Miracle-dz/UniFAR-FTUs huggingface dataset:
Information Retrieval Models, Techniques and Applications

— An Information Retrieval (IR) system focuses on the processing of data collection by means of representation, storage, and searching for the purpose of knowledge discovery in response to user request via query. The tendency of the IRS to produce relevant documents with high precision and recall to meet user’s need based on query input depends on the adoption of the appropriate techniques by the search engine. In this paper, we explain the concepts of IR and traditional models in which various IR techniques rely upon. We equally give detail description of IR techniques that have been successfully applied to store, manage and retrieve documents from huge amount of data available to users of IR systems. This shows that applications of these retrieval techniques in digital libraries, information filtering system, media search, search engine and domain-specific areas of IR are capable of increasing the throughput and minimize the access time of the user with respect to information needs .
Asymptotics of thermal spectral functions

We use operator product expansion (OPE) techniques to study the spectral functions of currents and stress tensors at finite temperature, in the high-energy timelike region {omega}>>T. The leading corrections to these spectral functions are proportional to {approx}T{sup 4} expectation values in general, and the leading corrections {approx}g{sup 2}T{sup 4} are calculated at weak coupling, up to an undetermined coefficient in the shear viscosity channel. Spectral functions are shown to be infrared safe, in the deeply virtual regime, up to order g{sup 8}T{sup 4}. The convergence of (vacuum subtracted) sum rules in the shear and bulk viscosity channels is established in QCD to all orders in perturbation theory, though numerically significant tails {approx}T{sup 4}/(log{omega}){sup 3} are shown to exist in the bulk viscosity channel. We argue that the spectral functions of currents and stress tensors in infinitely coupled N=4 super Yang-Mills theory do not receive any medium-dependent power correction.
The Quantum $A_{\infty}$-Relations on the Elliptic Curve

We define and prove the existence of the Quantum $A_{\infty}$-relations on the Fukaya category of the elliptic curve, using the notion of the Feynman transform of a modular operad, as defined by Getzler and Kapranov. Following Barannikov, these relations may be viewed as defining a solution to the quantum master equation of Batalin-Vilkovisky geometry.
Soliton solutions for the elastic metric on spaces of curves

In this article we investigate a first order reparametrization-invariant Sobolev metric on the space of immersed curves. Motivated by applications in shape analysis where discretizations of this infinite-dimensional space are needed, we extend this metric to the space of Lipschitz curves, establish the wellposedness of the geodesic equation thereon, and show that the space of piecewise linear curves is a totally geodesic submanifold. Thus, piecewise linear curves are natural finite elements for the discretization of the geodesic equation. Interestingly, geodesics in this space can be seen as soliton solutions of the geodesic equation, which were not known to exist for reparametrization-invariant Sobolev metrics on spaces of curves.
23040 symmetries of hyperbolic tetrahedra

We give a rigorous geometric proof of the Murakami-Yano formula for the volume of a hyperbolic tetrahedron. In doing so, we are led to consider generalized hyperbolic tetrahedra, which are allowed to be non-convex, and have vertices `beyond infinity'; and we uncover a group, which we call 22.5K, of 23040 scissors-class-preserving symmetries of the space of (suitably decorated) generalized hyperbolic tetrahedra. The group 22.5K contains the Regge symmetries as a subgroup of order 144. From a generic tetrahedron, 22.5K produces 30 distinct generalized tetrahedra in the same scissors class, including the 12 honest-to-goodness tetrahedra produced by the Regge subgroup. The action of 22.5K leads us to the Murakami-Yano formula, and to 9 others, which are similar but less symmetrical. From here, we can derive yet other volume formulas with pleasant algebraic and analytical properties. The key to understanding all this is a natural relationship between a hyperbolic tetrahedron and a pair of ideal hyperbolic octahedra.
In silico Study of Coumarins Derivatives With Potential Use in Systemic Diseases

