Comment on ''Properties of highly clustered networks"

We consider a procedure for generating clustered networks previously reported by Newman [Phys. Rev. E 68, 026121 (2003)]. In the same study, clustered networks generated according to the proposed model have been reported to have a lower epidemic threshold under susceptible-infective-recovered-type network epidemic dynamics. By rewiring networks generated by this model, such that the degree distribution is conserved, we show that the lower epidemic threshold can be closely reproduced by rewired networks with close to zero clustering. The reported lower epidemic threshold can be explained by different degree distributions observed in the networks corresponding to different levels of clustering. Clustering results in networks with high levels of heterogeneity in node degree, a higher proportion of nodes with zero connectivity, and links concentrated within highly interconnected components of small size. Hence, networks generated by this model differ in both clustering and degree distribution, and the lower epidemic threshold is not explained by clustering alone

Network Symmetry and Binocular Rivalry Experiments

Hugh Wilson has proposed a class of models that treat higher-level decision making as a competition between patterns coded as levels of a set of attributes in an appropriately defined network (Cortical Mechanisms of Vision, pp. 399–417, 2009; The Constitution of Visual Consciousness: Lessons from Binocular Rivalry, pp. 281–304, 2013). In this paper, we propose that symmetry-breaking Hopf bifurcation from fusion states in suitably modified Wilson networks, which we call rivalry networks, can be used in an algorithmic way to explain the surprising percepts that have been observed in a number of binocular rivalry experiments. These rivalry networks modify and extend Wilson networks by permitting different kinds of attributes and different types of coupling. We apply this algorithm to psychophysics experiments discussed by Kovács et al. (Proc. Natl. Acad. Sci. USA 93:15508–15511, 1996), Shevell and Hong (Vis. Neurosci. 23:561–566, 2006; Vis. Neurosci. 25:355–360, 2008), and Suzuki and Grabowecky (Neuron 36:143–157, 2002). We also analyze an experiment with four colored dots (a simplified version of a 24-dot experiment performed by Kovács), and a three-dot analog of the four-dot experiment. Our algorithm predicts surprising differences between the three- and four-dot experiments

Modeling and Analysis of Electrical Network Activity in Neuronal Systems.

Electrical activity in networks of neurons is an essential part of most brain functions. This dissertation deals with two different aspects in modeling and analysis of such activity in neuronal systems. Part I develops the first detailed mathematical model of the electrophysiology of the specific neuronal network responsible for the generation of circadian (~24-hour) rhythms in mammals. Part II is concerned with methods for inferring the functional connectivity of neuronal networks from multi-neuronal spike train data. Mammalian circadian rhythms are controlled by a group of about 20,000 neurons in the hypothalamus called the suprachiasmatic nucleus (SCN). We have developed a model of action potential firing in the SCN network. With this model we can simulate and track the action potentials of thousands of model SCN neurons, while experimentally it is only possible to record the activity of a few dozen SCN neurons at the same time. Our simulations predict that subgroups, or clusters, of SCN neurons form, within which neurons synchronize their firing at a millisecond time scale. Furthermore, our simulations demonstrate how this clustering leads to the silencing or adjustment of neurons whose firing is out of phase with the rest of the population at the 24-hour time scale, giving insight into how the circadian clock may operate at the network level. Temporal patterns of firing that are more complex than synchrony, such as precise firing sequences with fixed time delays between neurons, have been observed in multi-neuronal recordings from other brain areas. To determine whether the patterns detected are meaningful, it is important to know whether they are occurring more or less often than would be expected due to chance alone. To address this question, we have developed statistical methods for assessing when the number of occurrences of a precise firing sequence is significantly different from randomness and for estimating the magnitude of the connection strength. Our approach is computationally efficient and can discover patterns involving many neurons. The significant patterns discovered in multi-neuronal spike trains can be used to infer the functional connectivity between neurons and potentially identify circuits in the underlying neural tissue.Ph.D.Industrial and Operations Engineering and BioinformaticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/78984/1/diekman_1.pd

Minimizers with discontinuous velocities for the electromagnetic variational method

