text
stringlengths 1
3.65k
| source
stringlengths 15
79
|
|---|---|
crystals melt when thermal excitations or the concentration of defects in the lattice is sufficiently high. upon melting, the crystalline long - range order vanishes, turning the solid to a fluid. in contrast to this classical scenario of solid melting, here we demonstrate a counter - intuitive behavior of the occurrence of crystalline long - range order in an initially disordered matrix. this unusual solidification is demonstrated in a system of passive colloidal particles accommodating chemically active defects - - photocatalytic janus particles. the observed crystallization occurs when the amount of active - defect - induced fluctuations ( which is the measure of the effective temperature ) reaches critical value. the driving mechanism behind this unusual behavior is purely internal and resembles a blast - induced solidification. here the role of " internal micro - blasts " is played by the photochemical activity of defects residing in the colloidal matrix. the defect - induced solidification occurs under non - equilibrium conditions : the resulting solid exists as long as a constant supply of energy in the form of ion flow is provided by the catalytic photochemical reaction at the surface of active janus particle defects. our findings could be useful for understanding of the phase transitions of matter under extreme conditions far from thermodynamic equilibrium.
|
arxiv:2010.03794
|
pressure effect is overviewed for the cuprates and carbon - based superconductors, with an emphasis on how their orbital characters are modified by pressure. for the high - tc cuprates, we start from an observation for ambient pressure that, on top of the main orbital ( dx2 - y2 ), a hybridization with the second ( dz2 ) orbital around the fermi energy significantly affects tc in the spin - fluctuation mediated pairing, where the hybridization is dominated by material parameters. we can then show that applying pressures along a, b axes enhances tc while a c axis pressure suppresses tc, where not only the dz2 hybridization but also cu ( 4s ) hybridization exert an effect. for the multi - layer cuprates, inter - layer pair hopping is suggested to be important, which may contribute to pressure effect. pressure effect is also interesting in a recently discovered aromatic family of superconductors ( picene, etc ). there, we have again multi - band systems, which in this case derive from different molecular orbitals. the fermi surface is an intriguing composite of different pockets / sheets having different dimensionalities arising from anisotropic transfers between the molecular orbitals, and pressure effects should be an important probe of these.
|
arxiv:1307.5954
|
##x < 2x + 1 β€ 3x + 2, it is not possible to isolate x in any one part of the inequality through addition or subtraction. instead, the inequalities must be solved independently, yielding x < 1 / 2 and x β₯ β1 respectively, which can be combined into the final solution β1 β€ x < 1 / 2. occasionally, chained notation is used with inequalities in different directions, in which case the meaning is the logical conjunction of the inequalities between adjacent terms. for example, the defining condition of a zigzag poset is written as a1 < a2 > a3 < a4 > a5 < a6 >.... mixed chained notation is used more often with compatible relations, like <, =, β€. for instance, a < b = c β€ d means that a < b, b = c, and c β€ d. this notation exists in a few programming languages such as python. in contrast, in programming languages that provide an ordering on the type of comparison results, such as c, even homogeneous chains may have a completely different meaning. = = sharp inequalities = = an inequality is said to be sharp if it cannot be relaxed and still be valid in general. formally, a universally quantified inequality Ο is called sharp if, for every valid universally quantified inequality Ο, if Ο β Ο holds, then Ο Ο also holds. for instance, the inequality β r. a2 β₯ 0 is sharp, whereas the inequality β r. a2 β₯ β1 is not sharp. = = inequalities between means = = there are many inequalities between means. for example, for any positive numbers a1, a2,..., an we have h β€ g β€ a β€ q, { \ displaystyle h \ leq g \ leq a \ leq q, } where they represent the following means of the sequence : harmonic mean : h = n 1 a 1 + 1 a 2 + + 1 a n { \ displaystyle h = { \ frac { n } { { \ frac { 1 } { a _ { 1 } } } + { \ frac { 1 } { a _ { 2 } } } + \ cdots + { \ frac { 1 } { a _ { n } } } } } } geometric mean : g = a 1 β
a 2 a n n { \ displaystyle g = { \ sq
|
https://en.wikipedia.org/wiki/Inequality_(mathematics)
|
in this document, a nonlinear control law for a grid - tied converter is introduced. the converter topology consists of a voltage source inverter ( vsi ) linked to the grid through an inductive - capacitive second - order filter, its input being connected to a capacitive dc - link supplied by a renewable energy - based input power source. in order to achieve good performance in presence of large state excursions caused mainly by substantial set - point modifications and / or considerable disturbances, a nonlinear control law based on a complex - valued feedback linearization strategy is designed. specifically, a flat output is adopted, which is given by the summation of the energy stored in the dc - link capacitor and in the output filter ' s inductor and capacitor, as well as by the reactive energy at the output. after linearizing the system through a pertinent coordinate transformation and a nonlinear feedback, a linear trajectory tracking control law is implemented. the performance of the system controlled by applying the proposed strategy is tested via simulation for a very weak grid of unity x / r ratio, yielding satisfactory results.
|
arxiv:2502.18245
|
in this paper we study the existence of basins of attraction for germs of 2 - resonant biholomorphisms of $ \ c ^ n $ fixing a point, that is germs such that the eigenvalues of the differential at the fixed point have a 2 dimensional family of resonances.
|
arxiv:1211.3103
|
a sequential piecewise linear programming method is presented where bounded domains of non - convex functions are successively contracted about the solution of a piecewise linear program at each iteration of the algorithm. although feasibility and optimality are not guaranteed, we show that the method is capable of obtaining convergent and optimal solutions on a number of nonlinear programming ( nlp ) and mixed integer nonlinear programming ( minlp ) problems using only a small number of breakpoints and integer variables.
|
arxiv:2004.09474
|
the purpose of this work is to analyze the flow due to a potential point vortex pair in the vicinity of a symmetry line ( or " wall " ), in order to understand why the presence of the wall, even far from the vortices, accelerates fluid mixing around the vortex pair. an asymptotic analysis, in the limit of large distances to the wall, allows to approximate the wall effect as a constant translation of the vortex pair parallel to the wall, plus a straining flow which induces a natural blinking vortex mechanism with period half the rotation period. a melnikov analysis of lagrangian particles, in the frame translating and rotating with the vortices, shows that a homoclinic bifurcation indeed occurs, so that the various separatrices located near the vortex pair ( and rotating with it ) do not survive when a wall is present. the thickness of the resulting inner stochastic layer is estimated by using the separatrix map method, and is shown to scale like the inverse of the squared distance to the wall. this estimation provides a lower - bound to the numerical thickness measured from either poincar \ ' e sections or simulations of lagrangian particles transported by the exact potential velocity field in the laboratory frame. in addition, it is shown that the outer homoclinic cycle, separating the vortices from the external ( open ) flow, is also perturbed from inside by the rotation of the vortex pair. as a consequence, a stochastic layer is shown to exist also in the vicinity of this cycle, allowing fluid exchange between the vortices and the outer flow. however, the thickness of this outer stochastic zone is observed to be much smaller than the one of the inner stochastic zone near vortices, as soon as the distance to the wall is large enough.
|
arxiv:1109.2423
|
we study homotopic - to - the - identity torus homeomorphisms, whose rotation set has nonempty interior. we prove that any such map is monotonically semiconjugate to a homeomorphism that preserves the lebesgue measure, and that has the same rotation set. furthermore, the dynamics of the quotient map has several interesting chaotic traits : for instance, it is topologically mixing, has a dense set of periodic points and is continuum - wise expansive. in particular, this shows that a convex compact set of $ \ mathbb { r } ^ 2 $ with nonempty interior is the rotation set of the lift of a homeomorphism of $ \ mathbb { t } ^ 2 $ if and only if it is the rotation set of the lift of a conservative homeomorphism.
|
arxiv:2404.02341
|
optical computing systems provide an alternate hardware model which appears to be aligned with the demands of neural network workloads. however, the challenge of implementing energy efficient nonlinearities in optics - - a key requirement for realizing neural networks - - is a conspicuous missing link. in this work we introduce a novel method to achieve nonlinear computation in fully linear media. our method can operate at low power and requires only the ability to drive the optical system at a data - dependent spatial position. leveraging this positional encoding, we formulate a fully automated, topology - optimization - based hardware design framework for extremely specialized optical neural networks, drawing on modern advancements in optimization and machine learning. we evaluate our optical designs on machine learning classification tasks : demonstrating significant improvements over linear methods, and competitive performance when compared to standard artificial neural networks.
|
arxiv:2504.20401
|
we introduce a notion of position - space cuts of eikonal diagrams, the set of diagrams appearing in the perturbative expansion of the correlator of a set of straight semi - infinite wilson lines. the cuts are applied directly to the position - space representation of any such diagram and compute its imaginary part to the leading order in the dimensional regulator. our cutting prescription thus defines a position - space analog of the standard momentum - space cutkosky rules. unlike momentum - space cuts which put internal lines on shell, position - space cuts constrain a number of the gauge bosons exchanged between the energetic partons to be lightlike, leading to a vanishing and a non - vanishing imaginary part for space - and timelike kinematics, respectively.
|
arxiv:1410.5681
|
from medium - resolution radio images, dr 16 was suspected to be a large cometary nebula. to test this suggestion we obtained a higher resolution ( 15 \ arcsec ) vla continuum map. we also analyzed data from the canadian galactic plane survey in continuum, h i line, and ir. these data were supplemented by published near - infrared ( j, h, k ) stellar photometric results and msx 8. 28 micrometer data. we suggest that dr 16 is the diffuse h ii region of an ongoing star formation site at a distance of about 3 kpc. the complicated radio picture arises from the superposition of diffuse h ii with the remains of a giant bipolar outflow. the outflow was generated by a probable herbig aebe star, and the lobes are the remnants of its working surfaces. additional ring - like features are discussed. dr 16 is part of a larger volume of space in the local spiral arm where star formation is an ongoing process.
|
arxiv:astro-ph/0311243
|
gait recognition with radio frequency ( rf ) signals enables many potential applications requiring accurate identification. however, current systems require individuals to be within a line - of - sight ( los ) environment and struggle with low signal - to - noise ratio ( snr ) when signals traverse concrete and thick walls. to address these challenges, we present trgr, a novel transmissive reconfigurable intelligent surface ( ris ) - aided gait recognition system. trgr can recognize human identities through walls using only the magnitude measurements of channel state information ( csi ) from a pair of transceivers. specifically, by leveraging transmissive ris alongside a configuration alternating optimization algorithm, trgr enhances wall penetration and signal quality, enabling accurate gait recognition. furthermore, a residual convolution network ( rcnn ) is proposed as the backbone network to learn robust human information. experimental results confirm the efficacy of transmissive ris, highlighting the significant potential of transmissive ris in enhancing rf - based gait recognition systems. extensive experiment results show that trgr achieves an average accuracy of 97. 88 \ % in identifying persons when signals traverse concrete walls, demonstrating the effectiveness and robustness of trgr.
