Miracle-dz/UniFAR-FTUs huggingface dataset:
EMPIRICAL METHODS OF MODELING SELF-ORGANIZATION OF LEXICAL INNOVATIONS IN THE MENTAL LEXICON

The study Abstract. Owing to the large-scale national ideology for the modernization of public consciousness, it is relevant to consider the process of lexical innovations self-organization in a per-son’s mental lexicon along with other problems of Kazakh linguistics. A new style of scientific thinking – synergetics is proposed an appropriate methodology, universal principles to study such a complex system. It is possible to identify common patterns and processes of the evolution of the national language as a complex system and characterize lexical innovations in the Kazakh language by using a synergistic methodology. The synergetic methodological platform – is a complex of integrated theoretical and empirical methods as well as universal principles characterized by interdisciplinary features. The article analyzes the types of empirical methods and the possibility of achieving the results of synergetic modeling of self-organization of Kazakhized lexical innovations in the mental lexicon.
UNDER PRESSURE: STAR CLUSTERS AND THE NEUTRAL HYDROGEN MEDIUM OF TIDAL TAILS

Using archival data from ATCA, WHISP, and the Very Large Array, we have analyzed the H i emission of 22 tidal tail regions of the Mullan et al. sample of pairwise interacting galaxies. We have measured the column densities, line-of-sight velocity dispersions, and kinetic energy densities on ∼kpc scales. We also constructed a tracer of the line-of-sight velocity gradient over ∼10 kpc scales. We compared the distributions of these properties between regions that do and do not contain massive star cluster candidates (MV < −8.5; ∼104–106 M☉ as observed in Hubble Space Telescope WFPC2 VI data). In agreement with Maybhate et al., we find that a local, ∼kpc-scale column density of log ≳ 20.6 cm−2 is frequently required for detecting clustered star formation. This H i gas also tends to be turbulent, with line-of-sight velocity dispersions σlos ≈ 10–75 km s−1, implying high kinetic energy densities (log ΣKE > 46 erg pc−2). Thus, high H i densities and pressures, partly determined by the tail dynamical age and other interaction characteristics, are connected to large-scale cluster formation in tidal tails overall. Last, we find that the high mechanical energy densities of the gas are likely not generally due to feedback from star formation. Rather, these properties are more likely to be a cause of star formation than a result.
Note on Reversion, Rotation and Exponentiation in Dimensions Five and Six

The explicit matrix realizations of the reversion anti-automorphism and the spin group depend on the set of matrices chosen to represent a basis of 1 -vectors for a given Clifford algebra. On the other hand, there are iterative procedures to obtain bases of 1-vectors for higher dimensional Clifford algebras, starting from those for lower dimensional ones. For a basis of 1-vectors for Cl (0, 5), obtained by applying such procedures to the Pauli basis of 1-vectors for Cl(3,0), we find that the matrix form of reversion involves neither of the two standard representations of the symplectic bilinear form. However, by making use of the relation between 4 X 4 real matrices and the tensor product of the quaternions with themselves, the matrix form of reversion for this basis of 1-vectors is identified. The corresponding version of the Lie algebra of the spin group, has useful matrix properties which are explored. Next, the form of reversion for a basis of 1-vectors for Cl(0,6) obtained iteratively from Cl(0,0) is obtained. This is then applied to the task of computing exponentials of 5X 5 and 6X 6 real skew-symmetric matrices in closed form, by reducing this to the simpler task of computing exponentials of certain 4X 4 matrices. For the latter purpose closed form expressions for the minimal polynomials of these 4 X 4 matrices are obtained, without having to compute their eigenstructure. Finally, a novel representation of Sp(4)is provided which may be of independent interest. Among the byproducts of this work are natural interpretations for some members of an orthogonal basis for M(4, R) provided by the isomorphism with the quaternion tensor product, and a first principles approach to the spin groups in dimensions five and six.
Foot Drop Caused by Herpes Zoster L5 Radiculitis Mimicking Disk Herniation Electrophysiologically: A Case Report

