Miracle-dz/UniFAR-FTUs huggingface dataset:
Border Ranks of Positive and Invariant Tensor Decompositions: Applications to Correlations

The matrix rank and its positive versions are robust for small approximations, i.e. they do not decrease under small perturbations. In contrast, the multipartite tensor rank can collapse for arbitrarily small errors, i.e. there may be a gap between rank and border rank, leading to instabilities in the optimization over sets with fixed tensor rank. Can multipartite positive ranks also collapse for small perturbations? In this work, we prove that multipartite positive and invariant tensor decompositions exhibit gaps between rank and border rank, including tensor rank purifications and cyclic separable decompositions. We also prove a correspondence between positive decompositions and membership in certain sets of multipartite probability distributions, and leverage the gaps between rank and border rank to prove that these correlation sets are not closed. It follows that testing membership of probability distributions arising from resources like translational invariant Matrix Product States is impossible in finite time. Overall, this work sheds light on the instability of ranks and the unique behavior of bipartite systems.
Topology of Cut Complexes of Graphs

We define the $k$-cut complex of a graph $G$ with vertex set $V(G)$ to be the simplicial complex whose facets are the complements of sets of size $k$ in $V(G)$ inducing disconnected subgraphs of $G$. This generalizes the Alexander dual of a graph complex studied by Fr\"oberg (1990), and Eagon and Reiner (1998). We describe the effect of various graph operations on the cut complex, and study its shellability, homotopy type and homology for various families of graphs, including trees, cycles, complete multipartite graphs, and the prism $K_n \times K_2$, using techniques from algebraic topology, discrete Morse theory and equivariant poset topology.
HDR or SDR? A Subjective and Objective Study of Scaled and Compressed Videos

We conducted a large-scale study of human perceptual quality judgments of High Dynamic Range (HDR) and Standard Dynamic Range (SDR) videos subjected to scaling and compression levels and viewed on three different display devices. HDR videos are able to present wider color gamuts, better contrasts, and brighter whites and darker blacks than SDR videos. While conventional expectations are that HDR quality is better than SDR quality, we have found subject preference of HDR versus SDR depends heavily on the display device, as well as on resolution scaling and bitrate. To study this question, we collected more than 23,000 quality ratings from 67 volunteers who watched 356 videos on OLED, QLED, and LCD televisions. Since it is of interest to be able to measure the quality of videos under these scenarios, e.g. to inform decisions regarding scaling, compression, and SDR vs HDR, we tested several well-known full-reference and no-reference video quality models on the new database. Towards advancing progress on this problem, we also developed a novel no-reference model called HDRPatchMAX, that uses both classical and bit-depth sensitive distortion statistics more accurately than existing metrics.
Deformation and $K$-theoretic Index Formulae on Boundary Groupoids

Boundary groupoids were introduced by the second author, which can be used to model many analysis problems on singular spaces. In order to investigate index theory on boundary groupoids, we introduce the notion of {\em a deformation from the pair groupoid}. Under the assumption that a deformation from the pair groupoid $M \times M$ exists for Lie groupoid $\mathcal{G}\rightrightarrows M$, we construct explicitly a deformation index map relating the analytic index on $\mathcal{G}$ and the index on the pair groupoid. We apply this map to boundary groupoids of the form $\mathcal{G} = M_0 \times M_0 \sqcup G \times M_1 \times M_1 \rightrightarrows M=M_0\sqcup M_1$, where $G$ is an exponential Lie group, to obtain index formulae for (fully) elliptic (pseudo)-differential operators on $\mathcal{G}$, with the aid of the index formula by M. J. Pflaum, H. Posthuma, and X. Tang. These results recover and generalize our previous results for renormalizable boundary groupoids via the method of renormalized trace.
FairBalance: How to Achieve Equalized Odds With Data Pre-processing

