A simple vibrating reed apparatus for use at low temperatures

The authors report the design and construction of a very simple vibrating reed apparatus with automatic frequency locking capability where the resonance frequency and the internal friction can be recorded continuously as a function of temperature. The apparatus is particularly suitable for studies down to liquid helium temperatures or below.

Reed-Muller Canonical Forms in Multivalued Logic

Canonical forms for m-valued functions referred to as m-Reed-Muller canonical (m-RMC) forms that are a generalization of RMC forms of two-valued functions are proposed. m-RMC forms are based on the operations ?m (addition mod m) and .m (multiplication mod m) and do not, as in the cases of the generalizations proposed in the literature, require an m-valued function for m not a power of a prime, to be expressed by a canonical form for M-valued functions, where M > m is a power of a prime. Methods of obtaining the m-RMC forms from the truth vector or the sum of products representation of an m-valued function are discussed. Using a generalization of the Boolean difference to m-valued logic, series expansions for m-valued functions are derived.

A Note on Minimal Reed-Muller Canonical Forms of Switching Functions

A nonexhaustive procedure for obtaining minimal Reed-Muller canonical (RMC) forms of switching functions is presented. This procedure is a modification of a procedure presented earlier in the literature and enables derivation of an upper bound on the number of RMC forms to be derived to choose a minimal one. It is shown that the task of obtaining minimal RMC forms is simplified in the case of symmetric functions and self-dual functions.

On Generalized Reed-Muller Expansions

The generalized Reed-Muller expansions of a switching function are generated using a single Boolean matrix and step-by-step shifting of the principal column.

Pictorial Guide to Frogs and Toads of the Western Ghats

A unique colour pictorial guide exclusively on frogs and toads of the Western Ghats of India. The guide illustrates 73 species with quality photographs, pointers to key features, pictograms, distribution maps, habitat photographs and with minimal text. Scientific and common names, museum record, actual and relative sizes, habitats and current IUCN status of each species are also provided. Species are grouped on their habitat preferences, making it easy to use in the field.

The Treewidth of MDS and Reed-Muller Codes

The constraint complexity of a graphical realization of a linear code is the maximum dimension of the local constraint codes in the realization. The treewidth of a linear code is the least constraint complexity of any of its cycle-free graphical realizations. This notion provides a useful parameterization of the maximum-likelihood decoding complexity for linear codes. In this paper, we show the surprising fact that for maximum distance separable codes and Reed-Muller codes, treewidth equals trelliswidth, which, for a code, is defined to be the least constraint complexity (or branch complexity) of any of its trellis realizations. From this, we obtain exact expressions for the treewidth of these codes, which constitute the only known explicit expressions for the treewidth of algebraic codes.

On the treewidth of MDS and Reed-Muller codes

The treewidth of a linear code is the least constraint complexity of any of its cycle-free graphical realizations. This notion provides a useful parametrization of the maximum-likelihood decoding complexity for linear codes. In this paper, we compute exact expressions for the treewidth of maximum distance separable codes, and first- and second-order Reed-Muller codes. These results constitute the only known explicit expressions for the treewidth of algebraic codes.

Lineage delimitation and description of nine new species of bush frogs (Anura: Raorchestes, Rhacophoridae) from the Western Ghats Escarpment

Bush frogs of the genus Raorchestes are distributed mainly in the Western Ghats Escarpment of Peninsular India. The inventory of species in this genus is incomplete and there is ambiguity in the systematic status of species recognized by morphological criteria. To address the dual problem of taxon sampling and systematic uncertainty in bush frogs, we used a large-scale spatial sampling design, explicitly incorporating the geographic and ecological heterogeneity of the Western Ghats. We then used a hierarchical multi-criteria approach by combining mitochondrial phylogeny, genetic distance, geographic range, morphology and advertisement call to delimit bush frog lineages. Our analyses revealed the existence of a large number of new lineages with varying levels of genetic divergence. Here, we provide diagnoses and descriptions for nine lineages that exhibit divergence across multiple axes. The discovery of new lineages that exhibit high divergence across wide ranges of elevation and across the major massifs highlights the large gaps in historical sampling. These discoveries underscore the significance of addressing inadequate knowledge of species distribution, namely the ``Wallacean shortfall'', in addressing the problem of taxon sampling and unknown diversity in tropical hotspots. A biogeographically informed sampling and analytical approach was critical in detecting and delineating lineages in a consistent manner across the genus. Through increased taxon sampling, we were also able to discern a number of well-supported sub-clades that were either unresolved or absent in earlier phylogenetic reconstructions and identify a number of shallow divergent lineages which require further examination for assessment of their taxonomic status.

