Miracle-dz/UniFAR-FTUs huggingface dataset:
Count-min sketch with variable number of hash functions: an experimental study

Conservative Count-Min, an improved version of Count-Min sketch [Cormode, Muthukrishnan 2005], is an online-maintained hashing-based data structure summarizing element frequency information without storing elements themselves. Although several works attempted to analyze the error that can be made by Count-Min, the behavior of this data structure remains poorly understood. In [Fusy, Kucherov 2022], we demonstrated that under the uniform distribution of input elements, the error of conservative Count-Min follows two distinct regimes depending on its load factor. In this work, we provide a series of experimental results providing new insights into the behavior of conservative Count-Min. Our contributions can be seen as twofold. On one hand, we provide a detailed experimental analysis of the behavior of Count-Min sketch in different regimes and under several representative probability distributions of input elements. On the other hand, we demonstrate improvements that can be made by assigning a variable number of hash functions to different elements. This includes, in particular, reduced space of the data structure while still supporting a small error.
Text recognition on images using pre-trained CNN

A text on an image often stores important information and directly carries high level semantics, makes it as important source of information and become a very active research topic. Many studies have shown that the use of CNN-based neural networks is quite effective and accurate for image classification which is the basis of text recognition. It can also be more enhanced by using transfer learning from pre-trained model trained on ImageNet dataset as an initial weight. In this research, the recognition is trained by using Chars74K dataset and the best model results then tested on some samples of IIIT-5K-Dataset. The research results showed that the best accuracy is the model that trained using VGG-16 architecture applied with image transformation of rotation 15{\deg}, image scale of 0.9, and the application of gaussian blur effect. The research model has an accuracy of 97.94% for validation data, 98.16% for test data, and 95.62% for the test data from IIIT-5K-Dataset. Based on these results, it can be concluded that pre-trained CNN can produce good accuracy for text recognition, and the model architecture that used in this study can be used as reference material in the development of text detection systems in the future
A Feasibility-Seeking Approach to Two-stage Robust Optimization in Kidney Exchange

Kidney paired donation programs (KPDPs) match patients with willing but incompatible donors to compatible donors with an assurance that when they donate, their intended recipient receives a kidney in return from a different donor. A patient and donor join a KPDP as a pair, represented as a vertex in a compatibility graph, where arcs represent compatible kidneys flowing from a donor in one pair to a patient in another. A challenge faced in real-world KPDPs is the possibility of a planned match being cancelled, e.g., due to late detection of organ incompatibility or patient-donor dropout. We therefore develop a two-stage robust optimization approach to the kidney exchange problem wherein (1) the first stage determines a kidney matching solution according to the original compatibility graph, and then (2) the second stage repairs the solution after observing transplant cancellations. In addition to considering homogeneous failure, we present the first approach that considers non-homogeneous failure between vertices and arcs. To this end, we develop solution algorithms with a feasibility-seeking master problem and evaluate two types of recourse policies. Our framework outperforms the state-of-the-art kidney exchange algorithm under homogeneous failure on publicly available instances. Moreover, we provide insights on the scalability of our solution algorithms under non-homogeneous failure for two recourse policies and analyze their impact on highly-sensitized patients, patients for whom few kidney donors are available and whose associated exchanges tend to fail at a higher rate than non-sensitized patients.
Phantom scalar-tensor models and cosmological tensions

We study three different extended scalar-tensor theories of gravity by also allowing a negative sign for the kinetic term for the scalar field in the Jordan frame. Our scope is to understand how the observational constraints for these models cope with the volume of the parameter space in which the theory is healthy. Models with a negative kinetic term lead to decreasing effective gravitational constant with redshift and behave as an effective relativistic component with a negative energy density as opposite to their corresponding version with a standard kinetic term. As a consequence, we find that the extended branch with a negative sign for the kinetic term correspond in general to lower H 0 and σ 8 compared to ΛCDM. We find that in all the cases with a negative sign for the kinetic term studied here, cosmological observations constrain these models around GR and prefer a volume of the parameter space in which the theory is not healthy since the scalar field behave as a ghost also in the related Einstein frame. We show that also in the phantom branch early modify gravity with a quartic coupling can substantially reduce the H 0 tension fitting the combination of cosmic microwave background data from Planck, baryon acoustic oscillations from BOSS and eBOSS, and Supernovae from the Pantheon sample with calibration information by SH0ES.
An explicit Hecke's bound and exceptions of even unimodular quadratic forms

We prove an explicit Hecke's bound for the Fourier coefficients of holomorphic cusp forms for SL2(Z) and apply it to derive effectively computable constants c (m) for each dimension m, divisible by 8, for which every even integer is always represented by every even unimodular form of m variables.
The Role of Codeword-to-Class Assignments in Error-Correcting Codes: An Empirical Study

