text
stringlengths 1
3.65k
| source
stringlengths 15
79
|
|---|---|
the dirichlet series $ l _ m ( s ) $ are of fundamental importance in number theory. shanks defined the generalized euler and class numbers in connection with these dirichlet series, denoted by $ \ { s _ { m, n } \ } _ { n \ geq 0 } $. we obtain a formula for the exponential generating function $ s _ m ( x ) $ of $ s _ { m, n } $, where m is an arbitrary positive integer. in particular, for m > 1, say, $ m = bu ^ 2 $, where b is square - free and u > 1, we prove that $ s _ m ( x ) $ can be expressed as a linear combination of the four functions $ w ( b, t ) \ sec ( btx ) ( \ pm \ cos ( ( b - p ) tx ) \ pm \ sin ( ptx ) ) $, where p is an integer satisfying $ 0 \ leq p \ leq b $, $ t | u ^ 2 $ and $ w ( b, t ) = k _ bt / u $ with $ k _ b $ being a constant depending on b. moreover, the dirichlet series $ l _ m ( s ) $ can be easily computed from the generating function formula for $ s _ m ( x ) $. finally, we show that the main ingredient in the formula for $ s _ { m, n } $ has a combinatorial interpretation in terms of the m - signed permutations defined by ehrenborg and readdy. in principle, this answers a question posed by shanks concerning a combinatorial interpretation for the numbers $ s _ { m, n } $.
|
arxiv:1004.2168
|
we study heterostructures where a two - dimensional topological insulator ( ti ) is attached to two normal metal ( nm ) electrodes while an island of a ferromagnetic insulator ( fi ) with precessing magnetization covers a portion of its lateral edges to induce time - dependent exchange field underneath via the magnetic proximity effect. when the fi island covers both lateral edges, such device pumps pure spin current in the absence of any bias voltage, thereby acting as an efficient spin battery with giant output current even at very small microwave power input driving the precession. when only one lateral edge is covered by the fi island, both charge and spin current are pumped into the nm electrodes. we delineate conditions for the corresponding conductances ( current - to - microwave - frequency ratio ) to be quantized in a wide interval of precession cone angles, which is robust with respect to weak disorder and can be further extended by changes in device geometry.
|
arxiv:1005.3796
|
we review and extend our recent work on the planar ( large n ) equivalence between gauge theories with varying degree of supersymmetry. the main emphasis is made on the planar equivalence between n = 1 gluodynamics ( super - yang - mills theory ) and a non - supersymmetric " orientifold field theory. " we outline an " orientifold " large n expansion, analyze its possible phenomenological consequences in one - flavor massless qcd, and make a first attempt at extending the correspondence to three massless flavors. an analytic calculation of the quark condensate in one - flavor qcd starting from the gluino condensate in n = 1 gluodynamics is thoroughly discussed. we also comment on a planar equivalence involving n = 2 supersymmetry, on " chiral rings " in non - supersymmetric theories, and on the origin of planar equivalence from an underlying, non - tachyonic type - 0 string theory. finally, possible further directions of investigation, such as the gauge / gravity correspondence in large - n orientifold field theory, are briefly discussed.
|
arxiv:hep-th/0403071
|
this paper systematically compares two mathematical foundations for multitarget tracking : labeled random finite sets ( lrfs ' s ) and trajectory random finite sets ( trfs ' s ).
|
arxiv:2203.10972
|
optical - field emission from nanostructured solids such as subwavelength nanoantennas can be leveraged to create sub - femtosecond, phz - scale electronics for optical - field detection. one application that is of particular interest is the detection of an incident optical pulse ' s carrier - envelope phase. such carrier - envelope - phase detection requires few - cycle, broadband optical excitation where the resonant properties of the nanoantenna can strongly alter the response of the near field in time. little quantitative investigation has been performed to understand how the geometry and resonant properties of the antennae should be tuned to enhance the carrier - envelope phase sensitivity and signal to noise ratio. here we examine how the geometry and resonance frequency of planar plasmonic nanoantennas can be engineered for enhancing the emitted carrier - envelope - phase - sensitive photocurrent when driven by a few - cycle optical pulse. we find that with the simple addition of curved sidewalls leading to the apex, and proper tuning of the resonance wavelength, the net cep - sensitive current per nanoantenna can be improved by $ 5 $ - $ 10 \ times $, and the signal - to - noise - ratio by $ 50 $ - $ 100 \ times $ relative to simple triangular antennas operated on resonance. our findings will inform the next generation of nanoantenna designs for emerging applications in ultrafast photoelectron metrology and petahertz electronics.
|
arxiv:2103.08018
|
despite their immense success, deep neural networks ( cnns ) are costly to train, while modern architectures can retain hundreds of convolutional layers in network depth. standard convolutional operations are fundamentally limited by their linear nature along with fixed activations, where multiple layers are needed to learn complex patterns, making this approach computationally inefficient and prone to optimization difficulties. as a result, we introduce rkan ( residual kolmogorov - arnold network ), which could be easily implemented into stages of traditional networks, such as resnet. the module also integrates polynomial feature transformation that provides the expressive power of many convolutional layers through learnable, non - linear feature refinement. our proposed rkan module offers consistent improvements over the base models on various well - known benchmark datasets, such as cifar - 100, food - 101, and imagenet.
|
arxiv:2410.05500
|
we present a set of hydrodynamical / nbody controlled simulations of isolated gas rich galaxies that self - consistently include sn feedback and a detailed chemical evolution model, both tested in cosmological simulations. the initial conditions are motivated by the observed star forming galaxies at z ~ 2 - 3. we find that the presence of a multiphase interstellar media in our models promotes the growth of disc instability favouring the formation of clumps which in general, are not easily disrupted on timescales compared to the migration time. we show that stellar clumps migrate towards the central region and contribute to form a classical - like bulge with a sersic index, n > 2. our physically - motivated supernova feedback has a mild influence on clump survival and evolution, partially limiting the mass growth of clumps as the energy released per supernova event is increased, with the consequent flattening of the bulge profile. this regulation does not prevent the building of a classical - like bulge even for the most energetic feedback tested. our supernova feedback model is able to establish a self - regulated star formation, producing mass - loaded outflows and stellar age spreads comparable to observations. we find that the bulge formation by clumps may coexit with other channels of bulge assembly such as bar and mergers. our results suggest that galactic bulges could be interpreted as composite systems with structural components and stellar populations storing archaeological information of the dynamical history of their galaxy.
|
arxiv:1308.4396
|
we derive the effective equations for the out of equilibrium time evolution of the order parameter and the fluctuations of a scalar field theory in spatially flat frw cosmologies. the calculation is performed both to one - loop and in a non - perturbative, self - consistent hartree approximation. the method consists of evolving an initial functional thermal density matrix in time and is suitable for studying phase transitions out of equilibrium. the renormalization aspects are studied in detail and we find that the counterterms depend on the initial state. we investigate the high temperature expansion and show that it breaks down at long times. we also obtain the time evolution of the initial boltzmann distribution functions, and argue that to one - loop order or in the hartree approximation, the time evolved state is a ` ` squeezed ' ' state. we illustrate the departure from thermal equilibrium by numerically studying the case of a free massive scalar field in de sitter and radiation dominated cosmologies. it is found that a suitably defined non - equilibrium entropy per mode increases linearly with comoving time in a de sitter cosmology, whereas it is { \ it not } a monotonically increasing function in the radiation dominated case.
|
arxiv:hep-ph/9310319
|
the problem of particle creation from vacuum in a flat robertson - walker space - time is studied. two sets of exact solutions for the klein gordon equation are given. then the canonical method based on bogoliubov transformation is applied to calculate the pair creation probability and the density number of created particles. some particular cosmological models such as radiation dominated universe and milne universe are discussed. for the both cases the vacuum to vacuum transition probability is calculated and the imaginary part of the effective action is extracted.
|
arxiv:1108.0336
|
we present the first lattice qcd determination of the $ b _ c \ rightarrow j / \ psi $ vector and axial - vector form factors. these will enable experimental information on the rate for $ b _ c $ semileptonic decays to $ j / \ psi $ to be converted into a value for $ v _ { cb } $. our calculation covers the full physical $ q ^ 2 $ range of the decay and uses non - perturbatively renormalised lattice currents. we use the highly improved staggered quark ( hisq ) action for all valence quarks on the second generation milc ensembles of gluon field configurations including $ u $, $ d $, $ s $ and $ c $ hisq sea quarks. our hisq heavy quarks have masses ranging upwards from that of $ c $ ; we are able to reach that of the $ b $ on our finest lattices. this enables us to map out the dependence on heavy quark mass and determine results in the continuum limit at the $ b $. we use our form factors to construct the differential rates for $ b _ c ^ - \ rightarrow j / \ psi \ mu ^ - \ bar { \ nu } _ \ mu $ and obtain a total rate with $ 7 \ % $ uncertainty : $ \ gamma ( b _ c ^ - \ rightarrow j / \ psi \ mu ^ - \ bar { \ nu } _ { \ mu } ) / | \ eta _ { \ mathrm { ew } } v _ { cb } | ^ 2 = 1. 73 ( 12 ) \ times 10 ^ { 13 } ~ \ mathrm { s } ^ { - 1 } $. including values for $ v _ { cb } $, $ \ eta _ { \ mathrm { ew } } $ and $ \ tau _ { b _ c } $ yields a branching fraction for this decay mode of 0. 0150 ( 11 ) ( 10 ) ( 3 ) ~ with uncertainties from lattice qcd, $ \ eta _ \ mathrm { ew } v _ { cb } $ and $ \ tau _ { b _ c } $ respectively.
|
arxiv:2007.06957
|
we investigate the transport and the dynamical properties of tunnel - coupled double charge shuttles. the oscillation frequencies of two shuttles are mode - locked to integer multiples of the applied voltage frequency $ \ omega $. we show that left / right - symmetric double shuttles may generate direct net current due to bistable motions caused by parametric instability. the symmetry - broken direct current appears near $ \ omega = \ omega _ { 0 } / ( 2j - 1 ) $, ( $ j = 1, 2,... $ ), where $ \ omega _ { 0 } $ is the dressed resonance frequency of the relative motion of the two shuttles.
|
arxiv:cond-mat/0610287
|
the breakthrough paper of croot, lev, pach \ cite { clp } on progression - free sets in $ \ z _ 4 ^ n $ introduced a polynomial method that has generated a wealth of applications, such as ellenberg and gijswijt ' s solutions to the cap set problem \ cite { eg }. using this method, we bound the size of a set of polynomials over $ \ f _ q $ of degree less than $ n $ that is free of solutions to the equation $ \ sum _ { i = 1 } ^ k a _ if _ i ^ r = 0 $, where the coefficients $ a _ i $ are polynomials that sum to 0 and the number of variables satisfies $ k \ geq 2r ^ 2 + 1 $. the bound we obtain is of the form $ q ^ { cn } $ for some constant $ c < 1 $. this is in contrast to the best bounds known for the corresponding problem in the integers, which offer only a logarithmic saving, but work already with as few as $ k \ geq r ^ 2 + 1 $ variables.
