Embedding Of Non-Simple Lie-Groups, Coupling-Constant Relations And Non-Uniqueness Of Models Of Unification

A general derivation of the coupling constant relations which result on embedding a non-simple group like SU L (2) @ U(1) in a larger simple group (or graded Lie group) is given. It is shown that such relations depend only on the requirement (i) that the multiplet of vector fields form an irreducible representation of the unifying algebra and (ii) the transformation properties of the fermions under SU L (2). This point is illustrated in two ways, one by constructing two different unification groups containing the same fermions and therefore have same Weinberg angle; the other by putting different SU L (2) structures on the same fermions and consequently have different Weinberg angles. In particular the value sin~0=3/8 is characteristic of the sequential doublet models or models which invoke a large number of additional leptons like E 6, while addition of extra charged fermion singlets can reduce the value of sin ~ 0 to 1/4. We point out that at the present time the models of grand unification are far from unique.

Vibration spectra of ferroelectric alkali trihydrogen selenites and the nature of the hydrogen bond potential in these crystals

Raman spectra of the ferroelectric LiH3 (SeO3)2 and NaH3(SeO3)2 and the anti-ferroelectric KH3 (SeO3)2 have been recorded at room temperature using a He-Ne and also an Ar-ion laser source. The infrared absorption spectra of these crystals and their deuterated analogues have been recorded in the region 400–4000 cm−1 both below and above the Curie temperature. From an analysis of the spectrum in the region 400–900 cm−1 it is concluded that (i) in LiH3 (SeO3)2 the protons are ordered in an asymmetric double minimum potential with a low barrier and the spectrum can be interpreted in terms of HSeO3− and H2SeO3 vibrations, (ii) in NaH3 (SeO3)2 all three protons occupy a single minimum potential at room temperature and below the transition temperature the groups HSeO3− and H2SeO3 are present, (iii) the proton at the inversion centre in KH3(SeO3)2 is in a broad troughed potential well and the low temperature spectrum is more likely to be due to H3SeO3+ and SeO32− species. This deviation of the spectrum from that of the previous two crystals is attributed to the difference in H-bond scheme and hence the absence of any cooperative motion of protons in this crystal.

On the reactivity of carboxyl groups of ribonuclease-A in anhydrous methanol

The esterification of Ribonuclease-A in methanol/0.1 M hydrochloric acid has been studied by measuring the decrease in the number of titratable groups of the protein and estimating the amount of methanol incorporated. Esterification of nearly five of the 11 free carboxyl groups of the protein resulted in almost complete inactivation of the enzyme. The initial products of esterification have been chromatographed on Amberlite columns, and five partially active methyl ester derivatives of Ribonuclease-A have been isolated. The dimethyl ester, the initial product of esterification with reduced catalytic activity, has the carboxyl groups of Glu-49 and Asp-53 modified. Even in the non-aqueous solvent, as in the native structure of the protein in aqueous solution, these carboxyl groups are the fast reacting ones. Subsquently, the esterification reaction appears to proceed preferentially at the C-terminal region of the molecule. Comparison of the reactivities of carboxyl groups of Ribonuclease-A in acidic methanol to that known in aqueous solutions (with carbodiimides) suggests that the structure of Ribonuclease-A in the non-aqueous solvent resembles, at least in part, the structure in aqueous environment.

Synthesis of a one-dimensional coordination polymer containing pendant hydrosulfide groups

In view of the recent interest in compounds containing M-SH units, an organotin hydrosulfide compound, Me2Sn(SH)(O2CMe) (1) was prepared by controlled hydrolysis of the diorganotin thioacetate. Under similar mild hydrolytic conditions the corresponding benzoate could not be isolated. Instead, the thiobenzoate complex, Me2Sn(SOCPh)(2) (3) was obtained in excellent yields indicating that there was no hydrolysis. Both 1 and 3 were characterized by X-ray crystallography. Some properties of the polymeric compound 1, such as spectral, electrical conductivity and NLO response were also studied. The reactivity and properties were explained using density functional calculations.

Preparation of Palladium(II) Complexes of Isonitrosoacetylacetoneimines Having O- and N-Coordinated Isonitroso Groups

Methods for the preparation of palladium(II) complexes of the type Pd(R-IAI)(IAI'), where IAI' is the anion of isonitrosoacetylacetoneimine and R-IAI, its N-alkyl or N-aryl derivative, are given.

