Laws of Large Numbers for Cesàro alpha-integrable Random Variables under Dependence Condition AANA or AQSI

Both residual Cesàro alpha-integrability (RCI( α)) and strongly residual Cesàro alpha-integrability (SRCI(α)) are two special kinds of extensions to uniform integrability, and both asymp-totically almost negative association (AANA) and asymptotically quadrant sub-independence (AQSI) are two special kinds of dependence structures. By relating the RCI(α) property as well as the SRCI(α) property with dependence condition AANA or AQSI, we formulate some tail-integrability conditions under which for appropriate α the RCI(α) property yields L1-convergence results and the SRCI(α) property yields strong laws of large numbers, which is the continuation of the corresponding literature.     

GI/G/1排队系统队长的强大数定律和中心极限定理

本文首先证明当服务强度小于1时,GI/G/1排队系统的队长是一个特殊的马尔可夫骨架过程——正常返的Doob骨架过程,然后运用马尔可夫骨架过程的强大数定律和中心极限定理等重要结果,给出了队长的累积过程的期望和方差,并给出了该累积过程满足强大数定律和中心极限定理的充分条件。     

测量金属导线热导率的新方法

用双臂电桥测量一定温度下铜导线的电阻,进而计算得到铜线的电导率,再根据维德曼-夫兰兹定律得到铜线的热导率.     

Algebraic methods for inferring biochemical networks: A maximum likelihood approach

We present a novel method for identifying a biochemical reaction network based on multiple sets of estimated reaction rates in the corresponding reaction rate equations arriving from various (possibly different) experiments. The current method, unlike some of the graphical approaches proposed in the literature, uses the values of the experimental measurements only relative to the geometry of the biochemical reactions under the assumption that the underlying reaction network is the same for all the experiments. The proposed approach utilizes algebraic statistical methods in order to parametrize the set of possible reactions so as to identify the most likely network structure, and is easily scalable to very complicated biochemical systems involving a large number of species and reactions. The method is illustrated with a numerical example of a hypothetical network arising from a “mass transfer”-type model.     

Critically indecomposable graphs

An undirected graph G=(V,E) with a specific subset X⊂V is called X-critical if G and G(X), induced subgraph on X, are indecomposable but G(V−{w}) is decomposable for every w∈V−X. This is a generalization of critically indecomposable graphs studied by Schmerl and Trotter [J.H. Schmerl, W.T. Trotter, Critically indecomposable partially ordered sets, graphs, tournaments and other binary relational structures, Discrete Mathematics 113 (1993) 191-205] and Bonizzoni [P. Bonizzoni, Primitive 2-structures with the (n−2)-property, Theoretical Computer Science 132 (1994) 151-178], who deal with the case where X is empty.We present several structural results for this class of graphs and show that in every X-critical graph the vertices of V−X can be partitioned into pairs (a₁,b₁),(a₂,b₂),…,(a_m,b_m) such that G(V−{a_j1,b_j1,…,a_jk,b_jk}) is also an X-critical graph for arbitrary set of indices {j₁,…,j_k}. These vertex pairs are called commutative elimination sequence. If G is an arbitrary indecomposable graph with an indecomposable induced subgraph G(X), then the above result establishes the existence of an indecomposability preserving sequence of vertex pairs (x₁,y₁),…,(x_t,y_t) such that x_i,y_i∈V−X. As an application of the commutative elimination sequence of an X-critical graph we present algorithms to extend a 3-coloring (similarly, 1-factor) of G(X) to entire G.     

Displacement exponent for loop-erased random walk on the Sierpiński gasket

We prove that loop-erased random walks on the finite pre-Sierpiński gaskets can be extended to a loop-erased random walk on the infinite pre-Sierpiński gasket by using the ‘erasing-larger-loops-first’ method, and obtain the asymptotic behavior of the walk as the number of steps increases, in particular, the displacement exponent and a law of the iterated logarithm.     

Developing an algorithm for compression, multiplexing and enhancement of multiple images

Image compression is one of the important fields that has useful applications in data storage and transmission. In this research a new algorithm is developed and tested for multiple-image compression and enhancement. The algorithm, in addition, is applied to multiple noisy images. Also, the effect of compression ratio on the peak signal to noise ratio (PSNR) is explored by applying different compression ratios. The developed algorithm gives good compression and noise immunity. It can be used for storage/transmission of encrypted and compressed information.     

Evolutionary model of the growth and size of firms

The key idea of this model is that firms are the result of an evolutionary process. Based on demand and supply considerations the evolutionary model presented here derives explicitly Gibrat’s law of proportionate effects as the result of the competition between products. Applying a preferential attachment mechanism for firms, the theory allows to establish the size distribution of products and firms. Also established are the growth rate and price distribution of consumer goods. Taking into account the characteristic property of human activities to occur in bursts, the model allows also an explanation of the size–variance relationship of the growth rate distribution of products and firms. Further the product life cycle, the learning (experience) curve and the market size in terms of the mean number of firms that can survive in a market are derived. The model also suggests the existence of an invariant of a market as the ratio of total profit to total revenue. The relationship between a neo-classic and an evolutionary view of a market is discussed. The comparison with empirical investigations suggests that the theory is able to describe the main stylized facts concerning the size and growth of firms.     

On consistency of stationary points of stochastic optimization problems in a Banach space

Recently, Balaji and Xu studied the consistency of stationary points, in the sense of the Clarke generalized gradient, for the sample average approximations to a one-stage stochastic optimization problem in a separable Banach space with separable dual. We present an alternative approach, showing that the restrictive assumptions that the dual space is separable and the Clarke generalized gradient is a (norm) upper semicontinuous and compact-valued multifunction can be dropped. For that purpose, we use two results having independent interest: a strong law of large numbers and a multivalued Komlós theorem in the dual to a separable Banach space, and a result on the weak* closedness of the expectation of a random weak* compact convex set.