|
arxiv:1701.07196
|
we give a geometric invariant theory ( git ) construction of the log canonical model $ \ bar m _ g ( \ alpha ) $ of the pairs $ ( \ bar m _ g, \ alpha \ delta ) $ for $ \ alpha \ in ( 7 / 10 - \ epsilon, 7 / 10 ] $ for small $ \ epsilon \ in \ mathbb q _ + $. we show that $ \ bar m _ g ( 7 / 10 ) $ is isomorphic to the git quotient of the chow variety bicanonical curves ; $ \ bar m _ g ( 7 / 10 - \ epsilon ) $ is isomorphic to the git quotient of the asymptotically - linearized hilbert scheme of bicanonical curves. in each case, we completely classify the ( semi ) stable curves and their orbit closures. chow semistable curves have ordinary cusps and tacnodes as singularities but do not admit elliptic tails. hilbert semistable curves satisfy further conditions, e. g., they do not contain elliptic bridges. we show that there is a small contraction $ \ psi : \ bar m _ g ( 7 / 10 + \ epsilon ) \ to \ bar m _ g ( 7 / 10 ) $ that contracts the locus of elliptic bridges. moreover, by using the git interpretation of the log canonical models, we construct a small contraction $ \ psi ^ + : \ bar m _ g ( 7 / 10 - \ epsilon ) \ to \ bar m _ g ( 7 / 10 ) $ that is the mori flip of $ \ psi $.
|
arxiv:0806.3444
|
we construct morse - smale - witten complex for an effective orientable orbifold. for a global quotient orbifold, we also construct a morse - bott complex. we show that certain type of critical points of a morse function has to be discarded to construct such a complex, and gradient flows should be counted with suitable weights. the homology of these complexes are shown to be isomorphic to the singular homology of the quotient spaces under the self - indexing assumptions.
|
arxiv:1103.5528
|
in order to make the foundation model more efficient and effective, our idea is combining sequence transformation and state transformation. first, we prove the availability of rotary position embedding in the state space duality algorithm, which reduces the perplexity of the hybrid quadratic causal self - attention and state space duality by more than 4 %, to ensure that the combining sequence transformation unifies position encoding. second, we propose dynamic mask attention, which maintains 100 % accuracy in the more challenging multi - query associative recall task, improving by more than 150 % compared to quadratic causal self - attention and state space duality, to ensure that the combining sequence transformation selectively filters relevant information. third, we design cross domain mixture of experts, which makes the computational speed of expert retrieval with more than 1024 experts 8 to 10 times faster than the mixture of experts, to ensure that the combining state transformation quickly retrieval mixture. finally, we summarize these matrix algorithms that can form the foundation model : wonderful matrices, which can be a competitor to popular model architectures.
|
arxiv:2412.11834
|
link prediction is a key problem for network - structured data, attracting considerable research efforts owing to its diverse applications. the current link prediction methods focus on general networks and are overly dependent on either the closed triangular structure of networks or node attributes. their performance on sparse or highly hierarchical networks has not been well studied. on the other hand, the available tree - like benchmark datasets are either simulated, with limited node information, or small in scale. to bridge this gap, we present a new benchmark dataset telegraph, a highly sparse and hierarchical telecommunication network associated with rich node attributes, for assessing and fostering the link inference techniques. our empirical results suggest that most of the algorithms fail to produce a satisfactory performance on a nearly tree - like dataset, which calls for special attention when designing or deploying the link prediction algorithm in practice.
|
arxiv:2204.07703
|
superconductivity was discovered in a ni0 : 05tas2 single crystal. a ni0 : 05tas2 single crystal was successfully grown via the nacl / kcl flux method. the obtained lattice constant c of ni0 : 05tas2 is 1. 1999 nm, which is significantly smaller than that of 2h - tas2 ( 1. 208 nm ). electrical resistivity and magnetization measurements reveal that the superconductivity transition temperature of ni0 : 05tas2 is enhanced from 0. 8 k ( 2h - tas2 ) to 3. 9 k. the charge - density - wave transition of the matrix compound 2h - tas2 is suppressed in ni0 : 05tas2. the success of ni0 : 05tas2 single crystal growth via a nacl / kcl flux demonstrates that nacl / kcl flux method will be a feasible method for single crystal growth of the layered transition metal dichalcogenides.
|
arxiv:0811.2549
|
various theoretical obstacles are associated with a homogeneous and isotropic distribution of ` ` charge ' ' which is subject to a repulsive, long - range force. we show how these can be overcome, for all practical purposes, by the simple device of endowing the particle which carries the force with a small mass. the resulting situation may be relevant to a phase of cosmological acceleration which is triggered by the approach to masslessness of such a force carrier.
|
arxiv:gr-qc/0105072
|
context. fine - scale structures of the solar chromosphere, particularly fibrils, are known to host various types of magnetohydrodynamic ( mhd ) waves that can transport energy to the corona. in particular, absorption features observed in the h { \ alpha } channel have been widely detected that exhibit transverse oscillations. aims. we aimed to detect a high - frequency transverse oscillation in fibrils. methods. we conducted a case study on a high - frequency transverse oscillation in a chromospheric fibril. a chromospheric fibril was observed on 24 august 2018, in the h { \ alpha } spectral line, with the prototype microlensed hyperspectral imager ( mihi ) at the swedish 1 - meter solar telescope. the mihi instrument is an integral field spectrograph capable of achieving ultra - high resolution simultaneously in the spatial, temporal, and spectral domains. results. the detected oscillation characteristics include a period of 15 s and a displacement amplitude of 42 km. using the bisector method, we derived doppler velocities and determined that the polarisation of the oscillation was elliptical. conclusions. the energy contained in the oscillation ranges from 390 to 2300 w / m2, which is not sufficient to balance radiative losses of the chromosphere.
|
arxiv:2504.21857
|
we present two variants of wythoff ' s game. the first game is a restriction of wythoff ' s game in which removing tokens from the smaller pile is not allowed if the two entries are not equal. the second game is an extension of wythoff ' s game obtained by adjoining a move allowing players to remove k tokens from the smaller pile and l tokens from the other pile provided l < k. we show that both games preserve the p - positions of wythoff ' s game. this resolves a question raised by duchene, fraenkel, nowakowski and rigo. we give formulas for those positions which have sprague - grundy value 1. we also prove several results on the sprague - grundy functions.
|
arxiv:1202.3186
|
the temperature dependence of the magnetisation of a cu ( mn ) spin glass ( $ t _ g $ $ \ approx $ 57 k ) has been investigated using weak probing magnetic fields ( $ h $ = 0. 5 or 0 oe ) and specific thermal protocols. the behaviour of the zero - field cooled, thermoremanent and isothermal remanent magnetisation on ( re - ) cooling the system from a temperature ( 40 k ) where the system has been aged is investigated. it is observed that the measured magnetisation is formed by two parts : ( i ) a temperature - and observation time - dependent thermally activated relaxational part governed by the age - and temperature - dependent response function and the ( latest ) field change made at a lower temperature, superposed on ( ii ) a weakly temperature - dependent frozen - in part. interestingly we observe that the spin configuration that is imprinted during an elongated halt in the cooling, if it is accompanied by a field induced magnetisation, also includes a unidirectional excess magnetisation that is recovered on returning to the ageing temperature.
|
arxiv:1002.0612
|
we investigate the dynamics brought on by an impulse perturbation in two infinite - range quantum ising models coupled to each other and to a dissipative bath. we show that, if dissipation is faster the higher the excitation energy, the pulse perturbation cools down the low - energy sector of the system, at the expense of the high - energy one, eventually stabilising a transient symmetry - broken state at temperatures higher than the equilibrium critical one. such non - thermal quasi - steady state may survive for quite a long time after the pulse, if the latter is properly tailored.
|
arxiv:2105.01321
|
we study decoherence of one, two, and $ n $ non - interacting qubits. decoherence, measured in terms of purity, is calculated in linear response approximation, making use of the spectator configuration. the environment and its interaction with the qubits are modelled by random matrices. for two qubits, numerical studies reveal a simple one to one correspondence between its decoherence and its internal entanglement decay. using this relation we are able to give a formula for concurrence decay. for large environments the evolution induces a unital channel in the two qubits, providing a partial explanation for the relation above. using a kicked ising spin network, we study the exact evolution of two non - interacting qubits in the presence of a spin bath. we find that the entanglement ( as measured by concurrence ) of the two qubits has a close relation to the purity of the pair, and closely follows an analytic relation derived for werner states. as a collateral result we find that an integrable environment causes quadratic decay of concurrence as well as of purity, while a chaotic environment causes linear decay. both quantities display recurrences in some integrable environments. good agreement with the results found using random matrix theory is obtained. finally, we analyze decoherence of a quantum register in the absence of non - local operations. the problem is solved in terms of a sum rule which implies linear scaling in the number of qubits. each term involves a single qubit and its entanglement with the remaining ones. two conditions are essential : decoherence must be small and the coupling of different qubits must be uncorrelated in the interaction picture. we apply the result to the random matrix model, and illustrate its reach considering a ghz state coupled to a spin bath.
|
arxiv:0711.4642
|
. g. $ \ mathbb { z } ^ d $ or a free group ), and $ \ text { char } ( k ) = 0 $, all injective algebraic cellular automata $ \ tau \ colon \ mathbb { c } ^ g \ to \ mathbb { c } ^ g $ are of the form $ \ tau ( x ) ( h ) = a x ( g ^ { - 1 } h ) + b $ for all $ x \ in \ mathbb { c } ^ g, h \ in g $ for some $ g \ in g $, $ a \ in \ mathbb { c } ^ * $, $ b \ in \ mathbb { c } $.
|
arxiv:1804.06631
|
we show that there exists a quasi - isometric embedding of the product of $ n $ copies of $ \ mathbb { h } _ { \ mathbb { r } } ^ 2 $ into any symmetric space of non - compact type of rank $ n $, and there exists a bi - lipschitz embedding of the product of $ n $ copies of the $ 3 $ - regular tree $ t _ 3 $ into any thick euclidean building of rank $ n $ with co - compact affine weyl group. this extends a previous result of fisher - - whyte. the proof is purely geometrical, and the result also applies to the non bruhat - - tits buildings.
