Viability Kernels of Higher Order

AMS subject classification: Primary 34A60, Secondary 49K24.

Liquid polymorphism, order-disorder transitions and anomalous behavior: A Monte Carlo study of the Bell-Lavis model for water

The Bell-Lavis model for liquid water is investigated through numerical simulations. The lattice-gas model on a triangular lattice presents orientational states and is known to present a highly bonded low density phase and a loosely bonded high density phase. We show that the model liquid-liquid transition is continuous, in contradiction with mean-field results on the Husimi cactus and from the cluster variational method. We define an order parameter which allows interpretation of the transition as an order-disorder transition of the bond network. Our results indicate that the order-disorder transition is in the Ising universality class. Previous proposal of an Ehrenfest second order transition is discarded. A detailed investigation of anomalous properties has also been undertaken. The line of density maxima in the HDL phase is stabilized by fluctuations, absent in the mean-field solution. (C) 2009 American Institute of Physics. [doi:10.1063/1.3253297]

Design constraints for third-order PLL nodes in master-slave clock distribution networks

Clock signal distribution in telecommunication commercial systems usually adopts a master-slave architecture, with a precise time basis generator as a master and phase-locked loops (PLLs) as slaves. In the majority of the networks, second-order PLLs are adopted due to their simplicity and stability. Nevertheless, in some applications better transient responses are necessary and, consequently, greater order PLLs need to be used, in spite of the possibility of bifurcations and chaotic attractors. Here a master-slave network with third-order PLLs is analyzed and conditions for the stability of the synchronous state are derived, providing design constraints for the node parameters, in order to guarantee stability and reachability of the synchronous state for the whole network. Numerical simulations are carried out in order to confirm the analytical results. (C) 2009 Elsevier B.V. All rights reserved.

Using bifurcations in the determination of lock-in ranges for third-order phase-locked loops

Transmission and switching in digital telecommunication networks require distribution of precise time signals among the nodes. Commercial systems usually adopt a master-slave (MS) clock distribution strategy building slave nodes with phase-locked loop (PLL) circuits. PLLs are responsible for synchronizing their local oscillations with signals from master nodes, providing reliable clocks in all nodes. The dynamics of a PLL is described by an ordinary nonlinear differential equation, with order one plus the order of its internal linear low-pass filter. Second-order loops are commonly used because their synchronous state is asymptotically stable and the lock-in range and design parameters are expressed by a linear equivalent system [Gardner FM. Phaselock techniques. New York: John Wiley & Sons: 1979]. In spite of being simple and robust, second-order PLLs frequently present double-frequency terms in PD output and it is very difficult to adapt a first-order filter in order to cut off these components [Piqueira JRC, Monteiro LHA. Considering second-harmonic terms in the operation of the phase detector for second order phase-locked loop. IEEE Trans Circuits Syst [2003;50(6):805-9; Piqueira JRC, Monteiro LHA. All-pole phase-locked loops: calculating lock-in range by using Evan`s root-locus. Int J Control 2006;79(7):822-9]. Consequently, higher-order filters are used, resulting in nonlinear loops with order greater than 2. Such systems, due to high order and nonlinear terms, depending on parameters combinations, can present some undesirable behaviors, resulting from bifurcations, as error oscillation and chaos, decreasing synchronization ranges. In this work, we consider a second-order Sallen-Key loop filter [van Valkenburg ME. Analog filter design. New York: Holt, Rinehart & Winston; 1982] implying a third order PLL The resulting lock-in range of the third-order PLL is determined by two bifurcation conditions: a saddle-node and a Hopf. (C) 2008 Elsevier B.V. All rights reserved.

Truncation errors in finite difference models for solute transport equation with first-order reaction

The truncation errors associated with finite difference solutions of the advection-dispersion equation with first-order reaction are formulated from a Taylor analysis. The error expressions are based on a general form of the corresponding difference equation and a temporally and spatially weighted parametric approach is used for differentiating among the various finite difference schemes. The numerical truncation errors are defined using Peclet and Courant numbers and a new Sink/Source dimensionless number. It is shown that all of the finite difference schemes suffer from truncation errors. Tn particular it is shown that the Crank-Nicolson approximation scheme does not have second order accuracy for this case. The effects of these truncation errors on the solution of an advection-dispersion equation with a first order reaction term are demonstrated by comparison with an analytical solution. The results show that these errors are not negligible and that correcting the finite difference scheme for them results in a more accurate solution. (C) 1999 Elsevier Science B.V. All rights reserved.

