arXiv subjects

Congping Lin

Publications and source records attributed to Congping Lin.

6 recordsLinked to original sources

arXiv2018

Modelling brain-wide neuronal morphology via rooted Cayley trees

Neuronal morphology is an essential element for brain activity and function. We take advantage of current availability of brain-wide neuron digital reconstructions of the Pyramidal cells from a mouse brain, and analyze several emergent features of brain-wide neuronal morphology. We observe that axonal trees are self-affine while dendritic trees are self-similar. We also show that tree size appear to be random, independent of the number of dendrites within single neurons. Moreover, we consider inhomogeneous branching model which stochastically generates rooted 3-Cayley trees for the brain-wide neuron topology. Based on estimated order-dependent branching probability from actual axonal and dendritic trees, our inhomogeneous model quantitatively captures a number of topological features including size and shape of both axons and dendrites. This sheds lights on a universal mechanism behind the topological formation of brain-wide axonal and dendritic trees.

math.DS↗

arXiv2017

Simulations of Fractal Star Cluster Formation: I. New Insights for Measuring Mass Segregation of Star Clusters with SubStructure

We compare the existent methods including the minimum spanning tree based method and the local stellar density based method, in measuring mass segregation of star clusters. We find that the minimum spanning tree method reflects more the compactness, which represents the global spatial distribution of massive stars, while the local stellar density method reflects more the crowdedness, which provides the local gravitational potential information. It is suggested to measure the local and the global mass segregation simultaneously. We also develop a hybrid method that takes both aspects into account. This hybrid method balances the local and the global mass segregation in the sense that the predominant one is either caused either by dynamical evolution or purely accidental, especially when such information is unknown a priori. In addition, we test our prescriptions with numerical models and show the impact of binaries in estimating the mass segregation value. As an application, we use these methods on the Orion Nebula Cluster (ONC) observations and the Taurus cluster. We find that the ONC is significantly mass segregated down to the 20th most massive stars. In contrast, the massive stars of the Taurus cluster are sparsely distributed in many different subclusters, showing a low degree of compactness. The massive stars of Taurus are also found to be distributed in the high-density region of the subclusters, showing significant mass segregation at subcluster scales. Meanwhile, we also apply these methods to discuss the possible mechanisms of the dynamical evolution of the simulated substructured star clusters.

astro-ph.GA↗

arXiv2014

On the mixing properties of piecewise expanding maps under composition with permutations, II: Maps of non-constant orientation

For an integer $m \geq 2$, let $\mathcal{P}_m$ be the partition of the unit interval $I$ into $m$ equal subintervals, and let $\mathcal{F}_m$ be the class of piecewise linear maps on $I$ with constant slope $\pm m$ on each element of $\mathcal{P}_m$. We investigate the effect on mixing properties when $f \in \mathcal{F}_m$ is composed with the interval exchange map given by a permutation $\sigma \in S_N$ interchanging the $N$ subintervals of $\mathcal{P}_N$. This extends the work in a previous paper [N.P. Byott, M. Holland and Y. Zhang, DCDS, {\bf 33}, (2013) 3365--3390], where we considered only the "stretch-and-fold" map $f_{sf}(x)=mx \bmod 1$.

math.DS↗

arXiv2012

A model for motor-mediated bidirectional transport along an antipolar microtubule bundle

Long-distance bidirectional transport of organelles depends on the motor proteins kinesin and dynein. Using quantitative data obtained from a fungal model system, we previously developed ASEP-models of bidirectional motion of motors along unipolar microtubules (MTs) near the cell ends of the elongated hyphal cells (herein referred as "unipolar section"). However, recent quantitative live cell imaging in this system has demonstrated that long-range motility of motors and their endosomal cargo mainly occurs along extended antipolar microtubule bundles within the central part of the cell (herein referred to as "bipolar section"). Dynein and kinesin-3 motors coordinate their activity to move early endosomes (EEs) in a bidirectional fashion, with dynein mediating retrograde motility along the unipolar section near the cell poles, whereas kinesin-3 is responsible for bidirectional motions along the antipolar section. Here we extend our modelling approach to simulate bidirectional motility along an antipolar microtubule bundle. In our model, cargos (particles) change direction on each MT with a turning rate $Ω$ and the MTs are linked to each other at the minus ends where particles can hop between MTs with a rate $q_1$ (obstacle-induced switching rate) or $q_2$ (end-induced switching rate). By numerical simulations and mean-field approximations, we investigate the distribution of particles along the MTs for different overall densities $Θ$. We find that even if $Θ$ is low, the system can exhibit shocks in the density profiles near plus and minus ends caused by queueing of particles. We also discuss how the switching rates $q_{1,2}$ influence the type of motor that dominates the active transport in the bundle.

cond-mat.stat-mech↗

arXiv2011

Invariant Measures with Bounded Variation Densities for Piecewise Area Preserving Maps

We investigate the properties of absolutely continuous invariant probability measures (ACIPs), especially those measures with bounded variation densities, for piecewise area preserving maps (PAPs) on $\mathbb{R}^d$. This class of maps unifies piecewise isometries (PWIs) and piecewise hyperbolic maps where Lebesgue measure is locally preserved. Using a functional analytic approach, we first explore the relationship between topological transitivity and uniqueness of ACIPs, and then give an approach to construct invariant measures with bounded variation densities for PWIs. Our results "partially" answer one of the fundamental questions posed in \cite{Goetz03} - to determine all invariant non-atomic probability Borel measures in piecewise rotations. When restricting PAPs to interval exchange transformations (IETs), our results imply that for non-uniquely ergodic IETs with two or more ACIPs, these ACIPs have very irregular densities, i.e., they have unbounded variation.

math.DS↗

arXiv2011

Bidirectional transport and pulsing states in a multi-lane ASEP model

In this paper, we introduce an ASEP-like transport model for bidirectional motion of particles on a multi-lane lattice. The model is motivated by {\em in vivo} experiments on organelle motility along a microtubule (MT), consisting of thirteen protofilaments, where particles are propelled by molecular motors (dynein and kinesin). In the model, organelles (particles) can switch directions of motion due to "tug-of-war" events between counteracting motors. Collisions of particles on the same lane can be cleared by switching to adjacent protofilaments (lane changes). We analyze transport properties of the model with no-flux boundary conditions at one end of a MT ("plus-end" or tip). We show that the ability of lane changes can affect the transport efficiency and the particle-direction change rate obtained from experiments is close to optimal in order to achieve efficient motor and organelle transport in a living cell. In particular, we find a nonlinear scaling of the mean {\em tip size} (the number of particles accumulated at the tip) with injection rate and an associated phase transition leading to {\em pulsing states} characterized by periodic filling and emptying of the system.

nlin.CG↗