Error-correcting codes (ECC) are used to reduce multiclass classification tasks to multiple binary classification subproblems. In ECC, classes are represented by the rows of a binary matrix, corresponding to codewords in a codebook. Codebooks are commonly either predefined or problem dependent. Given predefined codebooks, codeword-to-class assignments are traditionally overlooked, and codewords are implicitly assigned to classes arbitrarily. Our paper shows that these assignments play a major role in the performance of ECC. Specifically, we examine similarity-preserving assignments, where similar codewords are assigned to similar classes. Addressing a controversy in existing literature, our extensive experiments confirm that similarity-preserving assignments induce easier subproblems and are superior to other assignment policies in terms of their generalization performance. We find that similarity-preserving assignments make predefined codebooks become problem-dependent, without altering other favorable codebook properties. Finally, we show that our findings can improve predefined codebooks dedicated to extreme classification.
Weight Ergodic Theorems for Probability Measures on Locally Compact Groups

Let $G$ be a locally compact group with the left Haar measure $m_{G}$. A probability measure ${\mu}$ on $G$ is said to be strictly aperiodic if the support of ${\mu}$ is not contained in a proper closed left coset of $G$. In this paper, we prove weight ergodic theorems for strictly aperiodic measures.
The Intrinsic Bayes Factor for Model Selection and Prediction

Abstract In the Bayesian approach to model selection or hypothesis testing with models or hypotheses of differing dimensions, it is typically not possible to utilize standard noninformative (or default) prior distributions. This has led Bayesians to use conventional proper prior distributions or crude approximations to Bayes factors. In this article we introduce a new criterion called the intrinsic Bayes factor, which is fully automatic in the sense of requiring only standard noninformative priors for its computation and yet seems to correspond to very reasonable actual Bayes factors. The criterion can be used for nested or nonnested models and for multiple model comparison and prediction. From another perspective, the development suggests a general definition of a “reference prior” for model comparison.
In-Context Learning with Many Demonstration Examples

Large pre-training language models (PLMs) have shown promising in-context learning abilities. However, due to the backbone transformer architecture, existing PLMs are bottlenecked by the memory and computational cost when scaling up to a large context size, leaving instruction tuning and in-context learning of many demonstration examples, as well as long-range language modeling under-explored. In this study, we propose a long-range language model EVALM based on an efficient transformer mechanism. EVALM is trained with 8k tokens per batch line and can test up to 256k-lengthed contexts with extrapolation, 128 times to the limit of existing PLMs (e.g. GPT3). Based on EVALM, we scale up the size of examples efficiently in both instruction tuning and in-context learning to explore the boundary of the benefits from more annotated data. Experimental results on a diverse set of tasks show that EVALM achieves 4.1% higher accuracy on average, and the average length of achieving the best accuracy score over tasks is around 12k. We find that in-context learning can achieve higher performance with more demonstrations under many-shot instruction tuning (8k), and further extending the length of instructions (16k) can further improve the upper bound of scaling in-context learning.
Boosting 3D Point Cloud Registration by Transferring Multi-modality Knowledge

The recent multi-modality models have achieved great performance in many vision tasks because the extracted features contain the multi-modality knowledge. However, most of the current registration descriptors have only concentrated on local geometric structures. This paper proposes a method to boost point cloud registration accuracy by transferring the multi-modality knowledge of pre-trained multi-modality model to a new descriptor neural network. Different to the previous multi-modality methods that requires both modalities, the proposed method only requires point clouds during inference. Specifically, we propose an ensemble descriptor neural network combining pre-trained sparse convolution branch and a new point-based convolution branch. By fine-tuning on a single modality data, the proposed method achieves new state-of-the-art results on 3DMatch and competitive accuracy on 3DLoMatch and KITTI. The code and the trained model will be released at https://github.com/phdymz/DBENet.git.
Computing a Best Response against a Maximum Disruption Attack

Inspired by scenarios where the strategic network design and defense or immunisation are of the central importance, Goyal et al. [3] defined a new Network Formation Game with Attack and Immunisation. The authors showed that despite the presence of attacks, the game has high social welfare properties and even though the equilibrium networks can contain cycles, the number of edges is strongly bounded. Subsequently, Friedrich et al. [10] provided a polynomial time algorithm for computing a best response strategy for the maximum carnage adversary which tries to kill as many nodes as possible, and for the random attack adversary, but they left open the problem for the case of maximum disruption adversary. This adversary attacks the vulnerable region that minimises the post-attack social welfare. In this paper we address our efforts to this question. We can show that computing a best response strategy given a player u and the strategies of all players but u, is polynomial time solvable when the initial network resulting from the given strategies is connected. Our algorithm is based on a dynamic programming and has some reminiscence to the knapsack-problem, although is considerably more complex and involved.
Predicting Out-of-Distribution Error with Confidence Optimal Transport