Choice of macroinvertebrate metrics to evaluate stream conditions in Atlantic Forest, Brazil

The development of biomonitoring programs based on the macroinvertebrate community requires the understanding of species distribution patterns, as well as of the responses of the community to anthropogenic stressors. In this study, 49 metrics were tested as potential means of assessing the condition of 29 first- and second-order streams located in areas of differing types of land use in So Paulo State, Brazil. Of the sampled streams, 15 were in well-preserved regions in the Atlantic Forest, 5 were among sugarcane cultivations, 5 were in areas of pasture, and 4 were among eucalyptus plantations. The metrics were assessed against the following criteria: (1) predictable response to the impact of human activity; (2) highest taxonomic resolution, and (3) operational and theoretical simplicity. We found that 18 metrics were correlated with the environmental and spatial predictors used, and seven of these satisfied the selection criteria and are thus candidates for inclusion in a multimetric system to assess low-order streams in So Paulo State. These metrics are family richness; Ephemeroptera, Plecoptera and Trichoptera (EPT) richness; proportion of Megaloptera and Hirudinea; proportion of EPT; Shannon diversity index for genus; and adapted Biological Monitoring Work Party biotic index.

Factorization by invariant embedding of elliptic problems: circular and star-shaped domains

Dissertação apresentada para obtenção do grau de Doutor em Matemática na especialidade de Equações Diferenciais, pela Universidade Nova de Lisboa,Faculdade de Ciências e Tecnologia

Contracting Institutions and Development

The quality of contracting institutions has been thought to be of second-order importance next to the impact that good property rights institutions can have on long-run growth. Using a large range of proxies for each type of institution, we find a robust negative link between the quality of contracting institutions and long-run growth when we condition on property rights and a number of additional macroeconomic variables. Although the result remains something of a puzzle, we present evidence which suggests that only when property rights institutions are good do contracting institutions appear also to be good for development. Good contracting institutions can reduce long-run growth when property rights are not secured, presumably because the gains from the (costly) contracting institutions cannot be realised. This suggests that contracting institutions can benefit growth, and that the sequence of institutional change can matter.

Evolutionary and convergence stability for continuous phenotypes in finite populations derived from two-allele models.

The evolution of a quantitative phenotype is often envisioned as a trait substitution sequence where mutant alleles repeatedly replace resident ones. In infinite populations, the invasion fitness of a mutant in this two-allele representation of the evolutionary process is used to characterize features about long-term phenotypic evolution, such as singular points, convergence stability (established from first-order effects of selection), branching points, and evolutionary stability (established from second-order effects of selection). Here, we try to characterize long-term phenotypic evolution in finite populations from this two-allele representation of the evolutionary process. We construct a stochastic model describing evolutionary dynamics at non-rare mutant allele frequency. We then derive stability conditions based on stationary average mutant frequencies in the presence of vanishing mutation rates. We find that the second-order stability condition obtained from second-order effects of selection is identical to convergence stability. Thus, in two-allele systems in finite populations, convergence stability is enough to characterize long-term evolution under the trait substitution sequence assumption. We perform individual-based simulations to confirm our analytic results.

GNSS signal detection based on first-order absolute statistics

Aquest projecte es centra principalment en el detector no coherent d’un GPS. Per tal de caracteritzar el procés de detecció d’un receptor, es necessita conèixer l’estadística implicada. Pel cas dels detectors no coherents convencionals, l’estadística de segon ordre intervé plenament. Les prestacions que ens dóna l’estadística de segon ordre, plasmada en la ROC, són prou bons tot i que en diferents situacions poden no ser els millors. Aquest projecte intenta reproduir el procés de detecció mitjançant l’estadística de primer ordre com a alternativa a la ja coneguda i implementada estadística de segon ordre. Per tal d’aconseguir-ho, s’usen expressions basades en el Teorema Central del Límit i de les sèries Edgeworth com a bones aproximacions. Finalment, tant l’estadística convencional com l’estadística proposada són comparades, en termes de la ROC, per tal de determinar quin detector no coherent ofereix millor prestacions en cada situació.

A reduction of order two for infinite-order Lagrangians

Given a Lagrangian system depending on the position derivatives of any order, and assuming that certain conditions are satisfied, a second-order differential system is obtained such that its solutions also satisfy the Euler equations derived from the original Lagrangian. A generalization of the singular Lagrangian formalism permits a reduction of order keeping the canonical formalism in sight. Finally, the general results obtained in the first part of the paper are applied to Wheeler-Feynman electrodynamics for two charged point particles up to order 1/c4.

The evolution of anti-social rewarding and its countermeasures in public goods games.

