N-dimensional dynamical systems exploiting instabilities in full

We report experimental and numerical results showing how certain N-dimensional dynamical systems are able to exhibit complex time evolutions based on the nonlinear combination of N-1 oscillation modes. The experiments have been done with a family of thermo-optical systems of effective dynamical dimension varying from 1 to 6. The corresponding mathematical model is an N-dimensional vector field based on a scalar-valued nonlinear function of a single variable that is a linear combination of all the dynamic variables. We show how the complex evolutions appear associated with the occurrence of successive Hopf bifurcations in a saddle-node pair of fixed points up to exhaust their instability capabilities in N dimensions. For this reason the observed phenomenon is denoted as the full instability behavior of the dynamical system. The process through which the attractor responsible for the observed time evolution is formed may be rather complex and difficult to characterize. Nevertheless, the well-organized structure of the time signals suggests some generic mechanism of nonlinear mode mixing that we associate with the cluster of invariant sets emerging from the pair of fixed points and with the influence of the neighboring saddle sets on the flow nearby the attractor. The generation of invariant tori is likely during the full instability development and the global process may be considered as a generalized Landau scenario for the emergence of irregular and complex behavior through the nonlinear superposition of oscillatory motions

Direct and indirect subsidies in markets with system goods in the presence of externalities. Preliminary version

This paper derives a model of markets with system goods and two technological standards. An established standard incurs lower unit production costs but causes a negative externality. The paper derives the conditions for policy intervention and compares the effect of direct and indirect cost-reducing subsidies in two markets with system goods in the presence of externalities. If consumers are committed to the technology by purchasing one of the components, direct subsidies are preferable. For a medium-low cost difference between technological standards and a low externality cost it is optimal to provide a direct subsidy only to the first technology adopter. As the higher the externality cost raises, the more technology adopters should be provided with direct subsidies. This effect is robust in all extensions. In the absence of consumers commitment to a technological standard indirect and direct subsidies are both desirable. In this case, the subsidy to the first adopter is lower then the subsidy to the second adopter. Moreover, for the low cost difference between technological standards and low externality cost the fi rst fi rm chooses a superior standard without policy intervention. Finally, a perfect compatibility between components based on different technological standards enhances an advantage of indirect subsidies for medium-high externality cost and cost difference between technological standards. Journal of Economic Literature Classi fication Numbers: C72, D21, D40, H23, L13, L22, L51, O25, O33, O38. Keywords: Technological standards; complementary products; externalities; cost-reducing subsidies; compatibility.

Emotional attention as a modulatory system of perception

Report for the scientific sojourn carried out at the University Medical Center, Swiss, from 2010 to 2012. Abundant evidence suggests that negative emotional stimuli are prioritized in the perceptual systems, eliciting enhanced neural responses in early sensory regions as compared with neutral information. This facilitated detection is generally paralleled by larger neural responses in early sensory areas, relative to the processing of neutral information. In this sense, the amygdala and other limbic regions, such as the orbitofrontal cortex, may play a critical role by sending modulatory projections onto the sensory cortices via direct or indirect feedback.The present project aimed at investigating two important issues regarding these mechanisms of emotional attention, by means of functional magnetic resonance imaging. In Study I, we examined the modulatory effects of visual emotion signals on the processing of task-irrelevant visual, auditory, and somatosensory input, that is, the intramodal and crossmodal effects of emotional attention. We observed that brain responses to auditory and tactile stimulation were enhanced during the processing of visual emotional stimuli, as compared to neutral, in bilateral primary auditory and somatosensory cortices, respectively. However, brain responses to visual task-irrelevant stimulation were diminished in left primary and secondary visual cortices in the same conditions. The results also suggested the existence of a multimodal network associated with emotional attention, presumably involving mediofrontal, temporal and orbitofrontal regions Finally, Study II examined the different brain responses along the low-level visual pathways and limbic regions, as a function of the number of retinal spikes during visual emotional processing. The experiment used stimuli resulting from an algorithm that simulates how the visual system perceives a visual input after a given number of retinal spikes. The results validated the visual model in human subjects and suggested differential emotional responses in the amygdala and visual regions as a function of spike-levels. A list of publications resulting from work in the host laboratory is included in the report.

