Miracle-dz/UniFAR-FTUs huggingface dataset:
On the metal abundance range in the Draco dwarf galaxy

This paper examines the evidence for and against a range in metal abundance in the Draco dwarf spheroidal galaxy. It is shown that (i) Zinn's scanner observations of 17 red giants in Draco provide strong evidence in favor of a significant dispersion in metallicity; (ii) the scatter in B-V color of the subgiant branch stars (i.e., 20.0< or =V< or =20.5) in Stetson's color-magnitude diagram is consistent with the dispersion in metallicity that is inferred from Zinn's observations, but the possibility that the errors in the measurements alone are responsible for the scatter cannot be ruled out; and (iii) the scatter in B-V of a brighter sample of red giants (i.e., 19.2< or =V<20.0) is also consistent with Zinn's observations, and in this case the scatter is clearly larger than that expected from the observational errors. It is concluded that there is no evidence against there being a dispersion in metallicity in Draco and that there is some substantial evidence in favor of this hypothesis.
Aspects of open strings in Rindler Space

We study open string configurations in Rindler space suspended from D-branes at finite distance from the Rindler horizon. This is a toy model for strings in the near horizon region of a black hole and has applications for the study of strings configurations of heavy quarks in the AdS/CFT duals of hot field theories, as well as other applications to the study of open strings ending on giant gravitons. We find that this setup produces very similar results to those that have been found in the AdS black hole setup, but it is much more tractable analytically. We also comment on some quantum applications of our studies to the understanding of the spectrum of strings ending on giant gravitons.
The KLS isoperimetric conjecture for generalized Orlicz balls

What is the optimal way to cut a convex bounded domain $K$ in Euclidean space $(\mathbb{R}^n,|\cdot|)$ into two halves of equal volume, so that the interface between the two halves has least surface area? A conjecture of Kannan, Lov\'asz and Simonovits asserts that, if one does not mind gaining a universal numerical factor (independent of $n$) in the surface area, one might as well dissect $K$ using a hyperplane. This conjectured essential equivalence between the former non-linear isoperimetric inequality and its latter linear relaxation, has been shown over the last two decades to be of fundamental importance to the understanding of volumetric and spectral properties of convex domains. In this work, we address the conjecture for the subclass of generalized Orlicz balls \[ K = \left \{x \in \mathbb{R}^n \; ; \; \sum_{i=1}^n V_i(x_i) \leq E \right \} , \] confirming its validity for certain levels $E \in \mathbb{R}$ under a mild technical assumption on the growth of the convex functions $V_i$ at infinity (without which we confirm the conjecture up to a $\log(1+n)$ factor). In sharp contrast to previous approaches for tackling the KLS conjecture, we emphasize that no symmetry is required from $K$. This significantly enlarges the subclass of convex bodies for which the conjecture is confirmed.
On the First Eigenvalue of the Degenerate $p$-Laplace Operator in Non-Convex Domains

In this paper we obtain lower estimates of the first non-trivial eigenvalues of the degenerate $p$-Laplace operator, $p>2$, in a large class of non-convex domains. This study is based on applications of the geometric theory of composition operators on Sobolev spaces that permits us to estimates constants of Poincar\'e-Sobolev inequalities and as an application to derive lower estimates of the first non-trivial eigenvalues for the Alhfors domains (i.e. to quasidiscs). This class of domains includes some snowflakes type domains with fractal boundaries.
Safe Markov Chains for Density Control of ON/OFF Agents with Observed Transitions