This research seeks to benefit the software engineering society by providing a simple yet effective pre-processing approach to achieve equalized odds fairness in machine learning software. Fairness issues have attracted increasing attention since machine learning software is increasingly used for high-stakes and high-risk decisions. Amongst all the existing fairness notions, this work specifically targets"equalized odds"given its advantage in always allowing perfect classifiers. Equalized odds requires that members of every demographic group do not receive disparate mistreatment. Prior works either optimize for an equalized odds related metric during the learning process like a black-box, or manipulate the training data following some intuition. This work studies the root cause of the violation of equalized odds and how to tackle it. We found that equalizing the class distribution in each demographic group with sample weights is a necessary condition for achieving equalized odds without modifying the normal training process. In addition, an important partial condition for equalized odds (zero average odds difference) can be guaranteed when the class distributions are weighted to be not only equal but also balanced (1:1). Based on these analyses, we proposed FairBalance, a pre-processing algorithm which balances the class distribution in each demographic group by assigning calculated weights to the training data. On eight real-world datasets, our empirical results show that, at low computational overhead, the proposed pre-processing algorithm FairBalance can significantly improve equalized odds without much, if any damage to the utility. FairBalance also outperforms existing state-of-the-art approaches in terms of equalized odds. To facilitate reuse, reproduction, and validation, we made our scripts available at https://github.com/hil-se/FairBalance.
Which Component of Solar Magnetic Field Drives the Evolution of Interplanetary Magnetic Field over the Solar Cycle?

The solar magnetic structure changes over the solar cycle. It has a dipole structure during solar minimum, where the open flux extends mainly from the polar regions into the interplanetary space. During maximum, a complex structure is formed with low-latitude active regions and weakened polar fields, resulting in spread open field regions. However, the components of the solar magnetic field that are responsible for long-term variations in the interplanetary magnetic field (IMF) are not clear, and the IMF strength estimated based on the solar magnetic field is known to be underestimated by a factor of 3–4 against the actual in situ observations (the open flux problem). To this end, we decomposed the coronal magnetic field into the components of the spherical harmonic function of degree and order (ℓ, m) using the potential field source surface model with synoptic maps from SDO/HMI for 2010–2021. As a result, we found that the IMF rapidly increased in 2014 December (7 months after the solar maximum), which coincided with the increase in the equatorial dipole, (ℓ, m) = (1, ±1), corresponding to the diffusion of active regions toward the poles and in the longitudinal direction. The IMF gradually decreased until 2019 December (solar minimum) and its variation corresponded to that of the nondipole component ℓ ≥ 2. Our results suggest that the understanding of the open flux problem may be improved by focusing on the equatorial dipole and the nondipole component and that the influence of the polar magnetic field is less significant.
Robust Non-Linear Feedback Coding via Power-Constrained Deep Learning

The design of codes for feedback-enabled communications has been a long-standing open problem. Recent research on non-linear, deep learning-based coding schemes have demonstrated significant improvements in communication reliability over linear codes, but are still vulnerable to the presence of forward and feedback noise over the channel. In this paper, we develop a new family of non-linear feedback codes that greatly enhance robustness to channel noise. Our autoencoder-based architecture is designed to learn codes based on consecutive blocks of bits, which obtains de-noising advantages over bit-by-bit processing to help overcome the physical separation between the encoder and decoder over a noisy channel. Moreover, we develop a power control layer at the encoder to explicitly incorporate hardware constraints into the learning optimization, and prove that the resulting average power constraint is satisfied asymptotically. Numerical experiments demonstrate that our scheme outperforms state-of-the-art feedback codes by wide margins over practical forward and feedback noise regimes, and provide information-theoretic insights on the behavior of our non-linear codes. Moreover, we observe that, in a long blocklength regime, canonical error correction codes are still preferable to feedback codes when the feedback noise becomes high.
Diurnal variations of the areas and temperatures in tropical cyclone clouds

