In this paper we consider the problem of establishing a value r0 such that almost all random graphs with n vertices and rn edges, r > r0, are asymptotically not 3-colorable. In our approach we combine the concept of rigid legal colorings introduced by Achlioptas and Molloy with the occupancy problem for random allocations of balls into bins. Using the sharp estimates obtained by Kamath et al. o...

We consider a real Gaussian process X with unknown smoothness r0 where r0 is a nonnegative integer and the mean-square derivative X (r0) is supposed to be locally stationary of index β0. From n + 1 equidistant observations, we propose and study an estimator of (r0, β0) based on results for quadratic variations of the underlying process. Various numerical studies of these estimators derive their...

Let Q = {Q1, . . . , Qn} be a set of past queries and let R = {R1, . . . , Rn} be their results. Moreover, let Q0 be a query newly submitted to the system and let R0 be its result. The task of optimizing the extraction of R0 using the knowledge provided by Q and R have been faced following two distinct approaches. In the first approach we search for a query Qi ∈ Q, such that R0 ⊆ Ri (in such a ...

Mice with a targeted disruption of the interferon gamma receptor gene (IFN-gamma R0/0 mice) and control wild-type mice were inoculated with the Bacillus Calmette-Guérin (BCG) strain of Mycobacterium bovis. BCG infection was not lethal for wild-type mice whereas all IFN-gamma R0/0 mice died approximately 7-9 wk after inoculation. Histological examination at 2 and 6 wk after BCG inoculation showe...

Let X be an m × n matrix of indeterminates, m ≤ n, and T a new indeterminate. Consider the polynomial rings R0 = K[X] and R = R0[T ]. For a given positive integer t ≤ m, consider the ideal It = It(X) generated by the t-minors (i. e. the determinants of the t× t submatrices) of X . Using all these determinantal ideals, we define a new ideal J in R = R0[T ], which we call the generic graph constr...

Dynamic models - often deterministic in nature - were used to estimate the basic reproductive number, R0, of the 2014-5 Ebola virus disease (EVD) epidemic outbreak in West Africa. Estimates of R0 were then used to project the likelihood for large outbreak sizes, e.g., exceeding hundreds of thousands of cases. Yet fitting deterministic models can lead to over-confidence in the confidence interva...

The aim of this study was to test the ability of a simple two segment model to describe the frequency dependence of resistive impedance in obstructive patients, and to investigate the significance of parameters derived from this model. The study was performed in 38 patients, in the basal state and after inhalation of 200 micrograms salbutamol. Impedance data measured over 4-32 Hz were fitted by...

Temperature is a major factor affecting population abundance and individual performance. Net reproductive rate (R0) and intrinsic rate of increase (r) differ in their response to different temperature regimes, and much of the difference is mediated by generation time (Tg). Here, we evaluate the effects of thermal mean and variability on R0, r and Tg, at four population densities in Drosophila m...

A precise definition of the basic reproduction number, R0, is presented for a general compartmental disease transmission model based on a system of ordinary differential equations. It is shown that, if R0 < 1, then the disease free equilibrium is locally asymptotically stable; whereas if R0 > 1, then it is unstable. Thus, R0 is a threshold parameter for the model. An analysis of the local centr...