arXiv subjects

Abd AlRahman R. AlMomani

Publications and source records attributed to Abd AlRahman R. AlMomani.

8 recordsLinked to original sources

arXiv2026

Graph conductance, synchronization, and a new local bottleneck measure for decentralized network optimization

The two most prominent bottleneck measures in graph theory, commonly known as the isoperimetric number and conductance, are both referred to in the literature as Cheeger constants. While these measures are useful for assessing barriers to flow in networked systems, neither is sufficient to characterize the stability of complete synchronization, i.e. the dynamic convergence of every node in the system toward a synchronization manifold. Conductance, in particular, does provide an effective bound on the coupling strength required to achieve bulk synchronization, but it often fails to differentiate between many chimera states. The Fiedler vector, which is the eigenvector associated with the algebraic connectivity of the graph, is similarly often able to correctly identify the limiting cut, however, it can fail as well being a global relaxation, especially in the presence of small-set bottlenecks. Furthermore, the computations of these properties are NP-Hard and require global information about the network structure, which is often unrealistic for many complex systems. We define a normalized \textit{synchronization bottleneck ratio} for each bi-partitioning graph cut. The minimum of this ratio over all such cuts gives the \textit{synchronization bottleneck measure} as a global network property, and the associated cut better identifies the true limiting bottleneck for complete synchrony for a specific class of network coupled dynamics. Obtaining this global minimizer is also NP-hard, but due to the use of only local information in the argument, heuristics based on the ratio itself can guide decentralized strategies for improving the synchronizability in man-made networked systems; having relevance in power grid stability, distributed database coherence, and other applications where the alignment of every node is required for the proper functioning of the system.

physics.soc-ph↗

arXiv2026

Scale Partitioning by Incremental Nested Entropy: A Measure-Oriented Theory of Multiscale Structure

Across complex systems science, networks, spatial structures, populations, spectra, and dynamical flows are often represented by object-level measures such as connectivity, frequency, geometric isolation, spectral strength, or deformation. Determining whether these values contain distinct scales commonly requires a chosen cutoff, a prescribed number of groups, or an assumed prevalence. We introduce Scale Partitioning by Incremental Nested Entropy (SPINE), a deterministic framework that identifies scale structure without these inputs. The central theory reduces an arbitrary positive prefix of ordered measure values to two entropy-effective descriptors: an effective number of contributing components and a characteristic measure scale. This reduction yields an exact finite-size criterion for when the next value produces an entropy-supported scale transition. As the effective size grows, the critical ratio converges to $e$, which emerges from the balance between increasing diversity and increasing dominance rather than from threshold calibration. The same critical relation also determines the exact aligned perturbation margin of a detected boundary. Successive local transitions produce a data-supported number of scale strata, while a measure with no resolvable separation returns a single stratum. Numerical experiments verify the critical and stability relations to numerical precision across heterogeneous prefixes and recover two, three, and four generated scales without being supplied their number once separation is sufficient. In a double-gyre flow, SPINE identifies a high-expansion structure occupying $12.85\%$ of the domain without prescribing a retained percentile. The framework applies to geometric, categorical, network, spectral, and dynamical measures.

math.DS↗

arXiv2026

Structural Causal Discovery and Predictive Sufficiency in High-Dimensional Dynamical Systems

High-dimensional environmental systems contain variables that may be predictive, causally informative, physically coupled, or redundant, and these roles need not coincide. We study this distinction in precipitation dynamics using High-Resolution Rapid Refresh atmospheric fields and Multi-Radar Multi-Sensor precipitation observations over the Southwestern United States. We introduce a projection-based, variable-level formulation of entropic regression that identifies candidate causal parents without constructing a global nonlinear expansion library. Ten physical variables are selected sequentially by conditional-information forward selection using linear regression projections. A quadratic library is then formed only over those variables, followed by two sequential variable-block eliminations that produce an eight-variable local representation. Applied across 1227 precipitation-guided superpixels, the method recovers a compact and spatially recurrent causal structure. Under the same final cardinality, entropic regression yields a substantially more concentrated recurrence profile than transfer entropy and causation entropy. Six variables exceed a recurrence threshold of 0.25: land-surface moisture availability, composite reflectivity, geometric vertical velocity, wind speed, convective available potential energy, and maximum upward vertical velocity. Predictive models restricted to these variables achieve strong one-hour discrimination of precipitation occurrence, with an area under the receiver operating characteristic curve of 0.948, while pointwise intensity prediction remains more limited. The results provide a scalable variable-level procedure for high-dimensional causal discovery and show that recurrent causal relevance and predictive sufficiency are distinct properties of a reduced dynamical representation.

