Miracle-dz/UniFAR-FTUs huggingface dataset:
High-temperature magnetization and entropy of the triangular lattice Hubbard model in a Zeeman field

We use strong coupling expansions to calculate the entropy function $S(T,h)$, the magnetization $M(T,h)$, and the double occupancy factor $D(T,h)$ for the half-filled triangular lattice Hubbard model as a function of temperature $T$ and Zeeman field $h$, for various values of the Hubbard parameter ratio $U/t$. These calculations converge well for temperatures larger than the exchange parameter $J=\frac{4t^2}{U}$ for moderate to large $U/t$ values. Setting $\mu=U/2$ suffices to obtain the density of half filling within a fraction of one percent at all temperatures studied for $U/t \geq 8$. We discuss the systematic variation of properties with $U/t$. The temperature dependence of entropy and the double occupancy parameter shows a mapping to an antiferromagnetic Mott insulating behavior at temperatures well above $T=J$ for $U/t\ge 10$. Convergence of the series is weaker at intermediate fields implying non-monotonic variation of spin-correlations with the Zeeman field. We discuss the relevance of the Hubbard model results to the triangular-lattice antiferromagnetic materials Lu$_3$Cu$_2$Sb$_3$O$_{14} $ (LCSO) studied recently by Yang et al [Yang et al arXiv:2102.09271 (2022)].
Multilevel Monte Carlo methods for stochastic convection-diffusion eigenvalue problems

We develop new multilevel Monte Carlo (MLMC) methods to estimate the expectation of the smallest eigenvalue of a stochastic convection-diffusion operator with random coefficients. The MLMC method is based on a sequence of finite element (FE) discretizations of the eigenvalue problem on a hierarchy of increasingly finer meshes. For the discretized, algebraic eigenproblems we use both the Rayleigh quotient (RQ) iteration and implicitly restarted Arnoldi (IRA), providing an analysis of the cost in each case. By studying the variance on each level and adapting classical FE error bounds to the stochastic setting, we are able to bound the total error of our MLMC estimator and provide a complexity analysis. As expected, the complexity bound for our MLMC estimator is superior to plain Monte Carlo. To improve the efficiency of the MLMC further, we exploit the hierarchy of meshes and use coarser approximations as starting values for the eigensolvers on finer ones. To improve the stability of the MLMC method for convection-dominated problems, we employ two additional strategies. First, we consider the streamline upwind Petrov--Galerkin formulation of the discrete eigenvalue problem, which allows us to start the MLMC method on coarser meshes than is possible with standard FEs. Second, we apply a homotopy method to add stability to the eigensolver for each sample. Finally, we present a multilevel quasi-Monte Carlo method that replaces Monte Carlo with a quasi-Monte Carlo (QMC) rule on each level. Due to the faster convergence of QMC, this improves the overall complexity. We provide detailed numerical results comparing our different strategies to demonstrate the practical feasibility of the MLMC method in different use cases. The results support our complexity analysis and further demonstrate the superiority over plain Monte Carlo in all cases.
Anisotropic weighted isoperimetric inequalities for star-shaped and $F$-mean convex hypersurface

We prove two anisotropic type weighted geometric inequalities that hold for star-shaped and $F$-mean convex hypersurfaces in $\mathbb{R}^{n+1}$. These inequalities involve the anisotropic $p$-momentum, the anisotropic perimeter and the volume of the region enclosed by the hypersurface. We show that the Wulff shape of $F$ is the unique minimizer of the corresponding functionals among all star-shaped and $F$-mean convex sets. We also consider their quantitative versions characterized by the Hausdorff distance between the hypersurface and a rescaled Wulff shape. As a corollary, we obtain the stability of the Weinstock inequality for star-shaped and strictly mean convex domains, which requires weaker convexity compared to \cite{Gavitone}.
The characteristic-based-split procedure: an efficient and accurate algorithm for fluid problems

In 1995 the two senior authors of the present paper introduced a new algorithm designed to replace the Taylor–Galerkin (or Lax–Wendroff) methods, used by them so far in the solution of compressible flow problems. The new algorithm was applicable to a wide variety of situations, including fully incompressible flows and shallow water equations, as well as supersonic and hypersonic situations, and has proved to be always at least as accurate as other algorithms currently used. The algorithm is based on the solution of conservation equations of fluid mechanics to avoid any possibility of spurious solutions that may otherwise result. The main aspect of the procedure is to split the equations into two parts, (1) a part that is a set of simple scalar equations of convective–diffusion type for which it is well known that the characteristic Galerkin procedure yields an optimal solution; and (2) the part where the equations are self-adjoint and therefore discretized optimally by the Galerkin procedure. It is possible to solve both the first and second parts of the system explicitly, retaining there the time step limitations of the Taylor–Galerkin procedure. But it is also possible to use semi-implicit processes where in the first part we use a much bigger time step generally governed by the Peclet number of the system while the second part is solved implicitly and is unconditionally stable. It turns out that the characteristic-based-split (CBS) process allows equal interpolation to be used for all system variables without difficulties when the incompressible or nearly incompressible stage is reached. It is hoped that the paper will help to make the algorithm more widely available and understood by the profession and that its advantages can be widely realised. Copyright © 1999 John Wiley & Sons, Ltd.
Empirical Localization of Observations for Serial Ensemble Kalman Filter Data Assimilation in an Atmospheric General Circulation Model

