We show that the graph isomorphism problem is hard under logarithmic space many-one reductions for the complexity classes NL, PL (probabilistic logarithmic space), for every logarithmic space modular class ModkL and for the class DET of problems NC1 reducible to the determinant. These are the strongest existing hardness results for the graph isomorphism problem, and imply a randomized logarithm...

The purpose of this paper is to establish fixed point results for a single mapping in a partially ordered modular metric space, and to prove a common fixed point theorem for two self-maps satisfying some weak contractive inequalities.

In this paper, we consider double sequence iteration processes for strongly $rho$-contractive mapping in modular space. It is proved, these sequences, convergence strongly to a fixed point of the strongly $rho$-contractive mapping.

This paper demonstrates the advantages of using a hybrid reinforcement–modular neural network architecture for non-linear control. Specifically, the method of ACTION-CRITIC reinforcement learning, modular neural networks, competitive learning and stochastic updating are combined. This provides an architecture able to both support temporal difference learning and probabilistic partitioning of th...

The prevalent strategy in the topology optimization phase is to select a subset of members existing in an excessively connected truss, called Ground Structure, such that the overall weight or cost is minimized. Although finding a good topology significantly reduces the overall cost, excessive growth of the size of topology space combined with existence of varied types of design variables challe...

Probabilistic programming languages (PPLs) allow programmers to construct statistical models and then simulate data or perform inference over them. Many PPLs restrict a particular instance of simulation inference, limiting their reusability. In other PPLs, are not readily composable. Using Haskell as the host language, we present an embedded domain specific language based on algebraic effects, ...

Causal message ordering (CMO) demands that messages directed to the same destinations must be delivered in an order consistent with their potential causality. In this paper, we present a modular decomposition of CMO, and evaluate the probability of breaking CMO by assuming two probabilistic models on message delays: exponential distribution and uniform distribution. These models represent the c...

a modular $k$-coloring, $kge 2,$ of a graph $g$ without isolated vertices is a coloring of the vertices of $g$ with the elements in $mathbb{z}_k$ having the property that for every two adjacent vertices of $g,$ the sums of the colors of the neighbors are different in $mathbb{z}_k.$ the minimum $k$ for which $g$ has a modular $k-$coloring is the modular chromatic number of $g.$ except for some s...