|
arxiv:2407.21566
|
the space $ t _ { poly } ( \ mathbb r ^ d ) $ of all tensor fields on $ \ mathbb r ^ d $, equipped with the schouten bracket is a lie algebra. the subspace of ascending tensors is a lie subalgebra of $ t _ { poly } ( \ mathbb r ^ d ) $. in this paper, we compute the cohomology of the adjoint representations of this algebra ( in itself and $ t _ { poly } ( \ mathbb r ^ d ) $ ), when we restrict ourselves to cochains defined by aerial kontsevitch ' s graphs like in our previous work ( pacific j of math, vol 229, no 2, ( 2007 ) 257 - 292 ). as in the vectorial graphs case, the cohomology is freely generated by all the products of odd wheels.
|
arxiv:1003.4191
|
in this paper, we first introduce the full express of the riemannian curvature tensor of a real hypersurface $ m $ in complex quadric $ q ^ { m } $ from the equation of gauss. next we derive a formula for the structure jacobi operator $ r _ { \ xi } $ and its derivative under the levi - civita connection of $ m $. we give a complete classification of hopf real hypersurfaces with reeb parallel structure jacobi operator, $ \ nabla _ { \ xi } r _ { \ xi } = 0 $, in the complex quadric $ q ^ { m } $, $ m \ geq 3 $.
|
arxiv:1907.04661
|
we study correlations in spatial orientation between galaxy clusters and their host superclusters using a hubble volume n - body realization of a concordance cosmology and an analytic model for tidally - induced alignments. we derive an analytic form for distributions of the alignment angle as functions of halo mass ( m ), ellipticity ( epsilon ), distance ( r ) and velocity ( v ) and show that the model, after tuning of three parameters, provides a good fit to the numerical results. the parameters indicate a high degree of alignment along anisotropic, collapsed filaments. the degree of alignment increases with m and epsilon while it decreases with r and is independent of v. we note the possibility of using the cluster - supercluster alignment effect as a cosmological probe to constrain the slope of the initial power spectrum.
|
arxiv:astro-ph/0608685
|
the concept of physical momentum associated to phonons in a crystal, complemented with some fundamental reasoning, implies measurable effects in crystals even at a macroscopic scale. we show that, in close analogy with the transfer of momentum in the kinetic theory of gases, physical momentum carried by of phonons couples the thermal and the velocity field in a vibrating crystal. therefore an heat flow applied to a vibrating crystal can sustain or damp the oscillation, depending on the interplay between the temperature and the velocity gradient. we derive the general equations of this effect and show that its experimental confirmation is within reach of current technology.
|
arxiv:1210.2847
|
recent work on the quantum mechanics of near - extremal non - supersymmetric black holes has identified a characteristic $ t ^ { 3 / 2 } $ scaling of the low temperature black hole partition function. this result has only been derived using the path integral in the near - horizon region and relies on many assumptions. we discuss how to derive the $ t ^ { 3 / 2 } $ scaling for the near - extremal rotating btz black hole from a calculation in the full black hole background using the denef - hartnoll - sachdev ( dhs ) formula, which expresses the 1 - loop determinant of a thermal geometry in terms of a product over the quasinormal mode spectrum. we also derive the spectral measure for fields of any spin in euclidean btz and use it to provide a new proof of the dhs formula and a new, direct derivation of the btz heat kernel. the computations suggest a path to proving the $ t ^ { 3 / 2 } $ scaling for the asymptotically flat 4d kerr black hole.
|
arxiv:2409.14928
|
we investigate nonequilibrium noise in a diffusive andreev interferometer, in which currents emerging from two normal metal / superconductor ( n - s ) interfaces can interfere. we observe a modulation of the shot noise when the phase difference between the two n - s interfaces is varied by a magnetic flux. this is the signature of phase - sensitive fluctuations in the normal metal. the effective charge inferred from the shot noise measurement is close to q _ eff = 2e but shows phase - dependent deviations from 2e at finite energy, which we interprete as due to pair correlations. experimental data are in good agreement with theoretical predictions based on an extended keldysh green ' s function approach.
|
arxiv:cond-mat/0208089
|
we present a model - based feature extractor to describe neighborhoods around keypoints by finite expansion, estimating the spatially varying orientation by harmonic functions. the iso - curves of such functions are highly symmetric w. r. t. the origin ( a keypoint ) and the estimated parameters have well defined geometric interpretations. the origin is also a unique singularity of all harmonic functions, helping to determine the location of a keypoint precisely, whereas the functions describe the object shape of the neighborhood. this is novel and complementary to traditional texture features which describe texture - shape properties i. e. they are purposively invariant to translation ( within a texture ). we report on experiments of verification and identification of keypoints in forensic fingerprints by using publicly available data ( nist sd27 ) and discuss the results in comparison to other studies. these support our conclusions that the novel features can equip single cores or single minutia with a significant verification power at 19 % eer, and an identification power of 24 - 78 % for ranks of 1 - 20. additionally, we report verification results of periocular biometrics using near - infrared images, reaching an eer performance of 13 %, which is comparable to the state of the art. more importantly, fusion of two systems, our and texture features ( gabor ), result in a measurable performance improvement. we report reduction of the eer to 9 %, supporting the view that the novel features capture relevant visual information, which traditional texture features do not.
|
arxiv:2311.01651
|
crash events identification and prediction plays a vital role in understanding safety conditions for transportation systems. while existing systems use traffic parameters correlated with crash data to classify and train these models, we propose the use of a novel sensory unit that can also accurately identify crash events : microphone. audio events can be collected and analyzed to classify events such as crash. in this paper, we have demonstrated the use of a deep convolutional neural network ( cnn ) for road event classification. important audio parameters such as mel frequency cepstral coefficients ( mfcc ), log mel - filterbank energy spectrum and fourier spectrum were used as feature set. additionally, the dataset was augmented with more sample data by the use of audio augmentation techniques such as time and pitch shifting. together with the feature extraction this data augmentation can achieve reasonable accuracy. four events such as crash, tire skid, horn and siren sounds can be accurately identified giving indication of a road hazard that can be useful for traffic operators or paramedics. the proposed methodology can reach accuracy up to 94 %. such audio systems can be implemented as a part of an internet of things ( iot ) platform that can complement video - based sensors without complete coverage.
|
arxiv:2203.06059
|
a common optimization problem in the areas of magnetized plasmas and fusion energy is the design of magnets to produce a given three - dimensional magnetic field distribution to high precision. when designing arrays of permanent magnets for stellarator plasma confinement, such problems have tens of thousands of degrees of freedom whose solutions, for practical reasons, should be constrained to discrete spaces. we perform a direct comparison between two algorithms that have been developed previously for this purpose, and demonstrate that composite procedures that apply both algorithms in sequence can produce substantially improved results. one approach uses a continuous, quasi - newton procedure to optimize the dipole moments of a set of magnets and then projects the solution onto a discrete space. the second uses an inherently discrete greedy optimization procedure that has been enhanced and generalized for this work. the approaches are both applied to design arrays cubic rare - earth permanent magnets to confine a quasi - axisymmetric plasma with a magnetic field on axis of 0. 5 t. the first approach tends to find solutions with higher field accuracy, whereas the second can find solutions with substantially ( up to 30 % ) fewer magnets. when the approaches are combined, they can obtain solutions with magnet quantities comparable to the second approach while matching the field accuracy of the first.
|
arxiv:2309.17244
|
image to image translation ( i2i ) is a challenging computer vision problem used in numerous domains for multiple tasks. recently, ophthalmology became one of the major fields where the application of i2i is increasing rapidly. one such application is the generation of synthetic retinal optical coherence tomographic ( oct ) scans. existing i2i methods require training of multiple models to translate images from normal scans to a specific pathology : limiting the use of these models due to their complexity. to address this issue, we propose an unsupervised multi - domain i2i network with pre - trained style encoder that translates retinal oct images in one domain to multiple domains. we assume that the image splits into domain - invariant content and domain - specific style codes, and pre - train these style codes. the performed experiments show that the proposed model outperforms state - of - the - art models like munit and cyclegan synthesizing diverse pathological scans.
|
arxiv:2112.06031
|
multivariate bernoulli autoregressive ( bar ) processes model time series of events in which the likelihood of current events is determined by the times and locations of past events. these processes can be used to model nonlinear dynamical systems corresponding to criminal activity, responses of patients to different medical treatment plans, opinion dynamics across social networks, epidemic spread, and more. past work examines this problem under the assumption that the event data is complete, but in many cases only a fraction of events are observed. incomplete observations pose a significant challenge in this setting because the unobserved events still govern the underlying dynamical system. in this work, we develop a novel approach to estimating the parameters of a bar process in the presence of unobserved events via an unbiased estimator of the complete data log - likelihood function. we propose a computationally efficient estimation algorithm which approximates this estimator via taylor series truncation and establish theoretical results for both the statistical error and optimization error of our algorithm. we further justify our approach by testing our method on both simulated data and a real data set consisting of crimes recorded by the city of chicago.
|
arxiv:1811.02979
|
it is shown that $ u _ k \ cdot v _ k $ converges weakly to $ u \ cdot v $ if $ u _ k \ weakto u $ weakly in $ l ^ p $ and $ v _ k \ weakly v $ weakly in $ l ^ q $ with $ p, q \ in ( 1, \ infty ) $, $ 1 / p + 1 / q = 1 $, under the additional assumptions that the sequences $ \ div u _ k $ and $ \ curl v _ k $ are compact in the dual space of $ w ^ { 1, \ infty } _ 0 $ and that $ u _ k \ cdot v _ k $ is equi - integrable. the main point is that we only require equi - integrability of the scalar product $ u _ k \ cdot v _ k $ and not of the individual sequences.
|
arxiv:0907.0397
|
only four star clusters are known within ~ 100 pc of earth. of these, the chi1 for cluster has barely been studied. we use the gaia dr2 catalog and other published data to establish the cluster membership, structure, and age. the age of and distance to the cluster are ~ 40 myr and 104 pc, respectively. a remarkable, unprecedented, aspect of the cluster is the large percentage of m - type stars with warm excess infrared emission due to orbiting dust grains - - these stars lie in an annulus that straddles the tidal radius of the cluster. the chi1 for cluster appears to be closely related to two extensive, previously known, groups of co - moving, coeval stars ( the tucana - horologium and columba associations ) that are spread over much of the southern sky. while tuc - hor and chi1 for are comoving and coeval, the difference in the frequency of their warm dusty debris disks at m - type stars could hardly be more dramatic.
