SU(4) Theory for Spin Systems with Orbital Degeneracy

The isotropic limit of spin systems with orbital degeneracy is shown to have global SU(4) symmetry. On many 2D lattices, the ground state does not posses long range order, which may explain the observed spin liquid properties of $LiNiO_2$. In the SU(4) Neel ordered state, spin-spin correlations can be antiferromagneitc between two neighboring sites with parallel magnetic moments.Comment: 11 pages, 2 figures. submitted to PR

Emergent L\'evy behavior in single-cell stochastic gene expression

Single-cell gene expression is inherently stochastic; its emergent behavior can be defined in terms of the chemical master equation describing the evolution of the mRNA and protein copy numbers as the latter tends to infinity. We establish two types of "macroscopic limits": the Kurtz limit is consistent with the classical chemical kinetics, while the L\'{e}vy limit provides a theoretical foundation for an empirical equation proposed in [Phys. Rev. Lett. 97:168302, 2006]. Furthermore, we clarify the biochemical implications and ranges of applicability for various macroscopic limits and calculate a comprehensive analytic expression for the protein concentration distribution in autoregulatory gene networks. The relationship between our work and modern population genetics is discussed.Comment: 10 pages, 2 figure

Relaxation rates of gene expression kinetics reveal the feedback signs of autoregulatory gene networks

The transient response to a stimulus and subsequent recovery to a steady state are the fundamental characteristics of a living organism. Here we study the relaxation kinetics of autoregulatory gene networks based on the chemical master equation model of single-cell stochastic gene expression with nonlinear feedback regulation. We report a novel relation between the rate of relaxation, characterized by the spectral gap of the Markov model, and the feedback sign of the underlying gene circuit. When a network has no feedback, the relaxation rate is exactly the decaying rate of the protein. We further show that positive feedback always slows down the relaxation kinetics while negative feedback always speeds it up. Numerical simulations demonstrate that this relation provides a possible method to infer the feedback topology of autoregulatory gene networks by using time-series data of gene expression.Comment: 17 page

Predictive protocol of flocks with small-world connection pattern

By introducing a predictive mechanism with small-world connections, we propose a new motion protocol for self-driven flocks. The small-world connections are implemented by randomly adding long-range interactions from the leader to a few distant agents, namely pseudo-leaders. The leader can directly affect the pseudo-leaders, thereby influencing all the other agents through them efficiently. Moreover, these pseudo-leaders are able to predict the leader's motion several steps ahead and use this information in decision making towards coherent flocking with more stable formation. It is shown that drastic improvement can be achieved in terms of both the consensus performance and the communication cost. From the industrial engineering point of view, the current protocol allows for a significant improvement in the cohesion and rigidity of the formation at a fairly low cost of adding a few long-range links embedded with predictive capabilities. Significantly, this work uncovers an important feature of flocks that predictive capability and long-range links can compensate for the insufficiency of each other. These conclusions are valid for both the attractive/repulsive swarm model and the Vicsek model.Comment: 10 pages, 12 figure

Semantic Memory Activation in Individuals at Risk for Developing Alzheimer Disease

Objective: To determine whether whole-brain, event-related fMRI can distinguish healthy older adults with known Alzheimer disease (AD) risk factors (family history, APOE ε4) from controls using a semantic memory task involving discrimination of famous from unfamiliar names. Methods: Sixty-nine cognitively asymptomatic adults were divided into 3 groups (n = 23 each) based on AD risk: 1) no family history, no ε4 allele (control [CON]); 2) family history, no ε4 allele (FH); and 3) family history and ε4 allele (FH+ε4). Separate hemodynamic response functions were extracted for famous and unfamiliar names using deconvolution analysis (correct trials only). Results: Cognitively intact older adults with AD risk factors (FH and FH+ε4) exhibited greater activation in recognizing famous relative to unfamiliar names than a group without risk factors (CON), especially in the bilateral posterior cingulate/precuneus, bilateral temporoparietal junction, and bilateral prefrontal cortex. The increased activation was more apparent in the FH+ε4 than in the FH group. Unlike the 2 at-risk groups, the control group demonstrated greater activation for unfamiliar than familiar names, predominately in the supplementary motor area, bilateral precentral, left inferior frontal, right insula, precuneus, and angular gyrus. These results could not be attributed to differences in demographic variables, cerebral atrophy, episodic memory performance, global cognitive functioning, activities of daily living, or depression. Conclusions: Results demonstrate that a low-effort, high-accuracy semantic memory activation task is sensitive to Alzheimer disease risk factors in a dose-related manner. This increased activation in at-risk individuals may reflect a compensatory brain response to support task performance in otherwise asymptomatic older adults