Miracle-dz/UniFAR-FTUs huggingface dataset:
Quantum Black Holes, Elliptic Genera and Spectral Partition Functions

We study M-theory and D-brane quantum partition functions for microscopic black hole ensembles within the context of the AdS/CFT correspondence in terms of highest weight representations of infinite-dimensional Lie algebras, elliptic genera, and Hilbert schemes, and describe their relations to elliptic modular forms. The common feature in our examples lie in the modular properties of the characters of certain representations of the pertinent affine Lie algebras, and in the role of spectral functions of hyperbolic three-geometry associated with q-series in the calculation of elliptic genera. We present new calculations of supergravity elliptic genera on local Calabi-Yau threefolds in terms of BPS invariants and spectral functions, and also of equivariant D-brane elliptic genera on generic toric singularities. We use these examples to conjecture a link between the black hole partition functions and elliptic cohomology.
Constrained and unconstrained modes - Some modeling aspects of flexible spacecraft

Spacecraft that are partially rigid and partially flexible may be dynamically modeled in terms of either 'constrained' modes of vibration, for which the rigid part is held motionless, or the 'unconstrained' modes of the whole vehicle. A model 'completeness index' is defined for each expansion and used as a truncation criterion. Using as an example a large flexible platform with a rigid body at the center, it is shown that as the rigid portion of the vehicle becomes very small, a great many constrained modes are needed to achieve satisfactory model completeness. Otherwise, one finds an erroneous distribution of angular momentum among the modes. It is also shown that the importance of unconstrained modes is not necessarily ordered by frequency.
On acoustic propagation in exponential ocean surface waveguides

It has been observed experimentally that bubbly layers generated by breaking waves form nearly exponential waveguides near ocean surfaces and that noise propagation in such waveguides occurs in distinct frequency bands [D. M. Farmer and S. Vagle, J. Acoust. Soc. Am. 86, 1897 (1989)]. It was conjectured that the well‐defined frequency bands are due to the normal mode propagation of sound. Motivated by the experimental observations, a theory is presented to investigate the normal mode propagation in exponential waveguides, by analogy with the optical waveguides formed by diffusion [Z. Ye, Appl. Phys. Lett. 65, 3173 (1994)]. The theoretical results compare favorably with the experimental data. In addition, we show that a waveguide with an exponential sound speed profile has great mathematical convenience in that it has simple characteristic equations which can be solved in a closed form. The number of normal modes, which is shown to correspond to the number of discrete acoustic bands, can be determined by wa.
On the formation of streamwise vortices by plasma vortex generators

Abstract The streamwise vortices generated by dielectric-barrier-discharge plasma actuators in the laminar boundary layer were investigated using particle image velocimetry to understand the vortex-formation mechanisms. The plasma vortex generator was oriented along the primary flow direction to produce a body force in the spanwise direction. This created a spanwise-directed wall jet which interacted with the oncoming boundary layer to form a coherent streamwise vortex. It was found that the streamwise vortices were formed by the twisting and folding of the spanwise vorticity in the oncoming boundary layer into the outer shear layer of the spanwise wall jet, which added its own vorticity to increase the circulation along the actuator length. This is similar to the delta-shaped, vane-type vortex generator, except that the circulation was enhanced by the addition of the vorticity in the plasma jet. It was also observed that the plasma vortex was formed close to the wall with an enhanced wall-ward entrainment, which created strong downwash above the actuator.
ON CLUSTER SYSTEMS OF TENSOR PRODUCT SYSTEMS OF HILBERT SPACES

It is known that the spatial product of two product systems is intrinsic. Here we extend this result by analyzing subsystems of the tensor product of product systems. A relation with cluster systems is established. In a special case, we show that the amalgamated product of product systems through strictly contractive units is independent of the choices of the units. The amalgamated product in this case is isomorphic to the tensor product of the spatial product of the two and the type I product system of index one.
Variational Convergence Analysis With Smoothed-TV Interpretation