A 63‐year‐old woman with severe pain in her left leg was admitted to an orthopedic clinic. Topical analgesic medication was initiated. After using the drugs, the patient experienced vesicular rashes on her leg. She discontinued the drug because she considered these rashes to be side effects. Lumbar magnetic resonance imaging (MRI) was performed because of increasing pain and motor weakness. MRI showed disc protrusion in three consecutive segments; however, there was no significant canal stenosis or root compression [Figure 1]. Therefore, the patient was referred to us on the 20th day of symptom onset.
A new proof of Halász’s theorem, and its consequences

Halász’s theorem gives an upper bound for the mean value of a multiplicative function $f$ . The bound is sharp for general such $f$ , and, in particular, it implies that a multiplicative function with $|f(n)|\leqslant 1$ has either mean value $0$ , or is ‘close to’ $n^{it}$ for some fixed $t$ . The proofs in the current literature have certain features that are difficult to motivate and which are not particularly flexible. In this article we supply a different, more flexible, proof, which indicates how one might obtain asymptotics, and can be modified to treat short intervals and arithmetic progressions. We use these results to obtain new, arguably simpler, proofs that there are always primes in short intervals (Hoheisel’s theorem), and that there are always primes near to the start of an arithmetic progression (Linnik’s theorem).
Slipknotting in Random Diagrams

The presence of slipknots in configurations of proteins and DNA has been shown to affect their functionality, or alter it entirely. Historically, polymers are modeled as polygonal chains in space. As an alternative to space curves, we provide a framework for working with subknots inside of knot diagrams via knotoid diagrams. We prove using a pattern theorem for knot diagrams that not only are almost all knot diagrams slipknotted, almost all unknot diagrams are slipknotted. This proves in the random diagram model a conjecture yet unproven in random space curve models. We also discuss conjectures on the enumeration of knotoid diagrams.
Semistable reduction for overconvergent F-isocrystals, IV: local semistable reduction at nonmonomial valuations

Abstract We complete our proof that given an overconvergent F-isocrystal on a variety over a field of positive characteristic, one can pull back along a suitable generically finite cover to obtain an isocrystal which extends, with logarithmic singularities and nilpotent residues, to some complete variety. We also establish an analogue for F-isocrystals overconvergent inside a partial compactification. By previous results, this reduces to solving a local problem in a neighborhood of a valuation of height 1 and residual transcendence degree zero. We do this by studying the variation of some numerical invariants attached to p-adic differential modules, analogous to the irregularity of a complex meromorphic connection. This allows for an induction on the transcendence defect of the valuation, i.e., the discrepancy between the dimension of the variety and the rational rank of the valuation.
Continuous orbit equivalence rigidity

We take the first steps towards a better understanding of continuous orbit equivalence, i.e., topological orbit equivalence with continuous cocycles. First, we characterize continuous orbit equivalence in terms of isomorphisms of $C^{\ast }$ -crossed products preserving Cartan subalgebras. This is the topological analogue of the classical result by Singer and Feldman-Moore in the measurable setting. Second, we turn to continuous orbit equivalence rigidity, i.e., the question whether for certain classes of topological dynamical systems, continuous orbit equivalence implies conjugacy. We show that this is not always the case by constructing topological dynamical systems (actions of free abelian groups and also non-abelian free groups) that are continuously orbit equivalent but not conjugate. Furthermore, we prove positive rigidity results. For instance, for solvable duality groups, general topological Bernoulli actions and certain subshifts of full shifts over finite alphabets are rigid.
Multiplicity estimates: A Morse-theoretic approach

The problem of estimating the multiplicity of the zero of a polynomial when restricted to the trajectory of a non-singular polynomial vector field, at one or several points, has been considered by authors in several different fields. The two best (incomparable) estimates are due to Gabrielov and Nesterenko. In this paper we present a refinement of Gabrielov's method which simultaneously improves these two estimates. Moreover, we give a geometric description of the multiplicity function in terms certain naturally associated polar varieties, giving a topological explanation for an asymptotic phenomenon that was previously obtained by elimination theoretic methods in the works of Brownawell, Masser and Nesterenko. We also give estimates in terms of Newton polytopes, strongly generalizing the classical estimates.
Limited packings of closed neighbourhoods in graphs

