Waves and Oscillations in Model Neuronal Networks

In this thesis methods from nonlinear dynamical systems, pattern formation and bifurcation theory, combined with numerical simulations, are applied to three models in neuroscience. In Chapter 1 we analyze the Wilson-Cowan equations for a single self-excited population of cells with absolute refractory period. We construct the normal form for a Hopf bifurcation, and prove that by increasing the refractory period the network switches from a steady state to an oscillatory behavior. Numerical simulations indicate that for large values of refractoriness the oscillation converges to a relaxation-like pattern, the period of which we estimate. Chapter 2 brings new results for the rate model introduced by Hansel and Sompolinsky who study feature selectivity in local cortical circuits. We study their model with a more general, nonlinear sigmoid gain function, and prove that the system can exhibit different kind of patterns such as stationary states, traveling waves and standing waves. Standing waves can be obtained only if the threshold is sufficiently high and only for intermediate values of the strength of adaptation. A large adaptation strength destabilizes the pattern. Therefore the localized activity starts to propagate along the network, resulting in a traveling wave. We construct the normal form for Hopf and Takens-Bogdanov with O(2)-symmetry bifurcations and study the interactions between spatial and spatio-temporal patterns in the neural network. Numerical simulations are provided.Chapter 3 addresses several questions with regard to the traveling wave propagation in a leaky-integrate-and-fire model for a network with purely excitatory (exponentially decaying) synaptic coupling. We analyze the case when the neurons fire multiple spikes and derive a formula for the voltage. We compute in a certain parameter space, the curves that delineate the region where single-spike traveling wave solutions exist, and show that there is a region of parameter space where neurons can propagate a two-spike traveling wave

Evidence for hybridization and introgression within a species-rich oak (Quercus spp.) community

<p>Abstract</p> <p>Background</p> <p>Analysis of interspecific gene flow is crucial for the understanding of speciation processes and maintenance of species integrity. Oaks (genus <it>Quercus</it>, <it>Fagaceae</it>) are among the model species for the study of hybridization. Natural co-occurrence of four closely related oak species is a very rare case in the temperate forests of Europe. We used both morphological characters and genetic markers to characterize hybridization in a natural community situated in west-central Romania and which consists of <it>Quercus robur</it>, <it>Q. petraea</it>, <it>Q. pubescen</it>s, and <it>Q. frainetto</it>, respectively.</p> <p>Results</p> <p>On the basis of pubescence and leaf morphological characters ~94% of the sampled individuals were assigned to pure species. Only 16 (~6%) individual trees exhibited intermediate morphologies or a combination of characters of different species. Four chloroplast DNA haplotypes were identified in the study area. The distribution of haplotypes within the white oak complex showed substantial differences among species. However, the most common haplotypes were present in all four species. Furthermore, based on a set of 7 isozyme and 6 microsatellite markers and using a Bayesian admixture analysis without any a priori information on morphology we found that four genetic clusters best fit the data. There was a very good correspondence of each species with one of the inferred genetic clusters. The estimated introgression level varied markedly between pairs of species ranging from 1.7% between <it>Q. robur </it>and <it>Q. frainetto </it>to 16.2% between <it>Q. pubescens </it>and <it>Q. frainetto</it>. Only nine individuals (3.4%) appeared to be first-generation hybrids.</p> <p>Conclusion</p> <p>Our data indicate that natural hybridization has occurred at relatively low rates. The different levels of gene flow among species might be explained by differences in flowering time and spatial position within the stand. In addition, a partial congruence between phenotypically and genetically intermediate individuals was found, suggesting that intermediate appearance does not necessarily mean hybridization. However, it appears that natural hybridization did not seriously affect the species identity in this area of sympatry.</p

Rheology in Wood Engineering

AbstractThe system strains under external loads in a certain amount of time and under the influence of the environmental factors define the rheological behavior. Rheological phenomena depend on many factors: temperature such as air humidity or moisture content of rheological system, radiations in term of intensity, duration, type - UV, IR, X, geometry of the parts; loadings in terms of intensity, variation, duration; defects; aggressive environment; composition, material properties; combinations of these factors. Rheology science is based on the theories of the strength of materials, thermodynamics, chemistry and materials science, but in terms of application, it provides a personalized analysis or diagnosis according to the condition of the structures/systems used. Wooden constructions are subjected to various loadings on both short and long durations. The joints can be elastic (flexible) if the failure occurs gradually, or plastic, if the failure occurs suddenly. Sudden failure of joints is caused by shear as predominant load because wood does not resist at shear stresses. In order to study the rheological behavior of the wood joints with metal rods under constant load, three types of joints in terms of diameters of bolts and stiffening systems were tested. They were stressed to traction force of 500 to 900N for 200 days, in real conditions of temperature (-7°C la +30°C) and humidity (from 47.8% to 83.8%). The aim of the tests were to determine the rheological behavior of wooden joints; variation of deformations in relation to the relative humidity and temperature; rate of strain and connections in determining rheological model of wood with threaded rods. It was found that the low temperatures during winter (-7…0°C) correlated with high relative humidity led to sudden changes in strain. It was observed that the high-speed deformation had a joint with the largest diameter rod (8mm). The paper highlights the rheological analysis of joints in wooden rods in real conditions of temperature and humidity, with regards to applied tension and the determination of the creep function that characterizes these types of connections, establishing the optimum diameter rods

