background: in recent years, epidemiologic and laboratory studies have implied that vitamin d deficiency has a role in the pathogenesis of breast cancer. it has shown that vitamin d can prevent tumor progression induced by carcinogens and inhibit the carcinogenic effects of high fat diet on breast tissue and growth of tumor cells. this study aimed to evaluate serum 25-hydroxyvitamin d level and...

The Majority is Stablest Theorem has numerous applications in hardness of approximation and social choice theory. We give a new proof of the Majority is Stablest Theorem by induction on the dimension of the discrete cube. Unlike the previous proof, it uses neither the ”invariance principle” nor Borell’s result in Gaussian space. The new proof is general enough to include all previous variants o...

Heterogeneous networks (HetNets) give users the opportunity to access different access points(APs), which will simultaneously affect user performance and system performance, so user association in HetNets plays a critical role in enhancing the load balancing and the system sum-throughput of networks. Meanwhile, the incremental sum-throughput currently fails to meet the escalating data demands. ...

We characterize the structure of maximum-size sum-free subsets of a random subset of an Abelian group G. In particular, we determine the threshold above which, with high probability as |G| → ∞, each such subset is contained in some maximum-size sum-free subset of G, whenever q divides |G| for some (fixed) prime q with q ≡ 2 (mod 3). Moreover, in the special case G = Z2n, we determine the sharp ...

We study optimal stochastic control problems under model uncertainty. We rewrite such problems as (zero-sum) stochastic differential games of forward-backward stochastic differential equations. We prove general stochastic maximum principles for such games, both in the zero-sum case (finding conditions for saddle points) and for the non-zero sum games (finding conditions for Nash equilibria). We...

Let G=(V,E) be an oriented graph whose edges are labelled by the elements of a group Γ and let A⊆V . An A-path is a path whose ends are both in A. The weight of a path P in G is the sum of the group values on forward oriented arcs minus the sum of the backward oriented arcs in P . (If Γ is not abelian, we sum the labels in their order along the path.) We give an efficient algorithm for finding ...

Abstract Automatic sequences are not suitable for cryptographic applications since both their subword complexity and expansion small, correlation measure of order 2 is large. These highly predictable despite having a large maximum complexity. However, recent results show that polynomial subsequences automatic sequences, such as the Thue–Morse sequence, better candidates pseudorandom sequences. ...