The k-limited packing number, $L_k(G)$, of a graph $G$, introduced by Gallant, Gunther, Hartnell, and Rall, is the maximum cardinality of a set $X$ of vertices of $G$ such that every vertex of $G$ has at most $k$ elements of $X$ in its closed neighbourhood. The main aim in this paper is to prove the best-possible result that if $G$ is a cubic graph, then $L_2(G) \geq |V (G)|/3$, improving the previous lower bound given by Gallant, \emph{et al.} In addition, we construct an infinite family of graphs to show that lower bounds given by Gagarin and Zverovich are asymptotically best-possible, up to a constant factor, when $k$ is fixed and $\Delta(G)$ tends to infinity. For $\Delta(G)$ tending to infinity and $k$ tending to infinity sufficiently quickly, we give an asymptotically best-possible lower bound for $L_k(G)$, improving previous bounds.
Selection-Mutation Differential Equations: Long-Time Behavior of Measure-Valued Solutions

We study the long-time behavior of solutions to a measure-valued selection-mutation model that we formulated in [10]. We establish permanence results for the full model, and we study the limiting behavior even when there is more than one strategy of a given fitness; a case that arises in applications. We show that for the pure selection case the solution of the dynamical system converges to a Dirac measure centered at the fittest strategy class provided that the support of the initial measure contains a fittest strategy; thus we term this Dirac measure an Asymptotically Stable Strategy (ASS). We also show that when the strategy space is discrete, the selection-mutation model with small mutation has a locally asymptotically stable equilibrium that attracts all initial conditions that are positive at the fittest strategy.
Ill-Posedness of the Third Order NLS Equation with Raman Scattering Term

We consider the ill-posedness and well-posedness of the Cauchy problem for the third order NLS equation with Raman scattering term on the one dimensional torus. It is regarded as a mathematical model for the photonic crystal fiber oscillator. Regarding the ill-posedness, we show the nonexistence of solutions in the Sobolev space and the norm inflation of the data-solution map under slightly different conditions, respectively. We also prove the local unique existence of solutions in the analytic function space.
Geometric structure of exact triangles consisting of projectively flat bundles on higher dimensional complex tori

The mirror dual objects corresponding to affine Lagrangian (multi) sections of a trivial special Lagrangian torus fibration T^{2n}--->T^n are holomorphic vector bundles on a mirror dual complex torus of dimension n via the homological mirror symmetry. In this paper, we construct a one-to-one correspondence between those holomorphic vector bundles and a certain kind of projectively flat bundles explicitly, by using the result of the classification of factors of automorphy of projectively flat bundles on complex tori. Furthermore, we give a geometric interpretation of the exact triangles consisting of projectively flat bundles on complex tori by focusing on the dimension of intersections of the corresponding affine Lagrangian submanifolds.
Containment Problems for Projections of Polyhedra and Spectrahedra

Spectrahedra are affine sections of the cone of positive semidefinite matrices which form a rich class of convex bodies that properly contains that of polyhedra. While the class of polyhedra is closed under linear projections, the class of spectrahedra is not. In this paper we investigate the problem of deciding containment of projections of polyhedra and spectrahedra based on previous works on containment of spectrahedra. The main concern is to study these containment problems by formulating them as polynomial nonnegativity problems. This allows to state hierarchies of (sufficient) semidefinite conditions by applying (and proving) sophisticated Positivstellens\"atze. We also extend results on a solitary sufficient condition for containment of spectrahedra coming from the polyhedral situation as well as connections to the theory of (completely) positive linear maps.
The critical probability for confetti percolation equals $1/2$

In the confetti percolation model, or two-coloured dead leaves model, radius one disks arrive on the plane according to a space-time Poisson process. Each disk is coloured back with probability p and white with probability 1−p. In this paper we show that the critical probability for confetti percolation equals 1/2. That is, if p > 1/2 then a.s. there is an unbounded curve in the plane all of whose points are black; while if p ≤ 1/2 then a.s. all connected components of the set of black points are bounded. This answers a question of Benjamini and Schramm [1].
Speed selection for coupled wave equations

