On a Ratio of Functions of Exponential Random Variables and Some Applications

Consider L independent and identically distributed exponential random variables (r.vs) X-1, X-2 ,..., X-L and positive scalars b(1), b(2) ,..., b(L). In this letter, we present the probability density function (pdf), cumulative distribution function and the Laplace transform of the pdf of the composite r.v Z = (Sigma(L)(j=1) X-j)(2) / (Sigma(L)(j=1) b(j)X(j)). We show that the r.v Z appears in various communication systems such as i) maximal ratio combining of signals received over multiple channels with mismatched noise variances, ii)M-ary phase-shift keying with spatial diversity and imperfect channel estimation, and iii) coded multi-carrier code-division multiple access reception affected by an unknown narrow-band interference, and the statistics of the r.v Z derived here enable us to carry out the performance analysis of such systems in closed-form.

Adaptive optimal load balancing in a nonhomogeneous multiserver system with a central job scheduler

A model comprising several servers, each equipped with its own queue and with possibly different service speeds, is considered. Each server receives a dedicated arrival stream of jobs; there is also a stream of generic jobs that arrive to a job scheduler and can be individually allocated to any of the servers. It is shown that if the arrival streams are all Poisson and all jobs have the same exponentially distributed service requirements, the probabilistic splitting of the generic stream that minimizes the average job response time is such that it balances the server idle times in a weighted least-squares sense, where the weighting coefficients are related to the service speeds of the servers. The corresponding result holds for nonexponentially distributed service times if the service speeds are all equal. This result is used to develop adaptive quasi-static algorithms for allocating jobs in the generic arrival stream when the load parameters are unknown. The algorithms utilize server idle-time measurements which are sent periodically to the central job scheduler. A model is developed for these measurements, and the result mentioned is used to cast the problem into one of finding a projection of the root of an affine function, when only noisy values of the function can be observed

Optimal explicit guidance of multistage launch vehicle along three-dimensional trajectory

Details of an efficient optimal closed-loop guidance algorithm for a three-dimensional launch are presented with simulation results. Two types of orbital injections, with either true anomaly or argument of perigee being free at injection, are considered. The resulting steering-angle profile under the assumption of uniform gravity lies in a canted plane which transforms a three-dimensional problem into an equivalent two-dimensional one. Effects of thrust are estimated using a series in a recursive way. Encke's method is used to predict the trajectory during powered flight and then to compute the changes due to actual gravity using two gravity-related vectors. Guidance parameters are evaluated using the linear differential correction method. Optimality of the algorithm is tested against a standard ground-based trajectory optimization package. The performance of the algorithm is tested for accuracy, robustness, and efficiency for a sun-synchronous mission involving guidance for a multistage vehicle that requires large pitch and yaw maneuver. To demonstrate applicability of the algorithm to a range of missions, injection into a geostationary transfer orbit is also considered. The performance of the present algorithm is found to be much better than others.

Occurrence of maximum Tc at an optimal carrier concentration in superconducting bismuth and thallium cuprates

The superconducting transition temperatures in Bi2Ca1−xLnxSr2Cu2O8+δ, TlCa1−xLnxSr2Cu2O6+δ, and Tl0.8Ca1−xLnxBa2Cu23O6+δ (Ln=Y or rare earth) vary with composition and show a maximum at a specific value of x or δ. This observation suggests that an optimal carrier concentration is required to attain maximum Tc in such cuprates which seem to be two‐band systems

An optimal parallel algorithm for sparse matrix bandwidth reduction on a linear array

A simple and efficient algorithm for the bandwidth reduction of sparse symmetric matrices is proposed. It involves column-row permutations and is well-suited to map onto the linear array topology of the SIMD architectures. The efficiency of the algorithm is compared with the other existing algorithms. The interconnectivity and the memory requirement of the linear array are discussed and the complexity of its layout area is derived. The parallel version of the algorithm mapped onto the linear array is then introduced and is explained with the help of an example. The optimality of the parallel algorithm is proved by deriving the time complexities of the algorithm on a single processor and the linear array.

A near-optimal initial seed value selection in K-means means algorithm using a genetic algorithm

The K-means algorithm for clustering is very much dependent on the initial seed values. We use a genetic algorithm to find a near-optimal partitioning of the given data set by selecting proper initial seed values in the K-means algorithm. Results obtained are very encouraging and in most of the cases, on data sets having well separated clusters, the proposed scheme reached a global minimum.

