pinecone/core-2020-05-10-deduplication huggingface dataset:
Probabilistic Performance Modelling when Using Partial Reconfiguration to Accelerate Streaming Applications with Non-deterministic Task Scheduling

Many streaming applications composed of multiple tasks self-adapt their tasks’ execution at runtime as response to the processed data. This type of application promises a better solution to context switches at the cost of a non-deterministic task scheduling. Partial reconfiguration is a unique feature of FPGAs that not only offers a higher resource reuse but also performance improvements when properly applied. In this paper, a probabilistic approach is used to estimate the acceleration of streaming applications with unknown task schedule thanks to the application of partial reconfiguration. This novel approach provides insights in the feasible acceleration when partially reconfiguring regions of the FPGA are partially reconfigured in order to exploit the available resources by processing multiple tasks in parallel. Moreover, the impact of how different strategies or heuristics affect to the final performance is included in this analysis. As a result, not only an estimation of the achievable acceleration is obtained, but also a guide at the design stage when searching for the highest performance
The zero sets of slice regular functions and the open mapping theorem

A new class of regular quaternionic functions, defined by power series in a
natural fashion, has been introduced in recent years. Several results of the
theory recall the classical complex analysis, whereas other results reflect the
peculiarity of the quaternionic structure. A more recent paper identified a
larger class of domains, on which the study of regular functions is most
natural and not limited to the study of quaternionic power series. In the
present paper we extend some basic results concerning the algebraic and
topological properties of the zero set to regular functions defined on these
domains. We then use these results to prove the Maximum and Minimum Modulus
Principles and a version of the Open Mapping Theorem in this new setting.Comment: 13 page
New views of crystal symmetry guided by profound admiration of the
  extraordinary works of Grassmann and Clifford

This paper shows how beginning with Justus Grassmann's work, Hermann
Grassmann was influenced in his mathematical thinking by crystallography. H.
Grassmann's Ausdehnungslehre in turn had a decisive influence on W.K. Clifford
in the genesis of geometric algebras. Geometric algebras have been expanded to
conformal geometric algebras, which provide an ideal framework for modern
computer graphics. Within this framework a new visualization of
three-dimensional crystallographic space groups has been created. The complex
beauty of this new visualization is shown by a range of images of a diamond
cell. Mathematical details are given in an appendix.Comment: 11 pages, 8 figures, 2 tables. arXiv admin note: substantial text
  overlap with arXiv:1306.159
Homological algebra of semimodules and semicontramodules: Semi-infinite
  homological algebra of associative algebraic structures

We develop the basic constructions of homological algebra in the
(appropriately defined) unbounded derived categories of modules over algebras
over coalgebras over noncommutative rings (which we call semialgebras over
corings). We define double-sided derived functors SemiTor and SemiExt of the
functors of semitensor product and semihomomorphisms, and construct an
equivalence between the exotic derived categories of semimodules and
semicontramodules.
  Certain (co)flatness and/or (co)projectivity conditions have to be imposed on
the coring and semialgebra to make the module categories abelian (and the
cotensor product associative). Besides, for a number of technical reasons we
mostly have to assume that the basic ring has a finite homological dimension
(no such assumptions about the coring and semialgebra are made).
  In the final sections we construct model category structures on the
categories of complexes of semi(contra)modules, and develop relative
nonhomogeneous Koszul duality theory for filtered semialgebras and
quasi-differential corings.
  Our motivating examples come from the semi-infinite cohomology theory.
Comparison with the semi-infinite (co)homology of Tate Lie algebras and graded
associative algebras is established in appendices, and the semi-infinite
homology of a locally compact topological group relative to an open profinite
subgroup is defined. An application to the correspondence between complexes of
representations of an infinite-dimensional Lie algebra on the complementary
central charge levels ($c$ and $26-c$ for the Virasoro) is worked out.Comment: Dedicated to the memory of my father. LaTeX 2e, 310 pages. With
  appendices coauthored by S.Arkhipov and D.Rumynin. v.12: changes in the
  Introduction, additions to Section 0 and Appendix D, small improvements in
  Appendix C and elsewhere, subtitle added -- this is intended as the final
  arXiv version; v.13: abstract updated, LaTeX file unchanged (the publisher's
  version is more complete
Transfer Functions for Pairs of Wandering Subspaces

