Linear spaces and transversal designs: k-anonymous combinatorial configurations for anonymous database search notes

Anonymous database search protocols allow users to query a database anonymously. This can be achieved by letting the users form a peer-to-peer community and post queries on behalf of each other. In this article we discuss an application of combinatorial configurations (also known as regular and uniform partial linear spaces) to a protocol for anonymous database search, as defining the key-distribution within the user community that implements the protocol. The degree of anonymity that can be provided by the protocol is determined by properties of the neighborhoods and the closed neighborhoods of the points in the combinatorial configuration that is used. Combinatorial configurations with unique neighborhoods or unique closed neighborhoods are described and we show how to attack the protocol if such configurations are used. We apply k-anonymity arguments and present the combinatorial configurations with k-anonymous neighborhoods and with k-anonymous closed neighborhoods. The transversal designs and the linear spaces are presented as optimal configurations among the configurations with k-anonymous neighborhoods and k-anonymous closed neighborhoods, respectively.     

Goodwill,inventory penalty,and adaptive supply chain management

Information visibility is generally useful for decision makers distributed across supply chains. Availability of information on inventory levels, price, lead times, demand, etc. can help reduce uncertainties as well as alleviate problems associated with bullwhip effect. A majority of extant literature in this area assume a static supply chain network configuration. While this was sufficient a few decades ago, advances in e-commerce and the ease with which order processing can be performed over the Internet necessitates appropriate dynamic (re)configuration of supply chains over time. Each node in the supply chain is modeled as an actor who makes independent decisions based on information gathered from the next level upstream. A knowledge-based framework is used for dynamic supply chain configuration and to consider the effects of inventory constraints and ‘goodwill,’ as well as their effects on the performance dynamics of supply chains. Preliminary results indicate that neither static nor dynamic configurations are consistently dominant. Scenarios where static configurations perform better than the modeled system are identified.     

Wiener path intersections and local time

We study intersection properties of Wiener processes in the plane. For each positive integer k we show that k independent Wiener processes intersect almost surely in a set of Hausdorff dimension two, and that the set of points a single process visits at least k distinct times also has dimension two. We construct a functional on configurations of k independent Wiener processes that measures the extent to which the trajectories of the k processes intersect. We prove certain L^p estimates for this functional and show that it is a local time for a certain vector-valued multiparameter stochastic process.     

Knowledge-based framework for automated dynamic supply chain configuration

Supply chain management has gained renewed interest among researchers in recent years. This is primarily due to the availability of timely information across the various stages of the supply chain, and therefore the need to effectively utilize the information for improved performance. Although information plays a major role in effective functioning of supply chains, there is a paucity of studies that deal specifically with the dynamics of supply chains and how data collected in these systems can be used to improve their performance. In this paper I develop a framework, with machine learning, for automated supply chain configuration. Supply chain configuration used to be mostly a one-shot problem. Once a supply chain is configured, researchers and practitioners were more interested in means to improve performance given that initial configuration. However, recent developments in e-commerce applications and faster communication over the Internet in general necessitates dynamic (re)configuration of supply chains over time to take advantage of better configurations. Using examples, I show performance improvements of the proposed adaptive supply chain configuration framework over static configurations.     

Characterization of affine Steiner triple systems and Hall triple systems

It is known that a Steiner triple system is projective if and only if it does not contain the four-triple configuration C₁₄. We find three configurations such that a Steiner triple system is affine if and only if it does not contain any of these configurations. Similarly, we characterize Hall triple systems, a superclass of affine Steiner triple systems, using two forbidden configurations.     

Geometric configurations of singularities for quadratic differential systems with three distinct real simple finite singularities

In this work we classify, with respect to the geometric equivalence relation, the global configurations of singularities, finite and infinite, of quadratic differential systems possessing exactly three distinct finite simple singularities. This relation is finer than the topological equivalence relation which does not distinguish between a focus and a node or between a strong and a weak focus or between foci (or saddles) of different orders. Such distinctions are, however, important in the production of limit cycles close to the foci (or loops) in perturbations of the systems. The notion of geometric equivalence relation of configurations of singularities allows us to incorporate all these important geometric features which can be expressed in purely algebraic terms. The geometric classification of all configurations of singularities, finite and infinite, of quadratic systems was initiated in a work published in 2013 when the classification was done for systems with total multiplicity m _f of finite singularities less than or equal to one. That work was continued in an article which is due to appear in 2014 where the geometric classification of configurations of singularities was done for the case m _f = 2. In this article we go one step further and obtain the geometric classification of singularities, finite and infinite, for the subclass mentioned above. We obtain 147 geometrically distinct configurations of singularities for this family. We give here the global bifurcation diagram of configurations of singularities, both finite and infinite, with respect to the geometric equivalence relation, for this class of systems. The bifurcation set of this diagram is algebraic. The bifurcation diagram is done in the 12-dimensional space of parameters and it is expressed in terms of polynomial invariants, a fact which gives us an algorithm for determining the geometric configuration of singularities for any quadratic system in this particular class.     

