Isoperimetric Problem and Meta-fibonacci Sequences

Let G = (V,E) be a simple, finite, undirected graph. For S ⊆ V, let $\delta(S,G) = \{ (u,v) \in E : u \in S \mbox { and } v \in V-S \}$ and $\phi(S,G) = \{ v \in V -S: \exists u \in S$ , such that (u,v) ∈ E} be the edge and vertex boundary of S, respectively. Given an integer i, 1 ≤ i ≤ ∣ V ∣, the edge and vertex isoperimetric value at i is defined as b e (i,G) =  min S ⊆ V; |S| = i |δ(S,G)| and b v (i,G) =  min S ⊆ V; |S| = i |φ(S,G)|, respectively. The edge (vertex) isoperimetric problem is to determine the value of b e (i, G) (b v (i, G)) for each i, 1 ≤ i ≤ |V|. If we have the further restriction that the set S should induce a connected subgraph of G, then the corresponding variation of the isoperimetric problem is known as the connected isoperimetric problem. The connected edge (vertex) isoperimetric values are defined in a corresponding way. It turns out that the connected edge isoperimetric and the connected vertex isoperimetric values are equal at each i, 1 ≤ i ≤ |V|, if G is a tree. Therefore we use the notation b c (i, T) to denote the connected edge (vertex) isoperimetric value of T at i. Hofstadter had introduced the interesting concept of meta-fibonacci sequences in his famous book “Gödel, Escher, Bach. An Eternal Golden Braid”. The sequence he introduced is known as the Hofstadter sequences and most of the problems he raised regarding this sequence is still open. Since then mathematicians studied many other closely related meta-fibonacci sequences such as Tanny sequences, Conway sequences, Conolly sequences etc. Let T 2 be an infinite complete binary tree. In this paper we related the connected isoperimetric problem on T 2 with the Tanny sequences which is defined by the recurrence relation a(i) = a(i − 1 − a(i − 1)) + a(i − 2 − a(i − 2)), a(0) = a(1) = a(2) = 1. In particular, we show that b c (i, T 2) = i + 2 − 2a(i), for each i ≥ 1. We also propose efficient polynomial time algorithms to find vertex isoperimetric values at i of bounded pathwidth and bounded treewidth graphs.

Synthesis and exploration of novel curcumin analogues as anti-malarial agents

Curcumin, a major yellow pigment and active component of turmeric, has been shown to possess anti-inflammatory and anti-cancer activities. Recent studies have indicated that curcumin inhibits chloroquine-sensitive (CQ-S) and chloroquine-resistant (CQ-R) Plasmodium falciparum growth in culture with an IC50 of not, vert, similar3.25 μM (MIC = 13.2 μM) and IC50 4.21 μM (MIC = 14.4 μM), respectively. In order to expand their potential as anti-malarials a series of novel curcumin derivatives were synthesized and evaluated for their ability to inhibit P. falciparum growth in culture. Several curcumin analogues examined show more effective inhibition of P. falciparumgrowth than curcumin. The most potent curcumin compounds 3, 6, and 11 were inhibitory for CQ-S P. falciparum at IC50 of 0.48, 0.87, 0.92 μM and CQ-R P. falciparum at IC50 of 0.45 μM, 0.89, 0.75 μM, respectively. Pyrazole analogue of curcumin (3) exhibited sevenfold higher anti-malarial potency against CQ-S and ninefold higher anti-malarial potency against CQ-R. Curcumin analogues described here represent a novel class of highly selective P. falciparum inhibitors and promising candidates for the design of novel anti-malarial agents.

Software Pipelined Execution of Stream Programs on GPUs

The StreamIt programming model has been proposed to exploit parallelism in streaming applications on general purpose multi-core architectures. This model allows programmers to specify the structure of a program as a set of filters that act upon data, and a set of communication channels between them. The StreamIt graphs describe task, data and pipeline parallelism which can be exploited on modern Graphics Processing Units (GPUs), as they support abundant parallelism in hardware. In this paper, we describe the challenges in mapping StreamIt to GPUs and propose an efficient technique to software pipeline the execution of stream programs on GPUs. We formulate this problem - both scheduling and assignment of filters to processors - as an efficient Integer Linear Program (ILP), which is then solved using ILP solvers. We also describe a novel buffer layout technique for GPUs which facilitates exploiting the high memory bandwidth available in GPUs. The proposed scheduling utilizes both the scalar units in GPU, to exploit data parallelism, and multiprocessors, to exploit task and pipelin parallelism. Further it takes into consideration the synchronization and bandwidth limitations of GPUs, and yields speedups between 1.87X and 36.83X over a single threaded CPU.

