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

A systolic array for linear MIMO detection based on an all-swap lattice reduction algorithm

A systolic array to implement lattice-reduction-aided lineardetection is proposed for a MIMO receiver. The lattice reductionalgorithm and the ensuing linear detections are operated in the same array, which can be hardware-efficient. All-swap lattice reduction algorithm (ASLR) is considered for the systolic design.ASLR is a variant of the LLL algorithm, which processes all lattice basis vectors within one iteration. Lattice-reduction-aided linear detection based on ASLR and LLL algorithms have very similarbit-error-rate performance, while ASLR is more time efficient inthe systolic array, especially for systems with a large number ofantennas.

Towards robust network based complex systems : from evolutionary cellular automata to biological models

Abstract Sitting between your past and your future doesn't mean you are in the present. Dakota Skye Complex systems science is an interdisciplinary field grouping under the same umbrella dynamical phenomena from social, natural or mathematical sciences. The emergence of a higher order organization or behavior, transcending that expected of the linear addition of the parts, is a key factor shared by all these systems. Most complex systems can be modeled as networks that represent the interactions amongst the system's components. In addition to the actual nature of the part's interactions, the intrinsic topological structure of underlying network is believed to play a crucial role in the remarkable emergent behaviors exhibited by the systems. Moreover, the topology is also a key a factor to explain the extraordinary flexibility and resilience to perturbations when applied to transmission and diffusion phenomena. In this work, we study the effect of different network structures on the performance and on the fault tolerance of systems in two different contexts. In the first part, we study cellular automata, which are a simple paradigm for distributed computation. Cellular automata are made of basic Boolean computational units, the cells; relying on simple rules and information from- the surrounding cells to perform a global task. The limited visibility of the cells can be modeled as a network, where interactions amongst cells are governed by an underlying structure, usually a regular one. In order to increase the performance of cellular automata, we chose to change its topology. We applied computational principles inspired by Darwinian evolution, called evolutionary algorithms, to alter the system's topological structure starting from either a regular or a random one. The outcome is remarkable, as the resulting topologies find themselves sharing properties of both regular and random network, and display similitudes Watts-Strogtz's small-world network found in social systems. Moreover, the performance and tolerance to probabilistic faults of our small-world like cellular automata surpasses that of regular ones. In the second part, we use the context of biological genetic regulatory networks and, in particular, Kauffman's random Boolean networks model. In some ways, this model is close to cellular automata, although is not expected to perform any task. Instead, it simulates the time-evolution of genetic regulation within living organisms under strict conditions. The original model, though very attractive by it's simplicity, suffered from important shortcomings unveiled by the recent advances in genetics and biology. We propose to use these new discoveries to improve the original model. Firstly, we have used artificial topologies believed to be closer to that of gene regulatory networks. We have also studied actual biological organisms, and used parts of their genetic regulatory networks in our models. Secondly, we have addressed the improbable full synchronicity of the event taking place on. Boolean networks and proposed a more biologically plausible cascading scheme. Finally, we tackled the actual Boolean functions of the model, i.e. the specifics of how genes activate according to the activity of upstream genes, and presented a new update function that takes into account the actual promoting and repressing effects of one gene on another. Our improved models demonstrate the expected, biologically sound, behavior of previous GRN model, yet with superior resistance to perturbations. We believe they are one step closer to the biological reality.

The achievable region approach to the optimal control of stochastic systems

The achievable region approach seeks solutions to stochastic optimisation problems by: (i) characterising the space of all possible performances(the achievable region) of the system of interest, and (ii) optimisingthe overall system-wide performance objective over this space. This isradically different from conventional formulations based on dynamicprogramming. The approach is explained with reference to a simpletwo-class queueing system. Powerful new methodologies due to the authorsand co-workers are deployed to analyse a general multiclass queueingsystem with parallel servers and then to develop an approach to optimalload distribution across a network of interconnected stations. Finally,the approach is used for the first time to analyse a class of intensitycontrol problems.

Assessment of speed of human locomotion using a differential satellite global positioning system.

PURPOSE: The objective was to explore whether a satellite-based navigation system, global positioning system used in differential mode (DGPS), could accurately assess the speed of running in humans. METHODS: A subject was equipped with a portable GPS receptor coupled to a receiver for differential corrections, while running outdoors on a straight asphalt road at 27 different speeds. Actual speed (reference method) was assessed by chronometry. RESULTS: The accuracy of speed prediction had a standard deviation (SD) of 0.08 km x h(-1) for walking, 0.11 km x h(-1) for running, yielding a coefficient of variation (SD/mean) of 1.38% and 0.82%, respectively. There was a highly significant linear relationship between actual and DGPS speed assessment (r2 = 0.999) with little bias in the prediction equation, because the slope of the regression line was close to unity (0.997). CONCLUSION: the DGPS technique appears to be a valid and inconspicuous tool for "on line" monitoring of the speed of displacement of individuals located on any field on earth, for prolonged periods of time and unlimited distance, but only in specific environmental conditions ("open sky"). Furthermore, the accuracy of speed assessment using the differential GPS mode was improved by a factor of 10 as compared to non-differential GPS.

