Негейзенберговский ферримагентик с одноионной анизотропией

We have investigated the effect of single-ion anisotropy of the "easy plane" type on the phase states of a ferrimagnet with S = 1 and σ=1/2 sublattices and non-Heisenberg (bilinear and biquadratic in spins) exchange interaction for the sublattice with S = 1. It is shown that taking into account both the non-Heisenberg exchange interaction and the single-ion anisotropy of the sublattice with S = 1 leads to the realization of a phase with vector order parameters (ferrimagnetic phase) and a phase characterized by both vector and tensor order parameters (quadrupole-ferrimagnetic). It is shown that taking into account single-ion anisotropy changes the type of phase transition in comparison with an isotropic non-Heisenberg ferrimagnet. A phase diagram is constructed, and the condition for the compensation of the sublattice spins is determined.

Curvature Potential Unveiled Topological Defect Attractors

We consider the theoretical and positional assembling of topological defects (TDs) in effectively two-dimensional nematic liquid crystal films. We use a phenomenological Helfrich–Landau–de Gennes-type mesoscopic model in which geometric shapes and nematic orientational order are expressed in terms of a curvature tensor field and a nematic tensor order parameter field. Extrinsic, intrinsic, and total curvature potentials are introduced using the parallel transport concept. These potentials reveal curvature seeded TD attractors. To test ground configurations, we used axially symmetric nematic films exhibiting spherical topology.

Higher order analysis of gene correlations by tensor decomposition

This study advances our understanding of inter- and intra-pathways higher order signaling in the cellular system and it leads to new discovery of multiple intracellular structures in signal transduction pathways in yeast Saccharomyces. We present a new tensor decomposition algorithm in reconstructing the pathways based on higher correlations among genes that compose a cellular system. The higher order gene correlation (HOGC) analysis has the power to elucidate gene’s higher interaction dependencies which has been barely understood. Recent studies i.e. [24] have experimentally revealed that multiple signaling proteins, yet sometimes infinite, may assemble to meaningful structure to transmit a receptor activation information. In this paper we reveal 3-order genomic correlations among significant component of the cellular system. This is the first time such a systematic and computational model provided for analysis of higher order correlations among genes. We use new fast algorithm to formulate a genes × genes × genes × decorrelated rank-1 sub-tensors (complexes) which can be associated with functionally independent pathways. Then we model higher order tensor decomposition which is constructed by K tensors of genes × genes × genes. Each new tensor is constructed by an orthogonal projection of data signal onto a designated basis signal to keep common sub-tensors in both signals. Our model for decomposing tensor order-4 approximates series of tensors as linear components of deccorelated rank-1 sub-tensors over tensor of order-3 and rank-3 triplings among sub-tensors. The linear components represent intra-pathway in cell signaling and triplings implicate inter-pathways higher order signaling. Through structural studies of inter- and intra-higher order signaling pathways, we uncover different scenario that involves triple formation of signaling proteins into higher order signaling machines for transmission of receptor activation information to cellular responses.

Scalable Bayesian inference for high-dimensional neural receptive fields

We examine the problem of rapidly and efficiently estimating a neuron’s linear receptive field (RF) from responses to high-dimensional stimuli. This problem poses important statistical and computational challenges. Statistical challenges arise from the need for strong regularization when using correlated stimuli in high-dimensional parameter spaces, while computational challenges arise from extensive time and memory costs associated with evidence-optimization and inference in high-dimensional settings. Here we focus on novel methods for scaling up automatic smoothness determination (ASD), an empirical Bayesian method for RF estimation, to high-dimensional settings. First, we show that using a zero-padded Fourier domain representation and a “coarse-to-fine” evidence optimization strategy gives substantial improvements in speed and memory, while maintaining exact numerical accuracy. We then introduce a suite of scalable approximate methods that exploit Kronecker and Toeplitz structure in the stimulus autocovariance, which can be related to the method of expected log-likelihoods [1]. When applied together, these methods reduce the cost of estimating an RF with tensor order D and d coefficients per tensor dimension from O(d3D) time and O(d2D) space for standard ASD to O(Dd log d) time and O(Dd) space. We show that evidence optimization for a linear RF with 160K coefficients using 5K samples of data can be carried out on a laptop in < 2s.