The problem of minimizing the least squares functional with a Fr\'echet differentiable, lower semi-continuous, convex penalizer $J$ is considered to be solved. The penalizer maps the functions of Banach space $\mathcal{V}$ into $\mathbb{R}_{+},$ $ J : \mathcal{V} \rightarrow \mathbb{R}_{+}. $ It is assumed that some given data $f^{\delta}$ is defined on a compact domain $\mathcal{G} \subset \mathbb{R}_{+}$ and in the class of Hilbert space, $f^{\delta} \in \mathcal{L}^{2}(\mathcal{G}). $ Then general Tikhonov functional associated with some given linear, compact and injective forward operator $\mathcal{T} : \mathcal{V} \rightarrow \mathcal{L}^{2}(\mathcal{G})$ is formulated as \begin{eqnarray} F_{\alpha}(\varphi, f^{\delta}) : & \mathcal{V} \times \mathcal{L}^{2}(\mathcal{G}) & \rightarrow \mathbb{R}_{+} \nonumber\\ & (\varphi, f^{\delta}) & \mapsto F_{\alpha}(\varphi, f^{\delta}) := \frac{1}{2}\Vert\mathcal{T}\varphi - f^{\delta}\Vert_{\mathcal{L}^{2}(\mathcal{G})}^2 + \alpha J(\varphi) . \nonumber \end{eqnarray} Convergence of the regularized solution $\varphi_{\alpha(\delta)} \in \mathrm{argmin}_{\varphi \in \mathcal{V}} F_{\alpha}(\varphi, f^{\delta})$ to the true solution $\varphi^{\dagger}$ is analysed by means of Bregman divergence. First part of this aims to provide some general convergence analysis for generally strongly convex functional $J$ in the cost functional $F_{\alpha}$. In this part the key observation is that strong convexity of the penalty term $J$ with its convexity modulus implies norm convergence in the Bregman metric sense. In the second part, this general analysis will be interepreted for the smoothed-TV functional. The result of this work is applicable for any strongly convex functional.
A note on some sub-Gaussian random variables

In [8] the author of this paper continued the research on the complex-valued discrete random variables $X_l(m,N)$ ($0\le l\le N-1$, $1\le M\le N)$ recently introduced and studied in [24]. Here we extend our results by considering $X_l(m,N)$ as sub-Gaussian random variables. Our investigation is motivated by the known fact thatthe so-called Restricted Isometry Property (RIP) introduced in [4] holds with high probability for any matrix generated by a sub-Gaussian random variable. Notice that sensing matrices with the RIP play a crucial role in Theory of compressive sensing. Our main results concern the proofs of the lower and upper bound estimates of the expected values of the random variables $|X_l(m,N)|$, $|U_l(m,N)|$ and $|V_l(m,N)|$, where $U_l(m,N)$ and $U_l(m,N)$ are the real and the imaginary part of $X_l(m,N)$, respectively. These estimates are also given in terms of related sub-Gaussian norm $\Vert \cdot\Vert_{\psi_2}$ considered in [28]. Moreover, we prove a refinement of the mentioned upper bound estimates for the real and the imaginary part of $X_l(m,N)$.
Twisted K-theory, Real $\mathcal{A}$-bundles and Grothendieck-Witt groups

We introduce a general framework to unify several variants of twisted topological $K$-theory. We focus on the role of finite dimensional real simple algebras with a product-preserving involution, showing that Grothendieck-Witt groups provide interesting examples of twisted $K$-theory. These groups are linked with the classification of algebraic vector bundles on real algebraic varieties.
Schr\"odinger operators with measure-valued potentials: semiboundedness and spectrum.

We study the 1-D Schr\"odinger operators in Hilbert space $L^{2}(\mathbb{R})$ with real-valued Radon measure $q'(x)$, $q\in \mathrm{BV}_{loc}(\mathbb{R})$ as potentials. New sufficient conditions for minimal operators to be bounded below and selfadjoint are found. For such operators a criterion for the discreteness of the spectrum is proved, which generalizes Molchanov's, Brinck's, and the Albeverio-Kostenko-Malamud criteria. The quadratic forms corresponding to the investigated operators are described.
Fast Newton Method for Sparse Logistic Regression