We discuss models for coupled wave equations describing interacting fields, focusing on the speed of travelling wave solutions. In particular, we propose a general mechanism for selecting and tuning the speed of the corresponding (multi-component) travelling wave solutions under certain physical conditions. A number of physical models (molecular chains, coupled Josephson junctions, propagation of kinks in chains of adsorbed atoms and domain walls) are considered as examples.
Topics in Open Topological Strings

This thesis is based on some selected topics in open topological string theory which I have worked on during my Ph.D. It comprises an introductory part where I have focused on the points most needed for the later chapters, trading completeness for conciseness and clarity. Then, following [12], we discuss tadpole cancellation for topological strings where we mainly show how its implementation is needed for ensuring the same "odd" moduli decoupling encountered in the closed theory. Next we move to analyse how the open and closed effective field theories for the B model interact writing the complete Lagrangian. We first check it deriving some already known tree level amplitudes in term of target space quantities, and then we extend the recipe to new results; later we implement open closed duality from a target field theory perspective. This last subject is also analysed from a worldsheet point of view extending the analysis of [13]. Some ideas for future research are briefly reported.
COMPUTABILITY THEORY, NONSTANDARD ANALYSIS, AND THEIR CONNECTIONS

Abstract We investigate the connections between computability theory and Nonstandard Analysis. In particular, we investigate the two following topics and show that they are intimately related. (T.1) A basic property of Cantor space $2^ $ is Heine–Borel compactness: for any open covering of $2^ $, there is a finite subcovering. A natural question is: How hard is it to compute such a finite subcovering? We make this precise by analysing the complexity of so-called fan functionals that given any $G:2^ \to $, output a finite sequence $\langle f_0 , \ldots ,f_n \rangle $ in $2^ $ such that the neighbourhoods defined from $\overline {f_i } G\left( {f_i } \right)$ for $i \le n$ form a covering of $2^ $. (T.2) A basic property of Cantor space in Nonstandard Analysis is Abraham Robinson’s nonstandard compactness, i.e., that every binary sequence is “infinitely close” to a standard binary sequence. We analyse the strength of this nonstandard compactness property of Cantor space, compared to the other axioms of Nonstandard Analysis and usual mathematics. Our study of (T.1) yields exotic objects in computability theory, while (T.2) leads to surprising results in Reverse Mathematics. We stress that (T.1) and (T.2) are highly intertwined, i.e., our study is holistic in nature in that results in computability theory yield results in Nonstandard Analysis and vice versa.
Baumslag–Solitar groups, relative profinite completions and measure equivalence rigidity

We introduce an algebraic invariant for aperiodic inclusions of probability measure preserving (pmp) equivalence relations. We use this invariant to prove that every stable orbit equivalence between free pmp actions of direct products of non‐amenable Baumslag–Solitar groups whose canonical subgroup acts aperiodically, forces the number of factors of the products to be the same and the factors to be isomorphic after permutation. This generalizes some of the results obtained by Kida [‘Invariants of orbit equivalence relations and B aumslag– Solitar groups’, Tohoku Math. J. (2) 66 (2014) 205–258] and, moreover, provides new measure equivalence rigidity phenomena for Baumslag–Solitar groups. We also obtain a complete classification of direct products of relative profinite completions of Baumslag–Solitar groups, continuing recent work of Elder and Willis [‘Totally disconnected groups from Baumslag–Solitar groups’, Preprint, 2013, arXiv:1301.4775].
Algorithme d'aides à la décision pour Optimiser l'Ordonnancement des tâches de maintenance en temps-réel

L'approche presentee dans cet article est une contribution a la recherche portant sur l'optimisation de l'ordonnancement des taches de maintenance. Ce travail repond aux objectifs suivants : Decision en temps-reel (planification et ordonnancement), Allocation/affectation de ressources, Assurer une disponibilite minimum requise, Minimiser les temps retard en inserant les tâches dynamiques « maintenance corrective »
Discrete Algebraic Dynamical Systems

In this paper, we use a duality between the vector space of the multi-indexed sequences over a field and the vector subspace of the sequences with finite support over this field to characterize the closed subpaces of multi-indexed sequences. Then we prove that the polynomial operator in the shift which Oberst and Willems have introduced to define time invariant discrete linear dynamical systems is the adjoint of the polynomial multiplication. We end this paper by describing these systems.
Subdivision rules and the eight model geometries

