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we study the metrics on the families of moduli spaces arising from probing with a brane the ten and eleven dimensional supergravity solutions corresponding to renormalisation group flows of supersymmetric large n gauge theory. in comparing the geometry to the physics of the dual gauge theory, it is important to identify appropriate coordinates, and starting with the case of su ( n ) gauge theories flowing from n = 4 to n = 1 via a mass term, we demonstrate that the metric is kahler, and solve for the kahler potential everywhere along the flow. we show that the asymptotic form of the kahler potential, and hence the peculiar conical form of the metric, follows from special properties of the gauge theory. furthermore, we find the analogous kahler structure for the n = 4 preserving coulomb branch flows, and for an n = 2 flow. in addition, we establish similar properties for two eleven dimensional flow geometries recently presented in the literature, one of which has a deformation of the conifold as its moduli space. in all of these cases, we notice that the kahler potential appears to satisfy a simple universal differential equation. we prove that this equation arises for all purely coulomb branch flows dual to both ten and eleven dimensional geometries, and conjecture that the equation holds much more generally.
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arxiv:hep-th/0107261
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a straightforward application of semi - supervised machine learning to the problem of treatment effect estimation would be to consider data as " unlabeled " if treatment assignment and covariates are observed but outcomes are unobserved. according to this formulation, large unlabeled data sets could be used to estimate a high dimensional propensity function and causal inference using a much smaller labeled data set could proceed via weighted estimators using the learned propensity scores. in the limiting case of infinite unlabeled data, one may estimate the high dimensional propensity function exactly. however, longstanding advice in the causal inference community suggests that estimated propensity scores ( from labeled data alone ) are actually preferable to true propensity scores, implying that the unlabeled data is actually useless in this context. in this paper we examine this paradox and propose a simple procedure that reconciles the strong intuition that a known propensity functions should be useful for estimating treatment effects with the previous literature suggesting otherwise. further, simulation studies suggest that direct regression may be preferable to inverse - propensity weight estimators in many circumstances.
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arxiv:2009.06183
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residual dynamic mode decomposition ( resdmd ) offers a method for accurately computing the spectral properties of koopman operators. it achieves this by calculating an infinite - dimensional residual from snapshot data, thus overcoming issues associated with finite truncations of koopman operators, such as spurious eigenvalues. these spectral properties include spectra and pseudospectra, spectral measures, koopman mode decompositions, and dictionary verification. in scenarios where there are fewer snapshots than dictionary size, particularly for exact dmd and kernelized edmd, resdmd has traditionally been applied by dividing snapshot data into a training set and a quadrature set. through a novel computational approach of solving a dual least - squares problem, we demonstrate how to eliminate the need for two datasets. we provide an analysis of these new residuals for exact dmd and kernelized edmd, demonstrating resdmd ' s versatility and broad applicability across various dynamical systems, including those modeled by high - dimensional and nonlinear observables. the utility of these new residuals is showcased through three diverse examples : the analysis of cylinder wake, the study of aerofoil cascades, and the compression of transient shockwave experimental data. this approach not only simplifies the application of resdmd but also extends its potential for deeper insights into the dynamics of complex systems.
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arxiv:2403.05891
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the symbolic ai community is increasingly trying to embrace machine learning in neuro - symbolic architectures, yet is still struggling due to cultural barriers. to break the barrier, this rather opinionated personal memo attempts to explain and rectify the conventions in statistics, machine learning, and deep learning from the viewpoint of outsiders. it provides a step - by - step protocol for designing a machine learning system that satisfies a minimum theoretical guarantee necessary for being taken seriously by the symbolic ai community, i. e., it discusses " in what condition we can stop worrying and accept statistical machine learning. " unlike most textbooks which are written for students trying to specialize in stat / ml / dl and willing to accept jargons, this memo is written for experienced symbolic researchers that hear a lot of buzz but are still uncertain and skeptical. information on stat / ml / dl is currently too scattered or too noisy to invest in. this memo prioritizes compactness, citations to old papers ( many in early 20th century ), and concepts that resonate well with symbolic paradigms in order to offer time savings. it prioritizes general mathematical modeling and does not discuss any specific function approximator, such as neural networks ( nns ), svms, decision trees, etc. finally, it is open to corrections. consider this memo as something similar to a blog post taking the form of a paper on arxiv.
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arxiv:2209.04049
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despite the remarkable success of large language models ( llms ), evaluating their outputs ' quality regarding * preference * remains a critical challenge. existing works usually leverage an llm as the judge for comparing llms ' output pairwisely, yet such model - based evaluator is * weak evaluator * due to * conflicting preference *, i. e., output a is better than b, b than c, but c than a, causing contradictory evaluation results. to address this, we introduce ged ( preference graph ensemble and denoise ), a novel approach that leverages multiple model - based evaluators to construct preference graphs, and then ensemble and denoise these graphs for better, non - contradictory evaluation results. in particular, our method consists of two primary stages : aggregating evaluations into a unified graph and applying a denoising process to eliminate cyclic inconsistencies, ensuring a directed acyclic graph ( dag ) structure. we provide theoretical guarantees for our framework, demonstrating its efficacy in recovering the ground truth preference structure. extensive experiments on ten benchmarks demonstrate ged ' s superiority in three applications : model ranking, response selection, and model alignment tasks. notably, ged combines small llm evaluators ( e. g., llama3 - 8b, mistral - 7b, qwen2 - 7b ) to outperform stronger ones ( e. g., qwen2 - 72b ), showcasing its effectiveness in enhancing evaluation reliability and improving model performance.
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arxiv:2410.12869
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gromov - witten theory is used to define an enumerative geometry of curves in calabi - yau 5 - folds. we find recursions for meeting numbers of genus 0 curves, and we determine the contributions of moving multiple covers of genus 0 curves to the genus 1 gromov - witten invariants. the resulting invariants, conjectured to be integral, are analogous to the previously defined bps counts for calabi - yau 3 and 4 - folds. we comment on the situation in higher dimensions where new issues arise. two main examples are considered : the local calabi - yau p ^ 2 with balanced normal bundle 3o ( - 1 ) and the compact calabi - yau hypersurface x _ 7 in p ^ 6. in the former case, a closed form for our integer invariants has been conjectured by g. martin. in the latter case, we recover in low degrees the classical enumeration of elliptic curves by ellingsrud and stromme.
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arxiv:0802.1640
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soft slender structures are ubiquitous in natural and artificial systems and can be observed at scales that range from the nanometric to the kilometric, from polymers to space tethers. we present a practical numerical approach to simulate the dynamics of filaments that, at every cross - section, can undergo all six possible modes of deformation, allowing the filament to bend, twist, stretch and shear, while interacting with complex environments via muscular activity, surface contact, friction and hydrodynamics. we examine the accuracy of our method by means of several benchmark problems with known analytic solutions. we then demonstrate the capabilities and robustness of our approach to solve forward problems in physics and mechanics related to solenoid and plectoneme formation in twisted, stretched filaments, and inverse problems related to active biophysics of limbless locomotion on solid surfaces and in bulk liquids. all together, our approach provides a robust computational framework to characterize the mechanical response and design of soft active slender structures.
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arxiv:1607.00430
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let $ a \ in \ r, $ and let $ k ( a ) $ be the largest constant such that $ sup \ vert cos ( na ) - cos ( nb ) \ vert \ textless { } k ( a ) $ for $ b \ in \ r $ implies that $ b \ in \ pm a + 2 \ pi \ z. $ we show that if a cosine sequence $ ( c ( n ) ) \ _ { n \ in \ z } $ with values in a banach algebra $ a $ satisfies $ sup \ _ { n \ ge 1 } \ vert c ( n ) - cos ( na ). 1 \ _ a \ vert \ textless { } k ( a ), $ then $ c ( n ) = cos ( na ) $ for $ n \ in \ z. $ since $ { \ sqrt 5 \ over 2 } \ le k ( a ) \ le { 8 \ over 3 \ sqrt 3 } $ for every $ a \ in \ r, $ this shows that if some cosine family $ ( c ( g ) ) \ _ { g \ in g } $ over an abelian group $ g $ in a banach algebra satisfies $ sup \ _ { g \ in g } \ vert c ( g ) - c ( g ) \ vert \ textless { } { \ sqrt 5 \ over 2 } $ for some scalar cosine family $ ( c ( g ) ) \ _ { g \ in g }, $ then $ c ( g ) = c ( g ) $ for $ g \ in g, $ and the constant $ { \ sqrt 5 \ over 2 } $ is optimal. we also describe the set of all real numbers $ a \ in [ 0, \ pi ] $ satisfying $ k ( a ) \ le { 3 \ over 2 }. $
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arxiv:1505.06064
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we investigate spin dynamics of resident holes in a p - modulation - doped gaas / al $ _ { 0. 3 } $ ga $ _ { 0. 7 } $ as single quantum well. time - resolved faraday and kerr rotation, as well as resonant spin amplification, are utilized in our study. we observe that nonresonant or high power optical pumping leads to a resident hole spin polarization with opposite sign with respect to the optically oriented carriers, while low power resonant optical pumping only leads to a resident hole spin polarization if a sufficient in - plane magnetic field is applied. the competition between two different processes of spin orientation strongly modifies the shape of resonant spin amplification traces. calculations of the spin dynamics in the electron - - hole system are in good agreement with the experimental kerr rotation and resonant spin amplification traces and allow us to determine the hole spin polarization within the sample after optical orientation, as well as to extract quantitative information about spin dephasing processes at various stages of the evolution.