|
arxiv:2405.02226
|
" unified science " can refer to any of three related strands in contemporary thought. belief in the unity of science was a central tenet of logical positivism. different logical positivists construed this doctrine in several different ways, e. g. as a reductionist thesis, that the objects investigated by the special sciences reduce to the objects of a common, putatively more basic domain of science, usually thought to be physics ; as the thesis that all of the theories and results of the various sciences can or ought to be expressed in a common language or " universal slang " ; or as the thesis that all the special sciences share a common method. the writings of edward haskell and a few associates, seeking to rework science into a single discipline employing a common artificial language. this work culminated in the 1972 publication of full circle : the moral force of unified science. the vast part of the work of haskell and his contemporaries remains unpublished, however. timothy wilken and anthony judge have recently revived and extended the insights of haskell and his coworkers. unified science has been a consistent thread since the 1940s in howard t. odum ' s systems ecology and the associated emergy synthesis, modeling the " ecosystem " : the geochemical, biochemical, and thermodynamic processes of the lithosphere and biosphere. modeling such earthly processes in this manner requires a science uniting geology, physics, biology, and chemistry ( h. t. odum 1995 ). with this in mind, odum developed a common language of science based on electronic schematics, with applications to ecology economic systems in mind ( h. t. odum 1994 ). = = see also = = consilience — the unification of knowledge, e. g. science and the humanities tree of knowledge system = = references = = odum, h. t. 1994. ecological and general systems : an introduction to systems ecology. colorado university press, colorado. odum, h. t. 1995. ' energy systems and the unification of science ', in hall, c. s. ( ed. ) maximum power : the ideas and applications of h. t. odum. colorado university press, colorado : 365 - 372. = = external links = = future positive timothy wilken ' s website, including a lot of material and diagrams on edward haskell ' s unified science cardioid attractor fundamental to sustainability - 8 transactional games forming the heart of sustainable relationship anthony
|
https://en.wikipedia.org/wiki/Unified_Science
|
we consider a continuous model of d - dimensional elastic ( polymerized ) manifold fluctuating in d - dimensional euclidean space, interacting with a single impurity via an attractive or repulsive delta - potential ( but without self - avoidance interactions ). except for d = 1 ( the polymer case ), this model cannot be mapped onto a local field theory. we show that the use of intrinsic distance geometry allows for a rigorous construction of the high - temperature perturbative expansion and for analytic continuation in the manifold dimension d. we study the renormalization properties of the model for 0 < d < 2, and show that for d < d * where d * = 2d / ( 2 - d ) is the upper critical dimension, the perturbative expansion is uv finite, while uv divergences occur as poles at d = d *. the standard proof of perturbative renormalizability for local field theories ( the bph theorem ) does not apply to this model. we prove perturbative renormalizability to all orders by constructing a subtraction operator based on a generalization of the zimmermann forests formalism, and which makes the theory finite at d = d *. this subtraction operation corresponds to a renormalization of the coupling constant of the model ( strength of the interaction with the impurity ). the existence of a wilson function, of an epsilon - expansion around the critical dimension, of scaling laws for d < d * in the repulsive case, and of non - trivial critical exponents of the delocalization transition for d > d * in the attractive case is thus established. to our knowledge, this provides the first proof of renormalizability for a model of extended objects, and should be applicable to the study of self - avoidance interactions for random manifolds.
|
arxiv:hep-th/9211038
|
let $ p _ t $ and $ c _ \ ell $ denote a path on $ t $ vertices and a cycle on $ \ ell $ vertices, respectively. in this paper we study the $ k $ - coloring problem for $ ( p _ t, c _ \ ell ) $ - free graphs. maffray and morel, and bruce, hoang and sawada, have proved that 3 - colorability of $ p _ 5 $ - free graphs has a finite forbidden induced subgraphs characterization, while hoang, moore, recoskie, sawada, and vatshelle have shown that $ k $ - colorability of $ p _ 5 $ - free graphs for $ k \ geq 4 $ does not. these authors have also shown, aided by a computer search, that 4 - colorability of $ ( p _ 5, c _ 5 ) $ - free graphs does have a finite forbidden induced subgraph characterization. we prove that for any $ k $, the $ k $ - colorability of $ ( p _ 6, c _ 4 ) $ - free graphs has a finite forbidden induced subgraph characterization. we provide the full lists of forbidden induced subgraphs for $ k = 3 $ and $ k = 4 $. as an application, we obtain certifying polynomial time algorithms for 3 - coloring and 4 - coloring $ ( p _ 6, c _ 4 ) $ - free graphs. ( polynomial time algorithms have been previously obtained by golovach, paulusma, and song, but those algorithms are not certifying ) ; to complement these results we show that in most other cases the $ k $ - coloring problem for $ ( p _ t, c _ \ ell ) $ - free graphs is np - complete. specifically, for $ \ ell = 5 $ we show that $ k $ - coloring is np - complete for $ ( p _ t, c _ 5 ) $ - free graphs when $ k \ ge 4 $ and $ t \ ge 7 $ ; for $ \ ell \ ge 6 $ we show that $ k $ - coloring is np - complete for $ ( p _ t, c _ \ ell ) $ - free graphs when $ k \ ge 5 $, $ t \ ge 6 $ ; and additionally, for $ \ ell = 7 $, we show that $ k $ - coloring is also np - complete for $ ( p _ t, c _ 7 ) $ - free graphs if $ k =
|
arxiv:1310.0340
|
eye - tracking research has proven valuable in understanding numerous cognitive functions. recently, frey et al. provided an exciting deep learning method for learning eye movements from fmri data. however, it needed to co - register fmri into standard space to obtain eyeballs masks, and thus required additional templates and was time consuming. to resolve this issue, in this paper, we propose a framework named mrgazer for predicting eye gaze points from fmri in individual space. the mrgazer consisted of eyeballs extraction module and a residual network - based eye gaze prediction. compared to the previous method, the proposed framework skips the fmri co - registration step, simplifies the processing protocol and achieves end - to - end eye gaze regression. the proposed method achieved superior performance in a variety of eye movement tasks than the co - registration - based method, and delivered objective results within a shorter time ( ~ 0. 02 seconds for each volume ) than prior method ( ~ 0. 3 seconds for each volume ).
|
arxiv:2311.13372
|
first, it is pointed out that hadron / nuclear physics based on qcd should be regarded as ` ` condensed matter physics ' ' of the qcd vacuum. we indicate that phase shift analyses which respect chiral symmetry ( chs ), analyticity and crossing symmetry of the scattering amplitude show the $ \ sigma $ meson pole in the s - channel in the low mass region as well as the $ \ rho $ meson pole in the $ t $ - channel in the \ pipi scattering in the scalar channel. we review recent developments in exploring possible precursory phenomena of partial restoration of \ chis in nuclear medium by examining the spectral function in the scalar and the vector channels. we emphasize that the wave function renormalization of the pion in the medium plays an essential role to induce the decrease of the pion decay constant as the order parameter of chiral transition. an emphasis is also put on the importance to examine the scalar and vector channels simultaneously for exploring the possible restoration of chiral symmetry.
|
arxiv:nucl-th/0306056
|
we present time - dependent density matrix renormalization group ( dmrg ) results for strongly interacting one dimensional fermionic systems at finite temperature. when interactions are strong the characteristic spin energy can be greatly suppressed relative to the characteristic charge energy, allowing for the possibility of spin - incoherent luttinger liquid physics when the temperature is high compared to the spin energy, but small compared to the charge energy. using dmrg we compute the spectral properties of the $ t - j $ model at arbitrary temperatures with respect to both spin and charge energies. we study the full crossover from the luttinger liquid regime to the spin - incoherent regime, focusing on small $ j / t $, where the signatures of spin - incoherent behavior are more manifest. our method allows us to access the analytically intractable regime where temperature is of the order of the spin energy, $ t \ sim j $. our results should be helpful in the interpretation of experiments that may be in the crossover regime, $ t \ sim j $, and apply to one - dimensional cold atomic gases where finite - temperature effects are appreciable. the technique may also be used to guide the development of analytical approximations for the crossover regime.
|
arxiv:0910.3957
|
coauthors ( ca ) of a " lead investigator " ( li ) can receive a rank ( r ) according to their " importance " in having published joint publications with the li. it is commonly accepted, without any proof, that publications in peer review journals and e. g. conference proceedings do not have the same " value " in a cv. same for papers contributed to encyclopedia and book chapters. it is here examined whether the relationship between the number ( j ) of publications of some scientist with her / his coauthors, ranked according to their decreasing importance, i. e. $ j \ propto 1 / r ^ { \ alpha } $, as found by ausloos, still holds if the overall publication list is broken into such specific types of publications. several authors, with different careers, but mainly having worked in the field of statistical mechanics, are studied here to sort out answers to the questions. the exponent $ \ alpha $ turns out to be weakly scientist dependent, only if the maximum value of j and r is large and is $ \ sim + 1 $ then. the $ m _ a $ core value, i. e. the core number of cas, for proceedings only is about half of the total one, i. e. when all publications are counted. contributions to the numerical values from both encyclopedia and book chapters are marginal. the role of a time span on $ m _ a $ is also examined in two cases in relation to career activity considerations. it can considered that the findings serve as a contrasting point of view on how to quantify an individual ( publication ) career as recently done by petersen et al., here emphasizing the collaboration size and evolution, rather than a citation count, moreover specifying the type of publication. through the various $ m _ a $ ' s one can distinguish different behavior patterns of a scientist publication with cas.
|
arxiv:1306.2604
|
= = = = references = = de crespigny, rafe ( 2007 ), a biographical dictionary of later han to the three kingdoms ( 23 – 220 ad ), leiden : koninklijke brill, isbn 978 - 90 - 04 - 15605 - 0. berggren, lennart ; borwein, jonathan m. ; borwein, peter b. ( 2004 ), pi : a source book, new york : springer, isbn 978 - 0 - 387 - 20571 - 7 boyer, c. b. ( 1991 ) [ 1989 ], a history of mathematics ( 2nd ed. ), new york : wiley, isbn 978 - 0 - 471 - 54397 - 8 cuomo, serafina ( 2001 ), ancient mathematics, london : routledge, isbn 978 - 0 - 415 - 16495 - 5 goodman, michael, k. j. ( 2016 ), an introduction of the early development of mathematics, hoboken : wiley, isbn 978 - 1 - 119 - 10497 - 1 { { citation } } : cs1 maint : multiple names : authors list ( link ) gullberg, jan ( 1997 ), mathematics : from the birth of numbers, new york : w. w. norton and company, isbn 978 - 0 - 393 - 04002 - 9 joyce, hetty ( july 1979 ), " form, function and technique in the pavements of delos and pompeii ", american journal of archaeology, 83 ( 3 ) : 253 – 63, doi : 10. 2307 / 505056, jstor 505056, s2cid 191394716. katz, victor j. ( 1998 ), a history of mathematics : an introduction ( 2nd ed. ), addison - wesley, isbn 978 - 0 - 321 - 01618 - 8 katz, victor j. ( 2007 ), the mathematics of egypt, mesopotamia, china, india, and islam : a sourcebook, princeton, nj : princeton university press, isbn 978 - 0 - 691 - 11485 - 9 needham, joseph ; wang, ling ( 1995 ) [ 1959 ], science and civilization in china : mathematics and the sciences of the heavens and the earth, vol. 3, cambridge : cambridge university press, isbn 978 - 0 - 521 - 05801 - 8 needham, joseph ; wang, ling ( 2000 ) [ 1965 ], science and civilization in china : physics and physical technology :
|
https://en.wikipedia.org/wiki/History_of_mathematics
|
a reaction - diffusion equation is studied in a time - dependent interval whose length varies with time. the reaction term is either linear or of kpp type. on a fixed interval, it is well - known that if the length is less than a certain critical value then the solution tends to zero. when the domain length may vary with time, we prove conditions under which the solution does and does not converge to zero in long time. we show that, even with the length always strictly less than the ' critical length ', either outcome may occur. examples are given. the proof is based on upper and lower estimates for the solution, which are derived in this paper for a general time - dependent interval.
