On the Compressibility of non-Abelian-Group Sources in a Distributed Source Coding Setting

We consider the problem of compression of a non-Abelian source.This is motivated by the problem of distributed function computation,where it is known that if one is only interested in computing a function of several sources, then one can often improve upon the compression rate required by the Slepian-Wolf bound. Let G be a non-Abelian group having center Z(G). We show here that it is impossible to compress a source with symbols drawn from G when Z(G) is trivial if one employs a homomorphic encoder and a typical-set decoder.We provide achievable upper bounds on the minimum rate required to compress a non-Abelian group with non-trivial center. Also, in a two source setting, we provide achievable upper bounds for compression of any non-Abelian group, using a non-homomorphic encoder.

Visualizing lone pairs in compounds containing heavier congeners of the carbon and nitrogen group elements

In this mini-review, I discuss some recent work on the stereochemistry and bonding of lone pairs of electrons in divalent compounds of the heavier carbon group elements (SnII, PbII) and in trivalent compounds of the heavier nitrogen group elements (BiIII). Recently developed methods that permit the real-space visualization of bonding patterns on the basis of density functional calculations of electronic structure, reveal details of the nature of s electron lone pairs in compounds of the heavier main group elements – their stereochemistry and their inertness (or lack thereof). An examination of tetragonal P4/nmm SnO, a-PbO and BiOF, and cubic Fm3m PbS provides a segue into perovskite phases of technological significance, including ferroelectric PbTiO3 and antiferroelectric/piezoelectric PbZrO3, in both of which the lone pairs on Pb atoms play a pivotal rôle.

Higgs Working Group Summary Report

Report of the Higgs working group for the Workshop "Physics at TeV Colliders", Les Houches, France 8-18 June 1999. It contains 6 separate sections: 1. Measuring Higgs boson couplings at the LHC. 2. Higgs boson production at hadron colliders at NLO. 3. Signatures of Heavy Charged Higgs Bosons at the LHC. 4. Light stop effects and Higgs boson searches at the LHC. 5. Double Higgs production at TeV Colliders in the MSSM. 6. Programs and Tools for Higgs Bosons.

Rhodium Carbenoid Mediated C-H Activation of a Tertiary Methyl Group: An Enantiospecific Approach to the Angular Triquinanes Norsilphiperfolane and Norcameroonanes

An enantiospecific synthesis of the angular triquinane system present in the sesquiterpenes cameroonanes and silphiperfolanes has been accomplished, starting from 5-isopropenyl-2-methylcyclopent-1-ene-1-methanol [readily available in three steps from (R)-limonene] employing an intramolecular rhodium carbenoid insertion into the C-H bond of a tertiary methyl group for the construction of the triquinane system.

On four-group ML decodable distributed space time codes for cooperative communication

A construction of a new family of distributed space time codes (DSTCs) having full diversity and low Maximum Likelihood (ML) decoding complexity is provided for the two phase based cooperative diversity protocols of Jing-Hassibi and the recently proposed Generalized Non-orthogonal Amplify and Forward (GNAF) protocol of Rajan et al. The salient feature of the proposed DSTCs is that they satisfy the extra constraints imposed by the protocols and are also four-group ML decodable which leads to significant reduction in ML decoding complexity compared to all existing DSTC constructions. Moreover these codes have uniform distribution of power among the relays as well as in time. Also, simulations results indicate that these codes perform better in comparison with the only known DSTC with the same rate and decoding complexity, namely the Coordinate Interleaved Orthogonal Design (CIOD). Furthermore, they perform very close to DSTCs from field extensions which have same rate but higher decoding complexity.

Incentive compatible mechanisms for group ticket allocation in software maintenance services

A customer reported problem (or Trouble Ticket) in software maintenance is typically solved by one or more maintenance engineers. The decision of allocating the ticket to one or more engineers is generally taken by the lead, based on customer delivery deadlines and a guided complexity assessment from each maintenance engineer. The key challenge in such a scenario is two folds, un-truthful (hiked up) elicitation of ticket complexity by each engineer to the lead and the decision of allocating the ticket to a group of engineers who will solve the ticket with in customer deadline. The decision of allocation should ensure Individual and Coalitional Rationality along with Coalitional Stability. In this paper we use game theory to examine the issue of truthful elicitation of ticket complexities by engineers for solving ticket as a group given a specific customer delivery deadline. We formulate this problem as strategic form game and propose two mechanisms, (1) Division of Labor (DOL) and (2) Extended Second Price (ESP). In the proposed mechanisms we show that truth telling by each engineer constitutes a Dominant Strategy Nash Equilibrium of the underlying game. Also we analyze the existence of Individual Rationality (IR) and Coalitional Rationality (CR) properties to motivate voluntary and group participation. We use Core, solution concept from co-operative game theory to analyze the stability of the proposed group based on the allocation and payments.

