On the average length of lexicographic paths

A bound is given for the average length of a lexicographic path, a definition that is motivated by degeneracies encountered when using the randomized simplex method.     

The combinatorial game Nofil played on Steiner triple systems

We introduce an impartial combinatorial game on Steiner triple systems called Next One to Fill Is the Loser (Nofil ). Players move alternately, choosing points of the triple system. If a player is forced to fill a block on their turn, they lose. By computing nim-values, we determine optimal strategies for Nofil on all Steiner triple systems up to order 15 and a sampling for orders 19, 21 and 25. The game Nofil can be thought of in terms of play on a corresponding hypergraph which will become a graph during play. At that point Nofil is equivalent to playing the game Node Kayles on the graph. We prove necessary conditions and sufficient conditions for a graph to reached playing Nofil. We conclude that the complexity of determining the outcome of the game Nofil on Steiner triple systems is PSPACE-complete for randomized reductions.     

The Newton modified barrier method for QP problems

The Modified Barrier Functions (MBF) have elements of both Classical Lagrangians (CL) and Classical Barrier Functions (CBF). The MBF methods find an unconstrained minimizer of some smooth barrier function in primal space and then update the Lagrange multipliers, while the barrier parameter either remains fixed or can be updated at each step. The numerical realization of the MBF method leads to the Newton MBF method, where the primal minimizer is found by using Newton's method. This minimizer is then used to update the Lagrange multipliers. In this paper, we examine the Newton MBF method for the Quadratic Programming (QP) problem. It will be shown that under standard second-order optimality conditions, there is a ball around the primal solution and a cut cone in the dual space such that for a set of Lagrange multipliers in this cut cone, the method converges quadratically to the primal minimizer from any point in the aforementioned ball, and continues, to do so after each Lagrange multiplier update. The Lagrange multipliers remain within the cut cone and converge linearly to their optimal values. Any point in this ball will be called a hot start. Starting at such a hot start, at mostO(In In ^-1) Newton steps are sufficient to perform the primal minimization which is necessary for the Lagrange multiplier update. Here, >0 is the desired accuracy. Because of the linear convergence of the Lagrange multipliers, this means that onlyO(In ^-1)O(In In ^-1) Newton steps are required to reach an -approximation to the solution from any hot start. In order to reach the hot start, one has to perform Newton steps, wherem characterizes the size of the problem andC>0 is the condition number of the QP problem. This condition number will be characterized explicitly in terms of key parameters of the QP problem, which in turn depend on the input data and the size of the problem.Partially supported by NASA Grant NAG3-1397 and National Science Foundation Grant DMS-9403218.     

The thermorheological complexity of photoelastic behaviour of 2-hydroxyethyl methacrylate — dodecyl methacrylate copolymers

The viscoelastic photoelastic behaviour of networks of 2-hydroxyethyl methacrylate — dodecyl methacrylate (DMA) copolymers in the main transition and rubberlike region was investigated. With increasing DMA content, photoelastic functions are quickly shifted to lower temperatures or shorter times; a detailed course of the functions suggests heterogeneity of the copolymers. Due to the existence of long side chains, optical function of all samples change the sign from positive to negative with increasing temperature. While the temperature dependences of the moduli of copolymers can be described by the two-phase Takayanagi model, the temperature dependences of optical functions cannot be described by using this model. It has been found, however, that the tempeature and time dependences of photoelastic functions can be described semiquantitatively by a three-phase model with a hypothetical statistical copolymer as the third component. The high values of the volume fraction of the hypothetical statistical copolymer found for the individual samples, suggest a considerable miscibility and a strong influence of the interphase boundary on the photoelastic behaviour of the copolymers.     

用方阵乘幂求和法求线性方程组的数值解

介绍了一种新型的,不同于传统的雅克比或高斯塞德尔迭代法的,求解线性方程组的方阵乘幂求和法,并引入了方阵意义上求积分的龙贝格法.该算法成立须以方阵A为实阵,非奇异且主对角元素占优.该法较雅克比或高斯塞德尔迭代的计算量小,特别有助于求解大型线性方程组的问题.     

