Search results for "Random"

Is there an absolutely continuous random variable with equal probability density and cumulative distribution functions in its support? Is it unique? …

2014

This paper inquires about the existence and uniqueness of a univariate continuous random variable for which both cumulative distribution and density functions are equal and asks about the conditions under which a possible extrapolation of the solution to the discrete case is possible. The issue is presented and solved as a problem and allows to obtain a new family of probability distributions. The different approaches followed to reach the solution could also serve to warn about some properties of density and cumulative functions that usually go unnoticed, helping to deepen the understanding of some of the weapons of the mathematical statistician’s arsenal.

On the use of fractional calculus for the probabilistic characterization of random variables

2009

In this paper, the classical problem of the probabilistic characterization of a random variable is re-examined. A random variable is usually described by the probability density function (PDF) or by its Fourier transform, namely the characteristic function (CF). The CF can be further expressed by a Taylor series involving the moments of the random variable. However, in some circumstances, the moments do not exist and the Taylor expansion of the CF is useless. This happens for example in the case of $\alpha$--stable random variables. Here, the problem of representing the CF or the PDF of random variables (r.vs) is examined by introducing fractional calculus. Two very remarkable results are o…

A method for the probabilistic analysis of nonlinear systems

1995

Abstract The probabilistic description of the response of a nonlinear system driven by stochastic processes is usually treated by means of evaluation of statistical moments and cumulants of the response. A different kind of approach, by means of new quantities here called Taylor moments, is proposed. The latter are the coefficients of the Taylor expansion of the probability density function and the moments of the characteristic function too. Dual quantities with respect to the statistical cumulants, here called Taylor cumulants, are also introduced. Along with the basic scheme of the method some illustrative examples are analysed in detail. The examples show that the proposed method is an a…

A True Extension of the Markov Inequality to Negative Random Variables

2020

The Markov inequality is a classical nice result in statistics that serves to demonstrate other important results as the Chebyshev inequality and the weak law of large numbers, and that has useful applications in the real world, when the random variable is unspecified, to know an upper bound for the probability that an variable differs from its expectation. However, the Markov inequality has one main flaw: its validity is limited to nonnegative random variables. In the very short note, we propose an extension of the Markov inequality to any non specified random variable. This result is completely new.

Exploiting seeding of random number generators for efficient domain decomposition parallelization of dissipative particle dynamics

2013

Abstract Dissipative particle dynamics (DPD) is a new promising method commonly used in coarse-grained simulations of soft matter and biomolecular systems at constant temperature. The DPD thermostat involves the evaluation of stochastic or random forces between pairs of neighboring particles in every time step. In a parallel computing environment, the transfer of these forces from node to node can be very time consuming. In this paper we describe the implementation of a seeded random number generator with three input seeds at each step which enables the complete generation of the pairwise stochastic forces in parallel DPD simulations with minimal communication between nodes.

Neue vorstellungen über statistische fadenknäuel

1967

In Losung liegen synthetische Fadenmolekule im allgemeinen als Knauel vor. Diese Aussage stellt jedoch noch keine sehr genaue Information uber die Gestalt eines Fadenmolekuls dar. Hierzu bedarf es einer Systematik der verschiedenen Knaueltypen. Die Aufstellung einer solchen Systematik ist ein rein geometrisches Problem. Zunachst wird zwischen irrflugartigen und nicht-irrflugartigen Knaueln unterschieden. Ein irrflugartiges Knauel ist ein solches, bei dem die relative Orientierung zweier Fadenelemente zueinander zufallig ist, wenn die Entfernung zwischen den beiden Fadenelementen – langs des Fadens gemessen – hinreichend gros ist. Beispiele fur irrflugartige Knauel sind das KUHNsche Segmentm…

Chemo-orientation responses in hymenopteran parasitoids induced by substrate-borne semiochemicals

2013

Hymenopteran parasitoids can utilize substrate-borne semiochemicals released by conspecifics or by their hosts, increasing the likelihood of successful mating and host location. According to the literature, two substrate-borne chemo-orientation patterns can occur: (1) biased random searching, a non-directional reaction toward the chemicals (kinesis), and (2) trailfollowing searching, a directional response toward the source emitting the chemical compounds (taxis). These two different strategies can be adopted by parasitoids to locate hosts and mates. In host location, random searching is induced by allelochemicals indirectly associated with the host, whereas trail-following behavior is indu…

Yeast β-glucans and microalgal extracts modulate the immune response and gut microbiome in Senegalese sole (Solea senegalensis)

2019

One bottleneck to sustainability of fish aquaculture is the control of infectious diseases. Current trends include the preventive application of immunostimulants and prebiotics such as polysaccharides. The present study investigated how yeast β-glucan (Y), microalgal polysaccharide-enriched extracts (MAe) and whole Phaeodactylum tricornutum cells (MA) modulated the gut microbiome and stimulated the immune system in Senegalese sole (Solea senegalensis) when administered by oral intubation. Blood, intestine and spleen samples were taken at 3 h, 24 h, 48 h and 7 days after treatment. The short-term response (within 48 h after treatment) consisted of up-regulation of il1b and irf7 expression in…

2021

To what extent the intake of fruit and vegetables (FV) influences inflammatory status remains elusive, particularly in older populations. The aim of the present study was to determine the effect of increased FV intake for 16 weeks on circulating biomarkers of inflammation in a population of older men and women. Sixty-six participants (65–70 years) randomly assigned to either FV or control (CON) groups were instructed to increase FV intake to five servings per day through nutritional counseling (FV) or to maintain habitual diet (CON). Dietary intake and physical activity level (PA) were determined using food frequency questionnaire and accelerometers, respectively, at the start and end of th…

A 1-year maintenance after early adjuvant intravesical chemotherapy has a limited efficacy in preventing recurrence of intermediate risk non-muscle-i…

2010

Study Type – Therapy (RCT) Level of Evidence 1b OBJECTIVE To evaluate the efficacy of 1-year maintenance after a 6-week cycle of early intravesical chemotherapy, as the role of maintenance in intravesical chemotherapy is debated. PATIENTS AND METHODS Between May 2002 and August 2003, 577 patients with non-muscle-invasive bladder cancer (NMI-BC) underwent transurethral resection (TUR) and early intravesical chemotherapy (epirubicin, 80 mg/50 mL). They were randomized between a 6-week induction cycle and the induction cycle plus maintenance with 10 monthly instillations. In all, 95 patients with T1G3, Tis or single and primary Ta–T1 G1–G2 tumours were excluded; 482 patients at intermediate ri…