|
arxiv:2110.06007
|
we demonstrate that combining cosmic microwave background anisotropy measurements from the 1st year wmap observations with clustering data from the sloan galaxy redshift survey yields an indication for primordial anisotropies in the cosmological neutrino background.
|
arxiv:astro-ph/0412066
|
in clinical trials, mixed effects models for repeated measures ( mmrm ) and pattern mixture models ( pmm ) are often used to analyze longitudinal continuous outcomes. we describe a simple missing data imputation algorithm for the mmrm that can be easily implemented in standard statistical software packages such as sas proc mi. we explore the relationship of the missing data distribution in the control - based and delta - adjusted pmms with that in the mmrm, and suggest an efficient imputation algorithm for these pmms. the unobserved values in pmms can be imputed by subtracting the mean difference in the posterior predictive distributions of missing data from the imputed values in mmrm. we also suggest a modification of the copy reference imputation procedure to avoid the possibility that after dropout, subjects from the active treatment arm will have better mean response trajectory than subjects who stay on the active treatment. the proposed methods are illustrated by the analysis of an antidepressant trial.
|
arxiv:1610.03580
|
we study ribbons of vanishing gaussian curvature, i. e., flat ribbons, constructed along a curve in $ \ mathbb { r } ^ { 3 } $. in particular, we first investigate to which extent the ruled structure determines a flat ribbon : in other words, we ask whether for a given curve $ \ gamma $ and ruling angle ( angle between the ruling line and the curve ' s tangent ) there exists a well - defined flat ribbon. it turns out that the answer is positive only up to an initial condition, expressed by a choice of normal vector at a point. we then study the set of infinitely narrow flat ribbons along a fixed curve $ \ gamma $ in terms of energy. by extending a well - known formula for the bending energy of the rectifying developable, introduced in the literature by sadowsky in 1930, we obtain an upper bound for the difference between the bending energies of two solutions of the initial value problem. we finally draw further conclusions under some additional assumptions on the ruling angle and the curve $ \ gamma $.
|
arxiv:2104.12382
|
the discovery of multiple superconducting phases in ute2 boosted research on correlated - electron physics. this heavy - fermion paramagnet was rapidly identified as a reference compound to study the interplay between magnetism and unconventional superconductivity with multiple degrees of freedom. the proximity to a ferromagnetic quantum phase transition was initially proposed as a driving force to triplet - pairing superconductivity. however, we find here that long - range incommensurate antiferromagnetic order is established under pressure. the propagation vector km = ( 0. 07, 0. 33, 1 ) of the antiferromagnetic phase is close to a wavevector where antiferromagnetic fluctuations have previously been observed at ambient pressure. these elements support that ute2 is a nearly - antiferromagnet at ambient pressure. our work appeals for theories modelling the evolution of the magnetic interactions and electronic properties, driving a correlated paramagnetic regime at ambient pressure to a long - range antiferromagnetic order under pressure. a deeper understanding of itinerant - f - electrons magnetism in ute2 will be a key for describing its unconventional superconducting phases.
|
arxiv:2311.05455
|
federated learning ( fl ) represents a paradigm shift in distributed machine learning ( ml ), enabling clients to train models collaboratively while keeping their raw data private. this paradigm shift from traditional centralized ml introduces challenges due to the non - iid ( non - independent and identically distributed ) nature of data across clients, significantly impacting fl ' s performance. existing literature, predominantly model data heterogeneity by imposing label distribution skew across clients. in this paper, we show that label distribution skew fails to fully capture the real - world data heterogeneity among clients in computer vision tasks beyond classification. subsequently, we demonstrate that current approaches overestimate fl ' s performance by relying on label / class distribution skew, exposing an overlooked gap in the literature. by utilizing pre - trained deep neural networks to extract task - specific data embeddings, we define task - specific data heterogeneity through the lens of each vision task and introduce a new level of data heterogeneity called embedding - based data heterogeneity. our methodology involves clustering data points based on embeddings and distributing them among clients using the dirichlet distribution. through extensive experiments, we evaluate the performance of different fl methods under our revamped notion of data heterogeneity, introducing new benchmark performance measures to the literature. we further unveil a series of open research directions that can be pursued.
|
arxiv:2503.14553
|
we provide a necessary and sufficient condition for the representability of a function as the classical multidimensional laplace transform, when the support of the representing measure is contained in some generalized semi - algebraic set. this is done by employing a method of putinar and vasilescu [ putinar, m. and vasilescu, f. - h., solving moment problems by dimensional extension, ann. of math. ( 2 ) 149 ( 1999 ), no. 3, 1087 - 1107 ] for the corresponding multidimensional moment problem.
|
arxiv:1202.1324
|
the mod - p cohomology ring of a non - trivial finite p - group is an infinite dimensional, finitely presented graded unital algebra over the field with p elements, with generators in positive degrees. we describe an effective algorithm to test if two such algebras are graded isomorphic. as application, we determine all graded isomorphisms between the mod - p cohomology rings of all p - groups of order at most 100.
|
arxiv:1503.04666
|
we report a variation with temperature ( $ t $ ) of the effective interdimeric interaction $ j ^ \ prime _ { \ mathrm { eff } } $ in the antiferromagnetic ( afm ) copper dimeric organic compound cu $ _ 2 $ [ tzts ] $ _ 4 $ [ n - thiazol - 2 - yl - toluenesulfonamidate cu $ ^ \ mathrm { ii } $ ]. this $ t $ dependence was obtained from measurements of the effects in the electron paramagnetic resonance ( epr ) spectra of the proposed quantum phase transition associated to the exchange narrowing processes. cu $ _ 2 $ [ tzts ] $ _ 4 $ contains exchange coupled pairs of cu $ ^ \ mathrm { ii } $ spins $ \ mathbf { s _ \ mathrm { a } } $ and $ \ mathbf { s _ \ mathrm { b } } $ ( $ s $ = 1 / 2 ), with intradimeric afm exchange coupling $ j _ 0 $ = ( - 115 $ \ pm $ 1 ) cm $ ^ { - 1 } $ ( $ \ mathcal { h } _ \ mathrm { ex } = - j _ \ mathrm { 0 } \ mathbf { s _ \ mathrm { a } } \ cdot \ mathbf { s _ \ mathrm { b } } $ ). the variation of the epr line width of single crystals with field orientation around a " magic angle " where the transitions intersect, as well as the integrated signal intensity of the so - called " u - peak " of the powder spectrum were measured as a function of $ t $. modeling these data using arguments of exchange narrowing in the adiabatic regime considering the angular variation of the single crystal spectra and a geometric description, we find that $ | j ^ \ prime _ { \ mathrm { eff } } | $ associated with the exchange frequency $ \ omega _ { ex } $ is negligible for $ t < < | j _ \ mathrm { 0 } / k _ \ mathrm { b } | $, when the units are uncoupled, and $ | j ^ \ prime _ { \ mathrm { eff } } | $ = ( 0. 080 $ \ pm $ 0. 005 ) cm $ ^ { - 1 } $ ( $ | j ^ \ prime _ { \ mathrm { eff } } / j _
|
arxiv:1704.06642
|
recently, takeoka, guha and wilde have established a new ( loose ) upper bound on the secret key capacity of a pure - loss bosonic channel that is several times larger than an error - free bb84 qkd channel with same transmittance. this suggests that new qkd protocols may exist with higher secret key rates and effective ranges larger than the metro - area limits of bb84 qkd over optical fiber. in this paper we illustrate such a possibility with a new protocol called amplified quantum key distribution ( aqkd ), which will be compatible with the optical amplification typically encountered on inter - city fiber spans. we analyze one instantiation of aqkd, in which the transmitter enclave contains an optical amplifier ( oa ), with security against passive optical tapping. for this scenario aqkd is shown to : give three times the secret key rate of bb84 at spans up to 100km, increasing to more than a ten - fold gain at 140km ; and double the maximum single - span optical fiber transmission range to inter - city distances ( 300km ). essential to these performance gains is a new information - theoretic protocol post - processing stage called generalized advantage distillation ( gad ). aqkd could be implemented with commercial off - the - shelf ( cots ) hardware as an augmentation of present - day bb84 qkd. aqkd avoids the expense, complexity and resource duplication of " trusted relay " approaches to qkd range extension. we expect aqkd to be compatible with fiber spans containing intermediate oas, which will facilitate its deployment as an overlay on existing fiber networks.
|
arxiv:1406.6990
|
we investigate ordering properties of two - dimensional granular materials using several shapes created by welding ball bearings together. ordered domains form much more easily in two than in three dimensions, even when configurations lack long - range order. the onset of ordered domains occurs near a packing density of 0. 8, a phenomenon observed previously for disks. one of our shapes, the trapezoid, has packings that remain disordered and near the transition density even after annealing by shaking. since random packings are unstable for disks and many other shapes in two dimensions, trapezoid packings provide a new approach to studying two - dimensional randomness. we also find that the rotational symmetry of a shape is an excellent predictor of how easily it orders, and a potential guide to identifying two - dimensional shapes that remain random after annealing.
|
arxiv:cond-mat/0102025
|
we deal with parameter estimation for a linear parabolic second - order stochastic partial differential equation in two space dimensions driven by two types of $ q $ - wiener processes based on high frequency data with respect to time and space. we propose minimum contrast estimators of the coefficient parameters based on temporal and spatial squared increments, and provide adaptive estimators of the coefficient parameters based on an approximate coordinate process. we also give an example and simulation results of the proposed estimators.
|
arxiv:2304.09441
|
large language models ( llms ) have been used in cybersecurity such as autonomous security analysis or penetration testing. capture the flag ( ctf ) challenges serve as benchmarks to assess automated task - planning abilities of llm agents for cybersecurity. early attempts to apply llms for solving ctf challenges used single - agent systems, where feedback was restricted to a single reasoning - action loop. this approach was inadequate for complex ctf tasks. inspired by real - world ctf competitions, where teams of experts collaborate, we introduce the d - cipher llm multi - agent framework for collaborative ctf solving. d - cipher integrates agents with distinct roles with dynamic feedback loops to enhance reasoning on complex tasks. it introduces the planner - executor agent system, consisting of a planner agent for overall problem - solving along with multiple heterogeneous executor agents for individual tasks, facilitating efficient allocation of responsibilities among the agents. additionally, d - cipher incorporates an auto - prompter agent to improve problem - solving by auto - generating a highly relevant initial prompt. we evaluate d - cipher on multiple ctf benchmarks and llm models via comprehensive studies to highlight the impact of our enhancements. additionally, we manually map the ctfs in nyu ctf bench to mitre att & ck techniques that apply for a comprehensive evaluation of d - cipher ' s offensive security capability. d - cipher achieves state - of - the - art performance on three benchmarks : 22. 0 % on nyu ctf bench, 22. 5 % on cybench, and 44. 0 % on hackthebox, which is 2. 5 % to 8. 5 % better than previous work. d - cipher solves 65 % more att & ck techniques compared to previous work, demonstrating stronger offensive capability.
