arXiv subjects

Harrison Hartle

Publications and source records attributed to Harrison Hartle.

18 recordsLinked to original sources

arXiv2026

Finite relaxation protocols with minimal dissipation

Work extraction from nonequilibrium systems is a major challenge across biological, chemical, physical, and engineering systems. Idealized protocols generally require a quasistatic relaxation stage in which the Hamiltonian is gradually adjusted through a continuum of intermediaries. Here, we consider protocols restricted to a finite number $N$ of intermediary Hamiltonians, consisting of a sequence of quench-relax steps. We determine the sequence of quenches that minimizes the dissipated work, which can be expressed in terms of a recurrence involving the Lambert function. The optimal sequence converges to the Fisher-Rao geodesic, saturating known leading-order dissipation bounds at large $N$. We obtain lower bounds on work extraction from a nonequilibrium distribution as a function of its Fisher-Rao distance to equilibrium. We extend and apply the framework in two simple models: (i) an optical trap experiment, showing that the optimal intermediary distribution can be bimodal even for unimodal initial and final distributions, and (ii) an enzyme-catalyzed reaction, showing that that accounting for relaxation time in addition to dissipation can favor barrier-lowering.

cond-mat.stat-mech↗

arXiv2026

The rank and layer distributions in random recursive trees

The distribution of node depths in a network is crucial for analyzing network structure. Two measures, rank and layer, quantify how deep inside a network a node is. The rank is the node's distance to the closest leaf, a node of degree 1. The layer is the number of times all leaves must be stripped off for the node to become a leaf. We derive exact recursive expressions for the rank and layer distributions in random recursive trees. We show that the rank and layer distributions decay factorially and geometrically, respectively, and prove the self-averaging of the numbers of nodes with fixed rank or layer. Unlike previous studies, our approach does not depend on labels or a root node, providing a more versatile framework for analyzing rank and layer distributions in complex networks.

math.PR↗

arXiv2026

Computational foundations of the human world

Human societies continuously transform scattered information into collective judgments and coordinated action, whether through markets discovering prices, governments allocating resources, communities enforcing norms, or science converging on reliable claims. Importantly, the computational difficulty of collective decision-making, particularly the time and communication required to reach solutions, imposes fundamental constraints on social organization. While theoretical computer science offers formal tools for analyzing such problems, for instance, by analyzing resource requirements, including time and memory, surprisingly, there is no domain of social science that focuses on the nature of computation in the human world. This perspective argues that we now have the opportunity to deploy these computational frameworks to study human social organization, opening research directions at the intersection of computer science and social science. We highlight core social phenomena that can be framed as computational, including (i) distributed consensus and coordinated action, (ii) societal restructuring with scale, (iii) hierarchical and modular structure, and (iv) externalized memory systems. We identify several concepts from theoretical computer science that may provide insight into these phenomena, especially emphasizing more recently developed approaches beyond the paradigm of Turing~Machines and worst-case computational complexity.

cs.SI↗

arXiv2026

Anomalous scaling in redirection networks

In networks that grow by isotropic redirection (IR), a new node selects an initial target node uniformly at random and attaches to a randomly chosen neighbor of the target. The emerging networks exhibit leaf proliferation, in which the number of nonleaves scales sublinearly as $N^\mu$ and the degree distribution has an algebraic tail with exponent $1+\mu$. To understand these mysterious properties, we introduce a class of models with redirection to leaves whenever possible. The resulting networks exhibit qualitatively similar phenomenology to IR networks, but avoid the inherent non-locality of the IR growth rule. These networks admit an analytical description of the leaf degree distribution, from which we extract the exponent $\mu$.

cond-mat.stat-mech↗

arXiv2026

Leaves of preferential attachment trees

We provide a local probabilistic description of the limiting statistics of large preferential attachment trees in terms of the ordinary degree (number of neighbors) but augmented with information on leafdegree (number of neighbors that are leaves). The full description is the joint degree-leafdegree distribution $n_{k,\ell}$, which we derive from its associated multivariate generating function. From $n_{k,\ell}$ we obtain the leafdegree distribution, $m_{\ell}$, as well as the fraction of vertices that are protected (nonleaves with leafdegree zero) as a function of degree, $n_{k,0}$, among numerous other results. We also examine fluctuations and concentration of joint degree-leafdegree empirical counts $N_{k,\ell}$. Although our main findings pertain to the preferential attachment tree, the approach we present is highly generalizable and can characterize numerous existing models, in addition to facilitating the development of tractable new models. We further demonstrate the approach by analyzing $n_{k,\ell}$ in two other models: the random recursive tree, and a redirection-based model.

