arXiv subjects

Da Zhou

Publications and source records attributed to Da Zhou.

36 records · Page 2Linked to original sources

arXiv2022

Phenotypic Equilibrium as Probabilistic Convergence in Multi-phenotype Cell Population Dynamics

We consider the cell population dynamics with $n$ different phenotypes. Both the Markovian branching process model (stochastic model) and the ordinary differential equation (ODE) system model (deterministic model) are presented, and exploited to investigate the dynamics of the phenotypic proportions. We will prove that in both models, these proportions will tend to constants regardless of initial population states ("phenotypic equilibrium") under weak conditions, which explains the experimental phenomenon in Gupta et al.'s paper. We also prove that Gupta et al.'s explanation is the ODE model under a special assumption. As an application, we will give sufficient and necessary conditions under which the proportion of one phenotype tends to $0$ (die out) or $1$ (dominate). We also extend our results to non-Markovian cases.

q-bio.PE↗

arXiv2020

Sudden collapse of magnetic order in oxygen deficient nickelate films

Oxygen vacancies play a crucial role in the control of the electronic, magnetic, ionic, and transport properties of functional oxide perovskites. Rare earth nickelates (RENiO$_{3-x}$) have emerged over the years as a rich platform to study the interplay between the lattice, the electronic structure, and ordered magnetism. In this study, we investigate the evolution of the electronic and magnetic structure in thin films of RENiO$_{3-x}$, using a combination of X-ray absorption spectroscopy and imaging, resonant X-ray scattering, and extended multiplet ligand field theory modeling. We find that oxygen vacancies modify the electronic configuration within the Ni-O orbital manifolds, leading to a dramatic evolution of long-range electronic transport pathways despite the absence of nanoscale phase separation. Remarkably, magnetism is robust to substantial levels of carrier doping, and only a moderate weakening of the $(1/4, 1/4, 1/4)_{pc}$ antiferromagnetic order parameter is observed, whereas the magnetic transition temperature is largely unchanged. Only at a certain point long-range magnetism is abruptly erased without an accompanying structural transition. We propose the progressive disruption of the 3D magnetic superexchange pathways upon introduction of point defects as the mechanism behind the sudden collapse of magnetic order in oxygen-deficient nickelates. Our work demonstrates that, unlike most other oxides, ordered magnetism in RENiO$_{3-x}$ is mostly insensitive to carrier doping. The sudden collapse of ordered magnetism upon oxygen removal may provide a new mechanism for solid-state magneto-ionic switching and new applications in antiferromagnetic spintronics.

cond-mat.str-el↗

arXiv2020

Stochastic stem cell models with mutation: A comparison of asymmetric and symmetric divisions

In order to fulfill cell proliferation and differentiation through cellular hierarchy, stem cells can undergo either asymmetric or symmetric divisions. Recent studies pay special attention to the effect of different modes of stem cell division on the lifetime risk of cancer, and report that symmetric division is more beneficial to delay the onset of cancer. The fate uncertainty of symmetric division is considered to be the reason for the cancer-delaying effect. In this paper we compare asymmetric and symmetric divisions of stem cells via studying stochastic stem cell models with mutations. Specially, by using rigorous mathematical analysis we find that both asymmetric and symmetric models show the same statistical average, but symmetric model shows higher fluctuation than asymmetric model. We further show that the difference between the two models would be more remarkable for lower mutation rates. Our work quantifies the uncertainty of cell division and highlights the significance of stochasticity for distinguishing between different modes of stem cell division.

q-bio.PE↗

arXiv2019

Flatness of Minima in Random Inflationary Landscapes

We study the likelihood which relative minima of random polynomial potentials support the slow-roll conditions for inflation. Consistent with renormalizability and boundedness, the coefficients that appear in the potential are chosen to be order one with respect to the energy scale at which inflation transpires. Investigation of the single field case illustrates a window in which the potentials satisfy the slow-roll conditions. When there are two scalar fields, we find that the probability depends on the choice of distribution for the coefficients. A uniform distribution yields a $0.05\%$ probability of finding a suitable minimum in the random potential whereas a maximum entropy distribution yields a $0.1\%$ probability.

