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pp. 167 – 184, doi : 10. 1017 / cbo9781139028172. 009, isbn 978 - 1 - 107 - 01439 - 8 schofield, malcolm ( 2014 ), " archytas ", in huffman, carl a. ( ed. ), a history of pythagoreanism, cambridge university press, pp. 69 – 87, doi : 10. 1017 / cbo9781139028172. 009, isbn 978 - 1 - 107 - 01439 - 8 = = further reading = = a. barker, porphyry ’ s commentary on ptolemy ’ s harmonics a. barker, greek musical writings, vol. 2 : harmonic and acoustic theory a. bernard, “ ancient rhetoric and greek mathematics : a response to a modern historiographical dilemma, ” i. bodnar, oenopides of chius : a survey of the modern literature with a collection of the ancient testimonia burton, david m. ( 1997 ), the history of mathematics : an introduction ( 3rd ed. ), the mcgraw - hill companies, inc., isbn 978 - 0 - 07 - 009465 - 9 m. f. burnyeat, “ plato on why mathematics is good for the soul, ” proceedings of the british academy 2000 m. f. burnyeat, “ the philosophical sense of theaetetus ’ mathematics, ” 1978 l. corry, a brief history of number s. cuomo, pappus of alexandria and the mathematics of late antiquity christianidis, jean, ed. ( 2004 ), classics in the history of greek mathematics, dordrecht : kluwer, isbn 978 - 1 - 4020 - 0081 - 2 cooke, roger ( 1997 ), the history of mathematics : a brief course, wiley - interscience, isbn 978 - 0 - 471 - 18082 - 1 derbyshire, john ( 2006 ), unknown quantity : a real and imaginary history of algebra, joseph henry press, isbn 978 - 0 - 309 - 09657 - 7 e. j. dijksterhuis, archimedes m. n. fried, and s. unguru, apollonius of perga ’ s conica : text, context, subtext heath, thomas little ( 1981 ) [ first published 1921 ], a history of greek mathematics, dover publications, isbn 978 - 0 - 486 - 2407
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https://en.wikipedia.org/wiki/Ancient_Greek_mathematics
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we develop analogues of the primal and mixed variational formulations of the conservation laws describing transport of scalar physical properties for topological spaces referred to as cell complexes. the development is restricted to cell complexes with cells having connectivity of simple polytopes. such spaces are suitable representations of physical systems composed of elements of different apparent topological dimensions, where all elements might have individual properties, and elements of a given dimension might interact via common elements of lower dimensions. this modelling foundation can be considered as intermediate between the foundation for particle - based modelling, which is the discrete topology, and the foundation for continuum modelling, which is the smooth topology. the new foundation offers advantages for the analysis of the behaviour of physical systems with complex internal structures. the development is based on a calculus with combinatorial differential forms which is a discrete analogue of the smooth exterior calculus with differential forms. we call the resulting calculus combinatorial mesh calculus ( cmc ) as it is based on combinatorial meshes, for which embedding is forgotten and only the connectivity between cells and measures of the cells are used in calculations. we discuss how the obtained formulation is specialised for several different problems, including mass diffusion, heat conduction, fluid flow in porous media, and charge diffusion, and provide details about the formulation of initial boundary value problems for these transport cases. examples and results for selected boundary value problems are given to demonstrate the capabilities of the cmc formulations.
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arxiv:2505.09443
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the study of nonlinear waves that collapse in finite time is a theme of universal interest, e. g. within optical, atomic, plasma physics, and nonlinear dynamics. here we revisit the quintessential example of the nonlinear schrodinger equation and systematically derive a normal form for the emergence of blowup solutions from stationary ones. while this is an extensively studied problem, such a normal form, based on the methodology of asymptotics beyond all algebraic orders, unifies both the dimension - dependent and power - law - dependent bifurcations previously studied ; it yields excellent agreement with numerics in both leading and higher - order effects ; it is applicable to both infinite and finite domains ; and it is valid in all ( subcritical, critical and supercritical ) regimes.
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arxiv:2008.08968
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let g be a complex simple lie algebra, f a nilpotent element of g. we show that ( 1 ) the center of the w - algebra $ w ^ { cri } ( g, f ) $ associated with ( g, f ) at the critical level coincides with the feigin - frenkel center of the affine lie algebra associated with g, ( 2 ) the centerless quotient $ w _ { \ chi } ( g, f ) $ of $ w ^ { cri } ( g, f ) $ corresponding to an oper $ \ chi $ on the disc is simple, ( 3 ) the simple quotient $ w _ { \ chi } ( g, f ) $ is a quantization of the jet scheme of the intersection of the slodowy slice at f with the nilpotent cone of g.
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arxiv:1111.6329
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recently, the higher order statistics ( hos ) and sparsity based array are most talked about techniques to estimate the direction of arrival ( doa ). they not only provide enhanced degree of freedom ( dof ) to handle underdetermined cases but also improve the estimation accuracy of the system. to achieve high accuracy and more number of dof with limited number of sensors, here we have proposed a method based on the fourth order statistics. the aperture of virtual array becomes o ( 16n ^ 4 ) using n physical sensors. proposed method can be extended to the hos which increases the dof by many folds. numeric simulation validates these claims that the proposed method increases the resolution capacity as well as maximize the dof among all the earlier proposed method.
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arxiv:1711.05923
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an \ emph { acyclic coloring } of a graph is a proper vertex coloring such that the union of any two color classes induces a disjoint collection of trees. the more restricted notion of \ emph { star coloring } requires that the union of any two color classes induces a disjoint collection of stars. we prove that every acyclic coloring of a cograph is also a star coloring and give a linear - time algorithm for finding an optimal acyclic and star coloring of a cograph. if the graph is given in the form of a cotree, the algorithm runs in o ( n ) time. we also show that the acyclic chromatic number, the star chromatic number, the treewidth plus one, and the pathwidth plus one are all equal for cographs.
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arxiv:1103.5531
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gravitational wave astronomy pipelines rely on template waveform models for searches and parameter estimation purposes. for coalescing binary neutron stars ( bns ), such models need to accurately reproduce numerical relativity ( nr ) up to merger, in order to provide robust estimate of the stars ' equation of state - dependent parameters. in this work we present an improved version of the effective one body ( eob ) model $ \ tt teobresums $ for gravitational waves from bns systems. building upon recent post - newtonian calculations, we include subleading order tidal terms in the waveform multipoles and eob metric potentials, as well as add up to 5. 5pn terms in the gyro - gravitomagnetic functions entering the spin - orbit sector of the model. in order to further improve the eob - nr agreement in the last few orbital cycles before merger, we introduce next - to - quasicircular corrections in the waveform - - informed by a large number of bns nr simulations - - and introduce a new nr - informed parameter entering the tidal sector of our conservative dynamics. the performance of our model is then validated against 14 new eccentricity reduced simulations of unequal mass, spinning binaries with varying equation of state. a time - domain phasing analysis and mismatch computations demonstrate that the new model overall improves over the previous version of $ \ tt teobresums $. finally, we present a closed - form frequency domain representation of the ( tidal ) amplitude and phase of the new model. this representation accounts for mass - ratio, aligned spin and ( resummed ) spin - quadrupole effects in the tidal phase and - - within the calibration region - - it is faithful to the original model.
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arxiv:2307.15125
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we perform ab - initio calculations on bi $ _ \ mathrm { { se } } $ antisite defects in the surface of bi $ _ 2 $ se $ _ 3 $, finding strong low - energy defect resonances with a spontaneous ferromagnetism, fixed to an out - of - plane orientation due to an exceptional large magnetic anisotropy energy. for antisite defects in the surface layer, we find semi - itinerant ferromagnetism and strong hybridization with the dirac surface state, generating a finite energy gap. for deeper lying defects, such hybridization is largely absent, the magnetic moments becomes more localized, and no energy gap is present.
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arxiv:2002.03962
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fractal structures appear in a vast range of physical systems. a literature survey including all experimental papers on fractals which appeared in the six physical review journals ( a - e and letters ) during the 1990 ' s shows that experimental reports of fractal behavior are typically based on a scaling range $ \ delta $ which spans only 0. 5 - 2 decades. this range is limited by upper and lower cutoffs either because further data is not accessible or due to crossover bends. focusing on spatial fractals, a classification is proposed into ( a ) aggregation ; ( b ) porous media ; ( c ) surfaces and fronts ; ( d ) fracture and ( e ) critical phenomena. most of these systems, [ except for class ( e ) ] involve processes far from thermal equilibrium. the fact that for self similar fractals [ in contrast to the self affine fractals of class ( c ) ] there are hardly any exceptions to the finding of $ \ delta \ le 2 $ decades, raises the possibility that the cutoffs are due to intrinsic properties of the measured systems rather than the specific experimental conditions and apparatus. to examine the origin of the limited range we focus on a class of aggregation systems. in these systems a molecular beam is deposited on a surface, giving rise to nucleation and growth of diffusion - limited - aggregation - like clusters. scaling arguments are used to show that the required duration of the deposition experiment increases exponentially with $ \ delta $. furthermore, using realistic parameters for surfaces such as al ( 111 ) it is shown that these considerations limit the range of fractal behavior to less than two decades in agreement with the experimental findings. it is conjectured that related kinetic mechanisms that limit the scaling range are common in other nonequilibrium processes which generate spatial fractals.
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arxiv:cond-mat/9801127
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an n - vertex graph is called c - ramsey if it has no clique or independent set of size c log n. all known constructions of ramsey graphs involve randomness in an essential way, and there is an ongoing line of research towards showing that in fact all ramsey graphs must obey certain " richness " properties characteristic of random graphs. motivated by an old problem of erd \ h { o } s and mckay, recently narayanan, sahasrabudhe and tomon conjectured that for any fixed c, every n - vertex c - ramsey graph induces subgraphs of $ \ theta ( n ^ 2 ) $ different sizes. in this paper we prove this conjecture.
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arxiv:1711.02937
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we study the scaling properties of the solid - on - solid front of the infinite cluster in two - dimensional gradient percolation. we show that such an object is self affine with a hurst exponent equal to 2 / 3 up to a cutoff - length proportional to the gradient to the power ( - 4 / 7 ). beyond this length scale, the front position has the character of uncorrelated noise. importantly, the self - affine behavior is robust even after removing local jumps of the front. the previously observed multi affinity, is due to the dominance of overhangs at small distances in the structure function. this is a crossover effect.
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arxiv:cond-mat/0511545
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we investigate the van der waals friction between graphene and an amorphous sio $ _ 2 $ substrate. we find that due to this friction the electric current is saturated at a high electric field, in agreement with experiment. the saturation current depends weakly on the temperature, which we attribute to the quantum friction between the graphene carriers and the substrate optical phonons. we calculate also the frictional drag between two graphene sheets caused by van der waals friction, and find that this drag can induce a voltage high enough to be easily measured experimentally.