Diurnal variations of the areas and temperatures in tropical cyclone convective cloud systems in the western North Pacific were estimated using pixel‐resolution infrared (IR) brightness temperature (BT) and best‐track data for 2000–2013. The mean areal extent of very cold cloud cover (IR BTs < 208 K) reached a maximum in the early morning (0000–0300 local solar time (LST)), then decreased after sunrise. This was followed by increasing cloud cover between 208 and 240 K, reaching its maximum areal extent in the afternoon (1500–1800 LST). The time at which cloud cover reached a maximum was sensitive to the temperature thresholds used over the ocean. IR BTs < 240 K reached minima in the morning (0300–0600 LST), and IR BTs > 240 K reached minima in the afternoon (1500–1800 LST). The out‐of‐phase relationships between IR BTs < 240 K and IR BTs > 240 K, and between the maximum coverage times of IR BTs < 208 K and 208 K < IR BTs < 240 K, can both lead to the radius‐averaged IR temperature having two minima per day. The different diurnal evolutions under different cloud conditions suggest tropical cyclone convective cloud systems are best described in terms of both areal extent and cloud‐top temperature. Maximum occurrence of clouds with IR BTs < 208 K in the morning and maximum occurrence of clouds with 208 K < IR BTs < 240 K in the afternoon suggest that two different mechanisms might be involved in causing diurnal variations under these two types of tropical cyclone cloud conditions.
Breakdown of Boltzmann-type Models for the Alignment of Self-propelled Rods

Studies in the collective motility of organisms use a range of analytical approaches to formulate continuous kinetic models of collective dynamics from rules or equations describing agent interactions. However, the derivation of these kinetic models often relies on Boltzmann's hypothesis of"molecular chaos", that correlations between individuals are short-lived. While this assumption is often the simplest way to derive tractable models, it is often not valid in practice due to the high levels of cooperation and self-organization present in biological systems. In this work, we illustrated this point by considering a general Boltzmann-type kinetic model for the alignment of self-propelled rods where rod reorientation occurs upon binary collisions. We examine the accuracy of the kinetic model by comparing numerical solutions of the continuous equations to an agent-based model that implements the underlying rules governing microscopic alignment. Even for the simplest case considered, our comparison demonstrates that the kinetic model fails to replicate the discrete dynamics due to the formation of rod clusters that violate statistical independence. Additionally, we show that introducing noise to limit cluster formation helps improve the agreement between the analytical model and agent simulations but does not restore agreement completely. These results highlight the need to both develop and disseminate improved moment-closure methods for modeling biological and active matter systems.
Structure Diagram Recognition in Financial Announcements

Accurately extracting structured data from structure diagrams in financial announcements is of great practical importance for building financial knowledge graphs and further improving the efficiency of various financial applications. First, we proposed a new method for recognizing structure diagrams in financial announcements, which can better detect and extract different types of connecting lines, including straight lines, curves, and polylines of different orientations and angles. Second, we developed a two-stage method to efficiently generate the industry's first benchmark of structure diagrams from Chinese financial announcements, where a large number of diagrams were synthesized and annotated using an automated tool to train a preliminary recognition model with fairly good performance, and then a high-quality benchmark can be obtained by automatically annotating the real-world structure diagrams using the preliminary model and then making few manual corrections. Finally, we experimentally verified the significant performance advantage of our structure diagram recognition method over previous methods.
Tensor network variational optimizations for real-time dynamics: Application to the time-evolution of spin liquids

