arXiv subjects

Horacio E. Castillo

Publications and source records attributed to Horacio E. Castillo.

At least 19 recordsLinked to original sources

arXiv2026

Approaching human parity in the quality of automated organoid image segmentation

Organoids are complex, three dimensional, self-organizing cell cultures which manifest organ-like features and represent a powerful platform for studying human disease and developing treatment options. Organoid development is characterized by dynamic morphological and cellular organization, which mimic some aspects of organ development. To study these rapid changes over the course of organoid development, advanced imaging and analytical tools are critical to accurately monitor the trajectory of organoid growth and investigate disease processes. In this work, we focus on computer vision and machine learning techniques to automatically measure the size and shape of developing spheroids derived from pluripotent stem cells (iPSCs), which are typically the starting material for generating organoid cultures. To facilitate this task, we introduce a composite method that combines the Segment Anything Model (SAM), a general-purpose foundation model, with an existing domain-specific tool. This composite method is evaluated together with several existing tools by testing them on organoid image data and comparing with the results of manual image segmentation. We find that no single existing tool is able to segment the test images with sufficient accuracy across all test conditions, but the newly introduced composite method produces consistent and accurate results for all but a very small fraction of the most challenging images. Finally, we compare the accuracy of this method to the variability between manual segmentations by independent annotators (inter-observer variability) and find that by one measure it performs at the level of inter-observer variability and by others it performs very close to it.

cs.CV↗

arXiv2023

A simple model for dynamic heterogeneity in glass-forming liquids

Liquids near the glass transition exhibit dynamical heterogeneity, i.e. local relaxation rates fluctuate strongly over space and time. Here we introduce a simple continuum model that allows for quantitative predictions for the correlators describing these fluctuations. We find remarkable agreement of the model predictions for the dynamic susceptibility $χ_4(t)$ with numerical results for a binary hard-sphere liquid and for a Kob-Andersen Lennard-Jones mixture. Under this model, the lifetime $τ_{\rm ex}$ of the heterogeneities has little effect on the position $t = t_4 \sim τ_α$ of the peak of $χ_4(t)$, but it controls the decay of $χ_4(t)$ after the peak, and we show how to estimate it from this decay.

cond-mat.soft↗

arXiv2021

Single particle fluctuations dominate the long-time dynamic susceptibility in glass-forming liquids

Liquids near the glass transition exhibit dynamical heterogeneity, i.e. correlated regions in the liquid relax at either a much faster rate or a much slower rate than the average. This collective phenomenon has been characterized by measurements of a dynamic susceptibility $χ_4(t)$, which are sometimes interpreted in terms of the size of those relaxing regions and the intensity of the fluctuations. We show that the results of those measurements can be affected not only by the collective fluctuations in the relaxation rate, but also by density fluctuations in the initial state and by single-particle fluctuations. We also show that at very long times the average overlap $C(t)$ probing the similarity between an initial and a final state separated by a time interval $t$ decays as a power law $C(t) \sim t^{-d/2}$. This is much slower than the stretched exponential behavior $C(t) \sim {\rm e}^{-(t/τ)^β}$ previously observed at times within one or two orders of magnitude of the $α$-relaxation time $τ_α$. We find that for times longer than $10-100 τ_α$, the dynamic susceptibility $χ_4(t)$ is dominated by single particle fluctuations, and that $χ_4(t) \approx C(t) \sim t^{-d/2}$. Finally, we introduce a method to extract the collective relaxation contribution to the dynamic susceptibility $χ_4(t)$ by subtracting the effects of single-particle fluctuations and initial state density fluctuations. We apply this method to numerical simulations of two glass forming models: a binary hard sphere system and a Kob-Andersen Lennard-Jones system. This allows us to extend the analysis of numerical data to timescales much longer than previously possible, and opens the door for further future progress in the study of dynamic heterogeneities, including the determination of the exchange time.

