Miracle-dz/UniFAR-FTUs huggingface dataset:
Derived Commutator Complete Algebras and Relative Koszul Duality for Operads

We prove that a connected commutator (or NC) complete associative algebra can be recovered in the derived setting from its abelianization together with its natural induced structure. Specifically, we prove an equivalence between connected derived commutator complete associative algebras and connected commutative algebras equipped with a coaction of the comonad arising from the adjunction between associative and commutative algebras. This provides a Koszul dual description of connected derived commutator (or NC) complete associative algebras and furthermore may be interpreted as a theory of relative Koszul duality for the associative operad relative to the commutative operad. We also prove analogous results in the setting of En-algebras. That is, we develop a theory of commutator complete En-algebras and a theory of relative Koszul duality for the En operad relative to the commutative operad. We relate the derived commutator filtration on associative and En-algebras to the filtration on the associative and En operad whose associated graded is the Poisson and shifted Poisson operad Pn. We argue that the derived commutator filtration on associative algebras (and En-algebras) are a relative analogue of the Goodwillie tower of the identity functor on the model category of associative algebras (and En-algebras) relative to the model category of commutative algebras.
An Overlapping Domain Decomposition Preconditioner for the Helmholtz equation

In this paper, based on the overlapping domain decomposition method (DDM) proposed in \cite{Leng2015}, an one step preconditioner is proposed to solve 2D high frequency Helmholtz equation. The computation domain is decomposed in both $x$ and $y$ directions, and the local solution on each subdomain is updated simultaneously in one iteration, thus there is no sweeping along certain directions. In these ways, the overlapping DDM is similar to the popular DDM for Poisson problem. The one step preconditioner simply take the restricted source on each subdomain, solve the local problems and summarize the local solutions on all subdomains including their PML area. The complexity of solving the problem with the preconditioner is $O(N n_{\text{iter}})$, where $n_{\text{iter}}$ is the number of iteration, and it is shown numerically that $n_{\text{iter}}$ is proportional to the number of subdomains in one direction. 2D Helmholtz problem with nearly a billion unknowns are solved efficiently with the preconditioner on massively parallel machines.
The MAXI mission on the International Space Station

Monitor of All-sky X-ray Image (MAXI) is the first astrophysical payload which will be mounted on the Japanese Experiment Module Exposed Facility of International Space Station in 2004. It is designed for monitoring all-sky in the x-ray band by scanning with slat collimators and slit apertures. Its angular resolution and scanning period are approximately 1 arc degree and 90 minutes, respectively. MAXI employs two types of X-ray camera. One is Gas slit Camera (GSC), the detectors of which are 1D position sensitive proportional counters. Its position resolution is approximately 1.0 mm along carbon anode wires. GSC covers the 2.0 - 30 keV energy band. We have found an interesting feature in the energy response: monochromatic X-rays are detected with a peculiar hard tail in the spectra. The physical mechanism causing the hard tail is still unclear. The other camera is Solid-state Slit Camera (SSC). We employ a pair of SSCs, each of which consists of sixteen CCD chips. Each CCD has 1024 X 1024 pixels, and each pixel is 24 X 24 micrometers. The CCDs are to be operated at -60 degree using Peltier coolers. SSC covers an energy range of 0.5 - 10.0 keV. The test counters and test chips are evaluated in NASDA, Riken, and Osaka-University. The continuous Ethernet down link will enable us to alert the astronomers in all over the world to the appearance of X-ray transients, novae, bursts, flares etc. In this paper we will report on the current status of the MAXI mission.
Mechanism of proton transport in hexagonal ice

In polycrystalline samples of hexagonal ice both Bjerrum defect dynamics and translational diffusion of protons have been identified by deuteron nuclear magnetic resonance stimulated echo experiments. The temperature dependence of these processes in combination with literature data of tracer diffusion coefficients reveals that the material transport originates from interstitial mediated diffusion of intact water molecules. The jump length of the self-interstitials can be estimated to be 1.5 to 4 times the size of interstitial cages. The time scale associated with the slower component of this two-step mechanism contradicts (in parts) the standard interpretation of the dielectric Debye relaxation.
Second-order Bounds of Gaussian Kernel-based Functions and its Application to Nonlinear Optimal Control with Stability

