Effects of Diversity and Procrastination in Priority Queuing Theory: the Different Power Law Regimes

Empirical analysis show that, after the update of a browser, the publication of the vulnerability of a software, or the discovery of a cyber worm, the fraction of computers still using the older version, or being not yet patched, or exhibiting worm activity decays as power laws $\sim 1/t^{\alpha}$ with $0 < \alpha \leq 1$ over time scales of years. We present a simple model for this persistence phenomenon framed within the standard priority queuing theory, of a target task which has the lowest priority compared with all other tasks that flow on the computer of an individual. We identify a "time deficit" control parameter $\beta$ and a bifurcation to a regime where there is a non-zero probability for the target task to never be completed. The distribution of waiting time ${\cal T}$ till the completion of the target task has the power law tail $\sim 1/t^{1/2}$, resulting from a first-passage solution of an equivalent Wiener process. Taking into account a diversity of time deficit parameters in a population of individuals, the power law tail is changed into $1/t^\alpha$ with $\alpha\in(0.5,\infty)$, including the well-known case $1/t$. We also study the effect of "procrastination", defined as the situation in which the target task may be postponed or delayed even after the individual has solved all other pending tasks. This new regime provides an explanation for even slower apparent decay and longer persistence.Comment: 32 pages, 10 figure

Equilibrium Properties of Temporally Asymmetric Hebbian Plasticity

A theory of temporally asymmetric Hebb (TAH) rules which depress or potentiate synapses depending upon whether the postsynaptic cell fires before or after the presynaptic one is presented. Using the Fokker-Planck formalism, we show that the equilibrium synaptic distribution induced by such rules is highly sensitive to the manner in which bounds on the allowed range of synaptic values are imposed. In a biologically plausible multiplicative model, we find that the synapses in asynchronous networks reach a distribution that is invariant to the firing rates of either the pre- or post-synaptic cells. When these cells are temporally correlated, the synaptic strength varies smoothly with the degree and phase of synchrony between the cells.Comment: 3 figures, minor corrections of equations and tex

The Darkening Cloud of Diabetes: Do trends in cardiovascular risk management provide a silver lining?

OBJECTIVE—We aimed to evaluate the changes in cardiovascular-related health care utilization (drug therapies, hospitalizations) and mortality for the diabetic population during a 9-year period in Saskatchewan, Canada

Causal trajectories description of atom diffraction by surfaces

9 pages, 7 figures -- PACS numbers: 79.20.Rf, 03.65.Sq, 03.65.BzThe method of quantum trajectories proposed by de Broglie and Bohm is applied to the study of atom diffraction by surfaces. As an example, a realistic model for the scattering of He off corrugated Cu is considered. In this way, the final angular distribution of trajectories is obtained by box-counting, which is in excellent agreement with the results calculated by standard S-matrix methods of scattering theory. More interestingly, the accumulation of quantum trajectories at the different diffraction peaks is explained in terms of the corresponding quantum potential. This non-local potential "guides" the trajectories causing a transition from a distribution near the surface, which reproduces its shape, to the final diffraction pattern observed in the asymptotic region, far from the diffracting object. These two regimes are homologous to the Fresnel and Fraunhofer regions described in undulatory optics. Finally, the turning points of the quantum trajectories provide a better description of the surface electronic density than the corresponding classical ones, usually employed for this task.This work was supported by DGES (Spain) under contracts No PB95-71, PB95-425 and PB96-76. A.S. Sanz also acknowledges the Universidad Autónoma de Madrid for a doctoral grant.Peer reviewe

Center or Limit Cycle: Renormalization Group as a Probe

Based on our studies done on two-dimensional autonomous systems, forced non-autonomous systems and time-delayed systems, we propose a unified methodology - that uses renormalization group theory - for finding out existence of periodic solutions in a plethora of nonlinear dynamical systems appearing across disciplines. The technique will be shown to have a non-trivial ability of classifying the solutions into limit cycles and periodic orbits surrounding a center. Moreover, the methodology has a definite advantage over linear stability analysis in analyzing centers