cond-mat.soft↗

arXiv2017

Slow and Long-ranged Dynamical Heterogeneities in Dissipative Fluids

A two-dimensional bidisperse granular fluid is shown to exhibit pronounced long-ranged dynamical heterogeneities as dynamical arrest is approached. Here we focus on the most direct approach to study these heterogeneities: we identify clusters of slow particles and determine their size, $N_c$, and their radius of gyration, $R_G$. We show that $N_c\propto R_G^{d_f}$, providing direct evidence that the most immobile particles arrange in fractal objects with a fractal dimension, $d_f$, that is observed to increase with packing fraction $ϕ$. The cluster size distribution obeys scaling, approaching an algebraic decay in the limit of structural arrest, i.e., $ϕ\toϕ_c$. Alternatively, dynamical heterogeneities are analyzed via the four-point structure factor $S_4(q,t)$ and the dynamical susceptibility $χ_4(t)$. $S_4(q,t)$ is shown to obey scaling in the full range of packing fractions, $0.6\leqϕ\leq 0.805$, and to become increasingly long-ranged as $ϕ\toϕ_c$. Finite size scaling of $χ_4(t)$ provides a consistency check for the previously analyzed divergences of $χ_4(t)\propto (ϕ-ϕ_c)^{-γ_χ}$ and the correlation length $ξ\propto (ϕ-ϕ_c)^{-γ_ξ}$. We check the robustness of our results with respect to our definition of mobility. The divergences and the scaling for $ϕ\toϕ_c$ suggest a non-equilibrium glass transition which seems qualitatively independent of the coefficient of restitution.

cond-mat.dis-nn↗

arXiv2016

Universal Scaling in the Aging of the Strong Glass Former SiO$_2$

We show that the aging dynamics of a strong glass former displays a strikingly simple scaling behavior, connecting the average dynamics with its fluctuations, namely the dynamical heterogeneities. We perform molecular dynamics simulations of SiO$_2$ with BKS interactions, quenching the system from high to low temperature, and study the evolution of the system as a function of the waiting time $t_{\rm w}$ measured from the instant of the quench. We find that both the aging behavior of the dynamic susceptibility $χ_4$ and the aging behavior of the probability distribution $P(f_{{\rm s},{\mathbf r}})$ of the local incoherent intermediate scattering function $f_{{\rm s},{\mathbf r}}$ can be described by simple scaling forms in terms of the global incoherent intermediate scattering function $C$. The scaling forms are the same that have been found to describe the aging of several fragile glass formers and that, in the case of $P(f_{{\rm s},{\mathbf r}})$, have been also predicted theoretically. A thorough study of the length scales involved highlights the importance of intermediate length scales. We also analyze directly the scaling dependence on particle type and on wavevector $q$, and find that both the average and the fluctuations of the slow aging dynamics are controlled by a unique aging clock, which is not only independent of the wavevector $q$, but is the same for O and Si atoms.

cond-mat.dis-nn↗

arXiv2015

Cellular reprogramming dynamics follow a simple one-dimensional reaction coordinate

Cellular reprogramming, the conversion of one cell type to another, has fundamentally transformed our conception of cell types. Cellular reprogramming induces global changes in gene expression involving hundreds of transcription factors and thousands of genes and understanding how cells globally alter their gene expression profile during reprogramming is an open problem. Here we reanalyze time-series data on cellular reprogramming from differentiated cell types to induced pluripotent stem cells (iPSCs) and show that gene expression dynamics during reprogramming follow a simple one-dimensional reaction coordinate. This reaction coordinate is independent of both the time it takes to reach the iPSC state as well as the details of experimental protocol used. Using Monte-Carlo simulations, we show that such a reaction coordinate emerges naturally from epigenetic landscape models of cell identity where cellular reprogramming is viewed as a "barrier-crossing" between the starting and ending cell fates. The model also provides gene-level insight into reprogramming dynamics and resolves a debate in the stem cell field about the different phases of reprogramming dynamics. Overall, our analysis and model suggest that gene expression dynamics during reprogramming follow a canonical trajectory consistent with the idea of an "optimal path" in gene expression space for reprogramming.

q-bio.MN↗

arXiv2015

Fluctuating Phases and Fluctuating Relaxation Times in Glass Forming Liquids

The presence of fluctuating local relaxation times, $τ_r(t)$ has been used for some time as a conceptual tool to describe dynamical heterogeneities in glass-forming systems. However, until now no general method is known to extract the full space and time dependent $τ_r(t)$ from experimental or numerical data. Here we report on a new method for determining the local phase field, $ϕ_r(t) = \int^{t} dt'/τ_r(t')$ from snapshots $\{r(t_i)\}_{i=1...M}$ of the positions of the particles in a system, and we apply it to extract $ϕ_r(t)$ and $τ_r(t)$ from numerical simulations. By studying how the phase field depends on the number of snapshots, we find that it is a well defined quantity. By studying fluctuations of the phase field, we find that they describe heterogeneities well at long distance scales.