Guaranteeing stability of a designed control system is a challenging problem in data-driven control approaches such as Gaussian process (GP)-based control. The reason is that the inequality conditions, which are used in ensuring the stability, should be evaluated for all states in the state space, meaning that an infinite number of inequalities must be evaluated. Previous research introduced the idea of using a finite number of sampled states with the bounds of the stability inequalities near the samples. However, high-order bounds with respect to the distance between the samples are essential to decrease the number of sampling. From the standpoint of control theory, the requirement is not only evaluating stability but also simultaneously designing a controller. This paper overcomes theses two issues to stabilize GP-based dynamical systems. Second-order bounds of the stability inequalities are derived whereas existing approaches use first-order bounds. The proposed method obtaining the bounds are widely applicable to various functions such as polynomials, Gaussian processes, Gaussian mixture models, and sum/product functions of them. Unifying the derived bounds and nonlinear optimal control theory yields a stabilizing (sub-)optimal controller for GP dynamics. A numerical simulation demonstrates the stability performance of the proposed approach.
On a twisted Reidemeister torsion

Given a finite simplicial complex, a unimodular representation of its fundamental group and a closed twisted cochain of odd degree, we define a twisted version of the Reidemeister torsion, extending a previous definition of V. Mathai and S. Wu. The main tool is a complex of piecewise smooth currents, defined by J. Dupont.
Quasi-projective relation algebras and directed cylindric algebras are categorially equivalent

We show that quasi-projective relation algebras and directed cylindric algebras are equivalent categorialy. We work out a Godels second incompleteness theorem for finite varibale fragments of first order logic. We show that distinct set theories (like one with CH, and another with its negation) give rise to equationally distinct simple directed cylindric algebras. This correspondance was worked out for quasi projective relation algebras (with a distinguished element corresponding to membership relation). The idea of the proof is that the Sagi representation of directed cylindric algebras preserve well-foundnes. Finally, using that the functor defined preserves order, we show that the class of directed cylindric algebras have the superamalgmation property.
Fully Adaptive Multilevel Stochastic Collocation Method for Randomized Elliptic PDEs

In this paper, we propose and analyse a new adaptive multilevel stochastic collocation method for randomized elliptic PDEs. A hierarchical sequence of adaptive mesh refinements for the spatial approximation is combined with adaptive anisotropic sparse Smolyak grids in the stochastic space in such a way as to minimize computational cost. We provide a rigorous analysis for the convergence and computational complexity of the adaptive multilevel algorithm. Two numerical examples demonstrate the reliability of an error control by adaptive methods and the significant decrease in complexity versus uniform spatial refinements and single-level stochastic sampling methods.
Energy Concentration for Min-Max Solutions of the Ginzburg-Landau Equations on Manifolds with $b_1(M)\neq 0$

We establish a new estimate for the Ginzburg-Landau energies $E_{\epsilon}(u)=\int_M\frac{1}{2}|du|^2+\frac{1}{4\epsilon^2}(1-|u|^2)^2$ of complex-valued maps $u$ on a compact, oriented manifold $M$ with $b_1(M)\neq 0$, obtained by decomposing the harmonic component $h_u$ of the one-form $ju:=u^1du^2-u^2du^1$ into an integral and fractional part. We employ this estimate to show that, for critical points $u_{\epsilon}$ of $E_{\epsilon}$ arising from the two-parameter min-max construction considered by the author in previous work, a nontrivial portion of the energy must concentrate on a stationary, rectifiable $(n-2)$-varifold as $\epsilon\to 0$.
Relative geodesics in the special Euclidean group