AbstractThe empirical localization algorithm described here uses the output from an observing system simulation experiment (OSSE) and constructs localization functions that minimize the root-mean-square (RMS) difference between the truth and the posterior ensemble mean for state variables. This algorithm can automatically provide an estimate of the localization function and does not require empirical tuning of the localization scale. It can compute an appropriate localization function for any potential observation type and kind of state variable. The empirical localization algorithm is investigated in the Community Atmosphere Model, version 5 (CAM5). The empirical localization function (ELF) is computed for the horizontal and vertical separately so that the vertical localization is explored explicitly. The horizontal and vertical ELFs are also computed for different geographic regions. The ELFs varying with region have advantages over the single global ELF in the horizontal and vertical, because different.
Resolutions of toric subvarieties by line bundles and applications

Given any toric subvariety $Y$ of a smooth toric variety $X$ of codimension $k$, we construct a length $k$ resolution of $\mathcal O_Y$ by line bundles on $X$. Furthermore, these line bundles can all be chosen to be direct summands of the pushforward of $\mathcal O_X$ under the map of toric Frobenius. The resolutions are built from a stratification of a real torus that was introduced by Bondal and plays a role in homological mirror symmetry. As a corollary, we obtain a virtual analogue of Hilbert's syzygy theorem for smooth projective toric varieties conjectured by Berkesch, Erman, and Smith. Additionally, we prove that the Rouquier dimension of the bounded derived category of coherent sheaves on a toric variety is equal to the dimension of the variety, settling a conjecture of Orlov for these examples. We also prove Bondal's claim that the pushforward of the structure sheaf under toric Frobenius generates the derived category of a smooth toric variety and formulate a refinement of Uehara's conjecture that this remains true for arbitrary line bundles.
Wigner kernels: body-ordered equivariant machine learning without a basis

Machine-learning models based on a point-cloud representation of a physical object are ubiquitous in scientific applications and particularly well-suited to the atomic-scale description of molecules and materials. Among the many different approaches that have been pursued, the description of local atomic environments in terms of their neighbor densities has been used widely and very succesfully. We propose a novel density-based method which involves computing ``Wigner kernels''. These are fully equivariant and body-ordered kernels that can be computed iteratively with a cost that is independent of the radial-chemical basis and grows only linearly with the maximum body-order considered. This is in marked contrast to feature-space models, which comprise an exponentially-growing number of terms with increasing order of correlations. We present several examples of the accuracy of models based on Wigner kernels in chemical applications, for both scalar and tensorial targets, reaching state-of-the-art accuracy on the popular QM9 benchmark dataset, and we discuss the broader relevance of these ideas to equivariant geometric machine-learning.
Recent Advances in Software Effort Estimation using Machine Learning

An increasing number of software companies have already realized the importance of storing project-related data as valuable sources of information for training prediction models. Such kind of modeling opens the door for the implementation of tailored strategies to increase the accuracy in effort estimation of whole teams of engineers. In this article we review the most recent machine learning approaches used to estimate software development efforts for both, non-agile and agile methodologies. We analyze the benefits of adopting an agile methodology in terms of effort estimation possibilities, such as the modeling of programming patterns and misestimation patterns by individual engineers. We conclude with an analysis of current and future trends, regarding software effort estimation through data-driven predictive models.
Ehrhart positivity for a certain class of panhandle matroids

We give a combinatorial formula for the Ehrhart coefficients of a certain class of weighted multi-hypersimplices. In a special case, where these polytopes coincide with the base polytope of the panhandle matroid $\textrm{Pan}_{k,n-2,n}$, we show that the Ehrhart coefficients are positive.
MAST: Masked Augmentation Subspace Training for Generalizable Self-Supervised Priors