Marginal/peripheral populations of forest tree species and their conservation status: report for southeastern Europe

The Southeastern Europe, which is usually known as Balkan Peninsula, harbours a vast number of plant species among which a great number of relict and endemic ones. This region was one of the main areas in Europe where plant species found shelter in refugia and survived during the last glaciation. These refugia were the source areas for the postglacial colonization of many forest tree species. Human impact has been reported in the region since antiquity resulting in fragmentation of forests and deforestation. Marginal/peripheral (MaP) populations could be identified for most of the forest tree species occurring in the region. However, detailed information about MaP populations is restricted to few cases. Most of the MaP populations identified by FP1202 experts are not located in protected areas. Thus, approximately 27 % of the MaP populations are included in Natura 2000 sites, and only one out of the four reported populations is included in a genetic conservation unit. Many MaP populations (40%) are registered as seed stands and only 14% are included in EUFGIS database. Conservation of forest genetic resources, including MaP populations, is a component of sustainable management of forests in many countries of the region

Patterns of contemporary hybridization inferred from paternity analysis in a four-oak-species forest

<p>Abstract</p> <p>Background</p> <p>Few studies address the issue of hybridization in a more than two-species context. The species-rich <it>Quercus </it>complex is one of the systems which can offer such an opportunity. To investigate the contemporary pattern of hybridization we sampled and genotyped 320 offspring from a natural mixed forest comprising four species of the European white oak complex: <it>Quercus robur</it>, <it>Q. petraea</it>, <it>Q. pubescens</it>, and <it>Q. frainetto</it>.</p> <p>Results</p> <p>A total of 165 offspring were assigned unambiguously to one of the pollen donors within the study plot. The minimum amount of effective pollen originating from outside the plot varied markedly among the seed parents, ranging from 0.18 to 0.87. The majority of the successful matings (64.1%) occurred between conspecific individuals indicating the existence of reproductive barriers between oak species. However, the isolation was not complete since we found strong evidence for both first-generation (8.4%) and later-generation hybrids (27.5%). Only two out of eight seed parents, belonging to <it>Q. petraea </it>and <it>Q. robur</it>, showed a high propensity to hybridize with <it>Q. pubescens </it>and <it>Q. petraea</it>, respectively. Significant structure of the effective pollen pools (<it>Φ</it>_{<it>pt </it>}= 0.069, P = 0.01) was detected in our sample. However, no support was found for the isolation by distance hypothesis. The proportion of hybrids was much higher (79%) in the seed generation when compared to the adult tree generation.</p> <p>Conclusion</p> <p>First-generation hybrids were observed only between three out of six possible species combinations. Hybrids between one pair of species preferred to mate with one of their parental species. The observation of first and later-generation hybrids in higher frequency in acorns than in adults might be explained by selection against hybrid genotypes, the history of this uneven-aged forest or past introgression between species.</p

Genetic evidence of human mediated, historical seed transfer from the Tyrolean Alps to the Romanian Carpathians in Larix decidua (Mill.) forests

International audienceKey messageHistoric transfer of larch from Alpine sources to Southern and Eastern Carpathians has been verified by means of nuclear genetic markers. Tyrolean populations can be differentiated into a north-western and south-eastern group, while Romanian populations are separated according to the Southern and Eastern Carpathians. Low-level introgression from Alpine sources is found in autochthonous Carpathian populations.ContextLarge scale human mediated transfer of forest reproductive material may have strongly modified the gene pool of European forests. Particularly in European larch, large quantities of seeds from Central Europe were used for plantations in Southern and Eastern Europe starting in the mid nineteenth century.AimsOur main objective was to provide DNA marker based evidence for the anthropogenic transfer of Alpine larch reproductive material to native Carpathian populations.MethodsWe studied and compared 12 populations (N = 771) of Larix decidua in the Alps (Austria, Italy) and in the Southern and Eastern Carpathians (Romania) using 13 microsatellites.ResultsHigh genetic diversity (He = 0.752; RS = 9.4) and a moderate genetic differentiation (FST = 0.13; G′ST = 0.28) among populations were found; Alpine and Carpathian populations were clearly separated by clustering methods. A Tyrolean origin of plant material was evident for one out of four adult Romanian populations. In the transferred population, a genetic influence from Carpathian sources was found neither in adults nor in juveniles, while the natural regeneration of two Romanian populations was genetically affected by Alpine sources to a minor degree (2.2 and 2.9% allochthonous individuals according to GeneClass and Structure, respectively). ConclusionTracing back of plant transfer by means of genetic tools is straightforward, and we propose further studies to investigate gene flow between natural and transferred populations

