Miracle-dz/UniFAR-FTUs huggingface dataset:
Tensor Based Multivariate Polynomial Modulo Multiplier for Cryptographic Applications

Modulo polynomial multiplication is an essential mathematical operation in the area of finite field arithmetic. Polynomial functions can be represented as tensors, which can be utilized as basic building blocks for various lattice-based post-quantum cryptography schemes. This paper presents a tensor-based novel modulo multiplication method for multivariate polynomials over <inline-formula><tex-math notation="LaTeX">$GF(2^{m})$</tex-math><alternatives><mml:math><mml:mrow><mml:mi>G</mml:mi><mml:mi>F</mml:mi><mml:mo>(</mml:mo><mml:msup><mml:mn>2</mml:mn><mml:mi>m</mml:mi></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="paul-ieq1-3215638.gif"/></alternatives></inline-formula> and is realized on the hardware platform (FPGA). The proposed method consumes <inline-formula><tex-math notation="LaTeX">$6.5\times$</tex-math><alternatives><mml:math><mml:mrow><mml:mn>6</mml:mn><mml:mo>. </mml:mo><mml:mn>5</mml:mn><mml:mo>×</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="paul-ieq2-3215638.gif"/></alternatives></inline-formula> less power and achieves more than <inline-formula><tex-math notation="LaTeX">$6\times$</tex-math><alternatives><mml:math><mml:mrow><mml:mn>6</mml:mn><mml:mo>×</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="paul-ieq3-3215638.gif"/></alternatives></inline-formula> speedup compared to other contemporary single variable polynomial multiplication implementations. Our method is embarrassingly parallel and easily scalable for multivariate polynomials. Polynomial functions of nine variables, where each variable is of degree 128, are tested with the proposed multiplier, and its corresponding area, power, and power-delay-area product (PDAP) are presented. The computational complexity of single variable and multivariate polynomial multiplications are <inline-formula><tex-math notation="LaTeX">$O(n)$</tex-math><alternatives><mml:math><mml:mrow><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="paul-ieq4-3215638.gif"/></alternatives></inline-formula> and <inline-formula><tex-math notation="LaTeX">$O(np)$</tex-math><alternatives><mml:math><mml:mrow><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mi>p</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="paul-ieq5-3215638.gif"/></alternatives></inline-formula>, respectively, where <inline-formula><tex-math notation="LaTeX">$n$</tex-math><alternatives><mml:math><mml:mi>n</mml:mi></mml:math><inline-graphic xlink:href="paul-ieq6-3215638.gif"/></alternatives></inline-formula> is the maximum degree of a polynomial having <inline-formula><tex-math notation="LaTeX">$p$</tex-math><alternatives><mml:math><mml:mi>p</mml:mi></mml:math><inline-graphic xlink:href="paul-ieq7-3215638.gif"/></alternatives></inline-formula> variables. Due to its high speed, low latency, and scalability, the proposed modulo multiplier can be used in a wide range of applications.
The Skorohod oblique reflection problem in time-dependent domains

The deterministic Skorohod problem plays an important role in the construction and analysis of diffusion processes with reflection. In the form studied here, the multidimensional Skorohod problem was introduced, in timeindependent domains, by H. Tanaka [61] and further investigated by P.-L. Lions and A. -S. Sznitman [42] in their celebrated article. Subsequent results of several researchers have resulted in a large literature on the Skorohod problem in time-independent domains. In this article we conduct a thorough study of the multidimensional Skorohod problem in time-dependent domains. In particular, we prove the existence of càdlàg solutions (x,λ) to the Skorohod problem, with oblique reflection, for (D, ,w) assuming, in particular, that D is a time-dependent domain (Theorem 1.2). In addition, we prove that if w is continuous, then x is continuous as well (Theorem 1.3). Subsequently, we use the established existence results to construct solutions to stochastic differential equations with oblique reflection (Theorem 1.9) in time-dependent domains. In the process of proving these results we establish a number of estimates for solutions to the Skorohod problem with bounded jumps and, in addition, several results concerning the convergence of sequences of solutions to Skorohod problems in the setting of time-dependent domains.
Analysis of The Relationship between Practices and Performance of Green Supply Chain Management in Indonesian Micro, Small, and Medium Enterprises (MSMEs)

