arXiv subjects

Baruch Barzel

Publications and source records attributed to Baruch Barzel.

At least 19 recordsLinked to original sources

arXiv2026

On the most reliable graphs with fixed redundancy

The all-terminal reliability of a graph $G$ is the probability that $G$ remains connected when each edge fails independently with probability $p$. For fixed $n$ and $m$, the uniformly most reliable problem asks which graph with $n$ vertices and $m$ edges maximizes reliability for all $p \in [0,1]$. Although such graphs do not always exist, optimal graphs in the regime $p \to 0$ always do and are determined by the structure of their minimal cut sets. We establish a structural characterization of graphs that are most reliable near $p=0$. Our results partially resolve a conjecture of Bourel et al., showing that, under suitable conditions, regular graphs with maximal girth are optimal. Extending this analysis to graphs with fixed redundancy $r=m-(n-1)$ and sufficiently large $n$, we show that the most reliable graphs are obtained by subdividing the most reliable cubic graphs with $2(r-1)$ vertices. The general conjecture remains open. Unlike previous results, which resolved only small redundancy cases or very dense regimes, our approach yields a substantial extension of the known range. We determine the unique cubic candidates for uniformly most reliable graphs for all redundancy levels $m-n \le 19$, and prove the non-existence of uniformly most reliable graphs for several infinite families with fixed redundancy and asymptotically large $n$. These results significantly enlarge both the candidate class and the range of provable non-existence.

math.CO↗

arXiv2025

Surface Optimisation Governs the Local Design of Physical Networks

The brain's connectome and the vascular system are examples of physical networks whose tangible nature influences their structure, layout, and ultimately their function. The material resources required to build and maintain these networks have inspired decades of research into wiring economy, offering testable predictions about their expected architecture and organisation. Here we empirically explore the local branching geometry of a wide range of physical networks, uncovering systematic violations of the long-standing predictions of length and volume minimisation. This leads to the hypothesis that predicting the true material cost of physical networks requires us to account for their full three-dimensional geometry, resulting in a largely intractable optimisation problem. We discover, however, an exact mapping of surface minimisation onto high-dimensional Feynman diagrams in string theory, predicting that with increasing link thickness, a locally tree-like network undergoes a transition into configurations that can no longer be explained by length minimisation. Specifically, surface minimisation predicts the emergence of trifurcations and branching angles in excellent agreement with the local tree organisation of physical networks across a wide range of application domains. Finally, we predict the existence of stable orthogonal sprouts, which not only are prevalent in real networks but also play a key functional role, improving synapse formation in the brain and nutrient access in plants and fungi.

physics.bio-ph↗

arXiv2025

Efficient treatment of heterogeneous malignant cell populations

When confronted with an undesired cell population, such as bacterial infections or tumors, we seek the most effective treatment, designed to eliminate the population as rapidly as possible. A common practice is to monitor the cells short-term response to the treatment, and from that, extrapolate the eventual treatment outcome, i.e. will it eradicate the cells, and if yes at what timescales. Underlying this approach is the assumption that the cells exhibit a homogeneous response to the treatment, and hence the early response patterns can be naturally extended to later times. Recent experiments on cancer cell populations, however, indicate a significant level of cellular heterogeneity, undermining this classic assessment protocol of treatment efficacy. We, therefore, develop here a stochastic framework, to analytically predict the temporal dynamics of a heterogeneous cell population. Quite often, we find, the average cellular parameters, governing the short-term response, fail to predict the actual treatment outcome. In contrast, our analysis, which also incorporates the populations variability, helps identify the relevant statistical parameters, which in turn, enable us to predict the full trajectory of the cell population, and specifically - the likelihood and typical timescales for remission.

physics.bio-ph↗

arXiv2024

Observing network dynamics through sentinel nodes

A fundamental premise of statistical physics is that the particles in a physical system are interchangeable, and hence the state of each specific component is representative of the system as a whole. This assumption breaks down for complex networks, in which nodes may be extremely diverse, and no single component can truly represent the state of the entire system. It seems, therefore, that to observe the dynamics of social, biological or technological networks, one must extract the dynamic states of a large number of nodes -- a task that is often practically prohibitive. Theoretical tools are also highly restrictive, given the analytically impenetrable combination of complex heterogeneous networks with nonlinear, often hidden, dynamics. To overcome this challenge, we use machine learning techniques to detect the network's sentinel nodes, a set of network components whose combined states can help approximate the average dynamics of the entire network. The method allows us to assess the equilibrium state of a large complex system by tracking just a small number of carefully selected nodes. We find that the sentinels are mainly determined by the network structure such that they can be extracted even with little knowledge of the system's specific interaction dynamics. Therefore, the network's sentinels offer a natural probe by which to observe the system's dynamic states. Intriguingly, sentinels tend to avoid the highly central nodes such as the hubs.

