A new mechanism of development and differentiation through slow binding/unbinding of regulatory proteins to the genes

Understanding the differentiation, a biological process from a multipotent stem or progenitor state to a mature cell is critically important. We develop a theoretical framework to quantify the underlying potential landscape and biological paths for cell development and differentiation. We propose a new mechanism of differentiation and development through binding/unbinding of regulatory proteins to the gene promoters. We found indeed the differentiated states can emerge from the slow promoter binding/unbinding processes. Furthermore, under slow promoter binding/unbinding, we found multiple meta-stable differentiated states. This can explain the origin of multiple states observed in the recent experiments. In addition, the kinetic time quantified by mean first passage transition time for the differentiation and reprogramming strongly depends on the time scale of the promoter binding/unbinding processes. We discovered an optimal speed for differentiation for certain binding/unbinding rates of regulatory proteins to promoters. More experiments in the future might be able to tell if cells differentiate at at that optimal speed. In addition, we quantify kinetic pathways for the differentiation and reprogramming. We found that they are irreversible. This captures the non-equilibrium dynamics in multipotent stem or progenitor cells. Such inherent time-asymmetry as a result of irreversibility of state transition pathways as shown may provide the origin of time arrow for cell development.Comment: 25 pages, 5 figure

An Ensemble EM Algorithm for Bayesian Variable Selection

We study the Bayesian approach to variable selection in the context of linear regression. Motivated by a recent work by Rockova and George (2014), we propose an EM algorithm that returns the MAP estimate of the set of relevant variables. Due to its particular updating scheme, our algorithm can be implemented efficiently without inverting a large matrix in each iteration and therefore can scale up with big data. We also show that the MAP estimate returned by our EM algorithm achieves variable selection consistency even when $p$ diverges with $n$. In practice, our algorithm could get stuck with local modes, a common problem with EM algorithms. To address this issue, we propose an ensemble EM algorithm, in which we repeatedly apply the EM algorithm on a subset of the samples with a subset of the covariates, and then aggregate the variable selection results across those bootstrap replicates. Empirical studies have demonstrated the superior performance of the ensemble EM algorithm

A Variational Algorithm for Bayesian Variable Selection

There has been an intense development on the estimation of a sparse regression coefficient vector in statistics, machine learning and related fields. In this paper, we focus on the Bayesian approach to this problem, where sparsity is incorporated by the so-called spike-and-slab prior on the coefficients. Instead of replying on MCMC for posterior inference, we propose a fast and scalable algorithm based on variational approximation to the posterior distribution. The updating scheme employed by our algorithm is different from the one proposed by Carbonetto and Stephens (2012). Those changes seem crucial for us to show that our algorithm can achieve asymptotic consistency even when the feature dimension diverges exponentially fast with the sample size. Empirical results have demonstrated the effectiveness and efficiency of the proposed algorithm

Multi-view Reconstructive Preserving Embedding for Dimension Reduction

With the development of feature extraction technique, one sample always can be represented by multiple features which locate in high-dimensional space. Multiple features can re ect various perspectives of one same sample, so there must be compatible and complementary information among the multiple views. Therefore, it's natural to integrate multiple features together to obtain better performance. However, most multi-view dimension reduction methods cannot handle multiple features from nonlinear space with high dimensions. To address this problem, we propose a novel multi-view dimension reduction method named Multi-view Reconstructive Preserving Embedding (MRPE) in this paper. MRPE reconstructs each sample by utilizing its k nearest neighbors. The similarities between each sample and its neighbors are primely mapped into lower-dimensional space in order to preserve the underlying neighborhood structure of the original manifold. MRPE fully exploits correlations between each sample and its neighbors from multiple views by linear reconstruction. Furthermore, MRPE constructs an optimization problem and derives an iterative procedure to obtain the low-dimensional embedding. Various evaluations based on the applications of document classification, face recognition and image retrieval demonstrate the effectiveness of our proposed approach on multi-view dimension reduction.Comment: 17 pages, 6 figure

Hysteresis from nonlinear dynamics of Majorana modes in topological Josephson junctions