hep-th↗

arXiv2019

Evolution of cooperation driven by active information spreading

Cooperators forgo their interest to benefit others. Thus cooperation should not be favored by natural selection. It challenges the evolutionists, since cooperation is widespread. As one of the resolutions, information spreading has been revealed to play a key role in the emergence of cooperation. Individuals, however, are typically assumed to be passive in the information spreading. Here we assume that individuals are active to spread the information via self-recommendation. Individuals with higher intensities of self-recommendation are likely to have more neighbors. We find that i) eloquent cooperators are necessary to promote cooperation; ii) individuals need to be open to the self-recommendation to enhance cooperation level; iii) the cost-to-benefit ratio should be smaller than one minus the ratio between self-recommendation intensities of defector and cooperator, which qualitatively measures the viscosity of the population. Our results highlight the importance of active information spreading on cooperation.

q-bio.PE↗

arXiv2018

A Boosting Method to Face Image Super-resolution

Recently sparse representation has gained great success in face image super-resolution. The conventional sparsity-based methods enforce sparse coding on face image patches and the representation fidelity is measured by $\ell_{2}$-norm. Such a sparse coding model regularizes all facial patches equally, which however ignores distinct natures of different facial patches for image reconstruction. In this paper, we propose a new weighted-patch super-resolution method based on AdaBoost. Specifically, in each iteration of the AdaBoost operation, each facial patch is weighted automatically according to the performance of the model on it, so as to highlight those patches that are more critical for improving the reconstruction power in next step. In this way, through the AdaBoost training procedure, we can focus more on the patches (face regions) with richer information. Various experimental results on standard face database show that our proposed method outperforms state-of-the-art methods in terms of both objective metrics and visual quality.

cs.CV↗

arXiv2017

A Bayesian statistical analysis of stochastic phenotypic plasticity model of cancer cells

The phenotypic plasticity of cancer cells has received special attention in recent years. Even though related models have been widely studied in terms of mathematical properties, a thorough statistical analysis on parameter estimation and model selection is still very lacking. In this study, we present a Bayesian approach on the relative frequencies of cancer stem cells (CSCs). Both Gibbs sampling and Metropolis-Hastings (MH) algorithm are used to perform point and interval estimations of cell-state transition rates between CSCs and non-CSCs. Extensive simulations demonstrate the validity of our model and algorithm. By applying this method to a published data on SW620 colon cancer cell line, the model selection favors the phenotypic plasticity model, relative to conventional hierarchical model of cancer cells. Moreover, it is found that the initial state of CSCs after cell sorting significantly influences the occurrence of phenotypic plasticity.

q-bio.CB↗

arXiv2016

Control of epidemics via social partnership adjustment

Epidemic control is of great importance for human society. Adjusting interacting partners is an effective individualized control strategy. Intuitively, it is done either by shortening the interaction time between susceptible and infected individuals or by increasing the opportunities for contact between susceptible individuals. Here, we provide a comparative study on these two control strategies by establishing an epidemic model with non-uniform stochastic interactions. It seems that the two strategies should be similar, since shortening the interaction time between susceptible and infected individuals somehow increases the chances for contact between susceptible individuals. However, analytical results indicate that the effectiveness of the former strategy sensitively depends on the infectious intensity and the combinations of different interaction rates, whereas the latter one is quite robust and efficient. Simulations are shown in comparison with our analytical predictions. Our work may shed light on the strategic choice of disease control.

q-bio.PE↗

arXiv2015

A Note on Discrete Einstein Metric

In this short note, we prove that the space of all admissible piecewise linear metrics parameterized by length square on a triangulated manifolds is a convex cone. We further study Regge's Einstein-Hilbert action and give a much more reasonable definition of discrete Einstein metric than our former version in \cite{G}. Finally, we introduce a discrete Ricci flow for three dimensional triangulated manifolds, which is closely related to the existence of discrete Einstein metrics.