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arxiv:1105.1338
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reconfigurable intelligent surface ( ris ) has been envisioned as a key technology in future wireless communication networks to enable smart radio environment. to further enhance the passive beamforming capability of ris, beyond diagonal ( bd ) - ris has been proposed considering reconfigurable interconnections among different ris elements. bd - ris has a unique feature that cannot be enabled by conventional diagonal ris ; it can be realized by non - reciprocal circuits and thus enables an asymmetric scattering matrix. this feature provides the capability to break the wireless channel reciprocity, and has the potential to benefit full - duplex ( fd ) systems. in this paper, we model the bd ris - assisted fd systems, where the impact of bd - ris non - reciprocity and that of structural scattering, which refers to the specular reflection generated by ris when the ris is turned off, are explicitly captured. to assess the benefits of non - reciprocal bd - ris, we optimise the scattering matrix, precoder and combiner to maximize the dl and ul sum - rates in the fd system. to tackle this optimization problem, we propose an iterative algorithm based on block coordination descent ( bcd ) and penalty dual decomposition ( pdd ). numerical results demonstrate surprising benefits of non - reciprocal bd - ris that it can achieve much higher dl and ul sum - rates in the fd scenario than reciprocal bd - ris and conventional diagonal ris.
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arxiv:2411.18523
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a set of new exact ground states of the generalized hubbard models in arbitrary dimensions with explicitly given parameter regions is presented. this is based on a simple method for constructing exact ground states for homogeneous quantum systems.
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arxiv:cond-mat/9802010
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we have studied a quinary fe - based superconductor sr $ _ 2 $ vfeaso $ _ 3 $ by the measurements of x - ray diffraction, x - ray absorption, m \ " { o } ssbauer spectrum, resistivity, magnetization and specific heat. this apparently undoped oxyarsenide is shown to be self doped via electron transfer from the v $ ^ { 3 + } $ ions. we observed successive magnetic transitions within the vo $ _ 2 $ layers : an antiferromagnetic transition at 150 k followed by a weak ferromagnetic transition at 55 k. the spin orderings within the vo $ _ 2 $ planes are discussed based on mixed valence of v $ ^ { 3 + } $ and v $ ^ { 4 + } $.
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arxiv:1007.3980
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as a preparation for the dynamical investigations, this paper begins with a short review of the three - layer gravastar model with distinguished attention to the structure of the pertinent parameter space of gravastars in equilibrium. then the radial stability of these types of gravastars is studied by determining their response for the totally inelastic collision of their surface layer with a dust shell. it is assumed that the dominant energy condition holds and the speed of sound does not exceed that of the light in the matter of the surface layer. while in the analytic setup the equation of state is kept to be generic, in the numerical investigations three functionally distinct classes of equations of states are applied. in the corresponding particular cases the maximal mass of the dust shell that may fall onto a gravastar without converting it into a black hole is determined. for those configurations which remain stable the excursion of their radius is assigned. it is found that even the most compact gravastars cannot get beyond the lower limit of the size of conventional stars, provided that the dominant energy condition holds in both cases. it is also shown - - - independent of any assumption concerning the matter interbridging the internal de sitter and the external schwarzschild regions - - - that the better is a gravastar in mimicking a black hole the easier is to get the system formed by a dust shell and the gravastar beyond the event horizon of the composite system. in addition, a generic description of the totally inelastic collision of spherical shells in spherically symmetric spacetimes is also provided in the appendix.
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arxiv:1008.0554
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multi - class classification algorithms are very widely used, but we argue that they are not always ideal from a theoretical perspective, because they assume all classes are characterized by the data, whereas in many applications, training data for some classes may be entirely absent, rare, or statistically unrepresentative. we evaluate one - sided classifiers as an alternative, since they assume that only one class ( the target ) is well characterized. we consider a task of identifying whether a substance contains a chlorinated solvent, based on its chemical spectrum. for this application, it is not really feasible to collect a statistically representative set of outliers, since that group may contain \ emph { anything } apart from the target chlorinated solvents. using a new one - sided classification toolkit, we compare a one - sided k - nn algorithm with two well - known binary classification algorithms, and conclude that the one - sided classifier is more robust to unexpected outliers.
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arxiv:1806.05455
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we study the hadron - quark phase transition in the interior of neutron stars ( ns ). for the hadronic sector, we use a microscopic equation of state ( eos ) involving nucleons and hyperons derived within the brueckner - hartree - fock approach. for the quark sector, we employ the mit bag model, as well as the nambu - - jona - lasinio ( njl ) and the color dielectric ( cd ) models, and find that the ns maximum masses lie in the interval between 1. 5 and 1. 8 solar masses.
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arxiv:nucl-th/0410040
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we introduce wecs ( wavelet energies correlation sreening ), an unsupervised sparse procedure to detect spatio - temporal change points on multi - temporal sar ( polsar ) images or even on sequences of very high resolution images. the procedure is based on wavelet approximation for the multi - temporal images, wavelet energy apportionment, and ultra - high dimensional correlation screening for the wavelet coefficients. we present two complimentary wavelet measures in order to detect sudden and / or cumulative changes, as well as for the case of stationary or non - stationary multi - temporal images. we show wecs performance on synthetic multi - temporal image data. we also apply the proposed method to a time series of 85 satellite images in the border region of brazil and the french guiana. the images were captured from november 08, 2015 to december 09 2017.
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arxiv:2103.14444
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hitchin ' s twistor treatment of schlesinger ' s equations is extended to the general isomonodromic deformation problem. it is shown that a generic linear system of ordinary differential equations with gauge group sl ( n, c ) on a riemann surface x can be obtained by embedding x in a twistor space z on which sl ( n, c ) acts. when a certain obstruction vanishes, the isomonodromic deformations are given by deforming x in z. this is related to a description of the deformations in terms of hamiltonian flows on a symplectic manifold constructed from affine orbits in the dual lie algebra of a loop group.
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arxiv:nlin/0007024
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we give a complete description of zero sets for some well - known subclasses of entire functions of exponential growth ( bounded on real axis, cartwright ' s class )
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arxiv:math/0701808
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in this paper we study the nonlinear elliptic problem with p ( x ) - laplacian ( hemivariational inequality ). we prove the existence of a nontrivial solution. our approach is based on critical point theory for locally lipschitz functionals due to chang.
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arxiv:1212.3688
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controlled abstractive summarization focuses on producing condensed versions of a source article to cover specific aspects by shifting the distribution of generated text towards a desired style, e. g., a set of topics. subsequently, the resulting summaries may be tailored to user - defined requirements. this paper presents a new transformer - based architecture capable of producing topic - focused summaries. the architecture modifies the cross - attention mechanism of the transformer to bring topic - focus control to the generation process while not adding any further parameters to the model. we show that our model sets a new state of the art on the newts dataset in terms of topic - focused abstractive summarization as well as a topic - prevalence score. moreover, we show via extensive experiments that our proposed topical cross - attention mechanism can be plugged into various transformer models, such as bart and t5, improving their performance on the cnn / dailymail and xsum benchmark datasets for abstractive summarization. this is achieved via fine - tuning, without requiring training from scratch. finally, we show through human evaluation that our model generates more faithful summaries outperforming the state - of - the - art frost model.
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arxiv:2311.06724
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the application of machine learning to transcriptomics data has led to significant advances in cancer research. however, the high dimensionality and complexity of rna sequencing ( rna - seq ) data pose significant challenges in pan - cancer studies. this study hypothesizes that gene sets derived from single - cell rna sequencing ( scrna - seq ) data will outperform those selected using bulk rna - seq in pan - cancer downstream tasks. we analyzed scrna - seq data from 181 tumor biopsies across 13 cancer types. high - dimensional weighted gene co - expression network analysis ( hdwgcna ) was performed to identify relevant gene sets, which were further refined using xgboost for feature selection. these gene sets were applied to downstream tasks using tcga pan - cancer rna - seq data and compared to six reference gene sets and oncogenes from oncokb evaluated with deep learning models, including multilayer perceptrons ( mlps ) and graph neural networks ( gnns ). the xgboost - refined hdwgcna gene set demonstrated higher performance in most tasks, including tumor mutation burden assessment, microsatellite instability classification, mutation prediction, cancer subtyping, and grading. in particular, genes such as dpm1, bad, and fkbp4 emerged as important pan - cancer biomarkers, with dpm1 consistently significant across tasks. this study presents a robust approach for feature selection in cancer genomics by integrating scrna - seq data and advanced analysis techniques, offering a promising avenue for improving predictive accuracy in cancer research.
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arxiv:2408.07233
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predicting motions of vessels in extreme sea states represents one of the most challenging problems in naval hydrodynamics. it involves computing complex nonlinear wave - body interactions, hence taxing heavily computational resources. here, we put forward a new simulation paradigm by training recurrent type neural networks ( rnns ) that take as input the stochastic wave elevation at a certain sea state and output the main vessel motions, e. g., pitch, heave and roll. we first compare the performance of standard rnns versus gru and lstm neural networks ( nns ) and show that lstm nns lead to the best performance. we then examine the testing error of two representative vessels, a catamaran in sea state 1 and a battleship in sea state 8. we demonstrate that good accuracy is achieved for both cases in predicting the vessel motions for unseen wave elevations. we train the nns with expensive cfd simulations offline, but upon training, the prediction of the vessel dynamics online can be obtained at a fraction of a second. this work is motivated by the universal approximation theorem for functionals [ 1 ], and it is the first implementation of such theory to realistic engineering problems.
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arxiv:1912.13382
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next - generation cosmological surveys will observe larger cosmic volumes than ever before, enabling us to access information on the primordial universe, as well as on relativistic effects. in a companion paper, we applied a fisher analysis to forecast the expected precision on $ f _ { \ rm nl } $ and the detectability of the lensing magnification and doppler contributions to the power spectrum. here we assess the bias on the best - fit values of $ f _ { \ rm nl } $ and other parameters, from neglecting these light - cone effects. we consider forthcoming 21cm intensity mapping surveys ( skao ) and optical galaxy surveys ( desi and euclid ), both individually and combined together. we conclude that lensing magnification at higher redshifts must be included in the modelling of spectroscopic surveys. if lensing is neglected in the analysis, this produces a bias of more than 1 $ \ sigma $ - not only on $ f _ { \ rm nl } $, but also on the standard cosmological parameters.