Research Aims: This study discusses the practice of green supply chain management (GSCM) on environmental performance and operational costs in micro, small and medium enterprises (MSMEs) in Indonesia's food and beverage industry. Especially to examine the existence of ecocentricity and supply chain traceability that moderates GSCM practices with environmental performance and operational costs. Design/Methodology/Approach: The judgement sampling method was used in this study, and 85 respondents contributed. Research questionnaires were distributed online, and data were analysed using Partial Least Square-Structural Equation Modelling (PLS-SEM). Research Findings: The results of this study indicate that GSCM practices have a significant relationship to environmental performance and operational costs of MSMEs in the food and beverage industry in Indonesia. Supply chain ecocentricity moderates the relationship between GSCM practices, environmental performance, and operating costs. However, supply chain traceability does not moderate the relationship between GSCM practices, environmental performance, and operational costs. Theoretical Contribution/Originality: The concept and practice of GSCM is gaining popularity in developing countries, but is still limited to the scope of MSMEs. Thus, research on GSCM still has to be extended to MSMEs because most research is limited to large organisations. Managerial Implication in the South East Asian Context: This research covers the concept and practice of GSCM on MSMEs in Indonesia. For MSMEs in the food and beverage industry, this research is expected to be taken into consideration in implementing GSCM for supply chain ecocentricity to improve business performance. Research Limitation & Implications: Respondents are limited to the Java and Bali area and the food and/or beverage industry group.
Exponential Convergence of the Discrete-Time Altafini Model

This paper considers the discrete-time version of Altafini's model for opinion dynamics in which the interaction among a group of agents is described by a time-varying signed digraph. Prompted by an idea from [1], exponential convergence of the system is studied using a graphical approach. Necessary and sufficient conditions for exponential convergence with respect to each possible type of limit states are provided. Specifically, under the assumption of repeatedly jointly strong connectivity, it is shown that (1) a certain type of two-clustering will be reached exponentially fast for almost all initial conditions if, and only if, the sequence of signed digraphs is repeatedly jointly structurally balanced corresponding to that type of two-clustering; (2) the system will converge to zero exponentially fast for all initial conditions if, and only if, the sequence of signed digraphs is repeatedly jointly structurally unbalanced. An upper bound on the convergence rate is also provided.
TRACING THE HERCULES STREAM AROUND THE GALAXY

It has been proposed that the Hercules stream, a group of co-moving stars in the solar neighborhood offset from the bulk of the velocity distribution, is the result of resonant interactions between stars in the outer disk and the Galactic bar. So far it has only been seen in the immediate solar neighborhood, but the resonance model makes a prediction over a large fraction of the Galactic disk. I predict the distribution of stellar velocities and the changing Hercules feature in this distribution as a function of location in the Galactic disk in a simple model for the Galaxy and the bar that produces the observed Hercules stream. The Hercules feature is expected to be strong enough to be unambiguously detected in the distribution of line-of-sight velocities in selected directions. I identify quantitatively the most promising lines of sight for detection in line-of-sight velocities using the Kullback–Leibler divergence between the predictions of the resonance model and an axisymmetric model; these directions are at 250° ≲ l ≲ 290°. The predictions presented here are only weakly affected by distance uncertainties, assumptions about the distribution function in the stellar disk, and the details of the Galactic potential including the effect of spiral structure. Gaia and future spectroscopic surveys of the Galactic disk such as APOGEE and HERMES will be able to robustly test the origin of the Hercules stream and constrain the properties of the Galactic bar.
Time-Dependent Degradation Mechanism of 1.2 kV SiC MOSFET Under Long-Term High-Temperature Gate Bias Stress

