Exploring Graphs with Time Constraints by Unreliable Collections of Mobile Robots

A graph environment must be explored by a collection of mobile robots. Some of the robots, a priori unknown, may turn out to be unreliable. The graph is weighted and each node is assigned a deadline. The exploration is successful if each node of the graph is visited before its deadline by a reliable robot. The edge weight corresponds to the time needed by a robot to traverse the edge. Given the number of robots which may crash, is it possible to design an algorithm, which will always guarantee the exploration, independently of the choice of the subset of unreliable robots by the adversary? We find the optimal time, during which the graph may be explored. Our approach permits to find the maximal number of robots, which may turn out to be unreliable, and the graph is still guaranteed to be explored. We concentrate on line graphs and rings, for which we give positive results. We start with the case of the collections involving only reliable robots. We give algorithms finding optimal times needed for exploration when the robots are assigned to fixed initial positions as well as when such starting positions may be determined by the algorithm. We extend our consideration to the case when some number of robots may be unreliable. Our most surprising result is that solving the line exploration problem with robots at given positions, which may involve crash-faulty ones, is NP-hard. The same problem has polynomial solutions for a ring and for the case when the initial robots' positions on the line are arbitrary. The exploration problem is shown to be NP-hard for star graphs, even when the team consists of only two reliable robots

Refined saddle-point preconditioners for discretized Stokes problems

This paper is concerned with the implementation of efficient solution algorithms for elliptic problems with constraints. We establish theory which shows that including a simple scaling within well-established block diagonal preconditioners for Stokes problems can result in significantly faster convergence when applying the preconditioned MINRES method. The codes used in the numerical studies are available online

Thermodynamics of an ideal generalized gas:II Means of order α\alpha

The property that power means are monotonically increasing functions of their order is shown to be the basis of the second laws not only for processes involving heat conduction but also for processes involving deformations. In an $L$-potentail equilibration the final state will be one of maximum entropy, while in an entropy equilibrium the final state will be one of minimum $L$. A metric space is connected with the power means, and the distance between means of different order is related to the Carnot efficiency. In the ideal classical gas limit, the average change in the entropy is shown to be proportional to the difference between the Shannon and R\'enyi entropies for nonextensive systems that are multifractal in nature. The $L$-potential, like the internal energy, is a Schur convex function of the empirical temperature, which satisfies Jensen's inequality, and serves as a measure of the tendency to uniformity in processes involving pure thermal conduction.Comment: 8 page

Modeling the scaling properties of human mobility

While the fat tailed jump size and the waiting time distributions characterizing individual human trajectories strongly suggest the relevance of the continuous time random walk (CTRW) models of human mobility, no one seriously believes that human traces are truly random. Given the importance of human mobility, from epidemic modeling to traffic prediction and urban planning, we need quantitative models that can account for the statistical characteristics of individual human trajectories. Here we use empirical data on human mobility, captured by mobile phone traces, to show that the predictions of the CTRW models are in systematic conflict with the empirical results. We introduce two principles that govern human trajectories, allowing us to build a statistically self-consistent microscopic model for individual human mobility. The model not only accounts for the empirically observed scaling laws but also allows us to analytically predict most of the pertinent scaling exponents

Reduced levels of dopamine and altered metabolism in brains of HPRT knock-out rats: a new rodent model of Lesch-Nyhan Disease

Lesch-Nyhan disease (LND) is a severe neurological disorder caused by loss-of-function mutations in the gene encoding hypoxanthine phosphoribosyltransferase (HPRT), an enzyme required for efficient recycling of purine nucleotides. Although this biochemical defect reconfigures purine metabolism and leads to elevated levels of the breakdown product urea, it remains unclear exactly how loss of HPRT activity disrupts brain function. As the rat is the preferred rodent experimental model for studying neurobiology and diseases of the brain, we used genetically-modified embryonic stem cells to generate an HPRT knock-out rat. Male HPRT-deficient rats were viable, fertile and displayed normal caged behaviour. However, metabolomic analysis revealed changes in brain biochemistry consistent with disruption of purine recycling and nucleotide metabolism. Broader changes in brain biochemistry were also indicated by increased levels of the core metabolite citrate and reduced levels of lipids and fatty acids. Targeted MS/MS analysis identified reduced levels of dopamine in the brains of HPRT-deficient animals, consistent with deficits noted previously in human LND patients and HPRT knock-out mice. The HPRT-deficient rat therefore provides a new experimental platform for future investigation of how HPRT activity and disruption of purine metabolism affects neural function and behaviour

Bound states of spin-half particles in a static gravitational field close to the black hole field