Cannon and Swenson have shown that each hyperbolic 3-manifold group has a natural subdivision rule on the space at infinity, and that this subdivision rule captures the action of the group on the sphere. Explicit subdivision rules have also been found for some closed and finite-volume hyperbolic manifolds, as well as a few non-hyperbolic knot complements. We extend these results by finding explicit finite subdivision rules for closed manifolds of the E3, H2XR, S2XR, S3, and SL2(R) manifolds by examining model manifolds. Because all manifolds in these geometries are the same up to finite covers, the subdivision rules for these model manifolds will be very similar to subdivision rules for all other manifolds in their respective geometries. We also discuss the existence of subdivision rules for Nil and Sol geometries. We use Ken Stephenson's Circlepack to visualize the subdivision rules and the resulting space at infinity.
Dilute oriented loop models

We study a model of dilute oriented loops on the square lattice, where each loop is compatible with a fixed, alternating orientation of the lattice edges. This implies that loop strands are not allowed to go straight at vertices, and results in an enhancement of the usual O ( n ) ? > symmetry to U ( n ) ? > . The corresponding transfer matrix acts on a number of representations (standard modules) that grows exponentially with the system size. We derive their dimension and those of the centralizer by both combinatorial and algebraic techniques. A mapping onto a field theory permits us to identify the conformal field theory governing the critical range, n ≤ 1 ? > . We establish the phase diagram and the critical exponents of low-energy excitations. For generic n, there is a critical line in the universality class of the dilute O ( 2 n ) ? > model, terminating in an SU ( n + 1 ) ? > point. The case n = 1 maps onto the critical line of the six-vertex model, along which exponents vary continuously.
Generic Newton points and the Newton poset in Iwahori-double cosets

Abstract We consider the Newton stratification on Iwahori-double cosets in the loop group of a reductive group. We describe a group-theoretic condition on the generic Newton point, called cordiality, under which the Newton poset (that is, the index set for non-empty Newton strata) is saturated and Grothendieck’s conjecture on closures of the Newton strata holds. Finally, we give several large classes of Iwahori-double cosets for which this condition is satisfied by studying certain paths in the associated quantum Bruhat graph.
Computation of Minimal Graded Free Resolutions over $\mathbb{N}$-Graded Solvable Polynomial Algebras

It is shown that the methods and algorithms, developed in (A. Capani et al., Computing minimal finite free resolutions, {\it Journal of Pure and Applied Algebra}, (117& 118)(1997), 105 -- 117; M. Kreuzer and L. Robbiano, {\it Computational Commutative Algebra 2}, Springer, 2005. ) for computing minimal homogeneous generating sets of graded submodules and graded quotient modules of free modules over a commutative polynomial algebra, can be adapted for computing minimal homogeneous generating sets of graded submodules and graded quotient modules of free modules over a weighted $\mathbb{N}$-graded solvable polynomial algebra, where solvable polynomial algebras are in the sense of (A. Kandri-Rody and V. Weispfenning, Non-commutative Grobner bases in algebras of solvable type. {\it J. Symbolic Comput.}, 9(1990), 1--26). Consequently, algorithmic procedures for computing minimal finite graded free resolutions over weighted $\mathbb{N}$-graded solvable polynomial algebras are achieved.
Investigation of Silicon Nitride Shadowed Selective Area Growth as an Enabling Technology for GaN Vertical Device Processing

Conventional processing routes for wide bandgap semiconductors such as SiC and GaN for power device applications are known to reduce device performance via the generation of high-leakage defects and deactivation of dopants. Here, the characterization of a novel masking method Silicon Nitride Shadowed, Selective Area Growth (SNS-SAG) is presented. The masks’ ability to enable the growth of tall vertical features with smooth sidewalls, arrest and prevent the formation of screw dislocations, and resist in-diffusion of constituent masking materials is demonstrated via Cathodoluminescence (CL), Conductive Atomic Force Microscopy (C-AFM), and X-ray Photoelectron Spectroscopy (XPS).