Recent Self-Supervised Learning (SSL) methods are able to learn feature representations that are invariant to different data augmentations, which can then be transferred to downstream tasks of interest. However, different downstream tasks require different invariances for their best performance, so the optimal choice of augmentations for SSL depends on the target task. In this paper, we aim to learn self-supervised features that generalize well across a variety of downstream tasks (e.g., object classification, detection and instance segmentation) without knowing any task information beforehand. We do so by Masked Augmentation Subspace Training (or MAST) to encode in the single feature space the priors from different data augmentations in a factorized way. Specifically, we disentangle the feature space into separate subspaces, each induced by a learnable mask that selects relevant feature dimensions to model invariance to a specific augmentation. We show the success of MAST in jointly capturing generalizable priors from different augmentations, using both unique and shared features across the subspaces. We further show that MAST benefits from uncertainty modeling to reweight ambiguous samples from strong augmentations that may cause similarity mismatch in each subspace. Experiments demonstrate that MAST consistently improves generalization on various downstream tasks, while being task-agnostic and efficient during SSL. We also provide interesting insights about how different augmentations are related and how uncertainty reflects learning difficulty.
On the Observer Dependence of the Quantum Effective Potential

In this short paper, we investigate the consequences of observer dependence of the quantum effective potential for an interacting field theory. Specializing to $d+2$ dimensional Euclidean Rindler space, we develop the formalism to calculate the effective potential. While the free energy diverges due to the presence of the Rindler horizon, the effective potential, which is a local function of space, is finite after the necessary renormalization procedure. We apply the results of our formalism to understand the restoration of spontaneously broken $\mathbb{Z}_2$ symmetry in three and four dimensions.
Proprioceptive Sensor-Based Simultaneous Multi-Contact Point Localization and Force Identification for Robotic Arms

In this paper, we propose an algorithm that estimates contact point and force simultaneously. We consider a collaborative robot equipped with proprioceptive sensors, in particular, joint torque sensors (JTSs) and a base force/torque (F/T) sensor. The proposed method has the following advan-tages. First, fast computation is achieved by proper preprocessing of robot meshes. Second, multi-contact can be identified with the aid of the base F/T sensor, while this is challenging when the robot is equipped with only JTSs. The proposed method is a modification of the standard particle filter to cope with mesh preprocessing and with available sensor data. In simulation validation, for a 7 degree-of-freedom robot, the algorithm runs at 2200Hz with 99.96% success rate for the single-contact case. In terms of the run-time, the proposed method was ≥3.5X faster compared to the existing methods. Dual and triple contacts are also reported in the manuscript.
Graph Decision Transformer

Offline reinforcement learning (RL) is a challenging task, whose objective is to learn policies from static trajectory data without interacting with the environment. Recently, offline RL has been viewed as a sequence modeling problem, where an agent generates a sequence of subsequent actions based on a set of static transition experiences. However, existing approaches that use transformers to attend to all tokens naively can overlook the dependencies between different tokens and limit long-term dependency learning. In this paper, we propose the Graph Decision Transformer (GDT), a novel offline RL approach that models the input sequence into a causal graph to capture potential dependencies between fundamentally different concepts and facilitate temporal and causal relationship learning. GDT uses a graph transformer to process the graph inputs with relation-enhanced mechanisms, and an optional sequence transformer to handle fine-grained spatial information in visual tasks. Our experiments show that GDT matches or surpasses the performance of state-of-the-art offline RL methods on image-based Atari and OpenAI Gym.
Rigidity and compactness with constant mean curvature in warped product manifolds

We prove the rigidity of rectifiable boundaries with constant distributional mean curvature in the Brendle class of warped product manifolds (which includes important models in General Relativity, like the deSitter--Schwarzschild and Reissner--Nordstrom manifolds). As a corollary we characterize limits of rectifiable boundaries whose mean curvatures converge, as distributions, to a constant. The latter result is new, and requires the full strength of distributional CMC-rigidity, even when one considers smooth boundaries whose mean curvature oscillations vanish in arbitrarily strong $C^k$-norms.
Toward a localized 
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-matrix theory

We formulate an S-matrix theory in which localisation effects of the particle interactions involved in a scattering process are consistently taken into account. In the limit of an infinite spread of all interactions, the S-matrix assumes its standard form. To better understand the significance of the emerging quantum phenomena in this formalism, we consider a solvable field-theoretic model with spatial Gaussian spreads at the interaction vertices. This solvable model, which was previously introduced in the literature, enables accurate descriptions of detection regions that are either close to or far from the source. In close analogy with light diffraction in classical optics, we call these two regions near-field and far-field zones, or the Fresnel and Fraunhofer regions. We revisit the question whether mixed mediators produce an oscillating pattern if their detection occurs in the Fresnel region. Besides corroborating certain earlier findings of the S-matrix amplitude in the forward Fresnel and Fraunhofer regimes, we observe several novel features with respect to its angular dependence which have not been accounted before in the literature. In particular, we obtain a ``quantum obliquity factor'' that suppresses particle propagation in the backwards direction, thereby providing an explicit quantum field-theoretic description for its origin in diffractive optics. Present and future colliders, as well as both short and long baseline neutrino experiments, would greatly benefit from the many predictions that can be offered from such a holistic localised S-matrix theory.
Can Membership Inferencing be Refuted?