Gohm, R. (2012)., Transfer functions for pairs of wandering subspaces, In: Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations, 221, pp.385-398 21st International Workshop on Operator Theory and Applications, Berlin, July 2010. Arendt, W., Ball, J. A., Behrndt, J., Forster, K-H., Mehrmann, V., Trunk, C. (eds.)To a pair of subspaces wandering with respect to a row isometry we associate a transfer function which in general is multi-Toeplitz and in interesting special cases is multi-analytic. Then we describe in an expository way how characteristic functions from operator theory as well as transfer functions from noncommutative Markov chains fit into this scheme.authorsversio
Computing Linear Matrix Representations of Helton-Vinnikov Curves

Helton and Vinnikov showed that every rigidly convex curve in the real plane
bounds a spectrahedron. This leads to the computational problem of explicitly
producing a symmetric (positive definite) linear determinantal representation
for a given curve. We study three approaches to this problem: an algebraic
approach via solving polynomial equations, a geometric approach via contact
curves, and an analytic approach via theta functions. These are explained,
compared, and tested experimentally for low degree instances.Comment: 19 pages, 3 figures, minor revisions; Mathematical Methods in
  Systems, Optimization and Control, Birkhauser, Base
Negative time delay for wave reflection from a one-dimensional
  semi-harmonic well

It is reported that the phase time of particles which are reflected by a
one-dimensional semi-harmonic well includes a time delay term which is negative
for definite intervals of the incoming energy. In this interval, the absolute
value of the negative time delay becomes larger as the incident energy becomes
smaller. The model is a rectangular well with zero potential energy at its
right and a harmonic-like interaction at its left.Comment: 6 pages, 5 eps figures. Talk presented at the XXX Workshop on
  Geometric Methods in Physics, Bialowieza, Poland, 201
A singularly perturbed Dirichlet problem for the Poisson equation in a
  periodically perforated domain. A functional analytic approach

Let $\Omega$ be a sufficiently regular bounded open connected subset of
$\mathbb{R}^n$ such that $0 \in \Omega$ and that $\mathbb{R}^n \setminus
\mathrm{cl}\Omega$ is connected. Then we take $(q_{11},\dots, q_{nn})\in
]0,+\infty[^n$ and $p \in Q\equiv \prod_{j=1}^{n}]0,q_{jj}[$. If $\epsilon$ is
a small positive number, then we define the periodically perforated domain
$\mathbb{S}[\Omega_{p,\epsilon}]^{-} \equiv \mathbb{R}^n\setminus \cup_{z \in
\mathbb{Z}^n}\mathrm{cl}\bigl(p+\epsilon \Omega +\sum_{j=1}^n
(q_{jj}z_j)e_j\bigr)$, where $\{e_1,\dots,e_n\}$ is the canonical basis of
$\mathbb{R}^n$. For $\epsilon$ small and positive, we introduce a particular
Dirichlet problem for the Poisson equation in the set
$\mathbb{S}[\Omega_{p,\epsilon}]^{-}$. Namely, we consider a Dirichlet
condition on the boundary of the set $p+\epsilon \Omega$, together with a
periodicity condition. Then we show real analytic continuation properties of
the solution as a function of $\epsilon$, of the Dirichlet datum on $p+\epsilon
\partial \Omega$, and of the Poisson datum, around a degenerate triple with
$\epsilon=0$.Comment: arXiv admin note: substantial text overlap with arXiv:1306.667
Transmutations and spectral parameter power series in eigenvalue
  problems