This work investigates the degradation mechanism of 1.2 kV silicon carbide (SiC) metal oxide semiconductor field-effect transistor (MOSFET) under positive or negative long-term high-temperature gate bias (HTGB) stress. After positive long-term HTGB stress, the device shows a positive shift in threshold voltage (<inline-formula> <tex-math notation="LaTeX">${V}_{\text {th}}{)}$ </tex-math></inline-formula> and an increase in ON-state resistance (<inline-formula> <tex-math notation="LaTeX">${R}_{ \mathrm{\scriptscriptstyle ON}}{)}$ </tex-math></inline-formula>, which mainly results from the electron traps at or near the SiC/SiO2 interface. While subjected to negative HTGB stress, the drift of <inline-formula> <tex-math notation="LaTeX">$V_{\text {th}}$ </tex-math></inline-formula> is time-dependent and correlated with the gate bias. For the device biased at a low gate voltage of −10 V, due to the hole traps at or near the interface, its <inline-formula> <tex-math notation="LaTeX">${V}_{\text {th}}$ </tex-math></inline-formula> exhibits negative shift all the time. But the drift of <inline-formula> <tex-math notation="LaTeX">${V}_{\text {th}}$ </tex-math></inline-formula> for the device biased at a higher voltage of −20 V is decreased first with the stress time, then is increased with the stress time, which may result from the hole traps and the additional electron traps introduced by the tunneling effect. Through the low-frequency noise technology, it is demonstrated that the trap density of the device biased at higher negative gate voltage of −20 V has been increased up to three times.
Non‐linear group actions with polynomial invariant rings and a structure theorem for modular Galois extensions

Let G be a finite p‐group and k be a field of characteristic p>0. We show that G has a non‐linear faithful action on a polynomial ring U of dimension n=log p(|G|) such that the invariant ring UG is also polynomial. This contrasts with the case of linear and graded group actions with polynomial rings of invariants, where the classical theorem of Chevalley–Shephard–Todd and Serre requires G to be generated by pseudo‐reflections. Our result is part of a general theory of ‘trace surjective G‐algebras’, which, in the case of p‐groups, coincide with the Galois ring extensions in the sense of Chase, Harrison and Rosenberg [‘Galois theory and Galois cohomology of commutative rings’, Mem. Amer. Math. Soc. 52 (1965) 15–33]. We consider the dehomogenized symmetric algebra Dk, a polynomial ring with non‐linear G‐action, containing U as a retract and we show that DGk is a polynomial ring. Thus, U turns out to be universal in the sense that every trace surjective G‐algebra can be constructed from U by ‘forming quotients and extending invariants’. As a consequence we obtain a general structure theorem for Galois extensions with given p‐group as Galois group and any prescribed commutative k‐algebra R as invariant ring. This is a generalization of the Artin–Schreier–Witt theory of modular Galois field extensions of degree ps.
Central Limit Theorems of a Recursive Stochastic Algorithm with Applications to Adaptive Designs

Stochastic approximation algorithms have been the subject of an enormous body of literature, both theoretical and applied. Recently, Laruelle and Pag\`es (2013) presented a link between the stochastic approximation and response-adaptive designs in clinical trials based on randomized urn models investigated in Bai and Hu (1999, 2005), and derived the asymptotic normality or central limit theorem for the normalized procedure using a central limit theorem for the stochastic approximation algorithm. However, the classical central limit theorem for the stochastic approximation algorithm does not include all cases of its regression function, creating a gap between the results of Laruelle and Pag\`es (2013) and those of Bai and Hu (2005) for randomized urn models. In this paper, we establish new central limit theorems of the stochastic approximation algorithm under the popular Lindeberg condition to fill this gap. Moreover, we prove that the process of the algorithms can be approximated by a Gaussian process that is a solution of a stochastic differential equation. In our application, we investigate a more involved family of urn models and related adaptive designs in which it is possible to remove the balls from the urn, and the expectation of the total number of balls updated at each stage is not necessary a constant. The asymptotic properties are derived under much less stringent assumptions than those in Bai and Hu (1999, 2005) and Laruelle and Pag\`es (2013).
The Arithmetic of Curves Defined by Iteration