Unified formalism for non-autonomous mechanical systems

We present a unified geometric framework for describing both the Lagrangian and Hamiltonian formalisms of regular and non-regular time-dependent mechanical systems, which is based on the approach of Skinner and Rusk (1983). The dynamical equations of motion and their compatibility and consistency are carefully studied, making clear that all the characteristics of the Lagrangian and the Hamiltonian formalisms are recovered in this formulation. As an example, it is studied a semidiscretization of the nonlinear wave equation proving the applicability of the proposed formalism.

Maximum-likelihood estimation of specific differential phase and attenuation in rain

Precise estimation of propagation parameters inprecipitation media is of interest to improve the performanceof communications systems and in remote sensing applications.In this paper, we present maximum-likelihood estimators ofspecific attenuation and specific differential phase in rain. Themodel used for obtaining the cited estimators assumes coherentpropagation, reflection symmetry of the medium, and Gaussianstatistics of the scattering matrix measurements. No assumptionsabout the microphysical properties of the medium are needed.The performance of the estimators is evaluated through simulateddata. Results show negligible estimators bias and variances closeto Cramer–Rao bounds.

Transcript profiling suggests that differential metabolic adaptation of mice to a high fat diet is associated with changes in liver to muscle lipid fluxes.

Genetically homogenous C57Bl/6 mice display differential metabolic adaptation when fed a high fat diet for 9 months. Most become obese and diabetic, but a significant fraction remains lean and diabetic or lean and non-diabetic. Here, we performed microarray analysis of "metabolic" transcripts expressed in liver and hindlimb muscles to evaluate: (i) whether expressed transcript patterns could indicate changes in metabolic pathways associated with the different phenotypes, (ii) how these changes differed from the early metabolic adaptation to short term high fat feeding, and (iii) whether gene classifiers could be established that were characteristic of each metabolic phenotype. Our data indicate that obesity/diabetes was associated with preserved hepatic lipogenic gene expression and increased plasma levels of very low density lipoprotein and, in muscle, with an increase in lipoprotein lipase gene expression. This suggests increased muscle fatty acid uptake, which may favor insulin resistance. In contrast, the lean mice showed a strong reduction in the expression of hepatic lipogenic genes, in particular of Scd-1, a gene linked to sensitivity to diet-induced obesity; the lean and non-diabetic mice presented an additional increased expression of eNos in liver. After 1 week of high fat feeding the liver gene expression pattern was distinct from that seen at 9 months in any of the three mouse groups, thus indicating progressive establishment of the different phenotypes. Strikingly, development of the obese phenotype involved re-expression of Scd-1 and other lipogenic genes. Finally, gene classifiers could be established that were characteristic of each metabolic phenotype. Together, these data suggest that epigenetic mechanisms influence gene expression patterns and metabolic fates.

Carbon stock and its compartments in a subtropical oxisol under long-term tillage and crop rotation systems

Soil organic matter (SOM) plays a crucial role in soil quality and can act as an atmospheric C-CO2 sink under conservationist management systems. This study aimed to evaluate the long-term effects (19 years) of tillage (CT-conventional tillage and NT-no tillage) and crop rotations (R0-monoculture system, R1-winter crop rotation, and R2- intensive crop rotation) on total, particulate and mineral-associated organic carbon (C) stocks of an originally degraded Red Oxisol in Cruz Alta, RS, Southern Brazil. The climate is humid subtropical Cfa 2a (Köppen classification), the mean annual precipitation 1,774 mm and mean annual temperature 19.2 ºC. The plots were divided into four segments, of which each was sampled in the layers 0-0.05, 0.05-0.10, 0.10-0.20, and 0.20-0.30 m. Sampling was performed manually by opening small trenches. The SOM pools were determined by physical fractionation. Soil C stocks had a linear relationship with annual crop C inputs, regardless of the tillage systems. Thus, soil disturbance had a minor effect on SOM turnover. In the 0-0.30 m layer, soil C sequestration ranged from 0 to 0.51 Mg ha-1 yr-1, using the CT R0 treatment as base-line; crop rotation systems had more influence on soil stock C than tillage systems. The mean C sequestration rate of the cropping systems was 0.13 Mg ha-1 yr-1 higher in NT than CT. This result was associated to the higher C input by crops due to the improvement in soil quality under long-term no-tillage. The particulate C fraction was a sensitive indicator of soil management quality, while mineral-associated organic C was the main pool of atmospheric C fixed in this clayey Oxisol. The C retention in this stable SOM fraction accounts for 81 and 89 % of total C sequestration in the treatments NT R1 and NT R2, respectively, in relation to the same cropping systems under CT. The highest C management index was observed in NT R2, confirming the capacity of this soil management practice to improve the soil C stock qualitatively in relation to CT R0. The results highlighted the diversification of crop rotation with cover crops as a crucial strategy for atmospheric C-CO2 sequestration and SOM quality improvement in highly weathered subtropical Oxisols.

