Trough the classical umbral calculus, we provide new, compact and easy to handle expressions of k-statistics, and more in general of U -statistics. In addition such a symbolic method can be naturally extended to multivariate case, i.e. to generalized k-statistics.

K-means is one of the most widely used algorithms for clustering in Data Mining applications, which attempts to minimize the sum of square of Euclidean distance of the points in the clusters from the respective means of the clusters. The simplicity and scalability of K-means makes it very appealing. However, K-means suffers from local minima problem, and comes with no guarantee to converge to t...

We give a comprehensive description for the irreversible growth of aggregates by migration from small to large aggregates. For a homogeneous rate K(i;j) at which monomers migrate from aggregates of size i to those of size j, that is, K(ai;aj)similar to a(lambda)K(i;j), the mean aggregate size grows with time as t(1/(2-lambda)) for lambda<2. The aggregate size distribution exhibits distinct regi...

We introduce a novel approach to calculating the Peierls energy barrier (and Peierls stress) based on the analysis of the dislocation migration dynamics, which we apply to 1/2a〈111〉 screw dislocations in bcc Ta. To study the migration of screw dislocations we use molecular dynamics with a first principles based embedded-atom method force field for Ta. We first distinguish the atoms belonging to...

—We determined the migration timing of fry-stocked smolts of Atlantic salmon Salmo salar, relative to environmental and physiological factors, by using net weirs and counting fences in three tributaries of the West River, Vermont. Smolt migration began in late April and early May when water temperature was 58C, peak movements occurred in early and mid-May at temperatures exceeding 88C, and migr...

Impairments in cell migration processes may cause various diseases, among which cancer cell metastasis, tumor angiogenesis, and the disability of immune cells to infiltrate into tumors are prominent ones. Mathematical modeling has been widely used to analyze the cell migration process. Cell migration is a complicated process and requires statistical methods such as random walk for proper analys...

A detailed analysis of the strong room-temperature photoluminescence ~PL! signal of size controlled nc-Si is reported. The size control of nc-Si is realized by evaporation of SiO/SiO2 superlattices and subsequent thermally induced phase separation. By this method the synthesis of completely SiO2 passivated Si nanocrystals with a controlled size is demonstrated. A strong blueshift of the photolu...

A detailed analysis of correlations between structural features and cation conductivity is performed for KAlO(2) polymorphs in a wide temperature range of 300-1023 K. To explore the migration maps of K(+) cations we have used neutron diffraction data for low- and high-temperature KAlO(2) polymorphs and applied for the first time a novel algorithm based on the natural tiling concept and implemen...

Hepatocyte growth factor (HGF) induces migration, proliferation, and branching in renal epithelial cells from the inner medullary collecting duct (mIMCD-3 cells). Microarray analysis after HGF stimulation of these cells revealed upregulation of the chemokine KC. We found that both the message and protein levels of KC are increased after HGF treatment and that mIMCD-3 cells express the KC recept...

in this paper, we prove the hyers-ulam stability in$beta$-homogeneous probabilistic modular spaces via fixed point method for the functional equation[f(x+ky)+f(x-ky)=f(x+y)+f(x-y)+frac{2(k+1)}{k}f(ky)-2(k+1)f(y)]for fixed integers $k$ with $kneq 0,pm1.$