arXiv subjects

Sara Najem

Publications and source records attributed to Sara Najem.

At least 19 recordsLinked to original sources

arXiv2026

The Heat Kernel Expansion: Curvature for Shock Detection in Higher-Order Financial Networks

This work follows the evolution of financial networks in Norway over a period of nine years at a monthly rate. The data consist of board directors and their affiliations to companies, which we model as simplicial complexes. In this framework, directors are represented as nodes and companies as faces of the complex. To characterize the latter, we focus on three topological measures: the Euler characteristic, computed through the Betti numbers, torsion computed through the reduced determinant of the higher-order Laplacians, and higher-order clustering coefficients. The first two fail to capture the effect of imposed law on representation, unlike our notion of curvature which is a geometrical measure computed from the coefficients of the series expansion of the heat kernel in powers of time, which is our major contribution in this work. In particular, the Euler characteristic integrates curvature, and thus local information is lost. Subsequently, not every topological measure can reliably capture shocks in networks. Further, the number of spanning trees may undergo significant changes at the lowest order, yet these changes need not be reflected in the torsion. Conversely, the change in the curvature revealed variation in the board interlock due to legislation, and serves as a sensitive measure for detecting shocks in networks. Inflection points in curvature are associated with external forcing, and minima with shock arrival times. Sharp transitions are also observed in the components of torsion, while smooth changes are observed in higher-order clustering.

physics.comp-ph↗

arXiv2026

Finding Graph Isomorphisms in Heated Spaces in Almost No Time

Determining whether two graphs are structurally identical is a fundamental problem with applications spanning mathematics, computer science, chemistry, and network science. Despite decades of study, graph isomorphism remains a challenging algorithmic task, particularly for highly regular structures. Here we introduce a new algorithmic approach based on ideas from spectral graph theory and geometry that constructs candidate correspondences between vertices using their curvatures. Any correspondence produced by the algorithm is explicitly verified, ensuring that non-isomorphic graphs are never incorrectly identified as isomorphic. Although the method does not yet guarantee success on all inputs, we find that it correctly resolves every instance tested in deterministic polynomial time, including a broad collection of graphs known to be difficult for classical techniques. These results demonstrate that enriched spectral methods can be far more powerful than previously understood, and suggest a promising direction for the practical resolution of the complexity of the graph isomorphism problem.

physics.comp-ph↗

arXiv2026

Discovery of Symbolic Hamiltonian Expressions with Buckingham-Symplectic Networks

Hamiltonian systems lie at the heart of modeling the physical world. Their defining scalar, the Hamiltonian, encodes both energy conservation and symplectic geometry in its phase-space trajectories. Recent deep learning approaches model Hamiltonian systems by embedding their properties either in the architecture or in the loss function. However, they typically ignore that: i) a Hamiltonian carries units of energy and/or ii) that every integrable Hamiltonian admits a canonical transformation to action-angle coordinates in which the dynamics reduce to a simple rotation on an invariant torus. We propose BuSyNet, a deep learning architecture that combines these two constraints via a dimensionally-consistent, symplectic transformation. A symplectic layer maps input trajectories to lower-dimensional latent action-angle variables, which are then combined with system parameters to discover a symbolic Hamiltonian expression in units of energy. Evaluated on the harmonic oscillator and the Kepler two-body problem (in 2D and 3D), BuSyNet recovers concise, closed-form Hamiltonians that outperform state-of-the-art neural architectures in long-term prediction accuracy and stability, while maintaining interpretability.

physics.comp-ph↗

arXiv2025

Geometric Features of Higher-Order Networks via the Spectral Triplet

Our work is concerned with simplicial complexes that describe higher-order interactions in real complex systems. This description allows to go beyond the pairwise node-to-node representation that simple networks provide and to capture a hierarchy of interactions of different orders. The prime contribution of this work is the introduction of geometric measures for these simplicial complexes. We do so by noting the non-commutativity of the algebra associated with their matrix representations and consequently we bring to bear the spectral triplet formalism of Connes on these structures and then notions of associated dimensions, curvature, and distance can be computed to serve as characterizing features in addition to known topological metrics.

cond-mat.stat-mech↗

arXiv2025

Higher-Order Network Representation of J. S. Bach's Solo Violin Sonatas and Partitas: Topological and Geometrical Explorations

Music is inherently complex, with structures and interactions that unfold across multiple layers. Complex networks have emerged as powerful structures for the quantitative analysis of Western classical music, revealing significant features of its harmonic and structural organization. Although notable works have used these approaches to study music, dyadic representations of interactions fall short in conveying the underlying complexity and depth. In recent years, the limitations of traditional graph representations have been questioned and challenged in the context of interactions that could be higher-dimensional. Effective musical analysis requires models that capture higher-order interactions and a framework that simultaneously captures transitions between them. Subsequently, in this paper, we present a topological framework for analyzing J. S. Bach's Solo Violin Sonatas and Partitas that uses higher-order networks where single notes are vertices, two-note chords are edges, three-notes are triangles, etc. We subsequently account for the flow of music, by modeling transitions between successive notes. We identify genre-specific patterns in the works' geometric and topological properties. In particular, we find signatures in the trends of the evolution of the Euler characteristic and curvature, as well as examining adherence to the Gauss-Bonnet theorem across different movement types. The distinctions are revealed between slow movements, Fugues, and Baroque dance movements through their simplicial complex representation.

