82 research outputs found
A proof of the Kikuta-Ruckle conjecture on cyclic caching of resources
No full textSuppose that a hider possesses a continuously divisible resource that he may distribute around a circle. The resources on a random arc in the circle are lost. The hider has a priori information on the length of the arc and he wants to maximize the probability that the retrieved portion exceeds a critical quantity, which is enough to survive on. We show that there exists an optimal resource distribution, which uses a finite number of point caches of equal size, establishing a conjecture of Kikuta and Ruckle. Our result is related to a conjecture of Samuels’ on-tail probabilities
Key role of the p110delta isoform of PI3K in B-cell antigen and IL-4 receptor signaling: comparative analysis of genetic and pharmacologic interference with p110delta function in B cells
No full textCrystal structure of a synthetic cyclodecapeptide for template-assembled synthetic protein design
No full textThe structural prototype of a new generation of regioselectively addressable functionalized templates (RAFTs) for use in protein de novo design has been synthesized and crystallized. The structure of the aromatically substituted cyclodecapeptide was determined by X-ray diffraction; it consists of an antiparallel β sheet spanned by heterochirally induced type II′ β turns, similar to that observed in gramicidin S. The three-dimensional structure of the artificial template was also examined by an NMR spectroscopic analysis in solution and shown to be compatible with a β-sheet plane suitable for accommodating secondary functional peptide fragments for the synthesis of template-assembled synthetic proteins (TASPs)
The novel therapeutic effect of phosphoinositide 3-kinase-γ inhibitor AS605240 in autoimmune diabetes
No full textType 1 diabetes (T1D) remains a major health problem worldwide, with a steadily rising incidence yet no cure. Phosphoinositide 3-kinase-γ (PI3Kγ), a member of a family of lipid kinases expressed primarily in leukocytes, has been the subject of substantial research for its role in inflammatory diseases. However, the role of PI3Kγ inhibition in suppressing autoimmune T1D remains to be explored. We tested the role of the PI3Kγ inhibitor AS605240 in preventing and reversing diabetes in NOD mice and assessed the mechanisms by which this inhibition abrogates T1D. Our data indicate that the PI3Kg pathway is highly activated in T1D. In NOD mice, we found upregulated expression of phosphorylated Akt (PAkt) in splenocytes. Notably, T regulatory cells (Tregs) showed significantly lower expression of PAkt compared with effector T cells. Inhibition of the PI3Kγ pathway by AS605240 efficiently suppressed effector T cells and induced Treg expansion through the cAMP response element-binding pathway. AS605240 effectively prevented and reversed autoimmune diabetes in NOD mice and suppressed T-cell activation and the production of inflammatory cytokines by autoreactive T cells in vitro and in vivo. These studies demonstrate the key role of the PI3Kγ pathway in determining the balance of Tregs and autoreactive cells regulating autoimmune diabetes
On I-lacunary statistical convergence of order α of sequences of sets
No full textThe idea of I-convergence of real sequences was introduced by Kostyrko et
al. [Kostyrko, P. ; Sal?t, T. and Wilczy?ski, W. I-convergence, Real
Anal. Exchange 26(2) (2000/2001), 669-686] and also independently by Nuray
and Ruckle [Nuray, F. and Ruckle,W. H. Generalized statistical convergence
and convergence free spaces, J. Math. Anal. Appl. 245(2) (2000), 513-527].
