Miracle-dz/UniFAR-FTUs huggingface dataset:
A survey of Drinfeld modular forms

The possibility of a theory of modular forms for function fields was perhaps implicit in Drinfeld’s original work, but the notion was only really introduced by Goss and Gekeler in the beginning of the eighties. A lot of it developped along “classical” lines (by the word “classical” we will always refer to modular forms for subgroups of SL(2,Z)), but there are also a few very intriguing novel facts to the function field side, and on these we want to concentrate. People who want to compare with the theory of classical modular forms are warmly refered to the well known classical literature. One can see this paper as a kind of (very personal) filter applied to the original works of Gekeler, Goss and Teitelbaum. It should serve as an introduction to (and motivation for) reading their original papers in the reference list, which inevitably contain much more information then can be presented here. In this paper, most interest will go to the “analytic” theory of modular forms and curves, and thus I have neglected parts of the intriguing theory of “algebraic” modular forms, developped in particular by Goss in 1980. For compensation, one should at least glimpse at his papers. Most novelties over function fields occur in connection with (a) the consideration of an arbitrary “ground ring” A, which already makes the moduli space without level structure look complicated; (b) the characteristic-p situation, which causes loss of information in taking derivatives of objects; (c) the analytic reduction of the upper half space to a combinatorial object, namely the Bruhat-Tits tree, and the interpretation of objects “down there”; (d) the fact that “modular forms” are only half of the story, the other side being complex valued Jacquet-Langlands like automorphic forms – and the interaction between these two notions. The organisation of the paper will be as follows: in the first paragraph I will show how modular forms arise naturally in the search for a genus formula for the moduli space without level for GL(2, A), and a few modular forms are introduced. The second paragraph contains a sketch of the explicit calculation of these genera. In the third part, function fields of modular curves are described by means of modular forms, and the fourth paragraph calculates the Hilbert function and presentation of a few rings of modular forms. In paragraph five, we present a few highlights in the theory of modular forms modulo primes and its connection with supersingular invariants. Paragraph six sketches the interpretation of modular forms on the tree via Teitelbaum’s residue-map, and its application to modular forms of low weight. In paragraph seven, the absolute value of some modular forms is studied as a complex-valued object on the tree. Needless to say, I do not claim originality in this survey, except for minor generalisations here and there, in particular in (1.5.3), (4.3) and (4.6.2).
Low sidelobe transmit antenna design for MIMO radar

Waveform diversity of MIMO radar provides more degrees of freedom for transmit beam-pattern design.Firstly,a min-max criterion is proposed for optimizing the correlation matrix of the transmit waveforms to solve the problem of low-sidelobe and high-gain transmit beam-pattern design under the uniform elemental power constraint.The constrained optimization problem is then converted into an unconstrained optimization problem,which can be solved by classical iterative algorithm.Simulation results show that the min-max sidelobe optimization method can obtain a transmit beam-pattern with flat sidelobe region and lower sidelobe level.Finally,phase-coded signals are optimized using the cyclic algorithm.The beam-pattern of designed phase-coded signals matches well with the theoretical results.
Generating Manga Images from Sketch Via GAN

Image generation has been a popular research topic in computer graphics and computer vision. However, most existing image generation works focus on real-life photographs rather than manga images. Generating manga images directly using photographic image generation methods often results in poor visual performance. We propose a novel manga generation method based on sketch images via GAN. The proposed method is irrelevant to real-life photographs and does not require explicit tags. The resulting manga images are generated based on the sketch images painted by the user. The generated manga image has consistent labels and outlines with the original sketch image and is rendered in manga style. Through our intensive experiments on the public dataset AnimeFace, comparing with the state-of-the-art methods Pix2Pix and SofGAN, the sketch detection model reduces 10.9% FID from SofGAN; and the PSNR of the proposed model is higher than Pix2Pix and SofGAN by 1.4% and 3.9%, respectively. The above qualitative and quantitative evaluations show that our manga generation method has excellent visual performance and serves a controllable and label-free generation of manga images. Statistically, the proposed method outperforms the state-of-the-art.
Formal Mathematics for the Masses