Optimal explicit terminal guidance for a launch vehicle

It is observed that general explicit guidance schemes exhibit numerical instability close to the injection point. This difficulty is normally attributed to the demand for exact injection which, in turn, calls for finite corrections to be enforced in a relatively short time. The deviations in vehicle state which need corrective maneuvers are caused by the off-nominal operating conditions. Hence, the onset of terminal instability depends on the type of off-nominal conditions encountered. The proposed separate terminal guidance scheme overcomes the above difficulty by minimizing a quadratic penalty on injection errors rather than demanding an exact injection. There is also a special requirement in the terminal phase for the faster guidance computations. The faster guidance computations facilitate a more frequent guidance update enabling an accurate terminal thrust cutoff. The objective of faster computations is realized in the terminal guidance scheme by employing realistic assumptions that are accurate enough for a short terminal trajectory. It is observed from simulations that one of the guidance parameters (P) related to the thrust steering angular rates can indicate the onset of terminal instability due to different off-nominal operating conditions. Therefore, the terminal guidance scheme can be dynamically invoked based on monitoring of deviations in the lone parameter P.

Optimal scheduling of a processor executing a communication protocol stack

We consider the problem of optimally scheduling a processor executing a multilayer protocol in an intelligent Network Interface Controller (NIC). In particular, we assume a typical LAN environment with class 4 transport service, a connectionless network service, and a class 1 link level protocol. We develop a queuing model for the problem. In the most general case this becomes a cyclic queuing network in which some queues have dedicated servers, and the others have a common schedulable server. We use sample path arguments and Markov decision theory to determine optimal service schedules. The optimal throughputs are compared with those obtained with simple policies. The optimal policy yields upto 25% improvement in some cases. In some other cases, the optimal policy does only slightly better than much simpler policies.

Processing of Ultrasonic Signal for Transducer Characterization and for Improving Signal-To-Noise Ratio

This paper describes the work related to characterisation of an ultrasonic transducer fabricated in the laboratory. The response of the medium to the ultrasonic wave was obtained by converting the time domain signal to frequency domain, using the FFT algorithm. Cross-correlation technique was adopted to increase the S/N ratio in the raw time domain signal and subsequently, to determine the ultrasonic velocity in the medium.

DNA Compaction by a Dendrimer

At physiological pH, a PAMAM dendrimer is positively charged and can effectively bind negatively charged DNA. Currently, there has been great interest in understanding this complexation reaction both for fundamental (as a model for complex biological reactions) as well as for practical (as a gene delivery material and probe for sensing DNA sequence) reasons. Here, we have studied the complexation between double-stranded DNA (dsDNA) and various generations of PAMAM dendrimers (G3-05) through atomistic molecular dynamics simulations in the presence of water and ions. We report the compaction of DNA on a nanosecond time scale. This is remarkable, given the fact that such a short DNA duplex with a length close to 13 nm is otherwise thought to be a rigid rod. Using several nanoseconds long MD simulations, we have observed various binding modes of dsDNA and dendrimers for various generations of PAMAM dendrimers at varying charge ratios, and it confirms some of the binding modes proposed earlier. The binding is driven by the electrostatic interaction, and the larger the dendrimer charge, the stronger the binding affinity. As DNA wraps/binds to the dendrimer, counterions originally condensed onto DNA (Na+) and the dendrimer (Cl-) get released. We calculate the entropy of counterions and show that there is gain in entropy due to counterion release during the complexation. MD simulations demonstrate that, when the charge ratio is greater than 1 (as in the case of the G5 dendrimer), the optimal wrapping of DNA is observed. Calculated binding energies of the complexation follow the trend G5 > 04 > 03, in accordance with the experimental data. For a lower-generation dendrimer, such as G3, and, to some extent, for G4 also, we see considerable deformation in the dendrimer structure due to their flexible nature. We have also calculated the various helicoidal parameters of DNA to study the effect of dendrimer binding on the structure of DNA. The B form of the DNA is well preserved in the complex, as is evident from various helical parameters, justifying the use of the PAMAM dendrimer as a suitable delivery vehicle.

