Miracle-dz/UniFAR-FTUs huggingface dataset:
Dynamic Transitions and Pattern Formations for Cahn-Hilliard Model with Long-Range Repulsive Interactions

The main objective of this article is to study the order-disorder phase transition and pattern formation for systems with long-range repulsive interactions. The main focus is on the Cahn-Hilliard model with a nonlocal term in the corresponding energy functional, representing the long-range repulsive interaction. First, we show that as soon as the linear problem loses stability, the system always undergoes a dynamic transition to one of the three types, forming different patterns/structures. The types of transition are then dictated by a nondimensional parameter, measuring the interactions between the long-range repulsive term and the quadratic and cubic nonlinearities in the model. The derived explicit form of this parameter offers precise information for the phase diagrams. Second, we obtain a novel and explicit pattern selection mechanism associated with the competition between the long-range repulsive interaction and the short-range attractive interactions. In particular, the hexagonal pattern is unique to the long-range interaction, and is associated with a novel two-dimensional reduced transition equations on the center manifold generated by the unstable modes, consisting of (degenerate) quadratic terms and non-degenerate cubic terms. Finally, explicit information on the metastability and basin of attraction of different disordered/ordered states and patterns are derived as well.
Unitary representations of the extended affine Lie algebra $\widetilde{\frak{gl}_{3}(\bc_q)}$

We use the idea of free fields to obtain highest weight representations for the extended affine Lie algebra $\widetilde{\frak{gl}_{2}(\bc_q)}$ coordinatized by the quantum torus $\bc_q$ and go on to construct a contravariant hermitian form. We further give a necessary and sufficient condition such that the contravariant hermitian form is positive definite.
Hypoelliptic heat kernel inequalities on H-type groups

We study inequalities related to the heat kernel for the hypoelliptic sublaplacian on an H-type Lie group. Specifically, we obtain precise pointwise upper and lower bounds on the heat kernel function itself. We then apply these bounds to derive an estimate on the gradient of solutions of the heat equation, which is known to have various significant consequences including logarithmic Sobolev inequalities. We also present a computation of the heat kernel, and a discussion of the geometry of H-type groups including their geodesics and Carnot-Caratheodory distance functions.
SOME OBSERVATIONS ABOUT GENERALIZED QUANTIFIERS IN LOGICS OF IMPERFECT INFORMATION

Abstract We analyse the two definitions of generalized quantifiers for logics of dependence and independence that have been proposed by F. Engström, comparing them with a more general, higher order definition of team quantifier. We show that Engström’s definitions (and other quantifiers from the literature) can be identified, by means of appropriate lifts, with special classes of team quantifiers. We point out that the new team quantifiers express a quantitative and a qualitative component, while Engström’s quantifiers only range over the latter. We further argue that Engström’s definitions are just embeddings of the first-order generalized quantifiers into team semantics, and fail to capture an adequate notion of team-theoretical generalized quantifier, save for the special cases in which the quantifiers are applied to flat formulas. We also raise several doubts concerning the meaningfulness of the monotone/nonmonotone distinction in this context. In the appendix we develop some proof theory for Engström’s quantifiers.
Continuation methods applied to the 2D Navier–Stokes equations at high Reynolds numbers

Nonlinearities arise in aerodynamic flows as a function of various parameters, such as angle of attack, Mach number and Reynolds number. These nonlinearities can cause the change from steady to unsteady flow or give rise to static hysteresis. Understanding these nonlinearities is important for safety validation and performance enhancement of modern aircraft. A continuation method has been developed to study nonlinear steady state solutions with respect to changes in parameters for two‐dimensional compressible turbulent flows at high Reynolds numbers. This is the first time that such flows have been analysed with this approach. Continuation methods allow the stable and unstable solutions to be traced as flow parameters are changed. Continuation has been carried out on two‐dimensional aerofoils for several parameters: angle of attack, Mach number, Reynolds number, aerofoil thickness and turbulent inflow as well as levels of dissipation applied to the models. A range of results are presented. Copyright © 2012 John Wiley & Sons, Ltd.
Automatic registration of multi-view range images based on statistical model