math.DG↗

arXiv2015

The phenotypic equilibrium of cancer cells: From average-level stability to path-wise convergence

The phenotypic equilibrium, i.e. heterogeneous population of cancer cells tending to a fixed equilibrium of phenotypic proportions, has received much attention in cancer biology very recently. In previous literature, some theoretical models were used to predict the experimental phenomena of the phenotypic equilibrium, which were often explained by different concepts of stabilities of the models. Here we present a stochastic multi-phenotype branching model by integrating conventional cellular hierarchy with phenotypic plasticity mechanisms of cancer cells. Based on our model, it is shown that: (i) our model can serve as a framework to unify the previous models for the phenotypic equilibrium, and then harmonizes the different kinds of average-level stabilities proposed in these models; and (ii) path-wise convergence of our model provides a deeper understanding to the phenotypic equilibrium from stochastic point of view. That is, the emergence of the phenotypic equilibrium is rooted in the stochastic nature of (almost) every sample path, the average-level stability just follows from it by averaging stochastic samples.

q-bio.CB↗

arXiv2015

The overshoot and phenotypic equilibrium in characterizing cancer dynamics of reversible phenotypic plasticity

The paradigm of phenotypic plasticity indicates reversible relations of different cancer cell phenotypes, which extends the cellular hierarchy proposed by the classical cancer stem cell (CSC) theory. Since it is still question able if the phenotypic plasticity is a crucial improvement to the hierarchical model or just a minor extension to it, it is worthwhile to explore the dynamic behavior characterizing the reversible phenotypic plasticity. In this study we compare the hierarchical model and the reversible model in predicting the cell-state dynamics observed in biological experiments. Our results show that the hierarchical model shows significant disadvantages over the reversible model in describing both long-term stability (phenotypic equilibrium) and short-term transient dynamics (overshoot) of cancer cells. In a very specific case in which the total growth of population due to each cell type is identical, the hierarchical model predicts neither phenotypic equilibrium nor overshoot, whereas thereversible model succeeds in predicting both of them. Even though the performance of the hierarchical model can be improved by relaxing the specific assumption, its prediction to the phenotypic equilibrium strongly depends on a precondition that may be unrealistic in biological experiments, and it also fails to capture the overshoot of CSCs. By comparison, it is more likely for the reversible model to correctly describe the stability of the phenotypic mixture and various types of overshoot behavior.

q-bio.CB↗

arXiv2015

Phase structures of the black D$p$-D$(p+4)$-brane system in various ensembles I: thermal stability

When the D$(p+4)$-brane ($p=0,1,2$) with delocalized D$p$ charges is put into equilibrium with a spherical thermal cavity, the two kinds of charges can be put into canonical or grand canonical ensemble independently by setting different conditions at the boundary. Using the thermal stability condition, we discuss the phase structures of various ensembles of this system formed in this way and find out the situations that the black brane could be the final stable phase in these ensembles. In particular, van der Waals-like phase transitions can happen when D0 and D4 charges are in different kinds of ensembles. Furthermore, our results indicate that the D$(p+4)$-branes and the delocalized D$p$-branes are equipotent.

hep-th↗

arXiv2015

Phase structures of the black D$p$-D$(p + 4)$-brane system in various ensembles II: electrical and thermodynamic stability

By incorporating the electrical stability condition into the discussion, we continue the study on the thermodynamic phase structures of the D$p$-D$(p + 4)$ black brane in GG, GC, CG, CC ensembles defined in our previous paper arXiv:1502.00261. We find that including the electrical stability conditions in addition to the thermal stability conditions does not modify the phase structure of the GG ensemble but puts more constraints on the parameter space where black branes can stably exist in GC, CG, CC ensembles. In particular, the van der Waals-like phase structure which was supposed to be present in these ensembles when only thermal stability condition is considered would no longer be visible, since the phase of the small black brane is unstable under electrical fluctuations. However, the symmetry of the phase structure by interchanging the two kinds of brane charges and potentials is still preserved, which is argued to be the result of T-duality.