Optimal pulse spacing for dynamical decoupling in the presence of a purely dephasing spin bath

Maintaining quantum coherence is a crucial requirement for quantum computation; hence protecting quantum systems against their irreversible corruption due to environmental noise is an important open problem. Dynamical decoupling (DD) is an effective method for reducing decoherence with a low control overhead. It also plays an important role in quantum metrology, where, for instance, it is employed in multiparameter estimation. While a sequence of equidistant control pulses the Carr-Purcell-Meiboom-Gill (CPMG) sequence] has been ubiquitously used for decoupling, Uhrig recently proposed that a nonequidistant pulse sequence the Uhrig dynamic decoupling (UDD) sequence] may enhance DD performance, especially for systems where the spectral density of the environment has a sharp frequency cutoff. On the other hand, equidistant sequences outperform UDD for soft cutoffs. The relative advantage provided by UDD for intermediate regimes is not clear. In this paper, we analyze the relative DD performance in this regime experimentally, using solid-state nuclear magnetic resonance. Our system qubits are C-13 nuclear spins and the environment consists of a H-1 nuclear spin bath whose spectral density is close to a normal (Gaussian) distribution. We find that in the presence of such a bath, the CPMG sequence outperforms the UDD sequence. An analogy between dynamical decoupling and interference effects in optics provides an intuitive explanation as to why the CPMG sequence performs better than any nonequidistant DD sequence in the presence of this kind of environmental noise.

MOSAICS: Multiplexed Optimal Signal Acquisition Involving Compressed Sensing

It is possible to sample signals at sub-Nyquist rate and still be able to reconstruct them with reasonable accuracy provided they exhibit local Fourier sparsity. Underdetermined systems of equations, which arise out of undersampling, have been solved to yield sparse solutions using compressed sensing algorithms. In this paper, we propose a framework for real time sampling of multiple analog channels with a single A/D converter achieving higher effective sampling rate. Signal reconstruction from noisy measurements on two different synthetic signals has been presented. A scheme of implementing the algorithm in hardware has also been suggested.

Explicit and Optimal Exact-Regenerating Codes for the Minimum-Bandwidth Point in Distributed Storage

In the distributed storage setting that we consider, data is stored across n nodes in the network such that the data can be recovered by connecting to any subset of k nodes. Additionally, one can repair a failed node by connecting to any d nodes while downloading beta units of data from each. Dimakis et al. show that the repair bandwidth d beta can be considerably reduced if each node stores slightly more than the minimum required and characterize the tradeoff between the amount of storage per node and the repair bandwidth. In the exact regeneration variation, unlike the functional regeneration, the replacement for a failed node is required to store data identical to that in the failed node. This greatly reduces the complexity of system maintenance. The main result of this paper is an explicit construction of codes for all values of the system parameters at one of the two most important and extreme points of the tradeoff - the Minimum Bandwidth Regenerating point, which performs optimal exact regeneration of any failed node. A second result is a non-existence proof showing that with one possible exception, no other point on the tradeoff can be achieved for exact regeneration.

Tunable Locally-Optimal Geographical Forwarding in Wireless Sensor Networks with Sleep-Wake Cycling Nodes

We consider a wireless sensor network whose main function is to detect certain infrequent alarm events, and to forward alarm packets to a base station, using geographical forwarding. The nodes know their locations, and they sleep-wake cycle, waking up periodically but not synchronously. In this situation, when a node has a packet to forward to the sink, there is a trade-off between how long this node waits for a suitable neighbor to wake up and the progress the packet makes towards the sink once it is forwarded to this neighbor. Hence, in choosing a relay node, we consider the problem of minimizing average delay subject to a constraint on the average progress. By constraint relaxation, we formulate this next hop relay selection problem as a Markov decision process (MDP). The exact optimal solution (BF (Best Forward)) can be found, but is computationally intensive. Next, we consider a mathematically simplified model for which the optimal policy (SF (Simplified Forward)) turns out to be a simple one-step-look-ahead rule. Simulations show that SF is very close in performance to BF, even for reasonably small node density. We then study the end-to-end performance of SF in comparison with two extremal policies: Max Forward (MF) and First Forward (FF), and an end-to-end delay minimising policy proposed by Kim et al. 1]. We find that, with appropriate choice of one hop average progress constraint, SF can be tuned to provide a favorable trade-off between end-to-end packet delay and the number of hops in the forwarding path.

High On-Off Ratio Bilayer Graphene Complementary Field Effect Transistors

In this paper, we propose a novel S/D engineering for dual-gated Bilayer Graphene (BLG) Field Effect Transistor (FET) using doped semiconductors (with a bandgap) as source and drain to obtain unipolar complementary transistors. To simulate the device, a self-consistent Non-Equilibrium Green's Function (NEGF) solver has been developed and validated against published experimental data. Using the simulator, we predict an on-off ratio in excess of 10(4) and a subthreshold slope of similar to 110mV/decade with excellent scalability and current saturation, for a 20nm gate length unipolar BLG FET. However, the performance of the proposed device is found to be strongly dependent on the S/D series resistance effect. The obtained results show significant improvements over existing reports, marking an important step towards bilayer graphene logic devices.