We reveal that topological Josephson junctions provide a natural platform for the interplay between the Josephson effect and the Landau-Zener effect through a two-level system formed by coupled Majorana modes. We build a quantum resistively shunted junction (RSJ) model by modifying the standard textbook RSJ model to take account of the two-level system from the Majorana modes at the junction. We show that the dynamics of the two-level system is governed by a nonlinear Schr\"odinger equation and solve the equations analytically via a mapping to a classical dynamical problem. This nonlinear dynamics leads to hysteresis in the I-V characteristics, which can give a quantitative explanation to recent experiments. We also predict the coexistence of two interference patterns with periods $h/e$ and $h/2e$ in topological superconducting quantum interference devices.Comment: 17 pages, 11figure

High-precision evaluation of Wigner's d-matrix by exact diagonalization

The precise calculations of the Wigner's d-matrix are important in various research fields. Due to the presence of large numbers, direct calculations of the matrix using the Wigner's formula suffer from loss of precision. We present a simple method to avoid this problem by expanding the d-matrix into a complex Fourier series and calculate the Fourier coefficients by exactly diagonalizing the angular-momentum operator $J_{y}$ in the eigenbasis of $J_{z}$. This method allows us to compute the d-matrix and its various derivatives for spins up to a few thousand. The precision of the d-matrix from our method is about $10^{-14}$ for spins up to $100$.Comment: 4 pages, 3 figures; a Fortran90 code is included; resubmitted to Phys. Rev.

All-optical transistor based on Rydberg atom-assisted opto-mechanical system

We study the optical response of double optomechanical cavity system assisted by Rydberg atomic ensembles. And atomic ensembles are only coupled with one side cavity by a single cavity mode. It has been realized that a long-range manipulation for optical properties of hybrid system, by controlling the Rydberg atomic ensembles decoupled with the optomechanical cavity. Switching on the coupling between atoms and cavity mode, the original time reversal symmetry of double cavity structure has been broken. Based on the controlled optical non-reciprocity, we put forward the theoretical schemes of all-optical controlled diode, rectifier and transistor

Opposite Changes in Gap Width of Opposite Spin States Induced by Rashba Effect in Anti-ferromagnetic Graphene on Ni(111)

Graphene is a promising candidate for applications in spintronics. In this paper, Density Functional Theory method is used to calculate the band structure and magnetic properties of graphene on Ni(111). Our results show that once there is antiferromagnetic order in graphene, an external electric field at the order of 10^9 V/m can induce a gap width difference of tens of meV for opposite spin states near the Fermi surface.Comment: 5 pages, 5 figure

Qualitative detection of oil adulteration with machine learning approaches

The study focused on the machine learning analysis approaches to identify the adulteration of 9 kinds of edible oil qualitatively and answered the following three questions: Is the oil sample adulterant? How does it constitute? What is the main ingredient of the adulteration oil? After extracting the high-performance liquid chromatography (HPLC) data on triglyceride from 370 oil samples, we applied the adaptive boosting with multi-class Hamming loss (AdaBoost.MH) to distinguish the oil adulteration in contrast with the support vector machine (SVM). Further, we regarded the adulterant oil and the pure oil samples as ones with multiple labels and with only one label, respectively. Then multi-label AdaBoost.MH and multi-label learning vector quantization (ML-LVQ) model were built to determine the ingredients and their relative ratio in the adulteration oil. The experimental results on six measures show that ML-LVQ achieves better performance than multi-label AdaBoost.MH.Comment: 18 pages, 4 figures, 5 table

Finite-volume formalism in the 2→HI+HI22 \xrightarrow[]{H_I+H_I} 2 transition: an application to the lattice QCD calculation of double beta decays

We present the formalism for connecting a second-order electroweak $2\xrightarrow[]{H_I+H_I}2$ transition amplitudes in the finite volume (with two hadrons in the initial and final states) to the physical amplitudes in the infinite volume. Our study mainly focus on the case where the low-lying intermediate state consists of two scattering hadrons. As a side product we also reproduce the finite-volume formula for $2\xrightarrow[]{H_I}2$ transition, originally obtained by Brice\~no and Hansen. With the available finite-volume formalism, we further discuss how to treat with the finite-volume problem in the double beta decays $nn\to pp ee\bar{\nu}\bar{\nu}$ and $nn\to pp ee$.Comment: 18 page