Scaling, self-similar solutions and shock waves for V-shaped field potentials

We investigate a (1+1)-dimensional nonlinear field theoretic model with the field potential $V(\phi)| = |\phi|.$ It can be obtained as the universal small amplitude limit in a class of models with potentials which are symmetrically V-shaped at their minima, or as a continuum limit of certain mechanical system with infinite number of degrees of freedom. The model has an interesting scaling symmetry of the 'on shell' type. We find self-similar as well as shock wave solutions of the field equation in that model.Comment: Two comments and one reference adde

Decision landscapes:Visualizing mouse-tracking data

Computerized paradigms have enabled gathering rich data on human behaviour, including information on motor execution of a decision, e.g. by tracking mouse cursor trajectories. These trajectories can reveal novel information about ongoing decision processes. As the number and complexity of mouse-tracking studies increase, more sophisticated methods are needed to analyse the decision trajectories. Here, we present a new computational approach to generating decision landscape visualizations based on mouse-tracking data. A decision landscape is an analogue of an energy potential field mathematically derived from the velocity of mouse movement during a decision. Visualized as a three-dimensional surface, it provides a comprehensive overview of decision dynamics. Employing the dynamical systems theory framework, we develop a new method for generating decision landscapes based on arbitrary number of trajectories. This approach not only generates three-dimensional illustration of decision landscapes, but also describes mouse trajectories by a number of interpretable parameters. These parameters characterize dynamics of decisions in more detail compared with conventional measures, and can be compared across experimental conditions, and even across individuals. The decision landscape visualization approach is a novel tool for analysing mouse trajectories during decision execution, which can provide new insights into individual differences in the dynamics of decision making

Besov priors for Bayesian inverse problems

We consider the inverse problem of estimating a function $u$ from noisy, possibly nonlinear, observations. We adopt a Bayesian approach to the problem. This approach has a long history for inversion, dating back to 1970, and has, over the last decade, gained importance as a practical tool. However most of the existing theory has been developed for Gaussian prior measures. Recently Lassas, Saksman and Siltanen (Inv. Prob. Imag. 2009) showed how to construct Besov prior measures, based on wavelet expansions with random coefficients, and used these prior measures to study linear inverse problems. In this paper we build on this development of Besov priors to include the case of nonlinear measurements. In doing so a key technical tool, established here, is a Fernique-like theorem for Besov measures. This theorem enables us to identify appropriate conditions on the forward solution operator which, when matched to properties of the prior Besov measure, imply the well-definedness and well-posedness of the posterior measure. We then consider the application of these results to the inverse problem of finding the diffusion coefficient of an elliptic partial differential equation, given noisy measurements of its solution.Comment: 18 page

Theory of differential inclusions and its application in mechanics

The following chapter deals with systems of differential equations with discontinuous right-hand sides. The key question is how to define the solutions of such systems. The most adequate approach is to treat discontinuous systems as systems with multivalued right-hand sides (differential inclusions). In this work three well-known definitions of solution of discontinuous system are considered. We will demonstrate the difference between these definitions and their application to different mechanical problems. Mathematical models of drilling systems with discontinuous friction torque characteristics are considered. Here, opposite to classical Coulomb symmetric friction law, the friction torque characteristic is asymmetrical. Problem of sudden load change is studied. Analytical methods of investigation of systems with such asymmetrical friction based on the use of Lyapunov functions are demonstrated. The Watt governor and Chua system are considered to show different aspects of computer modeling of discontinuous systems

Do Humans Optimally Exploit Redundancy to Control Step Variability in Walking?