cond-mat.dis-nn↗

arXiv2014

Strong Dynamical Heterogeneity and Universal Scaling in Driven Granular Fluids

Large scale simulations of two-dimensional bidisperse granular fluids allow us to determine spatial correlations of slow particles via the four-point structure factor $S_4(q,t)$. Both cases, elastic ($\varepsilon=1$) as well as inelastic ($\varepsilon < 1$) collisions, are studied. As the fluid approaches structural arrest, i.e. for packing fractions in the range $0.6 \le ϕ\le 0.805$, scaling is shown to hold: $S_4(q,t)/χ_4(t)=s(qξ(t))$. Both the dynamic susceptibility, $χ_4(τ_α)$, as well as the dynamic correlation length, $ξ(τ_α)$, evaluated at the $α$ relaxation time, $τ_α$, can be fitted to a power law divergence at a critical packing fraction. The measured $ξ(τ_α)$ widely exceeds the largest one previously observed for hard sphere 3d fluids. The number of particles in a slow cluster and the correlation length are related by a robust power law, $χ_4(τ_α) \approxξ^{d-p}(τ_α)$, with an exponent $d-p\approx 1.6$. This scaling is remarkably independent of $\varepsilon$, even though the strength of the dynamical heterogeneity increases dramatically as $\varepsilon$ grows.

cond-mat.stat-mech↗

arXiv2013

Fluctuations in the Time Variable and Dynamical Heterogeneity in Glass-Forming Systems

We test a hypothesis for the origin of dynamical heterogeneity in slowly relaxing systems, namely that it emerges from soft (Goldstone) modes associated with a broken continuous symmetry under time reparametrizations. We do this by constructing coarse grained observables and decomposing the fluctuations of these observables into transverse components, which are associated with the postulated time-fluctuation soft modes, and a longitudinal component, which represents the rest of the fluctuations. Our test is performed on data obtained in simulations of four models of structural glasses. As the hypothesis predicts, we find that the time reparametrization fluctuations become increasingly dominant as temperature is lowered and timescales are increased. More specifically, the ratio between the strengths of the transverse fluctuations and the longitudinal fluctuations grows as a function of the dynamical susceptibility, χ4, which represents the strength of the dynamical heterogeneity; and the correlation volumes for the transverse fluctuations are approximately proportional to those for the dynamical heterogeneity, while the correlation volumes for the longitudinal fluctuations remain small and approximately constant.

cond-mat.dis-nn↗

arXiv2011

Mapping dynamical heterogeneity in structural glasses to correlated fluctuations of the time variables

Dynamical heterogeneities -- strong fluctuations near the glass transition -- are believed to be crucial to explain much of the glass transition phenomenology. One possible hypothesis for their origin is that they emerge from soft (Goldstone) modes associated with a broken continuous symmetry under time reparametrizations. To test this hypothesis, we use numerical simulation data from four glass-forming models to construct coarse grained observables that probe the dynamical heterogeneity, and decompose the fluctuations of these observables into two transverse components associated with the postulated time-fluctuation soft modes and a longitudinal component unrelated to them. We find that as temperature is lowered and timescales are increased, the time reparametrization fluctuations become increasingly dominant, and that their correlation volumes grow together with the correlation volumes of the dynamical heterogeneities, while the correlation volumes for longitudinal fluctuations remain small.

cond-mat.soft↗

arXiv2011

Time reparametrization invariance in arbitrary range p-spin models: symmetric versus non-symmetric dynamics

We explore the existence of time reparametrization symmetry in p-spin models. Using the Martin-Siggia-Rose generating functional, we analytically probe the long-time dynamics. We perform a renormalization group analysis where we systematically integrate over short timescale fluctuations. We find three families of stable fixed points and study the symmetry of those fixed points with respect to time reparametrizations. One of those families is composed entirely of symmetric fixed points, which are associated with the low temperature dynamics. The other two families are composed entirely of non-symmetric fixed points. One of these two non-symmetric families corresponds to the high temperature dynamics. Time reparametrization symmetry is a continuous symmetry that is spontaneously broken in the glass state and we argue that this gives rise to the presence of Goldstone modes. We expect the Goldstone modes to determine the properties of fluctuations in the glass state, in particular predicting the presence of dynamical heterogeneity.

cond-mat.dis-nn↗

arXiv2008

Universal fluctuations in the relaxation of structural glasses

The presence of strong local fluctuations -- dynamical heterogeneities -- has been observed near the glass transitions of a wide variety of materials. Here we explore the possible presence of universality in those fluctuations. We compare the statistical properties of fluctuations obtained from numerical simulations of four different glass-forming systems: two polymer systems and two particle systems. We find strong evidence for universality, both in the qualitative behavior of the fluctuations and in the remarkable agreement of the scaling functions describing them.