|
arxiv:2502.10931
|
we study a singlet scalar extension of the standard model. the singlet scalar is coupled non - minimally to gravity and assumed to drive inflation, and also couple sufficiently strongly with the sm higgs field in order to provide for a strong first order electroweak phase transition. requiring the model to describe inflation successfully, be compatible with the lhc data, and yield a strong first order electroweak phase transition, we identify the regions of the parameter space where the model is viable. we also include a singlet fermion with scalar coupling to the singlet scalar to probe the sensitivity of the constraints on additional degrees of freedom and their couplings in the singlet sector. we also comment on the general feasibility of these fields to act as dark matter.
|
arxiv:1606.06063
|
in the rapidly evolving landscape of software development, addressing security vulnerabilities in open - source software ( oss ) has become critically important. however, existing research and tools from both academia and industry mainly relied on limited solutions, such as vulnerable version adjustment and adopting patches, to handle identified vulnerabilities. however, far more flexible and diverse countermeasures have been actively adopted in the open - source communities. a holistic empirical study is needed to explore the prevalence, distribution, preferences, and effectiveness of these diverse strategies. to this end, in this paper, we conduct a comprehensive study on the taxonomy of vulnerability remediation tactics ( rt ) in oss projects and investigate their pros and cons. this study addresses this oversight by conducting a comprehensive empirical analysis of 21, 187 issues from github, aiming to understand the range and efficacy of remediation tactics within the oss community. we developed a hierarchical taxonomy of 44 distinct rt and evaluated their effectiveness and costs. our findings highlight a significant reliance on community - driven strategies, like using alternative libraries and bypassing vulnerabilities, 44 % of which are currently unsupported by cutting - edge tools. additionally, this research exposes the community ' s preferences for certain fixing approaches by analyzing their acceptance and the reasons for rejection. it also underscores a critical gap in modern vulnerability databases, where 54 % of cves lack fixing suggestions, a gap that can be significantly mitigated by leveraging the 93 % of actionable solutions provided through github issues.
|
arxiv:2503.23357
|
to investigate the effects of muscle fatigue on force sense at the ankle joint, 10 young healthy adults were asked to perform an isometric contra - lateral force ankle - matching task in two experimental conditions of : ( 1 ) no - fatigue and ( 2 ) fatigue of the plantar - flexor muscles. measures of the overall accuracy and the variability of the force matching performances were determined using the absolute error and the variable error, respectively. results showed less accurate and less consistent force matching performances in the fatigue than no fatigue condition, as indicated by decreased absolute and variable errors, respectively. the present findings evidence that muscle fatigue degrades force sense at the ankle joint.
|
arxiv:0806.0084
|
causal inference methods based on electronic health record ( ehr ) databases must simultaneously handle confounding and missing data. vast scholarship exists aimed at addressing these two issues separately, but surprisingly few papers attempt to address them simultaneously. in practice, when faced with simultaneous missing data and confounding, analysts may proceed by first imputing missing data and subsequently using outcome regression or inverse - probability weighting ( ipw ) to address confounding. however, little is known about the theoretical performance of such $ \ textit { ad hoc } $ methods. in a recent paper levis $ \ textit { et al. } $ outline a robust framework for tackling these problems together under certain identifying conditions, and introduce a pair of estimators for the average treatment effect ( ate ), one of which is non - parametric efficient. in this work we present a series of simulations, motivated by a published ehr based study of the long - term effects of bariatric surgery on weight outcomes, to investigate these new estimators and compare them to existing $ \ textit { ad hoc } $ methods. while the latter perform well in certain scenarios, no single estimator is uniformly best. as such, the work of levis $ \ textit { et al. } $ may serve as a reasonable default for causal inference when handling confounding and missing data together.
|
arxiv:2407.06038
|
video diffusion models are able to generate high - quality videos by learning strong spatial - temporal priors on large - scale datasets. in this paper, we aim to investigate whether such priors derived from a generative process are suitable for video recognition, and eventually joint optimization of generation and recognition. building upon stable video diffusion, we introduce genrec, the first unified framework trained with a random - frame conditioning process so as to learn generalized spatial - temporal representations. the resulting framework can naturally supports generation and recognition, and more importantly is robust even when visual inputs contain limited information. extensive experiments demonstrate the efficacy of genrec for both recognition and generation. in particular, genrec achieves competitive recognition performance, offering 75. 8 % and 87. 2 % accuracy on ssv2 and k400, respectively. genrec also performs the best on class - conditioned image - to - video generation, achieving 46. 5 and 49. 3 fvd scores on ssv2 and ek - 100 datasets. furthermore, genrec demonstrates extraordinary robustness in scenarios that only limited frames can be observed. code will be available at https : / / github. com / wengzejia1 / genrec.
|
arxiv:2408.15241
|
double - fourier interferometry is the most viable path to sub - arcsecond spatial resolution for future astronomical instruments that will observe the universe at far - infrared wavelengths. the double transform spatio - spectral interferometry couples pupil plane beam combination with detector arrays to enable imaging spectroscopy of wide fields, that will be key to accomplishing top - level science goals. the wide field of view and the necessity for these instruments to fly above the opaque atmosphere create unique characteristics and requirements compared to instruments on ground - based telescopes. in this paper, we discuss some characteristics of single - baseline spatio - spectral interferometers. we investigate the impact of intensity and optical path difference noise on the interferogram and the spectral signal - to - noise ratio. we apply our findings to the special case of the balloon experimental twin telescope for infrared interferometry ( bettii ), a balloon payload that will be a first application of this technique at far - infrared wavelengths on a flying platform.
|
arxiv:1507.03961
|
program transformations in terms of abstract syntax trees compromise referential integrity by introducing variable capture. variable capture occurs when in the generated program a variable declaration accidentally shadows the intended target of a variable reference. existing transformation systems either do not guarantee the avoidance of variable capture or impair the implementation of transformations. we present an algorithm called name - fix that automatically eliminates variable capture from a generated program by systematically renaming variables. name - fix is guided by a graph representation of the binding structure of a program, and requires name - resolution algorithms for the source language and the target language of a transformation. name - fix is generic and works for arbitrary transformations in any transformation system that supports origin tracking for names. we verify the correctness of name - fix and identify an interesting class of transformations for which name - fix provides hygiene. we demonstrate the applicability of name - fix for implementing capture - avoiding substitution, inlining, lambda lifting, and compilers for two domain - specific languages.
|
arxiv:1404.5770
|
the partial transpose $ \ rho _ a ^ { t _ 2 } $ of the reduced density matrix $ \ rho _ a $ is the key object to quantify the entanglement in mixed states, in particular through the presence of negative eigenvalues in its spectrum. here we derive analytically the distribution of the eigenvalues of $ \ rho _ a ^ { t _ 2 } $, that we dub negativity spectrum, in the ground sate of gapless one - dimensional systems described by a conformal field theory ( cft ), focusing on the case of two adjacent intervals. we show that the negativity spectrum is universal and depends only on the central charge of the cft, similarly to the entanglement spectrum. the precise form of the negativity spectrum depends on whether the two intervals are in a pure or mixed state, and in both cases, a dependence on the sign of the eigenvalues is found. this dependence is weak for bulk eigenvalues, whereas it is strong at the spectrum edges. we also investigate the scaling of the smallest ( negative ) and largest ( positive ) eigenvalues of $ \ rho _ a ^ { t _ 2 } $. we check our results against dmrg simulations for the critical ising and heisenberg chains, and against exact results for the harmonic chain, finding good agreement for the spectrum, but showing that the smallest eigenvalue is affected by very large scaling corrections.
|
arxiv:1607.02992
|
noncatastrophic encoders are an important class of polynomial generator matrices of convolutional codes. when these polynomials have coefficients in a finite field, these encoders have been characterized are being polynomial left prime matrices. in this paper we study the notion of noncatastrophicity in the context of convolutional codes when the polynomial matrices have entries in a finite ring. in particular, we need to introduce two different notion of primeness in order to fully characterize noncatastrophic encoders over the finite ring z _ { p ^ r }. the second part of the paper is devoted to investigate the notion of free and column distance in this context when the convolutional code is a free finitely generated z _ { p ^ r } - module. we introduce the notion of b - degree and provide new bounds on the free distances and column distance. we show that this class of convolutional codes is optimal with respect to the column distance and to the free distance if and only if its projection on z _ p is.
|
arxiv:2104.06754
|
person re - identification is the task of matching pedestrian images across non - overlapping cameras. in this paper, we propose a non - linear cross - view similarity metric learning for handling small size training data in practical re - id systems. the method employs non - linear mappings combined with cross - view discriminative subspace learning and cross - view distance metric learning based on pairwise similarity constraints. it is a natural extension of xqda from linear to non - linear mappings using kernels, and learns non - linear transformations for efficiently handling complex non - linearity of person appearance across camera views. importantly, the proposed method is very computationally efficient. extensive experiments on four challenging datasets shows that our method attains competitive performance against state - of - the - art methods.
|
arxiv:1909.11316
|
as a straightforward application of the recently calculated two - loop heavy quarkonium hamiltonian, we evaluate the two - loop $ o ( \ epsilon ) $ term of the $ 1 / ( mr ^ 2 ) $ heavy quarkonium potential. compared to a previous calculation we find a small difference in the coefficient of the maximally non - abelian color factor $ c _ f c _ a ^ 2 $. we further examine this coefficient carefully.
|
arxiv:2411.07048
|
in this paper, we consider the relation between toeplitz operators and elements in von neumann algebras generated by certain graph groupoids.
|
arxiv:1007.2896
|
green hydrogen is a promising solution within carbon free energy systems with sub - saharan africa being a possibly well - suited candidate for its production. however, green hydrogen in sub - saharan africa is not yet investigated in detail. this work determines the green hydrogen cost - potential for green hydrogen within this region. therefore, a potential analysis for pv, wind and hydropower, groundwater analysis, and energy systems optimization are conducted. the results are evaluated under local socio - economic factors. results show that hydrogen costs start at 1. 6 eur / kg in mauritania with a total potential of ~ 259 twh / a under 2 eur / kg in 2050. two third of the regions experience groundwater limitations and need desalination at surplus costs of ~ 1 % of hydrogen costs. socio - economic analysis show, that green hydrogen deployment can be hindered along the upper guinea coast and the african great lakes, driven by limited energy access, low labor costs in west africa, and high labor potential in other regions.
|
arxiv:2408.10184
|
minimax optimization has found extensive applications in modern machine learning, in settings such as generative adversarial networks ( gans ), adversarial training and multi - agent reinforcement learning. as most of these applications involve continuous nonconvex - nonconcave formulations, a very basic question arises - - - " what is a proper definition of local optima? " most previous work answers this question using classical notions of equilibria from simultaneous games, where the min - player and the max - player act simultaneously. in contrast, most applications in machine learning, including gans and adversarial training, correspond to sequential games, where the order of which player acts first is crucial ( since minimax is in general not equal to maximin due to the nonconvex - nonconcave nature of the problems ). the main contribution of this paper is to propose a proper mathematical definition of local optimality for this sequential setting - - - local minimax, as well as to present its properties and existence results. finally, we establish a strong connection to a basic local search algorithm - - - gradient descent ascent ( gda ) : under mild conditions, all stable limit points of gda are exactly local minimax points up to some degenerate points.
