Miracle-dz/UniFAR-FTUs huggingface dataset:
A fast multilevel algorithm for graph clustering and community detection

One of the most useful measures of cluster quality is the modularity of a partition, which measures the difference between the number of the edges joining vertices from the same cluster and the expected number of such edges in a random (unstructured) graph. In this paper we show that the problem of finding a partition maximizing the modularity of a given graph G can be reduced to a minimum weighted cut problem on a complete graph with the same vertices as G. We then show that the resulted minimum cut problem can be efficiently solved with existing software for graph partitioning and that our algorithm finds clusterings of a better quality and much faster than the existing clustering algorithms.
Characterization of the law for 3D stochastic hyperviscous fluids

We consider the 3D hyperviscous Navier-Stokes equations in vorticity form, where the dissipative term $-\Delta \vec \xi$ of the Navier-Stokes equations is substituted by $(-\Delta)^{1+c} \vec \xi $. We investigate how big the correction term $c$ has to be in order to prove, by means of Girsanov transform, that the vorticity equations are equivalent (in law) to easier reference equations obtained by neglecting the stretching term. This holds as soon as $c>\frac 12$, improving previous results obtained with $c>\frac 32$ in a different setting in [5,14].
BOUNDARY LIMITATION OF WAVE NUMBERS IN TAYLOR-VORTEX FLOW

We report experimental results for a boundary-mediated wavenumber-adjustment mechanism and for a boundary-limited wavenumber-band of Taylor-vortex flow (TVF). The system consists of fluid contained between two concentric cylinders with the inner one rotating at an angular frequency $\Omega$. As observed previously, the Eckhaus instability (a bulk instability) is observed and limits the stable wavenumber band when the system is terminated axially by two rigid, non-rotating plates. The band width is then of order $\epsilon^{1/2}$ at small $\epsilon$ ($\epsilon \equiv \Omega/\Omega_c - 1$) and agrees well with calculations based on the equations of motion over a wide $\epsilon$-range. When the cylinder axis is vertical and the upper liquid surface is free (i.e. an air-liquid interface), vortices can be generated or expelled at the free surface because there the phase of the structure is only weakly pinned. The band of wavenumbers over which Taylor-vortex flow exists is then more narrow than the stable band limited by the Eckhaus instability. At small $\epsilon$ the boundary-mediated band-width is linear in $\epsilon$. These results are qualitatively consistent with theoretical predictions, but to our knowledge a quantitative calculation for TVF with a free surface does not exist.
Connectedness of the moduli of Sp(2p,2q)-Higgs bundles

Using the Morse-theoretic techniques introduced by Hitchin, we prove that the moduli space of $\Sp(2p,2q)$-Higgs bundles over a compact Riemann surface of genus $g\geq 2$ is connected. In particular, this implies that the moduli space of representations of the fundamental group of the surface in $\Sp(2p,2q)$ is connected.
Brown's moduli spaces of curves and the gravity operad

This paper is built on the following observation: the purity of the mixed Hodge structure on the cohomology of Brown's moduli spaces is essentially equivalent to the freeness of the dihedral operad underlying the gravity operad. We prove these two facts by relying on both the geometric and the algebraic aspects of the problem: the complete geometric description of the cohomology of Brown's moduli spaces and the coradical filtration of cofree cooperads. This gives a conceptual proof of an identity of Bergstr\"om-Brown which expresses the Betti numbers of Brown's moduli spaces via the inversion of a generating series. This also generalizes the Salvatore-Tauraso theorem on the nonsymmetric Lie operad.
Products of multisymplectic manifolds and homotopy moment maps

Multisymplectic geometry admits an operation that has no counterpart in symplectic geometry, namely, taking the product of two multisymplectic manifolds endowed with the wedge product of the multisymplectic forms. We show that there is an L-infinity-embedding of the L-infinity-algebra of observables of the individual factors into the observables of the product, and that homotopy moment maps for the individual factors induce a homotopy moment map for the product. As a by-product, we associate to every multisymplectic form a curved L-infinity-algebra, whose curvature is the multisymplectic form itself.
Finite Random Domino Automaton