Sparse logistic regression has been developed tremendously in recent two decades, from its origination the $\ell_1$-regularized version by Tibshirani(1996) to the sparsity constrained models by Bahmani, Raj, and Boufounos (2013); Plan and Vershynin (2013). This paper is carried out on the sparsity constrained logistic regression through the classical Newton method. We begin with analysing its first optimality condition to acquire a strong $\tau$-stationary point for some $\tau>0$. This point enables us to equivalently derive a stationary equation system which is able to be efficiently solved by Newton method. The proposed method FNSLR, an abbreviation for Newton method for sparse logistic regression, enjoys a very low computational complexity, local quadratic convergence rate and termination within finite steps. Numerical experiments on random data and real data demonstrate its superior performance when against with seven state-of-the-art solvers.
Static output feedback simultaneous stabilization: ILMI approach

In this note, the static output feedback simultaneous stabilization problem is addressed using a matrix inequality approach. A necessary and sufficient condition for simultaneous stabilizability of r proper MIMO plants via static output feedback is obtained. It is proven that the existence of a stabilizing feedback gain which simultaneously stabilizes this set of plants is equivalent to that of the solution of a set of coupled quadratic matrix inequalities. An iterative LMI (ILMI) algorithm based on the linear matrix inequality technique is proposed to obtain the feedback gain. Illustrated examples show its effectiveness.
Constraint Reasoning Embedded Structured Prediction

Many real-world structured prediction problems need machine learning to capture data distribution and constraint reasoning to ensure structure validity. Nevertheless, constrained structured prediction is still limited in real-world applications because of the lack of tools to bridge constraint satisfaction and machine learning. In this paper, we propose CO nstraint RE asoning embedded S tructured P rediction ( Core-Sp ), a scalable constraint reasoning and machine learning integrated approach for learning over structured domains. We propose to embed decision diagrams, a popular constraint reasoning tool, as a fully-diﬀerentiable module into deep neural networks for structured prediction. We also propose an iterative search algorithm to automate the searching process of the best Core-Sp structure. We evaluate Core-Sp on three applications: vehicle dispatching service planning, if-then program synthesis, and text2SQL generation. The proposed Core-Sp module demonstrates superior performance over state-of-the-art approaches in all three applications. The structures generated with Core-Sp satisfy 100% of the constraints when using exact decision diagrams. In addition, Core-Sp boosts learning performance by reducing the modeling space via constraint satisfaction.
Nondivisible cycles on products of very general Abelian varieties

In this paper, we give a recipe for producing infinitely many nondivisible codimension 2 2 cycles on a product of two or more very general Abelian varieties. In the process, we introduce the notion of “field of definition” for cycles in the Chow group modulo (a power of) a prime. We show that for a quite general class of codimension 2 2 cycles, that we call “primitive cycles”, the field of definition is a ramified extension of the function field of a modular variety. This ramification allows us to use Nori’s isogeny method (modified by Totaro) to produce infinitely many nondivisible cycles. As an application, we prove the Chow group modulo a prime of a product of three or more very general elliptic curves is infinite, generalizing work of Schoen.
D-branes, quivers, and ALE instantons

Effective field theories in type I and II superstring theories for D-branes located at points in the orbifold C^2/Z_n are supersymmetric gauge theories whose field content is conveniently summarized by a `quiver diagram,' and whose Lagrangian includes non-metric couplings to the orbifold moduli: in particular, twisted sector moduli couple as Fayet-Iliopoulos terms in the gauge theory. These theories describe D-branes on resolved ALE spaces. Their spaces of vacua are moduli spaces of smooth ALE metrics and Yang-Mills instantons, whose metrics are explicitly computable. For U(N) instantons, the construction exactly reproduces results of Kronheimer and Nakajima.
On the Unbounded Picture of KK-Theory

In the founding paper on unbounded $KK$-theory it was established by Baaj and Julg that the bounded transform, which associates a class in $KK$-theory to any unbounded Kasparov module, is a surjective homomorphism (under a separability assumption). In this paper, we provide an equivalence relation on unbounded Kasparov modules and we thereby describe the kernel of the bounded transform. This allows us to introduce a notion of topological unbounded $KK$-theory, which becomes isomorphic to $KK$-theory via the bounded transform. The equivalence relation is formulated entirely at the level of unbounded Kasparov modules and consists of homotopies together with an extra degeneracy condition. Our degenerate unbounded Kasparov modules are called spectrally decomposable since they admit a decomposition into a part with positive spectrum and a part with negative spectrum.
$(4,-(2n+5))$-torus knot with only 1 normal ruling

