arXiv subjects

Lizzy Teryoshin

Publications and source records attributed to Lizzy Teryoshin.

8 recordsLinked to original sources

arXiv2026

Selfless reduced amalgamated free products and HNN extensions

We find a general family of selfless inclusions in reduced amalgamated free products of C*-algebras. Apart from generalizing prior works due to McClanahan, Ivanov and Omland, our work yields a few other applications. We present a short new approach to construct HNN extensions of C*-algebras and find several new examples of selflessness using this. This generalizes results of Ueda, Ivanov and de la Harpe-Preaux. As another application our work yields a short proof of selflessness for arbitrary graph products of C*-algebras over graphs of more than 2 vertices and diameter greater than 3.

math.OA↗

arXiv2026

On free components of Artin and Coxeter groups

The number of connected components can be remembered by the von Neumann algebra among Artin groups, the only possible exception being the case that corresponds to the free group factor problem. In the case of Coxeter groups, this result is obtained in the absence of relatively hyperbolicity. We also discuss a specific case of the analogous problem in measure equivalence where each factor group is a product of nonabelian free groups.

math.GR↗

arXiv2026

Diffusive Spreading Across Dynamic Mitochondrial Network Architectures

In eukaryotic cells, mitochondria form networks that range from highly fused interconnected structures to fragmented populations of individual organelles that undergo transient interactions. These structures can be described as temporal networks of physical units, whose dynamic topology is determined by fusion, fission, and motion of the mitochondria through intracellular space. The heterogeneity of the mitochondrial population is governed by diffusive transport and inter-unit exchange of proteins, lipids, ions, and RNA within these networks. We present a unifying framework for the dispersion of material within temporal networks of spatially embedded units that span across a broad connectivity range. Specifically, we consider filling of the networks with a locally produced but globally consumed material, demonstrating that the steady-state content is determined by the balance of timescales for spatial encounter between clusters, local fusion, fission, and diffusive transport within a cluster. As the connectivity increases, filling behavior transitions from three-dimensional spread through a `social network' limited by cluster interactions to low-dimensional transport through a largely stationary `physical network' limited by material diffusivity. We extract parameters for mitochondrial networks in three human cell lines, demonstrating that different cells can access both the social and the physical network regimes. These results provide a quantitative basis for predicting the homogenization of biomolecules through a mitochondrial population. Our framework unifies a variety of temporal network structures into an overarching theory for transport through populations of interacting and interconnected units.

physics.bio-ph↗

arXiv2025

Encounter Times of Intermittently Running Particles

Intracellular processes often rely on the timely encounter of mobile reaction partners, including intermittently motor-driven organelles. The underlying cytoskeletal network presents a complex landscape that both directs particle movement and introduces quenched disorder through filament organization. We investigate the mean first encounter times for pairs of intermittently processive and diffusive particles, moving in two dimensions with and without a fixed filament network. In unstructured domains, increasing particle run-length enhances exploration of the domain, but tends to slow down the encounter times compared to equivalent diffusing particles. Encounters for long-running particles occur preferentially near the periphery, contrasting with bulk encounters for the purely diffusive case. When particles are unbiased in their runs along dense filament networks, encounters are shown to be well approximated by a continuum run-and-tumble model. For biased particles, regions of convergent filament orientation can serve as traps that slow the overall spatial exploration but can allow for faster encounter rates by funneling particles into regions of reduced dimensionality. These findings provide a framework for estimating intracellular encounter kinetics, highlighting the role of key physical features such as the effective diffusivity, run times, and network architecture.

physics.bio-ph↗

arXiv2025

Asymptotic invariants of symbolic powers of binomial edge ideals

To a graph $G$ one associates the binomial edge ideal $J_G$ generated by a collection of binomials corresponding to the edges of $G$. In this paper, we study the asymptotic behavior of symbolic powers of $J_G$, its lexicographic initial ideal $\mathrm{in}_<(J_G)$, and its multigraded generic initial ideal $\mathrm{gin}(J_G)$. We focus on the Waldschmidt constant, $\widehatα$, and asymptotic regularity, $\widehat{\mathrm{reg}}$, which capture linear growth of minimal generator degrees and Castelnuovo--Mumford regularity. We explicitly compute $\widehatα(J_G)$ and $\widehatα(\mathrm{in}_<(J_G))$, and compare the Betti numbers of the symbolic powers of $J_G$ and $J_H$, where $H$ is a subgraph of $G$. To analyze $\mathrm{in}_<(J_G)$ and $\mathrm{gin}(J_G)$, we use the symbolic polyhedron, a convex polyhedron that encodes the elements of the symbolic powers of a monomial ideal. We determine its vertices via $G$'s induced connected subgraphs and show that $\widehatα(\mathrm{gin}(J_G))=\widehatα(I_G)$, where $I_G$ is the edge ideal of $G$. This yields an alternate proof of known bounds for $\widehatα(I_G)$ in terms of $G$'s clique number and chromatic number.

