Dynamical principles in neuroscience

Dynamical modeling of neural systems and brain functions has a history of success over the last half century. This includes, for example, the explanation and prediction of some features of neural rhythmic behaviors. Many interesting dynamical models of learning and memory based on physiological experiments have been suggested over the last two decades. Dynamical models even of consciousness now exist. Usually these models and results are based on traditional approaches and paradigms of nonlinear dynamics including dynamical chaos. Neural systems are, however, an unusual subject for nonlinear dynamics for several reasons: (i) Even the simplest neural network, with only a few neurons and synaptic connections, has an enormous number of variables and control parameters. These make neural systems adaptive and flexible, and are critical to their biological function. (ii) In contrast to traditional physical systems described by well-known basic principles, first principles governing the dynamics of neural systems are unknown. (iii) Many different neural systems exhibit similar dynamics despite having different architectures and different levels of complexity. (iv) The network architecture and connection strengths are usually not known in detail and therefore the dynamical analysis must, in some sense, be probabilistic. (v) Since nervous systems are able to organize behavior based on sensory inputs, the dynamical modeling of these systems has to explain the transformation of temporal information into combinatorial or combinatorial-temporal codes, and vice versa, for memory and recognition. In this review these problems are discussed in the context of addressing the stimulating questions: What can neuroscience learn from nonlinear dynamics, and what can nonlinear dynamics learn from neuroscience?This work was supported by NSF Grant No. NSF/EIA-0130708, and Grant No. PHY 0414174; NIH Grant No. 1 R01 NS50945 and Grant No. NS40110; MEC BFI2003-07276, and Fundación BBVA

Network 'small-world-ness': a quantitative method for determining canonical network equivalence

Background: Many technological, biological, social, and information networks fall into the broad class of 'small-world' networks: they have tightly interconnected clusters of nodes, and a shortest mean path length that is similar to a matched random graph (same number of nodes and edges). This semi-quantitative definition leads to a categorical distinction ('small/not-small') rather than a quantitative, continuous grading of networks, and can lead to uncertainty about a network's small-world status. Moreover, systems described by small-world networks are often studied using an equivalent canonical network model-the Watts-Strogatz (WS) model. However, the process of establishing an equivalent WS model is imprecise and there is a pressing need to discover ways in which this equivalence may be quantified. Methodology/Principal Findings: We defined a precise measure of 'small-world-ness' S based on the trade off between high local clustering and short path length. A network is now deemed a 'small-world' if S. 1-an assertion which may be tested statistically. We then examined the behavior of S on a large data-set of real-world systems. We found that all these systems were linked by a linear relationship between their S values and the network size n. Moreover, we show a method for assigning a unique Watts-Strogatz (WS) model to any real-world network, and show analytically that the WS models associated with our sample of networks also show linearity between S and n. Linearity between S and n is not, however, inevitable, and neither is S maximal for an arbitrary network of given size. Linearity may, however, be explained by a common limiting growth process. Conclusions/Significance: We have shown how the notion of a small-world network may be quantified. Several key properties of the metric are described and the use of WS canonical models is placed on a more secure footing

Dynamics of coupled cell networks: synchrony, heteroclinic cycles and inflation

Copyright © 2011 Springer. The final publication is available at www.springerlink.comWe consider the dynamics of small networks of coupled cells. We usually assume asymmetric inputs and no global or local symmetries in the network and consider equivalence of networks in this setting; that is, when two networks with different architectures give rise to the same set of possible dynamics. Focussing on transitive (strongly connected) networks that have only one type of cell (identical cell networks) we address three questions relating the network structure to dynamics. The first question is how the structure of the network may force the existence of invariant subspaces (synchrony subspaces). The second question is how these invariant subspaces can support robust heteroclinic attractors. Finally, we investigate how the dynamics of coupled cell networks with different structures and numbers of cells can be related; in particular we consider the sets of possible “inflations” of a coupled cell network that are obtained by replacing one cell by many of the same type, in such a way that the original network dynamics is still present within a synchrony subspace. We illustrate the results with a number of examples of networks of up to six cells