An analogue of the big <Emphasis Type="Italic">q</Emphasis>-Jacobi polynomials in the algebra of symmetric functions

It is well known how to construct a system of symmetric orthogonal polynomials in an arbitrary finite number of variables from an arbitrary system of orthogonal polynomials on the real line. In the special case of the big q-Jacobi polynomials, the number of variables can be made infinite. As a result, in the algebra of symmetric functions, there arises an inhomogeneous basis whose elements are orthogonal with respect to some probability measure. This measure is defined on a certain space of infinite point configurations and hence determines a random point process.     

Dynamic multiple criteria decision making in changeable spaces: from habitual domains to innovation dynamics

Human behaviors involve dynamic, evolving, interactive and adaptive processes. Important decision makings usually are dynamic, involving multiple criteria in changeable spaces. This article introduces the behavior mechanism that integrates the findings of neural science, psychology, system science, optimization theory and multiple criteria decision making. It shows how our brain and mind operate and describes our behaviors and decision making as dynamic processes of multiple criteria decision making in changeable spaces. Unless extraordinary events occur or special effort exerted, the dynamic processes will be stabilized in certain domains, known as Habitual Domains. Habitual Domains, which play a vital role in upgrading the quality of our decision making and lives, will be explored. In addition, as important consequential derivatives, concepts of Competence Set Analysis and Innovation Dynamics will also be discussed. Note that these concepts involve transitions between dynamic and static states.     

The k-means range algorithm for personalized data clustering in e-commerce

This paper describes the k-means range algorithm, a combination of the partitional k-means clustering algorithm with a well known spatial data structure, namely the range tree, which allows fast range searches. It offers a real-time solution for the development of distributed interactive decision aids in e-commerce since it allows the consumer to model his preferences along multiple dimensions, search for product information, and then produce the data clusters of the products retrieved to enhance his purchase decisions. This paper also discusses the implications and advantages of this approach in the development of on-line shopping environments and consumer decision aids in traditional and mobile e-commerce applications.     

电子商务信息系统安全管理体系PRS-ISMS的研究

信息是电子商务至关重要的资产,电子商务的正常运转必须建立在安全的信息系统之上,因而电子商务信息系统安全问题成为人们日益关注的重点.根据电子商务信息系统特点,从信息系统过程(Process)、资源(Resource)和安全目标(Security)三个视角分析了电子商务信息安全风险的要素及其关系,构建了三维信息系统安全管理体系模型PRS-ISMS,提出了改进的信息安全风险管理过程PRS-PDCA.     

Simulation study on the formation and transition properties of cluster structures in liquid metals during rapid cooling processes

For the first time, a molecular dynamics simulation study has been performed for a liquid metal system consisting of 50000 atoms to deeply investigate the transitions of microstructure configurations dudng the rapid cooling processes. Especially, the cluster-type index method has been adopted to analyze the transforming and evolving processes of clusters and cluster configurations from liquid metal atoms. It has been found that the bigger cluster configurations in the system are formed by means of connecting some small clusters (they are combined by several smaller clusters), and not taken on the multi-shells configuration accumulated with an atom as the center and the surrounding atoms arranged according to some fixed pattern. With the decrease in temperature, the probability of repetitive appearance for clusters increases largely, which reveals that clusters are indeed possessing a certain relative stability and continuity (namely hereditary effect). These results will give us an important enlightenment to understand not only the forming mechanisms and microscopic processes of the short-order sections and disorder sparse sections in amorphous structures but also the freezing processes of liquid metals.``     

Stability properties of steady-states for a network of ferromagnetic nanowires

We investigate the problem of describing the possible stationary configurations of the magnetic moment in a network of ferromagnetic nanowires with length L connected by semiconductor devices, or equivalently, of its possible L-periodic stationary configurations in an infinite nanowire. The dynamical model that we use is based on the one-dimensional Landau–Lifshitz equation of micromagnetism. We compute all L-periodic steady-states of that system, define an associated energy functional, and these steady-states share a quantification property in the sense that their energy can only take some precise discrete values. Then, based on a precise spectral study of the linearized system, we investigate the stability properties of the steady-states.     

Optimal paths for minimizing entransy dissipation during heat transfer processes with generalized radiative heat transfer law

A common of finite-time heat transfer processes between high- and low-temperature sides with generalized radiative heat transfer law [q ∝ Δ(Tⁿ)] is studied in this paper. In general, the minimization of entropy generation in heat transfer processes is taken as the optimization objective. A new physical quantity, entransy, has been identified as a basis for optimizing heat transfer processes in terms of the analogy between heat and electrical conduction recently. Heat transfer analyses show that the entransy of an object describes its heat transfer ability, as the electrical energy in a capacitor describes its charge transfer ability. Entransy dissipation occurs during heat transfer processes, as a measure of the heat transfer irreversibility with the dissipation related thermal resistance. Under the condition of fixed heat load, the optimal configurations of hot and cold fluid temperatures for minimizing entransy dissipation are derived by using optimal control theory. The condition corresponding to the minimum entransy dissipation strategy with Newtonian heat transfer law (n = 1) is that corresponding to a constant heat flux rate, while the condition corresponding to the minimum entransy dissipation strategy with the linear phenomenological heat transfer law (n = −1) is that corresponding to a constant ratio of hot to cold fluid temperatures. Numerical examples for special cases with Newtonian, linear phenomenological and radiative heat transfer law (n = 4) are provided, and the obtained results are also compared with the conventional strategies of constant heat flux rate and constant hot fluid (reservoir) temperature operations and optimal strategies for minimizing entropy generation. Moreover, the effects of heat load changes on the optimal hot and fluid temperature configurations are also analyzed.     

