Miracle-dz/UniFAR-FTUs huggingface dataset:
$p$-adic formulas and unit root $F$-subcrystals of the hypergeometric system

We define the notion of {\it Dwork family of logarithmic $F$-crystals}, a typical example of which is the family of Gauss hypergeometricdifferential systems, viewed as parametrized by their exponents of algebraic monodromy. The $p$-adic analytic dependence of the Frobenius operation upon those exponents, is Dwork's "Boyarsky Principle". We discuss, in favorable cases, the $p$-adic analytic continuation of the unit root $F$-subcrystal in the open tube of a singularity, uniformly w.r. t. the exponents. We obtain a conceptual proof of the Koblitz-Diamond formula $p$-adically analog to Gauss' evaluation of $F(a,b,c;1)$.
Bottleneck-Stationary Compact Model Accelerator With Reduced Requirement on Memory Bandwidth for Edge Applications

State-of-the-art compact models such as MobileNets and EfficientNets are structured using a linear bottleneck and inverted residuals. Hardware architecture using a single dataflow strategy fails to balance the required memory bandwidth with the given computational resources. This work presents a heterogeneous dual-core accelerator that performs a block-wise pipelined process as a unit using a bottleneck-stationary (BS) dataflow. The BS greatly relieves the requirement on DRAM bandwidth and on-chip SRAM capacity. A look-behind-only attention is also proposed as a co-optimized algorithm. Compared to the state-of-the-art hardware scheme, the proposed accelerator demonstrates a reduction of 1.8-<inline-formula> <tex-math notation="LaTeX">$2.9\times $ </tex-math></inline-formula> in latency and 2.2-<inline-formula> <tex-math notation="LaTeX">$3\times $ </tex-math></inline-formula> in energy consumption, respectively.For verification, the accelerator with a 16-bit integer precision was implemented using 28nm CMOS process. Measurements show energy efficiencies of 0.5-to-3.75 TOPS/W in a supply voltage range of 0.55-to-1.15V.
Survival analysis of particle populations in branching random walks

Abstract It is a common practice to describe branching random walks in terms of birth, death and walk of particles, which makes it easier to use them in different applications. The main results obtained for the models of symmetric continuous-time heavy-tailed branching random walks on a multidimensional lattice. We will be mainly interested in studying the problems related to the limiting behavior of branching random walks such as the existence of phase transitions under change of various parameters, the properties of the limiting distribution and the survival probability of a particle population. Emphasis is made on the survival analysis. The answers to these and other questions essentially depend on numerous factors which affect the properties of a branching random walk. Therefore, we will try to describe how the properties of a branching random walk depend on such characteristics of the underlying random walk as finiteness or infiniteness of the variance of jumps. The presented results are based on the Green’s function representations of the transition probabilities of a branching random walk.
Loops and semidirect products

A \emph{loop} $(B,\cdot)$ is a set $B$ together with a binary operation $\cdot$ such that (i) for each $a\in B$, the left and right translation mappings $L_{a}:B\to B: x \mapsto a\cdot x$ and $R_{a}:B\to B: x \mapsto x\cdot a$ are bijections, and (ii) there exists a two-sided identity element $1\in B$. Thus loops can be thought of as "nonassociative groups". In this paper we study standard, internal and external semidirect products of loops with groups. These are generalizations of the familiar semidirect product of groups.
A non-iterative polynomial algorithm for linear programming

Consider a linear programming problem with n primal and m dual variables paired with n dual and m primal slack variables respectively, and aggregately denote these variables and slack variables as a vector z of length 2(n+m). Unlike existing algorithms such as simplex and interior point methods solving linear programming by iteratively generating a sequence of feasible points to approach the optimal solution, the paper defines a function f mapping the constraint matrix and the right-hand side and objective vectors defining the linear programming problem to a binary vector of length n+m. It is shown that, under the uniqueness assumption of the optimal solution z* and for each (primal or dual) variable z_i, f_i is zero if and only if the optimal value z*_i is zero, and f_i is one if and only if z*_i is positive. Computation of f_i for each i consists of solving two groups of linear equations using O(m^2n) operations. Computing f_i is then non-iterative and independent of computing f_j for j i. Hence, at most O(m^2n^2) operations are required to compute f and consequently to solve the linear programming problem. The non-iterative and mutually independent features of computing the elements of f enable a parallel polynomial algorithm for linear programming.
Dual-Band Bandpass Filter With Independently Tunable Attenuation Characteristics Using Graphene Nanoplates