|
arxiv:1902.00618
|
we describe powder and single - crystal inelastic neutron scattering experiments on a spinel - type antiferromagnet geco $ _ 2 $ o $ _ 4 $, represented by an effective total angular momentum j _ eff = 1 / 2. several types of non - dispersive short - range magnetic excitations were discovered. the scattering intensity maps in $ \ vec { q } $ space are well reproduced by dynamical structure factor analyses using molecular model hamiltonians. the results of analyses strongly suggest that the molecular excitations below t _ n arise from a hidden molecular - singlet ground state, in which ferromagnetic subunits are antiferromagnetically coupled. the quasielastic excitations above t _ n are interpreted as its precursor. a combination of frustration and j _ eff = 1 / 2 might induce these quantum phenomena.
|
arxiv:1102.4395
|
weak lensing causes spatially coherent fluctuations in flux of type ia supernovae ( sne ia ). this lensing magnification allows for weak lensing measurement independent of cosmic shear. it is free of shape measurement errors associated with cosmic shear and can therefore be used to diagnose and calibrate multiplicative error. although this lensing magnification is difficult to measure accurately in auto correlation, its cross correlation with cosmic shear and galaxy distribution in overlapping area can be measured to significantly higher accuracy. therefore these cross correlations can put useful constraint on multiplicative error, and the obtained constraint is free of cosmic variance in weak lensing field. we present two methods implementing this idea and estimate their performances. we find that, with $ \ sim 1 $ million sne ia that can be achieved by the proposed d2k survey with the lsst telescope ( zhan et al. 2008 ), multiplicative error of $ \ sim 0. 5 \ % $ for source galaxies at $ z _ s \ sim 1 $ can be detected and larger multiplicative error can be corrected to the level of $ 0. 5 \ % $. it is therefore a promising approach to control the multiplicative to the sub - percent level required for stage iv projects. the combination of the two methods even has the potential to diagnose and calibrate galaxy intrinsic alignment, which is another major systematic error in cosmic shear cosmology.
|
arxiv:1504.00733
|
synchronous programming is a paradigm of choice for the design of safety - critical reactive systems. runtime enforcement is a technique to ensure that the output of a black - box system satisfies some desired properties. this paper deals with the problem of runtime enforcement in the context of synchronous programs. we propose a framework where an enforcer monitors both the inputs and the outputs of a synchronous program and ( minimally ) edits erroneous inputs / outputs in order to guarantee that a given property holds. we define enforceability conditions, develop an online enforcement algorithm, and prove its correctness. we also report on an implementation of the algorithm on top of the kieler framework for the sccharts synchronous language. experimental results show that enforcement has minimal execution time overhead, which decreases proportionally with larger benchmarks.
|
arxiv:1612.05030
|
we demonstrate the power of a first principle - based and practicable method that allows for the perturbative computation of reduced density matrix elements of an open quantum system without making use of any master equations. the approach is based on techniques from non - equilibrium quantum field theory like thermo field dynamics, the schwinger - keldsyh formalism, and the feynman - vernon influence functional. it does not require the markov approximation and is essentially a lehmann - szymanzik - zimmermann - like reduction. in order to illustrate this method, we consider a real scalar field as an open quantum system interacting with an environment comprising another real scalar field. we give a general formula that allows for the perturbative computation of density matrix elements for any number of particles in a momentum basis. finally, we consider a simple toy model and use this formula to obtain expressions for some of the system ' s reduced density matrix elements.
|
arxiv:2204.08829
|
the rapid development of ai - mediated communication technologies ( aicts ), which are digital tools that use ai to augment interpersonal messages, has raised concerns about the future of interpersonal trust and prompted discussions about disclosure and uptake. this paper contributes to this discussion by assessing perceptions about the acceptability and use of open and secret aicts for oneself and others. in two studies with representative samples ( uk : n = 477, us : n = 765 ), we found that secret aict use is deemed less acceptable than open aict use, people tend to overestimate others ' aict use, and people expect others to use aicts irresponsibly. thus, we raise concerns about the potential for misperceptions and different expectations for others to drive self - fulfilling pessimistic outlooks about ai - mediated communication.
|
arxiv:2305.01670
|
we investigate the braid group representations arising from categories of representations of twisted quantum doubles of finite groups. for these categories, we show that the resulting braid group representations always factor through finite groups, in contrast to the categories associated with quantum groups at roots of unity. we also show that in the case of p - groups, the corresponding pure braid group representations factor through a finite p - group, which answers a question asked of the first author by v. drinfeld.
|
arxiv:math/0703274
|
we present a polarization - dependent infrared reflectivity study of the spin - ladder compound sr $ _ { 2. 5 } $ ca $ _ { 11. 5 } $ cu $ _ { 24 } $ o $ _ { 41 } $ under pressure. the optical response is strongly anisotropic, with the highest reflectivity along the ladders / chains ( \ textbf { e } $ \ | $ c ) revealing a metallic character. for the polarization direction perpendicular to the ladder plane, an insulating behavior is observed. with increasing pressure the optical conductivity for \ textbf { e } $ \ | $ c shows a strong increase, which is most pronounced below 2000 ~ cm $ ^ { - 1 } $. according to the spectral weight analysis of the \ textbf { e } $ \ | $ c optical conductivity the hole concentration in the ladders increases with increasing pressure and tends to saturate at high pressure. at $ \ sim $ 7. 5 ~ gpa the number of holes per cu atom in the ladders has increased by $ \ delta \ delta $ = 0. 09 ( $ \ pm $ 0. 01 ), and the cu valence in the ladders has reached the value + 2. 33. the optical data suggest that sr $ _ { 2. 5 } $ ca $ _ { 11. 5 } $ cu $ _ { 24 } $ o $ _ { 41 } $ remains electronically highly anisotropic up to high pressure, also at low temperatures.
|
arxiv:1411.7590
|
we study the derivative nonlinear schr \ " odinger equation on the real line and obtain global - in - time bounds on high order sobolev norms.
|
arxiv:2107.12297
|
increasing evidence of the effects of changing climate on physical ocean conditions and long - term changes in fish populations adds to the need to understand the effects of stochastic forcing on marine populations. cohort resonance is of particular interest because it involves selective sensitivity to specific time scales of environmental variability, including that of mean age of reproduction, and, more importantly, very low frequencies ( i. e., trends ). we present an age - structured model for two pacific salmon species with environmental variability in survival rate and in individual growth rate, hence spawning age distribution. we use computed frequency response curves and analysis of the linearized dynamics to obtain two main results. first, the frequency response of the population is affected by the life history stage at which variability affects the population ; varying growth rate tends to excite periodic resonance in age structure, while varying survival tends to excite low - frequency fluctuation with more effect on total population size. second, decreasing adult survival strengthens the cohort resonance effect at all frequencies, a finding that addresses the question of how fishing and climate change will interact.
|
arxiv:0912.2774
|
for mathematical convenience initial data sets in numerical relativity are often taken to be conformally flat. employing the dual - foliation formalism, we investigate the physical consequences of this assumption. working within a large class of asymptotically flat spacetimes we show that the adm linear momentum is governed by the leading lorentz part of a boost even in the presence of supertranslation - like terms. following up, we find that in spacetimes that are asymptotically flat, and admit spatial slices with vanishing linear momentum that are sufficiently close to conformal flatness, any boosted slice can not be conformally flat. consequently there are no conformally flat boosted slices of the schwarzschild spacetime. this confirms the previously anticipated explanation for the presence of junk - radiation in brandt - bruegmann puncture data.
|
arxiv:1909.06135
|
we present the cardinal mock galaxy catalogs, a new version of the buzzard simulation that has been updated to support ongoing and future cosmological surveys, including des, desi, and lsst. these catalogs are based on a one - quarter sky simulation populated with galaxies out to a redshift of $ z = 2. 35 $ to a depth of $ m _ { \ rm { r } } = 27 $. compared to the buzzard mocks, the cardinal mocks include an updated subhalo abundance matching ( sham ) model that considers orphan galaxies and includes mass - dependent scatter between galaxy luminosity and halo properties. this model can simultaneously fit galaxy clustering and group - - galaxy cross - correlations measured in three different luminosity threshold samples. the cardinal mocks also feature a new color assignment model that can simultaneously fit color - dependent galaxy clustering in three different luminosity bins. we have developed an algorithm that uses photometric data to improve the color assignment model further and have also developed a novel method to improve small - scale lensing below the ray - tracing resolution. these improvements enable the cardinal mocks to accurately reproduce the abundance of galaxy clusters and the properties of lens galaxies in the dark energy survey data. as such, these simulations will be a valuable tool for future cosmological analyses based on large sky surveys. the cardinal mock will be released upon publication at https : / / chunhaoto. com / cardinalsim.
|
arxiv:2303.12104
|
the emergence of cnns in mainstream deployment has necessitated methods to design and train efficient architectures tailored to maximize the accuracy under diverse hardware & latency constraints. to scale these resource - intensive tasks with an increasing number of deployment targets, once - for - all ( ofa ) proposed an approach to jointly train several models at once with a constant training cost. however, this cost remains as high as 40 - 50 gpu days and also suffers from a combinatorial explosion of sub - optimal model configurations. we seek to reduce this search space - - and hence the training budget - - by constraining search to models close to the accuracy - latency pareto frontier. we incorporate insights of compound relationships between model dimensions to build compofa, a design space smaller by several orders of magnitude. through experiments on imagenet, we demonstrate that even with simple heuristics we can achieve a 2x reduction in training time and 216x speedup in model search / extraction time compared to the state of the art, without loss of pareto optimality! we also show that this smaller design space is dense enough to support equally accurate models for a similar diversity of hardware and latency targets, while also reducing the complexity of the training and subsequent extraction algorithms.
|
arxiv:2104.12642
|
human brain possesses the ability to effectively focus on important environmental components, which enhances perception, learning, reasoning, and decision - making. inspired by this cognitive mechanism, we introduced a novel concept termed relevance for human - robot collaboration ( hrc ). relevance is a dimensionality reduction process that incorporates a continuously operating perception module, evaluates cue sufficiency within the scene, and applies a flexible formulation and computation framework. in this paper, we present an enhanced two - loop framework that integrates real - time and asynchronous processing to quantify relevance and leverage it for safer and more efficient human - robot collaboration ( hrc ). the two - loop framework integrates an asynchronous loop, which leverages llm world knowledge to quantify relevance, and a real - time loop, which performs scene understanding, human intent prediction, and decision - making based on relevance. hrc decision - making is enhanced by a relevance - based task allocation method, as well as a motion generation and collision avoidance approach that incorporates human trajectory prediction. simulations and experiments show that our methodology for relevance quantification can accurately and robustly predict the human objective and relevance, with an average accuracy of up to 0. 90 for objective prediction and up to 0. 96 for relevance prediction. moreover, our motion generation methodology reduces collision cases by 63. 76 % and collision frames by 44. 74 % when compared with a state - of - the - art ( sota ) collision avoidance method. our framework and methodologies, with relevance, guide the robot on how to best assist humans and generate safer and more efficient actions for hrc.