The campaign to transform traditional mathematical practice into a formal discipline appears to have been a great success. Several sophisticated proof assistants have been developed, a great deal of mathematical knowledge has been formalized, a growing number of researchers in computing and mathematics are now using proof assistants to check the theorems they prove, and a new area of computing called formal methods has been established in which formal mathematics is used in the development of hardware and software. However, the campaign has largely been a failure when viewed from a broader perspective. It has had almost no impact on mathematical practice. Far less than 1% of all mathematics practitioners have ever used a formal logic or a proof assistant in their work. We propose an alternative approach to formal mathematics that is characterized by (1) proofs are written in a traditional (infor-mal) style, (2) the underlying logic is as close to mathematical practice as possible, (3) mathematics is organized in accordance with the little theories method as a theory graph, and (4) supporting software systems are easy to build and use. We are pursuing a research program called Formal Mathematics for the Masses to make formal mathematics more useful, accessible, and natural to a wider range of mathematics practitioners by implementing this alternative approach.
Minimax Nonparametric Two-Sample Test under Adversarial Losses

In this paper, we consider the problem of two-sample hypothesis testing that aims at detecting the difference between two probability densities based on finite samples. The proposed test statistic is constructed by first truncating a sample version of a negative Besov norm and then normalizing it. Here, the negative Besov norm is the norm associated with a Besov space with negative exponent, and is shown to be closely related to a class of commonly used adversarial losses (or integral probability metrics) with smooth discriminators. Theoretically, we characterize the optimal detection boundary of two-sample testing in terms of the dimensionalities and smoothness levels of the underlying densities and the discriminator class defining the adversarial loss. We also show that the proposed approach can simultaneously attain the optimal detection boundary under many common adversarial losses, including those induced by the ℓ 1 , ℓ 2 distances and Wasserstein distances. Our numerical experiments show that the proposed test procedure tends to exhibit higher power and robustness in difference detection than existing state-of-the-art competitors.
Effects of non-uniform root zone salinity on water use, Na + recirculation, and Na + and H + ﬂux in cotton

A new split-root system was established through grafting to study cotton response to non-uniform salinity. Each root half was treated with either uniform (100/100 mM) or non-uniform NaCl concentrations (0/200 and 50/150 mM). In contrast to uniform control, non-uniform salinity treatment improved plant growth and water use, with more water absorbed from the non- and low salinity side. Non-uniform treatments decreased Na + concentrations in leaves. The [Na + ] in the ‘0’ side roots of the 0/200 treatment was signiﬁcantly higher than that in either side of the 0/0 control, but greatly decreased when the ‘0’ side phloem was girdled, suggesting that the increased [Na + ] in the ‘0’ side roots was possibly due to transportation of foliar Na + to roots through phloem. Plants under non-uniform salinity extruded more Na + from the root than those under uniform salinity. Root Na + efﬂux in the low salinity side was greatly enhanced by the higher salinity side. NaCl-induced Na + efﬂux and H + inﬂux were inhibited by amiloride and sodium orthovanadate, suggesting that root Na + extrusion was probably due to active Na + /H + antiport across the plasma membrane. Improved plant growth under non-uniform salinity was thus attributed to increased water use, reduced leaf Na + concentration, transport of excessive foliar Na + to the low salinity side, and enhanced Na + efﬂux from the low salinity root.
Analysis of the Problem of Ensuring the Reliability of the Information System

The article is devoted to the analysis of the problem of ensuring the operational reliability of communication equipment and automation and substantiating the approach to its solution based on the intellectualization of monitoring and diagnostics processes. The analysis of the state of the subject area of the study is carried out, the relevance of the topic of the work is substantiated, the problem situation is determined. A mathematical model of the influence of technical personnel training in troubleshooting on improving the operational reliability of communication equipment and automation has been developed, which is a formal modeling basis for the implementation of the process of knowledge formation for the diagnostic knowledge base on communication equipment and automation malfunctions
FIFO can be Better than LRU: the Power of Lazy Promotion and Quick Demotion