math.AC↗

arXiv2025

Simulated 3D $^{56}$Ni Distributions of Type IIp Supernovae

We present the first three-dimensional study of the asymptotic ejecta distributions for a suite of theoretical Type IIp supernovae originating from red supergiant progenitors. We simulate using the radiation-hydrodynamic code F{\sc{ornax}} from core bounce through the first seconds of the neutrino-driven explosion and then follow using a hydrodynamic variant of the code FLASH until shock breakout of the star and through to homologous expansion of the ejecta into the circumstellar environment. Our studied progenitor models range from 9 to 25 M$_{\odot}$, with explosion energies spanning $\sim$0.1$-$1 Bethe. The shock breakout times span the range $\sim$1$-$4 days, with a breakout time spread by direction ranging from hours to over a day. We find that the dipole orientation of the $^{56}$Ni ejecta is well-preserved from the first seconds out to shock breakout. The $^{56}$Ni ejecta penetrates through the initially outer oxygen shell, and its global structure is imprinted with small-scale clumping as the ejecta evolve through the stellar envelope. For the majority of our models, the neutron star kick is anti-aligned with the $^{56}$Ni ejecta. Models with strongly dipolar ejecta morphology and a massive hydrogen/helium envelope with an inner boundary located deep see as much as $\sim$70\% of the $^{56}$Ni ejecta mixed into that outer envelope, reaching asymptotic velocities ranging from $\sim$350 to 3200 km s$^{-1}$. Supernovae arising from red supergiant progenitors and exhibiting prominent nickel features generally display significant $^{56}$Ni mixing into the stellar envelope.

astro-ph.HE↗

arXiv2025

Some remarks on decay in countable groups and amalgamated free products

In this note, we first study the notion of subexponential decay (SD) for countable groups with respect to a length function, which generalizes the well-known rapid decay (RD) property, first discovered by Haagerup in 1979. Several natural properties and examples are studied, especially including groups that have SD, but not RD. This consideration naturally has applications in $C^*$-algebras. We also consider in this setting a permanence theorem for decay in amalgamated free products (proved also recently by Chatterji--Gautero), and demonstrate that it is in a precise sense optimal.

math.GR↗

arXiv2025

A 3D Simulation of a Type II-P Supernova: from Core Bounce to Beyond Shock Breakout

In order to better connect core-collapse supernovae (CCSN) theory with its observational signatures, we have developed a simulation pipeline from the onset of core collapse to beyond shock breakout. Using this framework, we present a three-dimensional simulation study following the evolution from five seconds to over five days of a 17-M$_{\odot}$ progenitor that explodes with $\sim$10$^{51}$ erg of energy and $\sim$0.1 M$_{\odot}$ of $^{56}$Ni ejecta. The early explosion is highly asymmetric, expanding most prominently along the southern hemisphere. This early asymmetry is preserved to shock breakout, $\sim$1 day later. Breakout itself evinces strong angle-dependence, with as much a day delay in shock breakout by direction. The nickel ejecta closely tails the forward shock, with velocities at breakout as high as $\sim$7000 km s$^{-1}$. A delayed reverse shock forming at the H/He interface on hour timescales leads to the formation of Rayleigh-Taylor instabilities, fast-moving nickel bullets, and almost complete mixing of the metal core into the hydrogen envelope. For the first time, we illustrate the angle-dependent emergent broadband and bolometric light curves from simulations evolved in three-dimensions in entirety, continuing through hydrodynamic shock breakout a CCSN model of a massive stellar progenitor evolved with detailed, late-time neutrino microphysics and transport. Our case study of a single progenitor suggests that 3D simulations initiated with detailed neutrino heating can begin to generically produce the cornucopia of suggested asymmetries and features in CCSNe observations, while establishing the methodology to study this problem in breadth.

astro-ph.HE↗