The converse of the Borel–Cantelli Lemma states that if {Ai}i=1∞ is a sequence independent events such ∑P(Ai)=∞, then almost surely infinitely many these will occur. Erdős and Rényi proved it sufficient to weaken condition independence pairwise independence. Later, several other weakenings appeared in literature. aim this paper provide collection conditions, all which imply occur, determine com...

The principle sPHPb (PV (α)) states that no oracle circuit can compute a surjection of a onto b. We show that sPHP P (a)(PV (α)) is independent of PV1(α)+ sPHP π(a) Π(a)(PV (α)) for various choices of the parameters π, Π, %, P . We also improve the known separation of iWPHP(PV ) from S 2 + sWPHP(PV ) under cryptographic assumptions.

We show that the class of social welfare functions that satisfy a weak independence condition identi…ed by Baigent (1987) is fairly rich and freed of a power concentration on a single individual. This positive result prevails when a weak pareto condition is imposed. Hence, under weak independence, both the Arrow (1951) and Wilson (1972) theorems vanish. We thank Goksel Asan, Irem Bozbay, Tugce ...

Previous experimental results have clearly demonstrated the effectiveness of utilizing context-specific independence (CSI) in probabilistic inference. However, CSI is a special case of a more general independence called contextual weak independence (CWI). In this paper, we show how CWI can be utilized for more efficient probabilistic inference. These results are quite significant as they sugges...

Let (Xi)i∈Z be a regular stationary process for a given filtration. The weak invariance principle holds under the condition ∑ i∈Z ‖P0(Xi)‖2 < ∞ (see [11], [2], [3]). In this paper, we show that this criterion is independent of other known criteria: the martingalecoboundary decomposition of Gordin (see [7], [8]), the criterion of Dedecker and Rio (see [4]) and the condition of Maxwell and Woodro...

The most simplified axiom systems of pseudo-weak-R0 algebras and pseudo-R0 algebras are obtained, and the mutually independence of axioms is proved. We introduce the notions of filters and normal filters in pseudo-weak-R0 algebras. The structures and properties of the generated filters and generated normal filters in pseudo-weak-R0 algebras are obtained. These can be seen as noncommutative gene...

In this paper we define ?-independent (a weak-version of independence), Kronecker and dissociate sets on hypergroups and study their properties and relationships among them and some other thin sets such as independent and Sidon sets. These sets have the lacunarity or thinness property and are very useful indeed. For example Varopoulos used the Kronecker sets to prove the Malliavin theorem. In t...

The Madagascar seasat dataset presents a problem where data are collected along crossing tracks. These tracks are not straight, and appear to be irregular in the model space. Previous methods assumed that the data were regularly sampled in the model space coordinate system. I warp the model space to look more like the data space, so that prediction-error filters can be estimated in the more reg...