Emotional attention as a modulatory system of perception

Report for the scientific sojourn carried out at the University Medical Center, Swiss, from 2010 to 2012. Abundant evidence suggests that negative emotional stimuli are prioritized in the perceptual systems, eliciting enhanced neural responses in early sensory regions as compared with neutral information. This facilitated detection is generally paralleled by larger neural responses in early sensory areas, relative to the processing of neutral information. In this sense, the amygdala and other limbic regions, such as the orbitofrontal cortex, may play a critical role by sending modulatory projections onto the sensory cortices via direct or indirect feedback.The present project aimed at investigating two important issues regarding these mechanisms of emotional attention, by means of functional magnetic resonance imaging. In Study I, we examined the modulatory effects of visual emotion signals on the processing of task-irrelevant visual, auditory, and somatosensory input, that is, the intramodal and crossmodal effects of emotional attention. We observed that brain responses to auditory and tactile stimulation were enhanced during the processing of visual emotional stimuli, as compared to neutral, in bilateral primary auditory and somatosensory cortices, respectively. However, brain responses to visual task-irrelevant stimulation were diminished in left primary and secondary visual cortices in the same conditions. The results also suggested the existence of a multimodal network associated with emotional attention, presumably involving mediofrontal, temporal and orbitofrontal regions Finally, Study II examined the different brain responses along the low-level visual pathways and limbic regions, as a function of the number of retinal spikes during visual emotional processing. The experiment used stimuli resulting from an algorithm that simulates how the visual system perceives a visual input after a given number of retinal spikes. The results validated the visual model in human subjects and suggested differential emotional responses in the amygdala and visual regions as a function of spike-levels. A list of publications resulting from work in the host laboratory is included in the report.

Role of the cannabinoid system in the effects induced by nicotine on anxiety-like behaviour in mice

Rationale: Acute behavioural effects and motivational responses induced by nicotine can be modulated by the endocannabinoid system supporting the existence of a physiological interaction between these two systems. Objectives: The present study was designed to examine the possible involvement of the cannabinoid system in the anxiolytic- and anxiogenic-like responses induced by nicotine in mice. Methods: Animals were only exposed once to nicotine. The acute administration of low (0.05, sc) or high (0.8 mg/kg, sc) doses of nicotine produced opposite effects in the elevated plus-maze, i.e., anxiolytic- and anxiogenic-like responses, respectively. The effects of the pretreatment with the CB1 cannabinoid receptor antagonist, rimonabant (0.25, 0.5 and 1 mg/kg, ip), and the cannabinoid agonist, 9-tetrahydrocannabinol (0.1 mg/kg, ip), were evaluated on the anxiolytic- and anxiogenic-like responses induced by nicotine. Results: Rimonabant completely abolished nicotine-induced anxiolytic-like effects and increased the anxiogenic-like responses of nicotine, suggesting an involvement of CB1 receptors in these behavioural responses. On the other hand, 9-tetrahydrocannabinol failed to modify nicotine anxiolytic-like responses, but attenuated its anxiogenic-like effects. In addition the association of non-effective doses of 9-tetrahydrocannabinol and nicotine produced clear anxiolytic-like responses. Conclusions: These results demonstrate that the endogenous cannabinoid system is involved in the regulation of nicotine anxiety-like behaviour in mice, and provide new findings to support the use of cannabinoid antagonists in the treatment of tobacco addiction.

A bi-dimensional genome scan for prolificacy traits in pigs shows the existence of multiple epistatic QTL

Background: Prolificacy is the most important trait influencing the reproductive efficiency of pig production systems. The low heritability and sex-limited expression of prolificacy have hindered to some extent the improvement of this trait through artificial selection. Moreover, the relative contributions of additive, dominant and epistatic QTL to the genetic variance of pig prolificacy remain to be defined. In this work, we have undertaken this issue by performing one-dimensional and bi-dimensional genome scans for number of piglets born alive (NBA) and total number of piglets born (TNB) in a three generation Iberian by Meishan F2 intercross. Results: The one-dimensional genome scan for NBA and TNB revealed the existence of two genome-wide highly significant QTL located on SSC13 (P < 0.001) and SSC17 (P < 0.01) with effects on both traits. This relative paucity of significant results contrasted very strongly with the wide array of highly significant epistatic QTL that emerged in the bi-dimensional genome-wide scan analysis. As much as 18 epistatic QTL were found for NBA (four at P < 0.01 and five at P < 0.05) and TNB (three at P < 0.01 and six at P < 0.05), respectively. These epistatic QTL were distributed in multiple genomic regions, which covered 13 of the 18 pig autosomes, and they had small individual effects that ranged between 3 to 4% of the phenotypic variance. Different patterns of interactions (a × a, a × d, d × a and d × d) were found amongst the epistatic QTL pairs identified in the current work.Conclusions: The complex inheritance of prolificacy traits in pigs has been evidenced by identifying multiple additive (SSC13 and SSC17), dominant and epistatic QTL in an Iberian × Meishan F2 intercross. Our results demonstrate that a significant fraction of the phenotypic variance of swine prolificacy traits can be attributed to first-order gene-by-gene interactions emphasizing that the phenotypic effects of alleles might be strongly modulated by the genetic background where they segregate.

Solving higher-dimensional continuous time stochastic control problems by value function regression

The paper develops a method to solve higher-dimensional stochasticcontrol problems in continuous time. A finite difference typeapproximation scheme is used on a coarse grid of low discrepancypoints, while the value function at intermediate points is obtainedby regression. The stability properties of the method are discussed,and applications are given to test problems of up to 10 dimensions.Accurate solutions to these problems can be obtained on a personalcomputer.

