Lee-Yang zeros and phase transitions in nonequilibrium steady states

We consider how the Lee-Yang description of phase transitions in terms of partition function zeros applies to nonequilibrium systems. Here one does not have a partition function, instead we consider the zeros of a steady-state normalization factor in the complex plane of the transition rates. We obtain the exact distribution of zeros in the thermodynamic limit for a specific model, the boundary-driven asymmetric simple exclusion process. We show that the distributions of zeros at the first and second order nonequilibrium phase transitions of this model follow the patterns known in the Lee-Yang equilibrium theory.Comment: 4 pages RevTeX4 with 4 figures; revised version to appear in Phys. Rev. Let

Yang-Lee zeros for a nonequilibrium phase transition

Equilibrium systems which exhibit a phase transition can be studied by investigating the complex zeros of the partition function. This method, pioneered by Yang and Lee, has been widely used in equilibrium statistical physics. We show that an analogous treatment is possible for a nonequilibrium phase transition into an absorbing state. By investigating the complex zeros of the survival probability of directed percolation processes we demonstrate that the zeros provide information about universal properties. Moreover we identify certain non-trivial points where the survival probability for bond percolation can be computed exactly.Comment: LaTeX, IOP-style, 13 pages, 10 eps figure

Spreading with immunization in high dimensions

We investigate a model of epidemic spreading with partial immunization which is controlled by two probabilities, namely, for first infections, $p_0$, and reinfections, $p$. When the two probabilities are equal, the model reduces to directed percolation, while for perfect immunization one obtains the general epidemic process belonging to the universality class of dynamical percolation. We focus on the critical behavior in the vicinity of the directed percolation point, especially in high dimensions $d>2$. It is argued that the clusters of immune sites are compact for $d\leq 4$. This observation implies that a recently introduced scaling argument, suggesting a stretched exponential decay of the survival probability for $p=p_c$, $p_0\ll p_c$ in one spatial dimension, where $p_c$ denotes the critical threshold for directed percolation, should apply in any dimension $d \leq 3$ and maybe for $d=4$ as well. Moreover, we show that the phase transition line, connecting the critical points of directed percolation and of dynamical percolation, terminates in the critical point of directed percolation with vanishing slope for $d<4$ and with finite slope for $d\geq 4$. Furthermore, an exponent is identified for the temporal correlation length for the case of $p=p_c$ and $p_0=p_c-\epsilon$, $\epsilon\ll 1$, which is different from the exponent $\nu_\parallel$ of directed percolation. We also improve numerical estimates of several critical parameters and exponents, especially for dynamical percolation in $d=4,5$.Comment: LaTeX, IOP-style, 18 pages, 9 eps figures, minor changes, additional reference

Genetic background influences the 5XFAD Alzheimer\u27s disease mouse model brain proteome.

There is an urgent need to improve the translational validity of Alzheimer’s disease (AD) mouse models. Introducing genetic background diversity in AD mouse models has been proposed as a way to increase validity and enable the discovery of previously uncharacterized genetic contributions to AD susceptibility or resilience. However, the extent to which genetic background influences the mouse brain proteome and its perturbation in AD mouse models is unknown. In this study, we crossed the 5XFAD AD mouse model on a C57BL/6J (B6) inbred background with the DBA/2J (D2) inbred background and analyzed the effects of genetic background variation on the brain proteome in F1 progeny. Both genetic background and 5XFAD transgene insertion strongly affected protein variance in the hippocampus and cortex (n = 3,368 proteins). Protein co-expression network analysis identified 16 modules of highly co-expressed proteins common across the hippocampus and cortex in 5XFAD and non- transgenic mice. Among the modules strongly influenced by genetic background were those related to small molecule metabolism and ion transport. Modules strongly influenced by the 5XFAD transgene were related to lysosome/stress responses and neuronal synapse/signaling. The modules with the strongest relationship to human disease—neuronal synapse/signaling and lysosome/stress response—were not significantly influenced by genetic background. However, other modules in 5XFAD that were related to human disease, such as GABA synaptic signaling and mitochondrial membrane modules, were influenced by genetic background. Most disease-related modules were more strongly correlated with AD genotype in the hippocampus compared with the cortex. Our findings suggest that the genetic diversity introduced by crossing B6 and D2 inbred backgrounds influences proteomic changes related to disease in the 5XFAD model, and that proteomic analysis of other genetic backgrounds in transgenic and knock-in AD mouse models is warranted to capture the full range of molecular heterogeneity in genetically diverse models of AD