Related papers: On two conjectures for M&m sequences
Two proofs of the Koml\'os-Major-Tusn\'ady embedding theorems, one for the uniform empirical process and one for the simple symmetric random walk, are given. More precisely, what are proved are the univariate coupling results needed in the…
A five-parameter distribution called the McDonald normal distribution is defined and studied. The new distribution contains, as special cases, several important distributions discussed in the literature, such as the normal, skew-normal,…
The dynamics of coupled intermittent maps is used to model the correlated structure of genomic sequences. The use of intermittent maps, as opposed to other simple chaotic maps, is particularly suited for the production of long range…
The famous MLC Conjecture states that the Mandelbrot set is locally connected, and it is considered by many to be the central conjecture in one-dimensional complex dynamics. Among others, it implies density of hyperbolicity in the quadratic…
In the finite dimensional case, mean-type mappings, their invariant means, relations between the uniqueness of invariant means and convergence of orbits of the mapping, are considered. In particular it is shown, that the uniqueness of an…
The contextuality problem connected with existence of joint probability distribution creating all the given marginals is studied. It is shown for several examples considered previously in literature that there exist some new solutions for…
In this paper; we prove that all sequences can be broken up in cycles. Each cycle follows the same pattern: 1) Upward trajectory. Odd and even numbers alternate until the cycle reaches an upper bound 2) Downward trajectory. Two or more…
The main purpose of this article is to study higher power mean values of generalized quadratic Gauss sums using estimates for character sums, analytic method and algebraic geometric methods. In this article, we prove two conjectures which…
Robustness of any statistics depends upon the number of assumptions it makes about the measured data. We point out the advantages of median statistics using toy numerical experiments and demonstrate its robustness, when the number of…
Network data arises through observation of relational information between a collection of entities. Recent work in the literature has independently considered when (i) one observes a sample of networks, connectome data in neuroscience being…
In systematic reviews and meta-analysis, researchers often pool the results of the sample mean and standard deviation from a set of similar clinical trials. A number of the trials, however, reported the study using the median, the minimum…
The presence of latent variables can greatly complicate inferences about causal relations between measured variables from statistical data. In many cases, the presence of latent variables makes it impossible to determine for two measured…
Mixture models are a fundamental tool in applied statistics and machine learning for treating data taken from multiple subpopulations. The current practice for estimating the parameters of such models relies on local search heuristics…
The universal law for percolation thresholds proposed by Galam and Mauger (GM) is found to apply also to dynamical situations. This law depends solely on two variables, the space dimension d and a coordinance numberq. For regular lattices,…
A mixed graph can be seen as a type of digraph containing some edges (two opposite arcs). Here we introduce the concept of sequence mixed graphs, which is a generalization of both sequence graphs and iterated line digraphs. These structures…
In this paper, we exhibit a new family of martingale couplings between two one-dimensional probability measures $\mu$ and $\nu$ in the convex order. This family is parametrised by two dimensional probability measures on the unit square with…
We consider perturbations of the complex quadratic map $ z \to z^2 +c$ and corresponding changes in their quasi-Mandelbrot sets. Depending on particular perturbation, visual forms of quasi-Mandelbrot set changes either sharply (when the…
We present a history of the Baum-Connes conjecture, the methods involved, the current status, and the mathematics it generated.
In a recent paper, Svante Janson has considered a conjecture suggested by Va\v{s}ek Chv\a'atal dealing with the probability that a binomial random variable with parameters $n$ and $m/n$ - where $m$ is an integer - exceeds its expectation…
The sample median is often used in statistical analyses of physical or astronomical data wherein a central value must be found from samples polluted by elements which do not belong to the population of interest or when the underlying…