Relaxing the Irrevocability Requirement for Online Graph Algorithms

Online graph problems are considered in models where the irrevocability requirement is relaxed. Motivated by practical examples where, for example, there is a cost associated with building a facility and no extra cost associated with doing it later, we consider the Late Accept model, where a request can be accepted at a later point, but any acceptance is irrevocable. Similarly, we also consider a Late Reject model, where an accepted request can later be rejected, but any rejection is irrevocable (this is sometimes called preemption). Finally, we consider the Late Accept/Reject model, where late accepts and rejects are both allowed, but any late reject is irrevocable. For Independent Set, the Late Accept/Reject model is necessary to obtain a constant competitive ratio, but for Vertex Cover the Late Accept model is sufficient and for Minimum Spanning Forest the Late Reject model is sufficient. The Matching problem has a competitive ratio of 2, but in the Late Accept/Reject model, its competitive ratio is 3/2

Mechanism of action of probiotics

The modern diet doesn't provide the required amount of beneficial bacteria. Maintenance of a proper microbial ecology in the host is the main criteria to be met for a healthy growth. Probiotics are one such alternative that are supplemented to the host where by and large species of Lactobacillus, Bifidobacterium and Saccharomyces are considered as main probiotics. The field of probiotics has made stupendous strides though there is no major break through in the identification of their mechanism of action. They exert their activity primarily by strengthening the intestinal barrier and immunomodulation. The main objective of the study was to provide a deep insight into the effect of probiotics against the diseases, their applications and proposed mechanism of action

Gold(I)-Catalyzed Coupling Reactions for the Synthesis of Diverse Small Molecules Using the Build/Couple/Pair Strategy

The build/couple/pair strategy has yielded small molecules with stereochemical and skeletal diversity by using short reaction sequences. Subsequent screening has shown that these compounds can achieve biological tasks considered challenging if not impossible (‘undruggable’) for small molecules. We have developed gold(I)-catalyzed cascade reactions of easily prepared propargyl propiolates as a means to achieve effective intermolecular coupling reactions for this strategy. Sequential alkyne activation of propargyl propiolates by a cationic gold(I) catalyst yields an oxocarbenium ion that we previously showed is trapped by C-based nucleophiles at an extrannular site to yield α-pyrones. Here, we report O-based nucleophiles react by ring opening to afford a novel polyfunctional product. In addition, by coupling suitable building blocks, we subsequently performed intramolecular pairing reactions that yield diverse and complex skeletons. These pairing reactions include one based on a novel aza-Wittig-6π-electrocyclization sequence and others based on ring-closing metathesis reactions.Chemistry and Chemical Biolog

On the competitive ratio for online facility location

Abstract. We consider the problem of Online Facility Location, where demands arrive online and must be irrevocably assigned to an open facility upon arrival. The objective is to minimize the sum of facility and assignment costs. We prove that the competitive log n ratio for Online Facility Location is Θ (). On the negative side, we show that no log log n randomized algorithm can achieve a competitive ratio better than Ω ( ) against an log log n oblivious adversary even if the demands lie on a line segment. On the positive side, we present log n a deterministic algorithm achieving a competitive ratio of O (). The analysis is based log log n on a hierarchical decomposition of the optimal facility locations such that each component either is relatively well-separated or has a relatively large diameter, and a potential function argument which distinguishes between the two kinds of components.

On the connectivity and superconnected graphs with small diameter

In this paper, first we prove that any graph G is 2-connected if diam(G)≤g−1 for even girth g, and for odd girth g and maximum degree Δ≤2δ−1 where δ is the minimum degree. Moreover, we prove that any graph G of diameter diam(G)≤g−2 satisfies that (i) G is 5-connected for even girth g and Δ≤2δ−5, and (ii) G is super-κ for odd girth g and Δ≤3δ/2−1

The Avant Garde as Exform

Peter Bürger’s critique of the historical avant garde accounts for its ineffectual nature as a political movement because of its relationship with institions. He argues for hermeneutics to be employed as a critique of ideology, and as a facet of the understanding of the ‘historicity of aesthetic categories’.’ The influence of institutions on music since 1968 has served as a central part of its critique: the work concept itself seems to enshrine political ineffectiveness and the bourgeois nature of art practice that ought to be critiqued by an avant-garde. In contrast, Bourriaud’s concept of the ‘exform’ re-conceives the avant-garde as outside of institutions and an idea of ‘progress’ that is aligned with a dominant capitalist ideology. He frames the task of the avant-garde artist as giving energy to ‘waste’, outside of political and ideological institutions. This type of avant-garde practice functions to ‘bring precarity to mind: to keep the notion alive that intervention in the world is possible.’ This article explores the exform with respect to the work of the British composer Chris Newman and the Swiss composer Annette Schmucki, and considers how Bourriaud’s approach to re-thinking the avant-garde might apply specifically to contemporary and experimental music in the present