On the cubicity of bipartite graphs

A unit cube in k-dimension (or a k-cube) is defined as the Cartesian product R-1 x R-2 x ... x R-k, where each R-i is a closed interval on the real line of the form [a(j), a(i), + 1]. The cubicity of G, denoted as cub(G), is the minimum k such that G is the intersection graph of a collection of k-cubes. Many NP-complete graph problems can be solved efficiently or have good approximation ratios in graphs of low cubicity. In most of these cases the first step is to get a low dimensional cube representation of the given graph. It is known that for graph G, cub(G) <= left perpendicular2n/3right perpendicular. Recently it has been shown that for a graph G, cub(G) >= 4(Delta + 1) In n, where n and Delta are the number of vertices and maximum degree of G, respectively. In this paper, we show that for a bipartite graph G = (A boolean OR B, E) with |A| = n(1), |B| = n2, n(1) <= n(2), and Delta' = min {Delta(A),Delta(B)}, where Delta(A) = max(a is an element of A)d(a) and Delta(B) = max(b is an element of B) d(b), d(a) and d(b) being the degree of a and b in G, respectively , cub(G) <= 2(Delta' + 2) bar left rightln n(2)bar left arrow. We also give an efficient randomized algorithm to construct the cube representation of G in 3 (Delta' + 2) bar right arrowIn n(2)bar left arrow dimension. The reader may note that in general Delta' can be much smaller than Delta.

Socio-environmental impact of idol immersion: dimensions and directions

India possesses a diverse and rich cultural heritage and is renowned as a 'land of festivals'. These festivals attract massive community involvement paving way to new materials such as 'Plaster of Paris' being used for 'modernizing' the representation of idols with very little thought given to the issues of toxicity and environmental impacts. Another dimension to the whole issue is the plight of the artisans and the workers involved in the trade. Owing to the unorganized nature of the industry there is minimal or no guidelines pertaining-to the worker safety and health risks of the people involved. This paper attempts to address the complexities of the inherent hazards as a consequence of these socio-environmental issues and trace the scientific rationale in addressing them in a practical and pragmatic way.

On optimum stratification with proportional allocation for a class of pareto distributions

Cum ./LSTA_A_8828879_O_XML_IMAGES/LSTA_A_8828879_O_ILM0001.gif rule [Singh (1975)] has been suggested in the literature for finding approximately optimum strata boundaries for proportional allocation, when the stratification is done on the study variable. This paper shows that for the class of density functions arising from the Wang and Aggarwal (1984) representation of the Lorenz Curve (or DBV curves in case of inventory theory), the cum ./LSTA_A_8828879_O_XML_IMAGES/LSTA_A_8828879_O_ILM0002.gif rule in place of giving approximately optimum strata boundaries, yields exactly optimum boundaries. It is also shown that the conjecture of Mahalanobis (1952) “. . .an optimum or nearly optimum solutions will be obtained when the expected contribution of each stratum to the total aggregate value of Y is made equal for all strata” yields exactly optimum strata boundaries for the case considered in the paper.

Software simulation of the EEG

The literature contains many examples of digital procedures for the analytical treatment of electroencephalograms, but there is as yet no standard by which those techniques may be judged or compared. This paper proposes one method of generating an EEG, based on a computer program for Zetterberg's simulation. It is assumed that the statistical properties of an EEG may be represented by stationary processes having rational transfer functions and achieved by a system of software fillers and random number generators.The model represents neither the neurological mechanism response for generating the EEG, nor any particular type of EEG record; transient phenomena such as spikes, sharp waves and alpha bursts also are excluded. The basis of the program is a valid ‘partial’ statistical description of the EEG; that description is then used to produce a digital representation of a signal which if plotted sequentially, might or might not by chance resemble an EEG, that is unimportant. What is important is that the statistical properties of the series remain those of a real EEG; it is in this sense that the output is a simulation of the EEG. There is considerable flexibility in the form of the output, i.e. its alpha, beta and delta content, which may be selected by the user, the same selected parameters always producing the same statistical output. The filtered outputs from the random number sequences may be scaled to provide realistic power distributions in the accepted EEG frequency bands and then summed to create a digital output signal, the ‘stationary EEG’. It is suggested that the simulator might act as a test input to digital analytical techniques for the EEG, a simulator which would enable at least a substantial part of those techniques to be compared and assessed in an objective manner. The equations necessary to implement the model are given. The program has been run on a DEC1090 computer but is suitable for any microcomputer having more than 32 kBytes of memory; the execution time required to generate a 25 s simulated EEG is in the region of 15 s.

