arXiv subjects

Daniel M. Abrams

Publications and source records attributed to Daniel M. Abrams.

At least 19 recordsLinked to original sources

arXiv2026

A coupled-oscillator model for the formation of planetary rings

We study the dichotomy between compact satellite and ring formation in proto-planetary disks. Specifically, we examine the behavior of a model system of $N$ identical particles locked into circular, gravitationally-bound orbits around a central body. We treat interactions as dominated by inter-particle collisions, and extract an effective two-particle interaction function based on both theory and simulations. We then demonstrate that the expected dynamics are equivalent to a variant of the Kuramoto model, which undergoes a phase transition as parameters vary. This offers a novel potential explanation for the transition between formation of rings versus moons.

astro-ph.EP↗

arXiv2026

A new method for augmenting short time series, with application to pain events in sickle cell disease

Researchers across different fields, including but not limited to ecology, biology, and healthcare, often face the challenge of sparse data. Such sparsity can lead to uncertainties, estimation difficulties, and potential biases in modeling. Here we introduce a novel data augmentation method that combines multiple sparse time series datasets when they share similar statistical properties, thereby improving parameter estimation and model selection reliability. We demonstrate the effectiveness of this approach through validation studies comparing Hawkes and Poisson processes, followed by application to subjective pain dynamics in patients with sickle cell disease (SCD), a condition affecting millions worldwide, particularly those of African, Mediterranean, Middle Eastern, and Indian descent.

stat.ME↗

arXiv2025

Information Criteria Fail for Dynamical Systems: Sampling Rate and Dimension Dependence

Information criteria such as Akaike's (AIC) and Bayes' (BIC) are widely used for model selection in physics and beyond, quantifying the tradeoff between model complexity and goodness-of-fit to enforce parsimony. However, their derivation assumes uncorrelated samples, an assumption systematically violated by dynamical systems data. Here, through analysis of simple but representative dynamical models -- exponential decay, harmonic oscillation, and chaos -- we demonstrate that model selection depends sensitively on sampling rate and system dimensionality. We derive explicit formulas predicting when standard information criteria fail that should be adaptable to many real-world scenarios, enabling experimentalists to design sampling protocols that avoid pathological regimes.

math.DS↗

arXiv2025

A universal animal communication tempo resonates with the receiver's brain

During fieldwork in Thailand we observed nearly identical frequencies of co-located flashing fireflies and chirping crickets. Motivated by this, we perform a meta-analysis and show an abundance of evolutionarily distinct species that communicate isochronously at ~0.5-4 Hz, suggesting that this might be a frequency "hotspot." We hypothesize that this timescale may have a universal basis in the biophysics of the receiver's neurons. We test this by demonstrating that small receiver circuits constructed from elements representing typical neurons will be most responsive in the observed frequency range.

q-bio.NC↗

arXiv2025

Modeling the evolution of collective synchrony

Group synchrony in the animal kingdom is usually associated with mating. Being in sync is likely advantageous, as it may help in luring the opposite sex. Yet there are also disadvantages -- such as the homogenization of the group -- which make it harder for individuals to stand-out. Here we address this tradeoff, bringing together the Kuramoto model with concepts from evolutionary game theory. We focus on the existence of self-interested ''cheaters,'' which have been extensively studied in a variety of species. In our scenario, cheating individuals take part in the synchronous group display but position themselves (in terms of phase) slightly ahead or behind the pack. This allows them to enjoy both the group benefit of advertisement and the individual benefit of being unique. But a group can only tolerate a limited number of such individuals while still achieving synchrony. We therefore incorporate a from of ''policing'' into our model: if an individual strays too far from the group's synchronous phase, they reveal themselves as dishonest and are punished. Our model offers testable predictions regarding natural population compositions, and will hopefully spur further investigation into not only how, but also why, natural systems synchronize.

q-bio.PE↗

arXiv2025

Equilibrium Moment Analysis of It\^o SDEs

Stochastic differential equations have proved to be a valuable governing framework for many real-world systems which exhibit ``noise'' or randomness in their evolution. One quality of interest in such systems is the shape of their equilibrium probability distribution, if such a thing exists. In some cases a straightforward integral equation may yield this steady-state distribution, but in other cases the equilibrium distribution exists and yet that integral equation diverges. Here we establish a new equilibrium-analysis technique based on the logic of finite-timestep simulation which allows us to glean information about the equilibrium regardless -- in particular, a relationship between the raw moments of the equilibrium distribution. We utilize this technique to extract information about one such equilibrium resistant to direct definition.

math.DS↗

arXiv2024

A Mexican hat dance: clustering in Ricker-potential particle systems

The dynamics and spontaneous organization of coupled particles is a classic problem in modeling and applied mathematics. Here we examine the behavior of particles coupled by the Ricker potential, exhibiting finite local repulsion transitioning to distal attraction, leading to an energy-minimizing ``preferred distance''. When compressed by a background potential well of varying severity, these particles exhibit intricate self-organization into ``stacks" with varying sizes and positions. We examine bifurcations of these high-dimensional arrangements, yielding tantalizing glimpses into a rich dynamical zoo of behavior.