We present a method for automatically registering multi-view range images. For each range image in the data set, corresponding point sets of its feature points are established, on the rest of the scans, by matching regional point descriptors. Then we build a statistic model to estimate the likelihood of the image overlapping with each of the rest ones to select candidate overlapping range images. Candidate overlapping pairs of range images are verified and registered by enforcing geometric constraints on point matches and ICP algorithm. Finally the absolute positions of all range images are established and fine-tuned. Experiment result demonstrates efficiency of the method in picking up potential overlapping images, and establishing initial transformation between overlapping pairs. The proposed method offers a good solution to automatically building complete 3D model of objects from unordered 3D scan data sets.
A Bregman Splitting Algorithm for Distributed Optimization over Networks

We consider distributed optimization problems in which a group of agents are to collaboratively seek the global optimum through peer-to-peer communication networks. The problem arises in various application areas, such as resource allocation, sensor fusion and distributed learning. We propose a general efficient distributed algorithm--termed Distributed Forward-Backward Bregman Splitting (D-FBBS)--to simultaneously solve the above primal problem as well as its dual based on Bregman method and operator splitting. The proposed algorithm allows agents to communicate asynchronously and thus lends itself to stochastic networks. This algorithm belongs to the family of general proximal point algorithms and is shown to have close connections with some existing well-known algorithms when dealing with fixed networks. However, we will show that it is generally different from the existing ones due to its effectiveness in handling stochastic networks. With proper assumptions, we establish a non-ergodic convergence rate of o(1/k) in terms of fixed point residuals over fixed networks both for D-FBBS and its inexact version (ID-FBBS) which is more computationally efficient and an ergodic convergence rate of O(1/k) for D-FBBS over stochastic networks respectively. We also apply the proposed algorithm to sensor fusion problems to show its superior performance compared to existing methods.
About the Chasm Separating the Goals of Hilbert's Consistency Program from the Second Incompletess Theorem

We have published several articles about generalizations and boundary-case exceptions to the Second Incompleteness Theorem during the last 25 years. The current paper will review some of our prior results and also introduce an `enriched' refinement of semantic tableaux deduction. While the Second Incompleteness Theorem is a strong result, we will emphasize its boundary-case exceptions are germane to Global Warming's threat because our systems can own a simultaneous knowledge about their own consistency, together with an understanding of the $\Pi_1$ implications of Peano Arithmetic.
Comparison of Different Techniques for the Determination of Platinized Cytostatic Drugs in Urine Samples

Platinum-based cytostatic drugs are one of the most widely used cancer treatments. They are excreted via the urinary tract and can reach the environment through wastewater, posing a risk to human health due to their side effects. Four identification and quantification techniques, including liquid chromatography (LC) separation coupled to (i) a diode array ultraviolet (UV(DAD)) (ii), mass spectrometer in single ion monitoring mode (LC-MS) and (iii) multiple reaction monitoring mode (LC-MS/MS) and (iv) derivatization with diethyldithiocarbamate prior to LC-MS/MS analysis, have been optimized and compared for the multiresidue determination of main platinized cytostatic drugs (cisplatin, carboplatin, and oxaliplatin) in urine samples. Parameters that affect the efficiency of the chromatographic separation and analytical determination of different methods (column, mobile phase, wavelength, precursor ions, fragmentor, and product ions) were optimized. Analytical features, such as matrix effect, sensitivity, precision, selectivity, and linearity, were calculated. In terms of selectivity, the derivatization technique was discarded since it was only applicable to the platinated sum. A high dilution of the sample with LC-UV(DAD) was needed to reduce the matrix effect. Overall, the LC-MS/MS method presented the best analytical features (% RSD ≤ 12.8%, R2 ≥ 0.991, or method-detection limits between 0.01–1 µg mL−1). The selected method was applied to the quantification of platinized cytostatic drugs in hospital urine samples from oncologic patients.
Range-based attacks on links in random scale-free networks