Membership inference (MI) attack is currently the most popular test for measuring privacy leakage in machine learning models. Given a machine learning model, a data point and some auxiliary information, the goal of an MI attack is to determine whether the data point was used to train the model. In this work, we study the reliability of membership inference attacks in practice. Specifically, we show that a model owner can plausibly refute the result of a membership inference test on a data point $x$ by constructing a proof of repudiation that proves that the model was trained without $x$. We design efficient algorithms to construct proofs of repudiation for all data points of the training dataset. Our empirical evaluation demonstrates the practical feasibility of our algorithm by constructing proofs of repudiation for popular machine learning models on MNIST and CIFAR-10. Consequently, our results call for a re-evaluation of the implications of membership inference attacks in practice.
Flow-Based Integrated Assignment and Path-Finding for Mobile Robot Sorting Systems

Express companies are deploying more robotic sorting systems, where mobile robots are used to sort incoming parcels by destination. In this study, we propose an integrated assignment and path-finding method for robots in such sorting systems. The method has two parts: offline and online. In the offline part, we represent the system as a traffic flow network, develop an approximate delay function using stochastic models, and solve the min-cost network flow problem. In the online part, robots are guided through the system according to the calculated optimal flow split probability. The online calculation of the method is decentralized and has linear complexity. Our method outperforms fast multi-agent path planning algorithms like prioritized planning because such algorithms lead to stochastic user equilibrium traffic assignment. In contrast, our method gives the approximated system-optimal traffic assignment. According to our simulations, our method can achieve 10%--20% higher throughput than zoning or random assignment. We also show that our method is robust even if the initial demand estimation is inaccurate.
Margin theory for the scenario-based approach to robust optimization in high dimension

This paper deals with the scenario approach to robust optimization. This relies on a random sampling of the possibly infinite number of constraints induced by uncertainties in the parameters of an optimization problem. Solving the resulting random program yields a solution for which the quality is measured in terms of the probability of violating the constraints for a random value of the uncertainties, typically unseen before. Another central issue is the determination of the sample complexity, i.e., the number of random constraints (or scenarios) that one must consider in order to guarantee a certain level of reliability. In this paper, we introduce the notion of margin to improve upon standard results in this field. In particular, using tools from statistical learning theory, we show that the sample complexity of a class of random programs does not explicitly depend on the number of variables. In addition, within the considered class, that includes polynomial constraints among others, this result holds for both convex and nonconvex instances with the same level of guarantees. We also derive a posteriori bounds on the probability of violation and sketch a regularization approach that could be used to improve the reliability of computed solutions on the basis of these bounds.
Apollonius circles and the number of irreducible factors of polynomials

We provide upper bounds for the sum of the multiplicities of the non-constant irreducible factors that appear in the canonical decomposition of a polynomial $f(X)\in\mathbb{Z}[X]$, in case all the roots of $f$ lie inside an Apollonius circle associated to two points on the real axis with integer abscissae $a$ and $b$, with ratio of the distances to these points depending on the admissible divisors of $f(a)$ and $f(b)$. In particular, we obtain such upper bounds for the case where $f(a)$ and $f(b)$ have few prime factors, and $f$ is an Enestr\"om-Kakeya polynomial, or a Littlewood polynomial, or has a large leading coefficient. Similar results are also obtained for multivariate polynomials over arbitrary fields, in a non-Archimedean setting.
New strategy on the existence of a spanning tree without small degree stems

For an integer $k\geq 2$, a spanning tree of a graph without no vertices of degree from $2$ to $k$ is call a {\it $[2,k]$-ST} of the graph. The concept of $[2,k]$-STs is a natural extension of a homeomorphically irreducible spanning tree (or HIST), which has been a well-studied graph-structure. In this paper, we give a new strategy for finding $[2,k]$-STs. By using the strategy, we refine or extend a known degree-sum condition for the existence of a HIST. Furthermore, we also investigate on a degree-product condition for the existence of a $[2,k]$-ST.
Non-Hermitian Hamiltonians violate the eigenstate thermalization hypothesis

The Eigenstate Thermalization Hypothesis (ETH) represents a cornerstone in the theoretical understanding of the emergence of thermal behavior in closed quantum systems. The ETH asserts that expectation values of simple observables in energy eigenstates are accurately described by smooth functions of the thermodynamic parameters, with fluctuations and off-diagonal matrix elements exponentially suppressed in the entropy. We investigate to what extent the ETH holds in non-Hermitian many-body systems and come to the surprising conclusion that the fluctuations between eigenstates is of equal order to the average, indicating no thermalization. We support this conclusion with mathematically rigorous results in the Ginibre ensemble and numerical results in other ensembles, including the non-Hermitian Sachdev-Ye-Kitaev model, indicating universality in chaotic non-Hermitian quantum systems.