Multigroup-Decodable STBCs from Clifford Algebras

A Space-Time Block Code (STBC) in K symbols (variables) is called g-group decodable STBC if its maximum-likelihood decoding metric can be written as a sum of g terms such that each term is a function of a subset of the K variables and each variable appears in only one term. In this paper we provide a general structure of the weight matrices of multi-group decodable codes using Clifford algebras. Without assuming that the number of variables in each group to be the same, a method of explicitly constructing the weight matrices of full-diversity, delay-optimal g-group decodable codes is presented for arbitrary number of antennas. For the special case of Nt=2a we construct two subclass of codes: (i) A class of 2a-group decodable codes with rate a2(a−1), which is, equivalently, a class of Single-Symbol Decodable codes, (ii) A class of (2a−2)-group decodable with rate (a−1)2(a−2), i.e., a class of Double-Symbol Decodable codes. Simulation results show that the DSD codes of this paper perform better than previously known Quasi-Orthogonal Designs.

Efficient space-time codes from cyclic division algebras

An overview of space-time code construction based on cyclic division algebras (CDA) is presented. Applications of such space-time codes to the construction of codes optimal under the diversity-multiplexing gain (D-MG) tradeoff, to the construction of the so-called perfect space-time codes, to the construction of optimal space-time codes for the ARQ channel as well as to the construction of codes optimal for the cooperative relay network channel are discussed. We also present a construction of optimal codes based on CDA for a class of orthogonal amplify and forward (OAF) protocols for the cooperative relay network

Some remarks on the symplectic pairing on the moduli space of representations of the fundamental group of surfaces

This work grew out of an attempt to understand a conjectural remark made by Professor Kyoji Saito to the author about a possible link between the Fox-calculus description of the symplectic structure on the moduli space of representations of the fundamental group of surfaces into a Lie group and pairs of mutually dual sets of generators of the fundamental group. In fact in his paper [3] , Prof. Kyoji Saito gives an explicit description of the system of dual generators of the fundamental group.

Families of asymptotic tensile crack tip stress fields in elastic-perfectly plastic single crystals

In this work, two families of asymptotic near-tip stress fields are constructed in an elastic-ideally plastic FCC single crystal under mode I plane strain conditions. A crack is taken to lie on the (010) plane and its front is aligned along the [(1) over bar 01] direction. Finite element analysis is first used to systematically examine the stress distributions corresponding to different constraint levels. The general framework developed by Rice (Mech Mater 6:317-335, 1987) and Drugan (J Mech Phys Solids 49:2155-2176, 2001) is then adopted to generate low triaxiality solutions by introducing an elastic sector near the crack tip. The two families of stress fields are parameterized by the normalized opening stress (tau(A)(22)/tau(o)) prevailing in the plastic sector in front of the tip and by the coordinates of a point where elastic unloading commences in stress space. It is found that the angular stress variations obtained from the analytical solutions show good agreement with finite element analysis.

X-ray Topographic Assessment of Dislocations in Crystals Grown from Solution

Crystals growing from solution, the vapour phase and from supercooled melt exhibit, as a rule, planar faces. The geometry and distribution of dislocations present within the crystals thus grown are strongly related to the growth on planar faces and to the different growth sectors rather than the physical properties of the crystals and the growth methods employed. As a result, many features of generation and geometrical arrangement of defects are common to extremely different crystal species. In this paper these commoner aspects of dislocation generation and configuration which permits one to predict their nature and distribution are discussed. For the purpose of imaging the defects a very versatile and widely applicable technique viz. x-ray diffraction topography is used. Growth dislocations in solution grown crystals follow straight path with strongly defined directions. These preferred directions which in most cases lie within an angle of ±15° to the growth normal depend on the growth direction and on the Burger's vector involved. The potential configuration of dislocations in the growing crystals can be evaluated using the theory developed by Klapper which is based on linear anisotropic elastic theory. The preferred line direction of a particular dislocation corresponds to that in which the dislocation energy per unit growth length is a minimum. The line direction analysis based on this theory enables one to characterise dislocations propagating in a growing crystal. A combined theoretical analysis and experimental investigation based on the above theory is presented.

A unified approach to the gauging of space-time and internal symmetries

The properties of the manifold of a Lie groupG, fibered by the cosets of a sub-groupH, are exploited to obtain a geometrical description of gauge theories in space-timeG/H. Gauge potentials and matter fields are pullbacks of equivariant fields onG. Our concept of a connection is more restricted than that in the similar scheme of Ne'eman and Regge, so that its degrees of freedom are just those of a set of gauge potentials forG, onG/H, with no redundant components. The ldquotranslationalrdquo gauge potentials give rise in a natural way to a nonsingular tetrad onG/H. The underlying groupG to be gauged is the groupG of left translations on the manifoldG and is associated with a ldquotrivialrdquo connection, namely the Maurer-Cartan form. Gauge transformations are all those diffeomorphisms onG that preserve the fiber-bundle structure.

Conformations Of Peptides Containing 1-Aminocyclohexane-Carboxylic Acid (Acc6) - Crystal-Structures Of 2 Model Peptides

The crystal structures of two peptides containing 1-aminocyclohexanecarboxylic acid (Acc6) are described. Boc-Aib-Acc6-NHMe · H2O adopts a β-turn conformation in the solid state, stabilized by an intramolecular 4 → 1 hydrogen bond between the Boc CO and methylamide NH groups. The backbone conformational angles (φAib = – 50.3°, ψAib = – 45.8°; φAcc6 = – 68.4°, ψAcc6 = – 15°) lie in between the values expected for ideal Type I or III β-turns. In Boc-Aib-Acc6-OMe, the Aib residue adopts a partially extended conformation (φAib = – 62.2°, ψAib = 143°) while the Acc6residue maintains a helical conformation (φAcc6 = 48°, ψAcc6= 42.6°). 1H n.m.r. studies in CDCl3 and (CD3)2SO suggest that Boc-Aib-Acc6-NHMe maintains the β-turn conformation in solution.

