Non-Self-Embedding Grammars, Constant-Height Pushdown Automata, and Limited Automata

Non-self-embedding grammars are a restriction of context-free grammars which does not allow to describe recursive structures and, hence, which characterizes only the class of regular languages. A double exponential gap in size from non-self-embedding grammars to deterministic finite automata is known. The same size gap is also known from constant-height pushdown automata and [Formula: see text]-limited automata to deterministic finite automata. Constant-height pushdown automata and [Formula: see text]-limited automata are compared with non-self-embedding grammars. It is proved that non-self-embedding grammars and constant-height pushdown automata are polynomially related in size. Furthermore, a polynomial size simulation by [Formula: see text]-limited automata is presented. However, the converse transformation is proved to cost exponential. Finally, a different simulation shows that also the conversion of deterministic constant-height pushdown automata into deterministic [Formula: see text]-limited automata costs polynomial.

l-Valued multiset automata and l-valued multiset languages

The reason for this work is to present and study deterministic multiset automata, multiset automata and their languages with membership values in complete residuated lattice without zero divisors. We build up the comparability of deterministic [Formula: see text]-valued multiset finite automaton and [Formula: see text]-valued multiset finite automaton in sense of recognizability of a [Formula: see text]-valued multiset language. Then, we relate multiset regular languages to a given [Formula: see text]-valued multiset regular languages and vice versa. At last, we present the concept of pumping lemma for [Formula: see text]-valued multiset automata theory, which we utilize to give a necessary and sufficient condition for a [Formula: see text]-valued multiset language to be non-constant.

Multiobjective Maximization of Monotone Submodular Functions with Cardinality Constraint

We consider the problem of multiobjective maximization of monotone submodular functions subject to cardinality constraint, often formulated as [Formula: see text]. Although it is widely known that greedy methods work well for a single objective, the problem becomes much harder with multiple objectives. In fact, it is known that when the number of objectives m grows as the cardinality k, that is, [Formula: see text], the problem is inapproximable (unless P = NP). On the other hand, when m is constant, there exists a a randomized [Formula: see text] approximation with runtime (number of queries to function oracle) the scales as [Formula: see text]. We focus on finding a fast algorithm that has (asymptotic) approximation guarantees even when m is super constant. First, through a continuous greedy based algorithm we give a [Formula: see text] approximation for [Formula: see text]. This demonstrates a steep transition from constant factor approximability to inapproximability around [Formula: see text]. Then using multiplicative-weight-updates (MWUs), we find a much faster [Formula: see text] time asymptotic [Formula: see text] approximation. Although these results are all randomized, we also give a simple deterministic [Formula: see text] approximation with runtime [Formula: see text]. Finally, we run synthetic experiments using Kronecker graphs and find that our MWU inspired heuristic outperforms existing heuristics.

Category of L-valued Multiset Automata and Brzozowski’s Algorithm

The purpose of this work is to use the concepts of reachability and coreachability maps to provide a solution of a well-known characterization for [Formula: see text]-valued multiset regular languages. In between, we associate two deterministic [Formula: see text]-valued multiset automata with a given deterministic [Formula: see text]-valued multiset automaton (DLMA) and show that the reachability and coreachability maps of the given DLMA turn out to be morphisms in the category of deterministic [Formula: see text]-valued multiset automata.

DEVELOPMENT EQUATION FOR DETERMINATION THE START TIME OF SEEPAGE UNDER HYDRAULIC STRUCTURE RESTING ON SOIL CONTAINING A CAVITY

This study aims to introduce a formula for determination the start time of seepage when single cavity presence at a specific location within the homogenous soil under a hydraulic structure. The investigation aims to observe the effect of cavity locations and size on the start time of seepage. The experimental work has been done in three stages, the first stage includes 36 models of 75mm in diameter cavity, while the second and the third stages includes eight models for each with 100mm and 34mm diameter of cavity respectively. The analysis of result shows that, generally, the effect of cavity was positive in term of increasing the time of starting the seepage. To generate the deterministic formula the SPSS statistical software was used and the results of multiple regressions are checked by statistical indices. By this process more realistic formula has been proposed with acceptable reliability.

Monotone submodular maximization over the bounded integer lattice with cardinality constraints

We consider the problem of maximizing monotone submodular function over the bounded integer lattice with a cardinality constraint. Function [Formula: see text] is submodular over integer lattice if [Formula: see text], [Formula: see text], where ∨ and ∧ represent elementwise maximum and minimum, respectively. Let [Formula: see text], and [Formula: see text], we study the problem of maximizing submodular function [Formula: see text] with constraints [Formula: see text] and [Formula: see text]. A random greedy [Formula: see text]-approximation algorithm and a deterministic [Formula: see text]-approximation algorithm are proposed in this paper. Both algorithms work in value oracle model. In the random greedy algorithm, we assume the monotone submodular function satisfies diminishing return property, which is not an equivalent definition of submodularity on integer lattice. Additionally, our random greedy algorithm makes [Formula: see text] value oracle queries and deterministic algorithm makes [Formula: see text] value oracle queries.

Probability Analysis of a Perturbed Epidemic System with Relapse and Cure

This paper is devoted to a continuous-time stochastic differential system which is derived by incorporating white noise to a deterministic [Formula: see text] epidemic model with mass action incidence, cure and relapse. We focus on the impact of a relapse on the asymptotic properties of the stochastic system. We show that the relapse encourages the persistence of the disease in the population and we determine the threshold of the relapse rate, above the threshold the disease prevails in the population. Furthermore, we show that there exists a unique density function of solutions which converges in [Formula: see text], under certain conditions of the parameters to an invariant density.

Exact Distribution of Linkage Disequilibrium in the Presence of Mutation, Selection or Minor Allele Frequency Filtering

ABSTRACTLinkage disequilibrium (LD), often expressed in terms of the squared correlation (r2) between allelic values at two loci, is an important concept in many branches of genetics and genomics. Genetic drift and recombination have opposite effects on LD, and thus r2 will keep changing until the effects of these two forces are counterbalanced. Several approximations have been used to determine the expected value of r2 at equilibrium in the presence or absence of mutation. In this paper, we propose a probability-based approach to compute the exact distribution of allele frequencies at two loci in a finite population at any generation t conditional on the distribution at generation t − 1. As r2 is a function of this distribution of allele frequencies, this approach can be used to examine the distribution of r2 over generations as it approaches equilibrium. The exact distribution of LD from our method is used to describe, quantify and compare LD at different equilibria, including equilibrium in the absence or presence of mutation, selection, and filtering by minor allele frequency. We also propose a deterministic formula for expected LD in the presence of mutation at equilibrium based on the exact distribution of LD.

BIPARTITE EXPANDER MATCHING IS IN NC

A work-efficient deterministic [Formula: see text] algorithm is presented for finding a maximum matching in a bipartite expander graph with any expansion factor β > 1. This improves upon a recently presented deterministic [Formula: see text] maximum matching algorithm which is restricted to those bipartite expanders with large expansion factors (β ≥ Δ∊, ∊ > 0), and is not work-efficient [1].