We give an overview of recent developments in Sturm-Liouville theory
concerning operators of transmutation (transformation) and spectral parameter
power series (SPPS). The possibility to write down the dispersion
(characteristic) equations corresponding to a variety of spectral problems
related to Sturm-Liouville equations in an analytic form is an attractive
feature of the SPPS method. It is based on a computation of certain systems of
recursive integrals. Considered as families of functions these systems are
complete in the $L_{2}$-space and result to be the images of the nonnegative
integer powers of the independent variable under the action of a corresponding
transmutation operator. This recently revealed property of the Delsarte
transmutations opens the way to apply the transmutation operator even when its
integral kernel is unknown and gives the possibility to obtain further
interesting properties concerning the Darboux transformed Schr\"{o}dinger
operators.
  We introduce the systems of recursive integrals and the SPPS approach,
explain some of its applications to spectral problems with numerical
illustrations, give the definition and basic properties of transmutation
operators, introduce a parametrized family of transmutation operators, study
their mapping properties and construct the transmutation operators for Darboux
transformed Schr\"{o}dinger operators.Comment: 30 pages, 4 figures. arXiv admin note: text overlap with
  arXiv:1111.444
Ordinary differential equations in algebras of generalized functions

A local existence and uniqueness theorem for ODEs in the special algebra of
generalized functions is established, as well as versions including parameters
and dependence on initial values in the generalized sense. Finally, a Frobenius
theorem is proved. In all these results, composition of generalized functions
is based on the notion of c-boundedness.Comment: LaTeX, 18 pages. An earlier version was presented at the 8th ISAAC
  Congress in Moscow, August 22 - 27, 2011. in S. Molahajloo, S. Pilipovi\'c,
  J. Toft, M.W. Wong (eds.): Pseudo-Differential Operators, Generalized
  Functions and Asymptotics. Operator Theory: Advances and Applications, vol.
  231, pp. 253--270, Birkh\"auser, Basel 201
A Survey on the Krein-von Neumann Extension, the corresponding Abstract
  Buckling Problem, and Weyl-Type Spectral Asymptotics for Perturbed Krein
  Laplacians in Nonsmooth Domains

In the first (and abstract) part of this survey we prove the unitary
equivalence of the inverse of the Krein--von Neumann extension (on the
orthogonal complement of its kernel) of a densely defined, closed, strictly
positive operator, $S\geq \varepsilon I_{\mathcal{H}}$ for some $\varepsilon
>0$ in a Hilbert space $\mathcal{H}$ to an abstract buckling problem operator.
  This establishes the Krein extension as a natural object in elasticity theory
(in analogy to the Friedrichs extension, which found natural applications in
quantum mechanics, elasticity, etc.).
  In the second, and principal part of this survey, we study spectral
properties for $H_{K,\Omega}$, the Krein--von Neumann extension of the
perturbed Laplacian $-\Delta+V$ (in short, the perturbed Krein Laplacian)
defined on $C^\infty_0(\Omega)$, where $V$ is measurable, bounded and
nonnegative, in a bounded open set $\Omega\subset\mathbb{R}^n$ belonging to a
class of nonsmooth domains which contains all convex domains, along with all
domains of class $C^{1,r}$, $r>1/2$.Comment: 68 pages. arXiv admin note: extreme text overlap with arXiv:0907.144
The expressiveness of spider diagrams augmented with constants

Spider diagrams are a visual language for expressing logical statements or constraints. Several sound and complete spider diagram systems have been developed and it has been shown that they are equivalent in expressive power to monadic first order logic with equality. However, these sound and complete spider diagram systems do not contain syntactic elements analogous to constants in first order predicate logic. We extend the spider diagram language to include constant spiders which represent specific individuals. Formal semantics are given for the extended diagram language. We prove that this extended system is equivalent in expressive power to the language of spider diagrams without constants and, hence, equivalent to monadic first order logic with equality
Notes on the Parity Conjecture

This is an expository article, based on a lecture course given at CRM
Barcelona in December 2009. The purpose of these notes is to prove, in a
reasonably self-contained way, that finiteness of the Tate-Shafarevich group
implies the parity conjecture for elliptic curves over number fields. Along the
way, we review local and global root numbers of elliptic curves and their
classification, and discuss some peculiar consequences of the parity
conjecture.Comment: minor corrections, to appear in a CRM Advanced Courses volume
  "Elliptic curves, Hilbert modular forms and Galois deformations"; 43 page
Hamilton-Jacobi-Bellman Equations on Multi-Domains

