General dd-position sets

The general $d$-position number ${\rm gp}_d(G)$ of a graph $G$ is the cardinality of a largest set $S$ for which no three distinct vertices from $S$ lie on a common geodesic of length at most $d$. This new graph parameter generalizes the well studied general position number. We first give some results concerning the monotonic behavior of ${\rm gp}_d(G)$ with respect to the suitable values of $d$. We show that the decision problem concerning finding ${\rm gp}_d(G)$ is NP-complete for any value of $d$. The value of ${\rm gp}_d(G)$ when $G$ is a path or a cycle is computed and a structural characterization of general $d$-position sets is shown. Moreover, we present some relationships with other topics including strong resolving graphs and dissociation sets. We finish our exposition by proving that ${\rm gp}_d(G)$ is infinite whenever $G$ is an infinite graph and $d$ is a finite integer.Comment: 16 page

What we talk about when we talk about capacitance measured with the voltage-clamp step method

Capacitance is a fundamental neuronal property. One common way to measure capacitance is to deliver a small voltage-clamp step that is long enough for the clamp current to come to steady state, and then to divide the integrated transient charge by the voltage-clamp step size. In an isopotential neuron, this method is known to measure the total cell capacitance. However, in a cell that is not isopotential, this measures only a fraction of the total capacitance. This has generally been thought of as measuring the capacitance of the “well-clamped” part of the membrane, but the exact meaning of this has been unclear. Here, we show that the capacitance measured in this way is a weighted sum of the total capacitance, where the weight for a given small patch of membrane is determined by the voltage deflection at that patch, as a fraction of the voltage-clamp step size. This quantifies precisely what it means to measure the capacitance of the “well-clamped” part of the neuron. Furthermore, it reveals that the voltage-clamp step method measures a well-defined quantity, one that may be more useful than the total cell capacitance for normalizing conductances measured in voltage-clamp in nonisopotential cells

Neuronal synchrony: peculiarity and generality

Synchronization in neuronal systems is a new and intriguing application of dynamical systems theory. Why are neuronal systems different as a subject for synchronization? (1) Neurons in themselves are multidimensional nonlinear systems that are able to exhibit a wide variety of different activity patterns. Their “dynamical repertoire” includes regular or chaotic spiking, regular or chaotic bursting, multistability, and complex transient regimes. (2) Usually, neuronal oscillations are the result of the cooperative activity of many synaptically connected neurons (a neuronal circuit). Thus, it is necessary to consider synchronization between different neuronal circuits as well. (3) The synapses that implement the coupling between neurons are also dynamical elements and their intrinsic dynamics influences the process of synchronization or entrainment significantly. In this review we will focus on four new problems: (i) the synchronization in minimal neuronal networks with plastic synapses (synchronization with activity dependent coupling), (ii) synchronization of bursts that are generated by a group of nonsymmetrically coupled inhibitory neurons (heteroclinic synchronization), (iii) the coordination of activities of two coupled neuronal networks (partial synchronization of small composite structures), and (iv) coarse grained synchronization in larger systems (synchronization on a mesoscopic scale

Role of transport performance on neuron cell morphology

The compartmental model is a basic tool for studying signal propagation in neurons, and, if the model parameters are adequately defined, it can also be of help in the study of electrical or fluid transport. Here we show that the input resistance, in different networks which simulate the passive properties of neurons, is the result of an interplay between the relevant conductances, morphology and size. These results suggest that neurons must grow in such a way that facilitates the current flow. We propose that power consumption is an important factor by which neurons attain their final morphological appearance.Comment: 9 pages with 3 figures, submitted to Neuroscience Letter

Post-thaw development of in vitro produced buffalo embryos cryopreserved by cytoskeletal stabilization and vitrification

The present study was conducted to examine post-thaw in vitro developmental competence of buffalo embryos cryopreserved by cytoskeletal stabilization and vitrification. In vitro produced embryos were incubated with a medium containing cytochalasin-b (cyto-b) in a CO2 incubator for 40 min for microfilament stabilization and were cryopreserved by a two-step vitrification method at 24℃ in the presence of cyto-b. Initially, the embryos were exposed to 10% ethylene glycol (EG) and 10% dimethylsulfoxide (DMSO) in a base medium for 4 min. After the initial exposure, the embryos were transferred to a 7 µl drop of 25% EG and 25% DMSO in base medium and 0.3 M sucrose for 45 sec. After warming, the embryos were cultured in vitro for 72 h. The post-thaw in vitro developmental competence of the cyto-b-treated embryos did not differ significantly from those vitrified without cyto-b treatment. The hatching rates of morulae vitrified without cyto-b treatment was significantly lower than the non-vitrified control. However, the hatching rate of cyto-b-treated vitrified morulae did not differ significantly from the non-vitrified control. This study demonstrates that freezing of buffalo embryos by cytoskeletal stabilization and vitrification is a reliable method for long-term preservation

A missing dimension in measures of vaccination impacts

Immunological protection, acquired from either natural infection or vaccination, varies among hosts, reflecting underlying biological variation and affecting population-level protection. Owing to the nature of resistance mechanisms, distributions of susceptibility and protection entangle with pathogen dose in a way that can be decoupled by adequately representing the dose dimension. Any infectious processes must depend in some fashion on dose, and empirical evidence exists for an effect of exposure dose on the probability of transmission to mumps-vaccinated hosts [1], the case-fatality ratio of measles [2], and the probability of infection and, given infection, of symptoms in cholera [3]. Extreme distributions of vaccine protection have been termed leaky (partially protects all hosts) and all-or-nothing (totally protects a proportion of hosts) [4]. These distributions can be distinguished in vaccine field trials from the time dependence of infections [5]. Frailty mixing models have also been proposed to estimate the distribution of protection from time to event data [6], [7], although the results are not comparable across regions unless there is explicit control for baseline transmission [8]. Distributions of host susceptibility and acquired protection can be estimated from dose-response data generated under controlled experimental conditions [9]–[11] and natural settings [12], [13]. These distributions can guide research on mechanisms of protection, as well as enable model validity across the entire range of transmission intensities. We argue for a shift to a dose-dimension paradigm in infectious disease science and community health

Spatial representation of temporal information through spike timing dependent plasticity

We suggest a mechanism based on spike time dependent plasticity (STDP) of synapses to store, retrieve and predict temporal sequences. The mechanism is demonstrated in a model system of simplified integrate-and-fire type neurons densely connected by STDP synapses. All synapses are modified according to the so-called normal STDP rule observed in various real biological synapses. After conditioning through repeated input of a limited number of of temporal sequences the system is able to complete the temporal sequence upon receiving the input of a fraction of them. This is an example of effective unsupervised learning in an biologically realistic system. We investigate the dependence of learning success on entrainment time, system size and presence of noise. Possible applications include learning of motor sequences, recognition and prediction of temporal sensory information in the visual as well as the auditory system and late processing in the olfactory system of insects.Comment: 13 pages, 14 figures, completely revised and augmented versio