Coumarins have been widely used in various human systemic diseases; however, their molecular action is not known in many cases. In silico studies are an option to explore the interaction of molecules with molecular targets and to obtain explanations for these biological activities. SwissTargetPrediction is an accepted tool to obtain potential biological targets for coumarin derivatives. Some carbonic anhydrases (CAs), enzymes related to the central nervous system (CNS), and estrogen receptors (ER) were evaluated vis à vis coumarins holding an electron donor (EDG) or an electron-withdrawing group (EWG). Molecular docking studies using Schrödinger carried out with some selected proteins showed that EDG and produces the best binding coupling energy (BCE) in CAs and ER. Substituents in the aromatic ring increased the BCE in targets related to CNS enzymes; EDG and EWG at positions 3 or 4 in coumarins had better activity in CAs. Also, in CAs, coumarins derivatives presented better BCE than commercial inhibitors. In ER, no competitive activity to estradiol was obtained from coumarins. All In silico results demonstrated the selective influence of the type of substitution and their position on the BCE that could permit better coumarin derivatives in protein targets implicated in human systemic diseases.
An Adaptive Discontinuous Galerkin Finite Elements Method for Advective Allen-Cahn Equation

We apply a space adaptive interior penalty discontinuous Galerkin method for solving advective Allen-Cahn (AC) equation with expanding and contracting velocity fields. The advective AC equation is first discretized in time and the resulting semi-linear elliptic PDE is solved by an adaptive algorithm using a residual-based a posteriori error estimator. The a posteriori error estimator contains additional terms due to the non-divergence-free velocity field. Numerical examples demonstrate the effectiveness and accuracy of the adaptive approach by resolving the sharp layers accurately.
Finite element exterior calculus for parabolic problems

In this paper, we consider the extension of the finite element exterior calculus from elliptic problems, in which the Hodge Laplacian is an appropriate model problem, to parabolic problems, for which we take the Hodge heat equation as our model problem. The numerical method we study is a Galerkin method based on a mixed variational formulation and using as subspaces the same spaces of finite element differential forms which are used for elliptic problems. We analyze both the semidiscrete and a fully-discrete numerical scheme.
Stability for the complete intersection theorem, and the forbidden intersection problem of Erdős and Sós

A family $F$ of sets is said to be $t$-intersecting if $|A \cap B| \geq t$ for any $A,B \in F$. The seminal Complete Intersection Theorem of Ahlswede and Khachatrian (1997) gives the maximal size $f(n,k,t)$ of a $t$-intersecting family of $k$-element subsets of $[n]=\{1,2,\ldots,n\}$, together with a characterisation of the extremal families. The forbidden intersection problem, posed by Erdős and Sos in 1971, asks for a determination of the maximal size $g(n,k,t)$ of a family $F$ of $k$-element subsets of $[n]$ such that $|A \cap B| \neq t-1$ for any $A,B \in F$. In this paper, we show that for any fixed $t \in \mathbb{N}$, if $o(n) \leq k \leq n/2-o(n)$, then $g(n,k,t)=f(n,k,t)$. In combination with prior results, this solves the above problem of Erdős and Sos for any constant $t$, except for in the ranges $n/2-o(n) < k < n/2+t/2$ and $k < 2t$. One key ingredient of the proof is the following sharp `stability' result for the Complete Intersection Theorem: if $k/n$ is bounded away from $0$ and $1/2$, and $F$ is a $t$-intersecting family of $k$-element subsets of $[n]$ such that $|F| \geq f(n,k,t) - O(\binom{n-d}{k})$, then there exists a family $G$ such that $G$ is extremal for the Complete Intersection Theorem, and $|F \setminus G| = O(\binom{n-d}{k-d})$. We believe this result to be of interest in its own right; indeed, it proves a conjecture of Friedgut from 2008. We prove it by combining classical `shifting' arguments with a `bootstrapping' method based upon an isoperimetric inequality. Another key ingredient is a `weak regularity lemma' for families of $k$-element subsets of $[n]$, where $k/n$ is bounded away from 0 and 1. This states that any such family $F$ is approximately contained within a `junta', such that the restriction of $F$ to each subcube determined by the junta is `pseudorandom' in a certain sense.
Corrosion Risk Estimation and Cause Analysis on Turbine Stator Blades of Turbofan Engine