cs.SD↗

arXiv2025

Networked Infectiousness: Cascades, Power Laws, and Kinetics

Networked SIR models have become essential workhorses in the modeling of epidemics, their inception, propagation and control. Here, and building on this venerable tradition, we report on the emergence of a remarkable self-organization of infectiousness in the wake of a propagating disease front. It manifests as a cascading power-law distribution of disease strength in networked SIR simulations, and is then confirmed with suitably defined kinetics, then stochastic modeling of surveillance data. Given the success of the networked SIR models which brought it to light, we expect this scale-invariant feature to be of universal significance, characterizing the evolution of disease within and across transportation networks, informing the design of control strategies, and providing a litmus test for the soundness of disease propagation models.

cond-mat.stat-mech↗

arXiv2024

Curvature of an Arbitrary Surface for Discrete Gravity and for $d=2$ Pure Simplicial Complexes

We propose a computation of curvature of arbitrary two-dimensional surfaces of three-dimensional objects, which is a contribution to discrete gravity with potential applications in network geometry. We begin by linking each point of the surface in question to its four closest neighbors, forming quads. We then focus on the simplices of $d=2$, or triangles embedded in these quads, which make up a pure simplicial complex with $d=2$. This allows us to numerically compute the local metric along with zweibeins, which subsequently leads to a derivation of discrete curvature defined at every triangle or face. We provide an efficient algorithm with $\mathcal{O}(N \log{N})$ complexity that first orients two-dimensional surfaces, solves the nonlinear system of equations of the spin-connections resulting from the torsion condition, and returns the value of curvature at each face.

gr-qc↗

arXiv2023

Black Hole in Discrete Gravity

We study the metric corresponding to a three-dimensional coset space $SO(4)/SO(3)$ in the lattice setting. With the use of three integers $n_1, n_2$, and $n_3$, and a length scale, $l_μ$, the continuous metric is transformed into a discrete space. The numerical outcomes are compared with the continuous ones. The singularity of the black hole is explored and different domains are studied.

hep-th↗

arXiv2023

Curvature Tensor in Discrete Gravity

We study numerically the curvature tensor in a three-dimensional discrete space. Starting from the continuous metric of a three-sphere, we transformed it into a discrete space using three integers $n_1, n_2$, and $n_3$. The numerical results are compared with the expected values in the continuous limit. We show that as the number of cells in the lattice increases, the continuous limit is recovered.

hep-th↗

arXiv2022

A Framework for Reconstructing COVID-19 Transmission Network to Inform Betweenness Centrality-Based Control Measures

In this paper, we propose a general framework for optimal control measures, which follows the evolution of COVID-19 infection counts collected by Surveillance Units on a country level. We employ an autoregressive model that allows to decompose the mean number of infections into three components that describe: intra-locality infections, inter-locality infections, and infections from other sources such as travelers arriving to a country from abroad. We identify the inter-locality term as a time-evolving network and when it drives the dynamics of the disease we focus on its properties. Tools from network analysis are then employed to get insight into its topology. Building on this, and particularly on the centrality of the nodes of the identified network, a strategy for intervention and disease control is devised.

physics.soc-ph↗

arXiv2022

Scalar Curvature in Discrete Gravity

We focus on studying, numerically, the scalar curvature tensor in a two-dimensional discrete space. The continuous metric of a two-sphere is transformed into that of a lattice using two possible slicings. In the first, we use two integers, while in the second we consider the case where one of the coordinates is ignorable. The numerical results of both cases are then compared with the expected values in the continuous limit as the number of cells of the lattice becomes very large.

hep-th↗

arXiv2021

Identifying urban air pollution hot-spots by dispersion modeling when data are scarce: application to diesel generators in Beirut, Lebanon

Diesel generators are emerging as community-initiated solutions to compensate for electricity shortage in cities marred by economical crisis and/or conflict. The resulting pollution distribution in dense urban environments is a major source of concern to the population. In the absence of periodic observations from properly distributed sensors, as is the case in Beirut, physically based computational modeling stand out as an effective tool for predicting the pollutant distribution in complex environments, and a cost-effective framework for investigating what-if scenarios and assessing mitigation strategies. Here, we present a Lagrangian transport model-based study of PM2.5 dispersion originating from a large number of diesel generators in Beirut. We explore large and small scale dispersion patterns in selected smalls domains and over the entire city. The scenarios considered investigate the impact of topography, atmospheric stability, presence of buildings, diesel generators distribution, and stacks elevations for representative meteorological conditions. Assessment of these scenarios is carried out in terms of small and large scale dispersion patterns and the mean concentration at street level and population exposure proxy indicators. We also report on the efficacy of elevating the stack height as a mitigation measure at different representative wind and atmospheric stability conditions.

