Spectral Efficiency of Channel-Aware Schedulers in Non-identical Composite Links with Interference

Accurate system planning and performance evaluation requires knowledge of the joint impact of scheduling, interference, and fading. However, current analyses either require costly numerical simulations or make simplifying assumptions that limit the applicability of the results. In this paper, we derive analytical expressions for the spectral efficiency of cellular systems that use either the channel-unaware but fair round robin scheduler or the greedy, channel-aware but unfair maximum signal to interference ratio scheduler. As is the case in real deployments, non-identical co-channel interference at each user, both Rayleigh fading and lognormal shadowing, and limited modulation constellation sizes are accounted for in the analysis. We show that using a simple moment generating function-based lognormal approximation technique and an accurate Gaussian-Q function approximation leads to results that match simulations well. These results are more accurate than erstwhile results that instead used the moment-matching Fenton-Wilkinson approximation method and bounds on the Q function. The spectral efficiency of cellular systems is strongly influenced by the channel scheduler and the small constellation size that is typically used in third generation cellular systems.

Conjugacy invariant pseudo-norms, representability and RNA secondary structures

To a reasonable approximation, a secondary structures of RNA is determined by Watson-Crick pairing without pseudo-knots in such a way as to minimise the number of unpaired bases: We show that this minimal number is determined by the maximal conjugacy-invariant pseudo-norm on the free group on two generators subject to bounds on the generators. This allows us to construct lower bounds on the minimal number of unpaired bases by constructing conjugacy invariant pseudo-norms. We show that one such construction, based on isometric actions on metric spaces, gives a sharp lower bound. A major goal here is to formulate a purely mathematical question, based on considering orthogonal representations, which we believe is of some interest independent of its biological roots.

An invariant subspace-based approach to the random eigenvalue problem of systems with clustered spectrum

The repeated or closely spaced eigenvalues and corresponding eigenvectors of a matrix are usually very sensitive to a perturbation of the matrix, which makes capturing the behavior of these eigenpairs very difficult. Similar difficulty is encountered in solving the random eigenvalue problem when a matrix with random elements has a set of clustered eigenvalues in its mean. In addition, the methods to solve the random eigenvalue problem often differ in characterizing the problem, which leads to different interpretations of the solution. Thus, the solutions obtained from different methods become mathematically incomparable. These two issues, the difficulty of solving and the non-unique characterization, are addressed here. A different approach is used where instead of tracking a few individual eigenpairs, the corresponding invariant subspace is tracked. The spectral stochastic finite element method is used for analysis, where the polynomial chaos expansion is used to represent the random eigenvalues and eigenvectors. However, the main concept of tracking the invariant subspace remains mostly independent of any such representation. The approach is successfully implemented in response prediction of a system with repeated natural frequencies. It is found that tracking only an invariant subspace could be sufficient to build a modal-based reduced-order model of the system. Copyright (C) 2012 John Wiley & Sons, Ltd.

Asymptotics of the invariant measure in mean field models with jumps

We consider the asymptotics of the invariant measure for the process of spatial distribution of N coupled Markov chains in the limit of a large number of chains. Each chain reflects the stochastic evolution of one particle. The chains are coupled through the dependence of transition rates on the spatial distribution of particles in the various states. Our model is a caricature for medium access interactions in wireless local area networks. Our model is also applicable in the study of spread of epidemics in a network. The limiting process satisfies a deterministic ordinary differential equation called the McKean-Vlasov equation. When this differential equation has a unique globally asymptotically stable equilibrium, the spatial distribution converges weakly to this equilibrium. Using a control-theoretic approach, we examine the question of a large deviation from this equilibrium.

Poincare invariant quantum field theories with twisted internal symmetries

Following up the work of 1] on deformed algebras, we present a class of Poincare invariant quantum field theories with particles having deformed internal symmetries. The twisted quantum fields discussed in this work satisfy commutation relations different from the usual bosonic/fermionic commutation relations. Such twisted fields by construction are nonlocal in nature. Despite this nonlocality we show that it is possible to construct interaction Hamiltonians which satisfy cluster decomposition principle and are Lorentz invariant. We further illustrate these ideas by considering global SU(N) symmetries. Specifically we show that twisted internal symmetries can provide a natural-framework for the discussion of the marginal deformations (beta-deformations) of the N = 4 SUSY theories.

Role of invariant water molecules and water-mediated ionic interactions in D-xylose isomerase from Streptomyces rubiginosus

The enzyme, D-xylose isomerase (D-xylose keto-isomerase; EC 5.3.1.5) is a soluble enzyme that catalyzes the conversion of the aldo-sugar D-xylose to the keto-sugar D-xylulose. A total of 27 subunits of D-xylose isomerase from Streptomyces rubiginosus were analyzed in order to identify the invariant water molecules and their water-mediated ionic interactions. A total of 70 water molecules were found to be invariant. The structural and/or functional roles of these water molecules have been discussed. These invariant water molecules and their ionic interactions may be involved in maintaining the structural stability of the enzyme D-xylose isomerase. Fifty-eight of the 70 invariant water molecules (83%) have at least one interaction with the main chain polar atom.

Joint Routing, Scheduling and Power Control in Multihop MIMO Networks with MAC and Broadcast Links

We consider the problem of joint routing, scheduling and power control in a multihop wireless network when the nodes have multiple antennas. We focus on exploiting the multiple degrees-of-freedom available at each transmitter and receiver due to multiple antennas. Specifically we use multiple antennas at each node to form multiple access and broadcast links in the network rather than just point to point links. We show that such a generic transmission model improves the system performance significantly. Since the complexity of the resulting optimization problem is very high, we also develop efficient suboptimal solutions for joint routing, scheduling and power control in this setup.