LRU has been the basis of cache eviction algorithms for decades, with a plethora of innovations on improving LRU's miss ratio and throughput. While it is well-known that FIFO-based eviction algorithms provide significantly better throughput and scalability, they lag behind LRU on miss ratio, thus, cache efficiency. We performed a large-scale simulation study using 5307 block and web cache workloads collected in the past two decades. We find that contrary to what common wisdom suggests, some FIFO-based algorithms, such as FIFO-Reinsertion (or CLOCK), are, in fact, more efficient (have a lower miss ratio) than LRU. Moreover, we find that qick demotion --- evicting most new objects very quickly --- is critical for cache efficiency. We show that when enhanced by qick demotion, not only can state-of-the-art algorithms be more efficient, a simple FIFO-based algorithm can outperform five complex state-of-the-art in terms of miss ratio.
A Bibliometric Analysis of Business Process Capabilities: Towards a Conceptual Model

This study presents a bibliometric analysis using the Web of Science core collection database to support the development of the business process capabilities domain, enhancing the knowledge about the key scientific journals, authors, and papers, besides the subject areas and the main definitions that shaped this topic. This bibliometric analysis comprises the following fundamental matters: (1) the number of studies published per year, (2) the most prolific and influential authors, (3) the assessment of studies citing business process capabilities, and (4) the main subject areas and definitions on this topic. Furthermore, based on the list of studies and the indicators identified, we mapped the business process capability concept and its main related concepts. This study provides helpful information for those attempting to analyze and deepen the business process capabilities in the literature while providing some insights concerning its conceptualization and growth.
Multiresolution Matrix Factorization and Wavelet Networks on Graphs

Multiresolution Matrix Factorization (MMF) is unusual amongst fast matrix factorization algorithms in that it does not make a low rank assumption. This makes MMF especially well suited to modeling certain types of graphs with complex multiscale or hierarchical strucutre. While MMF promises to yield a useful wavelet basis, finding the factorization itself is hard, and existing greedy methods tend to be brittle. In this paper, we propose a “learnable” version of MMF that carfully optimizes the factorization with a combination of reinforcement learning and Stiefel manifold optimization through backpropagating errors. We show that the resulting wavelet basis far outperforms prior MMF algorithms and provides the first version of this type of factorization that can be robustly deployed on standard learning tasks. Furthermore, we construct the wavelet neural networks (WNNs) learning graphs on the spectral domain with the wavelet basis produced by our MMF learning algorithm. Our wavelet networks are competitive against other state-of-the-art methods in molecular graphs classification and node classification on citation graphs. Our complete paper with the Appendix and more experiments is publicly available at https://arxiv.org/pdf/2111.01940. pdf. We release our implementation at https://github.com/risilab/Learnable_MMF/.
A Unconstrained Optimal Policy Pair

This is a common setting in many real-world 2-player cooperative games where the two players share the same action space and their joint action is the combined action from both parties. Moreover, we assume that both agents in this game, namely the teacher and the student, are fully rational, but their knowledge about the game differs: the teacher is omniscient and it knows all optimal policy pairs, while the student knows neither the optimal policies nor the reward function. We are interested in investigating how the two agents with misaligned information would behave in a cooperative game.
Ultrasound image de-noising study based on balanced orthogonal multiwavelet

There are inherent speckle noises in the medical ultrasound image.The image denoising is necessary for the lower image quality.The balanced orthogonal multiwavelet has both orthogonal and symmetry.It has higher resolution and better denoising effect than the scalar wavelet.Therefore,the ultrasound medical image is discomposed to multiwavelet domain.Then its coefficients are shrunk by fuzzy clustering with semi-soft threshold for image de-noising.The result indicates that the method is more effective than hard threshold and soft threshold.The speckle noise in the original image can be removed efficiently and at the same time the image details can be reserved.
Reliability of sleep deprivation-associated spontaneous brain activity and 1 behavior 2

