Evidences of the fractional kinetics in temperature region: Evolution of extreme points in ibuprofen

Based on a new approach presented in detail in this paper one can find new evidences of existence of the fractional kinetics not only in the frequency range. One can find rather general principles of detection of different collective motions in temperature region. These principles can be expressed in terms of an algorithm (defined in the paper as an approach). This approach includes some steps that help to separate a couple of the neighboring collective motions (expressed in the frequency range as a linear combination of two power-law exponents) from each other and establish the temperature evolution of the extreme point that follows to the generalized Vogel–Fulcher–Tamman (VFT)-equation. This experimentally confirmed fact gives new evidences for supporting of the theory of dielectric relaxation based on the fractional kinetics on the frequency/temperature domain. As an example for verification of this new approach the ibuprofen complex permittivity data measured in the wide frequency/temperature range were chosen. The reason of such selection was the following. It helps to compare the conventional study of this complex substance recently published in [1] and use possibilities of the developed approach that can add some new features to the picture obtained in the frame of the conventional treatment. We suppose that possibilities presented by new approach will be extremely useful for detection of different collective motions in other substances studied by the method of broadband dielectric spectroscopy (BDS).     

Obtaining exact value by approximate computations

Numerical approximate computations can solve large and complex problems fast.They have the advantage of high efficiency.However they only give approximate results,whereas we need exact results in some fields.There is a gap between approximate computations and exact results. In this paper,we build a bridge by which exact results can be obtained by numerical approximate computations.     

A generalized linear programming model for nurse scheduling

This paper presents a 0–1 column generation model with a resource constrained shortest path auxiliary problem for nurse scheduling. The master problem finds a configuration of individual schedules to satisfy the demand coverage constraints while minimizing salary costs and maximizing both employee preferences and team balance. A feasible solution of the auxiliary problem is an acceptable schedule for a given nurse, with respect to collective agreement requirements such as seniority, workload, rotations and days off. We define a new resource structure in the auxiliary problem in order to take into account the complex collective agreement rules specific to the nurse scheduling problem. This model generalizes further the previous formulations discussed in the literature and can be viewed as a general scheme for complex personnel scheduling problems, especially in the context of organizations which operate around the clock. Solution methods and preliminary test results are discussed.     

Bayesian Synthetic Likelihood

Having the ability to work with complex models can be highly beneficial. However, complex models often have intractable likelihoods, so methods that involve evaluation of the likelihood function are infeasible. In these situations, the benefits of working with likelihood-free methods become apparent. Likelihood-free methods, such as parametric Bayesian indirect likelihood that uses the likelihood of an alternative parametric auxiliary model, have been explored throughout the literature as a viable alternative when the model of interest is complex. One of these methods is called the synthetic likelihood (SL), which uses a multivariate normal approximation of the distribution of a set of summary statistics. This article explores the accuracy and computational efficiency of the Bayesian version of the synthetic likelihood (BSL) approach in comparison to a competitor known as approximate Bayesian computation (ABC) and its sensitivity to its tuning parameters and assumptions. We relate BSL to pseudo-marginal methods and propose to use an alternative SL that uses an unbiased estimator of the SL, when the summary statistics have a multivariate normal distribution. Several applications of varying complexity are considered to illustrate the findings of this article. Supplemental materials are available online. Computer code for implementing the methods on all examples is available at https://github.com/cdrovandi/Bayesian-Synthetic-Likelihood.     

Factors affecting the process of proficient mental addition and subtraction: case studies of flexible and inflexible computers

The relationship between mental computation and number sense is complex: mental computation can facilitate number sense when students are encouraged to be flexible, but flexibility and number sense is neither sufficient nor necessary for accuracy in mental computation. It is possible for familiarity with a strategy to compensate for a lack of number sense and inefficient processes. This study reports on six case studies exploring Year 3 students’ procedures for and understanding of mental addition and subtraction, and understanding of number sense and other cognitive, metacognitive, and affective factors associated with mental computation. The case studies indicate that the mental computation process is composed of four stages in which cognitive, metacognitive and affective factors operate differently for flexible and inflexible computers. The authors propose a model in which the differences between computer types are seen in terms of the application of different knowledges in number facts, numeration, effect of operation on number, and beliefs and metacognition on strategy choice and strategy implementation.     