Bud burst and flowering phenology in a mixed oak forest from Eastern Romania

Bud burst and flowering phenology have been observed in year 2008 ina natural white oak species complex situated in eastern Romania. A total of 300 mature individuals was mapped and identified based on leaf morphology. The community consists of four oak species: Quercus pedunculiflora, Q. robur, Q. pubescens and Q. petraea. A set of 28 individuals could not be unambiguously classified to one or another species. Data on bud burst showed a normal distribution and the differences among species were small. The "very late" flushing was recorded on 15th of April, three weeks later when compared to early flushing individuals. The time period between the bud burst and the complete development of leaves was nearly the same in all oak species, varying on average, between 18.4 and 20.6 days. The spatialdistribution of phenological groups within the complex appears to be non-randomly, because in many parts of the study plot exist groups in which most of the trees belong to the same phenological category. Our results indicate an overlap in flowering time for all oak species which occur in the area. The data support the hypothesis that interspecific gene flow is possible between closely related oak species

Dynamical characteristics common to neuronal competition models.

Shpiro A, Curtu R, Rinzel J, Rubin N. Dynamical characteristics common to neuronal competition models. J Neurophysiol 97: [462][463][464][465][466][467][468][469][470][471][472][473] 2007. First published October 25, 2006; doi:10.1152/jn.00604.2006. Models implementing neuronal competition by reciprocally inhibitory populations are widely used to characterize bistable phenomena such as binocular rivalry. We find common dynamical behavior in several models of this general type, which differ in their architecture in the form of their gain functions, and in how they implement the slow process that underlies alternating dominance. We focus on examining the effect of the input strength on the rate (and existence) of oscillations. In spite of their differences, all considered models possess similar qualitative features, some of which we report here for the first time. Experimentally, dominance durations have been reported to decrease monotonically with increasing stimulus strength (such as Levelt&apos;s &quot;Proposition IV&quot;). The models predict this behavior; however, they also predict that at a lower range of input strength dominance durations increase with increasing stimulus strength. The nonmonotonic dependency of duration on stimulus strength is common to both deterministic and stochastic models. We conclude that additional experimental tests of Levelt&apos;s Proposition IV are needed to reconcile models and perception. I N T R O D U C T I O N Binocular rivalry occurs when two different images are presented to the two eyes. With such ambiguous stimuli, only one of the images is perceived at any given moment, with dominance switching between the two images in a haphazard manner. The average dominance durations are typically a few seconds. Several stimulus parameters have been shown to influence the dynamical characteristics of the perceptual alternations. In particular, increasing the contrast of the rivaling images has been shown to increase the frequency of percept switching, which implies a decrease in the mean dominance times, an observation known as &quot;Levelt&apos;s Proposition IV&quot; Reciprocal inhibition architecture is widely used to describe binocular rivalry and bistable perception in general. The dominant side of the system exerts a strong inhibitory influence on the competing side, so that the latter is suppressed. The switching in dominance between the two sides is realized by a slow negative feedback process, such as spike-frequency adaptation or synaptic depression, that weakens the inhibition either by decreasing the activity of the dominant side or by decreasing the connectivity between the sides and allows the suppressed population to become active. These general principles have been incorporated in numerous mathematical models of binocular rivalry In addition to studying these two models as formulated, we also consider two variations of the model of We identify the parameter regimes where each model shows behavior that is consistent with Levelt&apos;s Proposition IV. In addition, we demonstrate that all the models predict previously unreported types of behavior. Using stimulation strength as the control variable, we focus on its effect on the existence and rate of oscillations. In spite of the differences in architecture and mathematical formulation of the explored models, we find substantial generalities in their behavior. In all models, for very high stimulus strengths the two populations are simultaneously active at a high level. Just below this regime is a range for stimulus strength where the behavior of the system is oscillatory, with the dominance period of each percept decreasing as stimulus strength increases, in accordance with Levelt&apos;s Proposition IV (decreasing duration, or DD behavior). However, for input strengths below this range new regimes of behavior are discovered: first, a winner-take-all (nonrivaling steady dominance) behavior appears. Next, as stimulus strength is further reduced, another range of rivalry (oscillatory) behavior appears, but this time with the dominance periods increasing with increasing input (increasing duration, or ID behavior). Finally, at very low input strengths there is again a range where the two populations are simultaneously active, this time at a low leve