physics.soc-ph↗

arXiv2023

Cost-effective network robustness

Modern society relies heavily on infrastructure networks, from communication to power systems, making their reliability under failure and disruption critical. Robustness typically requires redundancy, providing alternative paths that ensure continuous service, yet redundancy is costly and often limited. Real-world networks therefore operate under a fundamental trade-off between resource investment and reliability. Here we derive theoretical bounds governing this trade-off and identify the network architectures that minimize expected downtime under constraints of cost, component durability, and spatial embedding. We show that, in the relevant limit, optimal configurations consist of a 3-connected structural core linked by intermediate chains of uniform weight. This reveals a previously unrecognized family of spatial networks that achieves near-optimal robustness with orders-of-magnitude fewer resources. Distinct from commonly studied network models, these architectures expose general structural principles underlying the efficient organization of reliable infrastructure networks.

cs.DM↗

arXiv2023

Dense network motifs enhance dynamical stability

Network motifs are the building blocks of complex networks and are significantly involved in the network dynamics such as information processing and local operations in the brain, biological marks for drug targets, identifying and predicting protein complexes in PPI networks, as well as echo chambers in social networks. Here we show that dense motifs such as cliques have different stable states than the network itself. These stable states enhance the dynamical stability of the network and can even turn local stable states into global ones. Moreover, we show how cliques create polarization phenomena and global opinion changes.

physics.soc-ph↗

arXiv2022

Why are there six degrees of separation in a social network?

A wealth of evidence shows that real world networks are endowed with the small-world property i.e., that the maximal distance between any two of their nodes scales logarithmically rather than linearly with their size. In addition, most social networks are organized so that no individual is more than six connections apart from any other, an empirical regularity known as the six degrees of separation. Why social networks have this ultra-small world organization, whereby the graph's diameter is independent of the network size over several orders of magnitude, is still unknown. We show that the 'six degrees of separation' are the property featured by the equilibrium state of any network where individuals weigh between their aspiration to improve their centrality and the costs incurred in forming and maintaining connections. We show, moreover, that the emergence of such a regularity is compatible with all other features, such as clustering and scale-freeness, that normally characterize the structure of social networks. Thus, our results show how simple evolutionary rules of the kind traditionally associated with human cooperation and altruism can also account for the emergence of one of the most intriguing attributes of social networks.

physics.soc-ph↗

arXiv2022

Topological synchronization of chaotic systems

A chaotic dynamics is typically characterized by the emergence of strange attractors with their fractal or multifractal structure. On the other hand, chaotic synchronization is a unique emergent self-organization phenomenon in nature. Classically, synchronization was characterized in terms of macroscopic parameters, such as the spectrum of Lyapunov exponents. Recently, however, we attempted a microscopic description of synchronization, called topological synchronization, and showed that chaotic synchronization is, in fact, a continuous process that starts in low-density areas of the attractor. Here we analyze the relation between the two emergent phenomena by shifting the descriptive level of topological synchronization to account for the multifractal nature of the visited attractors. Namely, we measure the generalized dimension of the system and monitor how it changes while increasing the coupling strength. We show that during the gradual process of topological adjustment in phase space, the multifractal structures of each strange attractor of the two coupled oscillators continuously converge, taking a similar form, until complete topological synchronization ensues. According to our results, chaotic synchronization has a specific trait in various systems, from continuous systems and discrete maps to high dimensional systems: synchronization initiates from the sparse areas of the attractor, and it creates what we termed as the zipper effect, a distinctive pattern in the multifractal structure of the system that reveals the microscopic buildup of the synchronization process. Topological synchronization offers, therefore, a more detailed microscopic description of chaotic synchronization and reveals new information about the process even in cases of high mismatch parameters.

nlin.CD↗

arXiv2021

Epidemic spreading under mutually independent intra- and inter-host pathogen evolution

The dynamics of epidemic spreading is often reduced to the single control parameter $R_0$, whose value, above or below unity, determines the state of the contagion. If, however, the pathogen evolves as it spreads, $R_0$ may change over time, potentially leading to a mutation-driven spread, in which an initially sub-pandemic pathogen undergoes a breakthrough mutation. To predict the boundaries of this pandemic phase, we introduce here a modeling framework to couple the network spreading patterns with the intra-host evolutionary dynamics. For many pathogens these two processes, intra- and inter-host, are driven by different selection forces. And yet here we show that even in the extreme case when these two forces are mutually independent, mutations can still fundamentally alter the pandemic phase-diagram, whose transitions are now shaped, not just by $R_0$, but also by the balance between the epidemic and the evolutionary timescales. If mutations are too slow, the pathogen prevalence decays prior to the appearance of a critical mutation. On the other hand, if mutations are too rapid, the pathogen evolution becomes volatile and, once again, it fails to spread. Between these two extremes, however, we identify a broad range of conditions in which an initially sub-pandemic pathogen can break through to gain widespread prevalence.