Finite version of Random Domino Automaton (FRDA) - recently proposed a toy model of earthquakes - is investigated. Respective set of equations describing stationary state of the FRDA is derived and compared with infinite case. It is shown that for the system of big size, these equations are coincident with RDA equations. We demonstrate a non-existence of exact equations for size N bigger then 4 and propose appropriate approximations, the quality of which is studied in examples obtained within Markov chains framework. We derive several exact formulas describing properties of the automaton, including time aspects. In particular, a way to achieve a quasi-periodic like behaviour of RDA is presented. Thus, based on the same microscopic rule - which produces exponential and inverse-power like distributions - we extend applicability of the model to quasi-periodic phenomena.
Bounded eigenfunctions in the real hyperbolic space

The purpose of this paper is to describe the space Eλ. The Harnack inequality (see, e.g., [6, page 199]) implies that the gradient of a bounded λ-eigenfunction f is bounded by a constant which only depends on λ and on the sup norm of f. This implies, using the Ascoli theorem, that the space Eλ with the sup norm is a Banach space. For s ∈ C, we set λs = s(n − 1 − s). The basic example of a λs-eigenfunction is provided by x → P(x, ξ), where P(x, ξ) is the Poisson kernel of H and ξ is any point of the boundary at infinity ∂H of H. Any λs-eigenfunctions can be described in terms of hyperfunctions on ∂H. Namely, for any λs-eigenfunction, there is a hyperfunction on ∂H such that
Infrared divergences for free quantum fields in cosmological spacetimes

We investigate the nature of infrared divergences for the free graviton and inflaton two-point functions in flat Friedman–Lemaître–Robertson–Walker spacetime. These divergences arise because the momentum integral for these two-point functions diverges in the infrared. It is straightforward to see that the power of the momentum in the integrand can be increased by 2 in the infrared using large gauge transformations, which are sufficient for rendering these two-point functions infrared finite for slow-roll inflation. In other words, if the integrand of the momentum integral for these two-point functions behaves like , where p is the momentum, in the infrared, then it can be made to behave like by large gauge transformations. On the other hand, it is known that, if one smears these two-point functions in a gauge-invariant manner, the power of the momentum in the integrand is changed from to . This fact suggests that the power of the momentum in the integrand for these two-point functions can be increased by 4 using large gauge transformations. In this paper we show that this is indeed the case. Thus, the two-point functions for the graviton and inflaton fields can be made finite by large gauge transformations for a large class of potentials and states in single-field inflation.
Surgery on $\widetilde{\Bbb{SL}}\times\Bbb{E}^n$-manifolds

We show that closed S̃L×En-manifolds (with n ≥ 2) are topologically rigid, if n ≥ 2, and are rigid up to s-cobordism, if n = 1. The “Borel Conjecture” asserts that aspherical closed manifolds are topologically rigid, i.e. are determined up to homeomorphism by their fundamental groups. Farrell and Jones have proven this for infrasolvmanifolds (of dimensions ≥ 4) [5] and for smooth manifolds (of dimensions ≥ 5) with Riemannian metrics of nonpositive curvature [4], while Nicas and Stark have shown it to hold for manifolds (of dimensions ≥ 5) admitting an effective codimension-2 toral action of hyperbolic type [7]. The work of Farrell and Jones was used in [9] to establish topological rigidity for M ×Dk for all orientable closed irreducible 3-manifolds M with β1(M) > 0 and all k ≥ 3. In our main result (Theorem 4) we shall adapt the approach of [9] to show that manifolds with finite covering spaces admitting such toral actions are also topologically rigid. (These are the natural higher dimensional analogues of geometric Seifert fibred spaces.) In particular, all closed S̃L × E-manifolds with n ≥ 2 are topologically rigid, although such manifolds do not admit metrics of nonpositive curvature [2], and may not admit codimension-2 toral actions. (See Corollary A.) The most immediate applications of our work are to low dimensions. In Corollary B we complete the characterization of aspherical geometric 4-manifolds up to s-cobordism, in terms of fundamental group and Euler characteristic. (This was established for all other 4-dimensional geometries of aspherical type in Theorem 9.11 of [6].) In passing we also show (in Theorem 2) that noncompact complete S̃L-manifolds of finite volume are homeomorphic to complete H2×E1-manifolds of finite volume. (This was stated without proof in [10].) 1991 Mathematics Subject Classification. 57R67, 57N16.
Elements of Modern X-ray Physics