31 Recent studies have indicated that sleep deprivation (SD) alters intrinsic low-frequency 32 connectivity in the resting brain, mainly focusing on the default mode network (DMN) and its 33 anticorrelated network (ACN). These networks hold key functions in segregating internally and 34 externally directed awareness. However, far less attention has been paid to investigation of the 35 altered amplitude of these low-frequency fluctuations (ALFF) at the whole-brain level and more 36 importantly by what extent the sleep-deprived resting brain pattern can be reproducible and 37 predict individual behavioral performance. The aim of this study was to characterize more 38 clearly the influence of sleep on the whole brain level of ALFF changes and its relation with the 39 performance of a lexical decision task in the sleep deprivation. Sixteen healthy participants 40 underwent fMRI three times: once after a normal night of sleep in the rested wakefulness (RW) 41 state and two following approximately 24 h of total SD separated by an interval of two weeks 42 (SD1 and SD2). Our behavioral results showed that sleep stabilizes performance whereas two 43 sleep deprivation even at an interval of two weeks consistently deteriorates it. Sleep deprivation 44 attenuated the ALFF mainly in the bilateral orbitofrontal cortex (OFC), bilateral dorsolateral 45 prefrontal cortex (DLPFC) and right inferior parietal lobule (IPL). By contrast, the enhanced 46 ALFF emerged in the left sensorimotor cortex (SMA), visual cortex and left fusiform gyrus. 47 Conjunction analysis of SD1 and SD2 versus the control maps and voxel-wise ICC analysis 48 revealed that these SD induced ALFF changes showed a significantly high reliability (ICC ＞ 0.5). 49 Particularly, the attenuation of the right IPL presents a significant negative relation with the 50 behavior performance and can be reproducible for two SD at an interval of two weeks. Our 51 results suggest that ALFF is a stable measure in study of SD, and the right IPL may represent a 52 stable biomarker that responds to sleep loss. 53
Deep Reinforcement Learning for High-Frequency Market Making

High-frequency market making is a algorithmic trading strategy in which an agent provides liquidity at the same time as quoting a bid price and an ask price on a security. The strategy reap profits in the form of the spread between the quoted price placed on the buy and sell prices. Due to complexity in inventory risk, counterparties to trades and information asymmetry, the understanding of high-frequency market making algorithms is relatively unexplored by academics across disciplines. In this paper, we develop realistic simulations of limit order markets and use them to design a high-frequency market making agent using Deep Recurrent Q-Networks. Our approach outperforms a prominent benchmark strategy from literature, which uses temporal-difference reinforcement learning to design market making agents. Using the simulation framework, we analyse how the maker-take fee, a feature of market design, affects market quality and the agent’s profitability. The agents successfully reproduce stylised facts in historical trade data from each simulation.
Research on Network Prediction of Hidden Danger in Logistics Enterprises

In view of the large amount of manually recorded safety inspection data accumulated in the current logistics industry, as well as the problem of hidden danger neglect caused by lack of experience of inspectors and other reasons, this paper constructs a knowledge graph to show the structure of hidden danger of logistics enterprises in the form of graph data, targeted analysis of various unsafe hidden factors in logistics enterprises, based on the original unstructured data, To realize the construction of the relationship network between enterprises and the hidden danger factors, and analyse the relationship between the hidden danger of logistics enterprises. At the same time, the time sequence information is integrated, the graph data of continuous time slices is integrated, and the time-varying rule is analysed to realize the dynamic prediction of the hidden danger network of logistics enterprises. The accuracy of prediction is increased by learning historical data, so as to provide more targeted and specific inspection focus for the hidden danger inspection of logistics enterprises, and become an important auxiliary tool in manual inspection.
Formalization of Gambler's Ruin Problem (short paper)