Turbofan engine parts are subject to corrosion. This degradation is very difficult to observe outside of engine dismantling on predefined inspection dates. Moreover, it is necessary to specifically observe the impacted parts to notice this wear. This inspection process is long, expensive, and rarely carried out with the aim of detecting a corrosion effect. The provision of an indicator to alert on potential corrosion and to target parts is highly anticipated. Better still, if the origin of this corrosion can be identified by numerical methods, it will then be possible to improve the calculation of the lifespan of the part and to space out engine inspections. We propose a digital tool able to offer an indicator estimating if an engine part is corroded. In addition to the alert subject to this estimate, we also give a graphical means to interpret this detection. This application is intended for personnel involved in monitoring engines in operation (in-service support, airlines) or maintenance workshops. It not only alerts on degradation but also helps to optimize the calculation of engine inter-inspection intervals and even possibly helps to design new materials or coatings.
Outer automorphisms of classical algebraic groups

The so-called Tits class, associated to an adjoint absolutely almost simple algebraic group, provides a cohomological obstruction for this group to admit an outer automorphism. If the group has inner type, this obstruction is the only one. In this paper, we prove this is not the case for classical groups of outer type, except for groups of type $^2\mathsf{A}_n$ with $n$ even, or $n=5$. More precisely, we prove a descent theorem for exponent $2$ and degree $6$ algebras with unitary involution, which shows that their automorphism groups have outer automorphisms. In all other relevant classical types, namely $^2\mathsf{A}_n$ with $n$ odd, $n\geq3$ and $^2\mathsf{D}_n$, we provide explicit examples where the Tits class obstruction vanishes, and yet the group does not have outer automorphism. As a crucial tool, we use "generic" sums of algebras with involution.
Study on Conceptual Metaphor in Chinese Anti-epidemic Discourse from the Cultural Context Perspective

Metaphor widely exists in daily discourse and shines people’s extremely intelligent thinking. With the development of cognitive science, metaphor has become an indispensable cognitive tool. The awards ceremony for fighting against COVID-19 was held in Beijing Great Hall of the people and the speech of general secretary Present Xi at the conference was heartening. The speech contains a large number of metaphorical expressions, carrying the Chinese cultural information that was contained in the process of China’s anti-epidemic. Under the guidance of conceptual metaphor theory and combined with cultural context, interpreting the metaphorical expression in the speech will help to understand the great anti-epidemic spirit of the Chinese nation and the profound connotation of Chinese civilization. Research results showed that war metaphors were widely used in the speech, which carried forward the Chinese people’s brave and aggressive spirit in the process of fighting against COVID-19. The use of travel metaphors showed the confidence of the Chinese people to move forward bravely. The use of examination metaphors reflected the serious attitude and extraordinary wisdom of the Communist Party of China and the Chinese government towards the epidemic.
Studies on Synergistic Effects of Different Bio-Active Chemicals on Nuclearpolyherosis (Grasserie Disease) of Silkworm, Bombyx mori Linnaeus

Purpose: Larval hind gut of multivoltine breed silk worm Bombyx mori L. (Nistari) was studied in both favourable and unfavourable rearing seasons after Grasserie caused by Bombyx mori Nuclearpolyherosis Virus (BmNPV) using Histological Analysis, Scanning Electron Microscopy and Transmission Electronic Microscopy. Methodology: Chemical treatments using various bio active chemicals: Curcumin, Allicin and Azadirachtin were administered to minimize the extent of damage. Findings: The present study clearly indicates that Azadirachtin is more effective in comparison to its other counterparts and it is the major finding of this extensive study. Unique Contribution to Theory, Policy and Practice: The uniqueness of this type of bio chemical control of Grasserie disease which is not only a cost effective and eco-friendly technique, but also it is less hazardous and simple controlling procedure of Grasserie. Therefore, this extensive study may help the stakeholders to step ahead on the progression of sustainable agriculture while avoiding crop loss by means of cost-effective pathogen management technology.
A convergent linearized Lagrange finite element method for the magneto-hydrodynamic equations in 2D nonsmooth and nonconvex domains.