cond-mat.dis-nn↗

arXiv2008

Equilibrium and non-equilibrium fluctuations in a glass-forming liquid

Glass-forming liquids display strong fluctuations -- dynamical heterogeneities -- near their glass transition. By numerically simulating a binary Weeks-Chandler-Andersen liquid and varying both temperature and timescale, we investigate the probability distributions of two kinds of local fluctuations in the non-equilibrium (aging) regime and in the equilibrium regime; and find them to be very similar in the two regimes and across temperatures. We also observe that, when appropriately rescaled, the integrated dynamic susceptibility is very weakly dependent on temperature and very similar in both regimes.

cond-mat.dis-nn↗

arXiv2008

Growth of spatial correlations in the aging of a simple structural glass

We present a detailed numerical study of dynamical heterogeneities in the aging regime of a simple binary Lennard-Jones glass former. For most waiting times t_w and final times t, both the dynamical susceptibility χ_4(t,t_w) and the dynamical correlation length ξ_4(t,t_w) can be approximated as products of two factors: i) a waiting time dependent scale that grows as a power of t_w, and ii) a scaling function dependent on t,t_w only through the value of the intermediate scattering function C(t,t_w). We find that χ_4(t,t_w) is determined *only in part* by the correlation volume.

cond-mat.dis-nn↗

arXiv2008

Time reparametrization symmetry in spin glass models

We study the long-time aging dynamics of spin-glass models with two-spin interactions by performing a Renormalization Group transformation on the time variable in the non-equilibrium dynamical generating functional. We obtain the RG equations and find that the flow converges to an exact fixed point. We show that this fixed point is invariant under reparametrizations of the time variable. This continuous symmetry is broken, as evidenced by the fact that the observed correlations and responses are not invariant under it. We argue that this gives rise to the presence of Goldstone modes, and that those Goldstone modes shape the behavior of fluctuations in the nonequilibrium dynamics.

cond-mat.dis-nn↗

arXiv2006

Local fluctuations in the aging of a simple glass

The presence of dynamical heterogeneities, i.e. nanometer-scale regions containing molecules rearranging cooperatively at very different rates compared to the bulk, is increasingly being recognized as crucial in our understanding of the glass transition, from the non-exponential nature of relaxation, to the divergence of the relaxation times. Recently, dynamical heterogeneities have been directly observed experimentally. However a clear physical picture for the origin of these heterogeneities is still lacking. Here we investigate a possible physical mechanism for the origin of dynamical heterogeneities in the non-equilibrium dynamics of structural glasses. We test the predictions regarding universal scaling of fluctuations derived from this mechanism against simulation results in a simple binary Lennard-Jones glass model, and find that to a first approximation they are satisfied. We also propose to apply the same kind of analysis to experimental data from confocal microscopy in colloidal glasses.

cond-mat.dis-nn↗

arXiv2002

Spatially heterogeneous ages in glassy dynamics

We construct a framework for the study of fluctuations in the nonequilibrium relaxation of glassy systems with and without quenched disorder. We study two types of two-time local correlators with the aim of characterizing the heterogeneous evolution: in one case we average the local correlators over histories of the thermal noise, in the other case we simply coarse-grain the local correlators. We explain why the former describe the fingerprint of quenched disorder when it exists, while the latter are linked to noise-induced mesoscopic fluctuations. We predict constraints on the pdfs of the fluctuations of the coarse-grained quantities. We show that locally defined correlations and responses are connected by a generalized local out-of-equilibrium fluctuation-dissipation relation. We argue that large-size heterogeneities in the age of the system survive in the long-time limit. The invariance of the theory under reparametrizations of time underlies these results. We relate the pdfs of local coarse-grained quantities and the theory of dynamic random manifolds. We define a two-time dependent correlation length from the spatial decay of the fluctuations in the two-time local functions. We present numerical tests performed on disordered spin models in finite and infinite dimensions. Finally, we explain how these ideas can be applied to the analysis of the dynamics of other glassy systems that can be either spin models without disorder or atomic and molecular glassy systems.

cond-mat↗

arXiv2002

Heterogeneous aging in spin glasses

We introduce a set of theoretical ideas that form the basis for an analytical framework capable of describing nonequilibrium dynamics in glassy systems. We test the resulting scenario by comparing its predictions with numerical simulations of short-range spin glasses. Local fluctuations and responses are shown to be connected by a generalized local out-of-equilibrium fluctuation-dissipation relation. Scaling relationships are uncovered for the slow evolution of heterogeneities at all time scales.

cond-mat.stat-mech↗