A dual-band bandpass filter (BPF) with independently tunable attenuation based on graphene nanoplates is proposed. By utilizing dual coupling paths, the 1.2- and 2-GHz frequency bands realized by the multimode resonant structure can be completely controlled. The graphene nanoplates loaded close to the resonator are responsible for independently tunable attenuation. Meanwhile, the influence of the loaded graphene nanoplates on the original dual-band BPF is analyzed in detail. New branches are added to achieve a stronger coupling of source, load, and passband. Due to good separation of the dual coupling paths and the controllable attenuation of graphene to the signal, a novel dual-band BPF with independently tunable attenuation is obtained. The measured results show that the dual-band BPF achieves independently tunable attenuation of about −4 dB in two passbands with a low reflection of less than −10 dB.
Transports Regulators of Networks with Junctions Detected by Durations Functions

This study advocates a mathematical framework of ''transport relations'' on a network. They single out a subset of ''traffic states'' described by time, duration, position and other traffic attributes (called ''monads'' for short). Duration evolutions are non-negative, decreasing toward zero for incoming durations, increasing from zero for outgoing durations, allowing the detection of ''junction states'' defined as traffic states with ''zero duration''. A ''junction relation'' (crossroads, synapses, clearing houses, etc.) Is a subset of the transport relation made of junction states? The objective is to construct a ''transport regulator'' associating with traffic states a set of ''celerities'' that mobiles circulating in the network can use as velocities. In other word, a network is regarded as a ''provider of velocity information'' to the mobiles for travelling from one departure state to an arrival state across a junction relation (a kind of geodesic problem). This investigation assumes that a system governs the evolution of monads in function of time, duration and position using celerities as controls and provides the transport regulator, a feedback from transport states to celerities. The proposed mathematical framework can acclimate road or aerial networks, endocrine (hormonal) or synaptic (neurotransmitters) networks, financial or economic networks, which motivated this investigation. This framework could probably accommodate computer and even social networks. This investigation is restricted to junctions between two routes.
0^# and elementary end extensions of V_k

In this paper we prove that if k is a cardinal in L[0^#], then there is an inner model M such that M |= (V_k,E) has no elementary end extension. In particular if 0^# exists then weak compactness is never downwards absolute. We complement the result with a lemma stating that any cardinal greater than aleph_1 of uncountable cofinality in L[0^#] is Mahlo in every strict inner model of L[0^#].
Estimates for Minimal Volume and Minimal Curvature on 4-dimensional compact manifolds

In a remarkable article published in 1982, M. Gromov introduced the concept of minimal volume, namely, the minimal volume of a manifold $M^n$ is defined to be the greatest lower bound of the total volumes of $M^n$ with respect to complete Riemannian metrics whose sectional curvature is bounded above in absolute value by 1. While the minimal curvature, introduced by G. Yun in 1996, is the smallest pinching of the sectional curvature among metrics of volume 1. The goal of this article is to provide estimates to minimal volume and minimal curvature on 4-dimensional compact manifolds involving some differential and topological invariants. Among these ones, we get some sharp estimates for minimal curvature.
Boundedness of solutions in impulsive Duffing equations with polynomial potentials and $C^{1}$ time dependent coefficients