Range and load play key roles in the problem of attacks on links in random scale-free (RSF) networks. In this paper we obtain the approximate relation between range and load in RSF networks by the generating function theory, and then give an estimation about the impact of attacks on the efficiency of the network. The results show that short-range attacks are more destructive for RSF networks, and are confirmed numerically.
Locomotion mode recognition method based on inertial measurement units in exoskeleton robot

The lower limb exoskeleton robot is a wearable device that enhances the movement ability of human lower extremities. Locomotion mode recognition is an important prerequisite for controlling the lower limb exoskeleton robot. This proposed paper demonstrates a method of locomotion mode recognition of the lower limb exoskeleton robot based on residual networks. This article studies five common locomotion modes, including level ground walking, stair ascending, stair descending, ramp ascending and ramp descending. We collect locomotion data from 5 subjects using a set of 4 inertial sensors for 5 lower limb locomotion modes of different specificities. The residual network based hierarchical classifier is trained to classify the modes into a specified label hierarchy. The residual network can automatically learn mixed features without the participation of experts, avoiding manual feature extraction. It is noticeable to solve the degradation question and alleviate the problem of gradient disappearance. Some comparative experiments carried out on the selection of hyperparameters applied to optimize the residual network structure proposed. The results show that the average recognition rate reaches 96.95%, which has a prominent recognition effect on locomotion mode recognition.
Limiting Spectral Measures for Random Matrix Ensembles with a Polynomial Link Function

Consider the ensembles of real symmetric Toeplitz matrices and real symmetric Hankel matrices whose entries are i.i. d. random variables chosen from a fixed probability distribution p of mean 0, variance 1, and finite higher moments. Previous work on real symmetric Toeplitz matrices shows that the spectral measures, or densities of normalized eigenvalues, converge almost surely to a universal near-Gaussian distribution, while previous work on real symmetric Hankel matrices shows that the spectral measures converge almost surely to a universal non-unimodal distribution. Real symmetric Toeplitz matrices are constant along the diagonals, while real symmetric Hankel matrices are constant along the skew diagonals. We generalize the Toeplitz and Hankel matrices to study matrices that are constant along some curve described by a real-valued bivariate polynomial. Using the Method of Moments and an analysis of the resulting Diophantine equations, we show that the spectral measures associated with linear bivariate polynomials converge in probability and almost surely to universal non-semicircular distributions. We prove that these limiting distributions approach the semicircle in the limit of large values of the polynomial coefficients. We then prove that the spectral measures associated with the sum or difference of any two real-valued polynomials with different degrees converge in probability and almost surely to a universal semicircular distribution.
QUASI-STATIONARY DISTRIBUTIONS FOR STOCHASTIC APPROXIMATION ALGORITHMS WITH CONSTANT STEP SIZE

In this paper we investigate quasi-stationary distributions μ_N of stochastic approximation algorithms with constant step size which can be viewed as random perturbations of a time-continuous dynamical system. Inspired by ecological models these processes have a closed absorbing set corresponding to extinction. Under some large deviation assumptions and the existence of an interior attractor for the ODE, we show that the weak* limit points of the QSD μ_N are invariant measures for the ODE with support in the interior attractors.
BIM Style Restoration Based on Image Retrieval and Object Location Using Convolutional Neural Network

BIM is one of the main technical ways to realize building informatization, and the model’s texture is essential to its style design during BIM construction. However, the texture maps provided by mainstream BIM software are not realistic enough and monotonous to meet the actual needs of users for the model style. Therefore, an interior furniture BIM style restoration method was proposed based on image retrieval and object location using convolutional neural network. First, two types of furniture images, namely grayscale contour images from BIM software and real images from the Internet, were collected to train the following network model. Second, a multi-feature weighted fusion neural network model based on an attention mechanism (AM-rVGG) was proposed, which focused on the structural information of furniture images to retrieve the most similar real image, and then some furniture image patches from the retrieved one were generated with object location and random cropping techniques as the candidate texture maps of the furniture BIM. Finally, the candidate ones were fed back into the BIM software to realize the restoration of the furniture BIM style. The experimental results showed that the average retrieval accuracy of the proposed network model was 83.1%, and the obtained texture maps could effectively restore the real style of the furniture BIM. This work provides a new idea for restoring the realism in other BIM.
Dwarf nova outbursts – the ultraviolet delay and the effect of a weakly magnetized white dwarf