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arxiv:1409.0145
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this paper presents a compact system, openpneu, to support the pneumatic actuation for multi - chambers on soft robots. micro - pumps are employed in the system to generate airflow and therefore no extra input as compressed air is needed. our system conducts modular design to provide good scalability, which has been demonstrated on a prototype with ten air channels. each air channel of openpneu is equipped with both the inflation and the deflation functions to provide a full range pressure supply from positive to negative with a maximal flow rate at 1. 7 l / min. high precision closed - loop control of pressures has been built into our system to achieve stable and efficient dynamic performance in actuation. an open - source control interface and api in python are provided. we also demonstrate the functionality of openpneu on three soft robotic systems with up to 10 chambers.
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arxiv:2209.11318
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in the present paper, we investigate three scalar fields, \ qu field, phantom field and tachyon field, to explore the source of dark energy, using the gaussian processes method from the background data and perturbation growth rate data. the corresponding reconstructions all suggest that the dark energy should be dynamical. moreover, the quintom field, a combination between \ qu field and phantom field, is powerfully favored by the data within 68 \ % confidence level. using the mean values of scalar field $ \ phi $ and potential $ v $, we fit the function $ v ( \ phi ) $ in different fields. the fitted results imply that potential $ v ( \ phi ) $ in each scalar field may be a double exponential function or gaussian function. the gaussian processes reconstructions also indicate that the tachyon scalar field cannot be convincingly favored by the data and is at a disadvantage to describe the dark energy.
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arxiv:1809.08936
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the paper proposes a new recursive filter for non - linear systems that inherently computes a valid bound on the mean square estimation error. the proposed filter, bound based extended kalman, ( bekf ) is in the form of an extended kalman filter. the main difference of the proposed filter from the conventional extended kalman filter is in the use of a computed mean square error bound matrix, to calculate the filter gain, and to serve as bound on the actual mean square error. the paper shows that when the system is linear the proposed filtering algorithm reduces to the conventional kalman filter. the theory presented in the paper is applicable to a wide class of systems, but if the system is polynomial, then the recently developed theory of positive polynomials considerably simplifies the filter ' s implementation.
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arxiv:1410.0287
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anomaly detection based on 3d point cloud data is an important research problem and receives more and more attention recently. untrained anomaly detection based on only one sample is an emerging research problem motivated by real manufacturing industries such as personalized manufacturing that only one sample can be collected without any additional labels. how to accurately identify anomalies based on one 3d point cloud sample is a critical challenge in both industrial applications and the field of machine learning. this paper aims to provide a formal definition of untrained anomaly detection problem based on 3d point cloud data, discuss the differences between untrained anomaly detection and current unsupervised anomaly detection methods. unlike unsupervised learning, untrained methods do not rely on any data, including unlabeled data. instead, they leverage prior knowledge about the manufacturing surfaces and anomalies. examples are used to illustrate these prior knowledge and untrained machine learning model. afterwards, literature review on untrained anomaly detection based on 3d point cloud data is also provided, and the potential of untrained deep neural networks for anomaly detection is also discussed as outlooks.
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arxiv:2502.03876
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lipid bilayer membranes are not uniform and clusters of lipids in a more ordered state exist within the generally disorder lipid milieu of the membrane. these clusters of ordered lipids microdomains are now referred to as lipid rafts. recent reports attribute the formation of these microdomains to the geometrical and molecular mechanical mismatch of lipids of different species on the boundary. here we introduce the geodesic curvature to characterize the geometry of the domain boundary, and develop a geodesic curvature energy model to describe the formation of these microdomains as a result of energy minimization. our model accepts the intrinsic geodesic curvature of any binary lipid mixture as an input, and will produce microdomains of the given geodesic curvature as demonstrated by three sets of numerical simulations. our results are in contrast to the surface phase separation predicted by the classical surface cahn - hilliard equation, which tends to generate large domains as a result of the minimizing line tension. our model provides a direct and quantified description of the structure inhomogeneity of lipid bilayer membrane, and can be coupled to the investigations of biological processes on membranes for which such inhomogeneity plays essential roles.
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arxiv:1611.00103
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a quantum dot formed in a suspended carbon nanotube exposed to an external magnetic field is predicted to act as a thermoelectric unipolar spin battery which generates pure spin current. the built - in spin flip mechanism is a consequence of the spin - vibration interaction resulting from the interplay between the intrinsic spin - orbit coupling and the vibrational modes of the suspended carbon nanotube. on the other hand, utilizing thermoelectric effect, the temperature difference between the electron and the thermal bath to which the vibrational modes are coupled provides the driving force. we find that both magnitude and direction of the generated pure spin current are dependent on the strength of spin - vibration interaction, the sublevel configuration in dot, the temperatures of electron and thermal bath, and the tunneling rate between the dot and the pole. moreover, in the linear response regime, the kinetic coefficient is non - monotonic in the temperature $ t $ and it reaches its maximum when $ k _ bt $ is about one phonon energy. the existence of a strong intradot coulomb interaction is irrelevant for our spin battery, provided that high - order cotunneling processes are suppressed.
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arxiv:1702.07616
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quantum annealing ( qa ) has emerged as a powerful technique to solve optimization problems by taking advantages of quantum physics. in qa process, a bottleneck that may prevent qa to scale up is minor embedding step in which we embed optimization problems represented by a graph, called logical graph, to quantum processing unit ( qpu ) topology of quantum computers, represented by another graph, call hardware graph. existing methods for minor embedding require a significant amount of running time in a large - scale graph embedding. to overcome this problem, in this paper, we introduce a novel notion of adaptive topology which is an expandable subgraph of the hardware graph. from that, we develop a minor embedding algorithm, namely adaptive topology embedding ( atom ). atom iteratively selects a node from the logical graph, and embeds it to the adaptive topology of the hardware graph. our experimental results show that atom is able to provide a feasible embedding in much smaller running time than that of the state - of - the - art without compromising the quality of resulting embedding.
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arxiv:2307.01843
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we use the observed sizes and star formation rates of lyman - break galaxies ( lbgs ) to understand their properties expected in the hierarchical scenario of galaxy formation. the observed size distribution constrains the masses of the host haloes of lbgs from below, while the observed star - formation distribution constrains the masses from above. assuming a flat cdm model with a cosmological constant ( $ \ omega _ \ lambda = 0. 7 $ ), we find that consistency with observations requires the circular velocities of lbg host haloes to be in the range 100 - - $ 300 { \ rm km s ^ { - 1 } } $. the predicted comoving correlation length of these objects is $ \ sim 3 h ^ { - 1 } { \ rm mpc } $, and the predicted velocity dispersion of their stellar contents is typically $ 70 { \ rm km s ^ { - 1 } } $. the same prescription applied to larger haloes in the cdm cosmogony predicts the existence of galaxies with star formation rates $ \ sim 1000 { \ rm m _ \ odot yr ^ { - 1 } } $ at redshift $ z \ sim 3 $. we explore the possibility of identifying these galaxies to be the bright sub - millimeter ( sub - mm ) sources detected by scuba. the model predicts that the host haloes of these sub - mm sources are massive. these galaxies are predicted to be strongly correlated, with a comoving correlation length of $ \ sim 7 h ^ { - 1 } { \ rm mpc } $. the descendants of the bright sub - mm sources should reside in clusters of galaxies at the present time, and it is likely that these objects are the progenitors of giant ellipticals. the model predicts the existence of a relatively bright and red population of galaxies at $ z \ sim 3 $, which may be observed in the k - band.
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arxiv:astro-ph/0102436
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we consider the problems of language inclusion and language equivalence for vector addition systems with states ( vass ) with the acceptance condition defined by the set of accepting states ( and more generally by some upward - closed conditions ). in general, the problem of language equivalence is undecidable even for one - dimensional vass, thus to get decidability we investigate restricted subclasses. on the one hand, we show that the problem of language inclusion of a vass in k - ambiguous vass ( for any natural k ) is decidable and even in ackermann. on the other hand, we prove that the language equivalence problem is already ackermann - hard for deterministic vass. these two results imply ackermann - completeness for language inclusion and equivalence in several possible restrictions. some of our techniques can be also applied in much broader generality in infinite - state systems, namely for some subclass of well - structured transition systems.
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arxiv:2202.08033
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we obtain the quantum phase diagram of the ionic hubbard model including electron - hole symmetric density - dependent hopping. the boundaries of the phases are determined by crossing of excited levels with particular discrete symmetries, which coincide with jumps of charge and spin berry phases with a topological meaning. reducing the magnitude of the hopping terms that do not change the total number of singly occupied sites with respect to the other one, the region of the phase diagram occupied by the fully gapped spontaneously dimerized insulator ( which separates the band insulating and mott insulating phases ) is enlarged, particularly for small values of the alternating on - site energy. this result might be relevant for experiments in cold atoms in which topological charge pumping is observed when alternation in the hopping is included.
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arxiv:2304.04563
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in this paper we present observations, simulations, and analysis demonstrating the direct connection between the location of foreground emission on the sky and its location in cosmological power spectra from interferometric redshifted 21 cm experiments. we begin with a heuristic formalism for understanding the mapping of sky coordinates into the cylindrically averaged power spectra measurements used by 21 cm experiments, with a focus on the effects of the instrument beam response and the associated sidelobes. we then demonstrate this mapping by analyzing power spectra with both simulated and observed data from the murchison widefield array. we find that removing a foreground model which includes sources in both the main field - of - view and the first sidelobes reduces the contamination in high k _ parallel modes by several percent relative to a model which only includes sources in the main field - of - view, with the completeness of the foreground model setting the principal limitation on the amount of power removed. while small, a percent - level amount of foreground power is in itself more than enough to prevent recovery of any eor signal from these modes. this result demonstrates that foreground subtraction for redshifted 21 cm experiments is truly a wide - field problem, and algorithms and simulations must extend beyond the main instrument field - of - view to potentially recover the full 21 cm power spectrum.
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arxiv:1601.06177
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we study the possibility of using an uniformly coupled finite antiferromagnetic spin - 1 / 2 heisenberg chain as a channel for transmitting entanglement. one member of a pair of maximally entangled spins is initially appended to one end of a chain in its ground state and the dynamical propagation of this entanglement to the other end is calculated. we show that compared to the analogous scheme with a ferromagnetic chain in its ground state, here the entanglement is transmitted faster, with less decay, with a much higher purity and as a narrow pulse form rising non - analytically from zero. here non - zero temperatures and depolarizing environments are both found to be less destructive in comparison to the ferromagnetic case. the entanglement is found to propagate through the chain in a peculiar fashion whereby it hops to skip alternate sites.
