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The behavior of a Markov network with respect to an absorbing class: the target algorithm

Giacomo Aletti (2009)

RAIRO - Operations Research

In this paper, we face a generalization of the problem of finding the distribution of how long it takes to reach a “target” set T of states in Markov chain. The graph problems of finding the number of paths that go from a state to a target set and of finding the n-length path connections are shown to belong to this generalization. This paper explores how the state space of the Markov chain can be reduced by collapsing together those states that behave in the same way for the purposes of calculating...

The logic of neural networks.

Juan Luis Castro, Enric Trillas (1998)

Mathware and Soft Computing

This paper establishes the equivalence between multilayer feedforward networks and linear combinations of Lukasiewicz propositions. In this sense, multilayer forward networks have a logic interpretation, which should permit to apply logical techniques in the neural networks framework.

The Orderly Colored Longest Path Problem – a survey of applications and new algorithms

Marta Szachniuk, Maria Cristina De Cola, Giovanni Felici, Jacek Blazewicz (2014)

RAIRO - Operations Research - Recherche Opérationnelle

A concept of an Orderly Colored Longest Path (OCLP) refers to the problem of finding the longest path in a graph whose edges are colored with a given number of colors, under the constraint that the path follows a predefined order of colors. The problem has not been widely studied in the previous literature, especially for more than two colors in the color arrangement sequence. The recent and relevant application of OCLP is related to the interpretation of Nuclear Magnetic Resonance experiments for...

The Placement of Electronic Circuits Problem: A Neural Network Approach

M. Ettaouil, K. Elmoutaouakil, Y. Ghanou (2010)

Mathematical Modelling of Natural Phenomena

The goal of this paper is to apply the Continuous Hopfield Networks (CHN) to the Placement of Electronic Circuit Problem (PECP). This assignment problem has been expressed as Quadratic Knapsack Problem (QKP). To solve the PECP via the CHN, we choose an energy function which ensures an appropriate balance between minimization of the cost function and simultaneous satisfaction of the PECP constraints. In addition, the parameters of this function must...

The spectral test of the Boolean function linearity

Piotr Porwik (2003)

International Journal of Applied Mathematics and Computer Science

The paper discusses the problem of recognizing the Boolean function linearity. A spectral method of the analysis of Boolean functions using the Walsh transform is described. Linearity and nonlinearity play important roles in the design of digital circuits. The analysis of the distribution of spectral coefficients allows us to determine various combinatorial properties of Boolean functions, such as redundancy, monotonicity, self-duality, correcting capability, etc., which seems more difficult be...

Time-varying time-delay estimation for nonlinear systems using neural networks

Yonghong Tan (2004)

International Journal of Applied Mathematics and Computer Science

Nonlinear dynamic processes with time-varying time delays can often be encountered in industry. Time-delay estimation for nonlinear dynamic systems with time-varying time delays is an important issue for system identification. In order to estimate the dynamics of a process, a dynamic neural network with an external recurrent structure is applied in the modeling procedure. In the case where a delay is time varying, a useful way is to develop on-line time-delay estimation mechanisms to track the time-delay...

Towards a characterization of bipartite switching classes by means of forbidden subgraphs

Jurriaan Hage, Tero Harju (2007)

Discussiones Mathematicae Graph Theory

We investigate which switching classes do not contain a bipartite graph. Our final aim is a characterization by means of a set of critically non-bipartite graphs: they do not have a bipartite switch, but every induced proper subgraph does. In addition to the odd cycles, we list a number of exceptional cases and prove that these are indeed critically non-bipartite. Finally, we give a number of structural results towards proving the fact that we have indeed found them all. The search for critically...

TPM: Transition probability matrix - Graph structural feature based embedding

Sarmad N. Mohammed, Semra Gündüç (2023)

Kybernetika

In this work, Transition Probability Matrix (TPM) is proposed as a new method for extracting the features of nodes in the graph. The proposed method uses random walks to capture the connectivity structure of a node's close neighborhood. The information obtained from random walks is converted to anonymous walks to extract the topological features of nodes. In the embedding process of nodes, anonymous walks are used since they capture the topological similarities of connectivities better than random...

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