|
arxiv:1909.08764
|
we introduce an accurate and robust technique for accessing causality of network transfer functions given in the form of bandlimited discrete frequency responses. these transfer functions are commonly used to represent the electrical response of high speed digital interconnects used on chip and in electronic package assemblies. in some cases small errors in the model development lead to non - causal behavior that does not accurately represent the electrical response and may lead to a lack of convergence in simulations that utilize these models. the approach is based on hilbert transform relations or kramers - kronig dispersion relations and a construction of causal fourier continuations using a regularized singular value decomposition ( svd ) method. given a transfer function, non - periodic in general, this procedure constructs highly accurate fourier series approximations on the given frequency interval by allowing the function to be periodic in an extended domain. the causality dispersion relations are enforced spectrally and exactly. this eliminates the necessity of approximating the transfer function behavior at infinity and explicit computation of the hilbert transform. we perform the error analysis of the method and take into account a possible presence of a noise or approximation errors in data. the developed error estimates can be used in verifying causality of the given data. the performance of the method is tested on several analytic and simulated examples that demonstrate an excellent accuracy and reliability of the proposed technique in agreement with the obtained error estimates. the method is capable of detecting very small localized causality violations with amplitudes close to the machine precision.
|
arxiv:1411.3812
|
we investigate the eigenmodes of the massless dirac operator to extract the scale - dependent fermion mass anomalous dimension gamma _ m ( mu ). by combining simulations on multiple lattice volumes, and when possible several gauge couplings, we are able to measure the anomalous dimension across a wide range of energy scales. the method that we present is universal and can be applied to any lattice model of interest, including both conformal or chirally broken systems. we consider su ( 3 ) lattice gauge theories with nf = 4, 8 and 12 light or massless fermions. the 4 - flavor model behaves as expected for a qcd - like system and demonstrates that systematic effects are manageable in practical lattice calculations. our 12 - flavor results are consistent with the existence of an infrared fixed point, at which we predict the scheme - independent mass anomalous dimension gamma _ m ^ * = 0. 32 ( 3 ). for the 8 - flavor model we observe a large anomalous dimension across a wide range of energy scales. further investigation is required to determine whether nf = 8 is chirally broken and walking, or if it possesses a strongly - coupled conformal fixed point.
|
arxiv:1301.1355
|
, such as einstein and dirac, to be among the " real " mathematicians, but at the time that he was writing his apology, he considered general relativity and quantum mechanics to be " useless ", which allowed him to hold the opinion that only " dull " mathematics was useful. moreover, hardy briefly admitted that β just as the application of matrix theory and group theory to physics had come unexpectedly β the time may come where some kinds of beautiful, " real " mathematics may be useful as well. another insightful view is offered by american mathematician andy magid : i ' ve always thought that a good model here could be drawn from ring theory. in that subject, one has the subareas of commutative ring theory and non - commutative ring theory. an uninformed observer might think that these represent a dichotomy, but in fact the latter subsumes the former : a non - commutative ring is a not - necessarily - commutative ring. if we use similar conventions, then we could refer to applied mathematics and nonapplied mathematics, where by the latter we mean not - necessarily - applied mathematics... [ emphasis added ] friedrich engels argued in his 1878 book anti - duhring that " it is not at all true that in pure mathematics the mind deals only with its own creations and imaginations. the concepts of number and figure have not been invented from any source other than the world of reality ". : 36 he further argued that " before one came upon the idea of deducing the form of a cylinder from the rotation of a rectangle about one of its sides, a number of real rectangles and cylinders, however imperfect in form, must have been examined. like all other sciences, mathematics arose out of the needs of men... but, as in every department of thought, at a certain stage of development the laws, which were abstracted from the real world, become divorced from the real world, and are set up against it as something independent, as laws coming from outside, to which the world has to conform. " : 37 = = see also = = applied mathematics logic metalogic metamathematics = = references = = = = external links = = what is pure mathematics? β department of pure mathematics, university of waterloo the principles of mathematics by bertrand russell
|
https://en.wikipedia.org/wiki/Pure_mathematics
|
we study the existence of continuity points for mappings $ f : x \ times y \ to z $ whose $ x $ - sections $ y \ ni y \ to f ( x, y ) \ in z $ are fragmentable and $ y $ - sections $ x \ ni x \ to f ( x, y ) \ in z $ are quasicontinuous, where $ x $ is a baire space and $ z $ is a metric space. for the factor $ y $, we consider two infinite " point - picking " games $ g _ 1 ( y ) $ and $ g _ 2 ( y ) $ defined respectively for each $ y \ in y $ as follows : in the $ n $ th inning, player i gives a dense set $ d _ n \ subset y $, respectively, a dense open set $ d _ n \ subset y $, then player ii picks a point $ y _ n \ ind _ n $ ; ii wins if $ y $ is in the closure of $ \ { y _ n : n \ in \ mathbb n \ } $, otherwise i wins. it is shown that ( i ) $ f $ is cliquish if ii has a winning strategy in $ g _ 1 ( y ) $ for every $ y \ in y $, and ( ii ) $ f $ is quasicontinuous if the $ x $ - sections of $ f $ are continuous and the set of $ y \ in y $ such that ii has a winning strategy in $ g _ 2 ( y ) $ is dense in $ y $. item ( i ) extends substantially a result of debs ( 1986 ) and item ( ii ) indicates that the problem of talagrand ( 1985 ) on separately continuous maps has a positive answer for a wide class of " small " compact spaces.
|
arxiv:1010.0441
|
testing and characterizing the difference between two data samples is of fundamental interest in statistics. existing methods such as kolmogorov - smirnov and cramer - von - mises tests do not scale well as the dimensionality increases and provides no easy way to characterize the difference should it exist. in this work, we propose a theoretical framework for inference that addresses these challenges in the form of a prior for bayesian nonparametric analysis. the new prior is constructed based on a random - partition - and - assignment procedure similar to the one that defines the standard optional p \ ' olya tree distribution, but has the ability to generate multiple random distributions jointly. these random probability distributions are allowed to " couple ", that is to have the same conditional distribution, on subsets of the sample space. we show that this " coupling optional p \ ' olya tree " prior provides a convenient and effective way for both the testing of two sample difference and the learning of the underlying structure of the difference. in addition, we discuss some practical issues in the computational implementation of this prior and provide several numerical examples to demonstrate its work.
|
arxiv:1011.1253
|
let t be a tilting module. in this paper, some relative gorenstein projective and gortenstein injective modules are studied.
|
arxiv:1906.01457
|
the observed lyman - alpha ( lya ) line profile is a convolution of the complex lya radiative transfer taking place in the interstellar, circumgalactic and intergalactic medium ( ism, cgm, and igm, respectively ). discerning the different components of the lya line is crucial in order to use it as a probe of galaxy formation or the evolution of the igm. we present the second version of zelda ( redshift estimator for line profiles of distant lyman - alpha emitters ), an open - source python module focused on modeling and fitting observed lya line profiles. this new version of zelda focuses on disentangling the galactic from the igm effects. we build realistic lya line profiles that include the ism and igm contributions, by combining the monte carlo radiative transfer simulations for the so called " shell model " ( ism ) and igm transmission curves generated from illustristng100. we use these mock line profiles to train different artificial neural networks. these use as input the observed spectrum and output the outflow parameters of the best fitting " shell model " along with the redshift and lya emission igm escape fraction of the source. we measure the accuracy of zelda on mock lya line profiles. we find that zelda is capable of reconstructing the ism emerging lya line profile with high accuracy ( kolmogorov - smirnov < 0. 1 ) for 95 % of the cases for hst cos - like observations and 80 % for muse - wide - like. zelda is able to measure the igm transmission with the typical uncertainties below 10 % for hst - cos and muse - wide data. this work represents a step forward in the high - precision reconstruction of igm attenuated lya line profiles. zelda allows the disentanglement of the galactic and igm contribution shaping the lya line shape, and thus allows us to use lya as a tool to study galaxy and ism evolution.
|
arxiv:2501.04077
|
the ieee vis conference ( vis ) recently rebranded itself as a unified conference and officially positioned itself within the discipline of data science. driven by this movement, we investigated ( 1 ) who contributed to vis, and ( 2 ) where vis stands in the scientific world. we examined the authors and fields of study of 3, 240 vis publications in the past 32 years based on data collected from openalex and ieee xplore, among other sources. we also examined the citation flows from referenced papers ( i. e., those referenced in vis ) to vis, and from vis to citing papers ( i. e., those citing vis ). we found that vis has been becoming increasingly popular and collaborative. the number of publications, of unique authors, and of participating countries have been steadily growing. both cross - country collaborations, and collaborations between educational and non - educational affiliations, namely " cross - type collaborations ", are increasing. the dominance of the us is decreasing, and authors from china are now an important part of vis. in terms of author affiliation types, vis is increasingly dominated by authors from universities. we found that the topics, inspirations, and influences of vis research is limited such that ( 1 ) vis, and their referenced and citing papers largely fall into the computer science domain, and ( 2 ) citations flow mostly between the same set of subfields within computer science. our citation analyses showed that award - winning vis papers had higher citations. interactive visualizations, replication data, source code and supplementary material are available at https : / / 32vis. hongtaoh. com and https : / / osf. io / zkvjm.
|
arxiv:2208.03772
|
we report on the magnetic field dispersion of the exciton spin - splitting and diamagnetic shift in single inas / gaas quantum dots ( qds ) and dot molecules ( qdms ) up to $ b $ = 28 t. only for systems with strong geometric confinement, the dispersions can be well described by simple field dependencies, while for dots with weaker confinement considerable deviations are observed : most importantly, in the high field limit the spin - splitting shows a non - linear dependence on $ b $, clearly indicating light hole admixtures to the valence band ground state.
|
arxiv:cond-mat/0503271
|
due to their relevance in controller design, we consider the problem of determining the $ \ mathcal { l } ^ 2 $ - gain, passivity properties and conic relations of an input - output system. while, in practice, the input - output relation is often undisclosed, input - output data tuples can be sampled by performing ( numerical ) experiments. hence, we present sampling strategies for discrete time and continuous time linear time - invariant systems to iteratively determine the $ \ mathcal { l } ^ 2 $ - gain, the shortage of passivity and the cone with minimal radius that the input - output relation is confined to. these sampling strategies are based on gradient dynamical systems and saddle point flows to solve the reformulated optimization problems, where the gradients can be evaluated from only input - output data samples. this leads us to evolution equations, whose convergence properties are then discussed in continuous time and discrete time.
|
arxiv:1910.08919
|
we present the discovery of three late type ( > t4 ) brown dwarfs, including a probable y dwarf, in the wfc3 infrared spectroscopic parallels ( wisp ) survey. we use the g141 grism spectra to determine the spectral types of the dwarfs and derive distance estimates based on a comparison with nearby t dwarfs with known parallaxes. these are the most distant spectroscopically confirmed t / y dwarfs, with the farthest at an estimated distance of ~ 400 pc. we compare the number of cold dwarfs found in the wisp survey with simulations of the brown dwarf mass function. the number found is generally consistent with an initial stellar mass function dn / dm \ propto m ^ { - \ alpha } with \ alpha = 0. 0 - - 0. 5, although the identification of a y dwarf is somewhat surprising and may be indicative of either a flatter absolute magnitude / spectral type relation than previously reported or an upturn in the number of very late type brown dwarfs in the observed volume.