An Algorithm to Decide Feasibility of Linear Integer Constraints Occurrng in Decision Tables

Abstract-To detect errors in decision tables one needs to decide whether a given set of constraints is feasible or not. This paper describes an algorithm to do so when the constraints are linear in variables that take only integer values. Decision tables with such constraints occur frequently in business data processing and in nonnumeric applications. The aim of the algorithm is to exploit. the abundance of very simple constraints that occur in typical decision table contexts. Essentially, the algorithm is a backtrack procedure where the the solution space is pruned by using the set of simple constrains. After some simplications, the simple constraints are captured in an acyclic directed graph with weighted edges. Further, only those partial vectors are considered from extension which can be extended to assignments that will at least satisfy the simple constraints. This is how pruning of the solution space is achieved. For every partial assignment considered, the graph representation of the simple constraints provides a lower bound for each variable which is not yet assigned a value. These lower bounds play a vital role in the algorithm and they are obtained in an efficient manner by updating older lower bounds. Our present algorithm also incorporates an idea by which it can be checked whether or not an (m - 2)-ary vector can be extended to a solution vector of m components, thereby backtracking is reduced by one component.

The Saintly Madman : A Study of the Scholarly Reception History of Buile Shuibhne

This study examines the scholarly reception history of an early Irish text, Buile Shuibhne (The Frenzy of Suibhne), by focusing on the various theoretical and methodological presuppositions which have determined the scholars’ understanding of the text’s religious allegorical significance in the course of the 20th century. The reception-oriented inquiry takes the intersubjective aspect of literary interpretation as the basis for accentuating the importance of communally shared presumptions and reading strategies in the explication of interpretive variety. The materials of the study have been divided into four frameworks of interpretation: historical, pre-Christian, Christian and anthropological. This heuristic division does not denote mutually exclusive paradigms, but rather refers to perceived similarities within each group regarding the questions posed, and the evidence adduced, in textual analysis. The historical framework concentrates on the issues of the origins of the tale and the possible historicity of its main protagonist. The pre-Christian framework covers the theories of the shamanic, Indo-European and Celtic elements in the text, whereas the Christian framework includes readings emphasising the biblical, monastic and ascetic aspects of the tale. The anthropological framework in turn focuses on the parallels drawn between the narrative and the universal structure of the rites of passage. In addition to the examination of these four frameworks, the study also links the question of methodology with wider issues of authorship and textual integrity, and critically reconsiders the manner in which J.G. O'Keeffe's 1913 edition of the text has been reified in previous scholarship as a representation of a 12th century authorial original. The overall objective of the present case-study is to relate theoretical conceptions of literary theory, comparative religion and historiography to the study of early Irish narrative material by considering the communal and institutional dimension of meaning-making, and the implications of comparative methodology for historical research. In this aim, the prevailing methodological presuppositions informing the scholarly discourse on Buile Shuibhne are set against the wider context of Celtic Studies scholarship, in order to draw attention to the need to critically reflect upon the operations of knowledge production in future research.

A comment on the consistency of truncated nonlinear integral equation based theories of freezing

We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim–Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

Contributions to the Theory of Finite-State Based Grammars

This dissertation is a theoretical study of finite-state based grammars used in natural language processing. The study is concerned with certain varieties of finite-state intersection grammars (FSIG) whose parsers define regular relations between surface strings and annotated surface strings. The study focuses on the following three aspects of FSIGs: (i) Computational complexity of grammars under limiting parameters In the study, the computational complexity in practical natural language processing is approached through performance-motivated parameters on structural complexity. Each parameter splits some grammars in the Chomsky hierarchy into an infinite set of subset approximations. When the approximations are regular, they seem to fall into the logarithmic-time hierarchyand the dot-depth hierarchy of star-free regular languages. This theoretical result is important and possibly relevant to grammar induction. (ii) Linguistically applicable structural representations Related to the linguistically applicable representations of syntactic entities, the study contains new bracketing schemes that cope with dependency links, left- and right branching, crossing dependencies and spurious ambiguity. New grammar representations that resemble the Chomsky-Schützenberger representation of context-free languages are presented in the study, and they include, in particular, representations for mildly context-sensitive non-projective dependency grammars whose performance-motivated approximations are linear time parseable. (iii) Compilation and simplification of linguistic constraints Efficient compilation methods for certain regular operations such as generalized restriction are presented. These include an elegant algorithm that has already been adopted as the approach in a proprietary finite-state tool. In addition to the compilation methods, an approach to on-the-fly simplifications of finite-state representations for parse forests is sketched. These findings are tightly coupled with each other under the theme of locality. I argue that the findings help us to develop better, linguistically oriented formalisms for finite-state parsing and to develop more efficient parsers for natural language processing. Avainsanat: syntactic parsing, finite-state automata, dependency grammar, first-order logic, linguistic performance, star-free regular approximations, mildly context-sensitive grammars

A comment on the consistency of truncated nonlinear integral equation based theories of freezing