nlin.AO↗

arXiv2023

Pain Forecasting using Self-supervised Learning and Patient Phenotyping: An attempt to prevent Opioid Addiction

Sickle Cell Disease (SCD) is a chronic genetic disorder characterized by recurrent acute painful episodes. Opioids are often used to manage these painful episodes; the extent of their use in managing pain in this disorder is an issue of debate. The risk of addiction and side effects of these opioid treatments can often lead to more pain episodes in the future. Hence, it is crucial to forecast future patient pain trajectories to help patients manage their SCD to improve their quality of life without compromising their treatment. It is challenging to obtain many pain records to design forecasting models since it is mainly recorded by patients' self-report. Therefore, it is expensive and painful (due to the need for patient compliance) to solve pain forecasting problems in a purely supervised manner. In light of this challenge, we propose to solve the pain forecasting problem using self-supervised learning methods. Also, clustering such time-series data is crucial for patient phenotyping, anticipating patients' prognoses by identifying "similar" patients, and designing treatment guidelines tailored to homogeneous patient subgroups. Hence, we propose a self-supervised learning approach for clustering time-series data, where each cluster comprises patients who share similar future pain profiles. Experiments on five years of real-world datasets show that our models achieve superior performance over state-of-the-art benchmarks and identify meaningful clusters that can be translated into actionable information for clinical decision-making.

cs.AI↗

arXiv2023

Phase chimera states: frozen patterns of disorder

Coupled oscillators can serve as a testbed for larger questions of pattern formation across many areas of science and engineering. Much effort has been dedicated to the Kuramoto model and phase oscillators, but less has focused on oscillators with variable amplitudes. Here we examine the simplest such oscillators -- Stuart-Landau oscillators -- and attempt to elucidate some puzzling dynamics observed in simulation by us and others. We demonstrate the existence and stability of a previously unreported state which we call a ``phase chimera state.'' Remarkably, in this state, the amplitudes of all oscillators are identical, but one subset of oscillators phase-locks while another subset remains incoherent in phase. We also show that this state can take the form of a ``multitailed phase chimera state'' where a single phase-synchronous cluster of oscillators coexists with multiple groups of phase-incoherent oscillators.

nlin.CD↗

arXiv2022

Interpretation of generalized Langevin equations

Many real-world systems exhibit ``noisy'' evolution in time; interpreting their finitely-sampled behavior as arising from continuous-time processes (in the It\^o or Stratonovich sense) has led to significant success in modeling and analysis in a wide variety of fields. Yet such interpretation hinges on a fundamental linear separation of randomness from determinism in the underlying dynamics. Here we propose some theoretical systems which resist easy and self-consistent interpretation into this well-defined class of equations, requiring an expansion of the interpretive framework. We argue that a wider class of stochastic differential equations, where evolution depends nonlinearly on a random or effectively-random quantity, may be consistently interpreted and in fact exhibit finite-time stochastic behavior in line with an equivalent It\^o process, at which point many existing numerical and analytical techniques may be used. We put forward a method for this conversion, and demonstrate its use on both a toy system and on a system of direct physical relevance: the velocity of a meso-scale particle suspended in a turbulent fluid. This work enables the theoretical and numerical examination of a wide class of mathematical models which might otherwise be oversimplified due to a lack of appropriate tools.

math-ph↗

arXiv2021

A Dynamical Model for the Origin of Anisogamy

The vast majority of multi-cellular organisms are anisogamous, meaning that male and female sex cells differ in size. It remains an open question how this asymmetric state evolved, presumably from the symmetric isogamous state where all gametes are roughly the same size (drawn from the same distribution). Here, we use tools from the study of nonlinear dynamical systems to develop a simple mathematical model for this phenomenon. Using theoretical analysis and numerical simulation, we demonstrate that competition between individuals that is linked to the mean gamete size will almost inevitably result in a stable anisogamous equilibrium, and thus isogamy may naturally lead to anisogamy.

q-bio.PE↗

arXiv2021

Catalyzing collaborations: Prescribed interactions at conferences determine team formation

Collaboration plays a key role in knowledge production. Here, we show that patterns of interaction during conferences can be used to predict who will subsequently form a new collaboration, even when interaction is prescribed rather than freely chosen. We introduce a novel longitudinal dataset tracking patterns of interaction among hundreds of scientists during multi-day conferences encompassing different scientific fields over the span of 5 years. We find that participants who formed new collaborations interacted 63% more on average than those who chose not to form new teams, and that those assigned to a higher interaction scenario had more than an eightfold increase in their odds of collaborating. We propose a simple mathematical framework for the process of team formation that incorporates this observation as well as the effect of memory beyond interaction time. The model accurately reproduces the collaborations formed across all conferences and outperforms seven other candidate models. This work not only suggests that encounters between individuals at conferences play an important role in shaping the future of science, but that these encounters can be designed to better catalyze collaborations.