Higher-order colored-noise effects in multivariable systems

We extend the partial resummation technique of Fokker-Planck terms for multivariable stochastic differential equations with colored noise. As an example, a model system of a Brownian particle with colored noise is studied. We prove that the asymmetric behavior found in analog simulations is due to higher-order terms which are left out in that technique. On the contrary, the systematic ¿-expansion approach can explain the analog results.

Interfacial growth in driven diffusive systems

We have studied the growth of interfaces in driven diffusive systems well below the critical temperature by means of Monte Carlo simulations. We consider the region beyond the linear regime and of large values of the external field which has not been explored before. The simulations support the existence of interfacial traveling waves when asymmetry is introduced in the model, a result previously predicted by a linear-stability analysis. Furthermore, the generalization of the Gibbs-Thomson relation is discussed. The results provide evidence that the external field is a stabilizing effect which can be considered as effectively increasing the surface tension.

Intrinsic noise-induced phase transitions: Beyond the noise interpretation

We discuss intrinsic noise effects in stochastic multiplicative-noise partial differential equations, which are qualitatively independent of the noise interpretation (Itô vs Stratonovich), in particular in the context of noise-induced ordering phase transitions. We study a model which, contrary to all cases known so far, exhibits such ordering transitions when the noise is interpreted not only according to Stratonovich, but also to Itô. The main feature of this model is the absence of a linear instability at the transition point. The dynamical properties of the resulting noise-induced growth processes are studied and compared in the two interpretations and with a reference Ginzburg-Landau-type model. A detailed discussion of a different numerical algorithm valid for both interpretations is also presented.

Dynamical Systems approach to Saffman-Taylor fingering. A Dynamical Solvability Scenario

A dynamical systems approach to competition of Saffman-Taylor fingers in a Hele-Shaw channel is developed. This is based on global analysis of the phase space flow of the low-dimensional ordinary-differential-equation sets associated with the classes of exact solutions of the problem without surface tension. Some simple examples are studied in detail. A general proof of the existence of finite-time singularities for broad classes of solutions is given. Solutions leading to finite-time interface pinchoff are also identified. The existence of a continuum of multifinger fixed points and its dynamical implications are discussed. We conclude that exact zero-surface tension solutions taken in a global sense as families of trajectories in phase space are unphysical because the multifinger fixed points are nonhyperbolic, and an unfolding does not exist within the same class of solutions. Hyperbolicity (saddle-point structure) of the multifinger fixed points is argued to be essential to the physically correct qualitative description of finger competition. The restoring of hyperbolicity by surface tension is proposed as the key point to formulate a generic dynamical solvability scenario for interfacial pattern selection.

Dynamical properties of nonmarkovian stochastic differential equations

We study nonstationary non-Markovian processes defined by Langevin-type stochastic differential equations with an OrnsteinUhlenbeck driving force. We concentrate on the long time limit of the dynamical evolution. We derive an approximate equation for the correlation function of a nonlinear nonstationary non-Markovian process, and we discuss its consequences. Non-Markovicity can introduce a dependence on noise parameters in the dynamics of the correlation function in cases in which it becomes independent of these parameters in the Markovian limit. Several examples are discussed in which the relaxation time increases with respect to the Markovian limit. For a Brownian harmonic oscillator with fluctuating frequency, the non-Markovicity of the process decreases the domain of stability of the system, and it can change an infradamped evolution into an overdamped one.

Hamilton Jacobi theory for constrained systems

We extend the HamiltonJacobi formulation to constrained dynamical systems. The discussion covers both the case of first-class constraints alone and that of first- and second-class constraints combined. The HamiltonDirac equations are recovered as characteristic of the system of partial differential equations satisfied by the HamiltonJacobi function.