Preface. Acknowledgements. Notes on the Use of this Book. X-rays and Their Interaction with Matter. Sources of X-rays. Refraction and Reflection from Interfaces. Kinematical Diffraction. Diffraction by Perfect Crystals. Photoelectric Absorption. Resonant Scattering. Appendix A: Scattering and Absorption Cross-Sections. Appendix B: Classical Electric Dipole Radiation. Appendix C: Quantization of the Electromagnetic Field. Appendix D: Gaussian Statistics. Appendix E: Fourier Transforms. Appendix F: Comparison of X-rays with Neutrons. Appendix G: MATLAB Computer Programs. List of Tables. References. Index.
Laminar Branched Surfaces in 3-manifolds

We define a laminar branched surface to be a branched surface satisfying the following conditions: (1) Its horizontal boundary is incompressible; (2) there is no monogon; (3) there is no Reeb component; (4) there is no sink disk (after eliminating trivial bubbles in the branched surface). The first three conditions are standard in the theory of branched surfaces, and a sink disk is a disk branch of the branched surface with all branch directions of its boundary arcs pointing inwards. We will show in this paper that every laminar branched surface carries an essential lamination, and any essential lamination that is not a lamination by planes is carried by a laminar branched surface. This implies that a 3-manifold contains an essential lamination if and only if it contains a laminar branched surface.
Two-valued local sets of the 2D continuum Gaussian free field: connectivity, labels, and induced metrics

We study two-valued local sets, $\mathbb{A}_{-a,b}$, of the two-dimensional continuum Gaussian free field (GFF) with zero boundary condition in simply connected domains. Intuitively, $\mathbb{A}_{-a,b}$ is the (random) set of points connected to the boundary by a path on which the values of the GFF remain in $[-a,b]$. For specific choices of the parameters $a, b$ the two-valued sets have the law of the CLE$_4$ carpet, the law of the union of level lines between all pairs of boundary points, or, conjecturally, the law of the interfaces of the scaling limit of XOR-Ising model. Two-valued sets are the closure of the union of countably many SLE$_4$ type of loops, where each loop comes with a label equal to either $-a$ or $b$. One of the main results of this paper describes the connectivity properties of these loops. Roughly, we show that all the loops are disjoint if $a+b \geq 4\lambda$, and that their intersection graph is connected if $a + b < 4\lambda$. This also allows us to study the labels (the heights) of the loops. We prove that the labels of the loops are a function of the set $\mathbb{A}_{-a,b}$ if and only if $a\neq b$ and $2\lambda \leq a+b < 4\lambda$ and that the labels are independent given the set if and only if $a = b = 2\lambda$. We also show that the threshold for the level-set percolation in the 2D continuum GFF is $-2\lambda$. Finally, we discuss the coupling of the labelled CLE$_4$ with the GFF. We characterise this coupling as specific local set coupling, and show how to approximate these local sets. We see how in these approximations the labels naturally encode distances to the boundary.
Characterization and topological rigidity of Nöbeling manifolds

Table of Contents Introduction and preliminaries: * Introduction * Preliminaries Reducing the proof of the main results to the construction of $n$-regular and $n$-semiregular $\mathcal{N}_n$-covers: * Approximation within an $\mathcal{N}_n$-cover * Constructing closed $\mathcal{N}_{n}$-covers * Carrier and nerve theorems * Anticanonical maps and semiregularity * Extending homeomorphisms by the use of a "brick partitionings" technique * Proof of the main results Constructing $n$-semiregular and $n$-regular $\mathcal{N}_n$-covers: * Basic constructions in $\mathcal{N}_{n}$-spaces * Core of a cover * Proof of Theorem 6.7 * Bibliography * Index
Integral bounds on curvature and Gromov–Hausdorff limits

We develop a new approach to, and somewhat extend, results of Cheeger, Colding and Tian (Geom. Funct. Anal. 12 (2002) 873–914), which give restrictions on the singular sets that can arise as Gromov‐Hausdorff limits in the presence of integral bounds on the curvature. The foundation of this approach is provided by a rigidity result for flat singular spaces, which has independent interest.
Dual little strings and their partition functions