|
arxiv:1204.6320
|
bars are important in the secular evolution of galaxies. this study is aimed at exploring the reasons why some galaxies have bars at redshift $ z = 0 $ while others do not. we use ellipse fitting to measure the properties and evolution of bars in the illustristng cosmological simulation. by using the k - s two - sample test and tracing their evolutionary changes, we analyze the parameter differences between barred and unbarred galaxies. the properties of galaxies with short bars are also studied. when tracing all disk galaxies at $ z = 0 $ back to $ z = 1 $, all of them show similar bar features at $ z = 1 $. the fraction of bars increases in barred and short - bar galaxies but decreases in unbarred galaxies during $ z = 1 - 0 $. in the case of disk galaxies with stellar mass log $ ( m _ * / m _ \ odot ) > 10. 8 $, nurture ( mainly mergers ) plays the most important role in suppressing or destroying bars. bars are more likely to endure in galaxies that experience fewer mergers, which can be quantified by smaller stellar halos and ex - situ mass fractions. approximately 60 \ % of the unbarred galaxies in the local universe once had a bar. in contrast, the lack of responsiveness to bar instabilities ( a larger toomre - q parameter ) due to a less compact nature plays an important role in generating unbarred disk galaxies with stellar mass log $ ( m _ * / m _ \ odot ) < 10. 8 $. moreover, short bars generally form at a similar time to normal bars, during which they either grow mildly or contract significantly. the fact that illustristng simulations produce too many galaxies with short bars indicates that the dynamical properties of the central regions in illustristng galaxies are less affected by external factors, such as mergers and gas inflows.
|
arxiv:2412.02255
|
automatically detecting and recovering from failures is an important but challenging problem for autonomous robots. most of the recent work on learning to plan from demonstrations lacks the ability to detect and recover from errors in the absence of an explicit state representation and / or a ( sub - ) goal check function. we propose an approach ( blending learning with symbolic search ) for automated error discovery and recovery, without needing annotated data of failures. central to our approach is a neuro - symbolic state representation, in the form of dense scene graph, structured based on the objects present within the environment. this enables efficient learning of the transition function and a discriminator that not only identifies failures but also localizes them facilitating fast re - planning via computation of heuristic distance function. we also present an anytime version of our algorithm, where instead of recovering to the last correct state, we search for a sub - goal in the original plan minimizing the total distance to the goal given a re - planning budget. experiments on a physics simulator with a variety of simulated failures show the effectiveness of our approach compared to existing baselines, both in terms of efficiency as well as accuracy of our recovery mechanism.
|
arxiv:2405.18948
|
we investigate the collective dynamics of bursting neurons on clustered network. the clustered network is composed of subnetworks each presenting a small - world property, and in a given subnetwork each neuron has a probability to be connected to the other subnetworks. we give bounds for the critical coupling strength to obtain global burst synchronization in terms of the network structure, i. e., intracluster and intercluster probabilities connections. as the heterogeneity in the network is reduced the network global synchronization is improved. we show that the transitions to global synchrony may be abrupt or smooth depending on the intercluster probability.
|
arxiv:1012.4512
|
fluids in porous media are commonly studied with analytical or simulation methods, usually assuming that the host medium is rigid. by evaluating the substrate ' s response ( relaxation ) to the presence of the fluid we assess the error inherent in that assumption. one application is a determination of the ground state of 3he in slit and cylindrical pores. with the relaxation, there results a much stronger cohesion than would be found for a rigid host. similar increased binding effects of relaxation are found for classical fluids confined within slit pores or nanotube bundles.
|
arxiv:0810.0262
|
an ising model with local glauber dynamics is studied under the influence of additional kinetic restrictions for the spin - flip rates depending on the orientation of neighboring spins. even when the static interaction between the spins is completely eliminated and only an external field is taken into account the system offers a phase transition at a finite value of the applied field. the transition is realized due to a competition between the activation processes driven by the field and the dynamical rules for the spin - flips. the result is based on a master equation approach in a quantum formulation.
|
arxiv:cond-mat/9907414
|
c - based interpreters such as cpython make extensive use of c " extension " code, which is opaque to static analysis tools and faster runtimes with jit compilers, such as pypy. not only are the extensions opaque, but the interface between the dynamic language types and the c types can introduce impedance. we hypothesise that frequent calls to c extension code introduce significant overhead that is often unnecessary. we validate this hypothesis by introducing a simple technique, " typed methods ", which allow selected c extension functions to have additional metadata attached to them in a backward - compatible way. this additional metadata makes it much easier for a jit compiler ( and as we show, even an interpreter! ) to significantly reduce the call and return overhead. although we have prototyped typed methods in pypy, we suspect that the same technique is applicable to a wider variety of language runtimes and that the information can also be consumed by static analysis tooling.
|
arxiv:2403.02420
|
the cohen - kaplan - nelson bound is imposed on the grounds of logical consistency ( with classical general relativity ) upon local quantum field theories. this paper puts the bound into the context of a thermodynamic principle applicable to a field with a particular equation of state in an expanding universe. this is achieved without overtly appealing to either a decreasing density of states or a minimum coupling requirement, though they might still be consistent with the results described. we do so by defining an appropriate helmholtz free energy which when extremized relative to a key parameter ( the hubble radius l ) provides a scaling formula for the entropy with the hubble radius ( an exponent ' r ' used in the text ). we deduce that the ckn bound is one solution to this extremization problem ( with r = 3 / 2 ), but there are others consistent with r = 2. the paper establishes that the holographic principle applied to cosmology is consistent with minimizing the free energy of the universe in the canonical ensemble, upon the assumption that the ultraviolet cutoff is a function of the causal horizon scale.
|
arxiv:2111.07807
|
a model for the qcd vacuum based on a domainlike structured background gluon field with definite duality attributed to the domains has been shown elsewhere to give confinement of static quarks, a reasonable value for the topological susceptibility and indications that chiral symmetry is spontaneously broken. in this paper we study in detail the eigenvalue problem for the dirac operator in such a gluon mean field. a study of the local chirality parameter shows that the lowest nonzero eigenmodes possess a definite mean chirality correlated with the duality of a given domain. a probability distribution of the local chirality qualitatively reproduces histograms seen in lattice simulations.
|
arxiv:hep-ph/0208064
|
we consider the problem of enumerating the number of irreducible transformation shift registers. we give an asymptotic formula for the number of irreducible transformation shift registers in some special cases. moreover, we derive a short proof for the exact number of irreducible transformation shift registers of order two using a recent generalization of a theorem of carlitz.
|
arxiv:1506.02548
|
we show fully polynomial time randomized approximation schemes ( fpras ) for counting matchings of a given size, or more generally sampling / counting monomer - dimer systems in planar, not - necessarily - bipartite, graphs. while perfect matchings on planar graphs can be counted exactly in polynomial time, counting non - perfect matchings was shown by [ jer87 ] to be # p - hard, who also raised the question of whether efficient approximate counting is possible. we answer this affirmatively by showing that the multi - site glauber dynamics on the set of monomers in a monomer - dimer system always mixes rapidly, and that this dynamics can be implemented efficiently on downward - closed families of graphs where counting perfect matchings is tractable. as further applications of our results, we show how to sample efficiently using multi - site glauber dynamics from partition - constrained strongly rayleigh distributions, and nonsymmetric determinantal point processes. in order to analyze mixing properties of the multi - site glauber dynamics, we establish two notions for generating polynomials of discrete set - valued distributions : sector - stability and fractional log - concavity. these notions generalize well - studied properties like real - stability and log - concavity, but unlike them robustly degrade under useful transformations applied to the distribution. we relate these notions to pairwise correlations in the underlying distribution and the notion of spectral independence introduced by [ alo20 ], providing a new tool for establishing spectral independence based on geometry of polynomials. as a byproduct of our techniques, we show that polynomials avoiding roots in a sector of the complex plane must satisfy what we call fractional log - concavity ; this extends a classic result established by [ gar59 ] who showed homogeneous polynomials that have no roots in a half - plane must be log - concave over the positive orthant.
|
arxiv:2102.02708
|
typically, the deployment of face recognition models in the wild needs to identify low - resolution faces with extremely low computational cost. to address this problem, a feasible solution is compressing a complex face model to achieve higher speed and lower memory at the cost of minimal performance drop. inspired by that, this paper proposes a learning approach to recognize low - resolution faces via selective knowledge distillation. in this approach, a two - stream convolutional neural network ( cnn ) is first initialized to recognize high - resolution faces and resolution - degraded faces with a teacher stream and a student stream, respectively. the teacher stream is represented by a complex cnn for high - accuracy recognition, and the student stream is represented by a much simpler cnn for low - complexity recognition. to avoid significant performance drop at the student stream, we then selectively distil the most informative facial features from the teacher stream by solving a sparse graph optimization problem, which are then used to regularize the fine - tuning process of the student stream. in this way, the student stream is actually trained by simultaneously handling two tasks with limited computational resources : approximating the most informative facial cues via feature regression, and recovering the missing facial cues via low - resolution face classification. experimental results show that the student stream performs impressively in recognizing low - resolution faces and costs only 0. 15mb memory and runs at 418 faces per second on cpu and 9, 433 faces per second on gpu.
|
arxiv:1811.09998
|
in superfluid dark matter ( sfdm ), the phonon field plays a double role : it carries the superfluid ' s energy density and it mediates the mond - like phonon force. we show that these two roles are in tension with each other on galactic scales : a mond - like phonon force is in tension with a superfluid in equilibrium and with a significant superfluid energy density. to avoid these tensions, we propose a model where the two roles are split between two different fields. this also allows us to solve a stability problem in a more elegant way than standard sfdm. we argue that the standard estimates for the size of a galaxy ' s superfluid core need to be revisited.
|
arxiv:2009.03003
|
dielectric data on glycerol and propylene carbonate covering 18 decades of frequency are presented and compared to each other. both materials exhibit qualitatively similar behavior except for marked differences in the high - frequency region just below the boson peak. the results on both materials are consistent with the mode coupling theory of the glass transition.
|
arxiv:cond-mat/9812257
|
the original casimir effect results from the difference in the vacuum energies of the electromagnetic field, between that in a region of space with boundary conditions and that in the same region without boundary conditions. in this paper we develop the theory of a similar situation, involving a scalar field in spacetimes with compact spatial sections of negative spatial curvature.
