In [22], M. van de Berg made a “fundamental gap conjecture” in the context of a free boson gas confined in a container in Rn with hard walls, and in [24], Yau generalized the conjecture to what is now known as the “fundamental gap conjecture.” For a convex domain Ω ⊂ Rn, (0.1) ξ(Ω) := d (λ2(Ω)− λ1(Ω)) ≥ 3π where d is the diameter of the domain, and 0 < λ1(Ω) < λ2(Ω) are the first two eigenvalue...

In this paper, we study quantum OBDD model, it is a restricted version of read-once quantum branching programs, with respect to “width” complexity. It is known that the maximal gap between deterministic and quantum complexities is exponential. But there are few examples of functions with such a gap. We present a method (called “reordering”), which allows us to transform a Boolean function f int...

Gap junction channels mediate direct cell-cell communication via the exchange of second messengers, ions, and metabolites from one cell to another. Mutations in several human connexin (cx) genes, the subunits of gap junction channels, disturb the development and function of multiple tissues/organs. In particular, appropriate function of Cx43 is required for skeletal development in all vertebrat...

Gap junction communication (GJC) mediated by connexins is critical for heart function. To gain insight into the causal relationship of molecular mechanisms of disease pathology, it is important to understand which mechanisms contribute to impairment of gap junctional communication. Here, we present an update on the known modulators of connexins, including various interaction partners, kinases, ...

We give an application of our extender based Radin forcing to cardinal arithmetic. Assuming κ is a large enough cardinal we construct a model satisfying 2 = κ together with 2 = λ for each cardinal λ < κ, where 0 < n < ω. The cofinality of κ can be set arbitrarily or κ can remain inaccessible. When κ remains an inaccessible, Vκ is a model of ZFC satisfying 2 = λ for all cardinals λ.

ATP is a widely used extracellular signaling molecule. The mechanism of ATP release from cells is presently unresolved and may be either vesicular or channel-mediated. Erythrocytes release ATP in response to low oxygen or to shear stress. In the absence of vesicles, the release has to be through channels. Erythrocytes do not form gap junctions. Yet, here we show with immunohistochemical and ele...

We consider bilevel pseudomonotone equilibrium problems. We use a penalty function to convert a bilevel problem into one-level ones. We generalize a pseudo-∇-monotonicity concept from ∇monotonicity and prove that under pseudo-∇-monotonicity property any stationary point of a regularized gap function is a solution of the penalized equilibrium problem. As an application, we discuss a special case...

Despite the wealth of metagenomic sequencing data, the functions of most bacterial genes from the mammalian microbiota have remained poorly understood. In their recent study (Yaung et al 2015), Wang, Gerber, and colleagues present a platform which allows functional mining of bacterial genomes for genes that contribute to fitness in vivo and holds great potential for forward engineering microbes...

A well-known technique for the solution of quasi-variational inequalities (QVIs) consists in the reformulation of QVIs as a constrained or unconstrained optimization problem by means of so-called gap functions. In contrast to standard variational inequalities, however, these gap functions turn out to be nonsmooth in general. Here it is shown that one can obtain an unconstrained optimization ref...