We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim–Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

Playing "Nordic": The Women of Niskavuori, Agri/Culture, and Imagining Finland on the Third Reich Stage

The theatrical censorship of the Third Reich considered the playwright's race and politics alongside the content of the drama. Given the political stigma of its "leftist" author, it is rather surprising that Hella Wuolijoki's Niskavuoren naiset opened in 1938 at the Staatliches Schauspielhaus in Hamburg. The play ran for fourteen performances before being closed by the Reichsdramaturgie, apparently at the instigation of Finnish critics. Yet this was not the end of the play's or its author's fortunes in the Third Reich, as the possibility of staging the play was raised several times over the next four years, coming to a close in 1942. Playing "Nordic" examines the ideological and theatrical background of this extended "cultural performance," as a means to reopening and reconstructing the work of the 1938 Die Frauen auf Niskavuori. Written by a Finnish, northern, "Nordic" author, and preoccupied with the dynamics of rural culture in an increasingly urbanized world, Niskavuoren naiset was understood in the Third Reich to illustrate and reinforce the racial, agri/cultural themes of Blut und Boden ("veri ja maa"). Playing "Nordic" examines this thematic relationship in three phases. The first phase uses archival materials to investigate the Reichsdramaturgie's understanding of the play and its author, and its ongoing discussion of Wuolijoki from 1937 to 1942. Play evaluator Sigmund Graff's description of Niskavuoren naiset as hamsunartig, or "Hamsun-esque," inspires the second phase of the dissertation, which first elaborates the meanings of Blut und Boden through a reading of contemporary "racial" theory and anthropology, and then assesses the representation of Finland within this discourse, one of the dominant cultural paradigms of the Third Reich. Imaging Finland for German audiences, the play stood among analogous, continued efforts to represent Finland and the rural life in the Third Reich, colored by Blut und Boden: art and agricultural exhibitions, essays and propaganda literature, mass demonstrations of the peasantry. This wider framework for the performance of "Finland" materializes the abstract or theoretical program of Blut und Boden in its everyday performed meanings; as such it provides the essential background for reading the Hamburg production of Die Frauen auf Niskavuori, which sustains the third and final phase. The German translation and the Hamburg photographic record are compared with the Helsinki premiere to assess the impact of Blut und Boden on the representation of Wuolijoki's play in the Third Reich. The journalistic critical response illuminates the effect that the dramatic complex of rural and racial values - generically identified as Bauerndrama in the Third Reich - had on the reception of the play; at the same time, both visual and critical documents also suggest possible moments of theatrical dissent in the Hamburg production. Playing "Nordic" undertakes a documentary and cultural reading of the changing theatrical meanings of Wuolijoki's Niskavuoren naiset as it crossed the frontier from Finland to the stage of the Third Reich. It also provides a model for the ways theatrical signification operates within a network of cultural and ideological meanings, suggesting the ideological work of theatrical production depends on, reinforces, and contests that tissue of values. Although Finnish criticism of Niskavuoren naiset has assumed the play's Blut und Boden resonance contributed to Wuolijoki's success in the Third Reich, this study shows a considerably more complex situation. This revealing production dramatizes the changing uses of plays in a politicized national and transnational context. As part of the framing of "Nordic" identity on the wider stage of the Third Reich, Die Frauen auf Niskavuori exemplifies the conjunction of concurrent - sometimes independent, sometimes interlocking - "racial" and national ideologies.

On the Cubicity of Interval Graphs

A k-cube (or ``a unit cube in k dimensions'') is defined as the Cartesian product R-1 x . . . x R-k where R-i (for 1 <= i <= k) is an interval of the form [a(i), a(i) + 1] on the real line. The k-cube representation of a graph G is a mapping of the vertices of G to k-cubes such that the k-cubes corresponding to two vertices in G have a non-empty intersection if and only if the vertices are adjacent. The cubicity of a graph G, denoted as cub(G), is defined as the minimum dimension k such that G has a k-cube representation. An interval graph is a graph that can be represented as the intersection of intervals on the real line - i. e., the vertices of an interval graph can be mapped to intervals on the real line such that two vertices are adjacent if and only if their corresponding intervals overlap. We show that for any interval graph G with maximum degree Delta, cub(G) <= inverted right perpendicular log(2) Delta inverted left perpendicular + 4. This upper bound is shown to be tight up to an additive constant of 4 by demonstrating interval graphs for which cubicity is equal to inverted right perpendicular log(2) Delta inverted left perpendicular.