physics.ao-ph↗

arXiv2021

On Koopman Operator for Burgers' Equation

We consider the flow of Burgers' equation on an open set of (small) functions in $L^2([0,1])$. We derive explicitly the Koopman decomposition of the Burgers' flow. We identify the frequencies and the coefficients of this decomposition as eigenvalues and eigenfunctionals of the Koopman operator. We prove the convergence of the Koopman decomposition for $t>0$ for small Cauchy data, and up to $t=0$ for regular Cauchy data. The convergence up to $t=0$} leads to a `completeness' property for the basis of Koopman modes. We construct all modes and eigenfunctionals, including the eigenspaces involved in geometric multiplicity. This goes beyond the summation formulas provided by (Page & Kerswell, 2018), where only one term per eigenvalue was given. A numeric illustration of the Koopman decomposition is given and the Koopman eigenvalues compared to the eigenvalues of a Dynamic Mode Decomposition (DMD).

math.DS↗

arXiv2020

Buildings as Species: Competition and Scaling Rules in Cities

We look at buildings' competition over space in cities through the lens of ecology. Adopting the convex hull of the building's footprint perimeter as a definition of species yields parallels to forest trees' competition, which we expound on. Their perimeter distribution $p(r)$ follows a power-law behavior beyond a critical threshold of the density of the built environment. In this regime, the species coexistence likelihood $p(d)$, where $d$ is the distance to the nearest competitor, which we define to be a building with a larger $r$, bifurcates with the buildings' number $n$. This reveals two different predation laws: a vicious predatory one which is linked spatial homogeneity and segregation, as opposed to another favoring spatial diversity and intermixing between species.

physics.soc-ph↗

arXiv2020

Precarious trajectories: How far away is the next refugee drowning?

In this paper, we explore the analogy between the refugees' drownings in the sea and the earthquakes' occurrences and focus on the aspect that characterizes the statistics of their spatial and temporal successions. The former is shown to parallel the spatial distribution of consecutive drowning events with the difference that the latter exhibits short-range behavior below $κ= 4km$ and it is characterized by scale-free statistics, with a critical exponent $δ\approx 0.5$, falling within the range of the earthquakes' $δ= 0.65 \pm 0.20$, as well as finite size scaling beyond $κ= 4km$, while the distribution of events' rates exhibits no similarity with that of the earthquakes. Finally, the events' velocity distribution is also recovered. $κ$ is suspected to be related to the radar and mobile network's coverage ranges and thus effectively represents a cut-off in the ability of picking up signals on drownings in the sea.

physics.soc-ph↗

arXiv2020

Kinetic roughening of the urban skyline

\begin{abstract} In this Letter we follow the asymptotic spatial correlation of buildings' heights $G_{\infty}(r)$ in the whole of the Netherlands \cite{bag3d}, which comprises $\approx 10,000,000$ buildings, for the purpose of recovering its scaling with respect to space and time given respectively by the exponents $r^{2 α}$ and $t^{2β}$. This allows us to identify the universality class of the evolution of the urban skyline seen as a dynamically evolving interface. Two major classes of cities were identified based on the recovered value of $α=0.4$ and $α= 0$, which correspond respectively to the KPZ and the EW universality classes. Picking a discrete model from each of these classes and mapping it to physical rules for constructions in cities we conclude that imposed restrictions on buildings' heights are reflected in the exponent $α$ and thus have implications on how the skyline evolves.

cond-mat.stat-mech↗

arXiv2020

Machine learning for buildings characterization and power-law recovery of urban metrics

In this paper, we focus on a critical component of the city: its building stock, which holds much of its socio-economic activities. In our case, the lack of a comprehensive database about their features and its limitation to a surveyed subset lead us to adopt data-driven techniques to extend our knowledge to the near-city-scale. Neural networks and random forest are applied to identify the buildings' number of floors and construction periods' dependencies on a set of shape features: area, perimeter, and height along with the annual electricity consumption, relying on a surveyed data in the city of Beirut. The predicted results are then compared with established scaling laws of urban forms, which constitutes a further consistency check and validation of our work ow.

physics.soc-ph↗

arXiv2017

Debye-Hückel Theory for Refugees' Migration

In this Letter we follow the short-ranged Syrian refugees' migration to Lebanon as documented by the UNHCR. We propose a model inspired by the Debye-Hückel theory and show that it properly predicts the refugees' mobility while the gravity model fails. We claim that the interaction between origin cities attenuates and/or extenuates the flux to destinations, and consequently, in analogy with the effective charges of interacting particles in a plasma, these source cities are characterized by effective populations determined by their pairwise remoteness/closeness and defined by areas of control between the fighting parties.

physics.soc-ph↗