Модель определения оптимальных траекторий перемещения партий грузов

The suggested model for determining the optimal trajectories of moving consignments that form cargo flows in transport and logistics systems (TLS) is based on a combination of dynamic systems and multi-criteria optimization methods. This approach develops a methodology for solving applied control problems in TLS. Its main result is the principle of finding the maximum, subject to the criterion preferences, based on methods for determining the set of effective plans (Pareto set). At the same time, management in TLS should form models of cargo traffic taking into account the location of transport and storage complexes within the boundaries of the system being studied or designed, as well as should provide for movement of consignments according to specified performance criteria and the most rational trajectories using analytical modeling. Analytics together with digital technologies help to consider the core sense of TLS as of a subsystem of intelligent transport systems.Представленная модель определения оптимальных траекторий перемещения партий грузов, формирующих грузопотоки в транспортно-логистических системах (ТЛС), основана на совмещении динамических систем и методов многокритериальной оптимизации. Данный подход развивает методологию решения прикладных задач управления в ТЛС, центральным результатом которой является принцип нахождения максимума при условии соблюдения критериальных предпочтений, базирующийся на эффективном средстве решения проблемы – методах определения множества эффективных планов (множества Парето). При этом управление в ТЛС формирует модели грузопотоков с учётом месторасположения транспортно-складских комплексов в границах исследуемой или проектируемой системы и обеспечивает движение партий грузов по заданным критериям эффективности и наиболее рациональным траекториям с помощью методов аналитического моделирования. Аналитика в совокупности с цифровыми технологиями помогает увидеть суть ТЛС как подсистемы интеллектуальных транспортных систем

Macromolecular theory of solvation and structure in mixtures of colloids and polymers

The structural and thermodynamic properties of mixtures of colloidal spheres and non-adsorbing polymer chains are studied within a novel general two-component macromolecular liquid state approach applicable for all size asymmetry ratios. The dilute limits, when one of the components is at infinite dilution but the other concentrated, are presented and compared to field theory and models which replace polymer coils with spheres. Whereas the derived analytical results compare well, qualitatively and quantitatively, with mean-field scaling laws where available, important differences from ``effective sphere'' approaches are found for large polymer sizes or semi-dilute concentrations.Comment: 23 pages, 10 figure

Dynamics of Simple Balancing Models with State Dependent Switching Control

Time-delayed control in a balancing problem may be a nonsmooth function for a variety of reasons. In this paper we study a simple model of the control of an inverted pendulum by either a connected movable cart or an applied torque for which the control is turned off when the pendulum is located within certain regions of phase space. Without applying a small angle approximation for deviations about the vertical position, we see structurally stable periodic orbits which may be attracting or repelling. Due to the nonsmooth nature of the control, these periodic orbits are born in various discontinuity-induced bifurcations. Also we show that a coincidence of switching events can produce complicated periodic and aperiodic solutions.Comment: 36 pages, 12 figure

How spiking neurons give rise to a temporal-feature map

A temporal-feature map is a topographic neuronal representation of temporal attributes of phenomena or objects that occur in the outside world. We explain the evolution of such maps by means of a spike-based Hebbian learning rule in conjunction with a presynaptically unspecific contribution in that, if a synapse changes, then all other synapses connected to the same axon change by a small fraction as well. The learning equation is solved for the case of an array of Poisson neurons. We discuss the evolution of a temporal-feature map and the synchronization of the single cells’ synaptic structures, in dependence upon the strength of presynaptic unspecific learning. We also give an upper bound for the magnitude of the presynaptic interaction by estimating its impact on the noise level of synaptic growth. Finally, we compare the results with those obtained from a learning equation for nonlinear neurons and show that synaptic structure formation may profit from the nonlinearity