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arxiv:2108.05746
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unitarity along with precision measurements of sin2 \ beta, v _ { us } and v _ { cb } allows one to find a lower bound v _ { ub } \ geq 0. 0035 which, on using the recently measured angle \ alpha of the unitarity triangle, translates to v _ { ub } = 0. 0035 \ pm 0. 0002. this precise value, stable for a good deal of changes in \ alpha, along with cp violating phase \ delta found from unitarity allows the construction of a ` precise ' ckm matrix. the above unitarity based value of v _ { ub } is in agreement with the latest exclusive value used as input by utfit, ckmfitter, hfag, however underlines the so called ` tension ' faced by the latest inclusive v _ { ub } = 0. 00449 \ pm 0. 00033. further, using this inclusive value of v _ { ub } along with the latest sin2 \ beta, one finds \ delta = 23 ^ { \ rm o } - 39 ^ { \ rm o }, again in conflict with \ delta measured in b - decays. the calculated ranges of the elements of the ckm matrix are in excellent agreement with those obtained recently by utfit, ckmfitter and hfag. also, the ratio \ frac { v _ { ts } } { v _ { td } } is in agreement with its latest measured value, whereas there is some disagreement between the ` measured ' and the calculated v _ { td } values.
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arxiv:hep-ph/0608074
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on page 206 in his lost notebook, ramanujan recorded an incomplete septic theta function identity. motivated by the completion of this identity by the second author, we offer cubic and quintic analogues. using the theory generated by these two analogues and ramanujan ' s class invariants, we provide many evaluations for ramanujan ' s most prominent theta function, $ \ varphi ( q ) $ in his notation.
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arxiv:2312.15513
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we identify the category shv _ { nilp } ( bun _ g ) of automorphic sheaves with nilpotent singular support with its own dual, and relate this structure to the serre functor on shv _ { nilp } ( bun _ g ) and miraculous duality.
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arxiv:2012.07665
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clustering is a fundamental task in unsupervised learning. the focus of this paper is the correlation clustering functional which combines positive and negative affinities between the data points. the contribution of this paper is two fold : ( i ) provide a theoretic analysis of the functional. ( ii ) new optimization algorithms which can cope with large scale problems ( > 100k variables ) that are infeasible using existing methods. our theoretic analysis provides a probabilistic generative interpretation for the functional, and justifies its intrinsic " model - selection " capability. furthermore, we draw an analogy between optimizing this functional and the well known potts energy minimization. this analogy allows us to suggest several new optimization algorithms, which exploit the intrinsic " model - selection " capability of the functional to automatically recover the underlying number of clusters. we compare our algorithms to existing methods on both synthetic and real data. in addition we suggest two new applications that are made possible by our algorithms : unsupervised face identification and interactive multi - object segmentation by rough boundary delineation.
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arxiv:1112.2903
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fair representation learning ( frl ) is a broad set of techniques, mostly based on neural networks, that seeks to learn new representations of data in which sensitive or undesired information has been removed. methodologically, frl was pioneered by richard zemel et al. about ten years ago. the basic concepts, objectives and evaluation strategies for frl methodologies remain unchanged to this day. in this paper, we look back at the first ten years of frl by i ) revisiting its theoretical standing in light of recent work in deep learning theory that shows the hardness of removing information in neural network representations and ii ) presenting the results of a massive experimentation ( 225. 000 model fits and 110. 000 automl fits ) we conducted with the objective of improving on the common evaluation scenario for frl. more specifically, we use automated machine learning ( automl ) to adversarially " mine " sensitive information from supposedly fair representations. our theoretical and experimental analysis suggests that deterministic, unquantized frl methodologies have serious issues in removing sensitive information, which is especially troubling as they might seem " fair " at first glance.
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arxiv:2407.03834
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we prove : " if $ m $ is a compact hypersurface of the hyperbolic space, convex by horospheres and evolving by the volume preserving mean curvature flow, then it flows for all time, convexity by horospheres is preserved and the flow converges, exponentially, to a geodesic sphere ". in addition, we show that the same conclusions about long time existence and convergence hold if $ m $ is not convex by horospheres but it is close enough to a geodesic sphere.
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arxiv:math/0611216
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there are considerable advancements in medical health care in recent years, resulting in rising older population. as the workforce for such a population is not keeping pace, there is an urgent need to address this problem. having robots to stimulating recreational activities for older adults can reduce the workload for caretakers and give them time to address the emotional needs of the elderly. in this paper, we investigate the effects of the humanoid social robot nadine as an activity host for the elderly. this study aims to analyse if the elderly feels comfortable and enjoy playing game / activity with the humanoid robot nadine. we propose to evaluate this by placing nadine humanoid social robot in a nursing home as a caretaker where she hosts bingo game. we record sessions with and without nadine to understand the difference and acceptance of these two scenarios. we use computer vision methods to analyse the activities of the elderly to detect emotions and their involvement in the game. we envision that such humanoid robots will make recreational activities more readily available for the elderly. our results present positive enforcement during recreational activity, bingo, in the presence of nadine.
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arxiv:2105.01975
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for a general multipartite quantum state, we formulate a locally checkable condition, under which the expectation values of certain nonlocal observables are completely determined by the expectation values of some local observables. the condition is satisfied by ground states of gapped quantum many - body systems in two spatial dimensions, assuming a widely conjectured form of area law is correct. its implications on the studies of gapped quantum many - body systems, quantum state tomography, and quantum state verification are discussed. these results are based on a partial characterization of states with small yet nonzero conditional mutual information, which may be of independent interest.
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arxiv:1405.0137
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among all positional numeration systems, the widely studied bertrand numeration systems are defined by a simple criterion in terms of their numeration languages. in 1989, bertrand - mathis characterized them via representations in a real base $ \ beta $. however, the given condition turns to be not necessary. hence, the goal of this paper is to provide a correction of bertrand - mathis ' result. the main difference arises when $ \ beta $ is a parry number, in which case are derived two associated bertrand numeration systems. along the way, we define a non - canonical $ \ beta $ - shift and study its properties analogously to those of the usual canonical one.
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arxiv:2202.04938
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here we propose and demonstrate an all - optical wavelength - routing approach which uses a tuning mechanism based upon the optical gradient force in a specially - designed nano - optomechanical system. the resulting mechanically - compliant " spiderweb " resonantor realizes seamless wavelength routing over a range of 3000 times the intrinsic channel width, with a tuning efficiency of 309 - ghz / mw, a switching time of less than 200 - ns, and 100 % channel - quality preservation over the entire tuning range. these results indicate the potential for radiation pressure actuated devices to be used in a variety of photonics applications, such as channel routing / switching, buffering, dispersion compensation, pulse trapping / release, and widely tunable lasers.
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arxiv:0905.3336
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we provide theoretical and experimental evidence of statistical outliers in random laser emission that are not accounted for by the, now established, power - law tailed ( l \ ' evy ) distribution. such outliers manifest themselves as single, large isolated spikes over an otherwise smooth background. a statistical test convincingly shows that their probability is larger than the one extrapolated from lower - intensity events. to compare with experimental data, we introduced the anomaly parameter that allows for an identification of such rare events from experimental spectral measurements and that agrees as well with the simulations of our monte carlo model. a possible interpretation in terms of black swans or dragon kings, large events having a different generation mechanism from their peers, is discussed.
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arxiv:1811.04789
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we argue that the configurations that approach maximal entropy in five - dimensional asymptotically flat vacuum gravity, for fixed mass and angular momentum, are ` black saturns ' with a central, close to static, black hole and a very thin black ring around it. for any value of the angular momentum, the upper bound on the entropy is equal to the entropy of a static black hole of the same total mass. for fixed mass, spin and area there are families of multi - ring solutions with an arbitrarily large number of continuous parameters, so the total phase space is infinite - dimensional. somewhat surprisingly, the phases of highest entropy are not in thermal equilibrium. imposing thermodynamical equilibrium drastically reduces the phase space to a finite, small number of different phases.
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arxiv:hep-th/0702111
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we employed the fast folding algorithm ( ffa ) on l - band globular cluster ( gc ) observations taken with five - hundred - meter aperture spherical radio telescope ( fast ) to search for new pulsars, especially those with a long rotational period. we conducted a search across 16 gcs that collectively host 93 known pulsars, as well as 14 gcs that do not contain any known pulsars. the majority of these known pulsars were successfully re - detected in our survey. the few non - detections could be attributed to the high accelerations of these pulsars. additionally, we have discovered a new binary millisecond pulsar, namely m13i ( or psr j1641 + 3627i ) in gc m13 ( or ngc 6205 ), and obtained its phase - coherent timing solution using observations spanning 6 years. m13i has a spin period of 6. 37 ms, and an orbital period of 18. 23 days. the eccentricity of the binary orbit is 0. 064, with a companion mass range of approximately 0. 45 to 1. 37 m $ _ { \ odot } $. the orbital properties of m13i are remarkably different from those of the other known pulsars in m13, indicating that this pulsar has undergone a different evolutionary path compared to the rest.
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arxiv:2505.05021
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bayesian inference can quantify uncertainty in the predictions of neural networks using posterior distributions for model parameters and network output. by looking at these posterior distributions, one can separate the origin of uncertainty into aleatoric and epistemic contributions. one goal of uncertainty quantification is to inform on prediction accuracy. here we show that prediction accuracy depends on both epistemic and aleatoric uncertainty in an intricate fashion that cannot be understood in terms of marginalized uncertainty distributions alone. how the accuracy relates to epistemic and aleatoric uncertainties depends not only on the model architecture, but also on the properties of the dataset. we discuss the significance of these results for active learning and introduce a novel acquisition function that outperforms common uncertainty - based methods. to arrive at our results, we approximated the posteriors using deep ensembles, for fully - connected, convolutional and attention - based neural networks.