This paper presents a convex optimization approach to control the density distribution of autonomous mobile agents with two control modes: ON and OFF. The main new characteristic distinguishing this model from standard Markov decision models is the existence of the ON control mode and its observed actions. When an agent is in the ON mode, it can measure the instantaneous outcome of one of the actions corresponding to the ON mode and decides whether it should take this action or not based on this new observation. If it does not take this action, it switches to the OFF mode where it transitions to the next state based on a predetermined set of transitional probabilities, without making any additional observations. In this decision-making model, each agent acts autonomously according to an ON/OFF decision policy, and the discrete probability distribution for the agent's state evolves according to a discrete-time Markov chain that is a linear function of the stochastic environment (i.e., transition probabilities) and the ON/OFF decision policy. The relevant policy synthesis is formulated as a convex optimization problem where hard safety and convergence constraints are imposed on the resulting Markov matrix. We first consider the case where the ON mode has a single action and the OFF mode has deterministic transitions (rather than stochastic) to demonstrate the model and the ideas behind our approach, which is then generalized to the case where ON mode has multiple actions and OFF mode has stochastic transitions.
Random iteration and projection method

We show that under suitable conditions a random orbit generated by a system of nonexpansive maps recovers an invariant set via its omega-limit. In particular, this explains what happens to the Kaczmarz--von Neumann projection algorithm in the infeasible case, that is, when one deals with more than two affine varieties having empty intersection.
On compactly generated torsion pairs and the classification of co--structures for commutative noetherian rings

We classify compactly generated co-t-structures on the derived category of a commutative noetherian ring. In order to accomplish that, we develop a theory for compactly generated Hom-orthogonal pairs (also known as torsion pairs in the literature) in triangulated categories that resembles Bousfield localization theory. Finally, we show that the category of perfect complexes over a connected commutative noetherian ring admits only the trivial co-t-structures and (de)suspensions of the canonical co-t-structure and use this to describe all silting objects in the category.
Multiple photon Hamiltonian in linear quantum optical networks

We give an alternative derivation for the explicit formula of the effective Hamiltonian describing the evolution of the quantum state of any number of photons entering a linear optics multiport. The description is based on the effective Hamiltonian of the optical system for a single photon and comes from relating the evolution in the Lie group that describes the unitary evolution matrices in the Hilbert space of the photon states to the evolution in the Lie algebra of the Hamiltonians for one and multiple photons. We give a few examples of how a group theory approach can shed light on some properties of devices with two input ports.
Boolean polynomial threshold functions and random tensors

A simple way to generate a Boolean function is to take the sign of a real polynomial in $n$ variables. Such Boolean functions are called polynomial threshold functions. How many low-degree polynomial threshold functions are there? The partial case of this problem for degree $d=1$ was solved by Zuev in 1989, who showed that the number $T(n,1)$ of linear threshold functions satisfies $\log_2 T(n,d) \approx n^2$, up to smaller order terms. However the number of polynomial threshold functions for any higher degrees, including $d=2$, has remained open. We settle this problem for all fixed degrees $d \ge1$, showing that $ \log_2 T(n,d) \approx n^{d+1}/{d! }$. The solution relies on establishing connections between the theory of Boolean functions and high-dimensional probability theory and leads to a more general program of extending random matrix theory to random tensors.
Connectivity Preserving Flocking without Velocity Measurement

In this paper, we address the design of a decentralized controller for connectivity‐preserving flocking, where each agent only can access to the position information of the agents within its sensing zone. An output vector, based on the position information alone, is constructed to replace the role of velocity, and some bounded attractive and repulsive forces are integrated together to design the controller. We prove that the controller not only synchronizes all agents in a stable formation, but also enables collision avoidance and connectivity preserving all of the time, when the initial condition meets certain requirements. Moreover, a leader‐follower method is used to guide the group to a desired direction, where the followers can sense the leader only if the distance between them is less than the communication radius.
A Chevalley formula for the equivariant quantum $K$-theory of cominuscule varieties

We prove a type-uniform Chevalley formula for multiplication with divisor classes in the equivariant quantum $K$-theory ring of any cominuscule flag variety $G/P$. We also prove that multiplication with divisor classes determines the equivariant quantum $K$-theory of arbitrary flag varieties. These results prove a conjecture of Gorbounov and Korff concerning the equivariant quantum $K$-theory of Grassmannians of Lie type A.
Counting Hyperelliptic curves on Abelian surfaces with Quasi-modular forms