We show how the size of the Galois groups of iterates of a quadratic polynomial $f(x)$ can be parametrized by certain rational points on the curves $C_n:y^2=f^n(x)$ and their quadratic twists. To that end, we study the arithmetic of such curves over global and finite fields, translating key problems in the arithmetic of polynomial iteration into a geometric framework. This point of view has several dynamical applications. For instance, we establish a maximality theorem for the Galois groups of the fourth iterate of quadratic polynomials $x^2+c$, using techniques in the theory of rational points on curves. Moreover, we show that the Hall-Lang conjecture on integral points of elliptic curves implies a Serre-type finite index result for these dynamical Galois groups, and we use conjectural bounds for the Mordell curves to predict the index in the still unknown case when $f(x)=x^2+3$. Finally, we provide evidence that these curves defined by iteration have geometrical significance, as we construct a family of curves whose rational points we completely determine and whose geometrically simple Jacobians have complex multiplication and positive rank.
Discontinuation Rates of Tadalafil Alone and in Combination with a-Blockers in the Treatment of Male Lower Urinary Tract Symptoms with or without Coexisting Erectile Dysfunction: A Systematic Review and Meta-Analysis

Purpose We examined the discontinuation rates of tadalafil alone and in combination with a-blockers (ABs) for the treatment of male lower urinary tract symptoms (LUTS), with or without erectile dysfunction (ED). Materials and Methods We searched the EMBASE, PubMed, Web of Science, Scopus, Cochrane Library, and ClinicalTrials.gov databases for studies published until May 15, 2022. The discontinuation rates associated with LUTS medications were subsequently analyzed by meta-analysis. Results Forty-four studies, including 1724 discontinued patients, were included. The combined discontinuation rate was 12.78% (95% confidence interval (CI) 9.89–15.98%), and the discontinuation rates because of adverse events and lack of efficacy were 4.56% (95% CI 3.39–5.90%) and 3.30% (95% CI 1.53–5.72%), respectively. Conclusions The discontinuation rate of tadalafil alone or in combination with ABs for LUTS with or without ED was relatively low and varied according to the study type. Patients receiving monotherapy or combination therapy were similarly likely to abandon treatment. Treatment with a fixed-dose combination was associated with better persistence than with a free-dose combination. These data may help guide clinicians in selecting drug regimens when making decisions. Factors associated with treatment withdrawal need to be determined through high-quality clinical studies to reduce the drug discontinuation rate, which will ultimately reduce healthcare costs and improve patient outcomes.
Randomly trapped random walks on $\mathbb Z^d$

We give a complete classification of scaling limits of randomly trapped random walks and associated clock processes on $\mathbb Z^d$, $d\ge 2$. Namely, under the hypothesis that the discrete skeleton of the randomly trapped random walk has a slowly varying return probability, we show that the scaling limit of its clock process is either deterministic linearly growing or a stable subordinator. In the case when the discrete skeleton is a simple random walk on $\mathbb Z^d$, this implies that the scaling limit of the randomly trapped random walk is either Brownian motion or the Fractional Kinetics process, as conjectured in [BCCR13].
The Darboux transformation of the derivative nonlinear Schrödinger equation

The n-fold Darboux transformation (DT) is a 2 × 2 matrix for the Kaup–Newell (KN) system. In this paper, each element of this matrix is expressed by a ratio of the (n + 1) × (n + 1) determinant and n × n determinant of eigenfunctions. Using these formulae, the expressions of the q[n] and r[n] in the KN system are generated by the n-fold DT. Further, under the reduction condition, the rogue wave, rational traveling solution, dark soliton, bright soliton, breather solution and periodic solution of the derivative nonlinear Schrödinger equation are given explicitly by different seed solutions. In particular, the rogue wave and rational traveling solution are two kinds of new solutions. The complete classification of these solutions generated by one-fold DT is given.
On subspaces diskcyclicity

In this paper, we define and study subspace-diskcyclic operators. We show that subspace-diskcyclicity does not imply to diskcyclicity. We establish a subspace-diskcyclic criterion and use it to find a subspace-diskcyclic operator that is not subspace-hypercyclic for any subspaces. Also, we show that the inverse of invertible subspace-diskcyclic operators do not need to be subspace-diskcyclic for any subspaces. Finally, we prove that every finite-dimensional separable Hilbert space over the complex field supports a subspace-diskcyclic operator.
Random linear systems with sparse solutions -- asymptotics and large deviations