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arxiv:0706.4176
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in this paper, we investigate the holographic phase transition with dark matter sector in the ads black hole background away from the probe limit. we disclose the properties of phases mostly from the holographic topological entanglement entropy of the system. we find the entanglement entropy is a good probe to the critical temperature and the order of the phase transition in the general model. the behaviors of entanglement entropy at large strip size suggest that the area law still holds with dark matter sector. we also conclude that the holographic topological entanglement entropy is useful in detecting the stability of the phase transitions. furthermore, we derive the complete diagram of the effects of coupled parameters on the critical temperature through the entanglement entropy and analytical methods.
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arxiv:1507.07399
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given a real abelian field f with group g and an odd prime number { \ ell }, we define the circular subgroup of the pro - { \ ell } - group of logarithmic units and we show that for any galois morphism $ \ rho $ from the pro - { \ ell } - group of logarithmic units to z { \ ell } [ g ], the image of the circular subgroup annihilates the { \ ell } - group of logarithmic classes. we deduce from this a proof of a logarithmic version of solomon conjecture.
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arxiv:2003.12301
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this paper deals with the control generation of right linear grammars with unknown behaviors ( rlubs, for short ) in which derivation behavior is not determined completely. in particular, we consider a physical property of control devices used in control systems and formulate it as a partial order over control alphabet of the control system. we give necessary and sufficient conditions for given finite language classes to be generated by rlubs and their control systems using a given partial order over control alphabet.
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arxiv:2403.04301
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) $. and finally, we show that the running time of our new algorithm is at most $ g ( k ) \ exp [ - c ( k \ log \ log k ) / ( \ log k ) ^ 2 ( 1 + o ( 1 ) ) ] $ for a constant $ c > 0 $.
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arxiv:1907.08559
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the radio frequency ( rf ) superconducting quantum interference device ( squid ) is a highly nonlinear oscillator exhibiting rich dynamical behavior. it has been studied for many years and it has found numerous applications in magnetic field sensors, in biomagnetism, in non - destructive evaluation, and gradiometers, among others. despite its theoretical and practical importance, there is relatively very little work on its multistability, chaotic properties, and bifurcation structure. in the present work, the dynamical properties of the squid in the strongly nonlinear regime are demonstrated using a well - established model whose parameters lie in the experimentally accessible range of values. when driven by a time - periodic ( ac ) flux either with or without a constant ( dc ) bias, the squid exhibits extreme multistability at frequencies around the ( geometric ) resonance. this effect is manifested by a " snake - like " form of the resonance curve. in the presence of both ac and dc flux, multiple bifurcation sequences and secondary resonance branches appear at frequencies above and below the geometric resonance. in the latter case, the squid exhibits chaotic behavior in large regions of the parameter space ; it is also found that the state of the squid can be switched from chaotic to periodic or vice versa by a slight variation of the dc flux.
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arxiv:1712.10244
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utilization of non - linear tools to characterize the state of development of the electricity markets in italy and greece. this is equivalent to testing the efficient market hypothesis on these markets. the tools include a variety of complexity measures like maximal lyapunov and hurst exponents and hhi index for market concentration and entropy, a measure of uncertainty and complexity in a dynamical system, applied on the electricity wholesale marginal prices pun and smp of italy and greece. our aim is to measure the complexity and dimensionality of the manifold on which the underlying stochastic dynamical system, govenring the prices, evolve. we also use the conditional volatility of prices, which is a measure of the market risk, and its connection with stability, and hurst exponent to investigate the properties of the fluctuations of the prices which are the footprints of the idiosyncrracies of each market.
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arxiv:1711.10552
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we show that for any integer $ t \ geq 2 $, every properly edge - coloured graph on $ n $ vertices with more than $ n ^ { 1 + o ( 1 ) } $ edges contains a rainbow subdivision of $ k _ t $. note that this bound on the number of edges is sharp up to the $ o ( 1 ) $ error term. this is a rainbow analogue of some classical results on clique subdivisions and extends some results on rainbow tur \ ' an numbers. our method relies on the framework introduced by sudakov and tomon [ 2020 ] which we adapt to find robust expanders in the coloured setting.
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arxiv:2106.13803
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we consider the family of one - dimensional maps arising from the contracting lorenz attractors studied by rovella. benedicks - carleson techniques were used by rovella to prove that there is a one - parameter family of maps whose derivatives along their critical orbits increase exponentially fast and the critical orbits have slow recurrent to the critical point. metzger proved that these maps have a unique absolutely continuous ergodic invariant probability measure ( srb measure ). here we use the technique developed by freitas and show that the tail set ( the set of points which at a given time have not achieved either the exponential growth of derivative or the slow recurrence ) decays exponentially fast as time passes. as a consequence, we obtain the continuous variation of the densities of the srb measures and associated metric entropies with the parameter. our main result also implies some statistical properties for these maps.
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arxiv:1205.5639
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non - equilibrium molecular dynamics simulations, of crucial importance in sliding friction, are hampered by arbitrariness and uncertainties in the way joule heat is removed. we implement in a realistic frictional simulation a parameter - free, non - markovian, stochastic dynamics, which, as expected from theory, absorbs joule heat precisely as a semi - infinite harmonic substrate would. simulating stick - slip friction of a slider over a 2d lennard - jones solid, we compare our virtually exact frictional results with approximate ones from commonly adopted empirical dissipation schemes. while the latter are generally in serious error, we show that the exact results can be closely reproduced by a viscous langevin dissipation at the boundary layer, once the back - reflected frictional energy is variationally optimized.
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arxiv:1008.1711
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let $ p > 3 $ be a prime, and let $ a $ be a rational p - adic integer with $ a \ not \ equiv 0 \ pmod p $. in this paper we establish congruences for $ $ \ sum _ { k = 1 } ^ { ( p - 1 ) / 2 } \ frac { \ binom ak \ binom { - 1 - a } k } k, \ quad \ sum _ { k = 0 } ^ { ( p - 1 ) / 2 } k \ binom ak \ binom { - 1 - a } k \ quad \ text { and } \ quad \ sum _ { k = 0 } ^ { ( p - 1 ) / 2 } \ frac { \ binom ak \ binom { - 1 - a } k } { 2k - 1 } \ pmod { p ^ 2 } $ $ in terms of bernoulli and euler polynomials. we also give some transformation formulas for congruences modulo $ p ^ 2 $.
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arxiv:1605.09179
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in this work, we are interested in a non symmetric homogeneous space, namely $ so ( 2m ) / sp ( m ) $. we show that this space admits a structure of $ z _ 2 ^ 2 $ - symmetric space. we describe all the non degenerated metrics and classify the riemannian and lorentzian ones.
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arxiv:0704.1541
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methylammonium lead iodide ( ch3nh3pbi3 ) perovskite solar cell has produced a remarkable breakthrough in the photovoltaic history of solar cell technology because of its outstanding device based performance as a light - harvesting semiconductor. whereas the experimental and theoretical studies of this system in the solid state have been numerously reported in the last 4 years, its fundamental cluster physics is yet to be exploited. to this end, this study has performed theoretical investigations using dft - m06 - 2x / adzp to examine the principal geometrical, electronic, topological, and orbital properties of the ch3nh3pbi3 nanocluster blocks. these clusters are found to be unusually strongly bound, with binding energies lying between 93. 53 and 125. 11 kcal mol - 1 ( beyond the covalent limit, 40 kcal mol - 1 ), enabling us to characterize the underlying interactions as ultra - strong type. based on this, together with the unusually high charge transfers, strong hyperconjugative interactions, sophisticated topologies of the charge density, and short intermolecular distances uncovered, we have characterized the ch3nh3pbi3 as mulliken inner complexes. additionally, the consequences of these, as well as of the ultra - strong interactions, in designing novel functional nanomaterials are briefly discussed. the various new results obtained in this study are not in perfect agreement with those already reported experimentally ( nat. commun. 2015, 6, 7124 ), and computationally ( chem. commun., 2015, 51, 6434 ; sci. rep. 2016, doi : 10. 1038 / srep21687 ; chem. mater. 2016, 28, 4259 ; j. mat. chem a 2016, 4, 4728 ; j. phys. chem. lett. 2016, 7, 1596 ).
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arxiv:1703.10286
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the influence of raman scattering and higher order dispersions on solitons and frequency comb generation in silica microring resonators is investigated. the raman effect introduces a threshold value in the resonator quality factor above which the frequency locked solitons can not exist and, instead, a rich dynamics characterized by generation of self - frequency shift - ing solitons and dispersive waves is observed. a mechanism of broadening of the cherenkov radiation through hopf instability of the frequency locked solitons is also reported.
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arxiv:1503.00672
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we develop a unified, information theoretic interpretation of the number - phase complementarity that is applicable both to finite - dimensional ( atomic ) and infinite - dimensional ( oscillator ) systems, with number treated as a discrete hermitian observable and phase as a continuous positive operator valued measure ( povm ). the relevant uncertainty principle is obtained as a lower bound on { \ it entropy excess }, $ x $, the difference between the entropy of one variable, typically the number, and the knowledge of its complementary variable, typically the phase, where knowledge of a variable is defined as its relative entropy with respect to the uniform distribution. in the case of finite dimensional systems, a weighting of phase knowledge by a factor $ \ mu $ ( $ > 1 $ ) is necessary in order to make the bound tight, essentially on account of the povm nature of phase as defined here. numerical and analytical evidence suggests that $ \ mu $ tends to 1 as system dimension becomes infinite. we study the effect of non - dissipative and dissipative noise on these complementary variables for oscillator as well as atomic systems.
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arxiv:0905.3269
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we study distorted metrics on binary trees in the context of phylogenetic reconstruction. given a binary tree $ t $ on $ n $ leaves with a path metric $ d $, consider the pairwise distances $ \ { d ( u, v ) \ } $ between leaves. it is well known that these determine the tree and the $ d $ length of all edges. here we consider distortions $ \ d $ of $ d $ such that for all leaves $ u $ and $ v $ it holds that $ | d ( u, v ) - \ d ( u, v ) | < f / 2 $ if either $ d ( u, v ) < m $ or $ \ d ( u, v ) < m $, where $ d $ satisfies $ f \ leq d ( e ) \ leq g $ for all edges $ e $. given such distortions we show how to reconstruct in polynomial time a forest $ t _ 1,..., t _ { \ alpha } $ such that the true tree $ t $ may be obtained from that forest by adding $ \ alpha - 1 $ edges and $ \ alpha - 1 \ leq 2 ^ { - \ omega ( m / g ) } n $. metric distortions arise naturally in phylogeny, where $ d ( u, v ) $ is defined by the log - det of a covariance matrix associated with $ u $ and $ v $. of a covariance matrix associated with $ u $ and $ v $. when $ u $ and $ v $ are ` ` far ' ', the entries of the covariance matrix are small and therefore $ \ d ( u, v ) $, which is defined by log - det of an associated empirical - correlation matrix may be a bad estimate of $ d ( u, v ) $ even if the correlation matrix is ` ` close ' ' to the covariance matrix. our metric results are used in order to show how to reconstruct phylogenetic forests with small number of trees from sequences of length logarithmic in the size of the tree. our method also yields an independent proof that phylogenetic trees can be reconstructed in polynomial time from sequences of polynomial length under the standard assumptions in phylogeny. both the metric result and its applications to phylogeny are almost tight.