In this paper we produce a generating function for the number of hyperelliptic curves (up to translation) on a polarized Abelian surfaces using the crepant resolution conjecture and the Yau-Zaslow formula. We present a formula to compute these in terms of MacMahon's generalized sum-of-divisors functions, and prove that they are quasi-modular forms.
The Exterior Cubic L-function of GU(6) and Unitary Automorphic Induction

In this paper, we extend Ginzburg-Rallis' integral representation for the exterior cube automorphic $L$-function of ${\rm GL}_6\times {\rm GL}_1$ to that of the quasi-split unitary similitude group ${\rm GU}_6$ and establish its analytic properties to determine the poles of this $L$-function. Furthermore, we introduce the automorphic induction for automorphic representations of ${\rm GU}_n$ and then show that the weak Langlands functorial lift for the automorphic induction exists for generic cuspidal automorphic representations. By using this automorphic induction, we give a conjectural criterion on the existence of poles of $L(s,\pi,\wedge^{3}\otimes\chi)$ for discrete automorphic representations in the tempered spectrum.
Analysis of the Leray-{\alpha} model with Navier slip boundary condition

In this paper, we establish the existence and the regularity of a unique weak solution to turbulent flows in a bounded domain ${\Omega}\subset \mathbb R^3$ governed by the so-called Leray-{\alpha} model. We consider the Navier slip boundary conditions for the velocity. Furthermore, we show that, when the filter coefficient {\alpha} tends to zero, the weak solution constructed converges to a suitable weak solution to the incompressible Navier Stokes equations subject to the Navier boundary condition. Similarly, if {\lambda} tends to 1- we recover a solution to the Leray-{\alpha} model with the homogeneous Dirichlet boundary conditions.
Quantization of Drinfeld Zastava in type A

Drinfeld Zastava is a certain closure of the moduli space of maps from the projective line to the Kashiwara flag scheme of the affine Lie algebra $\hat{sl}_n$. We introduce an affine, reduced, irreducible, normal quiver variety $Z$ which maps to the Zastava space bijectively at the level of complex points. The natural Poisson structure on the Zastava space can be described on $Z$ in terms of Hamiltonian reduction of a certain Poisson subvariety of the dual space of a (nonsemisimple) Lie algebra. The quantum Hamiltonian reduction of the corresponding quotient of its universal enveloping algebra produces a quantization $Y$ of the coordinate ring of $Z$. The same quantization was obtained in the finite (as opposed to the affine) case generically in arXiv:math/0409031. We prove that, for generic values of quantization parameters, $Y$ is a quotient of the affine Borel Yangian.
Tracing galaxy orbits back in time

To test the assumption that galaxy clustering grew by gravity, a way to predict the motions is needed. The method presented here chooses trial orbits to minimize the action given the observed positions and assuming galaxies at high redshift have negligible peculiar velocities. Results are presented for the orbits of Local Group members, along with the Maffei and Sculptor systems treated as point particles. The solutions are checked by using them to generate initial conditions at high redshift for a conventional N-body integration forward in time; the results retrace the solution quite well. The predicted velocities generally resemble the observations, though there are discrepancies. 11 refs.
Energy band line-up of atomic layer deposited Al2O3 on β-Ga2O3

Electrical properties of atomic layer deposited Al2O3/β-Ga2O3 interface were investigated. We determined the conduction band offset and interface charge density of Al2O3/β-Ga2O3 interface by analyzing the capacitance-voltage characteristics. The conduction band offset at the Al2O3/β-Ga2O3 interface was found to be 1.7 eV. A large positive sheet charge density of 3.6 × 1012 cm−2 is induced at the Al2O3/β-Ga2O3 interface, which caused a non-zero field of 0.7 MV/cm in the Al2O3 under flat-band conditions in the β-Ga2O3. The forward current-voltage characteristics were found to be related to trap-assisted tunneling.
A Combined Input-state Feedback Linearization Scheme and Independent Component Analysis Filter for the Control of Chaotic Systems with Significant Measurement Noise