In this paper we revisit random linear under-determined systems with sparse solutions. We consider $\ell_1$ optimization heuristic known to work very well when used to solve these systems. A collection of fundamental results that relate to its performance analysis in a statistical scenario is presented. We start things off by recalling on now classical phase transition (PT) results that we derived in \cite{StojnicCSetam09,StojnicUpper10}. As these represent the so-called breaking point characterizations, we now complement them by analyzing the behavior in a zone around the breaking points in a sense typically used in the study of the large deviation properties (LDP) in the classical probability theory. After providing a conceptual solution to these problems we attack them on a "hardcore" mathematical level attempting/hoping to be able to obtain explicit solutions as elegant as those we obtained in \cite{StojnicCSetam09,StojnicUpper10} (this time around though, the final characterizations were to be expected to be way more involved than in \cite{StojnicCSetam09,StojnicUpper10}, simply, the ultimate goals are set much higher and their achieving would provide a much richer collection of information about the $\ell_1$'s behavior). Perhaps surprisingly, the final LDP $\ell_1$ characterizations that we obtain happen to match the elegance of the corresponding PT ones from \cite{StojnicCSetam09,StojnicUpper10}. Moreover, as we have done in \cite{StojnicEquiv10}, here we also present a corresponding LDP set of results that can be obtained through an alternative high-dimensional geometry approach. Finally, we also prove that the two types of characterizations, obtained through two substantially different mathematical approaches, match as one would hope that they do.
A natural generalization of Balanced Tableaux

We introduce the notion of ``type'' of a tableau, that allows us to define new families of tableaux including both balanced and standard Young tableaux. We use these new objects to describe the set of reduced decompositions of any permutation. We then generalize the work of Fomin \emph{et al.} by giving, among other things, a new proof of the fact that balanced and standard tableaux are equinumerous, and by exhibiting many new families of tableaux having similar combinatorial properties to those of balanced tableaux.
Preliminary Studies on the Intrahepatic Anatomy of the Venous Vasculature in Cats

Simple Summary The anatomy of the intrahepatic veins in cats has never been thoroughly described; thus, veterinary surgeons have based their techniques on previous knowledge about canine liver anatomy for hepatic surgeries in both dogs and cats. We used corrosion cast techniques and advanced imaging modalities on feline cadavers to describe the anatomy of the portal and hepatic veins in the feline liver. The anatomy seems consistent with that in previous studies in dogs; nevertheless, several relevant vascular differences could be identified between specimens and species and should be assessed pre-operatively to avoid surgical complications. Abstract Hepatic surgeries are often performed in cats to obtain a disease diagnosis, for the removal of masses, or for the treatment of shunts. Whereas the vascular anatomy of the liver has been studied in dogs, such evidence is lacking in cats. The current study used corrosion casts of portal and hepatic veins and computed tomography (CT) analysis of the casts to identify and describe the intrahepatic anatomy in healthy cat livers (n = 7). The results showed that feline livers had a consistent intrahepatic portal and venous anatomy, with only minor disparities in the numbers of secondary and tertiary branches. The feline portal vein consistently divided into two major branches and not three, as previously described in the literature for cats. The finding of a portal vein originating from the right medial lobe branch leading to the quadrate lobe in 4/7 specimens is a novelty of the feline anatomy that was not previously described in dogs. Partial to complete fusion of the caudate process of the caudate and the right lateral lobe, with a lack of clear venous separation between the lobes, was present in two specimens. These findings allowed a detailed description of the most common intrahepatic venous patterns in cats. Further anatomical studies should be encouraged to confirm the present findings and to investigate the utility of this information in surgical settings.
Reducible surgery in lens spaces and seiferters

The Cabling Conjecture states that surgery on hyperbolic knots in $S^3$ never produces reducible manifolds. In contrast, there do exist hyperbolic knots in some lens spaces with non-prime surgeries. Baker constructed a family of such hyperbolic knots and posed a conjecture that his examples encompass all hyperbolic knots in lens spaces with non-prime surgeries. Using the idea of seiferters we construct a counterexample to this conjecture. In the process of construction, we also derive an obstruction for a small Seifert fibred space to be obtainable by a surgery with a seiferter.