In this paper, we are concerned with the impulsive Duffing equation $$ x''+x^{2n+1}+\sum_{i=0}^{2n}x^{i}p_{i}(t)=0,\ t\neq t_{j}, $$ with impulsive effects $x(t_{j}+)=x(t_{j}-),\ x'(t_{j}+)=-x'(t_{j}-),\ j=\pm1,\pm2,\cdots$, where the time dependent coefficients $p_i(t)\in C^1(\mathbb{S}^1)\ (n+1\leq i\leq 2n)$ and $p_i(t)\in C^0(\mathbb{S}^1)\ (0\leq i\leq n)$ with $\mathbb{S}^1=\mathbb{R}/\mathbb{Z}$. If impulsive times are 1-periodic and $t_{2}-t_{1}\neq\frac{1}{2}$ for $0< t_{1}<t_{2}<1$, basing on a so-called large twist theorem recently established by X. Li, B. Liu and Y. Sun in \cite{XLi}, we find large invariant curves diffeomorphism to circles surrounding the origin and going to infinity, which confines the solutions in its interior and therefore leads to the boundedness of these solutions. Meanwhile, it turns out that the solutions starting at $t=0$ on the invariant curves are quasiperiodic.
Tomographic Inversion In Reflection Seismology

SUMMARY Recently there has been much interest in performing tomographic inversion on data acquired in seismic reflection configurations. Several approaches to dealing with the unknown geometry of reflectors have evolved, the most natural of which seems to be to parametrize them in a manner consistent with the velocity field discretization. the inversion may then be formulated to treat both sets of parameters equally, avoiding the possibility of in-built bias. One appropriate formulation may be a least-squares optimization with a priori and step-length damping terms, which may be accomplished by a multiple-parameter class subspace method. Unfortunately a standard, ‘naive’ application of such an optimization method appears to fall foul of trade-offs between reflector depth and near-reflector velocities. These are manifested in the poor reconstruction of the lower portion of test models from synthetic data. Considerations of determinacy, strategies for non-linear problems and regularization inspired the idea of a multiple-stage approach, in which successive stages admit progressively shorter scale lengths of variation in both velocity field and reflector. an algorithm implementing this approach demonstrates a significant improvement in the reconstruction of longer-wavelength components of test models. However the tests also suggest that the shorter-wavelength velocity-depth trade-offs at the reflector are unresolvable without further information.
Satisfiability Thresholds for Regular Occupation Problems

In the last two decades the study of random instances of constraint satisfaction problems (CSPs) has flourished across several disciplines, including computer science, mathematics and physics. The diversity of the developed methods, on the rigorous and non-rigorous side, has led to major advances regarding both the theoretical as well as the applied viewpoints. The two most popular types of such CSPs are the Erdős-Renyi and the random regular CSPs. Based on a ceteris paribus approach in terms of the density evolution equations known from statistical physics, we focus on a specific prominent class of problems of the latter type, the so-called occupation problems. The regular $r$-in-$k$ occupation problems resemble a basis of this class. By now, out of these CSPs only the satisfiability threshold - the largest degree for which the problem admits asymptotically a solution - for the $1$-in-$k$ occupation problem has been rigorously established. In the present work we take a general approach towards a systematic analysis of occupation problems. In particular, we discover a surprising and explicit connection between the $2$-in-$k$ occupation problem satisfiability threshold and the determination of contraction coefficients, an important quantity in information theory measuring the loss of information that occurs when communicating through a noisy channel. We present methods to facilitate the computation of these coefficients and use them to establish explicitly the threshold for the $2$-in-$k$ occupation problem for $k=4$. Based on this result, for general $k \ge 5$ we formulate a conjecture that pins down the exact value of the corresponding coefficient, which, if true, is shown to determine the threshold in all these cases.
Experimental and theoretical characterization of a lithium niobate photonic crystal

In this letter, we investigate the feasibility of tunable lithium niobate (LiNbO3) photonic crystals. The optical response through a LiNbO3 photonic structure is theoretically determined in order to obtain a photonic band gap with optimal tunability. We show by means of a finite difference time domain simulation that the optimal lattice parameters can provide a Δλ=7nm shift in the photonic band gap for a Δn=0.01 variation of the refractive index with an extinction ratio of −22.5dB. The fabrication process and the optical characterization of these novel photonic crystal structures are also reported. The extinction ratio of the measured photonic band gap is lower than −12dB.
Between countably compact and $\omega$-bounded

