Model Creation and Equivalence Proofs of Cellular Automata and Artificial Neural Networks

Computational methods and mathematical models have invaded arguably every scientific discipline forming its own field of research called computational science. Mathematical models are the theoretical foundation of computational science. Since Newton's time, differential equations in mathematical models have been widely and successfully used to describe the macroscopic or global behaviour of systems. With spatially inhomogeneous, time-varying, local element-specific, and often non-linear interactions, the dynamics of complex systems is in contrast more efficiently described by local rules and thus in an algorithmic and local or microscopic manner. The theory of mathematical modelling taking into account these characteristics of complex systems has to be established still. We recently presented a so-called allagmatic method including a system metamodel to provide a framework for describing, modelling, simulating, and interpreting complex systems. Implementations of cellular automata and artificial neural networks were described and created with that method. Guidance from philosophy were helpful in these first studies focusing on programming and feasibility. A rigorous mathematical formalism, however, is still missing. This would not only more precisely describe and define the system metamodel, it would also further generalise it and with that extend its reach to formal treatment in applied mathematics and theoretical aspects of computational science as well as extend its applicability to other mathematical and computational models such as agent-based models. Here, a mathematical definition of the system metamodel is provided. Based on the presented formalism, model creation and equivalence of cellular automata and artificial neural networks are proved. It thus provides a formal approach for studying the creation of mathematical models as well as their structural and operational comparison.Comment: 13 pages, 1 tabl

A Tutorial on Cross-layer Optimization Wireless Network System Using TOPSIS Method

Each other, leading to issues such as interference, limited bandwidth, and varying channel conditions. These challenges require specialized optimization techniques tailored to the wireless environment. In wireless communication networks is to maximize the overall system throughput while ensuring fairness among users and maintaining quality of service requirements. This objective can be achieved through resource allocation optimization, where the available network resources such as bandwidth, power, and time slots are allocated to users in an optimal manner. Optimization-based approaches in wireless resource allocation typically involve formulating the resource allocation problem as an optimization problem with certain constraints.. These techniques provide practical solutions with reduced computational complexity, although they may not guarantee optimality. In summary, optimization-based approaches have been instrumental in studying resource allocation problems in communication networks, including the wireless domain. While techniques from the Internet setting have influenced the understanding of congestion control and protocol design, specific challenges in wireless networks necessitate tailored optimization techniques that account for interference, limited bandwidth, and varying channel conditions. power allocation problem in wireless ad hoc networks Cross-layer optimization refers to the process of jointly optimizing the allocation of resources across different layers of wireless networks, the interactions between different layers become more complex due to the shared medium and time-varying channel conditions.  Nash equilibrium, where no user can unilaterally improve its own performance by changing its strategy. Game theory can capture the distributed nature of wireless networks and provide insights into the behavior of users in resource allocation scenarios Additionally, heuristics and approximation algorithms are often employed in wireless resource allocation due to the complexity of the optimization problems involved. In traditional cellular systems, each user is allocated a fixed time slot for transmission, regardless of their channel conditions. However, in opportunistic scheduling. Alternative parameters for “Data rate Ž kbps, Geographic coverage ,  Service requirements , cost ” Evaluation parameter for “Circuit-switched cell, CDPD, WLAN, Paging, Satellite.” “the first ranking training is obtained with the lowest quality of compensation.

Filtering Random Graph Processes Over Random Time-Varying Graphs

Graph filters play a key role in processing the graph spectra of signals supported on the vertices of a graph. However, despite their widespread use, graph filters have been analyzed only in the deterministic setting, ignoring the impact of stochastic- ity in both the graph topology as well as the signal itself. To bridge this gap, we examine the statistical behavior of the two key filter types, finite impulse response (FIR) and autoregressive moving average (ARMA) graph filters, when operating on random time- varying graph signals (or random graph processes) over random time-varying graphs. Our analysis shows that (i) in expectation, the filters behave as the same deterministic filters operating on a deterministic graph, being the expected graph, having as input signal a deterministic signal, being the expected signal, and (ii) there are meaningful upper bounds for the variance of the filter output. We conclude the paper by proposing two novel ways of exploiting randomness to improve (joint graph-time) noise cancellation, as well as to reduce the computational complexity of graph filtering. As demonstrated by numerical results, these methods outperform the disjoint average and denoise algorithm, and yield a (up to) four times complexity redution, with very little difference from the optimal solution

Fermionic Networks: Modeling Adaptive Complex Networks with Fermionic Gases

We study the structure of Fermionic networks, i.e., a model of networks based on the behavior of fermionic gases, and we analyze dynamical processes over them. In this model, particle dynamics have been mapped to the domain of networks, hence a parameter representing the temperature controls the evolution of the system. In doing so, it is possible to generate adaptive networks, i.e., networks whose structure varies over time. As shown in previous works, networks generated by quantum statistics can undergo critical phenomena as phase transitions and, moreover, they can be considered as thermodynamic systems. In this study, we analyze Fermionic networks and opinion dynamics processes over them, framing this network model as a computational model useful to represent complex and adaptive systems. Results highlight that a strong relation holds between the gas temperature and the structure of the achieved networks. Notably, both the degree distribution and the assortativity vary as the temperature varies, hence we can state that fermionic networks behave as adaptive networks. On the other hand, it is worth to highlight that we did not find relation between outcomes of opinion dynamics processes and the gas temperature. Therefore, although the latter plays a fundamental role in gas dynamics, on the network domain its importance is related only to structural properties of fermionic networks.Comment: 19 pages, 5 figure

Scalable dimensioning of resilient Lambda Grids

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