Достоверность данных первичного зоотехнического учёта в молочном скотоводстве

The purpose of this paper is to evaluate the primary databases of zootechnical records in western Siberia. The object of the study was the records on milk productivity (milk yield during the whole lactation, milk fat content, milk protein content, amount of milk fat, amount of milk protein), duration of lactation (service period, dry period, inter-breeding period), age of the first fruitful insemination and information on the origin of 20,000 Holstein cows. The validity of the raw data was assessed by assuming a Gaussian distribution without significant human influence. For this purpose, the Anderson-Darling test and corresponding visualization using histograms and quantile-quantile plots were applied. The list of traits of milk production was based on the values of the Anderson-Darling criterion. The authors found that the highest levels of this criterion were correlated with milk fat and protein. And the indicator «milk yield» was practically absent from the list of traits of dairy productivity. These results can be explained by the fact that in most enterprises, the value of milk yield was higher than the appraisal threshold values. An analysis of the genealogical trees of the studied breeding enterprises was carried out, along with the use of statistical criteria. This analysis revealed the inappropriate assignment of several dozen of offspring to a single mother. Thus, the presented approach can be used to identify outliers associated with human factors. And it can also be related to improper methodological support of the sampling process and errors in the work of the laboratories of selective milk quality control associated with the sampling and delivery of samples.Целью настоящей работы является оценка баз данных первичного зоотехнического учёта в Западной Сибири. Объектом исследований были записи о молочной продуктивности (удой за всю лактацию, содержание жира в молоке, содержание белка в молоке, количество молочного жира, количество молочного белка), длительности лактации (сервис-период, сухостойный период, межотельный период), возраст первого плодотворного осеменения и сведения о происхождении 20000 коров голштинской породы. Оценку достоверности исходных данных осуществляли исходя из предположения о гауссовом распределении при отсутствии значимого влияния человеческого фактора. С этой целью применяли критерий Андерсона-Дарлинга и соответствующую визуализацию с использованием гистограмм и графиков квантиль–квантиль. Список признаков молочной продуктивности был составлен исходя из значений критерия Андерсона–Дарлинга. Установлено, что самые высокие уровни данного критерия соотносились с такими показателями, как молочный жир и белок, тогда как удой практически отсутствовал в перечне признаков молочной продуктивности. Это объясняется тем, что у животных большинства предприятий величина удоя была выше пороговых значений бонитировки. Наряду с использованием статистических критериев, проведен анализ генеалогических деревьев исследуемых племенных предприятий, который позволил выявить неправомерное отнесение нескольких десятков потомков к одной матери. Таким образом, представленный подход может быть использован для выявления выбросов, сопряженных с человеческим фактором, неправильным методическим обеспечением процесса отбора проб и ошибками в работе лабораторий селекционного контроля качества молока, связанными с отбором проб и их доставкой

Formation of feedforward networks and frequency synchrony by spike-timing-dependent plasticity

Spike-timing-dependent plasticity (STDP) with asymmetric learning windows is commonly found in the brain and useful for a variety of spike-based computations such as input filtering and associative memory. A natural consequence of STDP is establishment of causality in the sense that a neuron learns to fire with a lag after specific presynaptic neurons have fired. The effect of STDP on synchrony is elusive because spike synchrony implies unitary spike events of different neurons rather than a causal delayed relationship between neurons. We explore how synchrony can be facilitated by STDP in oscillator networks with a pacemaker. We show that STDP with asymmetric learning windows leads to self-organization of feedforward networks starting from the pacemaker. As a result, STDP drastically facilitates frequency synchrony. Even though differences in spike times are lessened as a result of synaptic plasticity, the finite time lag remains so that perfect spike synchrony is not realized. In contrast to traditional mechanisms of large-scale synchrony based on mutual interaction of coupled neurons, the route to synchrony discovered here is enslavement of downstream neurons by upstream ones. Facilitation of such feedforward synchrony does not occur for STDP with symmetric learning windows.Comment: 9 figure

Rhythm Generation through Period Concatenation in Rat Somatosensory Cortex

Rhythmic voltage oscillations resulting from the summed activity of neuronal populations occur in many nervous systems. Contemporary observations suggest that coexistent oscillations interact and, in time, may switch in dominance. We recently reported an example of these interactions recorded from in vitro preparations of rat somatosensory cortex. We found that following an initial interval of coexistent gamma (∼25 ms period) and beta2 (∼40 ms period) rhythms in the superficial and deep cortical layers, respectively, a transition to a synchronous beta1 (∼65 ms period) rhythm in all cortical layers occurred. We proposed that the switch to beta1 activity resulted from the novel mechanism of period concatenation of the faster rhythms: gamma period (25 ms)+beta2 period (40 ms) = beta1 period (65 ms). In this article, we investigate in greater detail the fundamental mechanisms of the beta1 rhythm. To do so we describe additional in vitro experiments that constrain a biologically realistic, yet simplified, computational model of the activity. We use the model to suggest that the dynamic building blocks (or motifs) of the gamma and beta2 rhythms combine to produce a beta1 oscillation that exhibits cross-frequency interactions. Through the combined approach of in vitro experiments and mathematical modeling we isolate the specific components that promote or destroy each rhythm. We propose that mechanisms vital to establishing the beta1 oscillation include strengthened connections between a population of deep layer intrinsically bursting cells and a transition from antidromic to orthodromic spike generation in these cells. We conclude that neural activity in the superficial and deep cortical layers may temporally combine to generate a slower oscillation

Zinc oxide nanostructures doped with transitional metals: fabrication and properties

In this work ZnO nanostructured films doped with Co and Ni deposited by hydrothermal method on silicon substrates covered with ALD undoped ZnO sublayer were studied. According SEM images obtained ZnO films consist of densely packed vertical nanopillars. Doping ZnO films with Ni or Co concentration up to 1019 cm-3 quenches UV exciton photoluminescence of ZnO films and changed emission spectra. It also leads to slight ferromagnetic behavior of the obtained films