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arxiv:math/0403508
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the most discussed of ` ` live ' ' metaphors in physical sciences is that of the schr \ " odinger cat. introduced in the early, but mature days of the new quantum theory, in 1935, the parable of the cat has provoked and enlivened debates on the meaning of the quantum theory, on the ontology of the quantum wavefunction, on the puzzle of the collapse of the wavefunction, on the meaning of quantum measurement, and on the boundary between the quantum world and the classical world. in this article, i will discuss these issues of the quantum theory focussing on various aspects of the metaphor of the schr \ " odinger cat.
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arxiv:2107.10241
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semantic segmentation requires extensive pixel - level annotation, motivating unsupervised domain adaptation ( uda ) to transfer knowledge from labelled source domains to unlabelled or weakly labelled target domains. one of the most efficient strategies involves using synthetic datasets generated within controlled virtual environments, such as video games or traffic simulators, which can automatically generate pixel - level annotations. however, even when such datasets are available, learning a well - generalised representation that captures both domains remains challenging, owing to probabilistic and geometric discrepancies between the virtual world and real - world imagery. this work introduces a semantic segmentation method based on latent diffusion models, termed inter - coder connected latent diffusion ( iccld ), alongside an unsupervised domain adaptation approach. the model employs an inter - coder connection to enhance contextual understanding and preserve fine details, while adversarial learning aligns latent feature distributions across domains during the latent diffusion process. experiments on gta5, synthia, and cityscapes demonstrate that iccld outperforms state - of - the - art uda methods, achieving miou scores of 74. 4 ( gta5 $ \ rightarrow $ cityscapes ) and 67. 2 ( synthia $ \ rightarrow $ cityscapes ).
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arxiv:2412.16859
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in the paper the memory effect in the system consisting from a trajectory of process and an environment is considered. the environment is presented by scalar potential and noise. the evolution of system is interpreted as process of the continuous " measurement " of a trajectory by an environment and \ or on the contrary. in this sense the measured value is entropy - the information about embedding of the trajectory into configurations space. the concepts " measurement " and " interaction " are identified alike in quantum theory. thus, the entropy evolution is not only the effect of dynamics, but also its cause, if it is possible to speak about causality in this case. it is shown, that such non - elastic interaction leads to occurrence of memory in the system. the reflex memory mechanism is realized as a real conformal dynamic metrics. the metastable event ( attractor ) is defined and time of its life is estimated. it is shown, that in the system there is a change of dynamic modes from spatial localization to random walk ( fluctuation, relaxation ). on scale of the attractors dynamics the memory is appearing as a semi - regular ( in some information sense ) drift of the image of fluctuations in a power spectrum of environment to absolute minimum. the latter properties ( topological convergence ) attract the attention to algorithmic aspect of a considered system.
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arxiv:0708.1483
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i train models for the task of neural machine translation for english - hungarian and hungarian - english, using the hunglish2 corpus. the main contribution of this work is evaluating different data augmentation methods during the training of nmt models. i propose 5 different augmentation methods that are structure - aware, meaning that instead of randomly selecting words for blanking or replacement, the dependency tree of sentences is used as a basis for augmentation. i start my thesis with a detailed literature review on neural networks, sequential modeling, neural machine translation, dependency parsing and data augmentation. after a detailed exploratory data analysis and preprocessing of the hunglish2 corpus, i perform experiments with the proposed data augmentation techniques. the best model for hungarian - english achieves a bleu score of 33. 9, while the best model for english - hungarian achieves a bleu score of 28. 6.
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arxiv:2111.04099
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we report an exact analytical solution of so - called positron diffusion trapping model. this model have been widely used for the treatment of the experimental data for defect profiling of the adjoin surface layer using the variable energy positron ( vep ) beam technique. hovewer, up to now this model could be treated only numerically with so - called vepfit program. the explicit form of the solutions is obtained for the realistic cases when defect profile is described by a discreet step - like function and continuous exponential - like function. our solutions allow to derive the analytical expressions for typical positron annihilation characteristics including the positron lifetime spectrum. latter quantity could be measured using the pulsed, slow positron beam. our analytical results are in good coincidence with both the vepfit numerics and experimental data. the presented solutions are easily generalizable for defect profiles of other shapes and can be well used for much more precise treatment of above experimental data.
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arxiv:1308.0685
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in this work, we consider a random access internet of things iot wireless network assisted by two aggregators collecting information from two disjoint groups of sensors. the nodes and the aggregators are transmitting in a random access manner under slotted time, the aggregators perform network - level cooperation for the data collection. the aggregators are equipped with queues to store data packets that are transmitted by the network nodes and relaying them to the destination node. we characterize the throughput performance of the iot network and we obtain the stability conditions for the queues at the aggregators. we apply the theory of boundary value problems to analyze the delay performance. our results show that the presence of the aggregators provides significant gains in the iot network performance, in addition, we provide useful insights regarding the scalability of the iot network.
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arxiv:1806.10200
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the martensitic transformation in new - type all - d - metal heusler alloys pd2mnti and pt2mnti have been investigated based on first - principles investigations. the calculated results indicate that the martenstic transformation have great possibility to occur in both pd2mnti and pt2mnti. the energy differences between the cubic and tetragonal phases are 215. 12 mev and 329. 45 mev for pd2mnti and pt2mnti, respectively. the analysis of the electronic structure of cubic and tetragonal phases also support this conclusion. the magnetic properties are also investigated for the two compounds.
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arxiv:1910.13075
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we propose and benchmark a gross - pitaevskii - like equation for two - component bose mixtures with competing interactions in 1d. our approach follows the density - functional theory with the energy functional based on the exact quantum monte carlo ( qmc ) simulations. our model covers, but goes beyond, the popular approach with the lee - huang - yang corrections. we first benchmark our approach against available qmc data in all interaction regimes and then study dynamical properties, inaccessible by ab initio many - body simulations. our analysis includes a study of monopole modes and reveals the presence of anomalous dark solitons.
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arxiv:2301.04417
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transliterations play an important role in multilingual entity reference resolution, because proper names increasingly travel between languages in news and social media. previous work associated with machine translation targets transliteration only single between language pairs, focuses on specific classes of entities ( such as cities and celebrities ) and relies on manual curation, which limits the expression power of transliteration in multilingual environment. by contrast, we present an unsupervised transliteration model covering 69 major languages that can generate good transliterations for arbitrary strings between any language pair. our model yields top - ( 1, 20, 100 ) averages of ( 32. 85 %, 60. 44 %, 83. 20 % ) in matching gold standard transliteration compared to results from a recently - published system of ( 26. 71 %, 50. 27 %, 72. 79 % ). we also show the quality of our model in detecting true and false friends from wikipedia high frequency lexicons. our method indicates a strong signal of pronunciation similarity and boosts the probability of finding true friends in 68 out of 69 languages.
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arxiv:1611.06722
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korea astronomy and space science institute ( kasi ) has been developing a next - generation coronagraph ( ngc ) in cooperation with nasa to measure the coronal electron density, temperature, and speed simultaneously using four different filters around 400 nm. kasi organized an expedition team to demonstrate the coronagraph measurement scheme and the instrumental technology through the 2017 total solar eclipse ( tse ) across the usa. the observation site was in jackson hole, wyoming, usa. we built an eclipse observation system, so - called diagnostic coronal experiment ( dice ), which is composed of two identical telescopes to improve a signal to noise ratio. the observation was conducted with 4 wavelengths and 3 linear polarization directions according to the planned schedule in a limited total eclipse time of about 140 seconds. polarization information of corona from the data was successfully obtained but we were not able to obtain global information of coronal electron temperature and speed in the corona due to a low signal - to - noise ratio of the optical system and a strong emission from the prominence located in the western limb. in this study, we report the development of dice and observation results from the eclipse expedition. tse observation and analysis by using our own developed instrument gave an important lesson that a coronagraph should be carefully designed to achieve the scientific purpose of this study. and it was a very useful experience in the way for the success of follow - up nasa - kasi joint missions called the balloon - borne investigation of the temperature and speed of electrons in the corona ( bitse ) and coronal diagnostic experiment ( codex ).
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arxiv:2006.06155
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we construct continuous - time equilibrium models based on a finite number of exponential utility investors. the investors ' income rates as well as the stock ' s dividend rate are governed by discontinuous levy processes. our main result provides the equilibrium ( i. e., bond and stock price dynamics ) in closed - form. as an application, we show that the equilibrium sharpe ratio can be increased and the equilibrium interest rate can be decreased ( simultaneously ) when the investors ' income streams cannot be traded.
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arxiv:1507.02974
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i discuss three aspects of the notion of agency from the standpoint of physics : ( i ) what makes a physical system an agent ; ( ii ) the reason for agency ' s time orientation ; ( iii ) the source of the information generated in choosing an action. i observe that agency is the breaking of an approximation under which dynamics appears closed. i distinguish different notions of agency, and observe that the answer to the questions above differ in different cases. i notice a structural similarity between agency and memory, that allows us to model agency, trace its time asymmetry to thermodynamical irreversibility, and identify the source of the information generated by agency in the growth of entropy. agency is therefore a physical mechanism that transforms low entropy into information. this may be the general mechanism at the source of the whole information on which biology builds.
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arxiv:2007.05300
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effective and efficient graph representation learning is essential for enabling critical downstream tasks, such as node classification, link prediction, and subgraph search. however, existing graph neural network ( gnn ) architectures often struggle to adapt to diverse and complex graph structures, limiting their ability to produce structure - aware and task - discriminative representations. to address this challenge, we propose abg - nas, a novel framework for automated graph neural network architecture search tailored for efficient graph representation learning. abg - nas encompasses three key components : a comprehensive architecture search space ( cass ), an adaptive genetic optimization strategy ( agos ), and a bayesian - guided tuning module ( bgtm ). cass systematically explores diverse propagation ( p ) and transformation ( t ) operations, enabling the discovery of gnn architectures capable of capturing intricate graph characteristics. agos dynamically balances exploration and exploitation, ensuring search efficiency and preserving solution diversity. bgtm further optimizes hyperparameters periodically, enhancing the scalability and robustness of the resulting architectures. empirical evaluations on benchmark datasets ( cora, pubmed, citeseer, and corafull ) demonstrate that abg - nas consistently outperforms both manually designed gnns and state - of - the - art neural architecture search ( nas ) methods. these results highlight the potential of abg - nas to advance graph representation learning by providing scalable and adaptive solutions for diverse graph structures. our code is publicly available at https : / / github. com / sserranw / abg - nas.