cond-mat.stat-mech↗

arXiv2025

Deterministic construction of typical networks in network models

It is often desirable to assess how well a given dataset is described by a given model. In network science, for instance, one often wants to say that a given real-world network appears to come from a particular network model. In statistical physics, the corresponding problem is about how typical a given state, representing real-world data, is in a particular statistical ensemble. One way to address this problem is to measure the distance between the data and the most typical state in the ensemble. Here, we identify the conditions that allow us to define this most typical state. These conditions hold in a wide class of grand canonical ensembles and their random mixtures. Our main contribution is a deterministic construction of a state that converges to this most typical state in the thermodynamic limit. This construction involves rounds of derandomization procedures, some of which deal with derandomizing point processes, an uncharted territory. We illustrate the construction on one particular network model, deterministic hyperbolic graphs, and its application to real-world networks, many of which we find are close to the most typical network in the model. While our main focus is on network models, our results are very general and apply to any grand canonical ensembles and their random mixtures satisfying certain niceness requirements.

physics.soc-ph↗

arXiv2025

Statistics of leaves in growing random trees

Leaves, i.e., vertices of degree one, can play a significant role in graph structure, especially in sparsely connected settings in which leaves often constitute the largest fraction of vertices. We consider a leaf-based counterpart of the degree, namely, the leaf degree -- the number of leaves a vertex is connected to -- and the associated leaf degree distribution, analogous to the degree distribution. We determine the leaf degree distribution of random recursive trees (RRTs) and trees grown via a leaf-based preferential attachment mechanism that we introduce. The RRT leaf degree distribution decays factorially, in contrast with its purely geometric degree distribution. In the one-parameter leaf-based growth model, each new vertex attaches to an existing vertex with rate $\ell$ + a, where $\ell$ is the leaf degree of the existing vertex, and a > 0. The leaf degree distribution has a powerlaw tail when 0 < a < 1 and an exponential tail (with algebraic prefactor) for a > 1. The critical case of a = 1 has a leaf degree distribution with stretched exponential tail. We compute a variety of additional characteristics in these models and conjecture asymptotic equivalence of degree and leaf degree powerlaw tail exponent in the scale free regime. We highlight several avenues of possible extension for future studies.

cond-mat.stat-mech↗

arXiv2025

Growing unlabeled networks

Models of growing networks are a central topic in network science. In these models, vertices are usually labeled by their arrival time, distinguishing even those node pairs whose structural roles are identical. In contrast, unlabeled networks encode only structure, so unlabeled growth rules must be defined in terms of structurally distinguishable outcomes; network symmetries therefore play a key role in unlabeled growth dynamics. Here, we introduce and study models of growing unlabeled trees, defined in analogy to widely-studied labeled growth models such as uniform and preferential attachment. We develop a theoretical formalism to analyze these trees via tracking their leaf-based statistics. We find that while many characteristics of labeled network growth are retained, numerous critical differences arise, caused primarily by symmetries among leaves in common neighborhoods. In particular, degree heterogeneity is enhanced, with the strength of this enhancement depending on details of growth dynamics: mild enhancement for uniform attachment, and extreme enhancement for preferential attachment. These results and the developed analytical formalism may be of interest beyond the setting of growing unlabeled trees.

physics.soc-ph↗

arXiv2025

The Metric Dimension of Sparse Random Graphs

In 2013, Bollob\'as, Mitsche, and Pralat at gave upper and lower bounds for the likely metric dimension of random Erd\H{o}s-R\'enyi graphs $G(n,p)$ for a large range of expected degrees $d=pn$. However, their results only apply when $d \ge \log^5 n$, leaving open sparser random graphs with $d < \log^5 n$. Here we provide upper and lower bounds on the likely metric dimension of $G(n,p)$ from just above the connectivity transition, i.e., where $d=pn=c \log n$ for some $c > 1$, up to $d=\log^5 n$. Our lower bound technique is based on an entropic argument which is more general than the use of Suen's inequality by Bollob\'as, Mitsche, and Pralat, whereas our upper bound is similar to theirs.