International audienceA system of Hamilton Jacobi (HJ) equations on a partition of $\R^d$ is considered, and a uniqueness and existence result of viscosity solution is analyzed. While the notion of viscosity notion is by now well known, the question of uniqueness of solution, when the Hamiltonian is discontinuous, remains an important issue. A uniqueness result has been derived for a class of problems, where the behavior of the solution, in the region of discontinuity of the Hamiltonian, is assumed to be irrelevant and can be ignored (see reference [10]) . Here, we provide a new uniqueness result for a more general class of Hamilton-Jacobi equations
Hermitian clifford analysis

This paper gives an overview of some basic results on Hermitian Clifford analysis, a refinement of classical Clifford analysis dealing with functions in the kernel of two mutually adjoint Dirac operators invariant under the action of the unitary group. The set of these functions, called Hermitian monogenic, contains the set of holomorphic functions in several complex variables. The paper discusses, among other results, the Fischer decomposition, the Cauchy–Kovalevskaya extension problem, the axiomatic radial algebra, and also some algebraic analysis of the system associated with Hermitian monogenic functions. While the Cauchy–Kovalevskaya extension problem can be carried out for the Hermitian monogenic system, this system imposes severe constraints on the initial Cauchy data. There exists a subsystem of the Hermitian monogenic system in which these constraints can be avoided. This subsystem, called submonogenic system, will also be discussed in the paper
Discrete Clifford analysis

This survey is intended as an overview of discrete Clifford analysis and its current developments. Since in the discrete case one has to replace the partial derivative with two difference operators, backward and forward partial difference, one needs to modify the main tools for a development of a discrete function theory, such as the replacement of a real Clifford algebra by a complexified Clifford algebra or of the classic Weyl relations by so-called S-Weyl relations. The main results, like Cauchy integral formula, Fischer decomposition, CK-extension, and Taylor series, will be derived. To give a better idea of the differences between the discrete and continuous case, this chapter contains the problem of discrete Hardy spaces as well as some discrete objects which do not have an equivalent object in continuous Clifford analysis, such as the CK-extension of a discrete Delta function
Introductory clifford analysis

In this chapter an introduction is given to Clifford analysis and the underlying Clifford algebras. The functions under consideration are defined on Euclidean space and take values in the universal real or complex Clifford algebra, the structure and properties of which are also recalled in detail. The function theory is centered around the notion of a monogenic function, which is a null solution of a generalized Cauchy–Riemann operator, which is rotation invariant and factorizes the Laplace operator. In this way, Clifford analysis may be considered as both a generalization to higher dimension of the theory of holomorphic functions in the complex plane and a refinement of classical harmonic analysis. A notion of monogenicity may also be associated with the vectorial part of the Cauchy–Riemann operator, which is called the Dirac operator; some attention is paid to the intimate relation between both notions. Since a product of monogenic functions is, in general, no longer monogenic, it is crucial to possess some tools for generating monogenic functions: such tools are provided by Fueter’s theorem on one hand and the Cauchy–Kovalevskaya extension theorem on the other hand. A corner stone in this function theory is the Cauchy integral formula for representation of a monogenic function in the interior of its domain of monogenicity. Starting from this representation formula and related integral formulae, it is possible to consider integral transforms such as Cauchy, Hilbert, and Radon transforms, which are important both within the theoretical framework and in view of possible applications
Anatomy of quantum chaotic eigenstates

International audienceThe eigenfunctions of quantized chaotic systems cannot be described by explicit formulas, even approximate ones. This survey summarizes (selected) analytical approaches used to describe these eigenstates, in the semiclassical limit. The levels of description are macroscopic (one wants to understand the quantum averages of smooth observables), and microscopic (one wants informations on maxima of eigenfunctions, "scars" of periodic orbits, structure of the nodal sets and domains, local correlations), and often focusses on statistical results. Various models of "random wavefunctions" have been introduced to understand these statistical properties, with usually good agreement with the numerical data. We also discuss some specific systems (like arithmetic ones) which depart from these random models
Poisson smooth structures on stratified symplectic spaces

