Miracle-dz/UniFAR-FTUs huggingface dataset:
Off-Shell Strings II: Black Hole Entropy

In 1994, Susskind and Uglum argued that it is possible to derive the Bekenstein-Hawking entropy $A/4G_N$ from string theory. In this article we explain the conceptual underpinnings of this argument, while elucidating its relationship to induced gravity and ER=EPR. Following an off-shell calculation by Tseytlin, we explicitly derive the classical closed string effective action from sphere diagrams at leading order in $\alpha^{\prime}$. We then show how to use this to obtain black hole entropy from the RG flow of the NLSM on conical manifolds. (We also briefly discuss the more problematic ``open string picture'' of Susskind and Uglum, in which strings end on the horizon.) We then compare these off-shell results with the rival ``orbifold replica trick'' using the on-shell $\mathbb{C}/Z_{N}$ background, which does not account for the leading order Bekenstein-Hawking entropy -- unless perhaps tachyons are allowed to condense on the orbifold. Possible connections to the ER=EPR conjecture are explored. Finally, we discuss prospects for various extensions, including prospects for deriving holographic entanglement entropy in the bulk of AdS.
Fake It Till You Make It: Towards Accurate Near-Distribution Novelty Detection

We aim for image-based novelty detection. Despite considerable progress, existing models either fail or face a dramatic drop under the so-called"near-distribution"setting, where the differences between normal and anomalous samples are subtle. We first demonstrate existing methods experience up to 20% decrease in performance in the near-distribution setting. Next, we propose to exploit a score-based generative model to produce synthetic near-distribution anomalous data. Our model is then fine-tuned to distinguish such data from the normal samples. We provide a quantitative as well as qualitative evaluation of this strategy, and compare the results with a variety of GAN-based models. Effectiveness of our method for both the near-distribution and standard novelty detection is assessed through extensive experiments on datasets in diverse applications such as medical images, object classification, and quality control. This reveals that our method considerably improves over existing models, and consistently decreases the gap between the near-distribution and standard novelty detection performance. The code repository is available at https://github.com/rohban-lab/FITYMI.
Quasiparticle random-phase approximation calculations for 
M1
 transitions with the noniterative finite-amplitude method and application to neutron radiative capture cross sections

We derive the equations of quasiparticle random-phase approximation (QRPA) based on the finite amplitude method (FAM) with the Hartree-Fock+BCS (HF+BCS) single-particle states, and calculate the magnetic dipole (M1) transition for deformed gadolinium isotopes. Our QRPA calculation shows both large spin-flip transitions in the 5 to 10 MeV excitation energy and the low energy orbital transition that would correspond to the M1 scissors mode observed in nuclear experiments. Then, we calculate neutron capture reactions based on the statistical Hauser-Feshbach theory with the photoabsorption cross sections given by QRPA. We find that the capture cross section is enhanced due to the contribution from the low energy M1 transition although the calculated capture cross section still underestimates the experimental data. This issue in the calculated capture cross section could be improved by uncertainties of low energy E1 transition neglected in our QRPA calculation.
Stable capillary hypersurfaces and the partitioning problem in balls with radial weights

In a round ball $B\subset\mathbb{R}^{n+1}$ endowed with an $O(n+1)$-invariant metric we consider a radial function that weights volume and area. We prove that a compact two-sided hypersurface in $B$ which is stable capillary in weighted sense and symmetric about some line containing the center of $B$ is homeomorphic to a closed $n$-dimensional disk. When combined with Hsiang symmetrization and other stability results this allows to deduce that the interior boundary of any isoperimetric region in $B$ for the Gaussian weight is a closed $n$-disk of revolution. For $n=2$ we also show that a compact weighted stable capillary surface in $B$ of genus 0 is a closed disk of revolution.
A Survey of Relevant Text Mining Technology

Recent advances in text mining and natural language processing technology have enabled researchers to detect an authors identity or demographic characteristics, such as age and gender, in several text genres by automatically analysing the variation of linguistic characteristics. However, applying such techniques in the wild, i.e., in both cybercriminal and regular online social media, differs from more general applications in that its defining characteristics are both domain and process dependent. This gives rise to a number of challenges of which contemporary research has only scratched the surface. More specifically, a text mining approach applied on social media communications typically has no control over the dataset size, the number of available communications will vary across users. Hence, the system has to be robust towards limited data availability. Additionally, the quality of the data cannot be guaranteed. As a result, the approach needs to be tolerant to a certain degree of linguistic noise (for example, abbreviations, non-standard language use, spelling variations and errors). Finally, in the context of cybercriminal fora, it has to be robust towards deceptive or adversarial behaviour, i.e. offenders who attempt to hide their criminal intentions (obfuscation) or who assume a false digital persona (imitation), potentially using coded language. In this work we present a comprehensive survey that discusses the problems that have already been addressed in current literature and review potential solutions. Additionally, we highlight which areas need to be given more attention.
Construction of Multiple Constrained DNA Codes