The central configurations of four masses x, −x, y, −y

The configuration of a homothetic motion in the N-body problem is called a central configuration. In this paper, we prove that there are exactly three planar non-collinear central configurations for masses x, −x, y, −y with x≠y (a parallelogram and two trapezoids) and two planar non-collinear central configurations for masses x, −x, x, −x (two diamonds). Except the case studied here, the only known case where the four-body central configurations with non-vanishing masses can be listed is the case with equal masses (A. Albouy, 1995-1996), which requires the use of a symbolic computation program. Thanks to a lemma used in the proof of our result, we also show that a co-circular four-body central configuration has non-vanishing total mass or vanishing multiplier.     

Sojourn times in a processor sharing queue with multiple vacations

We study an M/G/1 processor sharing queue with multiple vacations. The server only takes a vacation when the system has become empty. If he finds the system still empty upon return, he takes another vacation, and so on. Successive vacations are identically distributed, with a general distribution. When the service requirements are exponentially distributed we determine the sojourn time distribution of an arbitrary customer. We also show how the same approach can be used to determine the sojourn time distribution in an M/M/1-PS queue of a polling model, under the following constraints: the service discipline at that queue is exhaustive service, the service discipline at each of the other queues satisfies a so-called branching property, and the arrival processes at the various queues are independent Poisson processes. For a general service requirement distribution we investigate both the vacation queue and the polling model, restricting ourselves to the mean sojourn time.     

Application of Computer Algebra System and the Mean-Value Theory for Evaluating Electrostatic Potential and Its Associated Field for Nontrivial Configurations

Evaluation of electrostatic potential at an arbitrary point within a two dimensional region free of electric charge containing geometrically dispersed nontrivial configurations electrified to constant potentials applying the standard classic approach, i.e. Laplace equation is challenging. The challenge stems from the fact that the solution of the Laplace equation needs to be adjusted to the boundary conditions imposed with the configurations. Numeric solution of the latter is challenging as it lacks generalities. There exist an alternative numeric method which is based on the application of The Mean-Value Theory. The latter is a pure numeric approach; although the output of its iterated refined version is successful, it is cumbersome. In this investigation utilizing the powerful features of Computer Algebra Systems, specifically Mathematica by a way of example we show an innovative approach. Our approach is based on a combination of numeric aspect of The Mean-Value Theory on one hand and Mathematica features on the other hand. This semi numeric-symbolic approach not only provides the desired output, but it also generates information beyond the scope of the standard classic method. By way of example we present the intricacies of our approach, showing (1) how the potential is evaluated and (2) how corollary essential information not addressed in classic cases such as electric field is calculated as well. Our method is applied to a two-dimensional case; its three dimensional version may easily be applied to cases of interest.     

Combinatoric enumeration of two-dimensional proper arrays

An n×mproper array is a two-dimensional rectangular array composed of directed cubes that obey certain constraints. Because of these constraints, the n×m proper arrays may be classified via a schema in which each n×m proper array is associated with a particular n×1 column. For a fixed n, the goal is to enumerate, modulo symmetry, all possible edge configurations associated with n×m proper arrays. By varying n, one constructs four combinatoric sequences, each of which enumerates a particular class of edge configurations. Convolution arguments and resultant calculations associate these sequences with cubic equations. These cubic equations allow one to predict M_n, the number of edge configurations, modulo symmetry, associated with n×m proper arrays.     

A BK inequality for randomly drawn subsets of fixed size

The BK inequality (van den Berg and Kesten in J Appl Probab 22:556?C569, 1985) says that, for product measures on {0, 1} ⁿ , the probability that two increasing events A and B ??occur disjointly?? is at most the product of the two individual probabilities. The conjecture in van den Berg and Kesten (1985) that this holds for all events was proved by Reimer (Combin Probab Comput 9:27?C32, 2000). Several other problems in this area remained open. For instance, although it is easy to see that non-product measures cannot satisfy the above inequality for all events, there are several such measures which, intuitively, should satisfy the inequality for all increasing events. One of the most natural candidates is the measure assigning equal probabilities to all configurations with exactly k 1??s (and probability 0 to all other configurations). The main contribution of this paper is a proof for these measures. We also point out how our result extends to weighted versions of these measures, and to products of such measures.