The main purpose of this paper is to provide an infinite family of counter examples of the open problem mentioned in [2]. In particular, we present an infinite family of a particular Legendrian $(4,-(2n+5))$-torus knot, for each $n \geq 0$, which has only 1 normal ruling, but do not satisfy the even number of clasps condition of Theorem 3 of [2]. Thus, these normal rulings cannot imply the existence of a decomposable exact Lagrandian filling.
On the classifying space of the family of virtually cyclic subgroups

We study the minimal dimension of the classifying space of the family of virtually cyclic subgroups of a discrete group. We give a complete answer for instance if the group is virtually poly-Z, word-hyperbolic or countable locally virtually cyclic. We give examples of groups for which the difference of the minimal dimensions of the classifying spaces of virtually cyclic and of finite subgroups is -1, 0 and 1, and show in many cases that no other values can occur.
An extremely low profile, compact, and broadband tightly coupled patch array

A tightly coupled patch array (TCPA) is introduced to realize small‐size, extremely low profile planar antennas with broadband performance. Past approaches have used frequency selective surfaces (FSSs) as part of the substrate or ground plane (i.e., in passive mode) for also realizing low‐profile antennas. In contrast, the proposed TCPA employs an FSS aperture as the radiating structure (i.e., array antenna). A key aspect of the TCPA is the exploitation of differences in FSSs when operating in radiating and passive modes. Tight element coupling and periodic excitation are the keys for achieving broadband operation. In this paper, a small‐size, finite array is designed along with a very thin and compact feeding network. The designed TCPA resonated at 2.07 GHz with 5.6% impedance bandwidth (∣S11∣ < −10 dB), 4.4 dB realized gain (86% efficiency), and 23% gain bandwidth (3 dB drop). Of importance is that the overall aperture dimensions were only λ0/3 × λ0/3 and λ0/42 thick (including feeding network) at the midfrequency of operation. A preliminary TCPA antenna prototype was fabricated and tested. Both simulated and measured data show enhanced bandwidth as compared to the conventional microstrip patch antennas of the same size and thickness. However, as common for such extremely low profile microstrip antennas, the conductivity losses were augmented. Thus, the measured TCPA efficiency (50%) was smaller than computed.
Extended changing crossover operators to solve the traveling salesman problem

In order to efficiently obtain an approximate solution of the traveling salesman problem (TSP), the use of extended changing crossover operators (ECXO) which can substitute for any crossover operator of genetic algorithms (GAs) and ant colony optimization (ACO) for another crossover operator at any time is proposed. In this investigation, ECXO uses both ACO or edge recombination crossover (EX) and edge exchange crossover (EXX) in the early generations in order to create local optimum subpaths, and it uses edge assembly crossover (EAX) to create a global optimum solution after a certain number of generations. In EX or ACO any individual or any ant determines the next city it visits from the lengths of the edges or the amounts of pheromone deposited on the edges, where the pheromone indicates the lengths of tours that other ants have completed, thus generating local optimum paths. In EXX, the generated paths converge to a provisional optimal path. In EAX, a parent exchanges edges with another parent to create subcyclic paths, before restructuring the total cyclic path by combining the subcyclic paths so as to minimize the distances between them. In this paper the validity of ECXO is experimentally verified by using medium-sized problems from TSPLIB, and it is shown that ECXO can find the best solution earlier than EAX. © 2010 Wiley Periodicals, Inc. Electron Comm Jpn, 93(7): 1–16, 2010; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecj.10313
Viscous effects on Kelvin–Helmholtz instability in a channel