Chaotic motion is an undesirable phenomenon in many engineering applications since it leads to a significant degradation of the system performance and restricts the feasible operational range. Therefore, the problem of controlling or suppressing chaos has attracted considerable attention in the literature. However, most chaos control schemes utilize a state feedback signal, and are therefore sensitive to measurement noise. Therefore, a requirement exists for filtering systems capable of separating the measurement noise from the chaotic signal in order to improve the performance of the controlled system. However, the chaotic signal and the measurement noise are both broadband signals, and thus the measurement noise can not be filtered using a low-pass filter since this causes a distortion of the chaotic signal. Accordingly, this paper presents a control scheme for chaotic dynamic systems with significant measurement noise featuring an input-state linearization scheme and a filter based upon an independent component analysis algorithm. The feasibility and effectiveness of the proposed approach are demonstrated by way of numerical simulations using a general Lorenz system for illustration purposes.
Generic Transversality for Unbranched Covers of Closed Pseudoholomorphic Curves

We prove that in closed almost complex manifolds of any dimension, generic perturbations of the almost complex structure suffice to achieve transversality for all unbranched multiple covers of simple pseudoholomorphic curves with deformation index 0. A corollary is that the Gromov‐Witten invariants (without descendants) of symplectic 4‐manifolds can always be computed as a signed and weighted count of honest J‐holomorphic curves for generic tame J: in particular, each such invariant is an integer divided by a weighting factor that depends only on the divisibility of the corresponding homology class. The transversality proof is based on an analytic perturbation technique, originally due to Taubes. © 2016 Wiley Periodicals, Inc.
Finitary Process Evolution I: Information Geometry of Configuration Space and the Process-Replicator Dynamics

This report presents some fundamental mathematical results towards elucidating the information-geometric underpinnings of evolutionary modelling schemes for (quasi-)stationary discrete stochastic processes. The model class under consideration is that of finite causal-state processes, known from the computational mechanics programme, along with their minimal unifilar hidden Markov generators. The respective configuration space is exhibited as a collection of combinatorially related Riemannian manifolds wherein the metric tensor field is an infinitesimal version of the relative entropy rate. Furthermore, a certain evolutionary inference iteration is defined which can be executed by generator-carrying agents and generalizes the Wright-Fisher model from population genetics. The induced dynamics on configuration space is studied from the large deviation point of view and it is shown that the associated asymptotic expectation dynamics follows the Riemannian gradient flow of a given fitness potential. In fact, this flow can formally be viewed as an information-geometric generalization of the replicator dynamics from population biology.
Viscosity methods for large deviations estimates for multiscale stochastic processes

We study singular perturbation problems for second order HJB equations in an unbounded setting. The main applications are large deviations estimates for the short maturity asymptotics of stochastic systems affected by a stochastic volatility, where the volatility is modelled by a process evolving at a faster time scale and satisfying some condition implying ergodicity.
The history of star formation of starburst galaxies

In this paper, we use different luminosity ratios to trace the histories of star formation of two different kinds of starburst galaxies: HII galaxies and starburst nucleus galaxies (SBNGs). The mean star formation rates (SFRs) for these galaxies is comparable, and compatible with a near constant star formation over a few Gyr period. We have also found an interesting difference between the burst stellar population of the SBNGs and the HII galaxies: SBNGs have an excess of intermediate-mass stars as compared to HII galaxies. We interpreted this difference as a sign that SBNGs have experienced a higher frequency of bursts of star formation than the HII galaxies. This interpretation is qualitatively consistent with the Stochastic Self Propagation of Star Formation (SSPSF) theory, which suggests that the starburst phenomenon depends on internal processes, regulated by the evolution of massive stars.
A Geometric Theory for Hypergraph Matching