DNA sequences are prone to creating secondary structures by folding back on themselves by non-specific hybridization among its nucleotides. The formation of secondary structures makes the sequences chemically inactive towards synthesis and sequencing processes. In this letter, our goal is to tackle the problems due to the creation of secondary structures in DNA sequences along with constraints such as not having a large homopolymer run length. In this paper, we have presented families of DNA codes with secondary structures of stem length at most two and homopolymer run length at most four. By mapping the error correcting codes over $\Z_{11}$ to DNA nucleotides, we obtained DNA codes with rates $0.5765$ times the rate of corresponding code over $\Z_{11}$, which include some new secondary structure free and better-performing codes for DNA based data storage and DNA computing purposes.
NoisyQuant: Noisy Bias-Enhanced Post-Training Activation Quantization for Vision Transformers

The complicated architecture and high training cost of vision transformers urge the exploration of post-training quantization. However, the heavy-tailed distribution of vision transformer activations hinders the effectiveness of previous post-training quantization methods, even with advanced quantizer designs. Instead of tuning the quantizer to better fit the complicated activation distribution, this paper proposes NoisyQuant, a quantizer-agnostic enhancement for the post-training activation quantization performance of vision transformers. We make a surprising theoretical discovery that for a given quantizer, adding a fixed Uniform noisy bias to the values being quantized can significantly reduce the quantization error under provable conditions. Building on the theoretical insight, NoisyQuant achieves the first success on actively altering the heavy-tailed activation distribution with additive noisy bias to fit a given quantizer. Extensive experiments show NoisyQuant largely improves the post-training quantization performance of vision transformer with minimal computation overhead. For instance, on linear uniform 6-bit activation quantization, NoisyQuant improves SOTA top-1 accuracy on ImageNet by up to 1.7%, 1.1% and 0.5% for ViT, DeiT, and Swin Transformer respectively, achieving on-par or even higher performance than previous nonlinear, mixed-precision quantization.
Progress on the study of the Ginibre ensembles I: GinUE

The Ginibre unitary ensemble (GinUE) consists of N × N random matrices with independent complex standard Gaussian entries. This was introduced in 1965 by Ginbre, who showed that the eigenvalues form a determinantal point process with an explicit correlation kernel, and after scaling they are supported on the unit disk with constant density. For some time now it has been appreciated that GinUE has a fundamental place within random matrix theory, both for its applications and for the richness of its theory. Here we review the progress on a number of themes relating to the study of GinUE. These are eigenvalue probability density functions and correlation functions, fluctuation formulas, sum rules and asymptotic behaviours of correlation functions, and normal matrix models. We discuss too applications in quantum many body physics and quantum chaos, and give an account of some statistical properties of the eigenvectors.
Fully Stochastic Trust-Region Sequential Quadratic Programming for Equality-Constrained Optimization Problems

We propose a trust-region stochastic sequential quadratic programming algorithm (TR-StoSQP) to solve nonlinear optimization problems with stochastic objectives and deterministic equality constraints. We consider a fully stochastic setting, where at each step a single sample is generated to estimate the objective gradient. The algorithm adaptively selects the trust-region radius and, compared to the existing line-search StoSQP schemes, allows us to utilize indefinite Hessian matrices (i.e., Hessians without modification) in SQP subproblems. As a trust-region method for constrained optimization, our algorithm must address an infeasibility issue -- the linearized equality constraints and trust-region constraints may lead to infeasible SQP subproblems. In this regard, we propose an adaptive relaxation technique to compute the trial step, consisting of a normal step and a tangential step. To control the lengths of these two steps while ensuring a scale-invariant property, we adaptively decompose the trust-region radius into two segments, based on the proportions of the rescaled feasibility and optimality residuals to the rescaled full KKT residual. The normal step has a closed form, while the tangential step is obtained by solving a trust-region subproblem, to which a solution ensuring the Cauchy reduction is sufficient for our study. We establish a global almost sure convergence guarantee for TR-StoSQP, and illustrate its empirical performance on both a subset of problems in the CUTEst test set and constrained logistic regression problems using data from the LIBSVM collection.
A Sampling Inspection Plan for Continuous Production

The plan of sampling inspection, described for individual parts, subassemblies, finished articles, and the like, is intended primarily for use in process inspection where there must be assurance that the percentage of defective units is kept down to a low prescribed figure. The system is particularly applicable to products manufactured by conveyer or similar straight-line continuous processes. The object of the plan is to establish a limiting value of “average outgoing quality,” expressed as a percentage of defective units, which will not be exceeded no matter what quality may be submitted to the inspector.
Anisotropic photon and electron scattering without ultrarelativistic approximation