|
arxiv:gr-qc/0205050
|
in this work, we consider the spread of a ' civilisation ' in an idealised homogeneous isotropic universe where all the planets of interest are habitable. following a framework that goes beyond the usual idea of percolation, we investigate the behaviour of the number of colonised planets with time, and the total colonisation time for three types of universes. these include static, dark energy - dominated, and matter - dominated universes. for all these types of universes, we find a remarkable fit with the logistic growth function for the number of colonised planets with time. this is in spite of the fact that for the matter - and dark - energy dominated universes, the space itself is expanding. for the total colonisation time, $ t $, the case for a dark energy - dominated universe is marked with divergence beyond the linear regime characterised by small values of the hubble parameter, $ h $. not all planets in a spherical section of this universe can be ' colonised ' due to the presence of a shrinking hubble sphere. in other words, the recession speeds of other planets go beyond the speed of light making them impossible to reach. on the other hand, for a matter - dominated universe, while there is an apparent horizon, the hubble sphere is growing instead of shrinking. this leads to a finite total colonisation time that depends on the hubble parameter characterising the universe ; in particular, we find $ t \ sim h $ for small $ h $ and $ t \ sim h ^ 2 $ for large $ h $.
|
arxiv:2309.06575
|
if a fluctuating medium is confined, the ensuing perturbation of its fluctuation spectrum generates casimir - like effective forces acting on its confining surfaces. near a continuous phase transition of such a medium the corresponding order parameter fluctuations occur on all length scales and therefore close to the critical point this effect acquires a universal character, i. e., to a large extent it is independent of the microscopic details of the actual system. accordingly it can be calculated theoretically by studying suitable representative model systems. we report on the direct measurement of critical casimir forces by total internal reflection microscopy ( tirm ), with femto - newton resolution. the corresponding potentials are determined for individual colloidal particles floating above a substrate under the action of the critical thermal noise in the solvent medium, constituted by a binary liquid mixture of water and 2, 6 - lutidine near its lower consolute point. depending on the relative adsorption preferences of the colloid and substrate surfaces with respect to the two components of the binary liquid mixture, we observe that, upon approaching the critical point of the solvent, attractive or repulsive forces emerge and supersede those prevailing away from it. based on the knowledge of the critical casimir forces acting in film geometries within the ising universality class and with equal or opposing boundary conditions, we provide the corresponding theoretical predictions for the sphere - planar wall geometry of the experiment. the experimental data for the effective potential can be interpreted consistently in terms of these predictions and a remarkable quantitative agreement is observed.
|
arxiv:0908.1795
|
existing image - based activity understanding methods mainly adopt direct mapping, i. e. from image to activity concepts, which may encounter performance bottleneck since the huge gap. in light of this, we propose a new path : infer human part states first and then reason out the activities based on part - level semantics. human body part states ( pasta ) are fine - grained action semantic tokens, e. g. < hand, hold, something >, which can compose the activities and help us step toward human activity knowledge engine. to fully utilize the power of pasta, we build a large - scale knowledge base pastanet, which contains 7m + pasta annotations. and two corresponding models are proposed : first, we design a model named activity2vec to extract pasta features, which aim to be general representations for various activities. second, we use a pasta - based reasoning method to infer activities. promoted by pastanet, our method achieves significant improvements, e. g. 6. 4 and 13. 9 map on full and one - shot sets of hico in supervised learning, and 3. 2 and 4. 2 map on v - coco and images - based ava in transfer learning. code and data are available at http : / / hake - mvig. cn /.
|
arxiv:2004.00945
|
we study the directed polymer model in dimension $ { 1 + 1 } $ when the environment is heavy - tailed, with a decay exponent $ \ alpha \ in ( 0, 2 ) $. we give all possible scaling limits of the model in the weak - coupling regime, i. e., when the inverse temperature temperature $ \ beta = \ beta _ n $ vanishes as the size of the system $ n $ goes to infinity. when $ \ alpha \ in ( 1 / 2, 2 ) $, we show that all possible transversal fluctuations $ \ sqrt { n } \ leq h _ n \ leq n $ can be achieved by tuning properly $ \ beta _ n $, allowing to interpolate between all super - diffusive scales. moreover, we determine the scaling limit of the model, answering a conjecture by dey and zygouras [ cf : dz ] - we actually identify five different regimes. on the other hand, when $ \ alpha < 1 / 2 $, we show that there are only two regimes : the transversal fluctuations are either $ \ sqrt { n } $ or $ n $. as a key ingredient, we use the entropy - controlled last passage percolation ( e - lpp ), introduced in a companion paper [ cf : bt _ elpp ].
|
arxiv:1802.03355
|
rig categories with finite biproducts are categories with two monoidal products, where one is a biproduct and the other distributes over it. in this work we present tape diagrams, a sound and complete diagrammatic language for these categories, that can be intuitively thought as string diagrams of string diagrams. we test the effectiveness of our approach against the positive fragment of tarski ' s calculus of relations.
|
arxiv:2210.09950
|
using density - functional theory ( dft ) we investigate the incorporation of oxygen directly below the rh ( 111 ) surface. we show that oxygen incorporation will only commence after nearly completion of a dense o adlayer ( \ theta _ tot = 1. 0 monolayer ) with o in the fcc on - surface sites. the experimentally suggested octahedral sub - surface site occupancy, inducing a site - switch of the on - surface species from fcc to hcp sites, is indeed found to be a rather low energy structure. our results indicate that at even higher coverages oxygen incorporation is followed by oxygen agglomeration in two - dimensional sub - surface islands directly below the first metal layer. inside these islands, the metastable hcp / octahedral ( on - surface / sub - surface ) site combination will undergo a barrierless displacement, introducing a stacking fault of the first metal layer with respect to the underlying substrate and leading to a stable fcc / tetrahedral site occupation. we suggest that these elementary steps, namely, oxygen incorporation, aggregation into sub - surface islands and destabilization of the metal surface may be more general and precede the formation of a surface oxide at close - packed late transition metal surfaces.
|
arxiv:cond-mat/0205257
|
the history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. from 3000 bc the mesopotamian states of sumer, akkad and assyria, followed closely by ancient egypt and the levantine state of ebla began using arithmetic, algebra and geometry for purposes of taxation, commerce, trade and also in the field of astronomy to record time and formulate calendars. the earliest mathematical texts available are from mesopotamia and egypt β plimpton 322 ( babylonian c. 2000 β 1900 bc ), the rhind mathematical papyrus ( egyptian c. 1800 bc ) and the moscow mathematical papyrus ( egyptian c. 1890 bc ). all of these texts mention the so - called pythagorean triples, so, by inference, the pythagorean theorem seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry. the study of mathematics as a " demonstrative discipline " began in the 6th century bc with the pythagoreans, who coined the term " mathematics " from the ancient greek ΞΌΞ±ΞΈΞ·ΞΌΞ± ( mathema ), meaning " subject of instruction ". greek mathematics greatly refined the methods ( especially through the introduction of deductive reasoning and mathematical rigor in proofs ) and expanded the subject matter of mathematics. the ancient romans used applied mathematics in surveying, structural engineering, mechanical engineering, bookkeeping, creation of lunar and solar calendars, and even arts and crafts. chinese mathematics made early contributions, including a place value system and the first use of negative numbers. the hindu β arabic numeral system and the rules for the use of its operations, in use throughout the world today evolved over the course of the first millennium ad in india and were transmitted to the western world via islamic mathematics through the work of muhammad ibn musa al - khwarizmi. islamic mathematics, in turn, developed and expanded the mathematics known to these civilizations. contemporaneous with but independent of these traditions were the mathematics developed by the maya civilization of mexico and central america, where the concept of zero was given a standard symbol in maya numerals. many greek and arabic texts on mathematics were translated into latin from the 12th century onward, leading to further development of mathematics in medieval europe. from ancient times through the middle ages, periods of mathematical discovery were often followed by centuries of stagnation. beginning in renaissance
|
https://en.wikipedia.org/wiki/History_of_mathematics
|
we introduce and study a one parameter deformation of the polynuclear growth ( png ) in $ ( 1 + 1 ) $ - dimensions, which we call the $ t $ - png model. it is defined by requiring that, when two expanding islands merge, with probability $ t $ they sprout another island on top of the merging location. at $ t = 0 $, this becomes the standard ( non - deformed ) png model that, in the droplet geometry, can be reformulated through longest increasing subsequences of uniformly random permutations or through an algorithm known as patience sorting. in terms of the latter, the $ t $ - png model allows errors to occur in the sorting algorithm with probability $ t $. we prove that the $ t $ - png model exhibits one - point tracy - widom gue asymptotics at large times for any fixed $ t \ in [ 0, 1 ) $, and one - point convergence to the narrow wedge solution of the kardar - parisi - zhang ( kpz ) equation as $ t $ tends to $ 1 $. we further construct distributions for an external source that are likely to induce baik - ben arous - peche type phase transitions. the proofs are based on solvable stochastic vertex models and their connection to the determinantal point processes arising from schur measures on partitions.
|
arxiv:2108.06018
|
data augmentation can effectively resolve a scarcity of images when training machine - learning algorithms. it can make them more robust to unseen images. we present a lesion conditional generative adversarial network lcgan to generate synthetic computed tomography ( ct ) images for data augmentation. a lesion conditional image ( segmented mask ) is an input to both the generator and the discriminator of the lcgan during training. the trained model generates contextual ct images based on input masks. we quantify the quality of the images by using a fully convolutional network ( fcn ) score and blurriness. we also train another classification network to select better synthetic images. these synthetic ct images are then augmented to our hemorrhagic lesion segmentation network. by applying this augmentation method on 2. 5 %, 10 % and 25 % of original data, segmentation improved by 12. 8 %, 6 % and 1. 6 % respectively.
|
arxiv:2003.13868
|
studies of diffuse magnetic scattering largely benefit from the use of a multi - detector covering wide scattering angles. therefore, the different contributions to the diffuse scattering that originate from magnetic, nuclear coherent, and nuclear spin - incoherent scattering can be separated by the so - called xyz - polarization analysis. in the past this method has been successfully applied to the analysis of diffuse scattering by polycrystalline samples of magnetic disordered materials. single crystal studies that exploit the vector properties of spin correlations are of particular interest for furthering our understanding of frustration effects in magnetism. based on the symmetry properties of polarised scattering a suitable extension of the conventional xyz method has been derived, which allows for the complete separation and the analysis of features of diffuse magnetic scattering from single crystals.
|
arxiv:1002.1228
|
we demonstrate the use of an optimized 5 core photonic lantern ( pl ) to simultaneously measure tip / tilt errors at the telescope focal plane, while also providing the input to an instrument. by replacing a single mode ( sm ) fiber with the pl we show that it is possible to stabilize the input psf to an instrument due to non - common path tip / tilt aberrations in an adaptive optics system. we show the pl in two different regimes, ( i ) using only the outer cores for tip / tilt measurements while feeding an instrument with the central core and, ( ii ) using all cores to measure tip / tilt when used in an instrument such as a spectrograph. in simulations our pl displays the ability to retrieve tip / tilt measurements in a linear range of + / - 55 milliarcseconds. at the designed central wavelength of 1. 55 microns, configuration ( i ) matches the throughput of an on - axis sm fiber but declines as we move away from this wavelength. in configuration ( ii ) we make use of the whole multimode input of the pl resulting in a potential increase of overall throughput compared to a sm fiber, while eliminating modal noise.