A new fully discrete linearized $H^1$-conforming Lagrange finite element method is proposed for solving the two-dimensional magneto-hydrodynamics equations based on a magnetic potential formulation. The proposed method yields numerical solutions that converge in general domains that may be nonconvex, nonsmooth and multi-connected. The convergence of subsequences of the numerical solutions is proved only based on the regularity of the initial conditions and source terms, without extra assumptions on the regularity of the solution. Strong convergence in $L^2(0,T;{\bf L}^2(\Omega))$ was proved for the numerical solutions of both ${\bm u}$ and ${\bm H}$ without any mesh restriction.
Group Approximation in Cayley Topology and Coarse Geometry, Part II: Fibred Coarse Embeddings

Abstract The objective of this series is to study metric geometric properties of disjoint unions of Cayley graphs of amenable groups by group properties of the Cayley accumulation points in the space of marked groups. In this Part II, we prove that a disjoint union admits a fibred coarse embedding into a Hilbert space (as a disjoint union) if and only if the Cayley boundary of the sequence in the space of marked groups is uniformly a-T-menable. We furthermore extend this result to ones with other target spaces. By combining our main results with constructions of Osajda and Arzhantseva–Osajda, we construct two systems of markings of a certain sequence of finite groups with two opposite extreme behaviors of the resulting two disjoint unions: With respect to one marking, the space has property A. On the other hand, with respect to the other, the space does not admit fibred coarse embeddings into Banach spaces with non-trivial type (for instance, uniformly convex Banach spaces) or Hadamard manifolds; the Cayley limit group is, furthermore, non-exact.
Some practical versions of boundary variation diminishing (BVD) algorithm

This short note presents some variant schemes of boundary variation diminishing (BVD) algorithm in one dimension with the results of numerical tests for linear advection equation to facilitate practical use. In spite of being presented in 1D fashion, all the schemes are simple and easy to implement in multi-dimensions on structured and unstructured grids for nonlinear and system equations.
AMBROSE–SINGER THEOREM ON DIFFEOLOGICAL BUNDLES AND COMPLETE INTEGRABILITY OF THE KP EQUATION

In this paper, we start from an extension of the notion of holonomy on diffeological bundles, reformulate the notion of regular Lie group or Frölicher Lie groups, state an Ambrose–Singer theorem that enlarges the one stated in [J.-P. Magnot, Structure groups and holonomy in infinite dimensions, Bull. Sci. Math.128 (2004) 513–529], and conclude with a differential geometric treatment of KP hierarchy. The examples of Lie groups that are studied are principally those obtained by enlarging some graded Frölicher (Lie) algebras such as formal q-series of the quantum algebra of pseudo-differential operators. These deformations can be defined for classical pseudo-differential operators but they are used here on formal pseudo-differential operators in order to get a differential geometric framework to deal with the KP hierarchy that is known to be completely integrable with formal power series. Here, we get an integration of the Zakharov–Shabat connection form by means of smooth sections of a (differential geometric) bundle with structure group, some groups of q-deformed operators. The integration obtained by Mulase [Complete integrability of the Kadomtsev–Petviashvili equation Adv. Math.54 (1984) 57–66], and the key tools he developed, are totally recovered on the germs of the smooth maps of our construction. The tool coming from (classical) differential geometry used in this construction is the holonomy group, on which we have an Ambrose–Singer-like theorem: the Lie algebra is spanned by the curvature elements. This result is proved for any connection a diffeological principal bundle with structure group a regular Frölicher Lie group. The case of a (classical) Lie group modeled on a complete locally convex topological vector space is also recovered and the work developed in [J.-P. Magnot, Difféologie du fibré d'Holonomie en dimension infinie, Math. Rep. Canadian Roy. Math. Soc.28(4) (2006); J.-P. Magnot, Structure groups and holonomy in infinite dimensions, Bull. Sci. Math. 128 (2004) 513–529] is completed.
On the Jones polynomial of 2n-plat presentations of knots

In this paper, a method is given to calculate the Jones polynomial of the 6-plat presentations of knots by using a representation of the braid group $\mathbb{B}_6$ into a group of $5\times 5$ matrices. We also can calculate the Jones polynomial of the $2n$-plat presentations of knots by generalizing the method for the 6-plat presentations of knots.
Immune Protective Efficacy of Recombinant Outer Membrane Protein H of Pasteurella multocida B:2 Associated with Hemorrhagic Septicemia in Pakistan

