Search results for "value"
showing 10 items of 5321 documents
A Bayesian analysis of a queueing system with unlimited service
1997
Abstract A queueing system occurs when “customers” arrive at some facility requiring a certain type of “service” provided by the “servers”. Both the arrival pattern and the service requirements are usually taken to be random. If all the servers are busy when customers arrive, they usually wait in line to get served. Queues possess a number of mathematical challenges and have been mainly approached from a probability point of view, and statistical analysis are very scarce. In this paper we present a Bayesian analysis of a Markovian queue in which customers are immediately served upon arrival, and hence no waiting lines form. Emergency and self-service facilities provide many examples. Techni…
Non-Markovianity and Coherence of a Moving Qubit inside a Leaky Cavity
2017
Non-Markovian features of a system evolution, stemming from memory effects, may be utilized to transfer, storage, and revive basic quantum properties of the system states. It is well known that an atom qubit undergoes non-Markovian dynamics in high quality cavities. We here consider the qubit-cavity interaction in the case when the qubit is in motion inside a leaky cavity. We show that, owing to the inhibition of the decay rate, the coherence of the traveling qubit remains closer to its initial value as time goes by compared to that of a qubit at rest. We also demonstrate that quantum coherence is preserved more efficiently for larger qubit velocities. This is true independently of the evol…
ArtiFuse—computational validation of fusion gene detection tools without relying on simulated reads
2019
Abstract Motivation Gene fusions are an important class of transcriptional variants that can influence cancer development and can be predicted from RNA sequencing (RNA-seq) data by multiple existing tools. However, the real-world performance of these tools is unclear due to the lack of known positive and negative events, especially with regard to fusion genes in individual samples. Often simulated reads are used, but these cannot account for all technical biases in RNA-seq data generated from real samples. Results Here, we present ArtiFuse, a novel approach that simulates fusion genes by sequence modification to the genomic reference, and therefore, can be applied to any RNA-seq dataset wit…
Dynamics of a financial market index after a crash
2002
We discuss the statistical properties of index returns in a financial market just after a major market crash. The observed non-stationary behavior of index returns is characterized in terms of the exceedances over a given threshold. This characterization is analogous to the Omori law originally observed in geophysics. By performing numerical simulations and theoretical modelling, we show that the nonlinear behavior observed in real market crashes cannot be described by a GARCH(1,1) model. We also show that the time evolution of the Value at Risk observed just after a major crash is described by a power-law function lacking a typical scale.
On delocalization of eigenvectors of random non-Hermitian matrices
2019
We study delocalization of null vectors and eigenvectors of random matrices with i.i.d entries. Let $A$ be an $n\times n$ random matrix with i.i.d real subgaussian entries of zero mean and unit variance. We show that with probability at least $1-e^{-\log^{2} n}$ $$ \min\limits_{I\subset[n],\,|I|= m}\|{\bf v}_I\| \geq \frac{m^{3/2}}{n^{3/2}\log^Cn}\|{\bf v}\| $$ for any real eigenvector ${\bf v}$ and any $m\in[\log^C n,n]$, where ${\bf v}_I$ denotes the restriction of ${\bf v}$ to $I$. Further, when the entries of $A$ are complex, with i.i.d real and imaginary parts, we show that with probability at least $1-e^{-\log^{2} n}$ all eigenvectors of $A$ are delocalized in the sense that $$ \min\l…
Brownian motion in trapping enclosures: Steep potential wells, bistable wells and false bistability of induced Feynman-Kac (well) potentials
2019
We investigate signatures of convergence for a sequence of diffusion processes on a line, in conservative force fields stemming from superharmonic potentials $U(x)\sim x^m$, $m=2n \geq 2$. This is paralleled by a transformation of each $m$-th diffusion generator $L = D\Delta + b(x)\nabla $, and likewise the related Fokker-Planck operator $L^*= D\Delta - \nabla [b(x)\, \cdot]$, into the affiliated Schr\"{o}dinger one $\hat{H}= - D\Delta + {\cal{V}}(x)$. Upon a proper adjustment of operator domains, the dynamics is set by semigroups $\exp(tL)$, $\exp(tL_*)$ and $\exp(-t\hat{H})$, with $t \geq 0$. The Feynman-Kac integral kernel of $\exp(-t\hat{H})$ is the major building block of the relaxatio…
Basing the Analysis of Comparative Bioavailability Trials on an Individualized Statistical Definition of Equivalence
1993
The conventional definition of bioequivalence in terms of population means only, is criticized for lacking relevance to the individual subject. Both approaches to bioequivalence assessment proposed here for avoiding this shortcoming, focus on the probability of an event induced by the response of a randomly selected subject to two formulations of a given active agent. The first approach leads to converting the basic idea underlying the well-known 75-rule into an exact statistical procedure. The second approach is of a parametric nature. It reduces bioequivalence assessment to testing against the alternative hypothesis that the standardized expected value of a Gaussian distribution is contai…
Pricing of Asian exchange rate options under stochastic interest rates as a sum of options
2002
The aim of the paper is to develop pricing formulas for long term European type Asian options written on the exchange rate in a two currency economy. The exchange rate as well as the foreign and domestic zero coupon bond prices are assumed to follow geometric Brownian motions. The emphasis is devoted to the discretely sampled Asian option. It is shown how the value of this option can be approximated as the sum of Black-Scholes options. The formula is obtained under the extension of results developed by Rogers and Shi (1995) and Jamshidian (1991). In addition bounds for the pricing error are determined. Comparing with Monte Carlo simulation the pricing is found to be very precise.
Juggler's exclusion process
2012
Juggler's exclusion process describes a system of particles on the positive integers where particles drift down to zero at unit speed. After a particle hits zero, it jumps into a randomly chosen unoccupied site. We model the system as a set-valued Markov process and show that the process is ergodic if the family of jump height distributions is uniformly integrable. In a special case where the particles jump according to a set-avoiding memoryless distribution, the process reaches its equilibrium in finite nonrandom time, and the equilibrium distribution can be represented as a Gibbs measure conforming to a linear gravitational potential.
Tests for real and complex unit roots in vector autoregressive models
2014
The article proposes new tests for the number of real and complex unit roots in vector autoregressive models. The tests are based on the eigenvalues of the sample companion matrix. The limiting distributions of the eigenvalues converging to the unit eigenvalues turn out to be of a non-standard form and expressible in terms of Brownian motions. The tests are defined such that the null distributions related to eigenvalues +/-1 are the same. The tests for the unit eigenvalues with nonzero imaginary part are defined independently of the angular frequency. When the tests are adjusted for deterministic terms, the null distributions usually change. Critical values are tabulated via simulations. Al…