New records of the River Shark Glyphis (Carcharhinidae) reported from Cape York Peninsula, northern Australia

The distribution of the river shark Glyphis in northern Australia is extended with new records of occurrence in the Gulf of Carpentaria and a reassessment of historical survey data from Cape York Peninsula. Nine new specimens of Glyphis sp. A were collected in 2005 from the Weipa region on the Queensland coast of the Gulf of Carpentaria. A re-examination of archival records from 1978-86 marine and estuarine fish surveys in the Gulf of Carpentaria and along the northern Queensland East Coast allowed a further nineteen Glyphis specimens to be identified. Combined this gives twenty-eight new records of Glyphis specimens from the coasts of Cape York Peninsula, Queensland. Common habitat characteristics for all captures were turbid, shallow, fast running tidal water in the upper reaches of coastal rivers. The substrate was generally muddy and the rivers lined with mangrove. In all surveys the representation of Glyphis was low, being less than 1% of the total shark captures historically and 0.002 sharks 50 m net hour-1 in Weipa 2005. The size range captured was 1000-1800 mm total length historically and 705-1200 mm total length from Weipa 2005, with none recorded as sexually mature. Diagnostic characteristics of the Weipa specimens, identified as Glyphis sp. A, were: lower jaw teeth protruding and "spear-like"; second dorsal fin greater than half the height of the first dorsal fin; the snout relatively short and fleshy in the lateral view; pectoral fin ventral surface black in colouration; the precaudal vertebral count between 118 and 123; and the total vertebral count between 204 and 209.

Intersex onscreen: An overview of recent fictional characters with intersex variations on television

Throughout history, people with intersex variations have been positioned somewhere between ‘prodigy literature and pornography, mythology and medical discourse’ (Gilbert 2000, 145). Indubitably, contemporary representations have changed in step with societal values, yet it could be argued there is still slippage, and, moreover, very little is seen or heard about intersex at all. Where once there was the awe and horror of the highly visible carnival sideshow or medical treatise, the intersex body is now rendered absent by medical intervention, which is invoked to fix the intersexed in both mind and body. This paper explores the fictional representation of people with intersex variations on screen – television and film in predominantly the genres of drama and comedy – arriving finally at characters originating from program-makers willing to work closely with the intersex community. Such texts disrupt unwarranted categorization and erasure by “owning” discursive practices, defying current medical interference and promoting ethical debates around the will-to-normalise what is considered to be aberrant, deviant and abject.

Growth and physiological response of six Australian rainforest tree species to a light gradient

An understanding of growth and photosynthetic potential of subtropical rainforest species to variations in light environment can be useful for determining the sequence of species introductions in rainforest restoration projects and mixed species plantations. We examined the growth and physiology of six Australian subtropical rainforest tree species in a greenhouse consisting of three artificial light environments (10%, 30%, and 60% full sunlight). Morphological responses followed the typical sun-shade dichotomy, with early and late secondary species (Elaeocarpus grandis, Flindersia brayleyana, Flindersia schottiana, and Gmelina leichhardtii) displaying higher relative growth rate (RGR) compared to mature stage species (Cryptocarya erythroxyion and Heritiera trifoliolatum). Growth and photosynthetic performance of most species reached a maximum in 30-60% full sunlight. Physiological responses provided limited evidence of a distinct dichotomy between early and late successional species. E. grandis and F brayleyana, provided a clear representation of early successional species, with marked increase in Am in high light and an ability to down regulate photosynthetic machinery in low light conditions. The remaining species (F. schottiana, G. leichhardtii, and H. trifoliolatum) were better represented as failing along a shade-tolerant continuum, with limited ability to adjust physiologically to an increase or decrease in light, maintaining similar A(max) across all light environments. Results show that most species belong to a shade-tolerant constituency, with an ability to grow and persist across a wide range of light environments. The species offer a wide range of potential planting scenarios and silvicultural options, with ample potential to achieve rapid canopy closure and rainforest restoration goals.

Studies on friction and formation of transfer layer when Al-4Mg alloy pins slid at various numbers of cycles on steel plates of different surface texture

In the present investigation, various kinds of textures, namely, unidirectional, 8-ground, and random were attained on the die surfaces. Roughness of the textures was varied using different grits of emery papers or polishing powders. Then pins made of Al-4Mg alloys were slid against steel plates at various numbers of cycles, namely 1, 2, 6, 10 and 20 under both dry and lubricated conditions using an inclined pin-on-plate sliding tester. The morphologies of the worn surfaces of the pins and the formation of transfer layer on the counter surfaces were observed using a scanning electron microscope. Surface roughness parameters of the plate were measured using an optical profilometer. It was observed that the coefficient of friction and formation of transfer layer during the first few cycles depend on the die surface textures under both dry and lubricated conditions. It was also observed that under lubricated condition, the coefficient of friction decreases with number of cycles for all kinds of textures. However, under dry condition, it ecreases for unidirectional and 8-ground surfaces while for random surfaces it increases with number of cycles