The electromagnetic two-body problem has \emph{neutral differential delay} equations of motion that, for generic boundary data, can have solutions with \emph{discontinuous} derivatives. If one wants to use these neutral differential delay equations with \emph{arbitrary} boundary data, solutions with discontinuous derivatives must be expected and allowed. Surprisingly, Wheeler-Feynman electrodynamics has a boundary value variational method for which minimizer trajectories with discontinuous derivatives are also expected, as we show here. The variational method defines continuous trajectories with piecewise defined velocities and accelerations, and electromagnetic fields defined \emph{by} the Euler-Lagrange equations \emph{% on} trajectory points. Here we use the piecewise defined minimizers with the Li{\'{e}}nard-Wierchert formulas to define generalized electromagnetic fields almost everywhere (but on sets of points of zero measure where the advanced/retarded velocities and/or accelerations are discontinuous). Along with this generalization we formulate the \emph{generalized absorber hypothesis} that the far fields vanish asymptotically \emph{almost everywhere%} and show that localized orbits with far fields vanishing almost everywhere \emph{must} have discontinuous velocities on sewing chains of breaking points. We give the general solution for localized orbits with vanishing far fields by solving a (linear) neutral differential delay equation for these far fields. We discuss the physics of orbits with discontinuous derivatives stressing the differences to the variational methods of classical mechanics and the existence of a spinorial four-current associated with the generalized variational electrodynamics.Comment: corrected minor typo: piecewise differentiable on closed instead of open interval

Ageing and the pathogenesis of osteoarthritis

Ageing-associated changes that affect articular tissues promote the development of osteoarthritis (OA). Although ageing and OA are closely linked, they are independent processes. Several potential mechanisms by which ageing contributes to OA have been elucidated. This Review focuses on the contributions of the following factors: age-related inflammation (also referred to as 'inflammaging'); cellular senescence (including the senescence-associated secretory phenotype (SASP)); mitochondrial dysfunction and oxidative stress; dysfunction in energy metabolism due to reduced activity of 5'-AMP-activated protein kinase (AMPK), which is associated with reduced autophagy; and alterations in cell signalling due to age-related changes in the extracellular matrix. These various processes contribute to the development of OA by promoting a proinflammatory, catabolic state accompanied by increased susceptibility to cell death that together lead to increased joint tissue destruction and defective repair of damaged matrix. The majority of studies to date have focused on articular cartilage, and it will be important to determine whether similar mechanisms occur in other joint tissues. Improved understanding of ageing-related mechanisms that promote OA could lead to the discovery of new targets for therapies that aim to slow or stop the progression of this chronic and disabling condition

Modeling the Neuroprotective Role of Enhanced Astrocyte Mitochondrial Metabolism during Stroke

AbstractA mathematical model that integrates the dynamics of cell membrane potential, ion homeostasis, cell volume, mitochondrial ATP production, mitochondrial and endoplasmic reticulum Ca2+ handling, IP3 production, and GTP-binding protein-coupled receptor signaling was developed. Simulations with this model support recent experimental data showing a protective effect of stimulating an astrocytic GTP-binding protein-coupled receptor (P2Y1Rs) following cerebral ischemic stroke. The model was analyzed to better understand the mathematical behavior of the equations and to provide insights into the underlying biological data. This approach yielded explicit formulas determining how changes in IP3-mediated Ca2+ release, under varying conditions of oxygen and the energy substrate pyruvate, affected mitochondrial ATP production, and was utilized to predict rate-limiting variables in P2Y1R-enhanced astrocyte protection after cerebral ischemic stroke

Cells exhibiting strong p16INK4a promoter activation in vivo display features of senescence