Out-of-distribution (OOD) data poses serious challenges in deployed machine learning models as even subtle changes could incur significant performance drops. Being able to estimate a model's performance on test data is important in practice as it indicates when to trust to model's decisions. We present a simple yet effective method to predict a model's performance on an unknown distribution without any addition annotation. Our approach is rooted in the Optimal Transport theory, viewing test samples' output softmax scores from deep neural networks as empirical samples from an unknown distribution. We show that our method, Confidence Optimal Transport (COT), provides robust estimates of a model's performance on a target domain. Despite its simplicity, our method achieves state-of-the-art results on three benchmark datasets and outperforms existing methods by a large margin.
Interstellar Magnetic Bubbles

A look is made at the available data on nearby (<1000 pc) large interstellar magnetic bubbles. Here the magnetic field strength B in a shell with gas of density n around an OB association is found to be a few times greater than that outside in the general interstellar medium. Typically, B varies like B∼n k , where k=1.0 and s.d. =0.1, as expected for a shocked medium
Deep Learning on Implicit Neural Representations of Shapes

Implicit Neural Representations (INRs) have emerged in the last few years as a powerful tool to encode continuously a variety of different signals like images, videos, audio and 3D shapes. When applied to 3D shapes, INRs allow to overcome the fragmentation and shortcomings of the popular discrete representations used so far. Yet, considering that INRs consist in neural networks, it is not clear whether and how it may be possible to feed them into deep learning pipelines aimed at solving a downstream task. In this paper, we put forward this research problem and propose inr2vec, a framework that can compute a compact latent representation for an input INR in a single inference pass. We verify that inr2vec can embed effectively the 3D shapes represented by the input INRs and show how the produced embeddings can be fed into deep learning pipelines to solve several tasks by processing exclusively INRs.
Q-system Completeness of Unitary Connections

A Q-system is a unitary version of a separable Frobenius algebra object in a C*-tensor category. In a recent joint work with P. Das, S. Ghosh and C. Jones, the author has categorified Bratteli diagrams and unitary connections by building a $2$-category \textbf{UC}. We prove that every $Q$-system in \textbf{UC} splits.
Magnetic catalysis in the (
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)-dimensional Gross-Neveu model

We study the Gross-Neveu model in $2+1$ dimensions in an external magnetic field $B$. We first summarize known mean-field results, obtained in the limit of large flavor number $N_\mathrm{f}$, before presenting lattice results using the overlap discretization to study one reducible fermion flavor, $N_\mathrm{f}=1$. Our findings indicate that the magnetic catalysis phenomenon, i.e., an increase of the chiral condensate with the magnetic field, persists beyond the mean-field limit for temperatures below the chiral phase transition and that the critical temperature grows with increasing magnetic field. This is in contrast to the situation in QCD, where the broken phase shrinks with increasing $B$ while the condensate exhibits a non-monotonic $B$-dependence close to the chiral crossover, and we comment on this discrepancy. We do not find any trace of inhomogeneous phases induced by the magnetic field.
A Laboratory Study of the Urban Heat Island in a Calm and Stably Stratified Environment. Part II: Velocity Field

Abstract A fully turbulent, low-aspect-ratio buoyant plume with no initial momentum under calm and stably stratified conditions is produced in a convection tank. The plume is generated by a circular heat island at the bottom of the tank. Two analytical models, a bulk convection model and a hydrostatic model, are developed to formulate similarity relations for the low-aspect-ratio plume. The convective velocity scale wD, suggested by the analytical models, is used as the similarity parameter for both the mean velocity and standard deviations of velocity fluctuations. The normalized standard deviations of horizontal and vertical velocities agree with each other for two heating rates, as well as with field observations in the center of Sapporo, Japan. The suggested scaling and empirical relations based on our experimental results may be applied to the velocity fields of other low-aspect-ratio plumes in calm and stably stratified environments. Further investigations are recommended to confirm the results of t.
Characterizing Graph Datasets for Node Classification: Homophily-Heterophily Dichotomy and Beyond