We develop a theory for the existence of perfect matchings in hypergraphs under quite general conditions. Informally speaking, the obstructions to perfect matchings are geometric, and are of two distinct types: 'space barriers' from convex geometry, and 'divisibility barriers' from arithmetic lattice-based constructions. To formulate precise results, we introduce the setting of simplicial complexes with minimum degree sequences, which is a generalisation of the usual minimum degree condition. We determine the essentially best possible minimum degree sequence for finding an almost perfect matching. Furthermore, our main result establishes the stability property: under the same degree assumption, if there is no perfect matching then there must be a space or divisibility barrier. This allows the use of the stability method in proving exact results. Besides recovering previous results, we apply our theory to the solution of two open problems on hypergraph packings: the minimum degree threshold for packing tetrahedra in 3-graphs, and Fischer's conjecture on a multipartite form of the Hajnal-Szemeredi Theorem. Here we prove the exact result for tetrahedra and the asymptotic result for Fischer's conjecture; since the exact result for the latter is technical we defer it to a subsequent paper.
A pulsation phase-dependent dust shell model of OH 26.5 + 0.6

The spectral energy distribution of the radio-luminous OH/IR star 26.5 + 0.6 was modeled as a function of pulsation phase, using standard radiative-transfer techniques but with more self-consistent input parameters based partly on pulsation model calculations. The changes in spectral shape and overall intensity are easily explained in terms of the radial movement of the dust condensation radius with the changing luminosity of the star. The derived amplitude of the bolometric light curve is only 1.2 mag, considerably less than expected. 30 refs.
Damped Lyman-Alpha Absorption by Disk Galaxies with Large Redshifts. I. The Lick Survey

On presente les spectres basse resolution (Δλ=10 A) de 68 QSO de grand deplacement vers le rouge. L'un des buts principaux de l'etude est de presenter une liste de raies d'absorption qui soient des candidats pour les «disques Ly α»
A Subblock Matrix Approach to Data-Reduction in Gait Recognition

We propose a novel method for data reduction in gait recognition, called Subblock Complete Two Dimensional Principal Component Analysis (SbC2DPCA). GEIs were divided into smaller sub-images and redundant subblocks were adaptively removed. Complete Two Dimensional Principal Component Analysis (C2DPCA) was then applied to every sub-image directly, to acquire a set of projection sub-vectors for both row and column directions and these were synthesized into whole features for subsequent classification using nearest neighbor classifier. We evaluate the proposed gait recognition method on the CASIA gait database. The experimental results and analysis show the recognition accuracy of SbC2DPCA to be superior to C2DPCA, with C2DPCA being a special case of SbC2DPCA. The novelty of the proposed method lies in the adaptive removal of redundant data while extracting local features. This translates to data reduction with very minimal loss of information, as demonstrated by the remarkable recognition accuracy when subjects change clothing or have a backpack.
Problem reduction, renormalization, and memory

Methods for the reduction of the complexity of computational problems are presented, as well as their connections to renormalization, scaling, and irreversible statistical mechanics. Several statistically stationary cases are analyzed; for time dependent problems averaging usually fails, and averaged equations must be augmented by appropriate memory and random forcing terms. Approximations are described and examples are given.
Quantum Singularity Theory for A_{r-1} and r-Spin Theory

We give a review of the quantum singularity theory of Fan-Jarvis-Ruan and the r-spin theory of Jarvis-Kimura-Vaintrob and describe the work of Abramovich-Jarvis showing that for the singularity A_{r-1} = x^r the stack of A_{r-1}-curves of is canonically isomorphic to the stack of r-spin curves. We prove that the A_{r-1}-theory satisfies all the axioms of Jarvis-Kimura-Vaintrob for an r-spin virtual class. Therefore, the results of Lee, Faber-Shadrin-Zovonkine, and Givental all apply to the A_{r-1}-theory. In particular, this shows that the Witten Integrable Hierarchies Conjecture is true for the A_{r-1}-theory; that is, the total descendant potential function of the A_{r-1}-theory satisfies the r-th Gelfand-Dikii hierarchy.
Finite element approximations for second-order stochastic differential equation driven by fractional Brownian motion

We consider finite element approximations for a one dimensional second order stochastic differential equation of boundary value type driven by a fractional Brownian motion with Hurst index $H\le 1/2$. We make use of a sequence of approximate solutions with the fractional noise replaced by its piecewise con- stant approximations to construct the finite element approximations for the equation. The error estimate of the approximations is derived through rigorous convergence analysis.