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arxiv:2211.14605
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in the frame of the scalar field model with non minimal kinetic coupling to gravity, we study the cosmological solutions of the chaplygin gas model of dark energy. by appropriately restricting the potential, we found the scalar field, the potential and coupling giving rise to the chaplygin gas solution. extensions to the generalized and modified chaplygin gas have been made.
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arxiv:1106.5482
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extremely powerful emission lines are observed in the x - ray afterglow of several grbs. the energy contained in the illuminating continuum which is responsible for the line production exceeds 10 $ ^ { 51 } $ erg, much higher than that of the collimated grbs. it constrains the models which explain the production of x - ray emission lines. in this paper, we argue that this energy can come from a continuous postburst outflow. focusing on a central engine of highly magnetized millisecond pulsar or magnetar we find that afterglow can be affected by the illuminating continuum, and therefore a distinct achromatic bump may be observed in the early afterglow lightcurves. with the luminosity of the continuous outflow which produces the line emission, we define the upper limit of the time when the bump feature appears. we argue that the reason why the achromatic bumps have not been detected so far is that the bumps should appear at the time too early to be observed.
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arxiv:astro-ph/0311368
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we study how equivalent nonisomorphic models of unsuperstable theories can be. we measure the equivalence by ehrenfeucht - fraisse games. this paper continues [ hysh : 474 ].
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arxiv:math/9202205
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the quasi - two - dimensional heisenberg spin $ s = 1 / 2 $ dimer system bis ( 2 - amino - 5 - fluoro - pyridinium ) tetrachlorocuprate ( ii ) is studied by means of inelastic neutron scattering, calorimetry and nuclear magnetic resonance ( nmr ) experiments. in the absence of an applied magnetic field we find dispersive triplet excitations with a spin gap of $ \ delta = 1. 112 ( 15 ) $ mev and a bandwidth of $ 0. 715 ( 15 ) $ mev within the layers and $ 0. 116 ( 15 ) $ mev between the layers, respectively. in an applied magnetic field of $ \ mu _ 0h _ c \ approx 8. 5 $ t the spin gap is closed and we find a field induced antiferromagnetically ordered phase.
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arxiv:1906.00602
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we have designed and experimentally realized an ultra - broadband acoustic metasurface ( ubam ) capable of going beyond the intrinsic limitation of bandwidth in existing designs of optical / acoustical metasurfaces. both the numerical and experimental results demonstrate that the ubam made of subwavelength gratings can manipulate the reflected phase - front within a bandwidth larger than 2 octaves. a simple physical model based on the phased array theory is developed for interpreting this extraordinary phenomenon as well as obtaining deeper insight to the underlying physics of our design. we anticipate the ubam to open new avenue to the design and application of broadband acoustical devices.
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arxiv:1409.1350
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nitrogen - vacancy ( nv ) center in diamond is a promising quantum sensor with remarkably versatile sensing capabilities. while scanning nv magnetometry is well - established, nv electrometry has been so far limited to bulk diamonds. here we demonstrate imaging external alternating ( ac ) and direct ( dc ) electric fields with a single nv at the apex of a diamond scanning tip under ambient conditions. a strong electric field screening effect is observed at low frequencies due to charge noise on the surface. we quantitatively measure its frequency dependence, and overcome this screening by mechanically oscillating the tip for imaging dc fields. our scanning nv electrometry achieved an ac e - field sensitivity of 26 mv um ^ ( - 1 ) hz ^ ( - 1 / 2 ), a dc e - field gradient sensitivity of 2 v um ^ ( - 2 ) hz ^ ( - 1 / 2 ), and sub - 100 nm resolution limited by the nv - sample distance. our work represents an important step toward building a scanning - probe - based multimodal quantum sensing platform.
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arxiv:2205.03952
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we present the { \ tt c + + } program \ texttt { relext } for standard model ( sm ) extensions that feature a dark matter ( dm ) candidate. the tool allows to efficiently scan the parameter spaces of these models to find parameter combinations that lead to relic density values which are compatible with the measured value within the uncertainty specified by the user. the code computes the relic density for freeze - out ( co - ) annihilation processes. the user can choose between several pre - installed models or any arbitrary other model featuring a discrete $ \ mathbb { z } _ 2 $ symmetry, by solely providing the corresponding \ texttt { feynrules } model files. the code automatically generates the required ( co - ) annihilation amplitudes and thermally averaged cross sections, including the total widths in the $ s $ - channel mediators, and solves the boltzmann equation to determine the relic density. it can easily be linked to other tools like e. g. ~ \ texttt { scanners } to check for the relevant theoretical and experimental constraints, or to \ texttt { bsmpt } to investigate the phase history of the model and possibly related gravitational waves signals.
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arxiv:2503.13087
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let $ n $ be a closed spin manifold with positive scalar curvature and $ d _ n $ the dirac operator on $ n $. let $ m _ 1 $ and $ m _ 2 $ be two galois covers of $ n $ such that $ m _ 2 $ is a quotient of $ m _ 1 $. then the quotient map from $ m _ 1 $ to $ m _ 2 $ naturally induces maps between the geometric $ c ^ * $ - algebras associated to the two manifolds. we prove, by a finite - propagation argument, that the \ emph { maximal } higher rho invariants of the lifts of $ d _ n $ to $ m _ 1 $ and $ m _ 2 $ behave functorially with respect to the above quotient map. this can be applied to the computation of higher rho invariants, along with other related invariants.
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arxiv:2005.01933
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typicality has always been in the minds of the founding fathers of probability theory when probabilistic reasoning is applied to the real world. however, the role of typicality is not always appreciated. an example is the paper " foundations of statistical mechanics and the status of born ' s rule in de broglie - bohm pilot - wave theory " by antony valentini, where he presents typicality and relaxation to equilibrium as distinct approaches to the proof of born ' s rule, while typicality is in fact an overriding necessity. moreover the " typicality approach " to born ' s rule of " the bohmian mechanics school " is claimed to be inherently circular. we wish to explain once more in very simple terms why the accusation is off target and why " relaxation to equilibrium " is neither necessary nor sufficient to justify born ' s rule.
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arxiv:1910.08049
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we study the ground state properties of the bond alternating $ s = 1 / 2 $ quantum spin chain whose hamiltonian is h = \ sum _ j ( s _ { 2j } ^ x s _ { 2j + 1 } ^ x + s _ { 2j } ^ y s _ { 2j + 1 } ^ y + \ lambda s _ { 2j } ^ z s _ { 2j + 1 } ^ z ) + \ beta \ sum _ j { \ bf s } _ { 2j - 1 } \ cdot { \ bf s } _ { 2j }. when $ \ beta = 0 $, the ground state is a collection of local singlets with a finite excitation gap. in the limit of strong ferromagnetic coupling $ \ beta \ to - \ infty $, this is equivalent to the $ s = 1 \ xxz $ hamiltonian. it has several ground state phases in the $ \ lambda $ - $ \ beta $ plane including the gapful haldane phase. they are characterized by a full breakdown, partial breakdowns and a non - breakdown of the hidden discrete $ z _ 2 \ times z _ 2 $ symmetry. the ground state phase diagram is obtained by series expansions.
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arxiv:cond-mat/9303010
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we propose a method to efficiently compute the minkowski sum, denoted by binary operator $ \ oplus $ in the paper, of convex polytopes in $ \ re ^ d $ using their face lattice structures as input. in plane, the minkowski sum of convex polygons can be computed in linear time of the total number of vertices of the polygons. in $ \ re ^ d $, we first show how to compute the minkowski sum, $ p \ oplus q $, of two convex polytopes $ p $ and $ q $ of input size $ n $ and $ m $ respectively in time $ o ( nm ) $. then we generalize the method to compute the minkowski sum of $ n $ convex polytopes, $ p _ 1 \ oplus p _ 2 \ oplus \ cdots \ oplus p _ n $, in $ \ re ^ d $ in time $ o ( \ prod _ { i } ^ { n } n _ i ) $, where $ p _ 1 $, $ p _ 2 $, $ \ dots $, $ p _ n $ are $ n $ input convex polytopes and for each $ i $, $ n _ i $ is size of the face lattice structure of $ p _ i $. our algorithm for minkowski sum of two convex polytopes is optimal in the worst case since the output face lattice structure of $ p \ oplus q $ for convex polytopes in $ \ re ^ d $ can be $ o ( nm ) $ in worst case.
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arxiv:1811.05812
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we perform a general analysis of the r - parity conserving dimension - five operators that can be present beyond the minimal supersymmetric standard model. not all these operators are actually independent. we present a method which employs spurion - dependent field redefinitions that removes this " redundancy " and establishes the minimal, irreducible set of these dimension - five operators. their potential effects on the mssm higgs sector are discussed to show that the tree level bound $ m _ h \ leq m _ z $ cannot be easily lifted within the approximations used, and quantum corrections are still needed to satisfy the lepii bound. an ansatz is provided for the structure of the remaining couplings in the irreducible set of d = 5 operators, which avoids phenomenological constraints from flavor changing neutral currents. the minimal set of operators brings new couplings in the effective lagrangian, notably " wrong " - higgs yukawa couplings and contact fermion - fermion - scalar - scalar interactions, whose effects are expected to be larger than those generated in the mssm at loop or even tree level. this has implications in particular for lhc searches for supersymmetry by direct squark production.