q-bio.PE↗

arXiv2020

Reviving a failed network through microscopic interventions

From mass extinction to cell death, complex networked systems often exhibit abrupt dynamic transitions between desirable and undesirable states. Such transitions are often caused by topological perturbations, such as node or link removal, or decreasing link strengths. The problem is that reversing the topological damage, namely retrieving the lost nodes or links, or reinforcing the weakened interactions, does not guarantee the spontaneous recovery to the desired functional state. Indeed, many of the relevant systems exhibit a hysteresis phenomenon, remaining in the dysfunctional state, despite reconstructing their damaged topology. To address this challenge, we develop a two-step recovery scheme: first - topological reconstruction to the point where the system can be revived, then dynamic interventions, to reignite the system's lost functionality. Applying this method to a range of nonlinear network dynamics, we identify the recoverable phase of a complex system, a state in which the system can be reignited by microscopic interventions, for instance, controlling just a single node. Mapping the boundaries of this dynamical phase, we obtain guidelines for our two-step recovery.

nlin.AO↗

arXiv2020

Alternating quarantine for sustainable epidemic mitigation

Absent a drug or vaccine, containing epidemic outbreaks is achieved by means of social distancing, specifically mobility restrictions and lock-downs. Such measures impose a hurtful toll on the economy, and are difficult to sustain for extended periods. As an alternative, we propose here an alternating quarantine strategy, in which at every instance, half of the population remains under lock-down while the other half continues to be active, maintaining a routine of weekly succession between activity and quarantine. This regime affords a dual partition:\ half of the population interacts for only half of the time, resulting in a dramatic reduction in transmission, comparable to that achieved by a population-wide lock-down. All the while, it enables socioeconomic continuity at $50\%$ capacity. The proposed weekly alternations also address an additional challenge, with specific relevance to COVID-19. Indeed, SARS-CoV-2 exhibits a relatively long incubation period, in which individuals experience no symptoms, but may already contribute to the spread. Unable to selectively isolate these invisible spreaders, we resort to population-wide restrictions. However, under the alternating quarantine routine, if an individual was exposed during their active week, by the time they complete their quarantine they will, in most cases, begin to exhibit symptoms. Hence this strategy isolates the majority of pre-symptomatic individuals during their infectious phase, leading to a rapid decline in the viral spread, thus addressing one of the main challenges in COVID-19 mitigation.

q-bio.PE↗

arXiv2020

Emergent stability in complex network dynamics

The stable functionality of networked systems is a hallmark of their natural ability to coordinate between their multiple interacting components. Yet, strikingly, real-world networks seem random and highly irregular, apparently lacking any design for stability. What then are the naturally emerging organizing principles of complex-system stability? Encoded within the system's stability matrix, the Jacobian, the answer is obscured by the scale and diversity of the relevant systems, their broad parameter space, and their nonlinear interaction mechanisms. To make advances, here we uncover emergent patterns in the structure of the Jacobian, rooted in the interplay between the network topology and the system's intrinsic nonlinear dynamics. These patterns help us analytically identify the few relevant control parameters that determine a system's dynamic stability. Complex systems, we find, exhibit discrete stability classes, from asymptotically unstable, where stability is unattainable, to sensitive, in which stability abides within a bounded range of the system's parameters. Most crucially, alongside these two classes, we uncover a third class, asymptotically stable, in which a sufficiently large and heterogeneous network acquires a guaranteed stability, independent of parameters, and therefore insensitive to external perturbation. Hence, two of the most ubiquitous characteristics of real-world networks - scale and heterogeneity - emerge as natural organizing principles to ensure stability in the face of changing environmental conditions.

nlin.AO↗

arXiv2020

Response times of nodes in a complex network environment -- two potential derivation tracks

The spread of perturbative signals in complex networks is governed by the combined effect of the network topology and its intrinsic nonlinear dynamics. Recently, the resulting spreading patterns have been analyzed and predicted, shown to depend on a single scaling relationship, linking a node's weighted degree $S_i$ to its intrinsic response time $τ_i$. The relevant scaling exponent $θ$ can be analytically traced to the system's nonlinear dynamics. Here we show that $θ$ can be obtained via two different derivation tracks, leading to seemingly different functions. Analyzing the resulting predictions, we find that, despite their distinct form, they are fully consistent, predicting the exact same scaling relationship under potentially diverse types of dynamics.