|
arxiv:1809.08131
|
a stability of nearly limiting stokes waves to superharmonic perturbations is considered numerically. the new, previously inaccessible branches of superharmonic instability were investigated. our numerical simulations suggest that eigenvalues of linearized dynamical equations, corresponding to the unstable modes, appear as a result of a collision of a pair of purely imaginary eigenvalues at the origin, and a subsequent appearance of a pair of purely real eigenvalues : a positive and a negative one that are symmetric with respect to zero. complex conjugate pairs of purely imaginary eigenvalues correspond to stable modes, and as the steepness of the underlying stokes wave grows, the pairs move toward the origin along the imaginary axis. moreover, when studying the eigenvalues of linearized dynamical we find that as the steepness of the stokes wave grows, the real eigenvalues follow a universal scaling law, that can be approximated by a power law. the asymptotic power law behaviour of this dependence for instability of stokes waves close to the limiting one is proposed. surface elevation profiles for several unstable eigenmodes are made available through http : / / stokeswave. org website.
|
arxiv:2206.00725
|
blackholecam is a project funded by a european research council synergy grant to build a complete astrophysical description of nearby supermassive black holes by using a combination of radio imaging, pulsar observations, stellar astrometry and general relativistic magneto - hydrodynamic models. blackholecam scientists are active partners of the event horizon telescope consortium. in this talk i will discuss the use of pulsars orbiting sagittarius a * for tests of general relativity, the current difficulties in detecting such sources, recent results from the galactic centre magnetar psr j1745 - 2900 and how blackholecam aims to search for undiscovered pulsars in the galactic centre.
|
arxiv:2306.01496
|
we study the periodic homogenization of first order front propagations. based on pde methods, we provide a simple proof that for $ n \ geq 3 $, the class of centrally symmetric polytopes with rational coordinates and nonempty interior is admissible as effective fronts, which was also established in [ 1, 10 ] in the form of stable norms as an extension of hedlund ' s classical result [ 7 ]. besides, we obtain the optimal convergence rate of the homogenization problem for this class.
|
arxiv:1909.11067
|
discovering the causal relationship via recovering the directed acyclic graph ( dag ) structure from the observed data is a well - known challenging combinatorial problem. when there are latent variables, the problem becomes even more difficult. in this paper, we first propose a dag structure recovering algorithm, which is based on the cholesky factorization of the covariance matrix of the observed data. the algorithm is fast and easy to implement and has theoretical grantees for exact recovery. on synthetic and real - world datasets, the algorithm is significantly faster than previous methods and achieves the state - of - the - art performance. furthermore, under the equal error variances assumption, we incorporate an optimization procedure into the cholesky factorization based algorithm to handle the dag recovering problem with latent variables. numerical simulations show that the modified " cholesky + optimization " algorithm is able to recover the ground truth graph in most cases and outperforms existing algorithms.
|
arxiv:2311.00674
|
we prove the bogomolov conjecture for an abelian variety a over a function field which is totally degenerate at a place v. we adapt zhang ' s proof of the number field case replacing the complex analytic tools by tropical analytic geometry. a key step is the tropical equidistribution theorem for a at the totally degenerate place. as an application, we obtain finiteness of torsion points with coordinates in the maximal unramified algebraic extension over v.
|
arxiv:math/0609387
|
this paper presents a method to reconstruct high - quality textured 3d models from single images. current methods rely on datasets with expensive annotations ; multi - view images and their camera parameters. our method relies on gan generated multi - view image datasets which have a negligible annotation cost. however, they are not strictly multi - view consistent and sometimes gans output distorted images. this results in degraded reconstruction qualities. in this work, to overcome these limitations of generated datasets, we have two main contributions which lead us to achieve state - of - the - art results on challenging objects : 1 ) a robust multi - stage learning scheme that gradually relies more on the models own predictions when calculating losses, 2 ) a novel adversarial learning pipeline with online pseudo - ground truth generations to achieve fine details. our work provides a bridge from 2d supervisions of gan models to 3d reconstruction models and removes the expensive annotation efforts. we show significant improvements over previous methods whether they were trained on gan generated multi - view images or on real images with expensive annotations. please visit our web - page for 3d visuals : https : / / research. nvidia. com / labs / adlr / progressive - 3d - learning
|
arxiv:2305.11102
|
the origins space telescope ( origins ) traces our cosmic history, from the formation of the first galaxies and the rise of metals to the development of habitable worlds and present - day life. origins does this through exquisite sensitivity to infrared radiation from ions, atoms, molecules, dust, water vapor and ice, and observations of extra - solar planetary atmospheres, protoplanetary disks, and large - area extragalactic fields. origins operates in the wavelength range 2. 8 to 588 microns and is 1000 times more sensitive than its predecessors due to its large, cold ( 4. 5 k ) telescope and advanced instruments. origins was one of four large missions studied by the community with support from nasa and industry in preparation for the 2020 decadal survey in astrophysics. this is the final study report.
|
arxiv:1912.06213
|
a main feature of high - energy scattering in qcd is saturation in the number density of gluons. this phenomenon is described by non - linear evolution equations, jimwlk and bk, which have been derived at leading logarithmic accuracy. in this paper we generalize this framework to include running coupling corrections to the evolution kernel. we develop a dispersive representation of the dressed gluon propagator in the background of weiszacker williams fields and use it to compute o ( beta _ 0 ^ { n - 1 } alpha _ s ^ n ) corrections to the kernel to all orders in perturbation theory. the resummed kernels present infrared - renormalon ambiguities, which are indicative of the form and importance of non - perturbative power corrections. we investigate numerically the effect of the newly computed perturbative corrections as well as the power corrections on the evolution and find that at present energies they are both significant.
|
arxiv:hep-ph/0609087
|
increasing amounts of scientific and social data are published in the resource description framework ( rdf ). although the rdf data can be queried using the sparql language, even the sparql - based operation has a limitation in implementing traversal or analytical algorithms. recently, a variety of graph database implementations dedicated to analyses on the property graph model have emerged. however, the rdf model and the property graph model are not interoperable. here, we developed a framework based on the graph to graph mapping language ( g2gml ) for mapping rdf graphs to property graphs to make the most of accumulated rdf data. using this framework, graph data described in the rdf model can be converted to the property graph model and can be loaded to several graph database engines for further analysis. future works include implementing and utilizing graph algorithms to make the most of the accumulated data in various analytical engines.
|
arxiv:1812.01801
|
we discuss the theorem on the existence of six points on a convex closed plane curve in which the curve has a contact of order six with the osculating conic. ( this is the ` ` projective version ' ' of the well known four vertices theorem for a curve in the euclidean plane. ) we obtain this classical fact as a corollary of some general sturm - type theorems.
|
arxiv:dg-ga/9510008
|
turbulence driven zonal flows play an important role in fusion devices since they improve plasma confinement by limiting the level of anomalous transport. current theories mostly focus on flow excitation but do not self - consistently describe the nearly stationary zonal flow turbulence equilibrium state. first - principles two - fluid turbulence studies are used to construct a reynolds stress response functional from observations in turbulent states. this permits, for the first time, a reliable charting of zonal flow turbulence equilibria.
|
arxiv:1106.1963
|
in this paper we study global distance estimates and uniform local volume estimates in a large class of sub - riemannian manifolds. our main device is the generalized curvature dimension inequality introduced by the first and the third author in \ cite { bg1 } and its use to obtain sharp inequalities for solutions of the sub - riemannian heat equation. as a consequence, we obtain a gromov type precompactness theorem for the class of sub - riemannian manifolds whose generalized ricci curvature is bounded from below in the sense of \ cite { bg1 }.
|
arxiv:1211.0221
|
we report results from a deep jansky very large array ( jvla ) search for co 1 - 0 line emission from galaxies in a candidate galaxy cluster at z ~ 1. 55 in the cosmos field. we target 4 galaxies with optical spectroscopic redshifts in the range z = 1. 47 - 1. 59. two of these 4 galaxies, id51613 and id51813, are nominally detected in co line emission at the 3 - 4 sigma level. we find co luminosities of 2. 4x10 ^ 10 k km / s pc ^ 2 and 1. 3x10 ^ 10 k km / s pc ^ 2, respectively. taking advantage from the clustering and 2 - ghz bandwidth of the jvla, we perform a search for emission lines in the proximity of optical sources within the field of view of our observations. we limit our search to galaxies with k < 23. 5 ( ab ) and z _ phot = 1. 2 - 1. 8. we find 2 bright optical galaxies to be associated with significant emission line peaks ( > 4 sigma ) in the data cube, which we identify with the co line emission. to test the reliability of the line peaks found, we performed a parallel search for line peaks using a bayesian inference method. monte carlo simulations show that such associations are statistically significant, with probabilities of chance association of 3. 5 % and 10. 7 % for id 51207 and id 51380, respectively. modeling of their optical / ir seds indicates that the co detected galaxies and candidates have stellar masses and sfrs in the range ( 0. 3 - 1. 1 ) x10 ^ 11 m _ sun and 60 - 160 m _ sun / yr, with sfes comparable to that found in other star - forming galaxies at similar redshifts. by comparing the space density of co emitters derived from our observations with the space density derived from previous co detections at z ~ 1. 5, and with semi - analytic predictions for the co luminosity function, we suggest that the latter tend to underestimate the number of co galaxies detected at high - redshift. finally, we argue about the benefits of future blind co searches in clustered fields with upcoming submm / radio facilities.
|
arxiv:1207.2795
|
text - to - video ( t2v ) generation has recently garnered significant attention thanks to the large multi - modality model sora. however, t2v generation still faces two important challenges : 1 ) lacking a precise open sourced high - quality dataset. the previous popular video datasets, e. g. webvid - 10m and panda - 70m, are either with low quality or too large for most research institutions. therefore, it is challenging but crucial to collect a precise high - quality text - video pairs for t2v generation. 2 ) ignoring to fully utilize textual information. recent t2v methods have focused on vision transformers, using a simple cross attention module for video generation, which falls short of thoroughly extracting semantic information from text prompt. to address these issues, we introduce openvid - 1m, a precise high - quality dataset with expressive captions. this open - scenario dataset contains over 1 million text - video pairs, facilitating research on t2v generation. furthermore, we curate 433k 1080p videos from openvid - 1m to create openvidhd - 0. 4m, advancing high - definition video generation. additionally, we propose a novel multi - modal video diffusion transformer ( mvdit ) capable of mining both structure information from visual tokens and semantic information from text tokens. extensive experiments and ablation studies verify the superiority of openvid - 1m over previous datasets and the effectiveness of our mvdit.
|
arxiv:2407.02371
|
the paper is withdrawn by the author because it is superseded by cond - mat / 0303357.
