Continuous-time formulation of reaction-diffusion processes on heterogeneous metapopulations

We present the derivation of the continuous-time equations governing the limit dynamics of discrete-time reaction-diffusion processes defined on heterogeneous metapopulations. We show that, when a rigorous time limit is performed, the lack of an epidemic threshold in the spread of infections is not limited to metapopulations with a scale-free architecture, as it has been predicted from dynamical equations in which reaction and diffusion occur sequentially in time

Mean first-passage time of continuous non-Markovian processes driven by colored noise

An equation for mean first-passage times of non-Markovian processes driven by colored noise is derived through an appropriate backward integro-differential equation. The equation is solved in a Bourret-like approximation. In a weak-noise bistable situation, non-Markovian effects are taken into account by an effective diffusion coefficient. In this situation, our results compare satisfactorily with other approaches and experimental data.

Mean first-passage time of continuous non-Markovian processes driven by colored noise

An equation for mean first-passage times of non-Markovian processes driven by colored noise is derived through an appropriate backward integro-differential equation. The equation is solved in a Bourret-like approximation. In a weak-noise bistable situation, non-Markovian effects are taken into account by an effective diffusion coefficient. In this situation, our results compare satisfactorily with other approaches and experimental data.

Exit times in non-Markovian drifting continuous-time random-walk processes

By appealing to renewal theory we determine the equations that the mean exit time of a continuous-time random walk with drift satisfies both when the present coincides with a jump instant or when it does not. Particular attention is paid to the corrections ensuing from the non-Markovian nature of the process. We show that when drift and jumps have the same sign the relevant integral equations can be solved in closed form. The case when holding times have the classical Erlang distribution is considered in detail.

Coupling and monotonicity of queueing processes

The main purpose of this work is to give a survey of main monotonicity properties of queueing processes based on the coupling method. The literature on this topic is quite extensive, and we do not consider all aspects of this topic. Our more concrete goal is to select the most interesting basic monotonicity results and give simple and elegant proofs. Also we give a few new (or revised) proofs of a few important monotonicity properties for the queue-size and workload processes both in single-server and multi- server systems. The paper is organized as follows. In Section 1, the basic notions and results on coupling method are given. Section 2 contains known coupling results for renewal processes with focus on construction of synchronized renewal instants for a superposition of independent renewal processes. In Section 3, we present basic monotonicity results for the queue-size and workload processes. We consider both discrete-and continuous-time queueing systems with single and multi servers. Less known results on monotonicity of queueing processes with dependent service times and interarrival times are also presented. Section 4 is devoted to monotonicity of general Jackson-type queueing networks with Markovian routing. This section is based on the notable paper [17]. Finally, Section 5 contains elements of stability analysis of regenerative queues and networks, where coupling and monotonicity results play a crucial role to establish minimal suficient stability conditions. Besides, we present some new monotonicity results for tandem networks.

Integrated random processes exhibiting long tails, finite moments, and power-law spectra

A dynamical model based on a continuous addition of colored shot noises is presented. The resulting process is colored and non-Gaussian. A general expression for the characteristic function of the process is obtained, which, after a scaling assumption, takes on a form that is the basis of the results derived in the rest of the paper. One of these is an expansion for the cumulants, which are all finite, subject to mild conditions on the functions defining the process. This is in contrast with the Lévy distribution¿which can be obtained from our model in certain limits¿which has no finite moments. The evaluation of the spectral density and the form of the probability density function in the tails of the distribution shows that the model exhibits a power-law spectrum and long tails in a natural way. A careful analysis of the characteristic function shows that it may be separated into a part representing a Lévy process together with another part representing the deviation of our model from the Lévy process. This

Parrondo-like behavior in continuous-time random walks with memory

The continuous-time random walk (CTRW) formalism can be adapted to encompass stochastic processes with memory. In this paper we will show how the random combination of two different unbiased CTRWs can give rise to a process with clear drift, if one of them is a CTRW with memory. If one identifies the other one as noise, the effect can be thought of as a kind of stochastic resonance. The ultimate origin of this phenomenon is the same as that of the Parrondo paradox in game theory.

Standardizing admission and discharge processes to improve patient flow: A cross sectional study

Background: The aim of this study was to evaluate how hospital capacity was managed focusing on standardizing the admission and discharge processes. Methods: This study was set in a 900-bed university affiliated hospital of the National Health Service, near Barcelona (Spain). This is a cross-sectional study of a set of interventions which were gradually implemented between April and December 2008. Mainly, they were focused on standardizing the admission and discharge processes to improve patient flow. Primary administrative data was obtained from the 2007 and 2009 Hospital Database. Main outcome measures were median length of stay, percentage of planned discharges, number of surgery cancellations and median number of delayed emergency admissions at 8:00 am. For statistical bivariate analysis, we used a Chi-squared for linear trend for qualitative variables and a Wilcoxon signed ranks test and a Mann–Whitney test for non-normal continuous variables. Results: The median patients’ global length of stay was 8.56 days in 2007 and 7.93 days in 2009 (p<0.051). The percentage of patients admitted the same day as surgery increased from 64.87% in 2007 to 86.01% in 2009 (p<0.05). The number of cancelled interventions due to lack of beds was 216 patients in 2007 and 42 patients in 2009. The median number of planned discharges went from 43.05% in 2007 to 86.01% in 2009 (p<0.01). The median number of emergency patients waiting for an in-hospital bed at 8:00 am was 5 patients in 2007 and 3 patients in 2009 (p<0.01). Conclusions: In conclusion, standardization of admission and discharge processes are largely in our control. There is a significant opportunity to create important benefits for increasing bed capacity and hospital throughput.

