arXiv subjects

Naghmeh Akhavan

Publications and source records attributed to Naghmeh Akhavan.

7 recordsLinked to original sources

arXiv2026

Dead Zones Enable Flexible Phase Organization in Coupled Oscillators

Coupled oscillator networks underlie many biological systems, from cardiac cycles to circadian rhythms. Phase-reduced models such as the Kuramoto model have been widely used to study synchronization, but they typically assume that oscillators remain continuously responsive to inputs and often produce tightly clustered phase distributions. Biological oscillators, however, commonly exhibit phase intervals during which inputs have little or no effect, called ``dead zones." Here, we extend the Kuramoto model by introducing receiver-gated dead zones, in which oscillators transiently ignore incoming signals. Using analytical and numerical approaches, we show that dead zones can reduce synchronization rates, modulate the distribution of phase-locked solutions, and modify the stability of phase-locked states. For identical oscillators, full synchrony remains locally exponentially stable and numerically dominant, although convergence times depend sensitively on the dead-zone width. For heterogeneous oscillators that admit phase-locked solutions when the coupling strength satisfies $K>K^*$, dead zones broaden the long-term phase distributions. Numerical exploration across dead zone widths reveals a transition in which steady phase gaps lose stability, resulting in dead zone-induced phase drifting. Overall, these results identify phase-response dead zones as a biologically plausible mechanism for flexible phase organization beyond classical Kuramoto dynamics.

math.DS↗

arXiv2026

A Data-Driven Measure of REM Sleep Propensity for Human and Rodent Sleep

Mammalian sleep is characterized by multiple alternations between episodes of rapid-eye-movement sleep (REMS) and non-REM sleep (NREMS). While the mechanisms governing the timing of these ultradian NREMS-REMS cycles remain poorly understood, the phenomenon of REMS pressure, namely a drive for REMS that builds up between REMS episodes, is thought to be a contributing factor. Prior analyses of NREMS-REMS cycles in mice has suggested that time in NREMS is a primary contributor to REMS pressure. Building on that finding, we previously introduced a REMS propensity measure defined as the probability to enter REMS before the accumulation of an additional amount of NREMS. Analyzing mouse ultradian cycle data, we showed that REMS propensity at REMS onset was positively correlated with REMS bout duration and with the probability of the occurrence of a REMS bout followed by a short inter-REMS interval, called a sequential REMS cycle. In this paper, we extend our analyses of REMS propensity to human and rat ultradian NREMS-REMS cycle data. We show that, as in mice, human and rat sleep contain both short NREMS-REMS sequential cycles and longer single NREMS-REMS cycles, though there are some differences in the relative distributions of cycle durations. Although rodents exhibit polyphasic sleep in contrast with the consolidated sleep of humans, the calculated REMS propensity measures in all three species show similar profiles as functions of time spent in NREMS: specifically, REMS propensity increases with time spent in NREMS until it reaches a peak value, and then it decays with additional time in NREMS. Positive correlations of REMS propensity at REMS onset with REMS bout duration were present in both human and rat data as in mouse data, suggesting that time spent in NREMS also influences REMS duration in these species.

q-bio.QM↗

arXiv2026

Cell Migration Boundary Motion in Drosophila Egg Chambers: A Combined Phase Field and Chemoattractant Model

In the Drosophila melanogaster egg chamber, the collective migration of border cells toward the oocyte is guided by spatial gradients of chemoattractants. While cellular responses to these cues are well characterized, the spatial distribution of chemoattractant within the tissue remains difficult to measure experimentally due to imaging limitations and extracellular complexity. In this study, we develop a spatially resolved mathematical framework to model local chemoattractant concentrations during border cell migration. We use a phase-field approach to represent the egg chamber geometry and define a diffusion-reaction system with spatially heterogeneous diffusivity that accounts for confinement by cellular domains. This framework allows chemoattractant diffusion to be restricted to extracellular space while remaining excluded from the interiors of nurse cells, the border cell cluster, and the oocyte, similar to what we observe in vivo. We simulate secretion from the oocyte and degradation throughout the domain, showing how geometry shapes the distribution of signaling molecules. We further couple this chemical field to a mechanical model of cluster migration that includes a tangential interface migration (TIM) force, allowing the cluster to respond to both chemoattractant gradients and cell-cell contact. Our results show that signal localization and tissue geometry jointly influence directional persistence and the speed of migration. Notably, geometric bottlenecks and intersections can flatten local gradients and slow migration, consistent with experimental observations. This modeling framework offers a tool to investigate how biophysical constraints shape signaling environments and guide collective cell movement in vivo.