Collective Mathematical Understanding as Improvisation

This article explores the phenomenon of mathematical understanding, and offers a response to the question raised by Martin (2001) at the Annual Meeting of the Psychology of Mathematics Education Group (North American Chapter) about the possibility for and nature of collective mathematical understanding. In referring to collective mathematical understanding, we point to the kinds of learning and understanding we may see occurring when a group of learners work together on a piece of mathematics. We characterize the growth of collective mathematical understanding as a creative and emergent improvisational process and illustrate how this can be observed in action. In doing this, we demonstrate how a collective perspective on mathematical understanding can more fully explain its growth. We also discuss how considering the growth of mathematical understanding as a collective process has implications for classroom practice and in particular for the setting of mathematical tasks.     

A No-Free-Lunch theorem for non-uniform distributions of target functions

The sharpened No-Free-Lunch-theorem (NFL-theorem) states that, regardless of the performance measure, the performance of all optimization algorithms averaged uniformly over any finite set F of functions is equal if and only if F is closed under permutation (c.u.p.). In this paper, we first summarize some consequences of this theorem, which have been proven recently: The number of subsets c.u.p. can be neglected compared to the total number of possible subsets. In particular, problem classes relevant in practice are not likely to be c.u.p. The average number of evaluations needed to find a desirable (e.g., optimal) solution can be calculated independent of the optimization algorithm in certain scenarios. Second, as the main result, the NFL-theorem is extended. Necessary and sufficient conditions for NFL-results to hold are given for arbitrary distributions of target functions. This yields the most general NFL-theorem for optimization presented so far.     

Failure in Complex Social Networks

A class of inhomogenously wired networks called “scale-free” networks have been shown to be more robust against failure than more homogenously connected exponential networks. The robustness of scale-free networks consists in their ability to remain connected even when failure occurs. The diffusion of information and disease across a network only requires a single contact between nodes, making network connectivity the crucial determinant of whether or not these “simple contagions” will spread. However, for “complex contagions,” such as social movements, collective behaviors, and cultural and social norms, multiple reinforcing ties are needed to support the spread of a behavior diffusion. I show that scale-free networks are much less robust than exponential networks for the spread of complex contagions, which highlights the value of more homogenously distributed social networks for the robust transmission of collective behavior.     

Task‐performing dynamics in irregular,biomimetic networks

Understanding self‐organized collective dynamics—especially in sparsely connected, noisy, and imperfect networks—has important implications for designing and optimizing task‐performing technological systems as well as for deciphering biological structures and functions. We note that stomatal arrays on plant leaves might provide an ideal example of task‐performance in this context. Guided by observations of stomatal networks, we examined a simple model of task‐performing, collective dynamics that included state noise, spatial rule heterogeneity, dynamic modules, and network rewiring. Our results indicate that task‐performance in such networks can actually be enhanced by various kinds of spatial and temporal irregularity. © 2007 Wiley Periodicals, Inc. Complexity 12: 14–21, 2007     

Emergence of order from chaos by cooperative non-biased learning between random bit-strings

Numerical experiments show that non-biased learning between families of independent and random bit-strings causes order. A parallel distributed learning between these bit-strings is performed by a neural network of the type pattern associator. The system allows emergence of some order in the learning matrix when a non-linear process is used, while a linear learning is unable to break the learning-matrix randomness. This neural network is in fact a complex and non-linear dynamical system, and consequently is able to self-organize order from chaos. It is also a model of collective proto-cognition that would describe biological evolution in species by cooperative learning. Our model suggests that the cause of evolution towards order in complex systems, can be just the learning process.     