We study the topological string partition function of a class of toric, double elliptically fibered Calabi-Yau threefolds $X_{N,M}$ at a generic point in the K\"ahler moduli space. These manifolds engineer little string theories in five dimensions or lower and are dual to stacks of M5-branes probing a transverse orbifold singularity. Using the refined topological vertex formalism, we explicitly calculate a generic building block which allows to compute the topological string partition function of $X_{N,M}$ as a series expansion in different K\"ahler parameters. Using this result we give further explicit proof for a duality found previously in the literature, which relates $X_{N,M}\sim X_{N',M'}$ for $NM=N'M'$ and $\text{gcd}(N,M)=\text{gcd}(N',M')$.
Conformal twists, Yang–Baxter σ-models & holographic noncommutativity

Expanding upon earlier results (Araujo et al 2017 Phys. Rev. D 95 105006), we present a compendium of σ-models associated with integrable deformations of AdS5 generated by solutions to homogenous classical Yang–Baxter equation. Each example we study from four viewpoints: conformal (Drinfeld) twists, closed string gravity backgrounds, open string parameters and proposed dual noncommutative (NC) gauge theory. Irrespective of whether the deformed background is a solution to supergravity or generalized supergravity, we show that the open string metric associated with each gravity background is undeformed AdS5 with constant open string coupling and the NC structure Θ is directly related to the conformal twist. One novel feature is that Θ exhibits ‘holographic noncommutativity’: while it may exhibit non-trivial dependence on the holographic direction, its value everywhere in the bulk is uniquely determined by its value at the boundary, thus facilitating introduction of a dual NC gauge theory. We show that the divergence of the NC structure Θ is directly related to the unimodularity of the twist. We discuss the implementation of an outer automorphism of the conformal algebra as a coordinate transformation in the AdS bulk and discuss its implications for Yang–Baxter σ-models and self-T-duality based on fermionic T-duality. Finally, we comment on implications of our results for the integrability of associated open strings and planar integrability of dual NC gauge theories.
Wave focusing and ensuing mean flow due to symmetry breaking in rotating fluids

Rotating fluids support waves. These inertial waves propagate obliquely through the fluid, with an angle that is fixed with respect to the rotation axis. Upon reflection, their wavelength is unchanged only when the wall obeys the local reflectional symmetry, that is, when it is either parallel or perpendicular to the rotation axis. For internal gravity waves in a density-stratified fluid, sloping boundaries thus break the symmetry of ray paths, in a two-dimensional container, predicting their focusing upon attractors: particular paths onto which the wave rays, and hence the energy, converge, and to which the wave energy returns after a small number of refections. Laboratory observations, presented here, show that, despite the intrinsic three-dimensionality of inertial waves, attractors still occur. The intensified wave energy on the attractor encourages centrifugal instabilities, leading to a mean flow. Evidence of this comes from dye spreading, observed to develop most rapidly over the location where the attractor reflects from the sloping wall, being the place where focusing and instabilities occur. This mean flow, resulting from the mixing of angular momentum, accompanying the intensification of the wave field at that location, has geophysical implications, because the ocean, atmosphere and Earth's liquid outer core can be regarded as asymmetrically contained. The relevance of wave focusing in a rotating, spherical shell, the modifications due to the addition of radial stratification, and its implications for observed equatorial current patterns and inertial oscillations are discussed. The well-known universality of oceanic, gravito-inertial wave spectra might reflect complementary, divergent (chaotic) wave-ray behaviour, which occurs in containers obeying the reflectional symmetry, but in which symmetry is broken in the horizontal plane. Periodic orbits still exist, but now repell.
K-theory of the moduli of bundles over a Riemann surface and deformations of the Verlinde algebra

I conjecture that index formulas for $K$-theory classes on the moduli of holomorphic $G$-bundles over a compact Riemann surface $\Sigma$ are controlled, in a precise way, by Frobenius algebra deformations of the Verlinde algebra of $G$. The Frobenius algebras in question are twisted $K$-theories of $G$, equivariant under the conjugation action, and the controlling device is the equivariant Gysin map along the "product of commutators" from $G^{2g}$ to $G$. The conjecture is compatible with naive virtual localization of holomorphic bundles, from $G$ to its maximal torus; this follows by localization in twisted $K$-theory.
Second-order symmetric Lorentzian manifolds: I. Characterization and general results