Given a property $P$ of subspaces of a $T_1$ space $X$, we say that $X$ is {\em $P$-bounded} iff every subspace of $X$ with property $P$ has compact closure in $X$. Here we study $P$-bounded spaces for the properties $P \in \{\omega D, \omega N, C_2 \}$ where $\omega D \, \equiv$ "countable discrete", $\omega N \, \equiv$ "countable nowhere dense", and $C_2 \,\equiv$ "second countable". Clearly, for each of these $P$-bounded is between countably compact and $\omega$-bounded. We give examples in ZFC that separate all these boundedness properties and their appropriate combinations. Consistent separating examples with better properties (such as: smaller cardinality or weight, local compactness, first countability) are also produced. We have interesting results concerning $\omega D$-bounded spaces which show that $\omega D$-boundedness is much stronger than countable compactness: $\bullet$ Regular $\omega D$-bounded spaces of Lindel\"of degree $< cov(\mathcal{M})$ are $\omega$-bounded. $\bullet$ Regular $\omega D$-bounded spaces of countable tightness are $\omega N$-bounded, and if $\mathfrak{b} > \omega_1$ then even $\omega$-bounded. $\bullet$ If a product of Hausdorff space is $\omega D$-bounded then all but one of its factors must be $\omega$-bounded. $\bullet$ Any product of at most $\mathfrak{t}$ many Hausdorff $\omega D$-bounded spaces is countably compact. As a byproduct we obtain that regular, countably tight, and countably compact spaces are discretely generated.
Price sensitivities for a general stochastic volatility model

We deal with the calculation of price sensitivities for stochastic volatility models. General forms for the dynamics of the underlying asset price and its volatility are considered. We make use of the chaotic (or Malliavin) calculus to compute the price sensitivities. The obtained results are applied to several recent stochastic volatility models as well as the existing ones that are commonly used by practitioners. Each price sensitivity is a source of financial risk. The suggested formulas are expected to improve on the hedging of the underlying risk.
W algebra, Cosets and VOA for 4d N = 2 SCFT from M5 branes

We identify vertex operator algebras (VOAs) of a class of Argyres-Douglas (AD) matters with two types of non-abelian flavor symmetries. They are the $W$ algebra defined using nilpotent orbit with partition $[q^m,1^s]$. Gauging above AD matters, we can find VOAs for more general $\mathcal{N}=2$ SCFTs engineered from 6d $(2,0)$ theories. For example, the VOA for general $(A_{N-1}, A_{k-1})$ theory is found as the coset of a collection of above $W$ algebras. Various new interesting properties of 2d VOAs such as level-rank duality, conformal embedding, collapsing levels, coset constructions for known VOAs can be derived from 4d theory.
Sign language Recognition System using Machine Learning

- Sign language is a good visual communication aid for those with auditory disabilities. This language is also prevalent for those with speech impairment. However, the general populous have little knowledge on sign language, and often find difficulty communicating with someone who is primarily versed in sign language. ISL is the primary sign language followed in India, but there is little work on it because there is a lack of standardized datasets. Additionally, it involves two-hand gestures, which increase the difficulty of recognition due to occlusion of the hands.
Non-adaptive fault diagnosis for low-degree networks via lightpath probing method

This paper considers the fault-diagnosis problem for low-degree all-optical networks. Failure-detection schemes which subject to topological constraints are proposed. Optical probe signals are sent in parallel along a set of designed lightpaths. The network health state is derived from the results of this end-to-end test (i.e., probe syndromes). The design objectives are to minimize the diagnosis cost which is represented by the number of probes. We obtain a lower bound of the number of the probes to identify any single link failure and implement this scheme in several networks as well.
Inverse source problem for wave equation and GPR data interpretation problem

The inverse problem of identifying the unknown spacewise dependent source F(x) in 1D wave equation is considered. Measured data are taken in the form g(t) := u(0; t). The relationship between that problem and Ground Penetrating Radar (GRR) data interpretation problem is shown. The non-iterative algorithm for reconstructing the unknown source F(x) is developed. The algorithm is based on the Fourier expansion of the source F(x) and the explicit representation of the direct problem solution via the function F(x). Then the minimization problem for discrete form of the Tikhonov functional is reduced to the linear algebraic system and solved numerically. Calculations show that the proposed algorithm allows to reconstruct the spacewise dependent source F(x) with enough accuracy for noise free and noisy data.
On modifications of the exponential integral with the Mittag-Leffler function