Postural Complexity during Listening in Young and Middle-Aged Adults

Postural behavior has traditionally been studied using linear assessments of stability (e.g., center of pressure ellipse area). While these assessments may provide valuable information, they neglect the nonlinear nature of the postural system and often lead to the conflation of variability with pathology. Moreover, assessing postural behavior in isolation or under otherwise unrealistic conditions may obscure the natural dynamics of the postural system. Alternatively, assessing postural complexity during ecologically valid tasks (e.g., conversing with others) may provide unique insight into the natural dynamics of the postural system across a wide array of temporal scales. Here, we assess postural complexity using Multiscale Sample Entropy in young and middle-aged adults during a listening task of varying degrees of difficulty. It was found that middle-aged adults exhibited greater postural complexity than did young adults, and that this age-related difference in postural complexity increased as a function of task difficulty. These results are inconsistent with the notion that aging is universally associated with a loss of complexity, and instead support the notion that age-related differences in complexity are task dependent.     

Formalising the Pathways to Life Using Assembly Spaces

Assembly theory (referred to in prior works as pathway assembly) has been developed to explore the extrinsic information required to distinguish a given object from a random ensemble. In prior work, we explored the key concepts relating to deconstructing an object into its irreducible parts and then evaluating the minimum number of steps required to rebuild it, allowing for the reuse of constructed sub-objects. We have also explored the application of this approach to molecules, as molecular assembly, and how molecular assembly can be inferred experimentally and used for life detection. In this article, we formalise the core assembly concepts mathematically in terms of assembly spaces and related concepts and determine bounds on the assembly index. We explore examples of constructing assembly spaces for mathematical and physical objects and propose that objects with a high assembly index can be uniquely identified as those that must have been produced using directed biological or technological processes rather than purely random processes, thereby defining a new scale of aliveness. We think this approach is needed to help identify the new physical and chemical laws needed to understand what life is, by quantifying what life does.     

基于复杂度分析logistic映射和Lorenz模型的研究

采用三次粗粒化方法得到了logistic映射和Lorenz模型的符号序列，运用动态非线性时间序 列分析方法——Lemper-Ziv复杂度，分别对两组符号序列进行了对比分析.对于logistic映 射，其复杂度反映了时间序列的演化；Lorenz模型三个分量的复杂度序列都具有混沌性质， 即由许多振幅非常接近而长度完全不同的循环所组成，反映了Lorenz模型内在的准周期特性 .进一步研究发现，当取不同的窗口长度时，复杂度序列的特征基本相同，并且复杂度反映 了时间序列的时空特性.因此，可以借助复杂度的计算来反演观测资料的动力学结构. 关键词： 三次粗粒化 Lemper-Ziv复杂度 logistic映射 Lorenz模型     

A logarithmic complexity floating frame of reference formulation with interpolating splines for articulated multi-flexible-body dynamics

An interpolating spline-based approach is presented for modeling multi-flexible-body systems in the divide-and-conquer (DCA) scheme. This algorithm uses the floating frame of reference formulation and piecewise spline functions to construct and solve the non-linear equations of motion of the multi-flexible-body system undergoing large rotations and translations. The new approach is compared with the flexible DCA (FDCA) that uses the assumed modes method [1]. The FDCA, in many cases, must resort to sub-structuring to accurately model the deformation of the system. We demonstrate, through numerical examples, that the interpolating spline-based approach is comparable in accuracy and superior in efficiency to the FDCA. The present approach is appropriate for modeling flexible mechanisms with thin 1D bodies undergoing large rotations and translations, including those with irregular shapes. As such, the present approach extends the current capability of the DCA to model deformable systems. The algorithm retains the theoretical logarithmic complexity inherent in the DCA when implemented in parallel.     

Dual Template Engaged Synthesis of Hollow Ball‐in‐Tube Asymmetrical Structured Ceria

Hollow materials with different configurations are of interest due to their unique structural features, which induce interesting properties e.g. catalysis. Here, the synthesis of asymmetrical hollow ball‐in‐tube (HBT) structured CeO₂ is reported, which is achieved using a dual template engaged solid–liquid interfacial reaction. In this reaction, the SiO₂ sphere (hard template)‐embedded Ce(OH)CO₃ nanorod (sacrificial template) composite is first treated with NaOH solution, followed by an acid wash to obtain asymmetrical hollow structured CeO₂. Such HBT structured CeO₂ is demonstrated to be a good support for Au nanoparticles toward CO oxidation as compared to simple hollow CeO₂ nanotubes, leading to significantly increase catalytic activity.