A Hypergraph Approach for Estimating Growth Mechanisms of Complex Networks

Temporal datasets that describe complex interactions between individuals over time are increasingly common in various domains. Conventional graph representations of such datasets may lead to information loss since higher-order relationships between more than two individuals must be broken into multiple pairwise relationships in graph representations. In those cases, a hypergraph representation is preferable since it can preserve higher-order relationships by using hyperedges. However, existing hypergraph models of temporal complex networks often employ some data-independent growth mechanism, which is the linear preferential attachment in most cases. In principle, this pre-specification is undesirable since it completely ignores the data at hand. Our work proposes a new hypergraph growth model with a data-driven preferential attachment mechanism estimated from observed data. A key component of our method is a recursive formula that allows us to overcome a bottleneck in computing the normalizing factors in our model. We also treat an often-neglected selection bias in modeling the emergence of new edges with new nodes. Fitting the proposed hypergraph model to 13 real-world datasets from diverse domains, we found that all estimated preferential attachment functions deviates substantially from the linear form. This demonstrates the need of doing away with the linear preferential attachment assumption and adopting a data-driven approach. We also showed that our model outperformed conventional models in replicating the observed first-order and second-order structures in these real-world datasets

An extension of the entropic chaos degree and its positive effect

The Lyapunov exponent is used to quantify the chaos of a dynamical system, by characterizing the exponential sensitivity of an initial point on the dynamical system. However, we cannot directly compute the Lyapunov exponent for a dynamical system without its dynamical equation, although some estimation methods do exist. Information dynamics introduces the entropic chaos degree to measure the strength of chaos of the dynamical system. The entropic chaos degree can be used to compute the strength of chaos with a practical time series. It may seem like a kind of fnite space Kolmogorov-Sinai entropy, which then indicates the relation between the entropic chaos degree and the Lyapunov exponent. In this paper, we attempt to extend the defnition of the entropic chaos degree on a d-dimensional Euclidean space to improve the ability to measure the stength of chaos of the dynamical system and show several relations between the extended entropic chaos degree and the Lyapunov exponen

Behavioral phenotypes of mice lacking purinergic P2X4 receptors in acute and chronic pain assays

A growing body of evidence indicates that P2X receptors (P2XRs), a family of ligand-gated cation channels activated by extracellular ATP, play an important role in pain signaling. In contrast to the role of the P2X3R subtype that has been extensively studied, the precise roles of others among the seven P2XR subtypes (P2X1R-P2X7R) remain to be determined because of a lack of sufficiently powerful tools to specifically block P2XR signaling in vivo. In the present study, we investigated the behavioral phenotypes of a line of mice in which the p2rx4 gene was disrupted in a series of acute and chronic pain assays. While p2rx4-/- mice showed no major defects in pain responses evoked by acute noxious stimuli and local tissue damage or in motor function as compared with wild-type mice, these mice displayed reduced pain responses in two models of chronic pain (inflammatory and neuropathic pain). In a model of chronic inflammatory pain developed by intraplantar injection of complete Freund's adjuvant (CFA), p2rx4-/- mice exhibited attenuations of pain hypersensitivity to innocuous mechanical stimuli (tactile allodynia) and also of the CFA-induced swelling of the hindpaw. A most striking phenotype was observed in a test of neuropathic pain: tactile allodynia caused by an injury to spinal nerve was markedly blunted in p2rx4-/- mice. By contrast, pain hypersensitivity to a cold stimulus (cold allodynia) after the injury was comparable in wild-type and p2rx4-/- mice. Together, these findings reveal a predominant contribution of P2X4R to nerve injury-induced tactile allodynia and, to the lesser extent, peripheral inflammation. Loss of P2X4R produced no defects in acute physiological pain or tissue damaged-induced pain, highlighting the possibility of a therapeutic benefit of blocking P2X4R in the treatment of chronic pain, especially tactile allodynia after nerve injury

Antidepressants Inhibit P2X4 Receptor Function: a Possible Involvement in Neuropathic Pain Relief

BACKGROUND: Neuropathic pain is characterized by pain hypersensitivity to innocuous stimuli (tactile allodynia) that is nearly always resistant to known treatments such as non-steroidal anti-inflammatory drugs or even opioids. It has been reported that some antidepressants are effective for treating neuropathic pain. However, the underlying molecular mechanisms are not well understood. We have recently demonstrated that blocking P2X(4 )receptors in the spinal cord reverses tactile allodynia after peripheral nerve injury in rats, implying that P2X(4 )receptors are a key molecule in neuropathic pain. We investigated a possible role of antidepressants as inhibitors of P2X(4 )receptors and analysed their analgesic mechanism using an animal model of neuropathic pain. RESULTS: Antidepressants strongly inhibited ATP-mediated Ca(2+ )responses in P2X(4 )receptor-expressing 1321N1 cells, which are known to have no endogenous ATP receptors. Paroxetine exhibited the most powerful inhibition of calcium influx via rat and human P2X(4 )receptors, with IC(50 )values of 2.45 μM and 1.87 μM, respectively. Intrathecal administration of paroxetine produced a striking antiallodynic effect in an animal model of neuropathic pain. Co-administration of WAY100635, ketanserin or ondansetron with paroxetine induced no significant change in the antiallodynic effect of paroxetine. Furthermore, the antiallodynic effect of paroxetine was observed even in rats that had received intrathecal pretreatment with 5,7-dihydroxytryptamine, which dramatically depletes spinal 5-hydroxytryptamine. CONCLUSION: These results suggest that paroxetine acts as a potent analgesic in the spinal cord via a mechanism independent of its inhibitory effect on serotonin transporters. Powerful inhibition on P2X(4 )receptors may underlie the analgesic effect of paroxetine, and it is possible that some antidepressants clinically used in patients with neuropathic pain show antiallodynic effects, at least in part via their inhibitory effects on P2X(4 )receptors

Convergence of simulated annealing by the generalized transition probability

We prove weak ergodicity of the inhomogeneous Markov process generated by the generalized transition probability of Tsallis and Stariolo under power-law decay of the temperature. We thus have a mathematical foundation to conjecture convergence of simulated annealing processes with the generalized transition probability to the minimum of the cost function. An explicitly solvable example in one dimension is analyzed in which the generalized transition probability leads to a fast convergence of the cost function to the optimal value. We also investigate how far our arguments depend upon the specific form of the generalized transition probability proposed by Tsallis and Stariolo. It is shown that a few requirements on analyticity of the transition probability are sufficient to assure fast convergence in the case of the solvable model in one dimension.Comment: 11 page

On-Line AdaTron Learning of Unlearnable Rules

We study the on-line AdaTron learning of linearly non-separable rules by a simple perceptron. Training examples are provided by a perceptron with a non-monotonic transfer function which reduces to the usual monotonic relation in a certain limit. We find that, although the on-line AdaTron learning is a powerful algorithm for the learnable rule, it does not give the best possible generalization error for unlearnable problems. Optimization of the learning rate is shown to greatly improve the performance of the AdaTron algorithm, leading to the best possible generalization error for a wide range of the parameter which controls the shape of the transfer function.)Comment: RevTeX 17 pages, 8 figures, to appear in Phys.Rev.