|
arxiv:2409.13998
|
environmental sound classification ( esc ) is an important and challenging problem. in contrast to speech, sound events have noise - like nature and may be produced by a wide variety of sources. in this paper, we propose to use a novel deep convolutional neural network for esc tasks. our network architecture uses stacked convolutional and pooling layers to extract high - level feature representations from spectrogram - like features. furthermore, we apply mixup to esc tasks and explore its impacts on classification performance and feature distribution. experiments were conducted on urbansound8k, esc - 50 and esc - 10 datasets. our experimental results demonstrated that our esc system has achieved the state - of - the - art performance ( 83. 7 % ) on urbansound8k and competitive performance on esc - 50 and esc - 10.
|
arxiv:1808.08405
|
this paper explores the problem of matching entities across different knowledge graphs. given a query entity in one knowledge graph, we wish to find the corresponding real - world entity in another knowledge graph. we formalize this problem and present two large - scale datasets for this task based on exiting cross - ontology links between dbpedia and wikidata, focused on several hundred thousand ambiguous entities. using a classification - based approach, we find that a simple multi - layered perceptron based on representations derived from rdf2vec graph embeddings of entities in each knowledge graph is sufficient to achieve high accuracy, with only small amounts of training data. the contributions of our work are datasets for examining this problem and strong baselines on which future work can be based.
|
arxiv:1903.06607
|
a hallmark of graph neural networks is their ability to distinguish the isomorphism class of their inputs. this study derives hardness results for the classification variant of graph isomorphism in the message - passing model ( mpnn ). mpnn encompasses the majority of graph neural networks used today and is universal when nodes are given unique features. the analysis relies on the introduced measure of communication capacity. capacity measures how much information the nodes of a network can exchange during the forward pass and depends on the depth, message - size, global state, and width of the architecture. it is shown that the capacity of mpnn needs to grow linearly with the number of nodes so that a network can distinguish trees and quadratically for general connected graphs. the derived bounds concern both worst - and average - case behavior and apply to networks with / without unique features and adaptive architecture - - they are also up to two orders of magnitude tighter than those given by simpler arguments. an empirical study involving 12 graph classification tasks and 420 networks reveals strong alignment between actual performance and theoretical predictions.
|
arxiv:2005.06649
|
this paper analyzes different models for evaluating investments in energy storage systems ( ess ) in power systems with high penetration of renewable energy sources ( res ). first of all, two methodologies proposed in the literature are extended to consider ess investment : a unit commitment model that uses the system states ( ss ) method of representing time ; and another one that uses a representative periods ( rp ) method. besides, this paper proposes two new models that improve the previous ones without a significant increase of computation time. the enhanced models are the system states reduced frequency matrix ( ss - rfm ) model which addresses short - term energy storage more approximately than the ss method to reduce the number of constraints in the problem, and the representative periods with transition matrix and cluster indices ( rp - tm & ci ) model which guarantees some continuity between representative periods, e. g. days, and introduces long - term storage into a model originally designed only for the short term. all these models are compared using an hourly unit commitment model as benchmark. while both system state models provide an excellent representation of long - term storage, their representation of short - term storage is frequently unrealistic. the rp - tm & ci model, on the other hand, succeeds in approximating both short - and long - term storage, which leads to almost 10 times lower error in storage investment results in comparison to the other models analyzed.
|
arxiv:1810.09539
|
we investigate the electronic structure and properties of atoms exposed to a magnetic quadrupole field. the spin - spatial as well as generalized time reversal symmetries are established and shown to lead to a two - fold degeneracy of the electronic states in the presence of the field. low - lying as well as highly excited rydberg states are computed and analyzed for a broad regime of field gradients. the delicate interplay between the coulomb and various magnetic interactions leads to complex patterns of the spatial spin polarization of individual excited states. electromagnetic transitions in the quadrupole field are studied in detail thereby providing the selection rules and in particular the transition wavelengths and corresponding dipole strengths. the peculiar property that the quadrupole magnetic field induces permanent electric dipole moments of the atoms is derived and discussed.
|
arxiv:physics/0402109
|
stack overflow ( so ) is the most popular question - and - answer website for software developers, providing a large amount of code snippets and free - form text on a wide variety of topics. like other software artifacts, questions and answers on so evolve over time, for example when bugs in code snippets are fixed, code is updated to work with a more recent library version, or text surrounding a code snippet is edited for clarity. to be able to analyze how content on so evolves, we built sotorrent, an open dataset based on the official so data dump. sotorrent provides access to the version history of so content at the level of whole posts and individual text or code blocks. it connects so posts to other platforms by aggregating urls from text blocks and comments, and by collecting references from github files to so posts. in this paper, we describe how we built sotorrent, and in particular how we evaluated 134 different string similarity metrics regarding their applicability for reconstructing the version history of text and code blocks. based on different analyses using the dataset, we present : ( 1 ) insights into the evolution of so posts, e. g., that post edits are usually small, happen soon after the initial creation of the post, and that code is rarely changed without also updating the surrounding text ; ( 2 ) a qualitative study investigating the close relationship between post edits and comments, ( 3 ) a first analysis of code clones on so together with an investigation of possible licensing risks. finally, since the initial presentation of the dataset, we improved the post block extraction and our predecessor matching strategy.
|
arxiv:1811.00804
|
an ensemble monte carlo method is used to study the spin injection through a ferromagnet - semiconductor junction where a schottky barrier is formed. it is shown that the schottky - barrier - induced electric field which is confined in the depletion region and parallel to the injection direction, is very large. this electric field can induce an effective magnetic field due to the rashba effect and cause strong spin dephasing.
|
arxiv:cond-mat/0506251
|
two fundamental problems for extraterrestrial intelligences ( etis ) attempting to establish interstellar communication are timing and energy consumption. humanity ' s study of exoplanets via their transit across the host star highlights a means of solving both problems. an eti ' a ' can communicate with eti ' b ' if b is observing transiting planets in a ' s star system, either by building structures to produce artificial transits observable by b, or by emitting signals at b during transit, at significantly lower energy consumption than typical electromagnetic transmission schemes. this can produce a network of interconnected civilisations, establishing contact via observing each other ' s transits. assuming that civilisations reside in a galactic habitable zone ( ghz ), i conduct monte carlo realisation simulations of the establishment and growth of this network, and analyse its properties in the context of graph theory. i find that at any instant, only a few civilisations are correctly aligned to communicate via transits. however, we should expect the true network to be cumulative, where a " handshake " connection at any time guarantees connection in the future via e. g. electromagnetic signals. in all our simulations, the cumulative network connects all civilisations together in a complete network. if civilisations share knowledge of their network connections, the network can be fully complete on timescales of order a hundred thousand years. once established, this network can connect any two civilisations either directly, or via intermediate civilisations, with a path much less than the dimensions of the ghz.
|
arxiv:1707.03730
|
the nonequilibrium thermodynamics of an open ( classical or quantum ) system in strong contact with a single heat bath can be conveniently described in terms of the hamiltonian of mean force. however, the conventional formulation is limited by the necessity to measure differences in equilibrium properties of the system - bath composite. we make use of the freedom involved in defining thermodynamic quantities, which leaves the thermodynamics unchanged, to show that the hamiltonian of mean force can be inferred from measurements on the system alone, up to that irrelevant freedom. in doing so, we refute a key criticism expressed in phys. rev. e 94, 022143 and arxiv : 1911. 11660. we also discuss the remaining part of the criticism.
|
arxiv:2001.08917
|
we compute, for the four - dimensional su ( 4 ) and su ( 6 ) gauge theories formulated on a lattice, the string tensions sigma _ k related to sources with z _ n charge k, using monte carlo simulations. our results are compatible with sigma _ k \ propto sin ( k pi / n ), and show sizeable deviations from casimir scaling.
|
arxiv:hep-lat/0110101
|
we propose a multi - scale extension of conformal prediction, an approach that constructs prediction sets with finite - sample coverage guarantees under minimal statistical assumptions. classic conformal prediction relies on a single notion of conformity, overlooking the multi - level structures that arise in applications such as image analysis, hierarchical data exploration, and multi - resolution time series modeling. in contrast, the proposed framework defines a distinct conformity function at each relevant scale or resolution, producing multiple conformal predictors whose prediction sets are then intersected to form the final multi - scale output. we establish theoretical results confirming that the multi - scale prediction set retains the marginal coverage guarantees of the original conformal framework and can, in fact, yield smaller or more precise sets in practice. by distributing the total miscoverage probability across scales in proportion to their informative power, the method further refines the set sizes. we also show that dependence between scales can lead to conservative coverage, ensuring that the actual coverage exceeds the nominal level. numerical experiments in a synthetic classification setting demonstrate that multi - scale conformal prediction achieves or surpasses the nominal coverage level while generating smaller prediction sets compared to single - scale conformal methods.
|
arxiv:2502.05565
|
context : the systems comprising a system of systems ( sos ) are inde - pendently acquired, operated, and managed. frequently, the architecture documentation of these existing systems addresses only a stand - alone perspective, and must be augmented to address concerns that arise in the integrated sos. objective : we evaluated an architecture documentation viewpoint to address the concerns of a sos architect about a constituent system, to support sos design and analysis involving that constituent system. method : we performed an expert review of documentation produced by applying the viewpoint to a system, using the active review method. results : the expert panel was able to used a view constructed using the baseline version of the viewpoint to answer questions related to all sos architect concerns about a constituent system, except for questions concerning the interaction of the constituent system with the platform and network infrastructure. conclusions : we found that the expert panel was unable to answer certain questions because the baseline version of the viewpoint had a gap in coverage related to relationship of software units of execution ( e. g., processes or services ) to computers and networks. the viewpoint was revised to add a deployment model to address these concerns, and is included in an appendix.
|
arxiv:1801.06837
|
by the theory of elliptic curves, we study the nontrivial rational parametric solutions and rational solutions of the diophantine equations $ z ^ 2 = f ( x ) ^ 2 \ pm f ( y ) ^ 2 $ for some simple laurent polynomials $ f $.
|
arxiv:1608.03810
|
we prove that, given a constant $ k > 2 $ and a bounded linear operator $ t $ from a jb $ ^ * $ - triple $ e $ into a complex hilbert space $ h $, there exists a norm - one functional $ \ psi \ in e ^ * $ satisfying $ $ \ | t ( x ) \ | \ leq k \, \ | t \ | \, \ | x \ | _ { \ psi }, $ $ for all $ x \ in e $. applying this result we show that, given $ g > 8 ( 1 + 2 \ sqrt { 3 } ) $ and a bounded bilinear form $ v $ on the cartesian product of two jb $ ^ * $ - triples $ e $ and $ b $, there exist norm - one functionals $ \ varphi \ in e ^ { * } $ and $ \ psi \ in b ^ { * } $ satisfying $ $ | v ( x, y ) | \ leq g \ \ | v \ | \, \ | x \ | _ { \ varphi } \, \ | y \ | _ { \ psi } $ $ for all $ ( x, y ) \ in e \ times b $. these results prove a conjecture pursued during almost twenty years.