The effects of viscosity on Kelvin–Helmholtz instability in a channel are studied using three different theories; a purely irrotational theory based on the dissipation method, an exact rotational theory and a hybrid irrotational–rotational theory. These new results are compared with previous results from a viscous irrotational theory. An analysis of the neutral state is conducted and its predictions are compared with experimental results related to the transition from a stratified-smooth to a stratified-wavy or slug flow. For values of the gas fraction greater than about 0.20, there is an interval of velocity differences for which the flow is unstable for an interval of wavenumbers between two cutoff wavenumbers, k− and k+. For unstable flows with a velocity difference above that interval or with gas fractions less than 0.20, k− = 0. The maximum critical relative velocity that determines the onset of instability can be found when the kinematic viscosity of the gas and liquid are the same. This critical value is surprisingly achieved when both fluids are inviscid. The neutral curves from the analyses of potential flow of viscous fluids and the hybrid method, the only theories that account for the viscosity of both fluids in this work, indicate that the critical velocity does not change with the viscosity ratio when the kinematic viscosity of the liquid is greater than a critical value. For smaller liquid viscosities, the critical relative velocity decreases.
Radiative association of H and D

Radiative association of H and D is re-examined taking careful account of the role played by the numerous quasi-bound states. Using the best available interaction potential and dipole moment, an enhancement by up to a factor of 70 over earlier calculations is obtained, with the largest factor occurring at a temperature of about 2000 K. Other formation processes for HD remain more important in the early universe.
Assessing Classification Accuracy using Cohen`s kappa in Data Mining

In this paper, Cohen`s kappa and weighted kappa are applied to measuring classification accuracy when performing classification in data minig. Cohen`s kappa compensates for classifications that may be due to chance and is used for the data with nominal or ordinal scales. Especially, for the ordinal data, weighted kappa which measures the classification accuracy by quantifying the classification errors as weights is used. We used two weights (linear weight, quadratic weight) for calculations of weighted kappa. Also for the calculation and comparison of kappa and weighted kappa we used a real data set, fat-liver data.
Electron impact excitation of atomic hydrogen and hydrogenic ions

The second-order potential model of Bransden and Coleman (1972) is used to calculate total cross sections for the excitation of the n=2 levels of one-electron ions in the energy interval 25Z2-250Z2 eV, enabling the range of validity of the Coulomb-Born approximation to be assessed. Previously reported work on the excitation of hydrogen is corrected and extended by the inclusion of exchange effects. Good agreement is obtained with the available experimental data.
Numerical Simulation of Turbulent Flow Around a Square Cylinder with Uniform Injection or Suction and Heat Transfer

In the present study, the turbulent flow around a square cylinder with uniform injection or suction through various surfaces has been numerically studied. The wall functions of the viscous sublayer and log-law layer for velocity and temperature on the cylinder have been modified to allow for the effect of the injection or suction through the cylinder. The finite-volume method has been used for solving the ensemble averaged Navier-Stokes equations for incompressible flow in conjunction with the k − ϵ turbulence model equations that include the Kato-Launder's modification. A nonuniform staggered grid arrangement has been used. The results show that the parameters taken into account such as drag coefficient, and Strouhal and Nusselt numbers have been influenced by the uniform injection and suction through certain surfaces of the square cylinder, as well as the flow field parameters.
Generic linear perturbations

In his celebrated paper "Generic projections", John Mather has shown that almost all linear projections from a submanifold of a vector space into a subspace are transverse with respect to a given modular submanifold. In this paper, an improvement of Mather's result is stated. Namely, we show that almost all linear perturbations of a smooth mapping from a submanifold of $\mathbb{R}^m$ into $\mathbb{R}^\ell$ yield a transverse mapping with respect to a given modular submanifold. Moreover, applications of this result are given.
Adaptive control of kinematically redundant robots

It is shown through careful problem formulation that the adaptive control of redundant robots can be addressed as a reference velocity tracking problem in the joint space. A control law which ensures the bounded estimation of the unknown dynamic parameters of the robot and the convergence to zero of the velocity tracking error is derived. In order to ensure that the joint motion on the self-motion manifold (SMM) remains bounded, a homeomorphic transformation is found. This transformation decomposes the velocity tracking error dynamics into a cascade system consisting of the dynamics in the end-effector error coordinates and the dynamics on the SMM. The dynamics on the SMM is directly shown to be related to the concept of zero-dynamics. It is shown that if the reference joint trajectory is selected to optimize a certain type of objective function, then stable dynamics on the SMM results. This ensures the overall stability of the adaptive system. Detailed simulations are given to verify the theoretical developments. The proposed adaptive scheme does not require measurements of the joint accelerations or the inversion of the inertia matrix of the robot. <<ETX>>