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arxiv:2504.21254
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the two - dimensional transition - metal dichalcogenides ( 2d tmdcs ) are an intriguing platform for studying light - matter interactions because they combine the electronic properties of conventional semiconductors with the optical resonances found in organic systems. however, the coupling strengths demonstrated in strong exciton - polariton coupling remain much lower than those found in organic systems. in this paper, we take on a new approach by utilizing the large oscillator strength of the above - band gap c exciton in few - layer molybdenum disulphide ( $ \ text { fl - mos } _ 2 $ ). we show a k - space rabi splitting of 293 mev when coupling $ \ text { fl - mos } _ 2 $ c excitons to surface plasmon polaritons at room temperature. this value is 11 % of the uncoupled exciton energy ( 2. 67 ev or 464 nm ), ~ 2x what is typically seen in the tmdcs, placing the system in the ultrastrong coupling regime. our results take a step towards finally achieving the efficient quantum coherent processes of ultrastrong coupling in a cmos - compatible system - - the 2d tmdcs - - in the visible spectrum.
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arxiv:2204.13768
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adversarial approach has been widely used for data generation in the last few years. however, this approach has not been extensively utilized for classifier training. in this paper, we propose an adversarial framework for classifier training that can also handle imbalanced data. indeed, a network is trained via an adversarial approach to give weights to samples of the majority class such that the obtained classification problem becomes more challenging for the discriminator and thus boosts its classification capability. in addition to the general imbalanced classification problems, the proposed method can also be used for problems such as graph representation learning in which it is desired to discriminate similar nodes from dissimilar nodes. experimental results on imbalanced data classification and on the tasks like graph link prediction show the superiority of the proposed method compared to the state - of - the - art methods.
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arxiv:1811.08812
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we calculate the non - zero ( na \ " { i } ve ) t - odd transverse momentum dependent transversity distribution $ h _ 1 ^ { \ perp } ( x, \ kp ^ 2 ) $ of the pion in a quark - spectator - antiquark model. the final - state interaction is modelled by the approximation of one gluon exchange between the quark and the antiquark spectator. using our model result we estimate the unsuppressed cos2 $ \ phi $ azimuthal asymmetry in unpolarized $ \ pi ^ - p $ drell - yan process. we find that the transverse momentum dependence of $ h _ 1 ^ { \ perp } ( x, \ kp ^ 2 ) $ of the pion is the same as that of $ h _ 1 ^ { \ perp } ( x, \ kp ^ 2 ) $ of the proton calculated from the quark - scalar - diquark model, although the $ x $ dependencies of them are different from each other. this suggests a connection between cos2 $ \ phi $ asymmetries in drell - yan processes with different initial hadrons.
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arxiv:hep-ph/0411043
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we show that, in general, there exist non - vanishing triple massey products in the cohomology with finite field coefficients of a complex hypersurface complement. in contrast, the massey products, triple and higher, in the rational cohomology of such a space are all known to vanish.
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arxiv:math/0505391
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this paper represents a theoretical and an experimental study of the spreading dynamics of a liquid droplet, generated by a needle free deposition system called the liquid needle droplet deposition technique. this technique utilizes a continuous liquid jet generated from a pressurized dosing system which generates a liquid drop on a substrate to be characterized by optical contact angle measurements. although many studies have explored the theoretical modelling of the droplet spreading scenario, a theoretical model representing the spreading dynamics of a droplet, generated by the jet impact and continuous addition of liquid mass, is yet to be addressed. in this study, we developed a theoretical model based on the overall energy balance approach which enables us to study on the physics of variation of droplet spreading under surrounding medium of various viscosities. the numerical solution of the non - linear ordinary differential equation has provided us the opportunity to comment on the variation of droplet spreading, as a function of weber number ( $ we $ ), reynolds number ( $ re $ ) and bond number ( $ bo $ ) ranging from 0. 5 - 3, 75 - 150, and 0. 001 - 0. 3, respectively. we have also presented a liquid jet impact model in order to predict the initial droplet diameter as an initial condition for the proposed governing equation. the model has been verified further with the experimental measurements and reasonable agreement has been observed. experimental observations and theoretical investigations also highlight the precision, repeatability and wide range of the applicability of liquid needle drop deposition technique.
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arxiv:2010.01154
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an improved amati correlation was constructed in ( apj 931 ( 2022 ) 50 ) by us recently. in this paper, we further study constraints on the $ \ lambda $ cdm and $ w $ cdm models from the gamma ray bursts ( grbs ) standardized with the standard and improved amati correlations, respectively. by using the pantheon type ia supernova sample to calibrate the latest a220 grb data set, the grb hubble diagram is obtained model - independently. we find that at the high redshift region ( $ z > 1. 4 $ ) the grb distance modulus from the improved amati correlation is larger apparently than that from the standard amati one. the grb data from the standard amati correlation only give a lower bound limit on the present matter density parameter $ \ omega _ { \ mathrm { m0 } } $, while the grbs from the improved amati correlation constrain the $ \ omega _ { \ mathrm { m0 } } $ with the $ 68 \ % $ confidence level to be $ 0. 308 ^ { + 0. 066 } _ { - 0. 230 } $ and $ 0. 307 ^ { + 0. 057 } _ { - 0. 290 } $ in the $ \ lambda $ cdm and $ w $ cdm models, respectively, which are consistent very well with those given by other current popular observational data including bao, cmb and so on. once the $ h ( z ) $ data are added in our analysis, the constraint on the hubble constant $ h _ 0 $ can be achieved. we find that two different correlations provide slightly different $ h _ 0 $ results but the marginalized mean values seem to be close to that from the planck 2018 cmb observations.
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arxiv:2207.00455
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using the analytical expressions for the genuine eigenfunctions $ \ varphi _ { \ mu \ nu } ( z ) $ and eigenvalues $ e _ { \ mu, \ nu } $, of open, bounded and quasi - bounded finite periodic systems, we derive the eigenfunctions space - inversion symmetry relations. the superlattice eigenfunctions symmetries, closely related with the symmetries and zeros of the chebyshev polynomials of the second kind $ u _ n $, are fully written in terms of the number of unit cells $ n $, the subband index $ \ mu $ and the intra - subband index $ \ nu $.
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arxiv:1607.02685
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quantum networks enable a broad range of practical and fundamental applications spanning distributed quantum computing to sensing and metrology. a cornerstone of such networks is an interface between telecom photons and quantum memories. here we demonstrate a novel approach based on cavity optomechanics that utilizes the susceptibility of spin qubits to strain. we use it to control electron spins of nitrogen - vacancy centers in diamond with photons in the 1550 nm telecommunications wavelength band. this method does not involve qubit optical transitions and is insensitive to spectral diffusion. furthermore, our approach can be applied to solid - state qubits in a wide variety of materials, expanding the toolbox for quantum information processing.
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arxiv:2102.04597
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a large, high - quality spectral data base of well - selected, moderate - redshift radio - loud and radio - quiet quasars is used to characterize the incidence of narrow associated civ lambda 1549 absorption, and how this may depend on some quasar properties, including radio - type. preliminary results of this study are presented.
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arxiv:astro-ph/0109382
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in the rotational sandpile model, either the clockwise or the anti - clockwise toppling rule is assigned to all the lattice sites. it has all the features of a stochastic sandpile model but belongs to a different universality class than the manna class. a crossover from rotational to manna universality class is studied by constructing a random rotational sandpile model and assigning randomly clockwise and anti - clockwise rotational toppling rules to the lattice sites. the steady state and the respective critical behaviour of the present model are found to have a strong and continuous dependence on the fraction of the lattice sites having the anti - clockwise ( or clockwise ) rotational toppling rule. as the anti - clockwise and clockwise toppling rules exist in equal proportions, it is found that the model reproduces critical behaviour of the manna model. it is then further evidence of the existence of the manna class, in contradiction with some recent observations of the non - existence of the manna class.
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arxiv:1501.01748
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big data analysis has become a crucial part of new emerging technologies such as the internet of things, cyber - physical analysis, deep learning, anomaly detection, etc. among many other techniques, dimensionality reduction plays a key role in such analyses and facilitates feature selection and feature extraction. randomized algorithms are efficient tools for handling big data tensors. they accelerate decomposing large - scale data tensors by reducing the computational complexity of deterministic algorithms and the communication among different levels of the memory hierarchy, which is the main bottleneck in modern computing environments and architectures. in this paper, we review recent advances in randomization for the computation of tucker decomposition and higher order svd ( hosvd ). we discuss random projection and sampling approaches, single - pass, and multi - pass randomized algorithms, and how to utilize them in the computation of the tucker decomposition and the hosvd. simulations on synthetic and real datasets are provided to compare the performance of some of the best and most promising algorithms.
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arxiv:2001.07124
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laminar - turbulent intermittency is intrinsic to the transitional regime of a wide range of fluid flows including pipe, channel, boundary layer and couette flow. in the latter turbulent spots can grow and form continuous stripes, yet in the stripe - normal direction they remain interspersed by laminar fluid. we carry out direct numerical simulations in a long narrow domain and observe that individual turbulent stripes are transient. in agreement with recent observations in pipe flow we find that turbulence becomes sustained at a distinct critical point once the spatial proliferation outweighs the inherent decaying process. by resolving the asymptotic size distributions close to criticality we can for the first time demonstrate scale invariance at the onset of turbulence.
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arxiv:1304.5446
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we study three - dimensional $ \ mathcal { n } = 2 $ supersymmetric gauge theories on $ \ mathcal { m } _ { g, p } $, an oriented circle bundle of degree $ p $ over a closed riemann surface, $ \ sigma _ g $. we compute the $ \ mathcal { m } _ { g, p } $ supersymmetric partition function and correlation functions of supersymmetric loop operators. this uncovers interesting relations between observables on manifolds of different topologies. in particular, the familiar supersymmetric partition function on the round $ s ^ 3 $ can be understood as the expectation value of a so - called " fibering operator " on $ s ^ 2 \ times s ^ 1 $ with a topological twist. more generally, we show that the 3d $ \ mathcal { n } = 2 $ supersymmetric partition functions ( and supersymmetric wilson loop correlation functions ) on $ \ mathcal { m } _ { g, p } $ are fully determined by the two - dimensional a - twisted topological field theory obtained by compactifying the 3d theory on a circle. we give two complementary derivations of the result. we also discuss applications to f - maximization and to three - dimensional supersymmetric dualities.