|
arxiv:1903.08931
|
paper deals with the singular sturm - liouville expressions $ $ l ( y ) = - ( py ' ) ' + qy $ $ on a finite interval with coefficients $ $ q = q ', \ quad 1 / p, q / p, q ^ 2 / p \ in l _ 1, $ $ where derivative of the function $ q $ is understood in the sense of distributions. due to a new regularization corresponding operators are correctly defined as quasi - differential. their resolvent approximation is investigated and all self - adjoint and maximal dissipative extensions and generalized resolvents are described in terms of homogeneous boundary conditions of the canonic form. some results are new for the case $ p ( t ) \ equiv 1 $ as well.
|
arxiv:1002.4371
|
a covariant, composite scalar diquark, fadde ' ev amplitude model for the nucleon is used to calculate pseudoscalar, isoscalar - and isovector - vector, axial - vector and scalar nucleon form factors. the last yields the nucleon sigma - term and on - shell sigma - nucleon coupling. the calculated form factors are soft, and the couplings are generally in good agreement with experiment and other determinations. elements in the dressed - quark - axial - vector vertex that are not constrained by the ward - takahashi identity contribute ~ 20 % to the magnitude of g _ a. the calculation of the nucleon sigma - term elucidates the only unambiguous means of extrapolating meson - nucleon couplings off the meson mass - shell.
|
arxiv:nucl-th/9911068
|
we prove that bernoulli convolutions are absolutely continuous provided the parameter lambda is an algebraic number sufficiently close to 1 depending on the mahler measure of lambda.
|
arxiv:1602.00261
|
in the present study, we show calculation of nonlinear compton scattering with circularly polarized photons in a cylindrical coordinate using feynman diagram to calculate photon vortex generation in intermediate states considering conservation of angular momentum. we take two different vortex wave functions based on bessel function for the emitted photon and the electron after emission of the photon, which are the eigenstate of z component of the total angular momentum ( ztam ) when a particle propagates along z axis. the result shows that when an electron absorbs n photons a photon vortex with a ztam = n is predominantly radiated, but there are still very small contributions of photons with a ztam = ( n - 1 ) and ( n + 1 ) due to the spin flip of the initial electron. this means even when an electron absorbs only a single photon, the electron may emit a photon vortex of a ztam of 2 h - bar. however, the numerical calculations show that the contribution of the spin flip is four orders of magnitude smaller than that of the dominant radiation. we also discuss the circular polarization for the generated photon vortices.
|
arxiv:2412.04709
|
this paper studies strategic decentralization in binary choice composite network congestion games. a player decentralizes if she lets some autonomous agents to decide respectively how to send different parts of her stock from the origin to the destination. this paper shows that, with convex, strictly increasing and differentiable arc cost functions, an atomic splittable player always has an optimal unilateral decentralization strategy. besides, unilateral decentralization gives her the same advantage as being the leader in a stackelberg congestion game. finally, unilateral decentralization of an atomic player has a negative impact on the social cost and on the costs of the other players at the equilibrium of the congestion game.
|
arxiv:1506.03479
|
numerous children diagnosed with autism spectrum disorder ( asd ) exhibit abnormal eye gaze pattern in communication and social interaction. due to the high cost of asd interventions and a shortage of professional therapists, researchers have explored the use of virtual reality ( vr ) systems as a supplementary intervention for autistic children. this paper presents the design of a novel vr - based system called the hide and seek virtual reality system ( hsvrs ). the hsvrs allows children with asd to enhance their ocular gaze abilities while engaging in a hide - and - seek game with a virtual avatar. by employing face and voice manipulation technology, the hsvrs provides the option to customize the appearance and voice of the avatar, making it resemble someone familiar to the child, such as their parents. we conducted a pilot study at the third affiliated hospital of sun yat - sen university, china, to evaluate the feasibility of hsvrs as an auxiliary intervention for children with autism ( n = 24 ). through the analysis of subjective questionnaires completed by the participants ' parents and objective eye gaze data, we observed that children in the vr - assisted intervention group demonstrated better performance compared to those in the control group. furthermore, our findings indicate that the utilization of face and voice manipulation techniques to personalize avatars in hide - and - seek games can enhance the efficiency and effectiveness of the system.
|
arxiv:2310.13482
|
the paper is a second step in the study of $ \ overline { m } _ { 0, n } $ started in arxiv : 1006. 0987 [ math. ag ]. we study fiber type morphisms of this moduli space via kapranov ' s beautiful description. our final goal is to understand if any dominant morphism $ f : \ overline { m } _ { 0, n } \ to x $ with positive dimensional fibers factors through forgetful morphisms. we prove that this is true if either $ n \ leq 7 $ or $ \ rm { dim } x \ leq 2 $ or the rational map induced on $ p ^ { n - 3 } $ has linear general fibers. along the way we give examples of forgetful morphisms whose fibers are connected curves of arbitrarily high positive genus, for $ n > > 0 $.
|
arxiv:1105.3293
|
stimulated emission can be defined as the process when an incoming photon stimulates an additional quantum of energy from an atom into the same electromagnetic mode as the impinging photon. hence, the two outgoing photons are identical. in a waveguide or free space, this intuition is typically found through fermi ' s golden rule, however, this does not properly account for the wave - like nature of the photons. here, i present an exact solution to stimulated emission from a quantum two - level atom that properly accounts for the incoming and outgoing electromagnetic modes. this result is valid over a huge range of incident photon numbers. for a single incident photon, it shows how the photon must properly mode match the two - level system to cause stimulated emission. for a fock state drive with large photon number, the exact solution shows how a two - level system rabi oscillates with the traveling fock mode as it passes by. i additionally use the same formalism to show that stimulated emission by a coherent pulse cannot be understood as an additional photon being emitted into the incident coherent state because the two - level system ' s state factorizes with the electromagnetic field ' s coherent state. recent advances in superconducting circuits make them an ideal platform to test these predictions.
|
arxiv:1806.04862
|
to provide stable and high data rate wireless access for passengers in the train, it is necessary to properly deploy base stations along the railway. we consider this issue from the perspective of service, which is defined as the integral of the time - varying instantaneous channel capacity. with large - scale fading assumption, it will be shown that the total service of each base station is inversely proportional to the velocity of the train. besides, we find that if the ratio of the service provided by a base station in its service region to its total service is given, the base station interval ( i. e. the distance between two adjacent base stations ) is a constant regardless of the velocity of the train. on the other hand, if a certain amount of service is required, the interval will increase with the velocity of the train. the above results apply not only to simple curve rails, like line rail and arc rail, but also to any irregular curve rail, provided that the train is travelling at a constant velocity. furthermore, the new developed results are applied to analyze the on - off transmission strategy of base stations.
|
arxiv:1311.6272
|
we develop quenched chiral perturbation theory for vector mesons made of light quarks, in the limit where the vector meson masses are much larger than the pion mass. we use this theory to extract the leading nonanalytic dependence of the vector meson masses on the masses of the light quarks. by comparing with analogous quantities computed in ordinary chiral perturbation theory, we estimate the size of quenching effects, observing that in general they can be quite large. this estimate is relevant to lattice simulations, where the $ \ rho $ mass is often used to set the lattice spacing.
|
arxiv:hep-ph/9610532
|
3d gaussian splatting ( 3dgs ) has recently emerged as a promising 3d representation. much research has been focused on reducing its storage requirements and memory footprint. however, the needs to compress and transmit the 3dgs representation to the remote side are overlooked. this new application calls for rate - distortion - optimized 3dgs compression. how to quantize and entropy encode sparse gaussian primitives in the 3d space remains largely unexplored. few early attempts resort to the hyperprior framework from learned image compression. but, they fail to utilize fully the inter and intra correlation inherent in gaussian primitives. built on scaffoldgs, this work, termed cat - 3dgs, introduces a context - adaptive triplane approach to their rate - distortion - optimized coding. it features multi - scale triplanes, oriented according to the principal axes of gaussian primitives in the 3d space, to capture their inter correlation ( i. e. spatial correlation ) for spatial autoregressive coding in the projected 2d planes. with these triplanes serving as the hyperprior, we further perform channel - wise autoregressive coding to leverage the intra correlation within each individual gaussian primitive. our cat - 3dgs incorporates a view frequency - aware masking mechanism. it actively skips from coding those gaussian primitives that potentially have little impact on the rendering quality. when trained end - to - end to strike a good rate - distortion trade - off, our cat - 3dgs achieves the state - of - the - art compression performance on the commonly used real - world datasets.
|
arxiv:2503.00357
|
. { \ textstyle e ^ { \ pi { \ sqrt { 58 } } } = 396 ^ { 4 } - 104. 000000177 \ dots. } this might be compared to heegner numbers, which have class number 1 and yield similar formulae. ramanujan ' s series for π converges extraordinarily rapidly and forms the basis of some of the fastest algorithms used to calculate π. truncating the sum to the first term also gives the approximation 9801√2 / 4412 for π, which is correct to six decimal places ; truncating it to the first two terms gives a value correct to 14 decimal places ( see also the more general ramanujan – sato series ). one of ramanujan ' s remarkable capabilities was the rapid solution of problems, illustrated by the following anecdote about an incident in which p. c. mahalanobis posed a problem : imagine that you are on a street with houses marked 1 through n. there is a house in between ( x ) such that the sum of the house numbers to the left of it equals the sum of the house numbers to its right. if n is between 50 and 500, what are n and x? ' this is a bivariate problem with multiple solutions. ramanujan thought about it and gave the answer with a twist : he gave a continued fraction. the unusual part was that it was the solution to the whole class of problems. mahalanobis was astounded and asked how he did it. ' it is simple. the minute i heard the problem, i knew that the answer was a continued fraction. which continued fraction, i asked myself. then the answer came to my mind ', ramanujan replied. " his intuition also led him to derive some previously unknown identities, such as ( 1 + 2 n = 1 ∞ cos ( n θ ) cosh ( n π ) ) − 2 + ( 1 + 2 n = 1 ∞ cosh ( n θ ) cosh ( n π ) ) − 2 = 2 γ 4 ( 3 4 ) π = 8 π 3 γ 4 ( 1 4 ) { \ displaystyle { \ begin { aligned } & \ left ( 1 + 2 \ sum _ { n = 1 } ^ { \ infty } { \ frac { \ cos ( n \ theta ) } { \ cosh ( n \ pi ) } } \ right ) ^ { - 2 } + \ left ( 1 + 2
|
https://en.wikipedia.org/wiki/Srinivasa_Ramanujan
|
deep learning - based joint source - channel coding ( jscc ) has shown excellent performance in image and feature transmission. however, the output values of the jscc encoder are continuous, which makes the constellation of modulation complex and dense. it is hard and expensive to design radio frequency chains for transmitting such full - resolution constellation points. in this paper, two methods of mapping the full - resolution constellation to finite constellation are proposed for real system implementation. the constellation mapping results of the proposed methods correspond to regular constellation and irregular constellation, respectively. we apply the methods to existing deep jscc models and evaluate them on awgn channels with different signal - to - noise ratios ( snrs ). experimental results show that the proposed methods outperform the traditional uniform quadrature amplitude modulation ( qam ) constellation mapping method by only adding a few additional parameters.
|
arxiv:2206.07008
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.