Cooperation in joint enterprises can easily break down when self-interests are in conflict with collective benefits, causing a tragedy of the commons. In such social dilemmas, the possibility for contributors to invest in a common pool-rewards fund, which will be shared exclusively among contributors, can be powerful for averting the tragedy, as long as the second-order dilemma (i.e. withdrawing contribution to reward funds) can be overcome (e.g. with second-order sanctions). However, the present paper reveals the vulnerability of such pool-rewarding mechanisms to the presence of reward funds raised by defectors and shared among them (i.e. anti-social rewarding), as it causes a cooperation breakdown, even when second-order sanctions are possible. I demonstrate that escaping this social trap requires the additional condition that coalitions of defectors fare poorly compared with pro-socials, with either (i) better rewarding abilities for the latter or (ii) reward funds that are contingent upon the public good produced beforehand, allowing groups of contributors to invest more in reward funds than groups of defectors. These results suggest that the establishment of cooperation through a collective positive incentive mechanism is highly vulnerable to anti-social rewarding and requires additional countermeasures to act in combination with second-order sanctions.

Increased eeg synchronization in schizophrenia patients by the glutathione precursor, n-acetyl-cysteine

Background: Glutathione (GSH) dysregulation at the gene, protein and functional levels observed in schizophrenia patients, and schizophrenia-like anomalies in GSH deficit experimental models, suggest that genetic glutathione synthesis impairments represent one major risk factor for the disease (Do et al., 2009). In a randomized, double blind, placebo controlled, add-on clinical trial of 140 patients, the GSH precursor N-Acetyl-Cysteine (NAC, 2 g/day, 6 months) significantly improved the negative symptoms and reduced side-effects due to antipsychotics (Berk et al., 2008). In a subset of patients (n=7), NAC (2 g/day, 2 months, cross-over design) also improved auditory evoked potentials, the NMDAdependent mismatch negativity (Lavoie et al, 2008). Methods: To determine whether increased GSH levels would modulate the topography of functional brain connectivity, we applied a multivariate phase synchronization (MPS) estimator (Knyazeva et al, 2008) to dense-array EEGs recorded during rest with eyes closed at the protocol onset, the point of crossover, and at its end. Phase synchronization phenomena are appealing because they can be associated to synchronized phases while the amplitudes stay uncorrelated. MPS measures the degree of interactions among the recorded neuronal oscillators by quantifiying to what extent they behave like a macro-oscillator (i.e. the oscillators are phase synchronous). To assess the whole-head synchronization topography, we computed the MPS sensor-wise over the cluster of locations defined by the sensor itself and he surrounding ones belonging to its second-order neighborhood (Carmeli et al, 2005). Such a cluster spans about 12 cm on average. Abstracts 245 Results: The whole-head imaging revealed a specific synchronization landscape in NAC compared to placebo condition. In particular, NAC increased MPS over frontal and left temporal regions in a frequency-specific manner. Importantly, the topography and direction of MPS changes were similar and robust in all 7 patients. Moreover, these changes correlated with the changes in the Liddle's score of disorganization (Liddle, 1987) thus linking EEG synchronization to the improvement of clinical picture. Discussion: The data suggest an important pathway towards new therapeutic strategies that target GSH dysregulation in schizophrenia. They also show the utility of MPS mapping as a marker of treatment efficacy.

Perception of acceleration in motion-in-depth with only monocular and both monocular and binocular information

Observers are often required to adjust actions with objects that change their speed. However, no evidence for a direct sense of acceleration has been found so far. Instead, observers seem to detect changes in velocity within a temporal window when confronted with motion in the frontal plane (2D motion). Furthermore, recent studies suggest that motion-in-depth is detected by tracking changes of position in depth. Therefore, in order to sense acceleration in depth a kind of second-order computation would have to be carried out by the visual system. In two experiments, we show that observers misperceive acceleration of head-on approaches at least within the ranges we used [600-800 ms] resulting in an overestimation of arrival time. Regardless of the viewing condition (only monocular or monocular and binocular), the response pattern conformed to a constant velocity strategy. However, when binocular information was available, overestimation was highly reduced.

Separação de espectros simulados e de luminescência total através do método generalizado de anulação do posto (GRAM)

A multivariate curve resolution method, "GENERALIZED RANK ANNIHILATION METHOD (GRAM)", is discussed and tested with simulated and experimental data. The analysis of simulated data provides general guidelines concerning the condition for uniqueness of a solution for a given problem. The second-order emission-excitation spectra of human and animal dental calculus deposits were used as an experimental data to estimate the performance of the above method. Three porphyrinic spectral profiles, for both human and cat, were obtained by the use of GRAM.