It is widely accepted that humans and animals minimize energetic cost while walking. While such principles predict average behavior, they do not explain the variability observed in walking. For robust performance, walking movements must adapt at each step, not just on average. Here, we propose an analytical framework that reconciles issues of optimality, redundancy, and stochasticity. For human treadmill walking, we defined a goal function to formulate a precise mathematical definition of one possible control strategy: maintain constant speed at each stride. We recorded stride times and stride lengths from healthy subjects walking at five speeds. The specified goal function yielded a decomposition of stride-to-stride variations into new gait variables explicitly related to achieving the hypothesized strategy. Subjects exhibited greatly decreased variability for goal-relevant gait fluctuations directly related to achieving this strategy, but far greater variability for goal-irrelevant fluctuations. More importantly, humans immediately corrected goal-relevant deviations at each successive stride, while allowing goal-irrelevant deviations to persist across multiple strides. To demonstrate that this was not the only strategy people could have used to successfully accomplish the task, we created three surrogate data sets. Each tested a specific alternative hypothesis that subjects used a different strategy that made no reference to the hypothesized goal function. Humans did not adopt any of these viable alternative strategies. Finally, we developed a sequence of stochastic control models of stride-to-stride variability for walking, based on the Minimum Intervention Principle. We demonstrate that healthy humans are not precisely “optimal,” but instead consistently slightly over-correct small deviations in walking speed at each stride. Our results reveal a new governing principle for regulating stride-to-stride fluctuations in human walking that acts independently of, but in parallel with, minimizing energetic cost. Thus, humans exploit task redundancies to achieve robust control while minimizing effort and allowing potentially beneficial motor variability

A model species for agricultural pest genomics: the genome of the Colorado potato beetle, Leptinotarsa decemlineata (Coleoptera: Chrysomelidae)

The Colorado potato beetle is one of the most challenging agricultural pests to manage. It has shown a spectacular ability to adapt to a variety of solanaceaeous plants and variable climates during its global invasion, and, notably, to rapidly evolve insecticide resistance. To examine evidence of rapid evolutionary change, and to understand the genetic basis of herbivory and insecticide resistance, we tested for structural and functional genomic changes relative to other arthropod species using genome sequencing, transcriptomics, and community annotation. Two factors that might facilitate rapid evolutionary change include transposable elements, which comprise at least 17% of the genome and are rapidly evolving compared to other Coleoptera, and high levels of nucleotide diversity in rapidly growing pest populations. Adaptations to plant feeding are evident in gene expansions and differential expression of digestive enzymes in gut tissues, as well as expansions of gustatory receptors for bitter tasting. Surprisingly, the suite of genes involved in insecticide resistance is similar to other beetles. Finally, duplications in the RNAi pathway might explain why Leptinotarsa decemlineata has high sensitivity to dsRNA. The L. decemlineata genome provides opportunities to investigate a broad range of phenotypes and to develop sustainable methods to control this widely successful pest

An update of the Worldwide Integrated Assessment (WIA) on systemic insecticides. Part 2: impacts on organisms and ecosystems

New information on the lethal and sublethal effects of neonicotinoids and fipronil on organisms is presented in this review, complementing the previous WIA in 2015. The high toxicity of these systemic insecticides to invertebrates has been confirmed and expanded to include more species and compounds. Most of the recent research has focused on bees and the sublethal and ecological impacts these insecticides have on pollinators. Toxic effects on other invertebrate taxa also covered predatory and parasitoid natural enemies and aquatic arthropods. Little, while not much new information has been gathered on soil organisms. The impact on marine coastal ecosystems is still largely uncharted. The chronic lethality of neonicotinoids to insects and crustaceans, and the strengthened evidence that these chemicals also impair the immune system and reproduction, highlights the dangers of this particular insecticidal classneonicotinoids and fipronil. , withContinued large scale – mostly prophylactic – use of these persistent organochlorine pesticides has the potential to greatly decreasecompletely eliminate populations of arthropods in both terrestrial and aquatic environments. Sublethal effects on fish, reptiles, frogs, birds and mammals are also reported, showing a better understanding of the mechanisms of toxicity of these insecticides in vertebrates, and their deleterious impacts on growth, reproduction and neurobehaviour of most of the species tested. This review concludes with a summary of impacts on the ecosystem services and functioning, particularly on pollination, soil biota and aquatic invertebrate communities, thus reinforcing the previous WIA conclusions (van der Sluijs et al. 2015)