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arxiv:0806.3778
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there are several instances where quantum anomalies of continuous and discrete classical symmetries play an important role in fundamental physics. examples come from chiral anomalies in the standard model of fundamental interactions and gravitational anomalies in string theories. their generic origin is the fact that classical symmetries may not preserve the domains of quantum operators like the hamiltonian. in this work, we show by simple examples that anomalous symmetries can often be implemented at the expense of working with mixed states having non - zero entropies. in particular there is the result on color breaking by non - abelian magnetic monopoles. this anomaly can be rectified by using impure states. we also argue that non - abelian groups of twisted bundles are always anomalous for pure states sharpening an earlier argument of sorkin and balachandran. this is the case of mapping class groups of geons indicating that " large " diffeos are anomalous for pure states in the presence of geons. nevertheless diffeo invariance may be restored by using impure states. this work concludes with examples of these ideas drawn from molecular physics. the above approach using impure states is entirely equivalent to restricting all states to the algebra of observables invariant under the anomalous symmetries. for anomalous gauge groups such as color, this would mean that we work with observables singlet under global gauge transformations. for color, this will mean that we work with color singlets, a reasonable constraint.
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arxiv:1108.3898
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this paper presents the first polynomial time algorithm to compute geodesics in a cat ( 0 ) cubical complex in general dimension. the algorithm is a simple iterative method to update breakpoints of a path joining two points using miller, owen and provan ' s algorithm ( 2015 ) as a subroutine. our algorithm is applicable to any cat ( 0 ) space in which geodesics between two close points can be computed, not limited to cat ( 0 ) cubical complexes.
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arxiv:1710.09932
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we propose and test a model that describes the morphology of cities, the scaling of the urban perimeter of individual cities, and the area distribution of systems of cities. the model is also consistent with observable urban growth dynamics, our results agreeing both qualitatively and quantitatively with urban data. the resulting growth morphology can be understood from interactions among the constituent units forming an urban region, and can be modeled using a correlated percolation model in the presence of a gradient.
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arxiv:cond-mat/9809431
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we calculate nuclear suppression $ r _ { aa } $ of heavy quarks produced from the initial fusion of partons in nucleus - nucleus collisions at rhic and lhc energies. we take the shadowing as well as the energy loss suffered by them while passing through quark gluon plasma into account. we obtain results for charm and bottom quarks at several rapidities using different mechanisms for energy loss, to see if we can distinguish between them.
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arxiv:1005.1208
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by using graded ( super ) lie algebras, we can construct noncommutative superspace on curved homogeneous manifolds. in this paper, we take a flat limit to obtain flat noncommutative superspace. we particularly consider $ d = 2 $ and $ d = 4 $ superspaces based on the graded lie algebras $ osp ( 1 | 2 ) $, $ su ( 2 | 1 ) $ and $ psu ( 2 | 2 ) $. jacobi identities of supersymmetry algebras and associativities of star products are automatically satisfied. covariant derivatives which commute with supersymmetry generators are obtained and chiral constraints can be imposed. we also discuss that these noncommutative superspaces can be understood as constrained systems analogous to the lowest landau level system.
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arxiv:hep-th/0306251
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the relation between rainfall and water accumulated in reservoirs comprises nonlinear feedbacks. here we show that they may generate alternative equilibrium regimes, one of high water - volume, the other of low water - volume. reservoirs can be seen as socio - environmental systems at risk of regime shifts, characteristic of tipping point transitions. we analyze data from stored water, rainfall, and water inflow and outflow in the main reservoir serving the metropolitan area of s \ ~ ao paulo, brazil, by means of indicators of critical regime shifts, and find a strong signal of a transition. we furthermore build a mathematical model that gives a mechanistic view of the dynamics and demonstrates that alternative stable states are an expected property of water reservoirs. we also build a stochastic version of this model that fits well to the data. these results highlight the broader aspect that reservoir management must account for their intrinsic bistability, and should benefit from dynamical systems theory. our case study illustrates the catastrophic consequences of failing to do so.
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arxiv:1506.07134
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mammography is the most widely used gold standard for screening breast cancer, where, mass detection is considered as the prominent step. detecting mass in the breast is, however, an arduous problem as they usually have large variations between them in terms of shape, size, boundary, and texture. in this literature, the process of mass detection is automated with the use of transfer learning techniques of deep convolutional neural networks ( dcnn ). pre - trained vgg19 network is used to extract features which are then followed by bagged decision tree for features selection and then a support vector machine ( svm ) classifier is trained and used for classifying between the mass and non - mass. area under roc curve ( auc ) is chosen as the performance metric, which is then maximized during classifier selection and hyper - parameter tuning. the robustness of the two selected type of classifiers, c - svm, and \ u { psion } - svm, are investigated with extensive experiments before selecting the best performing classifier. all experiments in this paper were conducted using the inbreast dataset. the best auc obtained from the experimental results is 0. 994 + / - 0. 003 i. e. [ 0. 991, 0. 997 ]. our results conclude that by using pre - trained vgg19 network, high - level distinctive features can be extracted from mammograms which when used with the proposed svm classifier is able to robustly distinguish between the mass and non - mass present in breast.
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arxiv:1907.04424
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the frequency dependent time delay correlation function $ k ( \ omega ) $ is studied analytically for a particle reflected from a finite one - dimensional disordered system. in the long sample limit $ k ( \ omega ) $ can be used to extract the resonance width distribution $ \ rho ( \ gamma ) $. both quantities are found to decay algebraically as $ \ gamma ^ { - \ nu } $, and $ \ omega ^ { - \ nu } $, $ \ nu \ simeq 1. 25 $ in a large range of arguments. numerical calculations for the resonance width distribution in 1d non - hermitian tight - binding model agree reasonably with the analytical formulas.
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arxiv:cond-mat/9909010
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in this paper we firstly introduce the concepts of capacity and cegrell ' s classes associated to any $ m $ - positive closed current $ t $. next, after investigating the most imporant related properties, we study the definition and the continuity of the complex hessian operator in several cases, generalizing then the work of demailly and xing in this direction. we also prove a xing - type comparison principle for the analogous cegrell class $ \ mathcal { f } ^ { m, t } $ of negative $ m $ - subharmonic functions. finally, we generalize the work of ben messaoud - el mir on the complex monge - amp \ ` ere operator and the lelong - skoda potential associated to a positive closed current.
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arxiv:1504.03519
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the striking recent putative detection of " dark oxygen " ( dark o $ _ 2 $ ) sources on the abyssal ocean floor in the pacific at $ \ sim 4 $ km depth raises the intriguing scenario that complex ( i. e., animal - like ) life could exist in underwater environments sans oxygenic photosynthesis. in this work, we thus explore the possible ( astro ) biological implications of this discovery. from the available data, we roughly estimate the concentration of dissolved o $ _ 2 $ and the corresponding o $ _ 2 $ partial pressure, as well as the flux of o $ _ 2 $ production, associated with dark oxygen sources. based on these values, we infer that organisms limited by internal diffusion may reach maximal sizes of $ \ sim 0. 1 - 1 $ mm in habitats with dark o $ _ 2 $, while those with circulatory systems might achieve sizes of $ \ sim 0. 1 - 10 $ cm. optimistically, the estimated dark oxygen flux can potentially support biomass densities up to $ \ sim 3 - 30 $ g m $ ^ { - 2 } $, perhaps surpassing typical reported densities at similar depths in global deep - sea surveys. finally, we outline how oceanic settings with dark o $ _ 2 $ may facilitate the origin ( s ) of life via the emergence of electrotrophy. our findings indicate that complex life fueled by dark oxygen is plausibly capable of inhabiting submarine environments devoid of photosynthesis on earth, conceivably extending likewise to extraterrestrial locations such as icy worlds with subsurface oceans ( e. g., enceladus and europa ), which are likely common throughout the universe.
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arxiv:2408.06841
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we present results from simultaneous modeling of 2d ( projected along the line of sight ) position, proper motion and line - of - sight velocity for \ textit { gaia } - and apogee - observed stars near the centre of the sagittarius ( sgr ) dwarf spheroidal galaxy. we use a mixture model that allows for independent sub - populations contributed by the sgr galaxy, its nuclear star cluster m54, and the milky way foreground. we find an offset of $ 0. 295 \ pm 0. 029 $ degrees between the inferred centroids of sgr and m54, corresponding to a ( projected ) physical separation of $ 0. 135 \ pm 0. 013 $ kpc. the detected offset might plausibly be driven by unmodelled asymmetry in sgr ' s stellar configuration ; however, standard criteria for model selection favour our symmetric model over an alternative that allows for bilateral asymmetry. we infer an offset between the proper motion centres of sgr and m54 of $ [ \ delta \ mu _ { \ alpha } \ cos \ delta, \ delta \ mu _ { \ delta } ] = [ 4. 9, - 19. 7 ] \ pm [ 6. 8, 6. 2 ] $ $ \ mu $ as yr $ ^ { - 1 } $ ( $ [ 0. 61, - 2. 46 ] \ pm [ 0. 85, 0. 77 ] $ km s $ ^ { - 1 } $ ), with magnitude similar to the covariance expected due to spatially - correlated systematic error. we infer an offset of $ 4. 1 \ pm 1. 2 $ km s $ ^ { - 1 } $ in line - of - sight velocity. using inferred values for the systemic positions and motions of sgr and m54 as initial conditions, we calculate the recent orbital history of a simplified sgr / m54 system, which we demonstrate to be sensitive to any line - of - sight distance offset between m54 and sgr, and to the distribution of dark matter within sgr.
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arxiv:2404.16184
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we study the dimensional aspect of the geometry of quantum spaces. introducing a physically motivated notion of the scaling dimension, we study in detail the model based on a fuzzy torus. we show that for a natural choice of a deformed laplace operator, this model demonstrates quite non - trivial behaviour : the scaling dimension flows from 2 in ir to 1 in uv. unlike another model with the similar property, the so - called horava - lifshitz model, our construction does not have any preferred direction. the dimension flow is rather achieved by a rearrangement of the degrees of freedom. in this respect the number of dimensions is deceptive. some physical consequences are discussed.