hep-th↗

arXiv2015

Seiberg Duality, Quiver Gauge Theories, and Ihara Zeta Function

We study Ihara zeta function for graphs in the context of quivers arising from gauge theories, especially under Seiberg duality transformations. The distribution of poles is studied as we proceed along the duality tree, in light of the weak and strong graph versions of the Riemann Hypothesis. As a by-product, we find a refined version of Ihara zeta function to be the generating function for the generic superpotential of the gauge theory.

hep-th↗

arXiv2014

The Statistics of Vacuum Geometry

We investigate the vacuum moduli space of supersymmetric gauge theories en masse by probing the space of such vacua from a statistical standpoint. Using quiver gauge theories with ${\cal N}=1$ supersymmetry as a testing ground, we sample over a large number of vacua as algebraic varieties, computing explicitly their dimension, degree and Hilbert series. We study the distribution of these geometrical quantities, and also address the question of how likely it is for the moduli space to be Calabi-Yau.

hep-th↗

arXiv2014

A multi-phenotypic cancer model with cell plasticity

The conventional cancer stem cell (CSC) theory indicates a hierarchy of CSCs and non-stem cancer cells (NSCCs), that is, CSCs can differentiate into NSCCs but not vice versa. However, an alternative paradigm of CSC theory with reversible cell plasticity among cancer cells has received much attention very recently. Here we present a generalized multi-phenotypic cancer model by integrating cell plasticity with the conventional hierarchical structure of cancer cells. We prove that under very weak assumption, the nonlinear dynamics of multi-phenotypic proportions in our model has only one stable steady state and no stable limit cycle. This result theoretically explains the phenotypic equilibrium phenomena reported in various cancer cell lines. Furthermore, according to the transient analysis of our model, it is found that cancer cell plasticity plays an essential role in maintaining the phenotypic diversity in cancer especially during the transient dynamics. Two biological examples with experimental data show that the phenotypic conversions from NCSSs to CSCs greatly contribute to the transient growth of CSCs proportion shortly after the drastic reduction of it. In particular, an interesting overshooting phenomenon of CSCs proportion arises in three-phenotypic example. Our work may pave the way for modeling and analyzing the multi-phenotypic cell population dynamics with cell plasticity.

q-bio.CB↗

arXiv2013

Sakai-Sugimoto model in D0-D4 background

We add smeared D0 charges to the D4 background and discuss Sakai-Sugimoto model under this background. The corresponding gauge theory develops a glue condensate $< tr (F_{μν}\tilde F^{μν})> $. The D8 branes go less deep than in the original S-S model and massless Goldstones are still found in the spectrum. The effects of the condensate on the meson spectra, pion decay constant, and couplings of the vector mesons and Goldstones are then investigated.

hep-th↗

arXiv2011

Fixation, transient landscape and diffusion's dilemma in stochastic evolutionary game dynamics

Agent-based stochastic models for finite populations have recently received much attention in the game theory of evolutionary dynamics. Both the ultimate fixation and the pre-fixation transient behavior are important to a full understanding of the dynamics. In this paper, we study the transient dynamics of the well-mixed Moran process through constructing a landscape function. It is shown that the landscape playing a central theoretical "device" that integrates several lines of inquiries: the stable behavior of the replicator dynamics, the long-time fixation, and continuous diffusion approximation associated with asymptotically large population. Several issues relating to the transient dynamics are discussed: (i) multiple time scales phenomenon associated with intra- and inter-attractoral dynamics; (ii) discontinuous transition in stochastically stationary process akin to Maxwell construction in equilibrium statistical physics; and (iii) the dilemma diffusion approximation facing as a continuous approximation of the discrete evolutionary dynamics. It is found that rare events with exponentially small probabilities, corresponding to the uphill movements and barrier crossing in the landscape with multiple wells that are made possible by strong nonlinear dynamics, plays an important role in understanding the origin of the complexity in evolutionary, nonlinear biological systems.

q-bio.PE↗