|
arxiv:cond-mat/0210674
|
we consider the dynamics of a mechanical failure induced by a shear stress in a strongly magnetized neutron - star crust. we show that even if the elastic properties of the crust allow the creation of a shear crack, the strongly sheared magnetic field around the crack leads to a back - reaction from the lorentz force which does not allow large relative displacement of the crack surfaces. instead, the global evolution of the crack proceeds on a slow resistive time scale, and is unable to release any substantial mechanical energy. our calculations demostrate that for { \ it some } magnetic - field configurations, the magnetic forces cause, effectively, a plastic deformation of the crust when the resulting elastic shear stress exceeds the critical value for mechanical failure.
|
arxiv:1204.2605
|
the last 10 - 20 years has seen a profound shift in views of how the galaxy ' s halo formed. the idea of a monolithic early collapse of a single system ( eggen, lynden - bell and sandage 1962 ) has been challenged by observations at high redshift and by cosmological models of structure formation. these findings imply that we should see clear evidence of hierarchical formation processes in nearby galaxies. recent studies of our galaxy, made possible by large - scale ccd surveys such as the sloan digital sky survey ( sdss ), have begun to reveal tantalizing evidence of substructure in the outer halo. we review evidence for tidal streams associated with known milky way satellites and for star streams whose progenitors are still unknown. this includes results from the sdss and our own ongoing pencil - beam halo survey, the spaghetti survey.
|
arxiv:astro-ph/0111097
|
the human visual system can spot an abnormal image, and reason about what makes it strange. this task has not received enough attention in computer vision. in this paper we study various types of atypicalities in images in a more comprehensive way than has been done before. we propose a new dataset of abnormal images showing a wide range of atypicalities. we design human subject experiments to discover a coarse taxonomy of the reasons for abnormality. our experiments reveal three major categories of abnormality : object - centric, scene - centric, and contextual. based on this taxonomy, we propose a comprehensive computational model that can predict all different types of abnormality in images and outperform prior arts in abnormality recognition.
|
arxiv:1512.01325
|
we present a monte carlo generator that implements significant theoretical improvements in the simulation of top - quark pair production and decay at the lhc. spin correlations and off - shell effects in top - decay chains are described in terms of exact matrix elements for $ p p \ to \ ell ^ + \ nu _ { \ scriptscriptstyle \ ell } \, l ^ - \ bar { \ nu } _ { \ scriptscriptstyle l } b \ bar { b } $ at nlo qcd, where the leptons $ \ ell $ and $ l $ belong to different families, and $ b $ quarks are massive. thus, the contributions from $ t \ bar { t } $ and $ wt $ single - top production as well as their quantum interference are fully included. matrix elements are matched to the pythia8 parton shower using a recently proposed method that allows for a consistent treatment of resonances in the powheg framework. these theoretical improvements are especially important for the interpretation of precision measurements of the top - quark mass, for single - top analyses in the $ wt $ channel, and for $ t \ bar { t } $ and $ wt $ backgrounds in the presence of jet vetoes or cuts that enhance off - shell effects. the new generator is based on a process - independent interface of the openloops amplitude generator with the powhegbox framework.
|
arxiv:1607.04538
|
we report the results of a full - stokes survey of all four 18 cm oh lines in 77 oh megamasers ( ohms ) using the arecibo observatory. this is the first survey of ohms that included observations of the oh satellite lines ; only 4 of the 77 ohms have existing satellite line observations in the literature. in 5 sources, satellite line emission is detected, with 3 of the 5 sources re - detections of previously published sources. the 2 sources with new detections of satellite line emission are iras f10173 + 0829, which was detected at 1720 mhz, and iras f15107 + 0724, for which both the 1612 mhz and 1720 mhz lines were detected. in iras f15107 + 0724, the satellite lines are partially conjugate, as 1720 mhz absorption and 1612 mhz emission have the same structure at some velocities within the source, along with additional broader 1612 mhz emission. this is the first observed example of conjugate satellite lines in an ohm. in the remaining sources, no satellite line emission is observed. the detections and upper limits are generally consistent with models of ohm emission in which all of the 18 cm oh lines have the same excitation temperature. there is no evidence for a significant population of strong satellite line emitters among ohms.
|
arxiv:1307.5071
|
in this paper, we propose an accurate finite difference method to discretize the $ d $ - dimensional ( for $ d \ ge 1 $ ) tempered integral fractional laplacian and apply it to study the tempered effects on the solution of problems arising in various applications. compared to other existing methods, our method has higher accuracy and simpler implementation. our numerical method has an accuracy of $ o ( h ^ \ epsilon ) $, for $ u \ in c ^ { 0, \ alpha + \ epsilon } ( \ bar { \ omega } ) $ if $ \ alpha < 1 $ ( or $ u \ in c ^ { 1, \ alpha - 1 + \ epsilon } ( \ bar { \ omega } ) $ if $ \ alpha \ ge 1 $ ) with $ \ epsilon > 0 $, suggesting the minimum consistency conditions. the accuracy can be improved to $ o ( h ^ 2 ) $, for $ u \ in c ^ { 2, \ alpha + \ epsilon } ( \ bar { \ omega } ) $ if $ \ alpha < 1 $ ( or $ u \ in c ^ { 3, \ alpha - 1 + \ epsilon } ( \ bar { \ omega } ) $ if $ \ alpha \ ge 1 $ ). numerical experiments confirm our analytical results and provide insights in solving the tempered fractional poisson problem. it suggests that to achieve the second order of accuracy, our method only requires the solution $ u \ in c ^ { 1, 1 } ( \ bar { \ omega } ) $ for any $ 0 < \ alpha < 2 $. moreover, if the solution of tempered fractional poisson problems satisfies $ u \ in c ^ { p, s } ( \ bar { \ omega } ) $ for $ p = 0, 1 $ and $ 0 < s \ le 1 $, our method has the accuracy of $ o ( h ^ { p + s } ) $. since our method yields a ( multilevel ) toeplitz stiffness matrix, one can design fast algorithms via the fast fourier transform for efficient simulations. finally, we apply it together with fast algorithms to study the tempered effects on the solutions of various tempered fractional pdes, including the allen - cahn equation and gray - scott equations.
|
arxiv:1808.02615
|
we show that limit cycle systems in langevin bath exhibit uncertainty in observables that define the limit - cycle plane, and maintain a positive lower bound. the uncertainty - bound depends on the parameters that determine the shape and periodicity of the limit cycle. in one dimension, we use the framework of canonical dissipative systems to construct the limit cycle, whereas in two dimensions, particle in central potentials with radial - dissipation provide us natural examples. we show that, the position - momenta uncertainty of particle in a central potential is larger than half the magnitude of the angular momentum ( conserved ) of the particle. we also investigate how uncertainties, which are absent in deterministic systems, increase with time when the systems are attached to a bath and eventually cross the lower bound before reaching the steady state.
|
arxiv:2502.13111
|
we study the compactification of om - theory on tori and show a simple heuristic derivation of the $ s $ - duals of noncommutative open string theory in diverse dimensions from the om - theoretical point of view. in particular, we identify the $ s $ - duality between noncommutative open string theory and noncommutative yang - mills theory in $ ( 3 + 1 ) $ dimensions as the exchange of two circles of a torus on which om - theory is compactified. also, we briefly discuss $ t $ - duality between noncommutative open string theories.
|
arxiv:hep-th/0006225
|
recommender systems have been applied successfully in a number of different domains, such as, entertainment, commerce, and employment. their success lies in their ability to exploit the collective behavior of users in order to deliver highly targeted, personalized recommendations. given that recommenders learn from user preferences, they incorporate different biases that users exhibit in the input data. more importantly, there are cases where recommenders may amplify such biases, leading to the phenomenon of bias disparity. in this short paper, we present a preliminary experimental study on synthetic data, where we investigate different conditions under which a recommender exhibits bias disparity, and the long - term effect of recommendations on data bias. we also consider a simple re - ranking algorithm for reducing bias disparity, and present some observations for data disparity on real data.
|
arxiv:1811.01461
|
we present a systematic theoretical study of the five smallest oligoacenes ( naphthalene, anthracene, tetracene, pentacene, and hexacene ) in their anionic, neutral, cationic, and dicationic charge states. we used density functional theory ( dft ) to obtain the ground - state optimised geometries, and time - dependent dft ( td - dft ) to evaluate the electronic absorption spectra. total - energy differences enabled us to evaluate the electron affinities and first and second ionisation energies, the quasiparticle correction to the homo - lumo energy gap and an estimate of the excitonic effects in the neutral molecules. electronic absorption spectra have been computed by combining two different implementations of td - dft : the frequency - space method to study general trends as a function of charge - state and molecular size for the lowest - lying in - plane long - polarised and short - polarised $ \ pi \ to \ pi ^ \ star $ electronic transitions, and the real - time propagation scheme to obtain the whole photo - absorption cross - section up to the far - uv. doubly - ionised pahs are found to display strong electronic transitions of $ \ pi \ to \ pi ^ \ star $ character in the near - ir, visible, and near - uv spectral ranges, like their singly - charged counterparts. while, as expected, the broad plasmon - like structure with its maximum at about 17 - 18 ev is relatively insensitive to the charge - state of the molecule, a systematic decrease with increasing positive charge of the absorption cross - section between about 6 and about 12 ev is observed for each member of the class.
|
arxiv:0707.3045
|
general fractional calculus offers an elegant and self - consistent path toward the generalization of fractional calculus to an enhanced class of kernels. prabhakar ' s theory can be thought of, to some extent, as an explicit realization of this scheme achieved by merging the prabhakar ( or, three - parameter mittag - leffler ) function with the general wisdom of the standard ( riemann - liouville and caputo ) formulation of fractional calculus. here i discuss some implications that emerge when attempting to frame prabhakar ' s theory within the program of general fractional calculus.
|
arxiv:1911.06695
|
we introduce a new class $ \ mathcal { g } $ of bipartite plane graphs and prove that each graph in $ \ mathcal { g } $ admits a proper square contact representation. a contact between two squares is \ emph { proper } if they intersect in a line segment of positive length. the class $ \ mathcal { g } $ is the family of quadrangulations obtained from the 4 - cycle $ c _ 4 $ by successively inserting a single vertex or a 4 - cycle of vertices into a face. for every graph $ g \ in \ mathcal { g } $, we construct a proper square contact representation. the key parameter of the recursive construction is the aspect ratio of the rectangle bounded by the four outer squares. we show that this aspect ratio may continuously vary in an interval $ i _ g $. the interval $ i _ g $ cannot be replaced by a fixed aspect ratio, however, as we show, the feasible interval $ i _ g $ may be an arbitrarily small neighborhood of any positive real.