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arxiv:1711.01461
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we study different types of localisations of a commutative noetherian ring. more precisely, we provide criteria to decide : ( a ) if a given flat ring epimorphism is a universal localisation in the sense of cohn and schofield ; and ( b ) when such universal localisations are classical rings of fractions. in order to find such criteria, we use the theory of support and we analyse the specialisation closed subset associated to a flat ring epimorphism. in case the underlying ring is locally factorial or of krull dimension one, we show that all flat ring epimorphisms are universal localisations. moreover, it turns out that an answer to the question of when universal localisations are classical depends on the structure of the picard group. we furthermore discuss the case of normal rings, for which the divisor class group plays an essential role to decide if a given flat ring epimorphism is a universal localisation. finally, we explore several ( counter ) examples which highlight the necessity of our assumptions.
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arxiv:1807.01982
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the spin - polarized superfluid $ ^ 3 $ he a $ _ 1 $ phase, which forms below 3 mk in external magnetic field, serves as a material in which theoretical notions of fundamental magnetic processes and macroscopic quantum spin phenomena may be tested. conventionally, the superfluid component of the a $ _ 1 $ phase is understood to contain only the majority spin condensate having energetically - favoured paired spins directed along the external field and no minority spin condensate having paired spins in the opposite direction. we have developed a novel mechanical spin density detector to measure the spin relaxation in the a $ _ 1 $ phase as functions of temperature, pressure and magnetic field. the mechanical spin detector is based in principle on the unique magnetic fountain effect occurring only in the a $ _ 1 $ phase ( occurring between two transition temperatures, t $ _ { c1 } $ and t $ _ { c2 } $ ). unexpectedly, the spin relaxation rate increases rapidly as the temperature is decreased towards t $ _ { c2 } $. our measurements, together with leggett - takagi and monien - tewordt theories, demonstrate that a minute presence of minority spin pairs is responsible for the unexpected spin relaxation phenomena in a $ _ 1 $ phase.
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arxiv:cond-mat/0611446
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in this paper, we find a holomorphic darboux chart around any immersed noncompact holomorphic legendrian curve in a complex contact manifold $ ( x, \ xi ) $. by using such a chart, we show that every holomorphic legendrian immersion $ r \ to x $ from an open riemann surface can be approximated on relatively compact subsets by holomorphic legendrian embeddings, and every holomorphic legendrian immersion $ m \ to x $ from a compact bordered riemann surface is a uniform limit of topological embeddings $ m \ hookrightarrow x $ such that $ \ mathring m \ hookrightarrow x $ is a complete holomorphic legendrian embedding. we also establish a contact neighborhood theorem for isotropic stein submanifolds, and we find a holomorphic darboux chart around any contractible isotropic stein submanifolds in an arbitrary complex contact manifold.
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arxiv:1702.00704
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we calculate for a binary mixture of lennard - jones particles the time dependence of the solution of the mode - coupling equations in which the full wave vector dependence is taken into account. in addition we also take into account the short time dynamics, which we model with a simple memory kernel. we find that the so obtained solution agrees very well with the time and wave vector dependence of the coherent and incoherent intermediate scattering functions as determined from molecular dynamics computer simulations. furthermore we calculate the wave vector dependence of the debye - waller factor for a realistic model of silica and compare these results with the ones obtained from a simulation of this model. we find that if the contribution of the three point correlation function to the vertices of the memory kernel are taken into account, the agreement between theory and simulation is very good. hence we conclude that mode coupling theory is able to give a correct quantitative description of the caging phenomena in fragile as well as strong glass - forming liquids.
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arxiv:cond-mat/0109285
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if g is a group with a presentation of the form < x, y | x ^ 3 = y ^ 5 = w ( x, y ) ^ 2 = 1 >, then either g is virtually soluble or g contains a free subgroup of rank 2. this provides additional evidence in favour of a conjecture of rosenberger.
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arxiv:1102.2073
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we prove the divisibility conjecture on sums of even powers of $ q $ - binomial coefficients, which was recently proposed by guo, schlosser and zudilin. our proof relies on two $ q $ - harmonic series congruences due to shi and pan.
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arxiv:2110.09906
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context dependence is central to the description of complexity. keying on the pairwise definition of " set complexity " we use an information theory approach to formulate general measures of systems complexity. we examine the properties of multi - variable dependency starting with the concept of interaction information. we then present a new measure for unbiased detection of multi - variable dependency, " differential interaction information. " this quantity for two variables reduces to the pairwise " set complexity " previously proposed as a context - dependent measure of information in biological systems. we generalize it here to an arbitrary number of variables. critical limiting properties of the " differential interaction information " are key to the generalization. this measure extends previous ideas about biological information and provides a more sophisticated basis for study of complexity. the properties of " differential interaction information " also suggest new approaches to data analysis. given a data set of system measurements differential interaction information can provide a measure of collective dependence, which can be represented in hypergraphs describing complex system interaction patterns. we investigate this kind of analysis using simulated data sets. the conjoining of a generalized set complexity measure, multi - variable dependency analysis, and hypergraphs is our central result. while our focus is on complex biological systems, our results are applicable to any complex system.
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arxiv:1302.6932
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we show that the average of the maximum teleportation fidelities between all pairs of nodes in a large quantum repeater network is a measure of the resourcefulness of the network as a whole. we use simple werner state - based models to characterise some fundamental ( loopless ) topologies ( star, chain, and some trees ) with respect to this measure in three ( semi ) realistic scenarios. most of our results are analytic and are applicable for arbitrary network sizes. we identify the parameter ranges where these networks can achieve quantum advantages and show the large - n behaviours.
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arxiv:2409.20304
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the search for light stops is of paramount importance, both in general as a promising path to the discovery of beyond the standard model physics and more specifically as a way of evaluating the success of the naturalness paradigm. while the lhc experiments have ruled out much of the relevant parameter space, there are " stop gaps ", i. e., values of sparticle masses for which existing lhc analyses have relatively little sensitivity to light stops. we point out that techniques involving on - shell constrained m _ 2 variables can do much to enhance sensitivity in this region and hence help close the stop gaps. we demonstrate the use of these variables for several benchmark points and describe the effect of realistic complications, such as detector effects and combinatorial backgrounds, in order to provide a useful toolkit for light stop searches in particular, and new physics searches at the lhc in general.
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arxiv:1411.0664
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in this article, we establish a sufficient condition for the existence of a primitive element $ \ alpha \ in { \ mathbb { f } _ { q ^ n } } $ such that the element $ \ alpha + \ alpha ^ { - 1 } $ is also a primitive element of $ { \ mathbb { f } _ { q ^ n } }, $ and $ tr _ { \ mathbb { f } _ { q ^ n } | \ mathbb { f } _ { q } } ( \ alpha ) = a $ for any prescribed $ a \ in \ mathbb { f } _ q $, where $ q = p ^ k $ for some prime $ p $ and positive integer $ k $. we prove that every finite field $ \ mathbb { f } _ { q ^ n } ~ ( n \ geq5 ), $ contains such primitive elements except for finitely many values of $ q $ and $ n $. indeed, by computation, we conclude that there are no actual exceptional pairs $ ( q, n ) $ for $ n \ geq5. $
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arxiv:1709.05540
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metric graphs are ubiquitous in science and engineering. for example, many data are drawn from hidden spaces that are graph - like, such as the cosmic web. a metric graph offers one of the simplest yet still meaningful ways to represent the non - linear structure hidden behind the data. in this paper, we propose a new distance between two finite metric graphs, called the persistence - distortion distance, which draws upon a topological idea. this topological perspective along with the metric space viewpoint provide a new angle to the graph matching problem. our persistence - distortion distance has two properties not shared by previous methods : first, it is stable against the perturbations of the input graph metrics. second, it is a continuous distance measure, in the sense that it is defined on an alignment of the underlying spaces of input graphs, instead of merely their nodes. this makes our persistence - distortion distance robust against, for example, different discretizations of the same underlying graph. despite considering the input graphs as continuous spaces, that is, taking all points into account, we show that we can compute the persistence - distortion distance in polynomial time. the time complexity for the discrete case where only graph nodes are considered is much faster. we also provide some preliminary experimental results to demonstrate the use of the new distance measure.
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arxiv:1503.07414
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in this paper, we can show that \ begin { align * } s _ { \ lambda } ( x ) = \ sum _ { 1 \ leq n \ leq x } \ lambda \ left ( \ left [ \ frac { x } { n } \ right ] \ right ) = \ sum _ { n = 1 } ^ { \ infty } \ frac { \ lambda ( n ) } { n ( n + 1 ) } x + o \ left ( x ^ { 7 / 15 + 1 / 195 + \ varepsilon } \ right ), \ end { align * } where $ \ lambda ( n ) $ is the von mangdolt function. moreover, we can also give a similar result related to the divisor function, which improves previous results.
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arxiv:2303.12347
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this paper is divided into three parts. in the first ( section 1 ), we demonstrate that all of quantum mechanics can be derived from the fundamental property that the propagation of a matter wave packet is described by the same gravitational and kinematic time dilation that applies to a clock. we will do so in several steps, first deriving the schroedinger equation for a nonrelativistic particle without spin in a weak gravitational potential, and eventually the dirac equation in curved space - time describing the propagation of a relativistic particle with spin in strong gravity. in the second part ( sections 2 - 4 ), we present interesting consequences of the above quantum mechanics : that it is possible to use wave packets as a reference for a clock, to test general relativity, and to realize a mass standard based on a proposed redefinition of the international system of units, wherein the planck constant would be assigned a fixed value. the clock achieved an absolute accuracy of 4 parts per billion ( ppb ). the experiment yields the fine structure constant $ \ alpha = 7. 297 \, 352 \, 589 ( 15 ) \ times 10 ^ { - 3 } $ with 2. 0 ppb accuracy. we present improvements that have reduced the leading systematic error about 8 - fold and improved the statistical uncertainty to 0. 33 ppb in 6 hours of integration time, referred to $ \ alpha $. in the third part ( sections 5 - 7 ), we present possible future experiments with atom interferometry : a gravitational aharonov - bohm experiment and its application as a measurement of newton ' s gravitational constant, antimatter interferometry, interferometry with charged particles, and interferometry in space. we will give a review of previously published material when appropriate, but will focus on new aspects that haven ' t been published before.
