This paper presents an investigation of genetic programming fitness landscapes. We propose a new indicator of problem hardness for tree-based genetic programming, called negative slope coefficient, based on the concept of fitness cloud. The negative slope coefficient is a predictive measure, i.e. it can be calculated without prior knowledge of the global optima. The fitness cloud is generated v...

Binomial coefficients have been used for centuries in a variety of fields and accumulated numerous definitions. In this paper, we introduce new way defining binomial as repeated sums ones. A multitude coefficient identities will be shown order to prove definition. Using definition, simplify some particular such the Harmonic sum Binomial-Harmonic sum. We derive formulae simplifying general <i...

We develop a simple statistic for comparing rates of rare adverse events between treatment groups in postmarketing safety studies where the events have uncertain status. In this setting, the statistic is asymptotically equivalent to the logrank statistic, but the limiting distribution has Poisson and binomial components instead of being Gaussian. We develop two new procedures for computing crit...

We study learning problems in which the conditional distribution of the output given the input varies as a function of additional task variables. In varying-coefficient models with Gaussian process priors, a Gaussian process generates the functional relationship between the task variables and the parameters of this conditional. Varying-coefficient models subsume multitask models—such as hierarc...

The Kneser graph K(n, k) has as vertices all the k-subsets of a fixed n-set and has as edges the pairs [A, B] of vertices such that A and B are disjoint. It is known that these graphs are Hamiltonian if ( n&1 k&1) ( n&k k ) for n 2k+1. We determine asymptotically for fixed k the minimum value n=e(k) for which this inequality holds. In addition we give an asymptotic formula for the solution of k...

Consider a linear elliptic partial differential equation in divergence form with random coefficient field. The solution-operator displays fluctuations around its expectation. recently-developed pathwise theory of stochastic homogenization reduces the characterization these to those so-called standard commutator. In this contribution, we investigate scaling limit key quantity: starting from Gaus...

Background: Alzheimer's disease (AD) is the most common disorder of dementia, which has not been cured after its occurrence. AD progresses indiscernible, first destroy the structure of the brain and subsequently becomes clinically evident. Therefore, the timely and correct diagnosis of these structural changes in the brain is very important and it can prevent the disease or stop its progress. N...

This paper develops the theory and methods for modeling a stationary count time series via Gaussian transformations. The techniques use latent process distributional transformation to construct with very flexible correlation features that can have any pre-specified marginal distribution, including classical Poisson, generalized negative binomial, binomial structures. pseudo-likelihood implied Y...

We show that the generalized q-gaussian von Neumann algebras with coefficients Γq(B,S⊗H) with B a finite dimensional factor, dim(Dk(S)) sub-exponential and the dimension of H finite and larger than a constant depending on q, have no non-trivial central sequences.

This paper presents a useful theorem for non-linear transformations of the sum of independent, zeromean, Gaussian random variables. It is proved that the linear regression coefficient of the non-linear transformation output with respect to the overall input is identical to the linear regression coefficient with respect to any Gaussian random variable that is part of the input. As a side-result,...