|
arxiv:2103.08719
|
the fact that not all measurements can be carried out simultaneously is a peculiar feature of quantum mechanics and responsible for many key phenomena in the theory, such as complementarity or uncertainty relations. for the special case of projective measurements quantum behavior can be characterized by the commutator but for generalized measurements it is not easy to decide whether two measurements can still be understood in classical terms or whether they show already quantum features. we prove that generalized measurements which do not fulfill the notion of joint measurability are nonclassical, as they can be used for the task of quantum steering. this shows that the notion of joint measurability is, among several definitions, the proper one to characterize quantum behavior. moreover, the equivalence allows to derive novel steering inequalities from known results on joint measurability and new criteria for joint measurability from known results on the steerability of states.
|
arxiv:1407.2224
|
blazars are the most violent steady / recurrent sources of high - energy gamma - ray emission in the known universe. they are prominent emitters of electromagnetic radiation throughout the entire electromagnetic spectrum. the observable radiation most likely originates in a relativistic jet oriented at a small angle with respect to the line of sight. this review starts out with a general overview of the phenomenology of blazars, including results from a recent multiwavelength observing campaign on 3c279. subsequently, issues of modeling broadband spectra will be discussed. spectral information alone is not sufficient to distinguish between competing models and to constrain essential parameters, in particular related to the primary particle acceleration and radiation mechanisms in the jet. short - term spectral variability information may help to break such model degeneracies, which will require snap - shot spectral information on intraday time scales, which may soon be achievable for many blazars even in the gamma - ray regime with the upcoming glast mission and current advances in atmospheric cherenkov telescope technology. in addition to pure leptonic and hadronic models of gamma - ray emission from blazars, leptonic / hadronic hybrid models are reviewed, and the recently developed hadronic synchrotron mirror model for tev gamma - ray flares which are not accompanied by simultaneous x - ray flares ( ` ` orphan tev flares ' ' ) is revisited.
|
arxiv:astro-ph/0608713
|
we propose rockmate to control the memory requirements when training pytorch dnn models. rockmate is an automatic tool that starts from the model code and generates an equivalent model, using a predefined amount of memory for activations, at the cost of a few re - computations. rockmate automatically detects the structure of computational and data dependencies and rewrites the initial model as a sequence of complex blocks. we show that such a structure is widespread and can be found in many models in the literature ( transformer based models, resnet, regnets,... ). this structure allows us to solve the problem in a fast and efficient way, using an adaptation of checkmate ( too slow on the whole model but general ) at the level of individual blocks and an adaptation of rotor ( fast but limited to sequential models ) at the level of the sequence itself. we show through experiments on many models that rockmate is as fast as rotor and as efficient as checkmate, and that it allows in many cases to obtain a significantly lower memory consumption for activations ( by a factor of 2 to 5 ) for a rather negligible overhead ( of the order of 10 % to 20 % ). rockmate is open source and available at https : / / github. com / topal - team / rockmate.
|
arxiv:2307.01236
|
two - dimensional ( 2d ) massless dirac electrons appear on a surface of three - dimensional topological insulators. the conductivity of such a 2d dirac electron system is studied for strong topological insulators in the case of the fermi level being located at the dirac point. the average conductivity $ \ langle \ sigma \ rangle $ is numerically calculated for a system of length $ l $ and width $ w $ under the periodic or antiperiodic boundary condition in the transverse direction, and its behavior is analyzed by applying a finite - size scaling approach. it is shown that $ \ langle \ sigma \ rangle $ is minimized at the clean limit, where it becomes scale - invariant and depends only on $ l / w $ and the boundary condition. it is also shown that once disorder is introduced, $ \ langle \ sigma \ rangle $ monotonically increases with increasing $ l $. hence, the system becomes a perfect metal in the limit of $ l \ to \ infty $ except at the clean limit, which should be identified as an unstable fixed point. although the scaling curve of $ \ langle \ sigma \ rangle $ strongly depends on $ l / w $ and the boundary condition near the unstable fixed point, it becomes almost independent of them with increasing $ \ langle \ sigma \ rangle $, implying that it asymptotically obeys a universal law.
|
arxiv:1608.07873
|
gamma cassiopeiae is an enigmatic be star with unusually strong hard x - ray emission. the suzaku observatory detected six rapid x - ray spectral hardening events called " softness dips " in a ~ 100 ksec duration observation in 2011. all the softness dip events show symmetric softness ratio variations, and some of them have flat bottoms apparently due to saturation. the softness dip spectra are best described by either ~ 40 % or ~ 70 % partial covering absorption to kt ~ 12 kev plasma emission by matter with a neutral hydrogen column density of ~ 2 - 8e21 cm - 2, while the spectrum outside of these dips is almost free of absorption. this result suggests the presence of two distinct x - ray emitting spots in the gamma cas system, perhaps on a white dwarf companion with dipole mass accretion. the partial covering absorbers may be blobs in the be stellar wind, the be disk, or rotating around the white dwarf companion. weak correlations of the softness ratios to the hard x - ray flux suggest the presence of stable plasmas at kt ~ 0. 9 and 5 kev, which may originate from the be or white dwarf winds. the formation of a be star and white dwarf binary system requires mass transfer between two stars ; gamma cas may have experienced such activity in the past.
|
arxiv:1608.01374
|
we present the first optical images of scattered light from large, detached gas / dust shells around two carbon stars, r scl and u ant, obtained in narrow band filters centred on the resonance lines of neutral k and na, and in a str. b filter ( only u ant ). they confirm results obtained in co radio line observations, but also reveal new and interesting structures. towards r scl the scattering appears optically thick in both the k and na filters, and both images outline almost perfectly circular disks with essentially uniform intensity out to a sharp outer radius of 21 ". these disks are larger - - by about a factor of two - - than the radius of the detached shell which has been marginally resolved in co radio line data. in u ant the scattering in the k filter appears to be, at least partially, optically thin, and the image is consistent with scattering in a geometrically thin ( 3 " ) shell ( radius 43 " ) with an overall spherical symmetry. the size of this shell agrees very well with that of the detached shell seen in co radio line emission. the scattering in the na filter appears more optically thick, and the image suggests the presence of at least one, possibly two, shells inside the 43 " shell. there is no evidence for such a multiple - shell structure in the co data, but this can be due to considerably lower masses for these inner shells. weak scattering appears also in a shell which is located outside the 43 " shell. the present data do not allow us to conclusively identify the scattering agent, but we argue that most of the emission in the k and na filter images is to due to resonance line scattering, and that there is also a weaker contribution from dust scattering in the u ant data. awaiting new observational data, our interpretation must be regarded as tentative.
|
arxiv:astro-ph/0104140
|
in this paper we study vector fields on the big phase space of gromov - witten theory which are idempotents of the quantum product. such vector fields can be used to simplify universal equations for higher genus gromov - witten invariants.
|
arxiv:math/0310409
|
in this note, we examine the jacobian ring description of the hodge structure of zero loci of vector bundle sections on a class of ambient varieties. we consider a set of cohomological vanishing conditions that imply such a description, and we verify these conditions for some new cases. we also observe that the method can be directly extended to log homogeneous varieties. we apply the jacobian ring to study the null varieties of period integrals and their derivatives, generalizing a result in [ 9 ] for projective spaces. as an additional application, we prove the hodge conjecture for very generic hypersurfaces in certain generalized flag varieties.
|
arxiv:1801.08261
|
low - rank matrix factorization ( mf ) is an important technique in data science. the key idea of mf is that there exists latent structures in the data, by uncovering which we could obtain a compressed representation of the data. by factorizing an original matrix to low - rank matrices, mf provides a unified method for dimension reduction, clustering, and matrix completion. in this article we review several important variants of mf, including : basic mf, non - negative mf, orthogonal non - negative mf. as can be told from their names, non - negative mf and orthogonal non - negative mf are variants of basic mf with non - negativity and / or orthogonality constraints. such constraints are useful in specific senarios. in the first part of this article, we introduce, for each of these models, the application scenarios, the distinctive properties, and the optimizing method. by properly adapting mf, we can go beyond the problem of clustering and matrix completion. in the second part of this article, we will extend mf to sparse matrix compeletion, enhance matrix compeletion using various regularization methods, and make use of mf for ( semi - ) supervised learning by introducing latent space reinforcement and transformation. we will see that mf is not only a useful model but also as a flexible framework that is applicable for various prediction problems.
|
arxiv:1507.00333
|
topological nodal superconductors are generally realized based on unconventional pairings. in this work, we propose a minimal model to realize these topological nodal phases with only $ s $ - wave interaction. in our model the linear and quadratic spin - orbit couplings along the two directions break the isotropy in momentum space and introduce effective unconventional pairings on the fermi surface. this model may support different nodal superconducting phases characterized by either winding number in bdi class or pfaffian in d class at the particle - hole invariant axes. in the vicinity of the nodal points the effective hamiltonian can be described by either type - i or type - ii dirac equation ; and the crossover between these two nodal points can be driven by external zeeman fields. we show that these nodal phases are robust against weak disorders, thus are possible to be realized in experiments with real materials. the smoking - gun evidences to verify these phases based on scanning tunneling spectroscopy are also briefly discussed.
|
arxiv:1706.01692
|
we present first results from the 3d - hst program, a near - ir spectroscopic survey performed with the wide field camera 3 on the hubble space telescope. we have used 3d - hst spectra to measure redshifts and halpha equivalent widths for a stellar mass - limited sample of 34 galaxies at 1 < z < 1. 5 with m ( stellar ) > 10 ^ 11 m ( sun ) in the cosmos, goods, and aegis fields. we find that a substantial fraction of massive galaxies at this epoch are forming stars at a high rate : the fraction of galaxies with halpha equivalent widths > 10 a is 59 %, compared to 10 % among sdss galaxies of similar masses at z = 0. 1. galaxies with weak halpha emission show absorption lines typical of 2 - 4 gyr old stellar populations. the structural parameters of the galaxies, derived from the associated wfc3 f140w imaging data, correlate with the presence of halpha : quiescent galaxies are compact with high sersic index and high inferred velocity dispersion, whereas star - forming galaxies are typically large two - armed spiral galaxies, with low sersic index. some of these star forming galaxies might be progenitors of the most massive s0 and sa galaxies. our results challenge the idea that galaxies at fixed mass form a homogeneous population with small scatter in their properties. instead we find that massive galaxies form a highly diverse population at z > 1, in marked contrast to the local universe.
|
arxiv:1108.6060
|
we show how kinetic theory, the statistics of classical particles obeying newtonian dynamics, can be formulated as a field theory. the field theory can be organized to produce a self - consistent perturbation theory expansion in an effective interaction potential. the need for a self - consistent approach is suggested by our interest in investigating ergodic - nonergodic transitions in dense fluids. the formal structure we develop has been implemented in detail for the simpler case of smoluchowski dynamics. one aspect of the approach is the identification of a core problem spanned by the variables \ rho the number density and b a response density. in this paper we set up the perturbation theory expansion with explicit development at zeroth and first order. we also determine all of the cumulants in the noninteracting limit among the core variables \ rho and b.
|
arxiv:1111.0571
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.