Enantioselective syntheses of diquinane and (cis, anti, cis)-linear triquinanes

The enantioselective syntheses of diquinane and cis, anti, cis-linear triquinanes, starting from the readily available (S)-campholenaldehyde, employing an intramolecular rhodium carbenoid CH insertion reaction, are described. (C) 2010 Elsevier Ltd. All rights reserved.

Robust heuristics for scalable optimization of complex SQL queries

Modern database systems incorporate a query optimizer to identify the most efficient "query execution plan" for executing the declarative SQL queries submitted by users. A dynamic-programming-based approach is used to exhaustively enumerate the combinatorially large search space of plan alternatives and, using a cost model, to identify the optimal choice. While dynamic programming (DP) works very well for moderately complex queries with up to around a dozen base relations, it usually fails to scale beyond this stage due to its inherent exponential space and time complexity. Therefore, DP becomes practically infeasible for complex queries with a large number of base relations, such as those found in current decision-support and enterprise management applications. To address the above problem, a variety of approaches have been proposed in the literature. Some completely jettison the DP approach and resort to alternative techniques such as randomized algorithms, whereas others have retained DP by using heuristics to prune the search space to computationally manageable levels. In the latter class, a well-known strategy is "iterative dynamic programming" (IDP) wherein DP is employed bottom-up until it hits its feasibility limit, and then iteratively restarted with a significantly reduced subset of the execution plans currently under consideration. The experimental evaluation of IDP indicated that by appropriate choice of algorithmic parameters, it was possible to almost always obtain "good" (within a factor of twice of the optimal) plans, and in the few remaining cases, mostly "acceptable" (within an order of magnitude of the optimal) plans, and rarely, a "bad" plan. While IDP is certainly an innovative and powerful approach, we have found that there are a variety of common query frameworks wherein it can fail to consistently produce good plans, let alone the optimal choice. This is especially so when star or clique components are present, increasing the complexity of th- e join graphs. Worse, this shortcoming is exacerbated when the number of relations participating in the query is scaled upwards.

A network representation of protein structures: Implications for protein stability

This study views each protein structure as a network of noncovalent connections between amino acid side chains. Each amino acid in a protein structure is a node, and the strength of the noncovalent interactions between two amino acids is evaluated for edge determination. The protein structure graphs (PSGs) for 232 proteins have been constructed as a function of the cutoff of the amino acid interaction strength at a few carefully chosen values. Analysis of such PSGs constructed on the basis of edge weights has shown the following: 1), The PSGs exhibit a complex topological network behavior, which is dependent on the interaction cutoff chosen for PSG construction. 2), A transition is observed at a critical interaction cutoff, in all the proteins, as monitored by the size of the largest cluster (giant component) in the graph. Amazingly, this transition occurs within a narrow range of interaction cutoff for all the proteins, irrespective of the size or the fold topology. And 3), the amino acid preferences to be highly connected (hub frequency) have been evaluated as a function of the interaction cutoff. We observe that the aromatic residues along with arginine, histidine, and methionine act as strong hubs at high interaction cutoffs, whereas the hydrophobic leucine and isoleucine residues get added to these hubs at low interaction cutoffs, forming weak hubs. The hubs identified are found to play a role in bringing together different secondary structural elements in the tertiary structure of the proteins. They are also found to contribute to the additional stability of the thermophilic proteins when compared to their mesophilic counterparts and hence could be crucial for the folding and stability of the unique three-dimensional structure of proteins. Based on these results, we also predict a few residues in the thermophilic and mesophilic proteins that can be mutated to alter their thermal stability.