Abstract In this paper we survey the properties of the Schelkunoff modification of the Exponential integral and we generalize it with the Mittag-Leffler function. So doing we get a new special function (as far as we know) that may be relevant in linear viscoelasticity because of its complete monotonicity properties in the time domain. We also consider the generalized sine and cosine integral functions.
Free subgroups in maximal subgroups of skew linear groups

The study of the existence of free groups in skew linear groups have begun since the last decades of the 20th century. The starting point is the theorem of Tits (1972), now often referred to as Tits’ Alternative, stating that every finitely generated subgroup of the general linear group [Formula: see text] over a field [Formula: see text] either contains a non-cyclic free subgroup or it is solvable-by-finite. In this paper, we study the existence of non-cyclic free subgroups in maximal subgroups of an almost subnormal subgroup of the general skew linear group over a locally finite division ring.
A High-Throughput Fluorescence Polarization-Based Assay for the SH2 Domain of STAT4

The signal transducer and activation of transcription (STAT) proteins are a family of Src homology 2 (SH2) domain-containing transcription factors. The family member STAT4 is a mediator of IL-12 signalling and has been implicated in the pathogenesis of multiple autoimmune diseases. The activity of STAT4 requires binding of phosphotyrosine-containing motifs to its SH2 domain. Selective inhibitors of the STAT4 SH2 domain have not been published to date. Here, we present a fluorescence polarization-based assay for the identification of inhibitors of the STAT4 SH2 domain. The assay is based on the interaction between the STAT4 SH2 domain and the fluorophore-labelled peptide 5-carboxyfluorescein-GpYLPQNID (Kd = 34 ± 4 nM). The assay is stable with respect to DMSO concentrations of up to 10% and incubation times of at least 8 h. The Z’-value of 0.85 ± 0.01 indicates that the assay is suited for use in high-throughput screening campaigns aimed at identifying new therapeutic modalities for the treatment of autoimmune diseases.
Spin‐valve structures exchange biased with a‐Tb0.23Co0.77 layers

Spin‐valve structures, glass/NiFeI/Cu/NiFeII/a‐TbCo/Cu, were prepared where the pinned Permalloy layer is exchanged biased by a 200 to 400 A thick a‐Tb0.23Co0. 77 layer. Exchange fields between 50 and 250 Oe were achieved with TbCo thicknesses below 400 A, for a pinned Permalloy layer 150 A thick. The exchange fields are strongly dependent on substrate bias. The magnetoresistance of these structures reaches 4.5% when thin Co layers are added at the NiFe/Cu interfaces.
Solution of Klein Gordon Equation for Some Diatomic Molecules with New Generalized Morse-like Potential Using SUSYQM

In quantum mechanics, the study of exact solutions of relativistic and non-relativistic equation with different potentials plays a significant role in Physics. The bound state solution of Klein Gordon equation (KGE) is of great important in nuclear and high energy physics. Klein Gordon equation is a relativistic wave equation that describes spinzero particles. It contains of two major objects, the vector potential V(r) and the scalar potential S(r). In D-dimension, the Klein Gordon equation is written as
Journal of Quantitative Analysis in Sports A Variance Decomposition of Individual Offensive Baseball Performance

This paper considers a variance decomposition of offensive baseball performance. Estimating the variance components of offensive baseball performance allows one to determine how much of the variability in performance can be accounted for by differences among teams and how much of the variability lies at the level of individual differences within teams. In addition to variance components, this paper examines the reliability estimates of the true team means in offensive baseball performance. Using offensive baseball data from the 2000 season, and replicated again for 2003, intra-class correlations and parameter reliabilities are obtained under the correct probability model for the performance measure in question. The results show that most of the variability in offensive baseball performance lies at the individual level with only a small number of measures where a sizeable amount variance is accounted for by differences among teams. Changes in the variance components and parameter reliabilities are observed from 2000 to 2003. Team level predictors are added to demonstrate the flexibility of the modelling approach. The paper concludes with a summary of the findings and implications for examining the contextual effects in baseball.