math.DS↗

arXiv2021

A Mathematical Model for the Origin of Name Brands and Generics

Firms in the U.S. spend over 200 billion dollars each year advertising their products to consumers, around one percent of the country's gross domestic product. It is of great interest to understand how that aggregate expenditure affects prices, market efficiency, and overall welfare. Here, we present a mathematical model for the dynamics of competition through advertising and find a surprising prediction: when advertising is relatively cheap compared to the maximum benefit advertising offers, rational firms split into two groups, one with significantly less advertising (a "generic" group) and one with significantly more advertising (a "name brand" group). Our model predicts that this segmentation will also be reflected in price distributions; we use large consumer data sets to test this prediction and find good qualitative agreement.

physics.soc-ph↗

arXiv2021

Clustering of Pain Dynamics in Sickle Cell Disease from Sparse, Uneven Samples

Irregularly sampled time series data are common in a variety of fields. Many typical methods for drawing insight from data fail in this case. Here we attempt to generalize methods for clustering trajectories to irregularly and sparsely sampled data. We first construct synthetic data sets, then propose and assess four methods of data alignment to allow for application of spectral clustering. We also repeat the same process for real data drawn from medical records of patients with sickle cell disease -- patients whose subjective experiences of pain were tracked for several months via a mobile app. We find that different methods for aligning irregularly sampled sparse data sets can lead to different optimal numbers of clusters, even for synthetic data with known properties. For the case of sickle cell disease, we find that three clusters is a reasonable choice, and these appear to correspond to (1) a low pain group with occasionally acute pain, (2) a group which experiences moderate mean pain that fluctuates often from low to high, and (3) a group that experiences persistent high levels of pain. Our results may help physicians and patients better understand and manage patients' pain levels over time, and we expect that the methods we develop will apply to a wide range of other data sources in medicine and beyond.

q-bio.QM↗

arXiv2020

Pain Intensity Assessment in Sickle Cell Disease patients using Vital Signs during Hospital Visits

Pain in sickle cell disease (SCD) is often associated with increased morbidity, mortality, and high healthcare costs. The standard method for predicting the absence, presence, and intensity of pain has long been self-report. However, medical providers struggle to manage patients based on subjective pain reports correctly and pain medications often lead to further difficulties in patient communication as they may cause sedation and sleepiness. Recent studies have shown that objective physiological measures can predict subjective self-reported pain scores for inpatient visits using machine learning (ML) techniques. In this study, we evaluate the generalizability of ML techniques to data collected from 50 patients over an extended period across three types of hospital visits (i.e., inpatient, outpatient and outpatient evaluation). We compare five classification algorithms for various pain intensity levels at both intra-individual (within each patient) and inter-individual (between patients) level. While all the tested classifiers perform much better than chance, a Decision Tree (DT) model performs best at predicting pain on an 11-point severity scale (from 0-10) with an accuracy of 0.728 at an inter-individual level and 0.653 at an intra-individual level. The accuracy of DT significantly improves to 0.941 on a 2-point rating scale (i.e., no/mild pain: 0-5, severe pain: 6-10) at an intra-individual level. Our experimental results demonstrate that ML techniques can provide an objective and quantitative evaluation of pain intensity levels for all three types of hospital visits.

cs.CY↗

arXiv2020

When Pull Turns to Shove: A Continuous-Time Model for Opinion Dynamics

Accurate modeling of opinion dynamics has the potential to help us understand polarization and what makes effective political discourse possible or impossible. Here, we use physics-based methods to model the evolution of political opinions within a continuously distributed population. We utilize a network-free system of determining political influence and a local-attraction, distal-repulsion dynamic for reaction to perceived content. Our approach allows for the incorporation of intergroup bias such that messages from trusted in-group sources enjoy greater leeway than out-group ones. We are able to extrapolate these nonlinear microscopic dynamics to macroscopic population distributions by using probabilistic functions representing biased environments. The framework we put forward can reproduce real-world political distributions and experimentally observed dynamics, and is amenable to further refinement as more data becomes available.

physics.soc-ph↗

arXiv2020

Why are U.S. Parties So Polarized? A "Satisficing" Dynamical Model

Since the 1960s, Democrats and Republicans in U.S. Congress have taken increasingly polarized positions, while the public's policy positions have remained centrist and moderate. We explain this apparent contradiction by developing a dynamical model that predicts ideological positions of political parties. Our approach tackles the challenge of incorporating bounded rationality into mathematical models and integrates the empirical finding of satisficing decision making---voters settle for candidates who are "good enough" when deciding for whom to vote. We test the model using data from the U.S. Congress over the past 150 years, and find that our predictions are consistent with the two major political parties' historical trajectory. In particular, the model explains how polarization between the Democrats and Republicans since the 1960s could be a consequence of increasing ideological homogeneity within the parties.

physics.soc-ph↗

arXiv2020

A Coupled Oscillator Model for the Origin of Bimodality and Multimodality

Perhaps because of the elegance of the central limit theorem, it is often assumed that distributions in nature will approach singly-peaked, unimodal shapes reminiscent of the Gaussian normal distribution. However, many systems behave differently, with variables following apparently bimodal or multimodal distributions. Here we argue that multimodality may emerge naturally as a result of repulsive or inhibitory coupling dynamics, and we show rigorously how it emerges for a broad class of coupling functions in variants of the paradigmatic Kuramoto model.

nlin.AO↗