Greedy Algorithms for Steiner Forest

In the Steiner Forest problem, we are given terminal pairs $\{s_i, t_i\}$, and need to find the cheapest subgraph which connects each of the terminal pairs together. In 1991, Agrawal, Klein, and Ravi, and Goemans and Williamson gave primal-dual constant-factor approximation algorithms for this problem; until now, the only constant-factor approximations we know are via linear programming relaxations. We consider the following greedy algorithm: Given terminal pairs in a metric space, call a terminal "active" if its distance to its partner is non-zero. Pick the two closest active terminals (say $s_i, t_j$), set the distance between them to zero, and buy a path connecting them. Recompute the metric, and repeat. Our main result is that this algorithm is a constant-factor approximation. We also use this algorithm to give new, simpler constructions of cost-sharing schemes for Steiner forest. In particular, the first "group-strict" cost-shares for this problem implies a very simple combinatorial sampling-based algorithm for stochastic Steiner forest

SLA-Oriented Resource Provisioning for Cloud Computing: Challenges, Architecture, and Solutions

Cloud computing systems promise to offer subscription-oriented, enterprise-quality computing services to users worldwide. With the increased demand for delivering services to a large number of users, they need to offer differentiated services to users and meet their quality expectations. Existing resource management systems in data centers are yet to support Service Level Agreement (SLA)-oriented resource allocation, and thus need to be enhanced to realize cloud computing and utility computing. In addition, no work has been done to collectively incorporate customer-driven service management, computational risk management, and autonomic resource management into a market-based resource management system to target the rapidly changing enterprise requirements of Cloud computing. This paper presents vision, challenges, and architectural elements of SLA-oriented resource management. The proposed architecture supports integration of marketbased provisioning policies and virtualisation technologies for flexible allocation of resources to applications. The performance results obtained from our working prototype system shows the feasibility and effectiveness of SLA-based resource provisioning in Clouds.Comment: 10 pages, 7 figures, Conference Keynote Paper: 2011 IEEE International Conference on Cloud and Service Computing (CSC 2011, IEEE Press, USA), Hong Kong, China, December 12-14, 201

Quantum phase interference (Berry phase) in single-molecule magnets of Mn12

Magnetization measurements of a molecular clusters Mn12 with a spin ground state of S = 10 show resonance tunneling at avoided energy level crossings. The observed oscillations of the tunnel probability as a function of the magnetic field applied along the hard anisotropy axis are due to topological quantum phase interference of two tunnel paths of opposite windings. Mn12 is therefore the second molecular clusters presenting quantum phase interference.Comment: 3 pages, 4 figures, MMM'01 conference (12-16 Nov.

Online Learning Models for Content Popularity Prediction In Wireless Edge Caching

Caching popular contents in advance is an important technique to achieve the low latency requirement and to reduce the backhaul costs in future wireless communications. Considering a network with base stations distributed as a Poisson point process (PPP), optimal content placement caching probabilities are derived for known popularity profile, which is unknown in practice. In this paper, online prediction (OP) and online learning (OL) methods are presented based on popularity prediction model (PPM) and Grassmannian prediction model (GPM), to predict the content profile for future time slots for time-varying popularities. In OP, the problem of finding the coefficients is modeled as a constrained non-negative least squares (NNLS) problem which is solved with a modified NNLS algorithm. In addition, these two models are compared with log-request prediction model (RPM), information prediction model (IPM) and average success probability (ASP) based model. Next, in OL methods for the time-varying case, the cumulative mean squared error (MSE) is minimized and the MSE regret is analyzed for each of the models. Moreover, for quasi-time varying case where the popularity changes block-wise, KWIK (know what it knows) learning method is modified for these models to improve the prediction MSE and ASP performance. Simulation results show that for OP, PPM and GPM provides the best ASP among these models, concluding that minimum mean squared error based models do not necessarily result in optimal ASP. OL based models yield approximately similar ASP and MSE, while for quasi-time varying case, KWIK methods provide better performance, which has been verified with MovieLens dataset.Comment: 9 figure, 29 page

Where we stand on structure dependence of ISGMR in the Zr-Mo region: Implications on K_\infty

Isoscalar giant resonances, being the archetypal forms of collective nuclear behavior, have been studied extensively for decades with the goal of constraining bulk nuclear properties of the equation of state, as well as for modeling dynamical behaviors within stellar environments. An important such mode is the isoscalar electric giant monopole resonance (ISGMR) that can be understood as a radially symmetric density vibration within the saturated nuclear volume. The field has a few key open questions, which have been proposed and remain unresolved. One of the more provocative questions is the extra high-energy strength in the $A\approx 90$ region, which manifested in large percentages of the $E0$ sum rule in $^{92}$Zr and $^{92}$Mo above the main ISGMR peak. The purpose of this article is to introduce these questions within the context of experimental investigations into the phenomena in the zirconium and molybdenum isotopic chains, and to address, via a discussion of previously published and preliminary results, the implications of recent experimental efforts on extraction of the nuclear incompressibility from this data.Comment: 9 pages, 7 figures, invited to be submitted to a special issue of EPJA honoring Prof. P. F. Bortigno

Berry-phase blockade in single-molecule magnets

We formulate the problem of electron transport through a single-molecule magnet (SMM) in the Coulomb blockade regime taking into account topological interference effects for the tunneling of the large spin of a SMM. The interference originates from spin Berry phases associated with different tunneling paths. We show that in the case of incoherent spin states it is essential to place the SMM between oppositely spin-polarized source and drain leads in order to detect the spin tunneling in the stationary current, which exhibits topological zeros as a function of the transverse magnetic field.Comment: 4 pages, Revtex 4, 4 EPS figure

Antimicrobial activity of skin secretions isolated from Indian toad, Bufo melanostictus Schneider 1799

Amphibians like toads have been known to secrete antimicrobial secretions outside their body into their environments, through skin pores and parotid glands. Toad skin-secretions contain four types of compounds namely, biogenic amines, bufadienolides, alkaloids & steroids and peptides & proteins. Bulk of research relating to amphibian antimicrobial secretions has been done on frogs. In toads, such research has only been done in South America, Europe and China. Antimicrobial secretions vary considerably from specie-to-specie and drastically across various biomes. This prompted us to examine and confirm presence of antimicrobial activity (if any) in Indian Common Toad (Bufo melanostictus Schneider 1799) skin secretions since; no such analysis had been previously done on this toad which is found all across the South-east Asia. The antibacterial potency of toad skin secretions was tested against the bacteria, Escherichia coli. After running preliminary antibacterial analysis assays, we found that these cutaneous secretions retrieved from Indian Common Toad possessed potential bactericidal activity. The results that we got confirmed that some unexplored bactericidal components were present in skin secretions of these toads. These conclusions call for further research into biochemistry and molecular characterization of these components