Soliton solutions and Bäcklund transformation for the complex Ginzburg-Landau equation

Symbolically investigated in this paper is the complex Ginzburg-Landau (CGL) equation. With the Hirota method, both bright and dark soliton solutions for the CGL equation are obtained simultaneously. New Bäcklund transformation in the bilinear form is derived. Relevant properties and features are discussed. Solitons can be compressed (amplified) when the nonlinear (linear) dispersion effect is enhanced. Meanwhile, central frequency of the soliton can be affected by the nonlinear and linear dispersion effects. Besides, directions of the movement for the soliton central frequency can be adjusted. Results of this paper would be of certain value to the studies on the soliton compression and amplification.     

Efficient automatic simulation of parallel computation on networks of workstations

Andrews et al. [Automatic method for hiding latency in high bandwidth networks, in: Proceedings of the ACM Symposium on Theory of Computing, 1996, pp. 257-265; Improved methods for hiding latency in high bandwidth networks, in: Proceedings of the Eighth Annual ACM Symposium on Parallel Algorithms and Architectures, 1996, pp. 52-61] introduced a number of techniques for automatically hiding latency when performing simulations of networks with unit delay links on networks with arbitrary unequal delay links. In their work, they assume that processors of the host network are identical in computational power to those of the guest network being simulated. They further assume that the links of the host are able to pipeline messages, i.e., they are able to deliver P packets in time O(P+d) where d is the delay on the link.In this paper we examine the effect of eliminating one or both of these assumptions. In particular, we provide an efficient simulation of a linear array of homogeneous processors connected by unit-delay links on a linear array of heterogeneous processors connected by links with arbitrary delay. We show that the slowdown achieved by our simulation is optimal. We then consider the case of simulating cliques by cliques; i.e., a clique of heterogeneous processors with arbitrary delay links is used to simulate a clique of homogeneous processors with unit delay links. We reduce the slowdown from the obvious bound of the maximum delay link to the average of the link delays. In the case of the linear array we consider both links with and without pipelining. For the clique simulation the links are not assumed to support pipelining.The main motivation of our results (as was the case with Andrews et al.) is to mitigate the degradation of performance when executing parallel programs designed for different architectures on a network of workstations (NOW). In such a setting it is unlikely that the links provided by the NOW will support pipelining and it is quite probable the processors will be heterogeneous. Combining our result on clique simulation with well-known techniques for simulating shared memory PRAMs on distributed memory machines provides an effective automatic compilation of a PRAM algorithm on a NOW.     

Binary games in constitutional form and collective choice

In this paper, we define the notion of binary game in constitutional form. For this game, we define a core and give a necessary and sufficient condition for a game to be stable.We define a representation of a collective choice rule by a binary game in constitutional form and characterize those collective choice rules which are representable.We finally introduce the notion of c-social decision function and characterize, as an application of our theorem on stability of binary constitutional games, the collective choice rules which are c-social decision functions.Our representation of a collective choice rule by a binary game in constitutional form is an obvious improvement of the classical representation by a simple game.     

Robin型离散Schwarz波形松弛算法的收敛性分析

Schwarz波形松弛(Schwarz waveform relaxation,SWR)是一种新型区域分解算法,是当今并行计算研究领域的焦点之一,但针对该算法的收敛性分析基本上都停留在时空连续层面.从实际计算角度看,分析离散SWR算法的收敛性更重要.本文考虑SWR研究领域中非常流行的Robin型人工边界条件,分析时空离散参数t和x、模型参数等因素对算法收敛速度的影响.Robin型人工边界条件中含有一个自由参数p,可以用来优化算法的收敛速度,但最优参数的选取却需要求解一个非常复杂的极小-极大问题.本文对该极小-极大问题进行深入分析,给出最优参数的计算方法.本文给出的数值实验结果表明所获最优参数具有以下优点:(1)相比连续情形下所获最优参数,利用离散情形下获得的参数可以进一步提高Robin型SWR算法在实际计算中的收敛速度,当固定t或x而令另一个趋于零时,利用离散情形下所获参数可以使算法的收敛速度具有鲁棒性(即收敛速度不随离散参数的减小而持续变慢).(2)相比连续情形下所获收敛速度估计,离散情形下获得的收敛速度估计可以更加准确地预测算法的实际收敛速度.     