In this paper we introduce the notion of a smooth structure on a stratified
space, the notion of a Poisson smooth structure and the notion of a weakly
symplectic smooth structure on a stratified symplectic space, refining the
concept of a stratified symplectic Poisson algebra introduced by Sjamaar and
Lerman. We show that these smooth spaces possess several important properties,
e.g. the existence of smooth partitions of unity. Furthermore, under mild
conditions many properties of a symplectic manifold can be extended to a
symplectic stratified space provided with a smooth Poisson structure, e.g. the
existence and uniqueness of a Hamiltonian flow, the isomorphism between the
Brylinski-Poisson homology and the de Rham homology, the existence of a
Leftschetz decomposition on a symplectic stratified space. We give many
examples of stratified symplectic spaces possessing a Poisson smooth structure
which is also weakly symplectic.Comment: 21 page, final version, to appear in the Proceedings of the 6-th
  World Conference on 21st Century Mathematic
The entropy of black holes: a primer

After recalling the definition of black holes, and reviewing their energetics
and their classical thermodynamics, one expounds the conjecture of Bekenstein,
attributing an entropy to black holes, and the calculation by Hawking of the
semi-classical radiation spectrum of a black hole, involving a thermal
(Planckian) factor. One then discusses the attempts to interpret the black-hole
entropy as the logarithm of the number of quantum micro-states of a macroscopic
black hole, with particular emphasis on results obtained within string theory.
After mentioning the (technically cleaner, but conceptually more intricate)
case of supersymmetric (BPS) black holes and the corresponding counting of the
degeneracy of Dirichlet-brane systems, one discusses in some detail the
``correspondence'' between massive string states and non-supersymmetric
Schwarzschild black holes.Comment: 51 pages, 4 figures, talk given at the "Poincare seminar" (Paris, 6
  December 2003), to appear in Poincare Seminar 2003 (Birkhauser
Looking back at superfluid helium

A few years after the discovery of Bose Einstein condensation in several
gases, it is interesting to look back at some properties of superfluid helium.
After a short historical review, I comment shortly on boiling and evaporation,
then on the role of rotons and vortices in the existence of a critical velocity
in superfluid helium. I finally discuss the existence of a condensate in a
liquid with strong interactions, and the pressure variation of its superfluid
transition temperature.Comment: Conference "Bose Einstein Condensation", Institut henri Poincare,
  Paris, 29 march 200
Work fluctuations, transient violations of the second law and
  free-energy recovery methods: Perspectives in Theory and Experiments

In this report I discuss fluctuation theorems and transient violations of the
second law of thermodynamics in small systems. Special emphasis is placed on
free-energy recovery methods in the framework of non-equilibrium
single-molecule pulling experiments. The treatment is done from a unified
theoretical-experimental perspective and emphasizes how these experiments
contribute to our understanding of the thermodynamic behavior of small systemsComment: 35 pages, 16 figures (Latex). Talk given at the Poincare semina
Regularity results and parametrices of semi-linear boundary problems of
  product type

This short note describes the benefit one obtains from a specific
construction of a family of parametrices for a class of elliptic boundary value
problems perturbed by non-linear terms of product type. The construction is
based on the Boutet de Monvel calculus of pseudo-differential boundary
operators for the linear elliptic parts, and on paradifferential operators for
the product terms.Comment: 7 pages. Conference proceeding in a preprint version. The final
  version was published by Springer in 200
Large deviations for polling systems

Related INRIA Research report available at : http://hal.inria.fr/docs/00/07/27/62/PDF/RR-3892.pdfInternational audienceWe aim at presenting in short the technical report, which states a sample path large deviation principle for a resealed process n-1 Qnt, where Qt represents the joint number of clients at time t in a single server 1-limited polling system with Markovian routing. The main goal is to identify the rate function. A so-called empirical generator is introduced, which consists of Q t and of two empirical measures associated with S t the position of the server at time t. The analysis relies on a suitable change of measure and on a representation of fluid limits for polling systems. Finally, the rate function is solution of a meaningful convex program
Learning programming with an RTS based Serious Game

International audienceThis paper presents a prototype of a Serious Game that aims to entice gamers to learn computer programming by using a multiplayer real time strategy game (RTS). In this type of game, a player gives orders to his/her units to carry out operations (i.e. moving, building, and so forth). Typically, these instructions are given by clicking on a map with the mouse. The goal of this project is to encourage players to give these orders through programming. This game is intended for computer science students in higher education and can be used across both university and professional curricula. The programming languages used are C or C++