We introduce a measurement (the discrepancy) of the minimum energy needed to transform from a standard parametrized planar curve c0 to an observed curve c1. To this end, we say that a curve of transformations in the special Euclidean group SE(2) is admissible if it maps the source curve to the target curve under the point-wise action of SE(2) on the plane. After endowing the group SE(2) with a left-invariant metric, we define a relative geodesic in SE(2) to be a critical point of the energy functional associated to the metric, over all admissible curves. The discrepancy is then defined as the value of the energy of the minimizing relative geodesic. In the first part of the paper, we derive a scalar ODE which is a necessary condition for a curve in SE(2) to be a relative geodesic, and we discuss some of the properties of the discrepancy. In the second part of the paper, we consider discrete curves, and by means of a variational principle, we derive a system of discrete equations for the relative geodesics. We finish with several examples.
A classification of small linear functors

We extend Goodwillie's classification of finitary linear functors to arbitrary small functors. That is we show that every small linear simplicial functor from spectra to simplicial sets is weakly equivalent to a filtered colimit of representable functors represented in cofibrant spectra. Moreover, we present this classification as a Quillen equivalence of the category of small functors from spectra to simplicial sets equipped with the linear model structure and the opposite of the pro-category of spectra with the strict model structure.
Top Local Cohomology Modules Are Almost Always Non-Artinian

Let $(R,\mathfrak m)$ be a Noetherian local ring, $I$ an ideal of $R$ and $M$ a weakly finite or a coatomic $R$-module of dimension $n$. In this article, we resolve the Artinianness and non-Artinianness of top local cohomology modules, $H^{cd(I,M)}_I(M)$, in all cases except in the case $cd(I,M)=n-1$ and $dim(R/{I+Ann(M)})>1$ for which we have some sorter results under certain conditions.
A new class of accelerated regularization methods, with application to bioluminescence tomography

In this paper we propose a new class of iterative regularization methods for solving ill-posed linear operator equations. The prototype of these iterative regularization methods is in the form of second order evolution equation with a linear vanishing damping term, which can be viewed not only as an extension of the asymptotical regularization, but also as a continuous analog of the Nesterov’s acceleration scheme. New iterative regularization methods are derived from this continuous model in combination with appropriate numerical discretization schemes such as damped symplectic methods. The regularization property as well as convergence rates and acceleration effects under the Hölder-type source conditions of both continuous and discretized methods are proven. The second part of this paper is concerned with the application of the newly developed accelerated iterative regularization methods to the diffusion-based bioluminescence tomography, which is modeled as an inverse source problem in elliptic partial differential equations with both Dirichlet and Neumann boundary data. A novel mathematical formulation is proposed so that the discrepancy principle can be applied to stop the iteration procedure without the usage of Sobolev embedding constants. Several numerical examples, as well as acomparison with the state-of-the-art methods, are given to show the accuracy and the acceleration effect of the new methods.
Hypoellipticity and Local Solvability in Gevrey Classes

Let P be a linear partial differential operator with coefficients in the Gevrey class Gs. We prove first that if P is s-hypoelliptic then its transposed operator tP is s-locally solvable, thus extending to the Gevrey classes the well-known analogous result in the C∞class. We prove also that if P is s-hypoelliptic then its null space is finite dimensional and its range is closed; this implies an index theorem for s-hypoelliptic operators. Generalizations of these results to other classes of functions are also considered.
Study of positive weak solutions to a degenerated singular problem

For any bounded smooth domain $\Omega$ of $\mathbb{R}^N$ with $N\geq 2$, we provide existence, uniqueness and regularity results for weak solutions to the degenerated singular problem \begin{gather*} \begin{cases} -\operatorname{div}(\mathcal A(x,\nabla u))=\frac{f}{u^\delta}\,\,\text{ in }\,\,\Omega, u>0\text{ in }\Omega,\,\, u = 0 \text{ on } \partial\Omega, \end{cases} \end{gather*} where $\delta>0$, $f$ be a non-negative function belong to some Lebesgue space and $\mathcal{A}:\Omega\times\mathbb{R}^N\to\mathbb{R}^N$ is a Carath\'eodory function satisfying some growth conditions depending upon an element lying in the Muckenhoupt class of weights.
Quantum one-cocycles for knots