Ethnobotany of the Monpa ethnic group at Arunachal Pradesh, India

Background: The present paper documents the uses of plants in traditional herbal medicine for human and veterinary ailments, and those used for dietary supplements, religious purpose, local beverage, and plants used to poison fish and wild animals. Traditional botanical medicine is the primary mode of healthcare for most of the rural population in Arunachal Pradesh. Materials and methods: Field research was conducted between April 2006 and March 2009 with randomly selected 124 key informants using semi-structured questionnaire. The data obtained was analyzed through informant consensus factor (F(IC)) to determine the homogeneity of informant's knowledge on medicinal plants. Results: We documented 50 plants species belonging to 29 families used for treating 22 human and 4 veterinary ailments. Of the medicinal plants reported, the most common growth form was herbs (40%) followed by shrubs, trees, and climbers. Leaves were most frequently used plant parts. The consensus analysis revealed that the dermatological ailments have the highest F(IC) (0.56) and the gastro-intestinal diseases have F(IC) (0.43). F(IC) values indicated that there was high agreement in the use of plants in dermatological and gastro-intestinal ailments category among the users. Gymnocladus assamicus is a critically rare and endangered species used as disinfectant for cleaning wounds and parasites like leeches and lice on livestocks. Two plant species (Illicium griffithii and Rubia cordifolia) are commonly used for traditional dyeing of clothes and food items. Some of the edible plants recorded in this study were known for their treatment against high blood pressure (Clerodendron colebrookianum), diabetes mellitus (Momordica charantia), and intestinal parasitic worms like round and tape worms (Lindera neesiana, Solanum etiopicum, and Solanum indicum). The Monpas of Arunachal Pradesh have traditionally been using Daphne papyracea for preparing hand-made paper for painting and writing religious scripts in Buddhist monasteries. Three plant species (Derris scandens, Aesculus assamica, and Polygonum hydropiper) were frequently used to poison fish during the month of June-July every year and the underground tuber of Aconitum ferrox is widely used in arrow poisoning to kill ferocious animals like bear, wild pigs, gaur and deer. The most frequently cited plant species; Buddleja asiatica and Hedyotis scandens were used as common growth supplements during the preparation of fermentation starter cultures. Conclusion: The traditional pharmacopoeia of the Monpa ethnic group incorporates a myriad of diverse botanical flora. Traditional knowledge of the remedies is passed down through oral traditions without any written document. This traditional knowledge is however, currently threatened mainly due to acculturation and deforestation due to continuing traditional shifting cultivation. This study reveals that the rural populations in Arunachal Pradesh have a rich knowledge of forest-based natural resources and consumption of wild edible plants is still an integral part of their socio-cultural life. Findings of this documentation study can be used as an ethnopharmacological basis for selecting plants for future phytochemical and pharmaceutical studies.

Fast-Group-Decodable STBCs via Codes over GF(4): Further Results

Recently in, a framework was given to construct low ML decoding complexity Space-Time Block Codes (STBCs) via codes over the finite field F4. In this paper, we construct new full-diversity STBCs with cubic shaping property and low ML decoding complexity via codes over F4 for number of transmit antennas N = 2m, m >; 1, and rates R >; 1 complex symbols per channel use. The new codes have the least ML decoding complexity among all known codes for a large set of (N, R) pairs. The new full-rate codes of this paper (R = N) are not only information-lossless and fully diverse but also have the least known ML decoding complexity in the literature. For N ≥ 4, the new full-rate codes are the first instances of full-diversity, information-lossless STBCs with low ML decoding complexity. We also give a sufficient condition for STBCs obtainable from codes over F4 to have cubic shaping property, and a sufficient condition for any design to give rise to a full-diversity STBC when the symbols are encoded using rotated square QAM constellations.

Low ML Decoding Complexity STBCs via Codes Over the Klein Group

In this paper, we give a new framework for constructing low ML decoding complexity space-time block codes (STBCs) using codes over the Klein group K. Almost all known low ML decoding complexity STBCs can be obtained via this approach. New full- diversity STBCs with low ML decoding complexity and cubic shaping property are constructed, via codes over K, for number of transmit antennas N = 2(m), m >= 1, and rates R > 1 complex symbols per channel use. When R = N, the new STBCs are information- lossless as well. The new class of STBCs have the least knownML decoding complexity among all the codes available in the literature for a large set of (N, R) pairs.

Group Actions and Elementary Number Theory

Abstract | In this article the shuffling of cards is studied by using the concept of a group action. We use some fundamental results in Elementary Number Theory to obtain formulas for the orders of some special shufflings, namely the Faro and Monge shufflings and give necessary and sufficient conditions for the Monge shuffling to be a cycle. In the final section we extend the considerations to the shuffling of multisets.

An analogue of the Wiener Tauberian Theorem for the Heisenberg Motion group

We show that the Wiener Tauberian property holds for the Heisenberg Motion group TnBgroups. However, our exposition is almost self contained and the techniques used in the proof are relatively simple.