This is a sequel of our previous work [8] on characterization of maximum sum rate of slotted Aloha networks. By extending the analysis to incorporate the capacity-achieving receiver structure, Successive Interference Cancellation (SIC), this paper aims to identify the rate loss due to random access. Specifically, two representative SIC receivers are considered, i.e, ordered SIC where packets ar...

The specific methods of the maximum average mutual information quantization are analyzed and deduced. With this method to quantify the initial message, the variable messages and check messages are converted into integers. Then the min-sum decoding algorithm based on integer arithmetic is implemented. Simulation results demonstrate that the decoding performance of min-sum algorithm based on inte...

We review the use of the Bird-Meertens Formalism as a vehicle for the construction of programs with massive implicit parallelism. We show that a simple result from the theory, concerning the expression of list homomorph-isms, can help us in our search for parallel algorithms and demonstrate its application to some simple problems including the maximum segment sum problem. Our main purpose is to...

The Balaban index of a connected graph G is defined as J(G) = |E(G)| μ+ 1 ∑ e=uv∈E(G) 1 √ DG(u)DG(v) , and the Sum-Balaban index is defined as SJ(G) = |E(G)| μ+ 1 ∑ e=uv∈E(G) 1 √ DG(u)+DG(v) , where DG(u) = ∑ w∈V (G) dG(u,w), and μ is the cyclomatic number of G. In this paper, the unicyclic graphs with the maximum Balaban index and the maximum Sum-Balaban index among all unicyclic graphs on n v...

this becomes false if (BI), (Be) and (B) are replaced by (Nt), (NM) and (N), respectively. This follows, even for p = 2 = q, from the above example proving that (NW) is not linear. Correspondingly, (Ne) cannot be interpreted as the dual space of (NP), since such an interpretation would involve the definition of a scalar product. 7. Let (Nt) denote the space which relates to the space (Nt) in th...

Sum-product networks (SPNs) are a class of probabilistic graphical models that allow tractable marginal inference. However, the maximum a posteriori (MAP) inference in SPNs is NP-hard. We investigate MAP inference in SPNs from both theoretical and algorithmic perspectives. For the theoretical part, we reduce general MAP inference to its special case without evidence and hidden variables; we als...

We study the problem of permuting each column of a given matrix to achieve minimum maximal row sum or maximum minimal row sum, a problem of interest in probability theory and quantitative finance where quantiles of a random variable expressed as the sum of several random variables with unknown dependence structure are estimated. If the minimum maximal row sum is equal to the maximum minimal row...

1.1 Algorithm 1: Brute Force Immediate from the definition is an algorithm with O(n3) work and O(log n) span. This algorithm examines all possible combinations of subsequences and for each one of them, it computes the sum and takes the maximum. Note that every subsequence of s can be represented by a starting position i and an ending position j. We will use the shorthand si.. j to denote the su...

We are given a sequence A of n real numbers which is to be preprocessed. In the Range Maximum-Sum Segment Query (RMSQ) problem, a query is comprised of two intervals [i, j] and [k, l] and our goal is to return the maximum-sum segment of A whose starting index lies in [i, j] and ending index lies in [k, l]. We propose the first known algorithm for this problem in O(n) preprocessing time and O(1)...

Previous work on the joint asymptotic distribution of the sum and maxima of Gaussian processes is extended here. In particular, it is shown that for a stationary sequence of standard normal random variables with correlation function r, the condition r(n) log n = o(1) as n →∞ suffices to establish the asymptotic independence of the sum and maximum.