We consider the bound-state energy levels of a spin-1/2 fermion in the gravitational field of a near-black hole object. In the limit that the metric of the body becomes singular, all binding energies tend to the rest-mass energy (i.e. total energy approaches zero). We present calculations of the ground state energy for three specific interior metrics (Florides, Soffel and Schwarzschild) for which the spectrum collapses and becomes quasi-continuous in the singular metric limit. The lack of zero or negative energy states prior to this limit being reached prevents particle pair production occurring. Therefore, in contrast to the Coulomb case, no pairs are produced in the non-singular static metric. For the Florides and Soffel metrics the singularity occurs in the black hole limit, while for the Schwarzschild interior metric it corresponds to infinite pressure at the centre. The behaviour of the energy level spectrum is discussed in the context of the semi-classical approximation and using general properties of the metric.Comment: 16 pages, 6 Figures. Submitted to General Relativity and Gravitatio

Young neutron stars with soft gamma ray emission and anomalous X-ray pulsar

The observational properties of Soft Gamma Repeaters and Ano\-malous X-ray Pulsars (SGR/AXP) indicate to necessity of the energy source different from a rotational energy of a neutron star. The model, where the source of the energy is connected with a magnetic field dissipation in a highly magnetized neutron star (magnetar) is analyzed. Some observational inconsistencies are indicated for this interpretation. The alternative energy source, connected with the nuclear energy of superheavy nuclei stored in the nonequilibrium layer of low mass neutron star is discussed.Comment: 29 pages, 13 figures, Springer International Publishing Switzerland 2016 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernova

Microfluidic systems for the analysis of the viscoelastic fluid flow phenomena in porous media

In this study, two microfluidic devices are proposed as simplified 1-D microfluidic analogues of a porous medium. The objectives are twofold: firstly to assess the usefulness of the microchannels to mimic the porous medium in a controlled and simplified manner, and secondly to obtain a better insight about the flow characteristics of viscoelastic fluids flowing through a packed bed. For these purposes, flow visualizations and pressure drop measurements are conducted with Newtonian and viscoelastic fluids. The 1-D microfluidic analogues of porous medium consisted of microchannels with a sequence of contractions/ expansions disposed in symmetric and asymmetric arrangements. The real porous medium is in reality, a complex combination of the two arrangements of particles simulated with the microchannels, which can be considered as limiting ideal configurations. The results show that both configurations are able to mimic well the pressure drop variation with flow rate for Newtonian fluids. However, due to the intrinsic differences in the deformation rate profiles associated with each microgeometry, the symmetric configuration is more suitable for studying the flow of viscoelastic fluids at low De values, while the asymmetric configuration provides better results at high De values. In this way, both microgeometries seem to be complementary and could be interesting tools to obtain a better insight about the flow of viscoelastic fluids through a porous medium. Such model systems could be very interesting to use in polymer-flood processes for enhanced oil recovery, for instance, as a tool for selecting the most suitable viscoelastic fluid to be used in a specific formation. The selection of the fluid properties of a detergent for cleaning oil contaminated soil, sand, and in general, any porous material, is another possible application

Including cognitive aspects in multiple criteria decision analysis

"First Online: 21 December 2016"Many Multiple Criteria Decision Analysis (MCDA) methods have been proposed over the last decades. Some of the most known methods share some similarities in the way they are used and configured. However, we live in a time of change and nowadays the decision-making process (especially when done in group) is even more demanding and dynamic. In this work, we propose a Multiple Criteria Decision Analysis method that includes cognitive aspects (Cognitive Analytic Process). By taking advantage of aspects such as expertise level, credibility and behaviour style of the decision-makers, we propose a method that relates these aspects with problem configurations (alternatives and criteria preferences) done by each decision-maker. In this work, we evaluated the Cognitive Analytic Process (CAP) in terms of configuration costs and the capability to enhance the quality of the decision. We have used the satisfaction level as a metric to compare our method with other known MCDA methods in literature (Utility function, AHP and TOPSIS). Our method proved to be capable to achieve higher satisfaction levels compared to other MCDA methods, especially when the decision suggested by CAP is different from the one proposed by those methods.This work was supported by COMPETE Programme (operational programme for competitiveness) within project POCI-01-0145-FEDER-007043, by National Funds through the FCT – Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) within the Projects UID/CEC/00319/2013, UID/EEA/00760/2013, and the João Carneiro PhD grant with the reference SFRH/BD/89697/2012.info:eu-repo/semantics/publishedVersio

Wet Granular Materials

Most studies on granular physics have focused on dry granular media, with no liquids between the grains. However, in geology and many real world applications (e.g., food processing, pharmaceuticals, ceramics, civil engineering, constructions, and many industrial applications), liquid is present between the grains. This produces inter-grain cohesion and drastically modifies the mechanical properties of the granular media (e.g., the surface angle can be larger than 90 degrees). Here we present a review of the mechanical properties of wet granular media, with particular emphasis on the effect of cohesion. We also list several open problems that might motivate future studies in this exciting but mostly unexplored field.Comment: review article, accepted for publication in Advances in Physics; tex-style change