math.CO↗

arXiv2024

Autocorrelation properties of temporal networks governed by dynamic node variables

We study synthetic temporal networks whose evolution is determined by stochastically evolving node variables - synthetic analogues of, e.g., temporal proximity networks of mobile agents. We quantify the long-timescale correlations of these evolving networks by an autocorrelative measure of edge persistence. Several distinct patterns of autocorrelation arise, including power-law decay and exponential decay, depending on the choice of node-variable dynamics and connection probability function. Our methods are also applicable in wider contexts; our temporal network models are tractable mathematically and in simulation, and our long-term memory quantification is analytically tractable and straightforwardly computable from temporal network data.

physics.soc-ph↗

arXiv2024

Work extraction with feedback control using limited resources

Many physical, biological, and even social systems are faced with the problem of how to efficiently harvest free energy from an environment that can have many possible states, yet only have a limited number of harvesting protocols to choose among. We investigate this scenario by extending earlier work on using feedback control to extract work from nonequilibirum systems. Specifically, in contrast to that previous work on the thermodynamics of feedback control, we analyze the combined and separate effects of noisy measurements, memory limitations, and limitations on the number of possible work extraction protocols. Our analysis provides a general recipe to construct repertoires of allowed harvesting protocols that minimize the expected thermodynamic losses during free energy harvesting, i.e., that minimize expected entropy production. In particular, our results highlight that the benefits of feedback control over uninformed (random) actions extend beyond just the associated information gain, often by many orders of magnitude. Our results also uncover the effects of limitations on the number of possible harvesting protocols when there is uncertainty about the distribution over states of the environment.

cond-mat.stat-mech↗

arXiv2023

Spatial scales of COVID-19 transmission in Mexico

During outbreaks of emerging infectious diseases, internationally connected cities often experience large and early outbreaks, while rural regions follow after some delay. This hierarchical structure of disease spread is influenced primarily by the multiscale structure of human mobility. However, during the COVID-19 epidemic, public health responses typically did not take into consideration the explicit spatial structure of human mobility when designing non-pharmaceutical interventions (NPIs). NPIs were applied primarily at national or regional scales. Here we use weekly anonymized and aggregated human mobility data and spatially highly resolved data on COVID-19 cases, deaths and hospitalizations at the municipality level in Mexico to investigate how behavioural changes in response to the pandemic have altered the spatial scales of transmission and interventions during its first wave (March - June 2020). We find that the epidemic dynamics in Mexico were initially driven by SARS-CoV-2 exports from Mexico State and Mexico City, where early outbreaks occurred. The mobility network shifted after the implementation of interventions in late March 2020, and the mobility network communities became more disjointed while epidemics in these communities became increasingly synchronised. Our results provide actionable and dynamic insights into how to use network science and epidemiological modelling to inform the spatial scale at which interventions are most impactful in mitigating the spread of COVID-19 and infectious diseases in general.

physics.soc-ph↗

arXiv2022

Dynamics of cold random hyperbolic graphs with link persistence

We consider and analyze a dynamic model of random hyperbolic graphs with link persistence. In the model, both connections and disconnections can be propagated from the current to the next snapshot with probability $\omega \in [0, 1)$. Otherwise, with probability $1-\omega$, connections are reestablished according to the random hyperbolic graphs model. We show that while the persistence probability $\omega$ affects the averages of the contact and intercontact distributions, it does not affect the tails of these distributions, which decay as power laws with exponents that do not depend on $\omega$. We also consider examples of real temporal networks, and we show that the considered model can adequately reproduce several of their dynamical properties. Our results advance our understanding of the realistic modeling of temporal networks and of the effects of link persistence on temporal network properties.

physics.soc-ph↗

arXiv2022

Entropy of labeled versus unlabeled networks

The structure of a network is an unlabeled graph, yet graphs in most models of complex networks are labeled by meaningless random integers. Is the associated labeling noise always negligible, or can it overpower the network-structural signal? To address this question, we introduce and consider the sparse unlabeled versions of popular network models, and compare their entropy against the original labeled versions. We show that labeled and unlabeled Erdos-Renyi graphs are entropically equivalent, even though their degree distributions are very different. The labeled and unlabeled versions of the configuration model may have different prefactors in their leading entropy terms, although this remains conjectural. Our main results are upper and lower bounds for the entropy of labeled and unlabeled one-dimensional random geometric graphs. We show that their unlabeled entropy is negligible in comparison with the labeled entropy. This means that in sparse networks the entropy of meaningless labeling may dominate the entropy of the network structure. The main implication of this result is that the common practice of using exchangeable models to reason about real-world networks with distinguishable nodes may introduce uncontrolled aberrations into conclusions made about these networks, suggesting a need for a thorough reexamination of the statistical foundations and key results of network science.

