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Linear mapping is widely used in dynamic modeling and empirical data analysis, but it suffers from the serious shortcoming that it does not work in the common case of time intervals being large. The fundamental cause of the failure is that the linear mapping does not take into account the coupling effects of multiple events within a discrete time interval. Here, we develop a theoretical framework to provide a nonlinear mapping between continuous- and discrete-time dynamics by accounting for the coupling effect. We have verified the effectiveness of our mapping by exploring classical susceptible-infected-susceptible and susceptible-infected-recovered models. In particular, we give a quantitative criterion that the sum of two transition probabilities â€"from one state to the other and vice versaâ€" must be strictly less than 1 for binary-state dynamics. [ABSTRACT FROM AUTHOR]

Summary: Aims: The G‐protein‐coupled estrogen receptor GPR30 (also referred to as GPER) has been implicated in the estrogenic regulation of hippocampal plasticity and spatial memory; however, the molecular mechanisms are largely unclear. Methods: In this study, we initially examined the levels of GPR30 in the hippocampus of postnatal, ovariectomy (OVX)‐ and letrozole (LET)‐treated female mice. Under G1, G15, and/or OVX treatment, the spatial memory, spine density, levels of ERα, ERβ, and SRC‐1, selected synaptic proteins, mTORC2 signals (Rictor and p‐AKT Ser473), and actin polymerization dynamics were subsequently evaluated. Furthermore, G1, G15, and/or E2 combined with SRC‐1 and/or PI3K inhibitors, actin cytoskeleton polymerization modulator JPK, and CytoD treatments were used to address the mechanisms that underlie GPR30 regulation in vitro. Finally, mTORC2 activator A‐443654 (A4) was used to explore the role of mTORC2 in GPR30 regulation of spatial memory. Results: The results showed that high levels of GPR30 were detected in the adult hippocampus and the levels were downregulated by OVX and LET. OVX induced an impairment of spatial memory, and changes in other parameters previously described were reversed by G1 and mimicked by G15. Furthermore, the E2 effects on SRC‐1 and mTORC2 signals, synaptic proteins, and actin polymerization were inhibited by G15, whereas G1 effects on these parameters were inhibited by the blockade of SRC‐1 or PI3K; the levels of synaptic proteins were regulated by JPK and CytoD. Importantly, G15‐induced actin depolymerization and spatial memory impairment were rescued by mTORC2 activation with A4. Conclusions: Taking together, these results demonstrated that decreased GPR30 induces actin depolymerization through SRC‐1 and PI3K/mTORC2 pathways and ultimately impairs learning and memory, indicating its potential role as a therapeutic target against hippocampus‐based, E2‐related memory impairments. [ABSTRACT FROM AUTHOR]

Summary: Aims: Estrogens play pivotal roles in hippocampal synaptic plasticity through nuclear receptors (nERs; including ERα and ERβ) and the membrane receptor (mER; also called GPR30), but the underlying mechanism and the contributions of nERs and mER remain unclear. Mammalian target of rapamycin complex 2 (mTORC2) is involved in actin cytoskeleton polymerization and long‐term memory, but whether mTORC2 is involved in the regulation of hippocampal synaptic plasticity by ERs is unclear. Methods: We treated animals with nER antagonists (MPP/PHTPP) or the mER antagonist (G15) alone or in combination with A‐443654, an activator of mTORC2. Then, we examined the changes in hippocampal SRC‐1 expression, mTORC2 signaling (rictor and phospho‐AKTSer473), actin polymerization (phospho‐cofilin and profilin‐1), synaptic protein expression (GluR1, PSD95, spinophilin, and synaptophysin), CA1 spine density, and synapse density. Results: All of the examined parameters except synaptophysin expression were significantly decreased by MPP/PHTPP and G15 treatment. MPP/PHTPP and G15 induced a similar decrease in most parameters except p‐cofilin, GluR1, and spinophilin expression. The ER antagonist‐induced decreases in these parameters were significantly reversed by mTORC2 activation, except for the change in SRC‐1, rictor, and synaptophysin expression. Conclusions: nERs and mER contribute similarly to the changes in proteins and structures associated with synaptic plasticity, and mTORC2 may be a novel target of hippocampal‐dependent dementia such as Alzheimer's disease as proposed by previous studies. [ABSTRACT FROM AUTHOR]