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arxiv:1312.6449
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the essay gives an overview on researches in the field of laser ion acceleration, focusing on two types of targets. there are many types of targets while they can all be divided into targets that apply single ion or multiple ions. mixed solid targets are proven efficient in accelerating heavy ions and generate high - quality ion beams with energy divergence lower than 5 %. traditional methods like tnsa are mainly used to accelerate protons or heavy ions and there are still many spaces for modification and improvement. applications of laser - driven ion beams are wide in fields like detector technology, cancer therapy and so on, which is promising and necessary.
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arxiv:2008.13349
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we propose a new strategy to search for a particular type of dark matter via nuclear capture. if the dark matter particle carries baryon number, as motivated by a class of theoretical explanations of the matter - antimatter asymmetry of the universe, it can mix with the neutron and be captured by an atomic nucleus. the resulting state de - excites by emitting a single photon or a cascade of photons with a total energy of up to several mev. the exact value of this energy depends on the dark matter mass. we investigate the prospects for detecting dark matter capture signals in current and future neutrino and dark matter direct detection experiments.
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arxiv:2005.04240
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we deal with locally free $ \ mathcal { o } _ x $ - modules with connection over a berkovich curve $ x $. as a main result we prove local and global decomposition theorems of such objects by the radii of convergence of their solutions. we also derive a bound of the number of edges of the controlling graph, in terms of the geometry of the curve and the rank of the equation. as an application we provide a classification result of such equations over elliptic curves.
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arxiv:1308.0859
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the present paper numerically investigates flow control over naca0021 ( national advisory committee for aeronautics ) airfoil by applying a leading - edge tubercle as a passive flow control device at transitional reynolds number ( re ) regime. the study includes simulations over the unmodified airfoil and modified airfoil operating at re = 120000 using kt - kl - { \ omega } based delayed detached eddy simulation ( ddes ) model. the calculations include both the pre - stall and post - stall regions, while the performance of the mean flow aerodynamic properties like pressure, lift, skin - friction, and drag coefficients are also investigated in the presence of tubercles. the spanwise flow over the modified airfoil interacts with the primary flow. the turbulent separation gets delayed compared to the unmodified airfoil, thereby significantly improving the stall behavior and flow behavior in the post - stall region. the modified airfoil provides the gradual stall behavior against the steep stall behavior for the unmodified airfoil. to optimize tubercle configuration, the study considers two modified airfoils with different combinations of amplitude and wavelength. the unsteady analysis, including the reduced - order modeling, i. e. 3d proper orthogonal decomposition ( pod ), characterizes the dominant vortical structure of the flow to evaluate the improvement in the aerodynamic performance of the modified airfoil. the model decomposition for flow over airfoil helps to provide a deeper understanding of the flow control phenomenon.
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arxiv:2103.08854
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_ { \ rm dg } \ sim 0. 55 $ toward the galactic anticentre, which is respectively about 23 and 124 per cent of the atomic and co - traced molecular gas in the same region. this result is consistent with the theoretical work of papadopoulos et al. but much larger than that expected in the $ \ rm h _ 2 $ cloud models by wolfire et al.
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arxiv:1501.03606
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this study investigates the charging - up effect on the topmetal - ii - chip in gas micro - pixel detectors ( gmpd ). it is found that this effect differs from the charging - up typically observed in gas detector multiplier devices and increases the relative gain of the detector. the research indicates that this effect originates from the accumulation of charges on the insulating layer of the chip ' s pixel surface. iterative simulations using comsol and garfield + + are employed to model the variation of detector relative gain with the charging - up effect, and a simple yet effective model is proposed, which aligns well with experimental data. the feasibility of validating the deposition of resistive materials and adjusting the local voltage distribution on the chip to suppress charging - up effects and enhance the relative gain is also verified.
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arxiv:2402.15077
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n _ h $ from 19 supernova remnants and 29 x - ray binaries for which $ n _ h $ was determined with subsolar abundances. we obtain $ { n _ h } / { a _ v } = ( 2. 47 \ pm0. 04 ) \ times10 ^ { 21 } { \ rm h \, cm ^ { - 2 } \, mag ^ { - 1 } } $ which exceeds that derived with solar abundances by $ \ sim $ 20 %. we suggest that in future studies one may simply scale $ n _ h $ derived from subsolar abundances by a factor of $ \ sim $ 1. 2 when converting to $ n _ h $ of solar abundances.
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arxiv:1706.07109
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some models providing shell - shaped static solutions with compact support ( compactons ) in 3 + 1 and 4 + 1 dimensions are introduced, and the corresponding exact solutions are calculated analytically. these solutions turn out to be topological solitons, and may be classified as maps $ s ^ 3 \ to s ^ 3 $ and suspended hopf maps, respectively. the lagrangian of these models is given by a scalar field with a non - standard kinetic term ( k field ) coupled to a pure skyrme term restricted to $ s ^ 2 $, rised to the appropriate power to avoid the derrick scaling argument. further, the existence of infinitely many exact shell solitons is explained using the generalized integrability approach. finally, similar models allowing for non - topological compactons of the ball type in 3 + 1 dimensions are briefly discussed.
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arxiv:0902.0880
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non - reciprocity in the critical current has been observed in a variety of superconducting systems and has been called the superconducting diode effect. the origin underlying the effect depends on the symmetry breaking mechanisms at play. we investigate superconducting micro bridges of nbn and also nbn / magnetic insulator ( mi ) hybrids. we observe a large diode efficiency of $ \ approx $ ~ 30 \ % when an out - of - plane magnetic field as small as 25 ~ mt is applied. in both nbn and nbn / mi hybrid, we find that the diode effect vanishes when the magnetic field is parallel to the sample plane. our observations are consistent with the critical current being determined by the vortex surface barrier. unequal barriers on the two edges of the superconductor strip result in the diode effect. furthermore, the rectification is observed up to a temperature $ \ sim $ 10 ~ k, which makes the device potential for diode based applications over larger temperature range than before.
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arxiv:2209.05754
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in authentication scenarios, applications of practical speaker verification systems usually require a person to read a dynamic authentication text. previous studies played an audio adversarial example as a digital signal to perform physical attacks, which would be easily rejected by audio replay detection modules. this work shows that by playing our crafted adversarial perturbation as a separate source when the adversary is speaking, the practical speaker verification system will misjudge the adversary as a target speaker. a two - step algorithm is proposed to optimize the universal adversarial perturbation to be text - independent and has little effect on the authentication text recognition. we also estimated room impulse response ( rir ) in the algorithm which allowed the perturbation to be effective after being played over the air. in the physical experiment, we achieved targeted attacks with success rate of 100 %, while the word error rate ( wer ) on speech recognition was only increased by 3. 55 %. and recorded audios could pass replay detection for the live person speaking.
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arxiv:2105.09022
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single - cell rna sequencing ( scrna - seq ) enables researchers to analyze gene expression at single - cell level. one important task in scrna - seq data analysis is unsupervised clustering, which helps identify distinct cell types, laying down the foundation for other downstream analysis tasks. in this paper, we propose a novel method called cluster - aware iterative contrastive learning ( cicl in short ) for scrna - seq data clustering, which utilizes an iterative representation learning and clustering framework to progressively learn the clustering structure of scrna - seq data with a cluster - aware contrastive loss. cicl consists of a transformer encoder, a clustering head, a projection head and a contrastive loss module. first, cicl extracts the feature vectors of the original and augmented data by the transformer encoder. then, it computes the clustering centroids by k - means and employs the student t - distribution to assign pseudo - labels to all cells in the clustering head. the projection - head uses a multi - layer perceptron ( mlp ) to obtain projections of the augmented data. at last, both pseudo - labels and projections are used in the contrastive loss to guide the model training. such a process goes iteratively so that the clustering result becomes better and better. extensive experiments on 25 real world scrna - seq datasets show that cicl outperforms the sota methods. concretely, cicl surpasses the existing methods by from 14 % to 280 %, and from 5 % to 133 % on average in terms of performance metrics ari and nmi respectively.
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arxiv:2312.16600
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$, at $ x $ $ \ sim $ 0. 015 is observed and probably is related to change of the fermi surface due to magnetic order. coherence lengths and the london penetration depths are also calculated based on $ h _ { c1 } $ and $ h _ { c2 } $ data. coherence lengths as the function of $ x $ also shows the changes near $ x $ = 0. 015.
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arxiv:2204.10925
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in this paper, we consider the three - dimensional full compressible viscous non - resistive mhd system. global well - posedness is proved for an initial - boundary value problem around a strong background magnetic field. it is also shown that the unique solution converges to the steady state at an almost exponential rate as time tends to infinity. the proof is based on the celebrated two - tier energy method, due to guo and tice [ \ emph { arch. ration. mech. anal. }, 207 ( 2013 ), pp. 459 - - 531 ; \ emph { anal. pde. }, 6 ( 2013 ), pp. 287 - - 369 ], reformulated in lagrangian coordinates. the obtained result may be viewed as an extension of tan and wang [ \ emph { siam j. math. anal. }, 50 ( 2018 ), pp. 1432 - - 1470 ] to the context of heat - conductive fluids. this in particular verifies the stabilization effects of vertical magnetic field in the full compressible non - resistive fluids.