Breeding in bamboo: a novel anuran reproductive strategy discovered in Rhacophorid frogs of the Western Ghats, India

Amphibians exhibit extraordinarily diverse sets of reproductive strategies among vertebrates. Understanding life history strategies in an evolutionary framework is lacking for many amphibian species in the tropics. Here, we report a novel reproductive mode where adult frogs enter hollow internodes of bamboo via a small opening, deposit direct developing eggs, and provide parental care. This behaviour is observed in two species of the frog genus Raorchestes. The first description of this unique life history and details of nest site characteristics and embryo development are provided along with ecological comparisons. Evolution of novel reproductive modes and parental care are discussed in context of natural selection. Dearth of natural history information on amphibians in the Western Ghats and much of the South-East Asian region is highlighted with suggestions for further studies.(c) 2014 The Linnean Society of London, Biological Journal of the Linnean Society, 2014, 114, 1-11.

Regional Differences in the Influence of Irrigation on Climate

A global climate model experiment is performed to evaluate the effect of irrigation on temperatures in several major irrigated regions of the world. The Community Atmosphere Model, version 3.3, was modified to represent irrigation for the fraction of each grid cell equipped for irrigation according to datasets from the Food and Agriculture Organization. Results indicate substantial regional differences in the magnitude of irrigation-induced cooling, which are attributed to three primary factors: differences in extent of the irrigated area, differences in the simulated soil moisture for the control simulation (without irrigation), and the nature of cloud response to irrigation. The last factor appeared especially important for the dry season in India, although further analysis with other models and observations are needed to verify this feedback. Comparison with observed temperatures revealed substantially lower biases in several regions for the simulation with irrigation than for the control, suggesting that the lack of irrigation may be an important component of temperature bias in this model or that irrigation compensates for other biases. The results of this study should help to translate the results from past regional efforts, which have largely focused on the United States, to regions in the developing world that in many cases continue to experience significant expansion of irrigated land.

A note on acyclic edge coloring of complete bipartite graphs

An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic (2-colored) cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and is denoted by a'(G). Let Delta = Delta(G) denote the maximum degree of a vertex in a graph G. A complete bipartite graph with n vertices on each side is denoted by K-n,K-n. Alon, McDiarmid and Reed observed that a'(K-p-1,K-p-1) = p for every prime p. In this paper we prove that a'(K-p,K-p) <= p + 2 = Delta + 2 when p is prime. Basavaraju, Chandran and Kummini proved that a'(K-n,K-n) >= n + 2 = Delta + 2 when n is odd, which combined with our result implies that a'(K-p,K-p) = p + 2 = Delta + 2 when p is an odd prime. Moreover we show that if we remove any edge from K-p,K-p, the resulting graph is acyclically Delta + 1 = p + 1-edge-colorable. (C) 2009 Elsevier B.V. All rights reserved.

Rectangular universal cellular array

A rectangular universal cellular array consisting of cells having three inputs and one output is described. This array is based on the Reed-Muller canonical expansion of a switching function. Although the total number of external input pins required in this array is the same as that of a rectangular array proposed in the literature, the number of cells is very much less.

A Note on Easily Testable Realizations for Logic Functions

It is shown that at most, n + 3 tests are required to detect any single stuck-at fault in an AND gate or a single faulty EXCLUSIVE OR (EOR) gate in a Reed-Muller canonical form realization of a switching function.

On the PAPR of cosets of linear codes

Employing an error control code is one of the techniques to reduce the Peak-to-Average Power Ratio (PAPR) in a Orthogonal Frequency Division Multiplexing system, a well known class of such codes being the cosets of Reed-Muller codes. In this paper, we consider the class of such coset-codes of arbitrary linear codes and present a method of doubling the size of such a code without increasing the PAPR, by combining two such binary coset-codes. We identify the conditions under which we can employ this doubling more than once with no marginal increase in the PAPR value. Given a PAPR and length, our method has enabled to get the best coset-code (in terms of the size). Also, we show that the PAPR information of the coset-codes of the extended codes is obtainable from the PAPR of the corresponding coset-codes of the parent code. We have also shown a special type of lengthening is useful in PAPR studies.