Resource allocation takes place in various kinds of real-world complex systems, such as traffic systems, social services institutions or organizations, or even ecosystems. The fundamental principle underlying complex resource-allocation dynamics is Boolean interactions associated with minority games, as resources are generally limited and agents tend to choose the least used resource based on available information. A common but harmful dynamical behavior in resource-allocation systems is herding, where there are time intervals during which a large majority of the agents compete for a few resources, leaving many other resources unused. Accompanying the herd behavior is thus strong fluctuations with time in the number of resources being used. In this paper, we articulate and establish that an intuitive control strategy, namely pinning control, is effective at harnessing the herding dynamics. In particular, by fixing the choices of resources for a few agents while leaving the majority of the agents free, herding can be eliminated completely. Our investigation is systematic in that we consider random and targeted pinning and a variety of network topologies, and we carry out a comprehensive analysis in the framework of mean-field theory to understand the working of control. The basic philosophy is then that, when a few agents waive their freedom to choose resources by receiving sufficient incentives, the majority of the agents benefit in that they will make fair, efficient, and effective use of the available resources. Our work represents a basic and general framework to address the fundamental issue of fluctuations in complex dynamical systems with significant applications to social, economical, and political systems. [ABSTRACT FROM AUTHOR]

Previous studies have shown that estrogen receptor beta (ERbeta) is the predominant estrogen receptor in the hypothalamic paraventricular nucleus (PVN) of mouse, mediating estrogen regulation of the neuroendocrine activities of the PVN, but the exact roles that ERbeta plays in the PVN remain unclear. In this study, we used immunocytochemistry to investigate the expression of ERbeta in the maternal PVN of mice during pregnancy (pregnant days 8, 10, 12, 15 and 18), lactation (postpartum days 1, 4 and 8) as well as in the PVN of the females from postnatal days 1, 3, 5, 7, 9, 15, 30 and 70. We found out that ERbeta was predominantly localized in the magnocellular divisions of PVN. In the pregnant female brain, generally, the ERbeta was lower than that of the postnatal development, the lowest level was found at gestational days 10–12; then from gestational day 18 to postpartum day 1, it increased to higher levels, followed by a decrease from postpartum day 4. During the postnatal development, the highest level of ERbeta was found at early postnatal days (before postnatal day 15), thereafter, it decreased to a lower level. The above results indicate that circulating sex steroids may differentially regulate the expression of ERbeta in the PVN of mice. It also suggests that this receptor may play important roles in the regulation of parturition and in the development, food intake and body weight increases of the newborns by acting on the neuropeptides, which were also detected in the PVN. [Copyright &y& Elsevier]

Studies have shown that estrogen plays important roles in regulating neural structure and function in the brain, but the mechanism remains unclear. The actions of estrogen were thought to be mediated by a single estrogen receptor until the identification of another estrogen receptor, namely estrogen receptor-β (ER-β). Here we report a comprehensive study of the localization of ER-β immunoreactivity and differences in the brains of adult male and female rats on the basis of a nickel ammonium sulfate-enhanced immunocytochemical method using a polyclonal antiserum sc-8974. The results of these studies revealed: (1) ER-β immunoactive material was mainly localized in the neuronal nucleus, but it was also detectable in the cytoplasm and neuronal processes; (2) in both male and female rats, high levels of ER-β immunopositive signals were detected in the anterior olfactory nucleus, cerebral cortex, Purkinje cells, vertical limb of the diagonal band, red nucleus, locus ceruleus, and motor trigeminal nucleus. Moderate levels were found in the medial septum, lateral amygdaloid nucleus, substantia nigra, and central gray. Weak signals were localized in other subregions of the hypothalamus and amygdaloid complex; (3) there was an obvious difference of ER-β immunoreactivity between male and female rats, and its intracellular distribution also showed a sex difference. The above results provide the first detailed evidence that ER-β protein is widely distributed in both male and female rat brains, but that distinctive sex differences also exist. Estrogen may exert its function in different brain regions in a gender-specific manner. [Copyright &y& Elsevier]

Grain refinement of beryllium deposits is studied as a significant subject for beryllium capsule in the Inertial Confinement Fusion project. The Be films were prepared on the Si (1 0 0) substrates by thermal evaporation with and without a magnetic field, respectively. The two separate groups of prepared Be films were characterized. The results showed the grain diameter in the Be film transited from 300 nm to 18 nm and the surface roughness of the Be film decreased from 61 nm to 3 nm by application of the magnetic field during the deposition process of Be coating. However, the Be film grown with the magnetic field was easily oxidized in comparison with that grown without magnetic field due to the refined grains, and the oxidation was gradually decreased with the increase of etching depth in the Be film. The reason for grain refinement of Be film was also qualitatively described. [ABSTRACT FROM AUTHOR]