Gauge theory of a group of diffeomorphisms. I. General principles

Any (N+M)-parameter Lie group G with an N-parameter subgroup H can be realized as a global group of diffeomorphisms on an M-dimensional base space B, with representations in terms of transformation laws of fields on B belonging to linear representations of H. The gauged generalization of the global diffeomorphisms consists of general diffeomorphisms (or coordinate transformations) on a base space together with a local action of H on the fields. The particular applications of the scheme to space-time symmetries is discussed in terms of Lagrangians, field equations, currents, and source identities. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Structural Polymorphism of the Nucleosomal DNA and Implications for Protein Binding

A nucleosome forms a basic unit of the chromosome structure. A biologically relevant question is how much of the nucleosomal conformational space is accessible to protein-free DNA, and what proportion of the nucleosomal conformations are induced by bound histones. To investigate this, we have analysed high resolution xray crystal structure datasets of DNA in protein-free as well as protein-bound forms, and compared the dinucleotide step parameters for the two datasets with those for high resolution nucleosome structures. Our analysis shows that most of the dinucleotide step parameter values for the nucleosome structures lie within the range accessible to protein-free DNA, indirectly indicating that the histone core plays more of a stabilizing role. The nucleosome structures are observed to assume smooth and nearly planar curvature, implying that ‘normal’ B-DNA like parameters can give rise to a curved geometry at the gross structural level. Different nucleosome

Representations and properties of para-Bose oscillator operators. I. Energy position and momentum eigenstates

Para-Bose commutation relations are related to the SL(2,R) Lie algebra. The irreducible representation [script D]alpha of the para-Bose system is obtained as the direct sum Dbeta[direct-sum]Dbeta+1/2 of the representations of the SL(2,R) Lie algebra. The position and momentum eigenstates are then obtained in this representation [script D]alpha, using the matrix mechanical method. The orthogonality, completeness, and the overlap of these eigenstates are derived. The momentum eigenstates are also derived using the wave mechanical method by specifying the domain of the definition of the momentum operator in addition to giving it a formal differential expression. By a careful consideration in this manner we find that the two apparently different solutions obtained by Ohnuki and Kamefuchi in this context are actually unitarily equivalent. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Flux balance analysis of biological systems: applications and challenges

Systems level modelling and simulations of biological processes are proving to be invaluable in obtaining a quantitative and dynamic perspective of various aspects of cellular function. In particular, constraint-based analyses of metabolic networks have gained considerable popularity for simulating cellular metabolism, of which flux balance analysis (FBA), is most widely used. Unlike mechanistic simulations that depend on accurate kinetic data, which are scarcely available, FBA is based on the principle of conservation of mass in a network, which utilizes the stoichiometric matrix and a biologically relevant objective function to identify optimal reaction flux distributions. FBA has been used to analyse genome-scale reconstructions of several organisms; it has also been used to analyse the effect of perturbations, such as gene deletions or drug inhibitions in silico. This article reviews the usefulness of FBA as a tool for gaining biological insights, advances in methodology enabling integration of regulatory information and thermodynamic constraints, and finally addresses the challenges that lie ahead. Various use scenarios and biological insights obtained from FBA, and applications in fields such metabolic engineering and drug target identification, are also discussed. Genome-scale constraint-based models have an immense potential for building and testing hypotheses, as well as to guide experimentation.

Bottleneck assignment problems under categorization

This paper considers two special cases of bottleneck grouped assignment problems when n jobs belong to m distinct categories (m < n). Solving these special problems through the available branch and bound algorithms will result in a heavy computational burden. Sequentially identifying nonopitmal variables, this paper provides more efficient methods for those cases. Propositions leading to the algorithms have been established. Numerical examples illustrate the respective algorithms.

Stereochemical studies on cyclic peptides. XIII. Energy minimization studies on cyclic hexapeptides having hydrogen bonds

The basic cyclic hexapeptide conformations which accommodate hydrogen bonded β and γ turns in the backbone have been worked out using stereochemical criteria and energy minimization procedures. It was found that cyclic hexapeptides can be made up of all possible combinations of 4 ± 1 hydrogen bonded types I, I', II and II' β turns, giving rise to symmetric conformations having twofold and inversion symmetries as well as nonsymmetric structures. Conformations having exclusive features of 3 ± 1 hydrogen bonded γ turns were found to be possible in threefold and S6 symmetric cyclic hexapeptides. The results show that the cyclic hexapeptides formed by the linking of two β turn tripeptide fragments differ mainly in (a) the hydrogen bonding scheme present in the β turn tripeptides and (b) the conformation at the α-carbon atoms where the two tripeptide fragments link. The different hydrogen bonding schemes found in the component β turns are: 1) a β turn with only a 4 ± 1 hydrogen bond, 2) a type I or I' β turn with 4 ± 1 and 3 ± 1 hydrogen bonds occurring in a bifurcated form and 3) a type II or II' β turn having both the 4 ± 1 and the 3 ± 1 hydrogen bonds with the same acceptor oxygen atom. The conformation at the linking α-carbon atoms was found to lie either in the extended region or in the 3 ± 1 hydrogen bonded γ turn or inverse γ turn regions. Further, the threefold and the S6 symmetric conformations have three γ turns interleaved by three extended regions or three inverse γ turns, respectively. The feasibility of accommodating alanyl residues of both isomeric forms in the CHP minima has been explored. Finally, the available experimental data are reviewed in the light of the present results.