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

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

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

Scale-free static and dynamical correlations in melts of monodisperse and Flory-distributed homopolymers: A review of recent bond-fluctuation model studies

It has been assumed until very recently that all long-range correlations are screened in three-dimensional melts of linear homopolymers on distances beyond the correlation length $\xi$ characterizing the decay of the density fluctuations. Summarizing simulation results obtained by means of a variant of the bond-fluctuation model with finite monomer excluded volume interactions and topology violating local and global Monte Carlo moves, we show that due to an interplay of the chain connectivity and the incompressibility constraint, both static and dynamical correlations arise on distances $r \gg \xi$. These correlations are scale-free and, surprisingly, do not depend explicitly on the compressibility of the solution. Both monodisperse and (essentially) Flory-distributed equilibrium polymers are considered.Comment: 60 pages, 49 figure

A pragmatic cluster randomized trial evaluating the impact of a community pharmacy intervention on statin adherence: rationale and design of the Community Pharmacy Assisting in Total Cardiovascular Health (CPATCH) study

<p>Abstract</p> <p>Background</p> <p>Traditional randomized controlled trials are considered the gold standard for evaluating the efficacy of a treatment. However, in adherence research, limitations to this study design exist, especially when evaluating real-world applicability of an intervention. Although adherence interventions by community pharmacists have been tested, problems with internal and external validity have limited the usefulness of these studies, and further well-designed and well-conducted research is needed. We aimed to determine the real-world effectiveness of a community pharmacy adherence intervention using a robust study design. This novel design integrates cluster randomization and an outcome evaluation of medication adherence using a population-based administrative data source in the province of Saskatchewan, Canada.</p> <p>Methods/Design</p> <p>Community pharmacies from across the province of Saskatchewan, Canada were randomized to deliver an adherence intervention to their patients or usual care. Intervention pharmacies were trained to employ a practical adherence strategy targeted at new users of statin medications. While randomization and implementation of the intervention occurred at the community pharmacy level, the outcome analysis will occur at the level of the individual subjects. The primary outcome is the mean statin adherence among all eligible new users of statin medications. Secondary outcomes include the proportion of new statin users who exhibit adherence ≥80%, and persistence with statin use.</p> <p>Discussion</p> <p>This novel study design was developed to combine the rigor of a randomized trial with a pragmatic approach to implementing and capturing the results in a real-world fashion. We believe this approach can serve as an example for future study designs evaluating practice-based adherence interventions.</p> <p>Trial Registration</p> <p>ClinicalTrials.gov no. NCT00971412.</p

Dynamical Mean-Field Theory

The dynamical mean-field theory (DMFT) is a widely applicable approximation scheme for the investigation of correlated quantum many-particle systems on a lattice, e.g., electrons in solids and cold atoms in optical lattices. In particular, the combination of the DMFT with conventional methods for the calculation of electronic band structures has led to a powerful numerical approach which allows one to explore the properties of correlated materials. In this introductory article we discuss the foundations of the DMFT, derive the underlying self-consistency equations, and present several applications which have provided important insights into the properties of correlated matter.Comment: Chapter in "Theoretical Methods for Strongly Correlated Systems", edited by A. Avella and F. Mancini, Springer (2011), 31 pages, 5 figure

Subsampling effects in neuronal avalanche distributions recorded in vivo

Background Many systems in nature are characterized by complex behaviour where large cascades of events, or avalanches, unpredictably alternate with periods of little activity. Snow avalanches are an example. Often the size distribution f(s) of a system's avalanches follows a power law, and the branching parameter sigma, the average number of events triggered by a single preceding event, is unity. A power law for f(s), and sigma=1, are hallmark features of self-organized critical (SOC) systems, and both have been found for neuronal activity in vitro. Therefore, and since SOC systems and neuronal activity both show large variability, long-term stability and memory capabilities, SOC has been proposed to govern neuronal dynamics in vivo. Testing this hypothesis is difficult because neuronal activity is spatially or temporally subsampled, while theories of SOC systems assume full sampling. To close this gap, we investigated how subsampling affects f(s) and sigma by imposing subsampling on three different SOC models. We then compared f(s) and sigma of the subsampled models with those of multielectrode local field potential (LFP) activity recorded in three macaque monkeys performing a short term memory task. Results Neither the LFP nor the subsampled SOC models showed a power law for f(s). Both, f(s) and sigma, depended sensitively on the subsampling geometry and the dynamics of the model. Only one of the SOC models, the Abelian Sandpile Model, exhibited f(s) and sigma similar to those calculated from LFP activity. Conclusions Since subsampling can prevent the observation of the characteristic power law and sigma in SOC systems, misclassifications of critical systems as sub- or supercritical are possible. Nevertheless, the system specific scaling of f(s) and sigma under subsampling conditions may prove useful to select physiologically motivated models of brain function. Models that better reproduce f(s) and sigma calculated from the physiological recordings may be selected over alternatives

Research into the effect Of SGLT2 inhibition on left ventricular remodelling in patients with heart failure and diabetes mellitus (REFORM) trial rationale and design

Background Heart failure (HF) and diabetes (DM) are a lethal combination. The current armamentarium of anti-diabetic agents has been shown to be less efficacious and sometimes even harmful in diabetic patients with concomitant cardiovascular disease, especially HF. Sodium glucose linked co-transporter type 2 (SGLT2) inhibitors are a new class of anti-diabetic agent that has shown potentially beneficial cardiovascular effects such as pre-load and after load reduction through osmotic diuresis, blood pressure reduction, reduced arterial stiffness and weight loss. This has been supported by the recently published EMPA-REG trial which showed a striking 38 and 35 % reduction in cardiovascular death and HF hospitalisation respectively. Methods The REFORM trial is a novel, phase IV randomised, double blind, placebo controlled clinical trial that has been ongoing since March 2015. It is designed specifically to test the safety and efficacy of the SLGT2 inhibitor, dapagliflozin, on diabetic patients with known HF. We utilise cardiac-MRI, cardio-pulmonary exercise testing, body composition analysis and other tests to quantify the cardiovascular and systemic effects of dapagliflozin 10 mg once daily against standard of care over a 1 year observation period. The primary outcome is to detect the change in left ventricular (LV) end systolic and LV end diastolic volumes. The secondary outcome measures include LV ejection fraction, LV mass index, exercise tolerance, fluid status, quality of life measures and others. Conclusions This trial will be able to determine if SGLT2 inhibitor therapy produces potentially beneficial effects in patients with DM and HF, thereby replacing current medications as the drug of choice when treating patients with both DM and HF