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arxiv:1701.03171
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under the multi - objective framework, this paper presents a hybrid algorithm to solve robust static output feedback control problem for continuous poly - topic uncertain system. to obtain static output feedback gain, a new hybrid algorithm is proposed by combination of a hybrid algorithm of the particle swarm optimization and differential evolution ( de ), and the linear matrix inequality method. the proposed algorithm is used to solve a optimization problem with a bi - linear matrix inequality constraints. the particle swarm optimization - de hybrid algorithm was used to obtain a population of controllers, and linear matrix inequality approach was used to optimize a performance criterion of the system. taking a hybrid h 2 / h infinite control problem as example, the detailed algorithm is presented to solve robust static output feedback control problem. the simulation results show that the proposed hybrid algorithm improves the convergence rate and accuracy of iterative methods and the original de - linear matrix inequality algorithm.
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arxiv:1603.02426
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in this letter we report a thorough analysis of the exciton dispersion in bulk hexagonal boron nitride. we solve the ab initio gw bethe - salpeter equation at finite $ \ mathbf { q } \ parallel \ gamma k $, and we compare our results with recent high - accuracy electron energy loss data. simulations reproduce the measured dispersion and the variation of the peak intensity. we focus on the evolution of the intensity, and we demonstrate that the excitonic peak is formed by the superposition of two groups of transitions that we call $ km $ and $ mk ' $ from the k - points involved in the transitions. these two groups contribute to the peak intensity with opposite signs, each damping the contributions of the other. the variations in number and amplitude of these transitions determine the changes in intensity of the peak. our results contribute to the understanding of electronic excitations in this systems along the $ \ gamma k $ direction, which is the relevant direction for spectroscopic measurements. they also unveil the non - trivial relation between valley physics and excitonic dispersion in h - - bn, opening the possibility to tune excitonic effects by playing with the interference between transitions. furthermore, this study introduces analysis tools and a methodology that are completely general. they suggest a way to regroup independent - particle transitions which could permit a deeper understanding of excitonic properties in any system.
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arxiv:1709.07397
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this paper presents a statistical forward model for a compton imaging system, called compton imager. this system, under development at the university of illinois urbana champaign, is a variant of compton cameras with a single type of sensors which can simultaneously act as scatterers and absorbers. this imager is convenient for imaging situations requiring a wide field of view. the proposed statistical forward model is then used to solve the inverse problem of estimating the location and energy of point - like sources from observed data. this inverse problem is formulated and solved in a bayesian framework by using a metropolis within gibbs algorithm for the estimation of the location, and an expectation - maximization algorithm for the estimation of the energy. this approach leads to more accurate estimation when compared with the deterministic standard back - projection approach, with the additional benefit of uncertainty quantification in the low photon imaging setting.
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arxiv:2402.07676
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two - sided group digraphs and graphs, introduced by iradmusa and praeger, provide a generalization of cayley digraphs and graphs in which arcs are determined by left and right multiplying by elements of two subsets of the group. we characterize when two - sided group digraphs and graphs are weakly and strongly connected and count connected components, using both an explicit elementary perspective and group actions. our results and examples address four open problems posed by iradmusa and praeger that concern connectedness and valency. we pose five new open problems.
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arxiv:1705.05827
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large language models ( llms ) have demonstrated the ability to solve complex tasks through in - context learning ( icl ), where models learn from a few input - output pairs without explicit fine - tuning. in this paper, we explore the capacity of llms to solve non - linear numerical computations, with specific emphasis on functions of the singular value decomposition. our experiments show that while llms perform comparably to traditional models such as stochastic gradient descent ( sgd ) based linear regression and neural networks ( nn ) for simpler tasks, they outperform these models on more complex tasks, particularly in the case of top - k singular values. furthermore, llms demonstrate strong scalability, maintaining high accuracy even as the matrix size increases. additionally, we found that llms can achieve high accuracy with minimal prior examples, converging quickly and avoiding the overfitting seen in classical models. these results suggest that llms could provide an efficient alternative to classical methods for solving high - dimensional problems. future work will focus on extending these findings to larger matrices and more complex matrix operations while exploring the effect of using different numerical representations in icl.
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arxiv:2411.15675
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domain - specific languages raise the level of abstraction in software development. while it is evident that programmers can more easily reason about very high - level programs, the same holds for compilers only if the compiler has an accurate model of the application domain and the underlying target platform. since mapping high - level, general - purpose languages to modern, heterogeneous hardware is becoming increasingly difficult, dsls are an attractive way to capitalize on improved hardware performance, precisely by making the compiler reason on a higher level. implementing efficient dsl compilers is a daunting task however, and support for building performance - oriented dsls is urgently needed. to this end, we present the delite framework, an extensible toolkit that drastically simplifies building embedded dsls and compiling dsl programs for execution on heterogeneous hardware. we discuss several building blocks in some detail and present experimental results for the optiml machine - learning dsl implemented on top of delite.
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arxiv:1109.0778
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in contrast to electrodynamics, einstein ' s gravitation equations are not invariant with respect to a wide class of the mapping of field variables which leave equations of motion of test particles in a given coordinate system invariant. it seems obvious enough that just these mappings should play a role of gauge transformations of the variables in differential equations of gravitational field. we consider here in short a gauge - invariant bimetric generalisation of the einstein equations which does not contradict availabel observation data. physical interpretation of the bimetricity based on relativity of space - time with respect to used reference frame, following conceptually from old poincar \ ' { e } fundamental ideas, is proposed..
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arxiv:0805.2688
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we propose how to generate macroscopic quantum superposition states using a microwave cavity containing a superconducting charge qubit. based on the measurement of charge states, we show that the superpositions of two macroscopically distinguishable coherent states of a single - mode cavity field can be generated by a controllable interaction between a cavity field and a charge qubit. after such superpositions of the cavity field are created, the interaction can be switched off by the classical magnetic field, and there is no information transfer between the cavity field and the charge qubit. we also discuss the generation of the superpositions of two squeezed coherent states.
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arxiv:quant-ph/0406058
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we propose a scheme to dynamically create a supersolid state in an optical lattice, using an attractive mixture of mass - imbalanced bosons. starting from a " molecular " quantum crystal, supersolidity is induced dynamically as an out - of - equilibrium state. when neighboring molecular wavefunctions overlap, both bosonic species simultaneously exhibit quasi - condensation and long - range solid order, which is stabilized by their mass imbalance. supersolidity appears in a perfect one - dimensional crystal, without the requirement of doping. our model can be realized in present experiments with bosonic mixtures that feature simple on - site interactions, clearing the path to the observation of supersolidity.
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arxiv:0906.1110
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the vortex phase diagram in the external rotation frequency versus temperature is calculated for dilute bose - einstein condensed gases. it is determined within the bogoliubov - popov theory for a finite temperature where the condensate and non - condensate fractions are treated in an equal footing. the temperature dependences of various thermodynamic instability lines for the vortex nucleation are computed to construct the phase diagram. experiments are proposed to resolve a recent controversy on the vortex creation problem associated with the quantized vortex observation in $ ^ { 87 } $ rb atom gases.
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arxiv:cond-mat/0104358
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by introducing a semi - honest third party ( tp ), we propose in this paper a novel qpc protocol using ( n + 1 ) - qubit ( n \ ge 2 ) greenberger - horne - zeilinger ( ghz ) states as information carriers. the parameter n not only determines the number of qubits contained in a ghz state, but also determines the probability that tp can successfully steal the participants ' data and the qubit efficiency. in the proposed protocol, we do not employ any other quantum technologies ( e. g., entanglement swapping and unitary operation ) except necessary technologies such as preparing quantum states and quantum measurements, which can reduce the need for quantum devices. we use the keys generated by quantum key distribution and bit - flipping for privacy protection, and decoy photons for eavesdropping checking, making both external and internal attacks invalid. specifically, for external attacks, we take several well - known attack means ( e. g., the intercept - resend attack and the measurement - resend attack ) as examples to show that the attackers outside the protocol can not steal the participants ' data successfully, in which we provide the security proof of the protocol against the entanglement - measurement attack. for internal attacks, we show that tp cannot steal the participants ' data and the participants cannot steal each other ' s data. we also show that the existing attack means against qpc protocols are invalid for our protocol.
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arxiv:1911.08075
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we present an alternative derivation of the pair correlation function for simple classical fluids by using a variational approach. that approach involves the conditional probability p ( 3,..., n / 1, 2 ) of an undefined system of n particles with respect to a given pair ( 1, 2 ), and the definition of a conditional entropy $ \ sigma $ ( 3,..., n / 1, 2 ). an additivity assumption of $ \ sigma $ ( 3,..., n / 1, 2 ) together with a superposition assumption for p ( 3 / 1, 2 ) allows deriving the pair probability p ( 1, 2 ). we then focus onto the case of simple classical fluids, which leads to an integral, non - linear equation that formally allows computing the pair correlation function g ( r ). that equation admits the one resulting from the hyper netted chain approximation ( and the percus - yevick approximation ) as a limit case.
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arxiv:2105.03191
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reciprocity in dyadic interactions is common and a topic of interest across disciplines. in some cases, reciprocity may be expected to be more or less prevalent among certain kinds of dyads. in response to interest among researchers in estimating dyadic reciprocity as a function of covariates, this paper proposes an extension to the multilevel social relations model. the outcome variable is assumed to be a binomial proportion, as is commonly encountered in observational and archival research. the approach draws on principles of multilevel modeling to implement random intercepts and slopes that vary among dyads. the corresponding variance function permits the computation of a dyadic reciprocity correlation. the modeling approach can potentially be integrated with other statistical models in the field of social network analysis.
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arxiv:2005.09827
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we present an algorithm for computing $ s $ - $ t $ maximum flows in directed graphs in $ \ widetilde { o } ( m ^ { 4 / 3 + o ( 1 ) } u ^ { 1 / 3 } ) $ time. our algorithm is inspired by potential reduction interior point methods for linear programming. instead of using scaled gradient / newton steps of a potential function, we take the step which maximizes the decrease in the potential value subject to advancing a certain amount on the central path, which can be efficiently computed. this allows us to trace the central path with our progress depending only $ \ ell _ \ infty $ norm bounds on the congestion vector ( as opposed to the $ \ ell _ 4 $ norm required by previous works ) and runs in $ o ( \ sqrt { m } ) $ iterations. to improve the number of iterations by establishing tighter bounds on the $ \ ell _ \ infty $ norm, we then consider the weighted central path framework of madry \ cite { m13, m16, cmsv17 } and liu - sidford \ cite { ls20 }. instead of changing weights to maximize energy, we consider finding weights which maximize the maximum decrease in potential value. finally, similar to finding weights which maximize energy as done in \ cite { ls20 } this problem can be solved by the iterative refinement framework for smoothed $ \ ell _ 2 $ - $ \ ell _ p $ norm flow problems \ cite { kpsw19 } completing our algorithm. we believe our potential reduction based viewpoint provides a versatile framework which may lead to faster algorithms for max flow.