In this paper we introduce the concepts of Wijsman I-lacunary statistical
convergence of order ? and Wijsman strongly I-lacunary statistical
convergence of order ?, and investigated between their relationship.</jats:p
Search Games on Hypergraphs
No full textThe main motivation behind this thesis is a certain type of win-lose games that are played on hypergraphs and can be translated into the following puzzle. Suppose there are two persons, say Alice and Bob. There are n biscuits, where n is a positive integer, and Alice chooses s of them uniformly at random. Bob possesses h grams of poison, where h is greater than or equal to 1, and the lethal dose is 1 gram. How should Bob distribute the poison over the biscuits in order to maximize the probability of poisoning Alice? This problem is due to Ken Kikuta and William Ruckle who, driven by less devious motives, formulated it in terms of accumulation games between two players. They conjectured that the optimal distribution of poison uses dosages of 1/j grams in as many biscuits as possible, where j is a positive integer that depends on h,n,s. In Chapter 1 we introduce the poisoning problem and discuss its relation to known results from the literature. The conjecture of Kikuta and Ruckle is related to two other conjectures, one from extremal combinatorics and one from the theory of probability. The combinatorial flavor of the Kikuta-Ruckle conjecture is its relation to the matching conjecture of Paul Erdos and its fractional analogue. Its probabilistic flavor is its relation to a conjecture of Stephen Samuels on a tail probability problem. We also consider a poisoning problem on more general ground spaces. This leads to a geometric problem that generalizes the isodiametric one. In Chapter 2 we settle the Kikuta-Ruckle conjecture in case n=2s-1. This case corresponds to the, so called, Odd graph. We also settle the conjecture for a few more cases using elementary combinatorial and game-theoretic arguments. In Chapter 3 we consider the poisoning game on the cyclic graph. In this game the n biscuits are arranged cyclically and Alice chooses s consecutive of them uniformly at random. We find the value of this game along with the optimal strategies of both players. In addition, we give a characterization of the fractional covering number of uniform hypergraphs obtained from the cyclic graph. Chapter 4 deals with the analysis of a network coloring game. This is a game that is motivated by conflict resolution situations and is played on a graph. The vertices of the graph are thought of as players having a fixed set of available colors. The game is played in rounds and in each round all players simultaneously and individually choose a color with the perspective of ending up with a color that is different from the colors chosen by their neighbors. We analyze the network game by introducing a very simple search game. The optimal strategy of the searchers in this game involves tosses of fair colored coins and leads to the following combinatorial probability problem that is interesting on its own. Suppose that you can color n fair coins with n colors. It is not allowed to colors both sides of a coin with the same color, but all other combinations are allowed. Let X be the number of different colors after a toss of the coins. In what way should you color the coins such that you maximize the median of X? We solve this problem and consider its natural generalization to the case of biased coins. The later case builds on the study of Bernoulli random variables whose total number of successes is of fixed parity.Applied mathematicsElectrical Engineering, Mathematics and Computer Scienc
Symmetric Coordinate Spaces and Symmetric Bases
No full textIn this paper properties of symmetric coordinate spaces and symmetric bases are investigated. Since a space which possesses a basis is essentially a space of sequences (12, p. 207), the interrelation of these two concepts naturally suggests itself.Section 2 is a summary of the terminology and methods employed, which fall into four categories: (1) set theoretical properties of coordinate spaces such as symmetry and dual spaces; (2) the notion of FK and BK space (12, p. 202; 13); (3) the theory of the Schauder basis in F-space applied to the case when (see § 2) is a basis for a coordinate space; (4) the concept of a sequential norm, which the author introduced in (7) to illustrate the underlying unity of the first three ideas.</jats:p
An Abstract Concept of the Sum of a Numerical Series
No full textOur aim in this paper, generally stated, is to formulate an abstract concept of the notion of the sum of a numerical series. More particularly, it is a study of the type of sequence space called “sum space”. The idea of sum space arose in connection with two distinct problems.1.1 The Köthe-Toeplitz dual of a sequence space T consists of all sequences t such that st ∈ l1 (absolutely summable sequences) for each s∈T. It is known that if cs or bs is used in place of l1, an analogous theory of duality for sequence spaces can be developed (cf. [2]). What other spaces of sequences can play a rôle analogous to l1? This problem is treated in [6].1.2. Let {xn, fn} be a complete biorthogonal sequence in (X, X*), where X is a locally convex linear topological space and X* is its topological dual space.</jats:p
The Strong <i>ϕ</i> Topology on Symmetric Sequence Spaces
No full textThe strong ϕ topology. Let S be a linear space of real sequences written in functional notationThere is a natural duality between S and the space ϕ of sequences which are eventually ϕ given by the equationThe series has only a finite number of nonzero terms since t is in ϕ.A subset B of ϕ is called S-bounded iffor each s in S.</jats:p
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