We investigate the effect on the properties of the outbursts of a dwarf nova (in the disc instability model) of the central white dwarf having a weak (∼10 4 G) magnetic field. We find that in quiescence the inner regions of the disc are evacuated by the presence of the field. This implies that at the beginning of the outburst there is a delay before the hotter inner disc regions are filled and radiating, and thus the optical flux can rise 12 h or so before the ultraviolet flux.
SISTEMAS DE CONTROLE GERENCIAL E EFICÁCIA DE EQUIPE: OS EFEITOS INTERVENIENTES DO COMPARTILHAMENTO DE INFORMAÇÕES E IDENTIFICAÇÃO ORGANIZACIONAL

Objetivo: O objetivo deste trabalho foi verificar a influência dos Sistemas de Controle Gerencial (SCG’s) na eficácia de equipe, moderados pela identificação organizacional e mediados pelo compartilhamento de informações. Método: Foi realizada uma pesquisa qualitativa e quantitativa realizada por meio de survey, que foi aplicada a 105 profissionais de um hospital militar localizado na região centro-oeste do Brasil. A modelagem de equações estruturais foi usada para análise. Resultados/Discussão: Os resultados mostraram que as características formais e informais dos SCG têm uma influência positiva e significativa na eficácia de equipe e que a relação entre o SCG e o compartilhamento de informações é moderada pela identificação organizacional. No entanto, a existência de uma relação significativa entre os SCG e a eficácia de equipe não foi mediada pelo compartilhamento de informações. Contribuições: Os gestores hospitalares devem estar atentos aos tipos de SCG, pois estão associados às atitudes e comportamentos dos indivíduos, que se refletem nos resultados organizacionais.
New class of 2D multirate filter bank for digital image coding

A new type of perfect reconstruction filter bank is presented in this paper. , This new class of filter bank has the following distinct features at the same time: linear-phase, distortion-free, IIR-FIR filter pair, closed form expression, orthogonal projection, and factorization-free. In contrast, the other existing filter banks do not possess all these properties simultaneously. For example, the classic Quadrature Mirror Filter (QMF) does not have the perfect reconstruction nature. Another example is the Conjugate Quadrature Filter (CQF), which lacks the linear- phase property. A qualitative comparison of different types of filter banks is also included. This newly developed perfect reconstruction IIR-FIR filter bank is then extended to the 2-D case. Both separable and non-separable filters are considered. In addition, both rectangular downsampling and non-rectangular downsampling schemes are discussed. Numerical optimization procedures are used to compute the optimal filter coefficients. The results are listed in tables for quick reference.
Generalized designs on graphs: Sampling, spectra, symmetries

Spherical designs are finite sets of points on the sphere S d with the property that the average of certain (low‐degree) polynomials in these points coincides with the global average of the polynomial on S d . They are evenly distributed and often exhibit a great degree of regularity and symmetry. We point out that a spectral definition of spherical designs transfers to finite graphs—these ‘graphical designs’ are subsets of vertices that are evenly spaced and capture the symmetries of the underlying graph (should they exist). Our main result states that good graphical designs either consist of many vertices or their neighborhoods have exponential volume growth. We show several examples, describe ways to find them and discuss problems.
An exact Lagrangian-mean wave activity for finite-amplitude disturbances to barotropic flow on a sphere

