For a class of integrate-and-fire, pulse-coupled networks with complex topology, we study the dependence of the pulse rate on the underlying architectural connectivity statistics. We derive the ...distribution of the pulse rate from this dependence and determine when the underlying scale-free architectural connectivity gives rise to a scale-free pulse-rate distribution. We identify the scaling of the pairwise coupling between the dynamical units in this network class that keeps their pulse rates bounded in the infinite-network limit. In the process, we determine the connectivity statistics for a specific scale-free network grown by preferential attachment.
Using the (1+1)D Majda-McLaughlin-Tabak model as an example, we present an extension of the wave turbulence (WT) theory to systems with strong nonlinearities. We demonstrate that nonlinear wave ...interactions renormalize the dynamics, leading to (i) a possible destruction of scaling structures in the bare wave systems and a drastic deformation of the resonant manifold even at weak nonlinearities, and (ii) creation of nonlinear resonance quartets in wave systems for which there would be no resonances as predicted by the linear dispersion relation. Finally, we derive an effective WT kinetic equation and show that our prediction of the renormalized Rayleigh-Jeans distribution is in excellent agreement with the simulation of the full wave system in equilibrium.
The study presents natural hazards in Slovenia's karst, focusing on flooding in karst poljes. A specific study was done on the flood dynamics of two typical and connected karst poljes (Cerknica and ...Planina) of the Classical Karst region. In the case of particularly extreme hydrological conditions in the autumn of 2008, detailed analyses of the recharge-discharge regime and the interrelationship of flooding on the two poljes were done. Daily precipitation, discharge, and water level values from several monitoring sites were analyzed and cross-correlated, and additional hydrological analyses were done using a digital elevation model in order to acquire water level increase and decrease intensity, flood water volumes, and the extent of flooding and to understand the conditions controlling karst flooding. The results reveal that the hydrological functioning of the studied karst poljes is influenced by the hydrogeological and temporary hydrological conditions in the catchment area. The response of the binary karst system (i.e., the influence of autogenic and allogenic recharge) is especially distinct. The study shows that during extremely intense recharge, the reactions of karst aquifer systems to precipitation are as rapid as the response of surface waters (the water level of Cerknica Lake increased with an intensity of 38-63 cm/day or 55 m3/s respectively) while retention capacities are negligible. In contrast to flash floods, floods in karst areas may last from several weeks to several months. For the observed period a three-dimensional simulation of the flooding was made. At the maximum recorded water level, the volume of water on the Cerknica polje was 51 million m
3
, and 26 million m
3
on the Planina polje. The maximum extent of flooding on the Cerknica polje was 23 km
2
and on the Planina polje 9.5 km
2
. On the basis of the study, information was provided regarding future hazard mitigation. However, the study demonstrated that a sufficiently dense monitoring network is necessary to predict the occurrence and duration of floods with greater certainty.
On the basis of a previously tested method, the cognition of the spatial extent of the Mediterranean in Slovenia is presented. The Mediterranean may be determined on the basis of numerous and very ...diverse criteria. It is therefore a very subjectively determined notion, where geographical and non-geographical definitions can be treated as equivalent. The research made use of a questionnaire method, which revealed the opinions of the inhabitants living in the area, generally regarded as being Mediterranean. The determination of the Mediterranean was achieved with the aid of a special question. Respondents were asked to graphically delineate its border in Slovenia on a specially prepared general map included in the questionnaire on the basis of their subjective complex perception of the characteristics by them understood as Mediterranean. The questionnaire was spatially structured by the following regions: Slovene Istria, the Vipava Valley, the Vipava Hills, the Goriska ravan, the Brda Hills, the Kras, the Pivka Basin, the Reka Valley, the Brkini Hills and the Matarsko podolje and Ljubljana with its surroundings. By drawing on the fuzzy logic theory and helped by computer techniques all the answers were merged on a special map showing the extent and membership of the fuzzy set "Mediterranean" within the crisp set "Slovenia". The border between the Mediterranean and non-Mediterranean part of Slovenia is in this way established as a continuous transition. The mean value of this transition goes from Sempeter, passes the eastern flank of Karst, beside Divaca and ends on the eastern side of Slavnik. A more restrictive criterion of the membership function value of 0.95, includes in the Slovenian Mediterranean only the sea and its most immediate hinterland. Particularly interesting proved differences in the spatial cognition of the Mediterranean's borders in Slovenia between different survey regions.
Celotno besedilo
Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, UILJ, UKNU, UL, UM, UPUK
Synchronous and asynchronous dynamics in all-to-all coupled networks of identical,
excitatory, current-based, integrate-and-fire (I&F) neurons with delta-impulse coupling currents and
Poisson ...spike-train external drive are studied. Repeating synchronous total firing events, during
which all the neurons fire simultaneously, are observed using numerical simulations and found to
be the attracting state of the network for a large range of parameters. Mechanisms leading to such
events are then described in two regimes of external drive: superthreshold and subthreshold. In
the former, a probabilistic argument similar to the proof of the Central Limit Theorem yields the
oscillation period, while in the latter, this period is analyzed via an exit time calculation utilizing a
diffusion approximation of the Kolmogorov forward equation. Asynchronous dynamics are observed
computationally in networks with random transmission delays. Neuronal voltage probability density
functions (PDFs) and gain curves—graphs depicting the dependence of the network firing rate on
the external drive strength—are analyzed using the steady solutions of the self-consistency problem
for a Kolmogorov forward equation. All the voltage PDFs are obtained analytically, and asymptotic
solutions for the gain curves are obtained in several physiologically relevant limits. The absence of
chaotic dynamics is proved for the type of network under investigation by demonstrating convergence
in time of its trajectories.
We present examples of theoretically-predicted invisibility cloaks with shapes other than spheres and cylinders, including cones and ellipsoids, as well as shapes spliced from parts of these simpler ...shapes. In addition, we present an example explicitly displaying the non-uniqueness of invisibility cloaks of the same shape. We depict rays propagating through these example cloaks using ray tracing for geometric optics.
► Theoretically-predicted conical and ellipsoidal invisibility cloaks. ► Non-smooth cloaks spliced from parts of simpler shapes. ► Example displaying non-uniqueness of invisibility cloaks of the same shape. ► Rays propagating through example cloaks depicted using geometric optics.
The present paper aims to address the sustainable management issues of karst water sources in Slovenia and Croatia. It focuses on the Mediterranean part of the Dinaric karst, which holds important ...groundwater reserves. The importance of selected karst aquifers for water supply is presented. In addition, national drinking water management strategies are examined to synthesise the issues relating to the exposure of groundwater to contamination and over-exploitation. Finally, the most significant problems, pressing needs and challenges are identified. These depend predominantly on revision of existing drinking water protection strategies and integration of karst-specific provisions, aspects of over-exploitation and proper water quality control. The need for harmonised multi-country policies regulating resource abstraction and contamination issues is stressed.
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