Within the Projected Entangled Pair State (PEPS) tensor network formalism, a simple update (SU) method has been used to investigate the time evolution of a two-dimensional U(1) critical spin-1/2 spin liquid under Hamiltonian quench [Phys. Rev. B 106, 195132 (2022)]. Here we introduce two different variational frameworks to describe the time dynamics of SU(2)-symmetric translationally-invariant PEPS, aiming to improve the accuracy. In one approach, after using a Trotter-Suzuki decomposition of the time evolution operator in term of two-site elementary gates, one considers a single bond embedded in an environment approximated by a Corner Transfer Matrix Renormalization Group (CTMRG). A variational update of the two tensors on the bond is performed under the application of the elementary gate and then, after symmetrization of the site tensors, the environment is updated. In the second approach, a cluster optimization is performed on a finite (periodic) cluster, maximizing the overlap of the exact time-evolved state with a symmetric finite-size PEPS ansatz. Observables are then computed on the infinite lattice contracting the infinite-PEPS (iPEPS) by CTMRG. We show that the variational schemes outperform the SU method and remain accurate over a significant time interval before hitting the entanglement barrier. Studying the spectrum of the transfer matrix, we find that the asymptotic correlations are very well preserved under time evolution, including the critical nature of the singlet correlations, as expected from the Lieb-Robinson (LR) bound theorem. Consistently, the system (asymptotic) boundary is found to be described by the same Conformal Field Theory of central charge c = 1c=1 during time evolution. We also compute the time-evolution of the short distance spin-spin correlations and estimate the LR velocity.
A two level approach for simulating Bose-Einstein condensates by localized orthogonal decomposition

In this work, we consider the numerical computation of ground states and dynamics of single-component Bose-Einstein condensates (BECs). The corresponding models are spatially discretized with a multiscale finite element approach known as Localized Orthogonal Decomposition (LOD). Despite the outstanding approximation properties of such a discretization in the context of BECs, taking full advantage of it without creating severe computational bottlenecks can be tricky. In this paper, we therefore present two fully-discrete numerical approaches that are formulated in such a way that they take special account of the structure of the LOD spaces. One approach is devoted to the computation of ground states and another one for the computation of dynamics. A central focus of this paper is also the discussion of implementation aspects that are very important for the practical realization of the methods. In particular, we discuss the use of suitable data structures that keep the memory costs economical. The paper concludes with various numerical experiments in 1d, 2d and 3d that investigate convergence rates and approximation properties of the methods and which demonstrate their performance and computational efficiency, also in comparison to spectral and standard finite element approaches.
A novel ISAR jamming method based on rotating angular reflectors

Based on the characteristic of rotating angular reflectors,this paper presents a novel jamming method for ISAR imaging.In this method,the radar echoes are frequency modulated along azimuth and thus lead to smeared imaging due to the rotation control of angular reflectors.Meanwhile,the barrage jamming along range is achieved via reflector array.In addition,the signal model,key parameter selection criteria and the arrangement of angular reflectors array are discussed in detail,providing a reference for the practical realization of this method.Finally,the results for both simulated and measured data proved the validity of this method.
Higher order Massey products for algebras over algebraic operads

We introduce higher-order Massey products for algebras over algebraic operads. This extends the work of Fernando Muro on secondary ones. We study their basic properties and behavior with respect to morphisms of algebras and operads and give some connections to formality. We prove that these higher-order operations represent the differentials in a naturally associated operadic Eilenberg--Moore spectral sequence. We also study the interplay between particular choices of higher-order Massey products and quasi-isomorphic $\mathcal P_\infty$-structures on the homology of a $\mathcal P$-algebra. We focus on Koszul operads over a characteristic zero field and explain how our results generalize to the non-Koszul case.
Characteristic Differences of Rainfall and Cloud-to-Ground Lightning Activity over South Korea during the Summer Monsoon Season

Abstract In this paper the characteristic variations of cloud-to-ground (CG) lightning and total precipitation during the Korean summer monsoon (June–August) season have been extensively analyzed for different climate regimes. The data used in this study consist of the monthly CG lightning flash count as detected by the lightning detection network installed at the Korean Meteorological Administration (KMA) and the monthly precipitation data from 23 meteorological observatories spread over the Korean peninsula for a period of 10 yr from 1988 to 1997. Temporal and spatial scales of 1 month and 102 km2, respectively, were considered to determine the seasonal values of rain yield or rain volume per CG flash (defined as the ratio of total precipitation to CG flash count over a common area). Seasonal values of rain yield have been compared with that of monthly values separately. The results of variation of the rain yield during the different months constituting the monsoon season are also presented. Results sho.
Synthetic Aperture Anomaly Imaging