The influence of esterification of carboxyl groups of ribonuclease-a on its structure and immunological activity

The effect of modification of carboxyl groups of Ribonuclease-Aa on the enzymatic activity and the antigenic structure of the protein has been studied. Modification of four of the eleven free carboxyl groups of the protein by esterification in anhydrous methanol/0.1 M hydrochloric acid resulted in nearly 80% loss in enzymatic activity but had very little influence on the antigenic structure of the protein. Further increases in the modification of the carboxyl groups caused a progressive loss in immunological activity, and the fully methylated RNase-A exhibited nearly 30% immunological activity. Concomitant with this change in the antigenic structure of the protein, the ability of the molecule to complement with RNase-S-protein increased, clearly indicating the unfolding of the peptide "tail" from the remainder of the molecule. The susceptibility to proteolysis, accessibility of methionine residues for orthobenzoquinone reaction and the loss in immunological activity of the more extensively esterified derivatives of RNase-A are suggestive of the more flexible conformation of these derivatives as compared with the compact native conformation. The fact that even the fully methylated RNase-A retains nearly 30% of its immunological activity suggested that the modified protein contained antibody recognizable residual native structure, which presumably accommodates some antigenic determinants.

Negotiation schemes for multi-agent cooperative search

Because of limited sensor and communication ranges, designing efficient mechanisms for cooperative tasks is difficult. In this article, several negotiation schemes for multiple agents performing a cooperative task are presented. The negotiation schemes provide suboptimal solutions, but have attractive features of fast decision-making, and scalability to large number of agents without increasing the complexity of the algorithm. A software agent architecture of the decision-making process is also presented. The effect of the magnitude of information flow during the negotiation process is studied by using different models of the negotiation scheme. The performance of the various negotiation schemes, using different information structures, is studied based on the uncertainty reduction achieved for a specified number of search steps. The negotiation schemes perform comparable to that of optimal strategy in terms of uncertainty reduction and also require very low computational time, similar to 7 per cent to that of optimal strategy. Finally, analysis on computational and communication requirement for the negotiation schemes is carried out.

Aggregation of apolar peptides in organic solvents. Concentration dependence of 1H-nmr parameters for peptide NH groups in 310 helical decapeptide fragment of suzukacillin

Peptide NH chemical shifts and their temperature dependences have been monitored as a function of concentration for the decapeptide, Boc-Aib-Pro-Val-Aib-Val-Ala-Aib-Ala-Aib-Aib-OMe in CDCl3 (0.001-0.06M) and (CD3)2SO (0.001-0.03M). The chemical shifts and temperature coefficients for all nine NH groups show no significant concentration dependence in (CD3)2SO. Seven NH groups yield low values of temperature coefficients over the entire range, while one yields an intermediate value. In CDCl3, the Aib(1) NH group shows a large concentration dependence of both chemical shift and temperature coefficient, in contrast to the other eight NH groups. The data suggest that in (CD3)2SO, the peptide adopts a 310 helical conformation and is monomeric over the entire concentration range. In CDCl3, the 310 helical peptide associates at a concentration of 0.01M, with the Aib(1) NH involved in an intermolecular hydrogen bond. Association does not disrupt the intramolecular hydrogen-bonding pattern in the decapeptide.

Cup products for groups and commutators

We give it description, modulo torsion, of the cup product on the first cohomology group in terms of the descriptions of the second homology group due to Hopf and Miller.

A non-orthogonal cooperative multiple access (NCMA) protocol and low ML decoding complexity codes

A half-duplex constrained non-orthogonal cooperative multiple access (NCMA) protocol suitable for transmission of information from N users to a single destination in a wireless fading channel is proposed. Transmission in this protocol comprises of a broadcast phase and a cooperation phase. In the broadcast phase, each user takes turn broadcasting its data to all other users and the destination in an orthogonal fashion in time. In the cooperation phase, each user transmits a linear function of what it received from all other users as well as its own data. In contrast to the orthogonal extension of cooperative relay protocols to the cooperative multiple access channels wherein at any point of time, only one user is considered as a source and all the other users behave as relays and do not transmit their own data, the NCMA protocol relaxes the orthogonality built into the protocols and hence allows for a more spectrally efficient usage of resources. Code design criteria for achieving full diversity of N in the NCMA protocol is derived using pair wise error probability (PEP) analysis and it is shown that this can be achieved with a minimum total time duration of 2N - 1 channel uses. Explicit construction of full diversity codes is then provided for arbitrary number of users. Since the Maximum Likelihood decoding complexity grows exponentially with the number of users, the notion of g-group decodable codes is introduced for our setup and a set of necesary and sufficient conditions is also obtained.