Abstract The finite-amplitude Rossby wave activity introduced recently by Nakamura and co-workers measures disturbances in terms of the areal displacement of potential vorticity (PV) from zonal symmetry and possesses exact Eliassen–Palm and non-acceleration theorems. This article investigates both theoretically and numerically how this wave activity, denoted ${A}^{\ensuremath{\ast} } $, relates to previously defined quantities such as the generalized Lagrangian-mean (GLM) pseudomomentum density and the impulse-Casimir (IC) wave activity in the context of barotropic flow on a sphere. It is shown that under the barotropic constraint both the new and GLM formalisms derive the non-acceleration theorem from the conservation of Kelvin’s circulation, but the two differ in the way the circulation is partitioned into a mean flow and wave activity/pseudomomentum density. The new wave activity differs from the (negative of) GLM pseudomomentum density by the Stokes correction to angular momentum density, which is not negligible even in the small-amplitude limit. In contrast, ${A}^{\ensuremath{\ast} } $ converges to the IC wave activity and the familiar linear pseudomomentum density in the conservative small-amplitude limit, provided that their reference states are identical. Both the GLM pseudomomentum density and the zonal-mean IC wave activity may be cast in a flux conservation form in equivalent latitude, which may then be related to an exact Eliassen–Palm theorem through a gauge transformation. However, of the three wave activity forms, only ${A}^{\ensuremath{\ast} } $ satisfies an exact non-acceleration theorem for the zonal-mean zonal wind $\bar {u} $. A simple jet forcing experiment is used to examine the quantitative differences among these diagnostics. In this experiment, ${A}^{\ensuremath{\ast} } $ and the IC wave activity behave similarly in the domain average; however, they differ substantially in the local profiles, the former being more closely related to the flow modification. Despite their close conceptual relationship, the GLM pseudomomentum fails to capture the meridional structure of ${A}^{\ensuremath{\ast} } $ because the Stokes correction term dominates the former. This demonstrates various advantages of ${A}^{\ensuremath{\ast} } $ as a diagnostic of eddy–mean flow interaction.
A method for generating a chaotic attractor by destabilization

We propose a method for generating a chaotic orbit by using destabilizing control for a stable equilibrium or a stable limit cycle in given differential equation. The controller is designed with the pole assignment technique, which is applied in many linear control systems. In the case of an equilibrium point, the poles of the characteristic equation are located in the right half plane. Control is started when the orbit flows into the point, and is activated during an appropriate interval. Then the orbit is repelled from the point and becomes chaotic. In the case of a limit cycle, the poles of the characteristic equation of the Poincare mapping for a fixed point are assigned as unstable poles. As illustrative examples, a stable equilibrium point of a gradient system, a stable limit cycle of the van der Pol equation, and the extended BVP equation are destabilized and chaotic attractors are obtained. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt. 3, 80(11): 73–81, 1997
On the degeneration of the Frölicher spectral sequence and small deformations

Abstract We study the behavior of the degeneration at the second step of the Frölicher spectral sequence of a 𝒞∞ family of compact complex manifolds. Using techniques from deformation theory and adapting them to pseudo-differential operators we prove a result à la Kodaira-Spencer for the dimension of the second step of the Frölicher spectral sequence and we prove that, under a certain hypothesis, the degeneration at the second step is an open property under small deformations of the complex structure.
Black-hole binaries, gravitational waves, and numerical relativity

Understanding the predictions of general relativity for the dynamical interactions of two black holes has been a long-standing unsolved problem in theoretical physics. Black-hole mergers are monumental astrophysical events, releasing tremendous amounts of energy in the form of gravitational radiation, and are key sources for both ground- and space-based gravitational-wave detectors. The black-hole merger dynamics and the resulting gravitational wave forms can only be calculated through numerical simulations of Einstein's equations of general relativity. For many years, numerical relativists attempting to model these mergers encountered a host of problems, causing their codes to crash after just a fraction of a binary orbit could be simulated. Recently, however, a series of dramatic advances in numerical relativity has allowed stable, robust black-hole merger simulations. This remarkable progress in the rapidly maturing field of numerical relativity and the new understanding of black-hole binary dynamics that is emerging is chronicled. Important applications of these fundamental physics results to astrophysics, to gravitational-wave astronomy, and in other areas are also discussed.