Interactions between photons and electrons are ubiquitous in astrophysics. Photons can be down scattered (Compton scattering) or up scattered (inverse Compton scattering) by moving electrons. Inverse Compton scattering, in particular, is an essential process for the production of astrophysical gamma rays. Computations of inverse Compton emission typically adopts an isotropic or an ultrarelativistic assumption to simplify the calculation, which makes them unable to broadcast the formula to the whole phase space of source particles. In view of this, we develop a numerical scheme to compute the interactions between anisotropic photons and electrons without taking ultrarelativistic approximations. Compared to the ultrarelativistic limit, our exact results show major deviations when target photons are down scattered or when they possess energy comparable to source electrons. We also consider two test cases of high-energy inverse Compton emission to validate our results in the ultrarelativistic limit. In general, our formalism can be applied to cases of anisotropic electron-photon scattering in various energy regimes, and for computing the polarizations of the scattered photons.
Neural Vocoder Feature Estimation for Dry Singing Voice Separation

Singing voice separation (SVS) is a task that separates singing voice audio from its mixture with instrumental audio. Previous SVS studies have mainly employed the spectrogram masking method which requires a large dimensionality in predicting the binary masks. In addition, they focused on extracting a vocal stem that retains the wet sound with the reverberation effect. This result may hinder the reusability of the isolated singing voice. This paper addresses the issues by predicting mel-spectrogram of dry singing voices from the mixed audio as neural vocoder features and synthesizing the singing voice waveforms from the neural vocoder. We experimented with two separation methods. One is predicting binary masks in the mel-spectrogram domain and the other is directly predicting the mel-spectrogram. Furthermore, we add a singing voice detector to identify the singing voice segments over time more explicitly. We measured the model performance in terms of audio, dereverberation, separation, and overall quality. The results show that our proposed model outperforms state-of-the-art singing voice separation models in both objective and subjective evaluation except the audio quality.
Inferencing Progenitor and Explosion Properties of Evolving Core-collapse Supernovae from Zwicky Transient Facility Light Curves

We analyze a sample of 45 Type II supernovae from the Zwicky Transient Facility public survey using a grid of hydrodynamical models in order to assess whether theoretically driven forecasts can intelligently guide follow-up observations supporting all-sky survey alert streams. We estimate several progenitor properties and explosion physics parameters, including zero-age main-sequence (ZAMS) mass, mass-loss rate, kinetic energy, 56Ni mass synthesized, host extinction, and the time of the explosion. Using complete light curves we obtain confident characterizations for 34 events in our sample, with the inferences of the remaining 11 events limited either by poorly constraining data or the boundaries of our model grid. We also simulate real-time characterization of alert stream data by comparing our model grid to various stages of incomplete light curves (Δt < 25 days, Δt < 50 days, all data), and find that some parameters are more reliable indicators of true values at early epochs than others. Specifically, ZAMS mass, time of the explosion, steepness parameter β, and host extinction are reasonably constrained with incomplete light-curve data, whereas mass-loss rate, kinetic energy, and 56Ni mass estimates generally require complete light curves spanning >100 days. We conclude that real-time modeling of transients, supported by multi-band synthetic light curves tailored to survey passbands, can be used as a powerful tool to identify critical epochs of follow-up observations. Our findings are relevant to identifying, prioritizing, and coordinating efficient follow-up of transients discovered by the Vera C. Rubin Observatory.
Exploring the Long-Term Generalization of Counting Behavior in RNNs

In this study, we investigate the generalization of LSTM, ReLU and GRU models on counting tasks over long sequences. Previous theoretical work has established that RNNs with ReLU activation and LSTMs have the capacity for counting with suitable configuration, while GRUs have limitations that prevent correct counting over longer sequences. Despite this and some positive empirical results for LSTMs on Dyck-1 languages, our experimental results show that LSTMs fail to learn correct counting behavior for sequences that are significantly longer than in the training data. ReLUs show much larger variance in behavior and in most cases worse generalization. The long sequence generalization is empirically related to validation loss, but reliable long sequence generalization seems not practically achievable through backpropagation with current techniques. We demonstrate different failure modes for LSTMs, GRUs and ReLUs. In particular, we observe that the saturation of activation functions in LSTMs and the correct weight setting for ReLUs to generalize counting behavior are not achieved in standard training regimens. In summary, learning generalizable counting behavior is still an open problem and we discuss potential approaches for further research.
Average-case and smoothed analysis of graph isomorphism