A hierarchical ant based clustering algorithm and its use in three real-world applications

In this paper is presented a new model for data clustering, which is inspired from the self-assembly behavior of real ants. Real ants can build complex structures by connecting themselves to each others. It is shown is this paper that this behavior can be used to build a hierarchical tree-structured partitioning of the data according to the similarities between those data. Several algorithms have been detailed using this model (called AntTree): deterministic or stochastic algorithms that may use or not global or local thresholds. Those algorithms have been evaluated using artificial and real databases. Our algorithms obtain competitive results when compared to the Kmeans, to ANTCLASS, and to Ascending Hierarchical Clustering. AntTree has been applied to three real world applications: the analysis of human healthy skin, the on-line mining of web sites usage, and the automatic construction of portal sites.     

Secure collaborative supply chain planning and inverse optimization – The JELS model

It is a well-acknowledged fact that collaboration between different members of a supply chain yields a significant potential to increase overall supply chain performance. Sharing private information has been identified as prerequisite for collaboration and, at the same time, as one of its major obstacles. One potential avenue for overcoming this obstacle is Secure Multi-Party Computation (SMC). SMC is a cryptographic technique that enables the computation of any (well-defined) mathematical function by a number of parties without any party having to disclose its input to another party. In this paper, we show how SMC can be successfully employed to enable joint decision-making and benefit sharing in a simple supply chain setting. We develop secure protocols for implementing the well-known “Joint Economic Lot Size (JELS) Model” with benefit sharing in such a way that none of the parties involved has to disclose any private (cost and capacity) data. Thereupon, we show that although computation of the model’s outputs can be performed securely, the approach still faces practical limitations. These limitations are caused by the potential of “inverse optimization”, i.e., a party can infer another party’s private data from the output of a collaborative planning scheme even if the computation is performed in a secure fashion. We provide a detailed analysis of “inverse optimization” potentials and introduce the notion of “stochastic security”, a novel approach to assess the additional information a party may learn from joint computation and benefit sharing. Based on our definition of “stochastic security” we propose a stochastic benefit sharing rule, develop a secure protocol for this benefit sharing rule, and assess under which conditions stochastic benefit sharing can guarantee secure collaboration.     

Dynamically stable control of articulated crowds

The synthesis of realistic complex body movements in real-time is a difficult problem in computer graphics and in robotics. High realism requires the accurate modeling of the details of the trajectories for a large number of degrees of freedom. At the same time, real-time animation necessitates flexible systems that can adapt and react in an online fashion to changing external constraints. Such behaviors can be modeled with nonlinear dynamical systems in combination with appropriate learning methods. The resulting mathematical models have manageable mathematical complexity, allowing to study and design the dynamics of multi-agent systems. We introduce Contraction Theory as a tool to treat the stability properties of such highly nonlinear systems. For a number of scenarios we derive conditions that guarantee the global stability and minimal convergence rates for the formation of coordinated behaviors of crowds. In this way we suggest a new approach for the analysis and design of stable collective behaviors in crowd simulation.     

An effective hybrid algorithm for computing symbolic determinants

A hybrid algorithm for computing the determinant of a matrix whose entries are polynomials is presented. It is based on the dimension-decreasing algorithm [22] and the parallel algorithm for computing a symbolic determinant of [19]. First, through the dimension-decreasing algorithm, a given multivariate matrix can be converted to a bivariate matrix. Then, the parallel algorithm can be applied to effectively compute the determinant of the bivariate matrix. Experimental results show that the new algorithm can not only reduce enormously the intermediate expression swell in the process of symbolic computation, but also achieve higher degree of parallelism, compared with the single parallel algorithm given in [19].     

行列式detVn-(x1,...,xn)的准确值及其应用

本文给出行列式Ｖ_n^-(x₁,...,x_n)的准确值，它是通常的Ｖａｎｄｅｒｍｏｄｅ行列式计算公式的推广，以及它在理论上的一些重要应用．