The phase transition of epidemic spreading model on networks is one of the most important concerns of physicists to theoretical epidemiology. In this paper, we present an analytical expression of epidemic threshold for interplay between epidemic spreading and human behavior on multiplex networks. The threshold formula proposed in this paper reveals the relation between the threshold on single-layer networks and that on multiplex networks, which means that the theoretical conclusions of single-layer networks can be used to improve the threshold accuracy of multiplex networks. To verify how well our formula works in different networks, we build a network model with constant total number of edges but gradually changing the heterogeneity of the network, from scale-free network to Erdős-Rényi random network. By use of theoretical analysis and computer simulations, we find that the heterogeneity of information layer behaves as a "double-edged sword" on the epidemic threshold: The strong heterogeneity can effectively improve the epidemic threshold (which means the disease outbreak requires a higher infection probability) when the awareness probability α is low, while the opposite effect takes place for high α. Meanwhile, the weak heterogeneity of the information layer is effective in suppressing the epidemic prevalence when the awareness probability is neither too high nor too low.

We investigate the occurrence of synchronous population activities in a neuronal network composed of both excitatory and inhibitory neurons and equipped with short-term synaptic plasticity. The collective firing patterns with different macroscopic properties emerge visually with the change of system parameters, and most long-time collective evolution also shows periodic-like characteristics. We systematically discuss the pattern-formation dynamics on a microscopic level and find a lot of hidden features of the population activities. The bursty phase with power-law distributed avalanches is observed in which the population activity can be either entire or local periodic-like. In the purely spike-to-spike synchronous regime, the periodic-like phase emerges from the synchronous chaos after the backward period-doubling transition. The local periodic-like population activity and the synchronous chaotic activity show substantial trial-to-trial variability, which is unfavorable for neural code, while they are contrary to the stable periodic-like phases. We also show that the inhibitory neurons can promote the generation of cluster firing behavior and strong bursty collective firing activity by depressing the activities of postsynaptic neurons partially or wholly.

Collective behaviors by self-organization are ubiquitous in nature and human society and extensive efforts have been made to explore the mechanisms behind them. Artificial intelligence (AI) as a rapidly developing field is of great potential for these tasks. By combining reinforcement learning with evolutionary game (RLEG), we numerically discover a rich spectrum of collective behaviors-explosive events, oscillation, and stable states, etc., that are also often observed in the human society. In this work, we aim to provide a theoretical framework to investigate the RLEGs systematically. Specifically, we formalize AI-agents' learning processes in terms of belief switches and behavior modes defined as a series of actions following beliefs. Based on the preliminary results in the time-independent environment, we investigate the stability at the mixed equilibrium points in RLEGs generally, in which agents reside in one of the optimal behavior modes. Moreover, we adopt the maximum entropy principle to infer the composition of agents residing in each mode at a strictly stable point. When the theoretical analysis is applied to the 2×2 game setting, we can explain the uncovered collective behaviors and are able to construct equivalent systems intuitively. Also, the inferred composition of different modes is consistent with simulations. Our work may be helpful to understand the related collective emergence in human society as well as behavioral patterns at the individual level and potentially facilitate human-computer interactions in the future.

Complex systems arising in a modern society typically have many resources and strategies available for their dynamical evolutions. To explore quantitatively the behaviors of such systems, we propose a class of models to investigate Minority Game (MG) dynamics with multiple strategies. In particular, agents tend to choose the least used strategies based on available local information. A striking finding is the emergence of grouping states defined in terms of distinct strategies. We develop an analytic theory based on the mean-field framework to understand the "bifurcations" of the grouping states. The grouping phenomenon has also been identified in the Shanghai Stock-Market system, and we discuss its prevalence in other real-world systems. Our work demonstrates that complex systems obeying the MG rules can spontaneously self-organize themselves into certain divided states, and our model represents a basic and general mathematical framework to address this kind of phenomena in social, economical and political systems.

The localization of the new estrogen receptor, ER-beta, in the rat brain was studied by immunocytochemical technique, and the results revealed that ER-beta immunoactive material was predominantly localized in the neuronal nucleus, but it was also detectable in the cytoplasm and neuronal processes. High levels of ER-beta immunopositive signals were detected in the cerebral cortex, vertical limb of the diagonal band, Purkinje cells, locus ceruleus, and motor trigeminal nucleus. Moderate levels were found in the medial septum, lateral amygdaloid nucleus, substantia nigra, and central gray. Weak signals were localized in some subregions of the hypothalamus and amygdaloid complex. Some differences of the expression of ER-beta immunoreactivity between male and female rats were also noticed. The above results provide the first detailed evidence that ER-beta protein is widely distributed in the rat brain, and ER-beta may be involved in some important brain function such as learning and memory.