We propose a simple and efficient local algorithm for graph isomorphism which succeeds for a large class of sparse graphs. This algorithm produces a low-depth canonical labeling, which is a labeling of the vertices of the graph that identifies its isomorphism class using vertices' local neighborhoods. Prior work by Czajka and Pandurangan showed that the degree profile of a vertex (i.e., the sorted list of the degrees of its neighbors) gives a canonical labeling with high probability when $n p_n = \omega( \log^{4}(n) / \log \log n )$ (and $p_{n} \leq 1/2$); subsequently, Mossel and Ross showed that the same holds when $n p_n = \omega( \log^{2}(n) )$. We first show that their analysis essentially cannot be improved: we prove that when $n p_n = o( \log^{2}(n) / (\log \log n)^{3} )$, with high probability there exist distinct vertices with isomorphic $2$-neighborhoods. Our first main result is a positive counterpart to this, showing that $3$-neighborhoods give a canonical labeling when $n p_n \geq (1+\delta) \log n$ (and $p_n \leq 1/2$); this improves a recent result of Ding, Ma, Wu, and Xu, completing the picture above the connectivity threshold. Our second main result is a smoothed analysis of graph isomorphism, showing that for a large class of deterministic graphs, a small random perturbation ensures that $3$-neighborhoods give a canonical labeling with high probability. While the worst-case complexity of graph isomorphism is still unknown, this shows that graph isomorphism has polynomial smoothed complexity.
Neutrino pair energy deposition in supernovae

The role of neutrino-antineutrino annihilation (producing an electron-positron pair) in delayed type II supernova explosions is investigated theoretically. The assumptions and analysis of Goodman et al. (1987) are examined in detail, with a focus on the need for a large density gradient at the edge of the neutrinosphere. It is found that the neutrino annihilation mechanism cannot contribute significantly to the energy of the explosion. 12 references.
Macroscopic wave propagation for 2D lattice with random masses

We consider a simple two‐dimensional harmonic lattice with random, independent, and identically distributed masses. Using the methods of stochastic homogenization, we prove that solutions with initial data, which varies slowly relative to the lattice spacing, converge in an appropriate sense to solutions of an effective wave equation. The convergence is strong and almost sure. In addition, the role of the lattice's dimension in the rate of convergence is discussed. The technique combines energy estimates with powerful classical results about sub‐Gaussian random variables.
Toward Accurate Modeling of Galaxy Clustering on Small Scales: Halo Model Extensions and Lingering Tension

This paper represents an effort to provide robust constraints on the galaxy–halo connection and simultaneously test the Planck ΛCDM cosmology using a fully numerical model of small-scale galaxy clustering. We explore two extensions to the standard Halo Occupation Distribution model: assembly bias, whereby halo occupation depends on both halo mass and the larger environment, and velocity bias, whereby galaxy velocities do not perfectly trace the velocity of the dark matter within the halo. Moreover, we incorporate halo mass corrections to account for the impact of baryonic physics on the halo population. We identify an optimal set of clustering measurements to constrain this “decorated” HOD model for both low- and high-luminosity galaxies in SDSS DR7. We find that, for low-luminosity galaxies, a model with both assembly bias and velocity bias provides the best fit to the clustering measurements, with no tension remaining in the fit. In this model, we find evidence for both central and satellite galaxy assembly bias at the 99% and 95% confidence levels, respectively. In addition, we find evidence for satellite galaxy velocity bias at the 99.9% confidence level. For high-luminosity galaxies, we find no evidence for either assembly bias or velocity bias, but our model exhibits significant tension with SDSS measurements. We find that all of these conclusions still stand when we include the effects of baryonic physics on the halo mass function, suggesting that the tension we find for high-luminosity galaxies may be due to a problem with our assumed cosmological model.
Toward a time domain approach to the linear sampling method

We consider an inverse scattering problem for time-dependent acoustic waves in an inhomogeneous medium. We wish to determine the support of the inhomogeneity from measurements of causal scattered waves by using the linear sampling method in the time domain. The performance of the algorithm is illustrated with several numerical examples, including the first examples of the use of the time domain linear sampling method in three dimensions.
Chaining Simultaneous Thoughts for Numerical Reasoning

Given that rich information is hidden behind ubiquitous numbers in text, numerical reasoning over text should be an essential skill of AI systems. To derive precise equations to solve numerical reasoning problems, previous work focused on modeling the structures of equations, and has proposed various structured decoders. Though structure modeling proves to be effective, these structured decoders construct a single equation in a pre-defined autoregressive order, potentially placing an unnecessary restriction on how a model should grasp the reasoning process. Intuitively, humans may have numerous pieces of thoughts popping up in no pre-defined order; thoughts are not limited to the problem at hand, and can even be concerned with other related problems. By comparing diverse thoughts and chaining relevant pieces, humans are less prone to errors. In this paper, we take this inspiration and propose CANTOR, a numerical reasoner that models reasoning steps using a directed acyclic graph where we produce diverse reasoning steps simultaneously without pre-defined decoding dependencies, and compare and chain relevant ones to reach a solution. Extensive experiments demonstrated the effectiveness of CANTOR under both fully-supervised and weakly-supervised settings.