math.DS↗

arXiv2025

Boltzmann-Shannon Index: A Geometric-Aware Measure of Clustering Balance

The Boltzmann-Shannon Index (BSI) for clustered continuous data is introduced as a normalized measure that captures the relationship between geometry-based and frequency-based probability distributions defined over the clusters. In essence, it quantifies the similarity across densities of the clusters, which are defined by a given labeling. This labeling may originate from a geometric partitioning of the state space itself, but need not in general. We illustrate its performance on synthetic Gaussian mixtures, the Iris benchmark data set, and a high-imbalance resource-allocation scenario, showing that the BSI provides a coherent assessment in cases where traditional metrics give incomplete or misleading signals. Moreover, in the resource-allocation setting where equal density may be associated with a "fair" distribution, we demonstrate that BSI not only detects inequality with high sensitivity, but also offers a numerically smooth measure that can be easily embedded in optimization frameworks as a regularization term for modern policy-making. Finally, the BSI also offers a new measure of the effectiveness for a given symbolic representation, i.e. coarse-grain states, for continuous-valued data recorded from complex dynamical systems.

cs.IT↗

arXiv2024

Generalizing Geometric Partition Entropy for the Estimation of Mutual Information in the Presence of Informative Outliers

The recent introduction of geometric partition entropy brought a new viewpoint to non-parametric entropy quantification that incorporated the impacts of informative outliers, but its original formulation was limited to the context of a one-dimensional state space. A generalized definition of geometric partition entropy is now provided for samples within a bounded (finite measure) region of a d-dimensional vector space. The basic definition invokes the concept of a Voronoi diagram, but the computational complexity and reliability of Voronoi diagrams in high dimension make estimation by direct theoretical computation unreasonable. This leads to the development of approximation schemes that enable estimation that is faster than current methods by orders of magnitude. The partition intersection ($π$) approximation, in particular, enables direct estimates of marginal entropy in any context resulting in an efficient and versatile mutual information estimator. This new measure-based paradigm for data driven information theory allows flexibility in the incorporation of geometry to vary the representation of outlier impact, which leads to a significant broadening in the applicability of established entropy-based concepts. The incorporation of informative outliers is illustrated through analysis of transient dynamics in the synchronization of coupled chaotic dynamical systems.

physics.soc-ph↗

arXiv2022

The Essential Synchronization Backbone Problem

Network optimization strategies for the process of synchronization have generally focused on the re-wiring or re-weighting of links in order to: (1) expand the range of coupling strengths that achieve synchronization, (2) expand the basin of attraction for the synchronization manifold, or (3) lower the average time to synchronization. A new optimization goal is proposed in seeking the minimum subset of the edge set of the original network that enables the same essential ability to synchronize in that the synchronization manifolds have conjugate stability. We call this type of minimal spanning subgraph an Essential Synchronization Backbone (ESB) of the original system, and we present two algorithms: one is a strategy for an exhaustive search for a true solution, while the other is a method of approximation for this combinatorial problem. The solution spaces that result from different choices of dynamical systems and coupling schemes vary with the level of hierarchical structure present and also the number of interwoven central cycles. Applications can include the important problem in civil engineering of power grid hardening, where new link creation may be costly, and the defense of certain key links to the functional process may be prioritized.

nlin.AO↗

arXiv2021

Entropic Causal Inference for Neurological Applications

The ultimate goal of cognitive neuroscience is to understand the mechanistic neural processes underlying the functional organization of the brain. Key to this study is understanding structure of both the structural and functional connectivity between anatomical regions. In this paper we follow previous work in developing a simple dynamical model of the brain by simulating its various regions as Kuramoto oscillators whose coupling structure is described by a complex network. However in our simulations rather than generating synthetic networks, we simulate our synthetic model but coupled by a real network of the anatomical brain regions which has been reconstructed from diffusion tensor imaging (DTI) data. By using an information theoretic approach that defines direct information flow in terms of causation entropy (CSE), we show that we can more accurately recover the true structural network than either of the popular correlation or LASSO regression techniques. We demonstrate the effectiveness of our method when applied to data simulated on the realistic DTI network, as well as on randomly generated small-world and Erdös-Rényi (ER) networks.

q-bio.NC↗

arXiv2019

How Entropic Regression Beats the Outliers Problem in Nonlinear System Identification

In this work, we developed a nonlinear System Identification (SID) method that we called Entropic Regression. Our method adopts an information-theoretic measure for the data-driven discovery of the underlying dynamics. Our method shows robustness toward noise and outliers and it outperforms many of the current state-of-the-art methods. Moreover, the method of Entropic Regression overcomes many of the major limitations of the current methods such as sloppy parameters, diverse scale, and SID in high dimensional systems such as complex networks. The use of information-theoretic measures in entropic regression poses unique advantages, due to the Asymptotic Equipartition Property (AEP) of probability distributions, that outliers and other low-occurrence events are conveniently and intrinsically de-emphasized as not-typical, by definition. We provide a numerical comparison with the current state-of-the-art methods in sparse regression, and we apply the methods to different chaotic systems such as the Lorenz System, the Kuramoto-Sivashinsky equations, and the Double Well Potential.

eess.SP↗