Optimal Mobility Control of Sensors in the Event of a Disaster

Disasters have caused serious damage on human beings throughout their long history. In a major natural disaster such as an earthquake, a key to mitigate the damage is evacuation. Evidently, secondary collateral disasters is account for more casualty than the initial one. In order to have citizens to evacuate safely for the sake of saving their lives, collecting information is vital. However at times of a disaster, it is a difficult task to gain environmental information about the area by conventional way. One of the solutions to this problem is crowd-sensing, which regards citizens as sensors nodes and collect information with their help. We considered a way of controlling the mobility of such sensor nodes under limitation of its mobility, caused by road blockage, for example. Aiming to make a mobility control scheme that enables high-quality information collection, our method uses preceding result of the measurement to control the mobility. Here it uses kriging variance to do that. We evaluated this method by simulating some measurements and it showed better accuracy than baseline. This is expected to be a method to enable a higher-quality input to the agent-based evacuation simulation, which helps to guide people to evacuate more safely.

VALEURS IMPAIRES DE LA FONCTION DE PARTITION p(n)

Let p(n) denote the number of partitions of n, and for i = 0 (resp. 1), Ai(x) denote the number of n ≤ x such that p(n) is even (resp. odd). In this paper, it is proved that for some constant K > 0, [Formula: see text] holds for x large enough. This estimation slightly improves a preceding result of S. Ahlgren who obtained the above lower bound for K = 0. Let [Formula: see text] and [Formula: see text]; the main tool is a result of J.-P. Serre about the distribution of odd values of τk(n). Effective lower bounds for A0(x) and A1(x) are also given.

On the Prime Ideals in a Commutative Ring

If n and m are positive integers, necessary and sufficient conditions are given for the existence of a finite commutative ring R with exactly n elements and exactly m prime ideals. Next, assuming the Axiom of Choice, it is proved that if R is a commutative ring and T is a commutative R-algebra which is generated by a set I, then each chain of prime ideals of T lying over the same prime ideal of R has at most 2|I| elements. A polynomial ring example shows that the preceding result is best-possible.

Characterization of convergence rates for the approximation of the stationary distribution of infinite monotone stochastic matrices

Let P be an infinite irreducible stochastic matrix, recurrent positive and stochastically monotone and Pn be any n × n stochastic matrix with Pn ≧ Tn , where Tn denotes the n × n northwest corner truncation of P. These assumptions imply the existence of limit distributions π and π n for P and Pn respectively. We show that if the Markov chain with transition probability matrix P meets the further condition of geometric recurrence then the exact convergence rate of π n to π can be expressed in terms of the radius of convergence of the generating function of π. As an application of the preceding result, we deal with the random walk on a half line and prove that the assumption of geometric recurrence can be relaxed. We also show that if the i.i.d. input sequence (A(m)) is such that we can find a real number r 0 > 1 with , then the exact convergence rate of π n to π is characterized by r 0. Moreover, when the generating function of A is not defined for |z| > 1, we derive an upper bound for the distance between π n and π based on the moments of A.

Characterization of convergence rates for the approximation of the stationary distribution of infinite monotone stochastic matrices

Let P be an infinite irreducible stochastic matrix, recurrent positive and stochastically monotone and Pn be any n × n stochastic matrix with Pn ≧ Tn, where Tn denotes the n × n northwest corner truncation of P. These assumptions imply the existence of limit distributions π and πn for P and Pn respectively. We show that if the Markov chain with transition probability matrix P meets the further condition of geometric recurrence then the exact convergence rate of πn to π can be expressed in terms of the radius of convergence of the generating function of π. As an application of the preceding result, we deal with the random walk on a half line and prove that the assumption of geometric recurrence can be relaxed. We also show that if the i.i.d. input sequence (A(m)) is such that we can find a real number r0 > 1 with , then the exact convergence rate of πn to π is characterized by r0. Moreover, when the generating function of A is not defined for |z| > 1, we derive an upper bound for the distance between πn and π based on the moments of A.