physics.soc-ph↗

arXiv2021

Dynamic Hidden-Variable Network Models

Models of complex networks often incorporate node-intrinsic properties abstracted as hidden variables. The probability of connections in the network is then a function of these variables. Real-world networks evolve over time, and many exhibit dynamics of node characteristics as well as of linking structure. Here we introduce and study natural temporal extensions of static hidden-variable network models with stochastic dynamics of hidden variables and links. The rates of the hidden variable dynamics and link dynamics are controlled by two parameters, and snapshots of networks in the dynamic models may or may not be equivalent to a static model, depending on the location in the parameter phase diagram. We quantify deviations from static-like behavior, and examine the level of structural persistence in the considered models. We explore temporal versions of popular static models with community structure, latent geometry, and degree-heterogeneity. We do not attempt to directly model real networks, but comment on interesting qualitative resemblances, discussing possible extensions, generalizations, and applications.

physics.soc-ph↗

arXiv2020

netrd: A library for network reconstruction and graph distances

Over the last two decades, alongside the increased availability of large network datasets, we have witnessed the rapid rise of network science. For many systems, however, the data we have access to is not a direct description of the underlying network. More and more, we see the drive to study networks that have been inferred or reconstructed from non-network data---in particular, using time series data from the nodes in a system to infer likely connections between them. Selecting the most appropriate technique for this task is a challenging problem in network science. Different reconstruction techniques usually have different assumptions, and their performance varies from system to system in the real world. One way around this problem could be to use several different reconstruction techniques and compare the resulting networks. However, network comparison is also not an easy problem, as it is not obvious how best to quantify the differences between two networks, in part because of the diversity of tools for doing so. The netrd Python package seeks to address these two parallel problems in network science by providing, to our knowledge, the most extensive collection of both network reconstruction techniques and network comparison techniques (often referred to as graph distances) in a single library (https://github.com/netsiphd/netrd). In this article, we detail the two main functionalities of the netrd package. Along the way, we describe some of its other useful features. This package builds on commonly used Python packages and is already a widely used resource for network scientists and other multidisciplinary researchers. With ongoing open-source development, we see this as a tool that will continue to be used by all sorts of researchers to come.

cs.SI↗

arXiv2020

Network comparison and the within-ensemble graph distance

Quantifying the differences between networks is a challenging and ever-present problem in network science. In recent years a multitude of diverse, ad hoc solutions to this problem have been introduced. Here we propose that simple and well-understood ensembles of random networks (such as Erd\H{o}s-R\'{e}nyi graphs, random geometric graphs, Watts-Strogatz graphs, the configuration model, and preferential attachment networks) are natural benchmarks for network comparison methods. Moreover, we show that the expected distance between two networks independently sampled from a generative model is a useful property that encapsulates many key features of that model. To illustrate our results, we calculate this within-ensemble graph distance and related quantities for classic network models (and several parameterizations thereof) using 20 distance measures commonly used to compare graphs. The within-ensemble graph distance provides a new framework for developers of graph distances to better understand their creations and for practitioners to better choose an appropriate tool for their particular task.

physics.soc-ph↗

arXiv2019

Classical Information Theory of Networks

Existing information-theoretic frameworks based on maximum entropy network ensembles are not able to explain the emergence of heterogeneity in complex networks. Here, we fill this gap of knowledge by developing a classical framework for networks based on finding an optimal trade-off between the information content of a compressed representation of the ensemble and the information content of the actual network ensemble. In this way not only we introduce a novel classical network ensemble satisfying a set of soft constraints but we are also able to calculate the optimal distribution of the constraints. We show that for the classical network ensemble in which the only constraints are the expected degrees a power-law degree distribution is optimal. Also, we study spatially embedded networks finding that the interactions between nodes naturally lead to non-uniform spread of nodes in the space, with pairs of nodes at a given distance not necessarily obeying a power-law distribution. The pertinent features of real-world air transportation networks are well described by the proposed framework.

physics.soc-ph↗