P. multocida B: 2 is a Gram-negative, small, non-flagellated, pleomorphic coccobacillus. It does possess different types of outer membrane proteins (OMP’s) which assist in interaction with host cells. The outer membrane protein H (OmpH) of Pasteurella multocida B:2 is a major transmembrane porin that can be used as a subunit vaccine and development of diagnostic kit against hemorrhagic septicemia (HS) because of its immunogenic nature. Pasteurella multocida has economic importance because of endemic and epizootic diseases in domestic and wild animals. This bacterium is an opportunistic pathogen of upper respiratory tracts of wild and domestic animals and birds as well as in livestock . The ompH gene was am- plified with in-house designed primers, the amplified gene (1002 bp) was cloned into pET 40-b (+) vector and transformed into E. coli BL21 (DE3) competent cells using heat shock transformation method to get expression. The product size was confirmed by restriction digestion. The rOmpH protein was purified by immobilized metal affinity chromatography by using His-Ni resins to get desired protein and charac- terized qualitatively by SDS-PAGE by using His antibodies and western blotting. Once purified the immunogenicity of rOmpH was evaluated in BALB/c mice. The expression of recombinant OmpH protein (rOmpH) resulted in its accumulation in cytosol. The purified rOmpH protein had a molecular weight of 36 kDa and concentration around 0.973 mg/mL. The BALB/c mice group injected with 100 ng of purified rOmpH exhibited significant protection (80%) when challenged with LD50 of P. multocida B:2. From the obtained results it is evident that rOmpH can be used as subunit vaccine against P. multocida B:2 and the purified rOmpH can also be further used to develop diagnostic test i.e., ELISA to screen and assess the immune response of cattle and buffaloes against P. multocida B:2 in developing countries like Pakistan.
Analytic lie extensions of number fields with cyclic fixed points and tame ramification

— Let p be a prime number and K an algebraic number field. What is the arithmetic structure of Galois extensions L/K having p-adic analytic Galois group Γ = Gal(L/K)? The celebrated Tame Fontaine-Mazur conjecture predicts that such extensions are either deeply ramified (at some prime dividing p) or ramified at an infinite number of primes. In this work, we take up a study (initiated by Boston) of this type of question under the assumption that L is Galois over some subfield k of K such that [K : k] is a prime = p. Letting σ be a generator of Gal(K/k), we study the constraints posed on the arithmetic of L/K by the cyclic action of σ on Γ, focusing on the critical role played by the fixed points of this action, and their relation to the ramification in L/K. The method of Boston works only when there are no non-trivial fixed points for this action. We show that even in the presence of arbitrarily many fixed points, the action of σ places severe arithmetic conditions on the existence of finitely and tamely ramified uniform p-adic analytic extensions over K, which in some instances leads us to be able to deduce the non-existence of such extensions over K from their non-existence over k.
Giant magneto-photoelectric effect in suspended graphene

We study the optical response of a suspended, monolayer graphene field-effect transistor structure in magnetic fields of up to 9 T (quantum Hall regime). With an illumination power of only 3 μW, we measure a photocurrent of up to 400 nA (without an applied bias) corresponding to a photo-responsivity of 0.13 A W−1, which we believe to be one of the highest values ever measured in single-layer graphene. We discuss possible mechanisms for generating this strong photo-response (17 electron–hole pairs per 100 incident photons). Based on our experimental findings, we believe that the most likely scenario is a ballistic two-stage process including carrier multiplication via Auger-type inelastic Coulomb scattering at the graphene edge.
Variational Methods and Planar Elliptic Growth

A nested family of growing or shrinking planar domains is called a Laplacian growth process if the normal velocity of each domain's boundary is proportional to the gradient of the domain's Green function with a fixed singularity on the interior. In this paper we review the Laplacian growth model and its key underlying assumptions, so that we may consider a generalization to so-called elliptic growth, wherein the Green function is replaced with that of a more general elliptic operator--this models, for example, inhomogeneities in the underlying plane. In this paper we continue the development of the underlying mathematics for elliptic growth, considering perturbations of the Green function due to those of the driving operator, deriving characterizations and examples of growth, developing a weak formulation of growth via balayage, and discussing of a couple of inverse problems in the spirit of Calder\'on. We conclude with a derivation of a more delicate, reregularized model for Hele-Shaw flow.