arXiv subjects

Georgios Argyris

Publications and source records attributed to Georgios Argyris.

3 recordsLinked to original sources

arXiv2023

Diagnosis of Small-world Bias in Random Graphs

Background: Imagine a paper with n nodes on it where each pair undergoes a coin toss experiment; if heads we connect the pair with an undirected link, while tails maintain the disconnection. This procedure yields a random graph. Now consider duplicating this network onto another paper with a slight bias-a fraction of its links (approximately 1/10) undergo rearrangement. If we shuffle the two papers, how can we distinguish the pure random graph from the biased one? Results: In response to this challenge, we propose a novel metric called Randomness Index (RI). The closer the metric to zero is, the higher degree of randomness in the graph. The RI can distinguish between dense small-world networks and dense random graphs; a distinction which is impossible by conventional small-world properties like clustering coefficient and average path length. To validate its effectiveness, we apply the RI to temporal correlation networks of stock indices. Our findings reveal a reduction in randomness during global economic recession periods. Conclusion: The RI emerges as a powerful metric capable of characterizing small-world topology, especially in scenarios where other network measures fail. Beyond its utility in network analysis, the RI is promising for change-point (anomaly) detection in dynamical systems studied by means of multivariate time series.

cs.SI↗

arXiv2023

Minimization of Dynamical Systems over Monoids

Quantitative notions of bisimulation are well-known tools for the minimization of dynamical models such as Markov chains and ordinary differential equations (ODEs). In \emph{forward bisimulations}, each state in the quotient model represents an equivalence class and the dynamical evolution gives the overall sum of its members in the original model. Here we introduce generalized forward bisimulation (GFB) for dynamical systems over commutative monoids and develop a partition refinement algorithm to compute the coarsest one. When the monoid is $(\mathbb{R}, +)$, we recover probabilistic bisimulation for Markov chains and more recent forward bisimulations for nonlinear ODEs. Using $(\mathbb{R}, \cdot)$ we get nonlinear reductions for discrete-time dynamical systems and ODEs where each variable in the quotient model represents the product of original variables in the equivalence class. When the domain is a finite set such as the Booleans $\mathbb{B}$, we can apply GFB to Boolean networks (BN), a widely used dynamical model in computational biology. Using a prototype implementation of our minimization algorithm for GFB, we find disjunction- and conjunction-preserving reductions on 60 BN from two well-known repositories, and demonstrate the obtained analysis speed-ups. We also provide the biological interpretation of the reduction obtained for two selected BN, and we show how GFB enables the analysis of a large one that could not be analyzed otherwise. Using a randomized version of our algorithm we find product-preserving (therefore non-linear) reductions on 21 dynamical weighted networks from the literature that could not be handled by the exact algorithm.

cs.LO↗

arXiv2021

Reducing Boolean Networks with Backward Boolean Equivalence

Boolean Networks (BNs) are established models to qualitatively describe biological systems. The analysis of BNs might be infeasible for medium to large BNs due to the state-space explosion problem. We propose a novel reduction technique called \emph{Backward Boolean Equivalence} (BBE), which preserves some properties of interest of BNs. In particular, reduced BNs provide a compact representation by grouping variables that, if initialized equally, are always updated equally. The resulting reduced state space is a subset of the original one, restricted to identical initialization of grouped variables. The corresponding trajectories of the original BN can be exactly restored. We show the effectiveness of BBE by performing a large-scale validation on the whole GINsim BN repository. In selected cases, we show how our method enables analyses that would be otherwise intractable. Our method complements, and can be combined with, other reduction methods found in the literature.

cs.CE↗