Extremal climatic states simulated by a 2-dimensional model Part I: Sensitivity of the model and present state

The criterion, based on the thermodynamics theory, that the climatic system tends to extremizesome function has suggested several studies. In particular, special attention has been devoted to the possibility that the climate reaches an extremal rate of planetary entropy production.Due to both radiative and material effects contribute to total planetary entropy production,climatic simulations obtained at the extremal rates of total, radiative or material entropy production appear to be of interest in order to elucidate which of the three extremal assumptions behaves more similar to current data. In the present paper, these results have been obtainedby applying a 2-dimensional (2-Dim) horizontal energy balance box-model, with a few independent variables (surface temperature, cloud-cover and material heat fluxes). In addition, climatic simulations for current conditions by assuming a fixed cloud-cover have been obtained. Finally,sensitivity analyses for both variable and fixed cloud models have been carried out

Extremal climatic states simulated by a 2-dimensional model Part II: Different climatic scenarios

Different climatic simulations have been obtained by using a 2-Dim horizontal energy balancemodel (EBM), which has been constrained to satisfy several extremal principles on dissipationand convection. Moreover, 2 different versions of the model with fixed and variable cloud-coverhave been used. The assumption of an extremal type of behaviour for the climatic system canacquire additional support depending on the similarities found with measured data for pastconditions as well as with usual projections for possible future scenarios

Trinocular System for 3D motion and Dense Stucture Estimation

The relief of the seafloor is an important source of data for many scientists. In this paper we present an optical system to deal with underwater 3D reconstruction. This system is formed by three cameras that take images synchronously in a constant frame rate scheme. We use the images taken by these cameras to compute dense 3D reconstructions. We use Bundle Adjustment to estimate the motion ofthe trinocular rig. Given the path followed by the system, we get a dense map of the observed scene by registering the different dense local reconstructions in a unique and bigger one

Critical behavior of a system with orientational and positional degrees of freedom: A Monte Carlo simulation study

The critical behavior of a system constituted by molecules with a preferred symmetry axis is studied by means of a Monte Carlo simulation of a simplified two-dimensional model. The system exhibits two phase transitions, associated with the vanishing of the positional order of the center of mass of the molecules and with the orientational order of the symmetry axis. The evolution of the order parameters and the specific heat is also studied. The transition associated with the positional degrees of freedom is found to change from a second-order to a first-order behavior when the two phase transitions are close enough, due to the coupling with the orientational degrees of freedom. This fact is qualitatively compared with similar results found in pure liquid crystals and liquid-crystal mixtures.

Vacancy-driven ordering in a two-dimensional binary alloy

Domain growth in a system with nonconserved order parameter is studied. We simulate the usual Ising model for binary alloys with concentration 0.5 on a two-dimensional square lattice by Monte Carlo techniques. Measurements of the energy, jump-acceptance ratio, and order parameters are performed. Dynamics based on the diffusion of a single vacancy in the system gives a growth law faster than the usual Allen-Cahn law. Allowing vacancy jumps to next-nearest-neighbor sites is essential to prevent vacancy trapping in the ordered regions. By measuring local order parameters we show that the vacancy prefers to be in the disordered regions (domain boundaries). This naturally concentrates the atomic jumps in the domain boundaries, accelerating the growth compared with the usual exchange mechanism that causes jumps to be homogeneously distributed on the lattice.

Hysteresis and avalanches in the T=0 random field ising model with 2-spin flip dynamics

We study the nonequilibrium behavior of the three-dimensional Gaussian random-field Ising model at T=0 in the presence of a uniform external field using a two-spin-flip dynamics. The deterministic, history-dependent evolution of the system is compared with the one obtained with the standard one-spin-flip dynamics used in previous studies of the model. The change in the dynamics yields a significant suppression of coercivity, but the distribution of avalanches (in number and size) stays remarkably similar, except for the largest ones that are responsible for the jump in the saturation magnetization curve at low disorder in the thermodynamic limit. By performing a finite-size scaling study, we find strong evidence that the change in the dynamics does not modify the universality class of the disorder-induced phase transition.

Pairing in two-dimensional boson-fermion mixtures

The possibilities of pairing in two-dimensional boson-fermion mixtures are carefully analyzed. It is shown that the boson-induced attraction between two identical fermions dominates the p wave pairing at low density. For a given fermion density, the pairing gap becomes maximal at a certain optimal boson concentration. The conditions for observing pairing in current experiments are discussed.

From subdiffusion to superdiffusion of particles on solid surfaces

We present a numerical and partially analytical study of classical particles obeying a Langevin equation that describes diffusion on a surface modeled by a two-dimensional potential. The potential may be either periodic or random. Depending on the potential and the damping, we observe superdiffusion, large-step diffusion, diffusion, and subdiffusion. Superdiffusive behavior is associated with low damping and is in most cases transient, albeit often long. Subdiffusive behavior is associated with highly damped particles in random potentials. In some cases subdiffusive behavior persists over our entire simulation and may be characterized as metastable. In any case, we stress that this rich variety of behaviors emerges naturally from an ordinary Langevin equation for a system described by ordinary canonical Maxwell-Boltzmann statistics.