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arxiv:2009.03260
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a " still life " is a subset s of the square lattice z ^ 2 fixed under the transition rule of conway ' s game of life, i. e. a subset satisfying the following three conditions : 1. no element of z ^ 2 - s has exactly three neighbors in s ; 2. every element of s has at least two neighbors in s ; 3. every element of s has at most three neighbors in s. here a ` ` neighbor ' ' of any x \ in z ^ 2 is one of the eight lattice points closest to x other than x itself. the " still - life conjecture " is the assertion that a still life cannot have density greater than 1 / 2 ( a bound easily attained, for instance by { ( x, y ) : x is even } ). we prove this conjecture, showing that in fact condition 3 alone ensures that s has density at most 1 / 2. we then consider variations of the problem such as changing the number of allowed neighbors or the definition of neighborhoods ; using a variety of methods we find some partial results and many new open problems and conjectures.
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arxiv:math/9905194
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series expansions have been a cornerstone of applied mathematics and engineering for centuries. in this paper, we revisit the taylor series expansion from a modern machine learning perspective. specifically, we introduce the fast continuous convolutional taylor transform ( fc2t2 ), a variant of the fast multipole method ( fmm ), that allows for the efficient approximation of low dimensional convolutional operators in continuous space. we build upon the fmm which is an approximate algorithm that reduces the computational complexity of n - body problems from o ( nm ) to o ( n + m ) and finds application in e. g. particle simulations. as an intermediary step, the fmm produces a series expansion for every cell on a grid and we introduce algorithms that act directly upon this representation. these algorithms analytically but approximately compute the quantities required for the forward and backward pass of the backpropagation algorithm and can therefore be employed as ( implicit ) layers in neural networks. specifically, we introduce a root - implicit layer that outputs surface normals and object distances as well as an integral - implicit layer that outputs a rendering of a radiance field given a 3d pose. in the context of machine learning, $ n $ and $ m $ can be understood as the number of model parameters and model evaluations respectively which entails that, for applications that require repeated function evaluations which are prevalent in computer vision and graphics, unlike regular neural networks, the techniques introduce in this paper scale gracefully with parameters. for some applications, this results in a 200x reduction in flops compared to state - of - the - art approaches at a reasonable or non - existent loss in accuracy.
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arxiv:2111.00110
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in zero - shot learning ( zsl ), conditional generators have been widely used to generate additional training features. these features can then be used to train the classifiers for testing data. however, some testing data are considered " hard " as they lie close to the decision boundaries and are prone to misclassification, leading to performance degradation for zsl. in this paper, we propose to learn clusterable features for zsl problems. using a conditional variational autoencoder ( cvae ) as the feature generator, we project the original features to a new feature space supervised by an auxiliary classification loss. to further increase clusterability, we fine - tune the features using gaussian similarity loss. the clusterable visual features are not only more suitable for cvae reconstruction but are also more separable which improves classification accuracy. moreover, we introduce gaussian noise to enlarge the intra - class variance of the generated features, which helps to improve the classifier ' s robustness. our experiments on sun, cub, and awa2 datasets show consistent improvement over previous state - of - the - art zsl results by a large margin. in addition to its effectiveness on zero - shot classification, experiments show that our method to increase feature clusterability benefits few - shot learning algorithms as well.
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arxiv:2010.03245
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this paper proposes fractional sliding control designs for single - degree - of - freedom fractional oscillators respectively of the kelvin - voigt type, the modified kelvin - voigt type and d \ " { u } ffing type, whose dynamical behaviors are described by second - order differential equations involving fractional derivatives. firstly, the differential equations of motion are transformed into non - commensurate fractional state equations by introducing state variables with physical significance. secondly, fractional sliding manifolds are constructed and stability of the corresponding sliding dynamics is addressed via the infinite state approach and lyapunov stability theory. thirdly, sliding control laws and adaptive sliding laws are designed for fractional oscillators respectively in cases that the bound of the external exciting force is known or unknown. finally, numerical simulations are carried out to validate the above control designs.
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arxiv:1608.04850
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researchers must ensure that the claims about the knowledge produced by their work are valid. however, validity is neither well - understood nor consistently established in design science, which involves the development and evaluation of artifacts ( models, methods, instantiations, and theories ) to solve problems. as a result, it is challenging to demonstrate and communicate the validity of knowledge claims about artifacts. this paper defines validity in design science and derives the design science validity framework and a process model for applying it. the framework comprises three high - level claim and validity types - criterion, causal, and context - as well as validity subtypes. the framework guides researchers in integrating validity considerations into projects employing design science and contributes to the growing body of research on design science methodology. it also provides a systematic way to articulate and validate the knowledge claims of design science projects. we apply the framework to examples from existing research and then use it to demonstrate the validity of knowledge claims about the framework itself.
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arxiv:2503.09466
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we present new 144 - mhz lofar observations of the prototypical ` x - shaped ' radio galaxy ngc 326, which show that the formerly known wings of the radio lobes extend smoothly into a large - scale, complex radio structure. we argue that this structure is most likely the result of hydrodynamical effects in an ongoing group or cluster merger, for which pre - existing x - ray and optical data provide independent evidence. the large - scale radio structure is hard to explain purely in terms of jet reorientation due to the merger of binary black holes, a previously proposed explanation for the inner structure of ngc 326. for this reason, we suggest that the simplest model is one in which the merger - related hydrodynamical processes account for all the source structure, though we do not rule out the possibility that a black hole merger has occurred. inference of the black hole - black hole merger rate from observations of x - shaped sources should be carried out with caution in the absence of deep, sensitive low - frequency observations. some x - shaped sources may be signposts of cluster merger activity, and it would be useful to investigate the environments of these objects more generally.
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arxiv:1907.03274
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we take into account the dynamics of three types of models of rotating galaxies in polar coordinates in a rotating frame. due to non - axisymmetric potential perturbations, the angular momentum varies with time, and the kinetic energy depends on the momenta and spatial coordinate. the existing explicit force - gradient symplectic integrators are not applicable to such hamiltonian problems, but the recently extended force - gradient symplectic methods proposed in a previous work are. numerical comparisons show that the extended force - gradient fourth - order symplectic method with symmetry is superior to the standard fourth - order symplectic method but inferior to the optimized extended force - gradient fourth - order symplectic method in accuracy. the optimized extended algorithm with symmetry is used to explore the dynamical features of regular and chaotic orbits in these rotating galaxy models. the gravity effects and the degree of chaos increase with an increase of the number of the radial terms in the series expansions of the potential. there are similar dynamical structures of regular and chaotical orbits in the three types of models for the same number of the radial terms in the series expansions, energy and initial conditions.
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arxiv:2302.06102
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we investigate the effect of a cosmological constant on the gravothermal catastrophe in the newtonian limit. a negative cosmological constant acts as a thermodynamic ` destabilizer '. the antonov radius gets smaller and the instability occurs, not only for negative but also for positive energy values. a positive cosmological constant acts as a ` stabilizer ' of the system, which, in this case, exhibits a novel ` reentrant behaviour '. in addition to the antonov radius we find a second critical radius, where an ` inverse antonov transition ' occurs ; a series of local entropy maxima is restored.
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arxiv:1206.2839
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we analyze the sector of dimension - three vector meson operators in the " hard wall " model of holographic qcd, including the vector and axial currents, dual to gauge fields in the bulk, and the tensor operator $ \ bar { \ psi } \ sigma ^ { \ mu \ nu } \ psi $, dual to a two - form field satisfying a complex self - duality condition. the model includes the effect of chiral symmetry breaking on vector mesons, that involves a coupling between the dual gauge field and the two - form field. we compute the leading logarithmic terms in the operator product expansion of two - point functions and the leading non - perturbative contribution to the tensor - vector correlator. the result is consistent with the operator product expansion of qcd. we also study the spectrum of vector mesons numerically.
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arxiv:1108.1191
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##20 and 49 npr 6 = 10068347520. however, the order of the 6 numbers is not significant for the payout. that is, if a ticket has the numbers 1, 2, 3, 4, 5, and 6, it wins as long as all the numbers 1 through 6 are drawn, no matter what order they come out in. accordingly, given any combination of 6 numbers, there are 6 × 5 × 4 × 3 × 2 × 1 = 6! or 720 orders in which they can be drawn. dividing 10, 068, 347, 520 by 720 gives 13, 983, 816, also written as 49! 6! ∗ ( 49 − 6 )! { \ displaystyle { 49! \ over 6! * ( 49 - 6 )! } }, or combin ( 49, 6 ) or 49 ncr 6 or more generally as ( n k ) = n! k! ( n − k )! { \ displaystyle { n \ choose k } = { n! \ over k! ( n - k )! } }, where n is the number of alternatives and k is the number of choices. further information is available at binomial coefficient and multinomial coefficient. this function is called the combination function, combin ( n, k ). for the rest of this article, we will use the notation ( n k ) { \ displaystyle { n \ choose k } }. " combination " means the group of numbers selected, irrespective of the order in which they are drawn. a combination of numbers is usually presented in ascending order. an eventual 7th drawn number, the reserve or bonus, is presented at the end. an alternative method of calculating the odds is to note that the probability of the first ball corresponding to one of the six chosen is 6 / 49 ; the probability of the second ball corresponding to one of the remaining five chosen is 5 / 48 ; and so on. this yields a final formula of ( n k ) = ( 49 6 ) = 49 6 ∗ 48 5 ∗ 47 4 ∗ 46 3 ∗ 45 2 ∗ 44 1 { \ displaystyle { n \ choose k } = { 49 \ choose 6 } = { 49 \ over 6 } * { 48 \ over 5 } * { 47 \ over 4 } * { 46 \ over 3 } * { 45 \ over 2 } * { 44 \ over 1 } } a 7th ball often is drawn as reserve ball, in the past only a second chance
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https://en.wikipedia.org/wiki/Lottery_mathematics
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is the evaporation of a black hole described by a unitary theory? in order to shed light on this question - - - especially aspects of this question such as a black hole ' s negative specific heat - - - we consider the real - time dynamics of a solitonic object in matrix quantum mechanics, which can be interpreted as a black hole ( black zero - brane ) via holography. we point out that the chaotic nature of the system combined with the flat directions of its potential naturally leads to the emission of d0 - branes from the black brane, which is suppressed in the large $ n $ limit. simple arguments show that the black zero - brane, like the schwarzschild black hole, has negative specific heat, in the sense that the temperature goes up when it evaporates by emitting d0 - branes. while the largest lyapunov exponent grows during the evaporation, the kolmogorov - sinai entropy decreases. these are consequences of the generic properties of matrix models and gauge theory. based on these results, we give a possible geometric interpretation of the eigenvalue distribution of matrices in terms of gravity. applying the same argument in the m - theory parameter region, we provide a scenario to derive the hawking radiation of massless particles from the schwarzschild black hole. finally, we suggest that by adding a fraction of the quantum effects to the classical theory, we can obtain a matrix model whose classical time evolution mimics the entire life of the black brane, from its formation to the evaporation.