The activation of cellular senescence throughout the lifespan promotes tumor suppression, whereas the persistence of senescent cells contributes to aspects of aging. This theory has been limited, however, by an inability to identify and isolate individual senescent cells within an intact organism. Toward that end, we generated a murine reporter strain by “knocking-in” a fluorochrome, tandem-dimer Tomato (tdTom), into exon 1α of the p16 INK4a locus. We used this allele (p16 tdTom ) for the enumeration, isolation, and characterization of individual p16 INK4a -expressing cells (tdTom + ). The half-life of the knocked-in transcript was shorter than that of the endogenous p16 INK4a mRNA, and therefore reporter expression better correlated with p16 INK4a promoter activation than p16 INK4a transcript abundance. The frequency of tdTom + cells increased with serial passage in cultured murine embryo fibroblasts from p16 tdTom/+ mice. In adult mice, tdTom + cells could be readily detected at low frequency in many tissues, and the frequency of these cells increased with aging. Using an in vivo model of peritoneal inflammation, we compared the phenotype of cells with or without activation of p16 INK4a and found that tdTom + macrophages exhibited some features of senescence, including reduced proliferation, senescence-associated β-galactosidase (SA-β-gal) activation, and increased mRNA expression of a subset of transcripts encoding factors involved in SA-secretory phenotype (SASP). These results indicate that cells harboring activation of the p16 INK4a promoter accumulate with aging and inflammation in vivo, and display characteristics of senescence

A Cellular Automata Model with Probability Infection and Spatial Dispersion

In this article, we have proposed an epidemic model by using probability cellular automata theory. The essential mathematical features are analyzed with the help of stability theory. We have given an alternative modelling approach for the spatiotemporal system which is more realistic and satisfactory from the practical point of view. A discrete and spatiotemporal approach are shown by using cellular automata theory. It is interesting to note that both size of the endemic equilibrium and density of the individual increase with the increasing of the neighborhood size and infection rate, but the infections decrease with the increasing of the recovery rate. The stability of the system around the positive interior equilibrium have been shown by using suitable Lyapunov function. Finally experimental data simulation for SARS disease in China and a brief discussion conclude the paper

Daily electrical activity in the master circadian clock of a diurnal mammal

From eLife via Jisc Publications RouterHistory: collection 2021, received 2021-03-08, accepted 2021-10-09, pub-electronic 2021-11-30Publication status: PublishedFunder: Biotechnology and Biological Sciences Research Council; FundRef: http://dx.doi.org/10.13039/501100000268; Grant(s): BB/P009182/1Funder: Biotechnology and Biological Sciences Research Council; FundRef: http://dx.doi.org/10.13039/501100000268; Grant(s): BB/S01764X/1Funder: Biotechnology and Biological Sciences Research Council; FundRef: http://dx.doi.org/10.13039/501100000268; Grant(s): BB/N014901/1Funder: Wellcome Trust; FundRef: http://dx.doi.org/10.13039/100004440; Grant(s): 210684/Z/18/ZFunder: National Science Foundation; FundRef: http://dx.doi.org/10.13039/100000001; Grant(s): DMS 155237Funder: Army Research Office; FundRef: http://dx.doi.org/10.13039/100000183; Grant(s): W911NF-16-1-0584Funder: US-UK Fulbright Commission; FundRef: http://dx.doi.org/10.13039/501100000592Funder: Engineering and Physical Sciences Research Council; FundRef: http://dx.doi.org/10.13039/501100000266; Grant(s): EP/N014391/1Circadian rhythms in mammals are orchestrated by a central clock within the suprachiasmatic nuclei (SCN). Our understanding of the electrophysiological basis of SCN activity comes overwhelmingly from a small number of nocturnal rodent species, and the extent to which these are retained in day-active animals remains unclear. Here, we recorded the spontaneous and evoked electrical activity of single SCN neurons in the diurnal rodent Rhabdomys pumilio, and developed cutting-edge data assimilation and mathematical modeling approaches to uncover the underlying ionic mechanisms. As in nocturnal rodents, R. pumilio SCN neurons were more excited during daytime hours. By contrast, the evoked activity of R. pumilio neurons included a prominent suppressive response that is not present in the SCN of nocturnal rodents. Our modeling revealed and subsequent experiments confirmed transient subthreshold A-type potassium channels as the primary determinant of this response, and suggest a key role for this ionic mechanism in optimizing SCN function to accommodate R. pumilio’s diurnal niche