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arxiv:2109.02799
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geometrically frustrated many - particle quantum systems are notoriously hard to study numerically but are of profound interest because of their unusual properties and emergent phenomena. in these systems energetic constraints cannot be minimized simultaneously, leading to large ground - state degeneracy and a variety of exotic quantum phases. here, we present a platform that enables unprecedentedly detailed experimental exploration of geometrically frustrated electronic systems on lattices with triangular geometry. we demonstrate the first realization of triangular atomic hubbard systems, directly image mott insulators in the triangular geometry with single - atom and single - site resolution, and measure antiferromagnetic spin - spin correlations for all nearest neighbors allowing for thermometry. this platform provides a powerful new approach for studying exotic quantum magnetism and direct detection of quantum spin liquid signatures in hubbard systems.
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arxiv:2210.14895
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ternary cubic perovskite compounds of the form a _ ( 1 / 3 ) a ' _ ( 1 / 3 ) a ' ' _ ( 1 / 3 ) bo _ 3 and ab _ ( 1 / 3 ) b ' _ ( 1 / 3 ) b ' ' _ ( 1 / 3 ) o _ 3, in which the differentiated cations form an alternating series of monolayers, are studied using first - principles methods. such compounds are representative of a possible new class of materials in which ferroelectricity is perturbed by compositional breaking of inversion symmetry. for isovalent substitution on either sublattice, the ferroelectric double - well potential is found to persist, but becomes sufficiently asymmetric that minority domains may no longer survive. the strength of the symmetry breaking is enormously stronger for heterovalent substitution, so that the double - well behavior is completely destroyed. possible means of tuning between these behaviors may allow for the optimization of resulting materials properties.
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arxiv:cond-mat/0003264
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we identify a large class of objects - dissipative measure - valued ( dmv ) solutions to the navier - stokes - fourier system - in which the strong solutions are stable. more precisely, a dmv solution coincides with the strong solution emanating from the same initial data as long as the latter exists. the dmv solutions are represented by parameterized families of measures satisfying certain compatibility conditions. they can be seen as an analogue to the dissipative measure - valued solutions introduced earlier in the context of the ( inviscid ) euler system.
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arxiv:1802.01785
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in social choice theory, ( kemeny ) rank aggregation is a well - studied problem where the goal is to combine rankings from multiple voters into a single ranking on the same set of items. since rankings can reveal preferences of voters ( which a voter might like to keep private ), it is important to aggregate preferences in such a way to preserve privacy. in this work, we present differentially private algorithms for rank aggregation in the pure and approximate settings along with distribution - independent utility upper and lower bounds. in addition to bounds in the central model, we also present utility bounds for the local model of differential privacy.
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arxiv:2112.14652
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in this paper we consider sparse approximation problems, that is, general $ l _ 0 $ minimization problems with the $ l _ 0 $ - " norm " of a vector being a part of constraints or objective function. in particular, we first study the first - order optimality conditions for these problems. we then propose penalty decomposition ( pd ) methods for solving them in which a sequence of penalty subproblems are solved by a block coordinate descent ( bcd ) method. under some suitable assumptions, we establish that any accumulation point of the sequence generated by the pd methods satisfies the first - order optimality conditions of the problems. furthermore, for the problems in which the $ l _ 0 $ part is the only nonconvex part, we show that such an accumulation point is a local minimizer of the problems. in addition, we show that any accumulation point of the sequence generated by the bcd method is a saddle point of the penalty subproblem. moreover, for the problems in which the $ l _ 0 $ part is the only nonconvex part, we establish that such an accumulation point is a local minimizer of the penalty subproblem. finally, we test the performance of our pd methods by applying them to sparse logistic regression, sparse inverse covariance selection, and compressed sensing problems. the computational results demonstrate that our methods generally outperform the existing methods in terms of solution quality and / or speed.
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arxiv:1205.2334
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despite the ubiquity of ice, a molecular - resolution image of ice crystallized from liquid water or the resulting defect structure has never been obtained. here, we report the stabilization and angstrom - resolution electron imaging of ice ih crystallized from liquid water by developing cryogenic liquid - cell transmission electron microscopy ( cryolic - tem ). we combine lattice mapping with molecular dynamics simulations to reveal that ice formation is highly tolerant to nanoscale defects such as misoriented subdomains and trapped gas bubbles, which are stabilized by molecular - scale structural motifs. importantly, bubble surfaces adopt low - energy nanofacets and create negligible strain fields in the surrounding crystal. these bubbles can dynamically nucleate, grow, migrate, dissolve, and coalesce under electron irradiation and be monitored in situ near a steady state. this work opens the door to understanding water crystallization behaviors at an unprecedented spatial resolution.
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arxiv:2406.00915
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partial suppression of superconductivity by fast cooling has been observed in the organic superconductor $ \ kappa $ - ( bedt - ttf ) $ _ 2 $ cu [ n ( cn ) $ _ 2 $ ] br by two means : a marked sample size effect on the magnetic susceptibility and direct imaging of insulating regions by scanning microregion infrared reflectance spectroscopy. macroscopic insulating regions are found in the vicinity of the crystalline surface after fast cooling, with diameters of 50 - - 100 $ \ mu $ m and depths of a few $ \ mu $ m. the very large in - plane penetration depth reported to date ( $ \ sim $ 24 - - 100 $ \ mu $ m ) can be explained by the existence of the insulating regions.
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arxiv:cond-mat/0507155
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for any partial combinatory algebra ( pca for short ) a, the class of a - representable partial functions from n to a quotiented by the filter of cofinite sets of n, is a pca such that the representable partial functions are exactly the limiting partial functions of a - representable partial functions ( akama, " limiting partial combinatory algebras " theoret. comput. sci. vol. 311 2004 ). the n - times iteration of this construction results in a pca that represents any n - iterated limiting partial recursive functions, and the inductive limit of the pcas over all n is a pca that represents any arithmetical, partial function. kleene ' s realizability interpretation over the former pca interprets the logical principles of double negation elimination for \ sigma ^ 0 _ n - formulas, and that over the latter pca interprets peano ' s arithmetic ( pa for short ). a hierarchy of logical systems between heyting ' s arithmetic and pa is used to discuss the prenex normal form theorem, the relativized independence - of - premise schemes, and " pa is an unbounded extension of ha. "
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arxiv:1307.5521
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our team participate in the challenge of task 1 : lesion boundary segmentation, and use a combined network, one of which is designed by ourselves named updcnn net and another is an improved vgg 16 - layer net. updcnn net uses reduced size images for training, and vgg 16 - layer net utilizes large size images. image enhancement is used to get a richer data set. we use boxes in the vgg 16 - layer net network for local attention regularization to fine - tune the loss function, which can increase the number of training data, and also make the model more robust. in the test, the model is used for joint testing and achieves good results.
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arxiv:1807.07391
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we investigate the conditions to entangle two qubits interacting with local environments driven by a continuous - variable correlated field. we find the conditions to transfer the entanglement from the driving field to the qubits both in dynamical and steady - state cases. we see how the quantum correlations initially present in the driving field play a critical role in the entanglement - transfer process. the system we treat is general enough to be adapted to different physical setups.
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arxiv:quant-ph/0403180
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the success of long short - term memory ( lstm ) neural networks in language processing is typically attributed to their ability to capture long - distance statistical regularities. linguistic regularities are often sensitive to syntactic structure ; can such dependencies be captured by lstms, which do not have explicit structural representations? we begin addressing this question using number agreement in english subject - verb dependencies. we probe the architecture ' s grammatical competence both using training objectives with an explicit grammatical target ( number prediction, grammaticality judgments ) and using language models. in the strongly supervised settings, the lstm achieved very high overall accuracy ( less than 1 % errors ), but errors increased when sequential and structural information conflicted. the frequency of such errors rose sharply in the language - modeling setting. we conclude that lstms can capture a non - trivial amount of grammatical structure given targeted supervision, but stronger architectures may be required to further reduce errors ; furthermore, the language modeling signal is insufficient for capturing syntax - sensitive dependencies, and should be supplemented with more direct supervision if such dependencies need to be captured.
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arxiv:1611.01368
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we investigate the use of transformer sequence models as dynamics models ( tdms ) for control. we find that tdms exhibit strong generalization capabilities to unseen environments, both in a few - shot setting, where a generalist tdm is fine - tuned with small amounts of data from the target environment, and in a zero - shot setting, where a generalist tdm is applied to an unseen environment without any further training. here, we demonstrate that generalizing system dynamics can work much better than generalizing optimal behavior directly as a policy. additional results show that tdms also perform well in a single - environment learning setting when compared to a number of baseline models. these properties make tdms a promising ingredient for a foundation model of control.
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arxiv:2305.10912
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the search for a material platform for topological quantum computation has recently focused on unconventional superconductors. such material systems, where the superconducting order parameter breaks a symmetry of the crystal point group, are capable of hosting novel phenomena, including emergent majorana quasiparticles. unique among unconventional superconductors is the recently discovered ute2, where spin - triplet superconductivity emerges from a paramagnetic normal state. although ute2 could be considered a relative of a family of known ferromagnetic superconductors, the unique crystal structure of this material and experimentally suggested zero curie temperature pose a great challenge to determining the symmetries, magnetism, and topology underlying the superconducting state. these emergent properties will determine the utility of ute2 for future spintronics and quantum information applications. here, we report observations of a non - zero polar kerr effect and of two transitions in the specific heat upon entering the superconducting state, which together show that the superconductivity in ute2 is characterized by an order parameter with two components that breaks time reversal symmetry. these data allow us to place firm constraints on the symmetries of the order parameter, which strongly suggest that ute2 is a weyl superconductor that hosts chiral fermi arc surface states.
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arxiv:2002.02539
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