We give a method to construct non symmetric solutions of a global tetrahedron equation from solutions of the Yang-Baxter equation. The solution in the HOMFLYPT case gives rise to the rst combinatorial quantum 1-cocycle which represents a non trivial cohomology class in the topological moduli space of long knots. We conjecture that the quotient of its values on Hatchers loop and on the rotation around the long axis is related to the simplicial volume of the knot complement in the 3-sphere and we prove this for the gure eight knot. Surprisingly, the formula for the solution in the HOMFLYPT case of the positive global tetrahedron equation gives also a solution in the case of the 2-variable Kauman
Lectures on Three-point Functions in N=4 Supersymmetric Yang-Mills Theory

This is a pedagogical review on the integrability-based approach to the three-point function in N=4 supersymmetric Yang-Mills theory. We first discuss the computation of the structure constant at weak coupling and show that the result can be recast as a sum over partitions of the rapidities of the magnons. We then introduce a non-perturbative framework, called the "hexagon approach", and explain how one can use the symmetries (i.e. superconformal and gauge symmetries) and integrability to determine the structure constants. This article is based on the lectures given in Les Houches Summer School "Integrability: From statistical systems to gauge theory" in June 2016.
Invariant measure of the stochastic Allen-Cahn equation: the regime of small noise and large system size

We study the invariant measure of the one-dimensional stochastic Allen Cahn equation for a small noise strength and a large but finite system with so-called Dobrushin boundary conditions, i.e., inhomogeneous $\pm 1$ Dirichlet boundary conditions that enforce at least one transition layer from $-1$ to $1$. (Our methods can be applied to other boundary conditions as well.) We are interested in the competition between the "energy'' that should be minimized due to the small noise strength and the "entropy'' that is induced by the large system size. Specifically, in the context of system sizes that are exponential with respect to the inverse noise strength---up to the ``critical'' exponential size predicted by the heuristics---we study the extremely strained large deviation event of seeing \emph{more than the one transition layer} between $\pm 1$ that is forced by the boundary conditions. We capture the competition between energy and entropy through upper and lower bounds on the probability of these unlikely extra transition layers. Our bounds are sharp on the exponential scale and imply in particular that the probability of having one and only one transition from $-1$ to $+1$ is exponentially close to one. Our second result then studies the distribution of the transition layer. In particular, we establish that, on a super-logarithmic scale, the position of the transition layer is approximately uniformly distributed. In our arguments we use local large deviation bounds, the strong Markov property, the symmetry of the potential, and measure-preserving reflections.
BLACK STRINGS, BLACK RINGS AND STATE-SPACE MANIFOLD

State-space geometry is considered, for diverse three and four parameter nonspherical horizon rotating black brane configurations, in string theory and M-theory. We have explicitly examined the case of unit Kaluza–Klein momentum D1D5P black strings, circular strings, small black rings and black supertubes. An investigation of the state-space pair correlation functions shows that there exist two classes of brane statistical configurations, viz. the first category divulges a degenerate intrinsic equilibrium basis, while the second yields a nondegenerate, curved, intrinsic Riemannian geometry. Specifically, the solutions with finitely many branes expose that the two charged rotating D1D5 black strings and three charged rotating small black rings consort real degenerate state-space manifolds. Interestingly, arbitrary valued M5-dipole charged rotating circular strings and Maldacena–Strominger–Witten black rings exhibit nondegenerate, positively curved, comprehensively regular state-space configurations. Furthermore, the state-space geometry of single bubbled rings admits a well-defined, positive definite, everywhere regular and curved intrinsic Riemannian manifold; except for the two finite values of conserved electric charge. We also discuss the implication and potential significance of this work for the physics of black holes in string theory.
PROTESTING IS NOT EVERYTHING: ANALYZING TWITTER USE DURING ELECTORAL EVENTS IN NON-DEMOCRATIC CONTEXT

