Relaxation time of processes driven by multiplicative noise

We consider systems described by nonlinear stochastic differential equations with multiplicative noise. We study the relaxation time of the steady-state correlation function as a function of noise parameters. We consider the white- and nonwhite-noise case for a prototype model for which numerical data are available. We discuss the validity of analytical approximation schemes. For the white-noise case we discuss the results of a projector-operator technique. This discussion allows us to give a generalization of the method to the non-white-noise case. Within this generalization, we account for the growth of the relaxation time as a function of the correlation time of the noise. This behavior is traced back to the existence of a non-Markovian term in the equation for the correlation function.

Electrical conductivity of soil irrigated with swine wastewater estimated by time-domain reflectometry¹

Wastewater application to soil is an alternative for fertilization and water reuse. However, particular care must be taken with this practice, since successive wastewater applications can cause soil salinization. Time-domain reflectometry (TDR) allows for the simultaneous and continuous monitoring of both soil water content and apparent electrical conductivity and thus for the indirect measurement of the electrical conductivity of the soil solution. This study aimed to evaluate the suitability of TDR for the indirect determination of the electrical conductivity (ECse) of the saturated soil extract by using an empirical equation for the apparatus TDR Trase 6050X1. Disturbed soil samples saturated with swine wastewater were used, at soil proportions of 0, 0.45, 0.90, 1.80, 2.70, and 3.60 m³ m-3. The probes were equipped with three handmade 0.20 cm long rods. The fit of the empirical model that associated the TDR measured values of electrical conductivity (EC TDR) to ECse was excellent, indicating this approach as suitable for the determination of electrical conductivity of the soil solution.

Follicular lymphoma at relapse after rituximab containing regimens: comparison of time to event intervals prior to and after (90) Y-ibritumomab-tiuxetan.

Radioimmunotherapies with Zevalin® (RIT-Z) showed encouraging results in patients with relapsed/refractory follicular lymphoma (FL), leading frequently to failure-free intervals longer than those achieved by the last previous therapy. We compared time-to-event variables obtained before and after RIT-Z in patients with relapsed FL, previously exposed to rituximab. All patients with relapsed non-transformed, non-refractory, non-rituximab-naïve FL who have been treated with RIT-Z in two different centres in Europe were included. Staging and response were assessed by contrast-enhanced CT in all patients; PET/CT was performed according to local availability. Event-free survival (EFS) and time to next treatment (TTNT) following the last previous therapy and after RIT-Z were compared. Pre-therapy characteristics were tested in univariate analyses for prediction of outcomes. A description of the patterns of relapse was also provided. Among 70 patients treated, only 16 fulfilled the inclusion criteria. They were treated with a median of 3 prior lines of chemo-immunotherapies, including a median of 2 rituximab-containing regimens; 6 patients had undergone myeloablative chemotherapy with autologous stem cell rescue (ASCT). Overall response rates were 10 (62%) CR/CRu, 3 (19%) PR and 3 (19%) PD; response rates were similar in patients with prior ASCT. After RIT-Z only few patients obtained EFS and TTNT longer than after the last previous therapy. All four patients receiving rituximab maintenance were without progression 12 months after RIT-Z. Relapses occurred in both previously and newly involved sites; a significant association was found between the number of pathologic sites involved prior to RIT-Z and subsequent TTNT. Despite the excellent response rate, the duration of response was shorter than the previous one confirming the known trend of relapses to occur earlier after subsequent treatments. Rituximab maintenance after RIT-Z showed encouraging results in terms of prolonging EFS, warranting further studies. Copyright © 2010 John Wiley & Sons, Ltd.

Linking Real Time and Location in Scheduling Demand-Responsive Transit, September 1996

The role of rural demand-responsive transit is changing, and with that change is coming an increasing need for technology. As long as rural transit was limited to a type of social service transportation for a specific set of clients who primarily traveled in groups to common meal sites, work centers for the disabled, or clinics in larger communities, a preset calendar augmented by notes on a yellow legal pad was sufficient to develop schedules. Any individual trips were arranged at least 24 to 48 hours ahead of time and were carefully scheduled the night before in half-hour or twenty-minute windows by a dispatcher who knew every lane in the service area. Since it took hours to build the schedule, any last-minute changes could wreak havoc with the plans and raise the stress level in the dispatch office. Nevertheless, given these parameters, a manual scheduling system worked for a small demand-responsive operation.

External dichotomous noise: The problem of the mean-first-passage time

A retarded backward equation for a non-Markovian process induced by dichotomous noise (the random telegraphic signal) is deduced. The mean-first-passage time of this process is exactly obtained. The Gaussian white noise and the white shot noise limits are studied. Explicit physical results in first approximation are evaluated.