Cultural Trauma and Life Stories

The purpose of this work is to use the concepts of human time and cultural trauma in a biographical study of the turning points in the recent history of Estonia. This research is primarily based on 148 in-depth biographical interviews conducted in Estonia and Sweden in 1995-2005, supplemented by excerpts from 5 collections and 10 individually published autobiographies. The main body of the thesis consists of six published and of two forthcoming separate refereed articles, summarised in the theoretical introduction, and Appendix of the full texts of three particular life stories. The topic of the first article is the generational composition and the collective action frames of anti-Soviet social mobilisation in Estonia in 1940-1990. The second article details the differentiation of the rites of passage and the calendar traditions as a strategy to adapt to the rapidly changed political realities, comparatively in Soviet Estonia and among the boat-refugees in Sweden. The third article investigates the life stories of the double-minded strategic generation of the Estonian-inclined Communists, who attempted to work within the Soviet system while professing to uphold the ideals of pre-war Estonia. The fourth article is concentrated on the problems of double mental standards as a coping strategy in a contradictory social reality. The fifth article implements the theory of cultural trauma for the social practice of singing nationalism in Estonia. The sixth article bridges the ideas of Russian theoreticians concerning cultural dialogue and the Western paradigm of cultural trauma, with examples from Estonian Russian life stories. The seventh article takes a biographical look at the logic of the unraveling of cultural trauma through four Soviet decades. The eighth article explores the re-shaping of citizen activities as a strategy of coping with the loss of the independent nation state, comparatively in Soviet Estonia and among Swedish Estonians. Cultural trauma is interpreted as the re-ordering of the society s value-normative constellation due to sharp, violent, usually political events. The first one under consideration was caused by the occupations of the Republic of Estonia by the Soviet army in 1940-45. After half a century of suppression the memories of these events resurfaced as different stories describing the long-term, often inter-generational strategies of coping with the value collapse. The second cultural trauma is revealed together with the collapse of the Soviet power and ideology in Estonia in 1991. According to empirical data, the following three trauma discourses have been reconstructed: - the forced adaptation to Soviet order of the homeland Estonians; - the difficulty of preserving Estonian identity in exile (Sweden); - the identity crisis of the Russian population of Estonia. Comparative analyses of these discourses have shown that opposing experiences and worldviews cause conflicting interpretations of the past. Different social and ethnic groups consider coping with cultural trauma as a matter of self-defence and create appropriate usable pasts to identify with. Keywords: human time, cultural trauma, frame analysis, discourse, life stories

Synthesis and exploration of novel curcumin analogues as anti-malarial agents

Curcumin, a major yellow pigment and active component of turmeric, has been shown to possess anti-inflammatory and anti-cancer activities. Recent studies have indicated that curcumin inhibits chloroquine-sensitive (CQ-S) and chloroquine-resistant (CQ-R) Plasmodium falciparum growth in culture with an IC50 of similar to 3.25 mu M (MIC = 13.2 mu M) and IC50 4.21 mu M (MIC = 14.4 mu M), respectively. In order to expand their potential as anti-malarials a series of novel curcumin derivatives were synthesized and evaluated for their ability to inhibit P. falciparum growth in culture. Several curcumin analogues examined show more effective inhibition of P. falciparum growth than curcumin. The most potent curcumin compounds 3, 6, and 11 were inhibitory for CQ-S P. falciparum at IC50 of 0.48, 0.87, 0.92 mu M and CQ-R P. falcipartan at IC50 of 0.45 mu M, 0.89, 0.75 mu M, respectively. Pyrazole analogue of curcumin (3) exhibited sevenfold higher anti-malarial potency against CQ-S and ninefold higher anti-malarial potency against CQ-R. Curcumin analogues described here represent a novel class of highly selective P. falcipartan inhibitors and promising candidates for the design of novel anti-malarial agents. (C) 2007 Elsevier Ltd. All rights reserved.

Effect of anti-luteinizing hormone serum on the ovulation of rats

IN the cyclic female albino rat, a release of pituitary luteinizing hormone (LH) occurs on the afternoon of proestrus1-5. This apparently induces ovulation, for ova are seen in the Fallopian tube 12 h later. Similarly, it is well known that in immature rats primed with pregnant mare serum gonadotrophin (PMS), ovulation can be induced by the administration of human chorionic gonadotrophin (HCG) or LH, the ova being seen in the Fallopian tube 12 h later. No information is available, however, about the mode of action of LH, released or administered, in bringing about ovulation. We have approached this problem by blocking the action of the ovulating hormone (LH) at various times after administration. © 1970 Nature Publishing Group.