Despite the fact that during political protests, Twitter usage has been substantially studied in various contexts, there are still some significant gaps in our understanding of the ways that this microblogging network is employed in regular political happenings, e.g., elections, particularly in authoritarian countries. As a result, it remains unclear if citizens in non-democratic countries use Twitter to protest at the time of regular political events as the time of uprisings or not. This investigation tries to address this gap by providing some empirical evidence from the Iranian Twittersphere during the 2017 presidential election. Having employed networked framing theory, we combined textual and network analytic approaches to investigate a sample of 10,416 tweets of the most influential users in the retweet (RT) network. Findings demonstrate that Iranian users did not significantly challenge the regime and power relations in Iran. They framed the election in a non-critical way dealing with routine political and election frays and debates. They also preferred to attack politicians rather than discuss contentious and deliberate politics. Thus, this research reveals that Twitter is not always a tool for protesting against non-democratic regimes. At the time of electoral events, it could be used as an ordinary communication platform.
A Minimal Model Program without flips

We introduce a new vector space associated to projective variety, the Weil Neron-Severi space, which we show is finitely generated and contains the usual Neron-Severi space as a subspace. We define the Nef cone of Weil divisor and the cone of Weil curves. We study these cones, and prove a new Cone theorem. We use this theorem to propose a Minimal Model Program without flips.
An analytical study of ion-acoustic solitary waves in a plasma consisting of two-temperature electrons and warm drift ions

Propagation of ion-acoustic waves in a multicomponent plasma consisting of warm positive ions with stream velocity and two-temperature electrons has been theoretically investigated. New analytical solutions with sufficient and necessary conditions are obtained for the existence of ion-acoustic solitary waves in the plasma. It is seen that the drifting ions and two temperature electrons have key roles on the formation of ion-acoustic solitary waves in a multicomponent plasma. The critical values of the ion temperature and phase velocity of the solitary waves have been numerically estimated, which would be applicable to various physical situations.
A GRAPHICAL CALCULUS FOR 2-BLOCK SPALTENSTEIN VARIETIES

Abstract We generalise statements known about Springer fibres associated to nilpotents with two Jordan blocks to Spaltenstein varieties. We study the geometry of generalised irreducible components (i.e. Bialynicki-Birula cells) and their pairwise intersections. In particular, we develop a graphical calculus that encodes their structure as iterated fibre bundles with ℂℙ1 as base spaces, and compute their cohomology. At the end, we present a connection with coloured cobordisms generalising the construction of Khovanov (M. Khovanov, A categorification of the Jones polynomial, Duke Math. J. 101(3) (2000), 359–426) and Stroppel (C. Stroppel, Parabolic category O, perverse sheaves on Grassmannians, Springer fibres and Khovanov homology, Compositio Mathematica145(4) (2009), 954–992).
Basic zeta functions and some applications in physics

It is the aim of these lectures to introduce some basic zeta functions and their uses in the areas of the Casimir effect and Bose-Einstein condensation. A brief introduction into these areas is given in the respective sections. We will consider exclusively spectral zeta functions, that is zeta functions arising from the eigenvalue spectrum of suitable differential operators. There is a set of technical tools that are at the very heart of understanding analytical properties of essentially every spectral zeta function. Those tools are introduced using the well-studied examples of the Hurwitz, Epstein and Barnes zeta function. It is explained how these different examples of zeta functions can all be thought of as being generated by the same mechanism, namely they all result from eigenvalues of suitable (partial) differential operators. It is this relation with partial differential operators that provides the motivation for analyzing the zeta functions considered in these lectures. Motivations come for example from the questions "Can one hear the shape of a drum? " and "What does the Casimir effect know about a boundary? ". Finally "What does a Bose gas know about its container? "
Optical detection of quasi-static actuation of nanoelectromechanical systems

An all optical method designed to test the functionality of nanoelectromechanical systems is presented. Silicon tweezers consisting of freestanding nanometer-sized prongs are prepared using electron beam lithography. Images of the tweezers structures are taken by scanning confocal microscopy while the prongs are electrostatically actuated under a low frequency ac voltage. The images, which are demodulated at the actuation frequency and its higher harmonics, clearly resolve the actuating parts of the tweezers. An actuation amplitude down to 6 pm (rms)/Hz can be detected.