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arxiv:1602.01473
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the deferred acceptance algorithm is an elegant solution to the stable matching problem that guarantees optimality and truthfulness for one side of the market. despite these desirable guarantees, it is susceptible to strategic misreporting of preferences by the agents on the other side. we study a novel model of strategic behavior under the deferred acceptance algorithm : manipulation through an accomplice. here, an agent on the proposed - to side ( say, a woman ) partners with an agent on the proposing side - - an accomplice - - to manipulate on her behalf ( possibly at the expense of worsening his match ). we show that the optimal manipulation strategy for an accomplice comprises of promoting exactly one woman in his true list ( i. e., an inconspicuous manipulation ). this structural result immediately gives a polynomial - time algorithm for computing an optimal accomplice manipulation. we also study the conditions under which the manipulated matching is stable with respect to the true preferences. our experimental results show that accomplice manipulation outperforms self manipulation both in terms of the frequency of occurrence as well as the quality of matched partners.
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arxiv:2012.04518
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in a phase ii dose - finding study with a placebo control, a new drug with several dose levels is compared with a placebo to test for the effectiveness of the new drug. the main focus of such studies often lies in the characterization of the dose - response relationship followed by the estimation of a target dose that leads to a clinically relevant effect over the placebo. this target dose is known as the minimum effective dose ( med ) in a drug development study. several approaches exist that combine multiple comparison procedures with modeling techniques to efficiently estimate the dose - response model and thereafter select the target dose. despite the flexibility of the existing approaches, they cannot completely address the model uncertainty in the model - selection step and may lead to target dose estimates that are biased. in this article, we propose two new med estimation approaches based on weighted regression modeling that are robust against deviations from the dose - response model assumptions. these approaches are compared with existing approaches with regard to their accuracy in point and interval estimation of the med. we illustrate by a simulation study that by integrating one of the new dose estimation approaches with the existing dose - response profile estimation approaches one can take into account the uncertainty of the model selection step.
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arxiv:2007.05974
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two - dimensional ( spin - $ 2 $ ) affleck - kennedy - lieb - tasaki ( aklt ) type valence bond solids on the square lattice are known to be symmetry protected topological ( spt ) gapped spin liquids [ shintaro takayoshi, pierre pujol, and akihiro tanaka phys. rev. b $ { \ bf 94 } $, 235159 ( 2016 ) ]. using the projected entangled pair state ( peps ) framework, we extend the construction of the aklt state to the case of $ su ( 3 ) $, relevant for cold atom systems. the entanglement spectrum is shown to be described by an alternating $ su ( 3 ) $ chain of " quarks " and " antiquarks ", subject to exponentially decaying ( with distance ) heisenberg interactions, in close similarity with its $ su ( 2 ) $ analog. we discuss the spt feature of the state.
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arxiv:1708.00848
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we show how heavy quark symmetry constraints on doubly heavy baryon semileptonic decay widths can be used to test the validity of different quark model calculations. the large discrepancies in the results observed between different quark model approaches can be understood in terms of a severe violation of heavy quark spin symmetry constraints by some of those models.
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arxiv:0710.1186
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thermophotovoltaic ( tpv ) converters are capable of generating electrical energy from infrared radiation emitted by an emitter powered by waste heat or solar energy. key performance metrics for tpv converters are power output density ( pod ), which represents the electrical energy per unit area of the photovoltaic ( pv ) cell, and converter efficiency ( ce ), which indicates the proportion of radiative energy converted into electrical energy. a common method to significantly enhance pod is maintaining a sub - micron vacuum gap between the emitter and pv cell to leverage the near - field thermal radiation. on the other hand, bifacial tpv conversion, operating in the far - field regime, has been proposed to enhance ce by efficiently recycling the sub - bandgap energy radiation. however, bifacial tpv converters face a challenge in cooling the pv cell because the excess heat should be transferred in the lateral direction to side - edge cooling channels. therefore, careful thermal engineering and management are required when employing near - field thermal radiation effects on bifacial tpv converters. in this study, we propose a bifacial near - field tpv ( nf - tpv ) converter that incorporates intrinsic si intermediate layers, aiming to enhance both pod and ce. si layers cover both sides of the pv cell to play a crucial role in pv cell cooling while addressing surface mode photonic loss in nf - tpv converters. we comprehensively analyze the influences of design parameters for a practical design of the bifacial nf - tpv converter. our results demonstrate that a single - junction inas cell can harvest 4. 38 w / cm $ ^ 2 $ of electrical energy with 27. 2 \ % ce from 1000 k graphite emitters at a 100 nm vacuum gap. despite the challenge in the cooing, our bifacial nf - tpv converter demonstrates 2. 4 times larger pod with 2. 7 \ % larger ce compared to conventional nf - tpv converters.
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arxiv:2306.02529
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we present a deterministic algorithm for the efficient evaluation of imaginary time diagrams based on the recently introduced discrete lehmann representation ( dlr ) of imaginary time green ' s functions. in addition to the efficient discretization of diagrammatic integrals afforded by its approximation properties, the dlr basis is separable in imaginary time, allowing us to decompose diagrams into linear combinations of nested sequences of one - dimensional products and convolutions. focusing on the strong coupling bold - line expansion of generalized anderson impurity models, we show that our strategy reduces the computational complexity of evaluating an $ m $ th - order diagram at inverse temperature $ \ beta $ and spectral width $ \ omega _ { \ max } $ from $ \ mathcal { o } ( ( \ beta \ omega _ { \ max } ) ^ { 2m - 1 } ) $ for a direct quadrature to $ \ mathcal { o } ( m ( \ log ( \ beta \ omega _ { \ max } ) ) ^ { m + 1 } ) $, with controllable high - order accuracy. we benchmark our algorithm using third - order expansions for multi - band impurity problems with off - diagonal hybridization and spin - orbit coupling, presenting comparisons with exact diagonalization and quantum monte carlo approaches. in particular, we perform a self - consistent dynamical mean - field theory calculation for a three - band hubbard model with strong spin - orbit coupling representing a minimal model of ca $ _ 2 $ ruo $ _ 4 $, demonstrating the promise of the method for modeling realistic strongly correlated multi - band materials. for both strong and weak coupling expansions of low and intermediate order, in which diagrams can be enumerated, our method provides an efficient, straightforward, and robust black - box evaluation procedure. in this sense, it fills a gap between diagrammatic approximations of the lowest order, which are simple and inexpensive but inaccurate, and those based on monte carlo sampling of high - order diagrams.
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arxiv:2307.08566
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the electronic structure of sr2ruo4 is investigated by high angular resolution arpes at several incident photon energies. we address the controversial issues of the fermi surface ( fs ) topology and of the van hove singularity at the m point, showing that a surface state and the replica of the primary fs due to ( sqrt2 x sqrt2 ) surface reconstruction are responsible for previous conflicting interpretations. the fs thus determined by arpes is consistent with the de haas - van alphen results, and it provides additional information on the detailed shape of the alpha, beta and gamma sheets.
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arxiv:cond-mat/0008462
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annotating lidar point clouds for autonomous driving is a notoriously expensive and time - consuming task. in this work, we show that the quality of recent self - supervised lidar scan representations allows a great reduction of the annotation cost. our method has two main steps. first, we show that self - supervised representations allow a simple and direct selection of highly informative lidar scans to annotate : training a network on these selected scans leads to much better results than a random selection of scans and, more interestingly, to results on par with selections made by sota active learning methods. in a second step, we leverage the same self - supervised representations to cluster points in our selected scans. asking the annotator to classify each cluster, with a single click per cluster, then permits us to close the gap with fully - annotated training sets, while only requiring one thousandth of the point labels.
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arxiv:2407.15797
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we study spectral and steady - state properties of generic markovian dissipative systems described by quadratic fermionic liouvillian operators of the lindblad form. the hamiltonian dynamics is modeled by a generic random quadratic operator, i. e., as a featureless superconductor of class d, whereas the markovian dissipation is described by $ m $ random linear jump operators. by varying the dissipation strength and the ratio of dissipative channels per fermion, $ m = m / ( 2n _ f ) $, we find two distinct phases where the support of the single - particle spectrum has one or two connected components. in the strongly dissipative regime, this transition occurs for $ m = 1 / 2 $ and is concomitant with a qualitative change in both the steady - state and the spectral gap that rules the large - time dynamics. above this threshold, the spectral gap and the steady - state purity qualitatively agree with the fully generic ( i. e., non - quadratic ) case studied recently. below $ m = 1 / 2 $, the spectral gap closes in the thermodynamic limit and the steady - state decouples into an ergodic and a nonergodic sector yielding a non - monotonic steady - state purity as a function of the dissipation strength. our results show that some of the universal features previously observed for fully random liouvillians are generic for a sufficiently large number of jump operators. on the other hand, if the number of dissipation channels is decreased the system can exhibit nonergodic features, rendering it possible to suppress dissipation in protected subspaces even in the presence of strong system - environment coupling.
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arxiv:2210.07959
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temperature - dependent gap equations in the su ( 4 ) model of high - tc superconductivity are derived and analytical solutions are obtained. based on these solutions, a generic gap diagram describing the features of energy gaps as functions of doping p is presented and a phase diagram illustrating the phase structure as a function of temperature t and doping p is sketched. a special doping point p _ q occurs naturally in the solutions that separates two phases at temperature t = 0 : a pure superconducting phase on one side ( p > p _ q ) and a phase with superconductivity strongly suppressed by antiferromagnetism on the other ( p < p _ q ). we interpret p _ q as a quantum phase transition point. moreover, the pairing gap is found to have two solutions for p < p _ q : a small gap that is associated with competition between superconductivity and antiferromagnetism and is responsible for the ground state superconductivity, and a large gap without antiferromagnetic suppression that corresponds to a collective excited state. a pseudogap appears in the solutions that terminates at p _ q and originates from the competition between d - wave superconductivity and antiferromagnetism. nevertheless, this conclusion does not contradict the preformed pair picture conceptually if the preformed pairs are generally defined as any pairs formed before pairing condensation.
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arxiv:cond-mat/0508081
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