The n-dimensional Lorentzian manifolds with vanishing second covariant derivative of the Riemann tensor—2–symmetric spacetimes—are characterized and classified. The main result is that either they are locally symmetric or they have a covariantly constant null vector field, in this case defining a subfamily of Brinkmann's class in n dimensions. Related issues and applications are considered, and new open questions presented.
Homotopy morphisms between convolution homotopy Lie algebras

In previous works by the authors, a bifunctor was associated to any operadic twisting morphism, taking a coalgebra over a cooperad and an algebra over an operad, and giving back the space of (graded) linear maps between them endowed with a homotopy Lie algebra structure. We build on this result by using a more general notion of $\infty$-morphism between (co)algebras over a (co)operad associated to a twisting morphism, and show that this bifunctor can be extended to take such $\infty$-morphisms in either one of its two slots. We also provide a counterexample proving that it cannot be coherently extended to accept $\infty$-morphisms in both slots simultaneously. We apply this theory to rational models for mapping spaces.
A solution for the differences in the continuity of continuum among mathematicians

There are the longstanding differences in the continuity of continuum among mathematicians. Starting from studies on a mathematical model of contact, we construct a set that is in contact everywhere by using the original idea of Dedekind's cut and weakening Order axioms to violate Order axiom 1. It is proved that the existence of the set constructed can eliminate the differences in the continuity.
Two-node queueing network with a heavy-tailed random input: the strong stability case

We consider a two-node fluid network with batch arrivals of random size having a heavy-tailed distribution. We are interested in the tail asymptotics for the stationary distribution of a two-dimensional queue-length process. The tail asymptotics have been well studied for two-dimensional reflecting processes where jumps have either a bounded or an unbounded light-tailed distribution. However, presence of heavy tails totally changes the asymptotics. Here we focus on the case of strong stability where both nodes release fluid with su? ciently high speeds to minimise their mutual influence. We show that, like in the one-dimensional case, big jumps provide the main cause for queues to become large, but now they may have multi-dimensional features. For deriving these results, we develop an analytic approach that diff? ers from the traditional tail asymptotic studies, and obtain various weak tail equivalences. Then, in the case of one-dimensional subexponential jump-size distributions, we fi? nd the exact asymptotics based on the sample-path arguments.
Dynamical construction of K\"{a}hler-Einstein metrics

In this paper, I give a new construction of a K\"{a}hler-Einstein metrics on a smooth projective variety with ample canonical bundle. This result can be generalized to the construction of a singular K\"{a}hler-Einstein metric on a smooth projective variety of general type which gives an AZD of the canonical bundle. Also the variation of Bergman kernels and K\"{a}hler-Einstein volume form have been considered.
Finiteness Properties of Chevalley Groups over the Laurent Polynomial Ring over a Finite Field

We show that if G is a Chevalley group of rank n and F_q[t,t^{-1}] is the ring of Laurent polynomials over a finite field, then G(F_q[t,t^{-1}]) is of type F_{2n-1}. This bound is optimal because it is known -- and we show again -- that the group is not of type F_{2n}.
Cosmetic surgery and the link volume of hyperbolic 3–manifolds

We prove that for any V>0, there exist a hyperbolic manifold M_V, so that Vol(M_V) V. The proof requires study of cosmetic surgery on links (equivalently, fillings of manifolds with boundary tori). There is no bound on the number of components of the link (or boundary components). For statements, see the second part of the introduction. Here are two examples of the results we obtain: 1) Let K be a component of a link L in S^3. Then "most" slopes on K cannot be completed to a cosmetic surgery on L, unless K becomes a component of a Hopf link. 2) Let X be a manifold and \epsilon>0. Then all but finitely many hyperbolic manifolds obtained by filling X admit a geodesic shorter than \epsilon\ (note that this finite set may correspond to an infinitely many fillings).
On the inverse Magnus effect in free molecular flow

A Newton-inspired particle interaction model is introduced to compute the sideways force on spinning projectiles translating through a rarefied gas. The simple model reproduces the inverse Magnus force on a sphere reported by Borg, Soderholm and Essen [Phys. Fluids 15, 736 (2003)] using probability theory. Further analyses given for cylinders and parallelepipeds of rectangular and regular polygon section point to a universal law for this class of geometric shapes: when the inverse Magnus force is steady, it is proportional to one-half the mass M of gas displaced by the body.