Related papers: A sufficient condition for mobile sampling in term…
We give necessary conditions for when a subset of $\mathbb{T}^n$ can contain the support of some non-zero RP-measure. Among other things we show that the support of a positive RP-measure cannot be contained in reflections of inverse images…
We establish necessary and sufficient conditions for the existence of factorizable steady states of the Generalized Zero Range Process. This process allows transitions from a site $i$ to a site $i+q$ involving multiple particles with rates…
In this paper, by reviewing the concept of subcovering and semicovering maps, we extend the notion of subcovering map to subsemicovering map. We present some necessary or sufficient conditions for a local homeomorphism to be a…
We present a topological proof of the existence of invariant manifolds for maps with normally hyperbolic-like properties. The proof is conducted in the phase space of the system. In our approach we do not require that the map is a…
We describe a very simple method for `consistent sampling' that allows for sampling with replacement. The method extends previous approaches to consistent sampling, which assign a pseudorandom real number to each element, and sample those…
Some properties of random Conley index are obtained and then a sufficient condition for the existence of abstract bifurcation points for both discrete-time and continuous-time random dynamical systems is presented. This stochastic…
To help future mobile agents plan their movement in harsh environments,a predictive model has been designed to determine what areas would be favorable for Global Navigation Satellite System (GNSS) positioning. The model is able to predict…
A new sufficient condition is proved for the existence of stochastic semigroups generated by the sum of two unbounded operators. It is applied to one-dimensional piecewise deterministic Markov processes, where we also discuss the existence…
In many areas of applied statistics and machine learning, generating an arbitrary number of independent and identically distributed (i.i.d.) samples from a given distribution is a key task. When the distribution is known only through…
We provide the analytic forms of the distributions for the sum of ordered spacings. We do this both for the case where the boundaries are included in the calculation of the spacings and the case where they are excluded. Both the probability…
In this paper, we are concerned with the problem of creating flattening maps of simply-connected open surfaces in $\mathbb{R}^3$. Using a natural principle of density diffusion in physics, we propose an effective algorithm for computing…
We establish a necessary and sufficient condition for the quantile process based on iid sampling to converge in distribution in $L^1(0,1)$. The condition is that the quantile function is locally absolutely continuous and satisfies a slight…
The electronic properties of a semi-infinite metal surface without a bulk gap are studied by a formalism able to account for the continuous spectrum of the system. The density of states at the surface is calculated within the $GW$…
This paper establishes a necessary and sufficient condition for the asymptotic normality of the nonparametric estimator of sample coverage proposed by Good [Biometrica 40 (1953) 237--264]. This new necessary and sufficient condition extends…
We present a necessary and sufficient condition for the reachable set, i.e., the set of states reachable from a ball of initial states at some time, of an ordinary differential equation to be convex. In particular, convexity is guaranteed…
Theoretical results for importance sampling rely on the existence of certain moments of the importance weights, which are the ratios between the proposal and target densities. In particular, a finite variance ensures square root convergence…
Motility is a ubiquitous feature of microbial life on Earth, and is widely regarded as a promising biosignature candidate. In the search for motile organisms, it is therefore valuable to have rough estimates for the number of such microbes…
Researchers are developing mobile sensing platforms to facilitate public awareness of environmental conditions. However, turning such awareness into practical community action and political change requires more than just collecting and…
Understanding human mobility is of vital importance for urban planning, epidemiology, and many other fields that aim to draw policies from the activities of humans in space. Despite recent availability of large scale data sets related to…
A method is suggested to separately determine the surface density of positively and negatively charged impurities that limit the mobility in a graphene monolayer. The method is based on the exact result for the transport cross-section,…