A transform approach to linear network coding for acyclic networks with delay

The algebraic formulation for linear network coding in acyclic networks with each link having an integer delay is well known. Based on this formulation, for a given set of connections over an arbitrary acyclic network with integer delay assumed for the links, the output symbols at the sink nodes at any given time instant is a Fq-linear combination of the input symbols across different generations, where Fq denotes the field over which the network operates. We use finite-field discrete Fourier transform (DFT) to convert the output symbols at the sink nodes at any given time instant into a Fq-linear combination of the input symbols generated during the same generation. We call this as transforming the acyclic network with delay into n-instantaneous networks (n is sufficiently large). We show that under certain conditions, there exists a network code satisfying sink demands in the usual (non-transform) approach if and only if there exists a network code satisfying sink demands in the transform approach. Furthermore, assuming time invariant local encoding kernels, we show that the transform method can be employed to achieve half the rate corresponding to the individual source-destination mincut (which are assumed to be equal to 1) for some classes of three-source three-destination multiple unicast network with delays using alignment strategies when the zero-interference condition is not satisfied.

Precoding-Based Network Alignment Using Transform Approach for Acyclic Networks With Delay

The algebraic formulation for linear network coding in acyclic networks with the links having integer delay is well known. Based on this formulation, for a given set of connections over an arbitrary acyclic network with integer delay assumed for the links, the output symbols at the sink nodes, at any given time instant, is a F(p)m-linear combination of the input symbols across different generations, where F(p)m denotes the field over which the network operates (p is prime and m is a positive integer). We use finite-field discrete Fourier transform to convert the output symbols at the sink nodes, at any given time instant, into a F(p)m-linear combination of the input symbols generated during the same generation without making use of memory at the intermediate nodes. We call this as transforming the acyclic network with delay into n-instantaneous networks (n is sufficiently large). We show that under certain conditions, there exists a network code satisfying sink demands in the usual (nontransform) approach if and only if there exists a network code satisfying sink demands in the transform approach. When the zero-interference conditions are not satisfied, we propose three precoding-based network alignment (PBNA) schemes for three-source three-destination multiple unicast network with delays (3-S 3-D MUN-D) termed as PBNA using transform approach and time-invariant local encoding coefficients (LECs), PBNA using time-varying LECs, and PBNA using transform approach and block time-varying LECs. We derive sets of necessary and sufficient conditions under which throughputs close to n' + 1/2n' + 1, n'/2n' + 1, and n'/2n' + 1 are achieved for the three source-destination pairs in a 3-S 3-D MUN-D employing PBNA using transform approach and time-invariant LECs, and PBNA using transform approach and block time-varying LECs, where n' is a positive integer. For PBNA using time-varying LECs, we obtain a sufficient condition under which a throughput demand of n(1)/n, n(2)/n, and n(3)/n can be met for the three source-destination pairs in a 3-S 3-D MUN-D, where n(1), n(2), and n(3) are positive integers less than or equal to the positive integer n. This condition is also necessary when n(1) + n(3) = n(1) + n(2) = n where n(1) >= n(2) >= n(3).

Performance analysis of FSO links under strong atmospheric turbulence conditions using various modulation schemes

Strong atmospheric turbulence is a major hindrance in wireless optical communication systems. In this paper, the performance of a wireless optical communication system is analyzed using different modulation formats such as, binary phase shift keying-subcarrier intensity modulation (BPSK-SIM), differential phase shift keying (DPSK), differential phase shift keying-subcarrier intensity modulation (DPSK-SIM), Mary pulse position modulation (M-PPM) and polarization shift keying (PoISK). The atmospheric channel is modeled for strong atmospheric turbulences with combined effect of turbulence and pointing errors. Novel closed-form analytical expressions for average bit error rate (BER), channel capacity and outage probability for the various modulation techniques, viz. BPSK-SIM, DPSK, DPSK-SIM, PoISK and M-PPM are derived. The simulated results for BER, channel capacity and outage probability of various modulation techniques are plotted and analyzed. (C) 2014 Elsevier GmbH. All rights reserved.

Matrix-Assisted Refolding, Purification and Activity Assessment Using a `Form Invariant' Assay for Matrix Metalloproteinase 2 (MMP2)

Matrix metalloproteinases expression is used as biomarker for various cancers and associated malignancies. Since these proteinases can cleave many intracellular proteins, overexpression tends to be toxic; hence, a challenge to purify them. To overcome these limitations, we designed a protocol where full length pro-MMP2 enzyme was overexpressed in E. coli as inclusion bodies and purified using 6xHis affinity chromatography under denaturing conditions. In one step, the enzyme was purified and refolded directly on the affinity matrix under redox conditions to obtain a bioactive protein. The pro-MMP2 protein was characterized by mass spectrometry, CD spectroscopy, zymography and activity analysis using a simple in-house developed `form invariant' assay, which reports the total MMP2 activity independent of its various forms. The methodology yielded higher yields of bioactive protein compared to other strategies reported till date, and we anticipate that using the protocol, other toxic proteins can also be overexpressed and purified from E. coli and subsequently refolded into active form using a one step renaturation protocol.

Open loop Model for WDM Links

Wavelength Division Multiplexing (WDM) techniques overfibrelinks helps to exploit the high bandwidth capacity of single mode fibres. A typical WDM link consisting of laser source, multiplexer/demultiplexer, amplifier and detectoris considered for obtaining the open loop gain model of the link. The methodology used here is to obtain individual component models using mathematical and different curve fitting techniques. These individual models are then combined to obtain the WDM link model. The objective is to deduce a single variable model for the WDM link in terms of input current to system. Thus it provides a black box solution for a link. The Root Mean Square Error (RMSE) associated with each of the approximated models is given for comparison. This will help the designer to select the suitable WDM link model during a complex link design.