We solve several multi-parameter families of binomial Thue equations of arbitrary degree; for example, we solve the equation 5x − 23y = ±1, in non-zero integers x, y and positive integers u, r, s and n ≥ 3. Our approach uses several Frey curves simultaneously, Galois representations and level-lowering, new lower bounds for linear forms in 3 logarithms due to Mignotte and a famous theorem of Ben...

Current prediction models for usability evaluations are based on stochastic distributions derived from series of Bernoulli processes. The underlying assumption of these models is a homogeneous detection probability despite of it being intuitively unrealistic. This paper contributes a simple statistical test for existence of heterogeneity in the process. The compound beta-binomial model is propo...

Analysis of somatic mutations in V regions of Ig genes is important for understanding various biological processes. It is customary to estimate Ag selection on Ig genes by assessment of replacement (R) as opposed to silent (S) mutations in the complementary-determining regions and S as opposed to R mutations in the framework regions. In the past such an evaluation was performed using a binomial...

Probabilistic proofs and interpretations are given for the q-binomial theorem, q-binomial series, two of Euler's fundamental partition identities, and for q-analogs of product expansions for the Riemann zeta and Euler phi functions. The underlying processes involve Bernoulli trials with variable probabilities. Also presented are several variations on the classical derangement problem inherent i...

Spatial statistical models are applied in many problems for which dependence in observed random variables is not easily explained by a direct scientific mechanism. In such situations there may be a latent spatial process that acts to produce the observed spatial pattern. Scientific interest often centers on the latent process and the degree of spatial dependence that characterizes it. Such late...

The construction of multi-scale image pyramids is used in state-of-the-art methods that perform robust object recognition, such as SIFT and SURF. However, building such image pyramids is computationally expensive, especially when implementations in embedded systems with limited computing resources are considered. Therefore, the use of alternative less expensive approaches are necessary if near ...

the present article discusses and presents a new and comprehensive approachaimed at measuring the maturity and quality of software processes. this method has beendesigned on the basis of the software capability maturity model (sw-cmm) and themulti-level fuzzy inference model and is used as a measurement and analysis tool. among themost important characteristics of this method one can mention si...

this article focuses on the estimation of population proportion when the study variable is sensitive in nature. two implicit randomized response techniques are proposed where the unrelated trait can be chosen subjectively. in addition to unbiased estimation of population proportion and variance, an empirical study is conducted to inspect the relative efficiency facet of the proposed techniques....

A binomial approximation to a diffusion is defined as “computationally simple” if the number of nodes grows at most linearly in the number of time intervals. It is shown how to construct computationally simple binomial processes that converge weakly to commonly employed diffusions in financial models. The convergence of the sequence of bond and European option prices from these processes to the...