Standardizing admission and discharge processes to improve patient flow: A cross sectional study

Background: The aim of this study was to evaluate how hospital capacity was managed focusing on standardizing the admission and discharge processes. Methods: This study was set in a 900-bed university affiliated hospital of the National Health Service, near Barcelona (Spain). This is a cross-sectional study of a set of interventions which were gradually implemented between April and December 2008. Mainly, they were focused on standardizing the admission and discharge processes to improve patient flow. Primary administrative data was obtained from the 2007 and 2009 Hospital Database. Main outcome measures were median length of stay, percentage of planned discharges, number of surgery cancellations and median number of delayed emergency admissions at 8:00¿am. For statistical bivariate analysis, we used a Chi-squared for linear trend for qualitative variables and a Wilcoxon signed ranks test and a Mann¿Whitney test for non-normal continuous variables. Results:The median patients' global length of stay was 8.56 days in 2007 and 7.93 days in 2009 (p<0.051). The percentage of patients admitted the same day as surgery increased from 64.87% in 2007 to 86.01% in 2009 (p<0.05). The number of cancelled interventions due to lack of beds was 216 patients in 2007 and 42 patients in 2009. The median number of planned discharges went from 43.05% in 2007 to 86.01% in 2009 (p<0.01). The median number of emergency patients waiting for an in-hospital bed at 8:00¿am was 5 patients in 2007 and 3 patients in 2009 (p<0.01). Conclusions: In conclusion, standardization of admission and discharge processes are largely in our control. There is a significant opportunity to create important benefits for increasing bed capacity and hospital throughput.

Monotonic continuous-time random walks with drift and stochastic reset events

In this paper we consider a stochastic process that may experience random reset events which suddenly bring the system to the starting value and analyze the relevant statistical magnitudes. We focus our attention on monotonic continuous-time random walks with a constant drift: The process increases between the reset events, either by the effect of the random jumps, or by the action of the deterministic drift. As a result of all these combined factors interesting properties emerge, like the existence (for any drift strength) of a stationary transition probability density function, or the faculty of the model to reproduce power-law-like behavior. General formulas for two extreme statistics, the survival probability, and the mean exit time, are also derived. To corroborate in an independent way the results of the paper, Monte Carlo methods were used. These numerical estimations are in full agreement with the analytical predictions.

Some remarks on the class of continuous (Semi-) strictcly quasiconvex functions

Vegeu el resum a l'inici del document del fitxer adjunt

Clarke critical values of subanalytic Lipschitz continuous functions

We prove that any subanalytic locally Lipschitz function has the Sard property. Such functions are typically nonsmooth and their lack of regularity necessitates the choice of some generalized notion of gradient and of critical point. In our framework these notions are defined in terms of the Clarke and of the convex-stable subdifferentials. The main result of this note asserts that for any subanalytic locally Lipschitz function the set of its Clarke critical values is locally finite. The proof relies on Pawlucki's extension of the Puiseuxlemma. In the last section we give an example of a continuous subanalytic function which is not constant on a segment of "broadly critical" points, that is, points for which we can find arbitrarily short convex combinations of gradients at nearby points.

Forecasting volatility using a continuous time model

This paper evaluates the forecasting performance of a continuous stochastic volatility model with two factors of volatility (SV2F) and compares it to those of GARCH and ARFIMA models. The empirical results show that the volatility forecasting ability of the SV2F model is better than that of the GARCH and ARFIMA models, especially when volatility seems to change pattern. We use ex-post volatility as a proxy of the realized volatility obtained from intraday data and the forecasts from the SV2F are calculated using the reprojection technique proposed by Gallant and Tauchen (1998).

The possibility for continuous growth with exhaustible resources: unknowingly an agreement has been reached, but it may not be correct

It is the size of the elasticity of substitution that has been the central issue in the long debate over the possibility of continuous growth in the presence of exhaustible resources. This paper reviews the debate and comes to the surprising conclusion that , unnoticed by the pessimists, the optimist position has gradually evolved so that it now approximates that of the pessimists. The paper also summarises some preliminary work by the author that indicates that this common position may not be correct

Selecting negotiation processes with Health Care

We address the question of how a third-party payer (e.g. an insurer) decides what providers to contract with. Three different mechanisms are studied and their properties compared. A first mechanism consists in the third-party payer setting up a bargaining procedure with both providers jointly and simultaneously. A second mechanism envisages the outcome of the same simultaneous bargaining but independently with every provider. Finally, the last mechanism is of different nature. It is the so-called "any willing provider" where the third-party payer announces a contract and every provider freely decides to sign it or not. The main finding is that the decision of the third-party payer depends on the surplus to be shared. When it is relatively high the third-party payer prefers the any willing provider system. When, on the contrary, the surplus is relatively low, the third-party payer will select one of the other two systems accor ing to how bargaining power is distributed.