Effect of impulsive change of wall velocity and wall temperature in viscous heat-conducting gas

A study of compression waves produced in a viscous heat-conducting gas by the impulsive start of a one-dimensional piston and by the inpulsive change of piston wall temperature is made using Laplace Transform Technique for Prandt1 number unity. Expressions for velocity, temperature and density have also been obtained using small-time expansion procedure in this case. For arbitrary Prandt1 number solutions have been developed using large-time expansion procedure. A number of graphs exhibiting the distribution of the fluid velocity, temperature and density have been drawn.

Harmonic and anharmonic oscillations of a cylindrical plasma in the presence of a uniform axial magnetic field and a steady axial current

In the present note we have studied the harmonic and anharmonic oscillations of cylindrical plasma using Lagrangian formalism. In order to study the harmonic oscillations, the equations are linearized and the resulting equation for the displacement has been numerically solved. For situations present in thermonuclear reactors, the presence of axial magnetic field is found necessary to make the periods of oscillation to become comparable with the time required for the thermonuclear reactions to set in. A detailed analysis of the anharmonic oscillations reveals that the significant interaction is between the first and the second mode. The fundamental period of anharmonic oscillation is more than the corresponding period of harmonic oscillations by 9·2%. Graphs have been drawn for the amplitudes of relative variations in density and magnetic field and of the time-varying part of anharmonic oscillation.

Vibration of simply-supported trapezoidal plates I. Symmetric trapezoids

A detailed investigation of the natural frequencies and mode shapes of simply supported symmetric trapezoidal plates is undertaken in this paper. For numerical calculations, the relationship that exists between the eigenvalue problem of a polygonal simply supported plate and the eigenvalue problem of polygonal membrane of the same shape is utilized with advantage. The deflection surface is expressed in terms of a Fourier sine series in transformed coordinates and the Galerkin method is used. Results are presented in the form of tables and graphs. Several features like the crossing of frequency curves and the metamorphosis of some of the nodal patterns are observed. By a suitable interpretation of the modes of those symmetric trapezoidal plates which have the median as the nodal line, the results for some of the modes of unsymmetrical trapezoidal plates are also deduced.

Transition metal complexes of 3-aryl-2-substituted 1,2-dihydroquinazolin-4(3H)-one derivatives: New class of analgesic and anti-inflammatory agents

Five-coordinate, neutral transition metal complexes of newly designed pyridine-2-ethyl-(3-carboxyhdeneamino)-3-(2-phenyl)-1,2-dihydroquinazoli n-4(3H)-one (L) were synthesized and characterized The structure of ligand is confirmed by single crystal X-ray diffraction studies The compounds were evaluated for the anti-inflammatory activity by carrageenan-induced rat paw edema model while their analgesic activity was determined by acetic acid-induced writhing test in mice wherein the transition metal complexes were found to be more active than the free ligand (C) 2010 Elsevier Masson SAS All rights reserved.

Studies in stereochemistry—I : Stereospecific routes to trans- anti- and cis- syn-Δ8-dodecahydrophenanthrenes

Reduction of trans-1-oxo-7-methoxy-1,2,3,4,9,10,11,12-octahydrophenanthrene (XI) by lithium tri-t-butoxyaluminohydride gave trans-1β-hydroxy-7-methoxy-1,2,3,4,9,10,11,12-octahydrophenanthrene (XII) which on lithium-liquid ammonia reduction gave trans-anti-1β-hydroxy-7-oxo-Δ8(14)-dodecahydrophenanthrene (XIII). Reduction of cis-1-oxo-7-methoxy-1,2,3,4,9,10,11,12-octahydrophenanthrene (XV) by sodium borohydride gave cis-1α-hydroxy-7-methoxy-1,2,3,4,9,10,11,12-octahydrophenanthrene (XVI) which on lithium-liquid ammonia reduction gave cis-syn-1α-hydroxy-7-oxo-Δ8(14)-dodecahydrophenanthrene (XVII).

On compressible boundary layer on a flat plate with uniform suction

A quartic profile in terms of the normal distance from the wall has been taken and coefficients are evaluated by satisfying one more boundary condition on the wall than the usual one. By doing so, the limitations about the Reynolds number of the quartic profile adopted by Lew (1949) has been removed. The Kármán (1921) Momentum Integral Equation has been used to evaluate the various characteristics of the flow. A comparative study of Lew's quartic profile and exponential profile together with the quartic profile of the present paper has been undertaken and the graphs for the various characteristics of the flow for a number of Mach numbers and suction coefficients have been drawn. At the end, certain conclusions of general nature about the velocity profiles have been recorded.