On the Locally Polynomial Complexity of the Projection-Gradient Method for Solving Piecewise Quadratic Optimisation Problems

This paper proposes a method for solving optimisation problems involving piecewise quadratic functions. The method provides a solution in a finite number of iterations, and the computational complexity of the proposed method is locally polynomial of the problem dimension, i.e., if the initial point belongs to the sufficiently small neighbourhood of the solution set. Proposed method could be applied for solving large systems of linear inequalities.     

A Traditional Scientific Perspective on the Integrated Information Theory of Consciousness

This paper assesses two different theories for explaining consciousness, a phenomenon that is widely considered amenable to scientific investigation despite its puzzling subjective aspects. I focus on Integrated Information Theory (IIT), which says that consciousness is integrated information (as ϕ^Max) and says even simple systems with interacting parts possess some consciousness. First, I evaluate IIT on its own merits. Second, I compare it to a more traditionally derived theory called Neurobiological Naturalism (NN), which says consciousness is an evolved, emergent feature of complex brains. Comparing these theories is informative because it reveals strengths and weaknesses of each, thereby suggesting better ways to study consciousness in the future. IIT’s strengths are the reasonable axioms at its core; its strong logic and mathematical formalism; its creative “experience-first” approach to studying consciousness; the way it avoids the mind-body (“hard”) problem; its consistency with evolutionary theory; and its many scientifically testable predictions. The potential weakness of IIT is that it contains stretches of logic-based reasoning that were not checked against hard evidence when the theory was being constructed, whereas scientific arguments require such supporting evidence to keep the reasoning on course. This is less of a concern for the other theory, NN, because it incorporated evidence much earlier in its construction process. NN is a less mature theory than IIT, less formalized and quantitative, and less well tested. However, it has identified its own neural correlates of consciousness (NCC) and offers a roadmap through which these NNCs may answer the questions of consciousness using the hypothesize-test-hypothesize-test steps of the scientific method.     

ϕ-Informational Measures: Some Results and Interrelations

In this paper, we focus on extended informational measures based on a convex function ϕ: entropies, extended Fisher information, and generalized moments. Both the generalization of the Fisher information and the moments rely on the definition of an escort distribution linked to the (entropic) functional ϕ. We revisit the usual maximum entropy principle—more precisely its inverse problem, starting from the distribution and constraints, which leads to the introduction of state-dependent ϕ-entropies. Then, we examine interrelations between the extended informational measures and generalize relationships such the Cramér–Rao inequality and the de Bruijn identity in this broader context. In this particular framework, the maximum entropy distributions play a central role. Of course, all the results derived in the paper include the usual ones as special cases.     

大学物理教学改革实践浅析——“问题导向”式学习的意义及应用

针对当前我国高校大学物理教学中存在诸多问题的现状,提出"问题导向"式教学的解决途径."问题导向"学习中"教"与"学"的方式有较大跨度的转变,它以学生为中心,以问题为导向,其中问题的设置环节对师生良好互动的实现至关重要.文章就振动内容问题的设计和提出进行简单应用尝试,以期为后续大学物理教学改革的持续进行提供帮助.     

初中物理运动观念的内涵分析及培养策略研究

阐述了初中物理中由运动概念向运动观念转变的过程,对运动观念的定义和表现进行了分析.基于初中物理课程标准,将运动观念分解为运动的属性观、运动的描述观、运动的形式观和运动的规律观4个子观念,对每个子观念的内涵及教学策略进行了讨论,提出了通过创设本原性综合问题情境构建学生运动观念的设想.     

QCD as a topologically ordered system

We argue that QCD belongs to a topologically ordered phase similar to many well-known condensed matter systems with a gap such as topological insulators or superconductors. Our arguments are based on an analysis of the so-called “deformed QCD” which is a weakly coupled gauge theory, but nevertheless preserves all the crucial elements of strongly interacting QCD, including confinement, nontrivial θ$\theta$ dependence, degeneracy of the topological sectors, etc. Specifically, we construct the so-called topological “BF” action which reproduces the well known infrared features of the theory such as non-dispersive contribution to the topological susceptibility which cannot be associated with any propagating degrees of freedom. Furthermore, we interpret the well known resolution of the celebrated U(1)_A$U{\left(1\right)}_A$ problem where the would be η^′${\eta }^{\prime }$ Goldstone boson generates its mass as a result of mixing of the Goldstone field with a topological auxiliary field characterizing the system. We then identify the non-propagating auxiliary topological field of the BF formulation in deformed QCD with the Veneziano ghost (which plays the crucial role in resolution of the U(1)_A$U{\left(1\right)}_A$ problem). Finally, we elaborate on relation between “string-net” condensation in topologically ordered condensed matter systems and long range coherent configurations, the “skeletons”, studied in QCD lattice simulations.     

Cooling Characteristics During Bath Quenching of Test Probe Using Inverse Heat Transfer

It is of engineering importance to accurately predict the surface cooling characteristics in bath quenching of metals and alloys. In this investigation, the surface cooling characteristics in quenching of Wolfson probe are estimated with reasonable accuracy by solving an inverse heat conduction problem. Regularization method is used for smoothening the input temperature measurements at probe center, for superior inversion estimates. The reverse pool-boiling curve is captured on bath quenching characteristic, plotted as cooling velocity versus surface temperature. The prime advantage is the bypassing of convection coefficients, which are uncertain in pool boiling.     

Application of a Factorial Design Method to Determine the Accuracy of a Solution to an Inverse Heat Conduction Problem

A numerical/experimental inverse procedure was employed to estimate the temperature-dependent thermal conductivity of a solid body in which 1D heat conduction in a top heated cylindrical sample is assumed. The emphasis is focused on the issue of sensitivity of results to selected assumptions made in inverse calculations. It has been found that the accuracy of heat capacity evaluation brings the largest contribution to final errors (up to 74%). Density accounts for one-fourth to one-third of the total error of determination. The failure to ensure unidirectional heat conduction in a sample during an experiment is important only at elevated temperatures.     

An upper bound for the first eigenvalue of a spherical cap

By working with suitable test functions, we obtain an upper bound for the principal eigenvalue of a geodesic ball on a sphere of arbitrary dimension. This bound is sharp in the limiting case when the radius of the ball approaches the diameter of the sphere.This research was supported by ARO Grant 28905-MA.     

Integral global optimization method for solution of nonlinear complementarity problems

The mapping in a nonlinear complementarity problem may be discontinuous. The integral global optimization algorithm is proposed to solve a nonlinear complementarity problem with a robust piecewise continuous mapping. Numerical examples are given to illustrate the effectiveness of the algorithm.