math.AP↗

arXiv2025

Phase-Field Modeling of Border Cell Cluster Migration in Drosophila

Collective cell migration is a fundamental biological process that drives events such as embryonic development, wound healing, and cancer metastasis. In this study, we develop a biophysically informed phase-field model to investigate the collective migration of the border cell cluster in the Drosophila melanogaster egg chamber. Our model captures key aspects of the egg chamber architecture, including the oocyte, nurse cells, and surrounding epithelium, and incorporates both mechanical forces and biochemical cues that guide cell migration. We introduce the Tangential Interface Migration (TIM) force which captures contact-mediated propulsion generated along interfaces between the border cell cluster and surrounding nurse cells. Our simulations reveal three key features of TIM-driven migration that distinguish it from previous forms of chemotaxis: (1) the necessity of border cell-nurse cell overlap to initiate movement (i.e., border cells cannot move without a nurse cell substrate), (2) motion is tangential to border cell-nurse cell interfaces, and (3) persistent migration even in regions where the spatial slope of chemoattractant is decreasing. Additionally, we demonstrate that with or without geometry-mediated alterations in chemoattractant distribution such as at intercellular junctions we can vary induced migration pauses, independent of mechanical confinement. We capture an experimentally observed transition to dorsal migration at the oocyte with a sustained medio-lateral chemical cue of small amplitude. The results show how spatial constraints and interfacial forces shape collective cell movement and highlight the utility of phase-field models in capturing the interplay between tissue geometry, contact forces, and chemical signaling.

q-bio.CB↗

arXiv2023

Topological conjugacy and its relations for symbolic matrices

In 1988 Boyle and Krieger defined sub-matrices for representation matrices of sofic shift. This paper presents some details of relations between integral sub-matrices and representation matrices. Besides, we express a new version of the Decomposition Theorem by sub-matrices. Generally, strong shift equivalence (conjugacy) of sub-matrices does not apply to representation matrices, but we show that this result can be achieved by the fixed diagonal integral sub-matrix.

math.DS↗

arXiv2023

Extinction of multiple populations and a team of Die-out Lyapunov functions

The extinction of species is a major problem of concern with a large literature. Our investigation gives insight into when species extinctions must occur, with an emphasis on determining which species might possibly die out and on how fast they die out. We investigate a differential equations model for population interactions with the goal of determining when several species (\ie, coordinates of a bounded solution) must die out or ``go extinct'' and must do so exponentially fast. Typically each coordinate represents the population density of a different species. For our main tool, we create what we call ``die-out'' Lyapunov functions. A given system may have several or many such functions, each of which is a function of a different set of coordinates. That die-out function implies that one of the species in its subset must die out exponentially fast -- for almost every choice of coefficients of the system. We create a ``team'' of die-out functions that work together to show that $k$ species must die, where $k$ is determined separately. Secondly, we present a ``trophic'' condition for generalized Lotka-Volterra systems that guarantees that there is a trapping region that is globally attracting. That implies that all solutions are bounded.

math.DS↗

arXiv2019

Population collapse in Elite-dominated societies: A differential equations model without differential equations

The HANDY model of Motesharrei, Rivas, and Kalnay examines interactions with the environment by human populations, both between poor and rich people, i.e., "Commoners" and "Elites". The Elites control the society's wealth and consume it at a higher rate than Commoners, whose work produces the wealth. We say a model is "Elite-dominated" when the Elites' per capita population change rate is always at least as large as the Commoners'. We can show the HANDY model always exhibits population crashes for all choices of parameter values for which it is Elite-dominated. But any such model with explicit equations raises questions of how the resulting behaviors depend on the details of the models. How important are the particular design features codified in the differential equations? In this paper, we first replace the explicit equations of HANDY with differential equations that are only described conceptually or qualitatively - using only conditions that can be verified for explicit systems. Next, we discard the equations entirely, replacing them with qualitative conditions, and we prove these conditions imply population collapse must occur. In particular, one condition is that the model is Elite-dominated. We show that the HANDY model with Elite-dominated parameters satisfies our hypotheses and thus must undergo population collapse. Our approach of introducing qualitative mathematical hypotheses can better show the underlying features of the model that lead to collapse. We also ask how societies can avoid collapse.

math.DS↗