Previous research has shown that in the presence of foliage occlusion, anomaly detection performs significantly better in integral images resulting from synthetic aperture imaging compared to applying it to conventional aerial images. In this article, we hypothesize and demonstrate that integrating detected anomalies is even more effective than detecting anomalies in integrals. This results in enhanced occlusion removal, outlier suppression, and higher chances of visually as well as computationally detecting targets that are otherwise occluded. Our hypothesis was validated through both: simulations and field experiments. We also present a real-time application that makes our findings practically available for blue-light organizations and others using commercial drone platforms. It is designed to address use-cases that suffer from strong occlusion caused by vegetation, such as search and rescue, wildlife observation, early wildfire detection, and sur-veillance.
VARIATION OF COSMIC ULTRAVIOLET RADIATION MEASUREMENTS IN AHVAZ AT DIFFERENT MONTHS OF YEAR

Background and Objective: Ultraviolet radiation (UVR), in comparison with the other non-ionizing radiations is more energetic and could produce some biological effects. WHO has reported some of UV effects such as skin cancer and cataract. As a result, the integral observation of UV levels and their effects at ground level is important to assess present and future environmental and health implications of atmospheric UV radiation. Since the amount of UVR has not previously been measured in Khuzestan, the aim of the present study was to measure the amount in Ahvaz area in different months of the year and allocate the maximum UVR during day time. Materials and Methods: In this research, daily quantity of solar UVR were measured in Ahvaz during one year 2007-2008 using a Hand-held Lux-uv-Ir-meter. Three measurements in each day: at noon, and 2 hours before and 2 hours after noon. Results: Averaging the UVR measurements for each month showed that the maximum and the minimum amount of UVR were in Khordad (June-July) and Azar (January-February) respectively. Comparison of UVR measurements during a single day showed that the maximum was at noon hours. Conclusion: Although UV radiation levels are influenced by geographical and climate situations and therefore any comparison between the results of UV measurements at different areas of the world is inappropriate. However, it is possible to compare the average of the measured data in this study with those from the relatively near areas. According to the results the amount of solar UV is highest in summer time, it is recommended to wear appropriate sunglasses and limit time of exposure in the midday sunshine during this period. Sci Med J 2010;9(1):45-51
Test for symmetry in $2 \times 2$ contingency tables with nonignorable nonresponses

The McNemar test evaluates the hypothesis that two correlated proportion is common in $2 \times 2$ contingency tables with the same categories. This study discusses a test for symmetry in $2 \times 2$ contingency tables with nonignorable nonresponses. The proposed method is based on Takai and Kano (2008), which discusses a test for independence because a dependency assumption between the two observed outcomes is required to obtain an identification. Here, we focus on three models and propose a test for symmetry in $2 \times 2$ contingency tables with nonignorable nonresponses.
Determination of the moments of the proton charge density

A global analysis of proton electric form factor experimental data from Rosenbluth separation and low squared four-momentum transfer experiments is discussed for the evaluation of the spatial moments of the proton charge density based on the recently published integral method~\cite{Hob20}. Specific attention is paid to the evaluation of the systematic errors of the method, particularly the sensitivity to the choice of the mathematical expression of the form factor fitting function. Within this comprehensive analysis of proton electric form factor data, the moments of the proton charge density are determined for integer order moments, particularly: $\langle r^2 \rangle$=0.682(02)$_{Sta. }$(11)$_{Sys. }$~fm$^2$, $\langle r^3 \rangle$=0.797(10)$_{Sta. }$(58)$_{Sys. }$~fm$^3$, and $\langle r^4 \rangle$=1.02(05)$_{Sta. }$(31)$_{Sys. }$~fm$^4$.