nlin.AO↗

arXiv2019

Unusual changeover in the transition nature of local-interaction Potts models

A combinatorial approach is used to study the critical behavior of a $q$-state Potts model with a round-the-face interaction. Using this approach it is shown that the model exhibits a first order transition for $q>3$. A second order transition is numerically detected for $q=2$. Based on these findings, it is deduced that for some two-dimensional ferromagnetic Potts models with completely local interaction, there is a changeover in the transition order at a critical integer $q_c\leq 3$. This stands in contrast to the standard two-spin interaction Potts model where the maximal integer value for which the transition is continuous is $q_c=4$. A lower bound on the first order critical temperature is additionally derived.

cond-mat.stat-mech↗

arXiv2018

Synchronization of chaotic systems: A microscopic description

The synchronization of coupled chaotic systems represents a fundamental example of self organization and collective behavior. This well-studied phenomenon is classically characterized in terms of macroscopic parameters, such as Lyapunov exponents, that help predict the systems transitions into globally organized states. However, the local, microscopic, description of this emergent process continues to elude us. Here we show that at the microscopic level, synchronization is captured through a gradual process of topological adjustment in phase space, in which the strange attractors of the two coupled systems continuously converge, taking similar form, until complete topological synchronization ensues. We observe the local nucleation of topological synchronization in specific regions of the systems attractor, providing early signals of synchrony, that appear significantly before the onset of complete synchronization. This local synchronization initiates at the regions of the attractor characterized by lower expansion rates, in which the chaotic trajectories are least sensitive to slight changes in initial conditions. Our findings offer an alternative description of synchronization in chaotic systems, exposing its local embryonic stages that are overlooked by the currently established global analysis. Such local topological synchronization enables the identification of configurations where prediction of the state of one system is possible from measurements on that of the other, even in the absence of global synchronization.

nlin.CD↗

arXiv2018

Predicting the patterns of spatio-temporal signal propagation in complex networks

A major achievement in the study of complex networks is the observation that diverse systems, from sub-cellular biology to social networks, exhibit universal topological characteristics. Yet this universality does not naturally translate to the dynamics of these systems , hindering our progress towards a general theoretical framework of network dynamics. The source of this theoretical gap is the fact that the behavior of a complex system cannot be uniquely predicted from its topology, but rather depends also on the dynamic mechanisms of interaction between the nodes, hence systems with similar structure may exhibit profoundly different dynamic behavior. To bridge this gap, we derive here the patterns of network information transmission, indeed, the essence of a network's behavior, by offering a systematic translation of topology into the actual spatio-temporal propagation of perturbative signals. We predict, for an extremely broad range of nonlinear dynamic models, that the propagation rules condense around three highly distinctive dynamic universality classes, characterized by the interplay between network paths, degree distribution and the interaction dynamics. Our formalism helps us leverage the major advances in the mapping of real world networks, into predictions on the actual dynamic propagation, from the spread of viruses in social networks to the discussion of genetic information in cellular systems.

physics.soc-ph↗

arXiv2018

Perfect synchronization in networks of phase-frustrated oscillators

Synchronizing phase frustrated Kuramoto oscillators, a challenge that has found applications from neuronal networks to the power grid, is an eluding problem, as even small phase-lags cause the oscillators to avoid synchronization. Here we show, constructively, how to strategically select the optimal frequency set, capturing the natural frequencies of all oscillators, for a given network and phase-lags, that will ensure perfect synchronization. We find that high levels of synchronization are sustained in the vicinity of the optimal set, allowing for some level of deviation in the frequencies without significant degradation of synchronization. Demonstrating our results on first and second order phase-frustrated Kuramoto dynamics, we implement them on both model and real power grid networks, showing how to achieve synchronization in a phase frustrated environment.

nlin.AO↗

arXiv2017

Characterizing departure delays of flights in passenger aviation network of United States

Flight delay happens every day in airports all over the world. However, systemic investigation in large scales remains a challenge. We collect primary data of domestic departure records from Bureau of Transportation Statistics of United States, and do empirical statistics with them in form of complementary cumulative distributions functions (CCDFs) and transmission function of the delays. Fourteen main airlines are characterized by two types of CCDFs: shifted power-law and exponentially truncated shifted power-law. By setting up two phenomenological models based on mean-field approximation in temporal regime, we convert effect from other delay factors into a propagation one. Three parameters meaningful in measuring airlines emerge as universal metrics. Moreover, method used here could become a novel approach to revealing practical meanings hidden in temporal big data in wide fields.

physics.soc-ph↗