A cooperative game theoretic approach to prototype selection

In this paper we consider the task of prototype selection whose primary goal is to reduce the storage and computational requirements of the Nearest Neighbor classifier while achieving better classification accuracies. We propose a solution to the prototype selection problem using techniques from cooperative game theory and show its efficacy experimentally.

Biologically Inspired Cooperative Routing for Wireless Mobile Sensor Networks

Biological systems present remarkable adaptation, reliability, and robustness in various environments, even under hostility. Most of them are controlled by the individuals in a distributed and self-organized way. These biological mechanisms provide useful resources for designing the dynamical and adaptive routing schemes of wireless mobile sensor networks, in which the individual nodes should ideally operate without central control. This paper investigates crucial biologically inspired mechanisms and the associated techniques for resolving routing in wireless sensor networks, including Ant-based and genetic approaches. Furthermore, the principal contributions of this paper are as follows. We present a mathematical theory of the biological computations in the context of sensor networks; we further present a generalized routing framework in sensor networks by diffusing different modes of biological computations using Ant-based and genetic approaches; finally, an overview of several emerging research directions are addressed within the new biologically computational framework.

Diversity and degrees of freedom of cooperative wireless networks

Two key parameters in the outage characterization of a wireless fading network are the diversity and the degrees of freedom (DOF). These two quantities represent the two endpoints of the diversity multiplexing gain tradeoff, In this paper, we present max-flow min-cut type theorems for computing both the diversity and the DOF of arbitrary single-source single-sink networks with nodes possessing multiple antennas. We also show that an amplify-and-forward protocol is sufficient to achieve the same. The DOF characterization is obtained using a conversion to a deterministic wireless network for which the capacity was recently found. This conversion is operational in the sense that a capacity-achieving scheme for the deterministic network can be converted into a DOF-achieving scheme for the fading network. We also show that the diversity result easily extends to multisource multi-sink networks whereas the DOF result extends to a single-source multi-cast network. Along the way, we prove that the zero error capacity of the deterministic network is the same as its c-error capacity.

DMT of Multi-hop Cooperative Networks-Part II: Layered and Multi-Antenna Networks

We consider single-source, single-sink (ss-ss) multi-hop relay networks, with slow-fading Rayleigh links. This two part paper aims at giving explicit protocols and codes to achieve the optimal diversity-multiplexing tradeoff (DMT) of two classes of multi-hop networks: K-parallel-path (KPP) networks and Layered networks. While single-antenna KPP networks were the focus of the first part, we consider layered and multi-antenna networks in this second part. We prove that a linear DMT between the maximum diversity d(max). and the maximum multiplexing gain of 1 is achievable for single-antenna fully-connected layered networks under the half-duplex constraint. This is shown to be equal to the optimal DMT if the number of relaying layers is less than 4. For the multiple-antenna case, we provide an achievable DMT, which is significantly better than known lower bounds for half duplex networks. Along the way, we compute the DMT of parallel MIMO channels in terms of the DMT of the component channel. For arbitrary ss-ss single-antenna directed acyclic networks with full-duplex relays, we prove that a linear tradeoff between maximum diversity and maximum multiplexing gain is achievable using an amplify-and-forward (AF) protocol. Explicit short-block-length codes are provided for all the proposed protocols. Two key implications of the results in the two-part paper are that the half-duplex constraint does not necessarily entail rate loss by a factor of two as previously believed and that simple AN protocols are often sufficient to attain the best possible DMT.

DMT of Multi-hop Cooperative Networks-Part I: K-Parallel-Path Networks

We consider single-source, single-sink multi-hop relay networks, with slow-fading Rayleigh fading links and single-antenna relay nodes operating under the half-duplex constraint. While two hop relay networks have been studied in great detail in terms of the diversity-multiplexing tradeoff (DMT), few results are available for more general networks. In this two-part paper, we identify two families of networks that are multi-hop generalizations of the two hop network: K-Parallel-Path (KPP) networks and Layered networks. In the first part, we initially consider KPP networks, which can be viewed as the union of K node-disjoint parallel paths, each of length > 1. The results are then generalized to KPP(I) networks, which permit interference between paths and to KPP(D) networks, which possess a direct link from source to sink. We characterize the optimal DMT of KPP(D) networks with K >= 4, and KPP(I) networks with K >= 3. Along the way, we derive lower bounds for the DMT of triangular channel matrices, which are useful in DMT computation of various protocols. As a special case, the DMT of two-hop relay network without direct link is obtained. Two key implications of the results in the two-part paper are that the half-duplex constraint does not necessarily entail rate loss by a factor of two, as previously believed and that, simple AF protocols are often sufficient to attain the best possible DMT.