Homophily is a graph property describing the tendency of edges to connect similar nodes; the opposite is called heterophily. It is often believed that heterophilous graphs are challenging for standard message-passing graph neural networks (GNNs), and much effort has been put into developing efficient methods for this setting. However, there is no universally agreed-upon measure of homophily in the literature. In this work, we show that commonly used homophily measures have critical drawbacks preventing the comparison of homophily levels across different datasets. For this, we formalize desirable properties for a proper homophily measure and verify which measures satisfy which properties. In particular, we show that a measure that we call adjusted homophily satisfies more desirable properties than other popular homophily measures while being rarely used in graph learning literature. Then, we go beyond the homophily-heterophily dichotomy and propose a new characteristic allowing one to further distinguish different sorts of heterophily. The proposed label informativeness (LI) characterizes how much information a neighbor's label provides about a node's label. We analyze LI via the same theoretical framework and show that it is comparable across different datasets. We also observe empirically that LI better agrees with GNN performance compared to homophily measures, which confirms that it is a useful characteristic of the graph structure.
A point process on the unit circle with antipodal interactions

We study the point process \begin{align*} \frac{1}{Z_{n}}\prod_{1 \leq j<k \leq n} |e^{i\theta_{j}}+e^{i\theta_{k}}|^{\beta}\prod_{j=1}^{n} d\theta_{j}, \qquad \theta_{1},\ldots,\theta_{n} \in (-\pi,\pi], \quad \beta>0, \end{align*} where $Z_{n}$ is the normalization constant. The feature of this process is that the points $e^{i\theta_{1}},\ldots,e^{i\theta_{n}}$ are repelled by the antipodal points $-e^{i\theta_{1}},\ldots,-e^{i\theta_{n}}$. We consider linear statistics of the form $\sum_{j=1}^{n}g(\theta_{j})$ as $n \to \infty$, where $g$ is H\"{o}lder continuous and $2\pi$-periodic. We prove that the leading order fluctuations around the mean are of order $n$ and given by $\smash{\big(g(U)-\int_{-\pi}^{\pi}g(\theta) \frac{d\theta}{2\pi}}\big)n$, where $U \sim \mathrm{Uniform}(-\pi,\pi]$. We also conjecture that if $g \in C^{1,q}$, then the subleading fluctuations around the mean are of order $\sqrt{n}$ and of the form $\mathcal{N}_{\mathbb{R}}(0,4g'(U)^{2}/\beta)\sqrt{n}$, i.e. that the subleading fluctuations are given by a Gaussian random variable that itself has a random variance. We also derive large $n$ asymptotics for $Z_{n}$ (and some generalizations), up to and including the term of order $1$. Our proof uses techniques developed by McKay and Isaev [7,5] to obtain asymptotics of related $n$-fold integrals.
Solar Term Anomaly in China Stock Market: Evidence from Shanghai Index

This paper investigates the solar term effect in China stock market as a supplementary to the existing literature of calender effect. Based on a regression framework, this paper verifies the existence of solar term effect in Shanghai Index in multiple dimensions: inter-solar-term analysis, full sample analysis at mean level and risk level as well as the turn of solar term effect. Several solar terms have been found to cause significant positive and negative value to the return such as solar term 1,3 and 4. and bring high volatility such as solar term 8, 11 and 14. The result is reliable and robust under the Extreme Bound Analysis and various assumptions of errors distribution in IGARCH model. These findings give readers a new perspective to view calender effect under the influence of traditional Chinese culture that solar terms affect the market through affecting investors mood, expectation, enthusiasm, etc. which is a good evidence to the Culture bonus hypothesis proposed by Chen and Chien and the possible influence by the Chinese culture in other Asian markets.
Design and construction of a small-scale model of a high-temperature superconducting magnetically levitated vehicle

The design of a small-scale model of a magnetically levitated vehicle is presented in the paper. The model has been constructed on the basis of the calculation of the magnetic field and forces between permanent magnets and high temperature superconducting materials prepared by different fabrication techniques. The fabrication of the superconductor play a fundamental role in designing the vehicle since large enough levitation forces can be achieved only with superconductors that have large pinning forces. The fabrication processes, the design with a special emphasis on the calculation of the magnetic field and model construction are reported.
Dislocation scattering in a two‐dimensional electron gas of an AlxGa1−xN/GaN heterostructure

The theoretical electron mobility limited by dislocation scattering of a two‐dimensional electron gas confined near the interface of an AlxGa1−xN/GaN heterostructure is calculated. The accurate wave functions and electron distributions of the three lowest subbands for a typical structure are obtained by solving the Schrödinger and Poisson equations self‐consistently. Based on the model of treating dislocation as a charged line, a simple scattering potential, a square‐well potential, is utilized. The estimated mobility suggests that such a choice can simplify the calculation without introducing significant deviation from experimental data. It is also found that the dislocation scattering dominates both the low‐ and moderate‐temperature mobilities and accounts for the nearly flattening‐out behavior with increasing temperature. To clarify the role of dislocation scattering all standard scattering mechanisms are included in the calculation. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)