The gambler’s ruin problem is an exciting application of probability theory which is generally used to analyze various practical scenarios like the security of bitcoin protocol. In this article, we provide a complete analysis of the formalization of the gambler’s ruin problem in Isabelle/HOL. First, we present a comprehensive background and pen-and-paper calculation. Second, we summarise how to quantify the gambler’s ruin problem and prepare all necessary intermediate conclusions. Third, we explain the difficulties we faced during the final formalization and analyze the strategies to overcome these barriers. Our final result: The recursive probability equation aims to establish the complete quantitative analysis of random walks and assist others in developing advanced probability analysis based on what we endeavour here.
Pelvic Girdle Pain in Pregnancy: A Review

Importance Pelvic girdle pain is often thought to be a recent phenomenon, but this condition was described as early as 400 BC by Hippocrates. Despite being identified for years, confusion continues about the definition and management of this ailment affecting many pregnancies. Objectives The purpose of the review is to assess the incidence, etiology, pathophysiology, risk factors, diagnosis, management, and pregnancy outcomes/recovery of current pregnancies, and outcomes of future pregnancies complicated by pelvic girdle pain. Evidence Acquisition Electronic databases (PubMed and Embase) were searched from 1980 to 2021 with the only limitation being that the articles were in English. Studies were selected that examined associations between pelvic pain/pelvic girdle pain and pregnancy. Results There were 343 articles identified. After reviewing the abstracts, 88 were used in this review. Pelvic girdle pain is a common condition of pregnancy, affecting a reported 20% of pregnant women. The pathophysiology is poorly understood and likely multifactorial, involving both hormonal and biomechanical changes that occur during pregnancy. Several risk factors have been identified. This diagnosis is most commonly made based on symptoms related to pelvic pain during pregnancy. Treatment should be multimodal, including pelvic girdle support, stabilizing exercises, analgesia, and potentially complementary therapies. The effects on future pregnancies are uncertain, although some limited information suggests an increased risk of recurrent PGP in subsequent pregnancies. Conclusions Pelvic girdle pain in pregnancy is a common condition that is often overlooked as a normal part of pregnancy but has a significant impact on quality of life during, after, and in subsequent pregnancies. Multimodal therapies are available and are largely low cost and noninvasive. Relevance Our aim is to increase the awareness of pelvic girdle pain in pregnancy as a common but often underdiagnosed and undertreated condition. Target Audience Obstetricians and gynecologist, family physicians. Learning Objectives After completing this activity, the learner should be better able to describe the diagnosis, etiology, and pathophysiology of pelvic girdle pain; identify risk factors and appropriate management; and predict reoccurrence in a subsequent pregnancy.
A Novel Tamil Character Recognition Using Decision Tree Classifier

Abstract Tamil is a South Indian language spoken widely in Tamil Nadu, one of the states of India. It is one of the oldest languages in the world, and the Tamil script is used to write the Tamil language in India, Sri Lanka, Singapore, and parts of Malaysia, as well as to write minority languages such as Badaga. This paper presents an efficient method for recognizing Tamil characters based on extracted features like horizontal lines, vertical lines, loops, and curves. The extracted features are fed to Back Propagation based Neural Network (BPNN) classifier system, Support Vector Machine (SVM) classifier, and Decision Tree (DT) classifier. The DT classifier system has achieved very good recognition rate on the Tamil character database and shows improved performance as compared to BPNN classifier and SVM classifiers.
Adaptive Observer for DC Voltages in a cascaded H-bridge multilevel converter

Abstract Using an instantaneous model of a cascaded H-bridge multilevel converter a nonlinear adaptive observer is proposed. The model of the system is arranged as a set of subsystems, in order to take advantage of the converter structure, for designing the observer. This observer scheme can be used to replace the voltage sensors needed to control and monitoring the system capacitor voltages even in the presence of system parameter uncertainties. Simulation results are used to validate the performance of the proposed observer when the multilevel converter is used as an electrical network compensator.