Explicit Construction of Optimal Exact Regenerating Codes for Distributed Storage

Erasure coding techniques are used to increase the reliability of distributed storage systems while minimizing storage overhead. Also of interest is minimization of the bandwidth required to repair the system following a node failure. In a recent paper, Wu et al. characterize the tradeoff between the repair bandwidth and the amount of data stored per node. They also prove the existence of regenerating codes that achieve this tradeoff. In this paper, we introduce Exact Regenerating Codes, which are regenerating codes possessing the additional property of being able to duplicate the data stored at a failed node. Such codes require low processing and communication overheads, making the system practical and easy to maintain. Explicit construction of exact regenerating codes is provided for the minimum bandwidth point on the storage-repair bandwidth tradeoff, relevant to distributed-mail-server applications. A sub-space based approach is provided and shown to yield necessary and sufficient conditions on a linear code to possess the exact regeneration property as well as prove the uniqueness of our construction. Also included in the paper, is an explicit construction of regenerating codes for the minimum storage point for parameters relevant to storage in peer-to-peer systems. This construction supports a variable number of nodes and can handle multiple, simultaneous node failures. All constructions given in the paper are of low complexity, requiring low field size in particular.

A mathematical programming approach to optimal Markovian switching of Poisson arrival streams to queueing systems

Motivated by certain situations in manufacturing systems and communication networks, we look into the problem of maximizing the profit in a queueing system with linear reward and cost structure and having a choice of selecting the streams of Poisson arrivals according to an independent Markov chain. We view the system as a MMPP/GI/1 queue and seek to maximize the profits by optimally choosing the stationary probabilities of the modulating Markov chain. We consider two formulations of the optimization problem. The first one (which we call the PUT problem) seeks to maximize the profit per unit time whereas the second one considers the maximization of the profit per accepted customer (the PAC problem). In each of these formulations, we explore three separate problems. In the first one, the constraints come from bounding the utilization of an infinite capacity server; in the second one the constraints arise from bounding the mean queue length of the same queue; and in the third one the finite capacity of the buffer reflect as a set of constraints. In the problems bounding the utilization factor of the queue, the solutions are given by essentially linear programs, while the problems with mean queue length constraints are linear programs if the service is exponentially distributed. The problems modeling the finite capacity queue are non-convex programs for which global maxima can be found. There is a rich relationship between the solutions of the PUT and PAC problems. In particular, the PUT solutions always make the server work at a utilization factor that is no less than that of the PAC solutions.

Parallel circuit partitioning on a reduced array architecture

The physical design of a VLSI circuit involves circuit partitioning as a subtask. Typically, it is necessary to partition a large electrical circuit into several smaller circuits such that the total cross-wiring is minimized. This problem is a variant of the more general graph partitioning problem, and it is known that there does not exist a polynomial time algorithm to obtain an optimal partition. The heuristic procedure proposed by Kernighan and Lin1,2 requires O(n2 log2n) time to obtain a near-optimal two-way partition of a circuit with n modules. In the VLSI context, due to the large problem size involved, this computational requirement is unacceptably high. This paper is concerned with the hardware acceleration of the Kernighan-Lin procedure on an SIMD architecture. The proposed parallel partitioning algorithm requires O(n) processors, and has a time complexity of O(n log2n). In the proposed scheme, the reduced array architecture is employed with due considerations towards cost effectiveness and VLSI realizability of the architecture.The authors are not aware of any earlier attempts to parallelize a circuit partitioning algorithm in general or the Kernighan-Lin algorithm in particular. The use of the reduced array architecture is novel and opens up the possibilities of using this computing structure for several other applications in electronic design automation.

Crystal structure of 2-thiophene-2-yl-3(thiophene-2-carboxylideneamino)-1,2-dihydroquinazolin-4(3H)-one and the synthesis, spectral and thermal studies of its transition metal(II) complexes

The synthesis of manganese(II), cobalt(II), nickel(II), copper(II), zinc(II) and cadmium(II) complexes of a new ligand 2-thiophene-2-yl-3(thiophene-2-carboxylidene-amino)-1,2-dihydroquinazolin-4(3H)-one (TTCADQ) is described. The ligand and metal complexes were characterized by elemental analysis, conductivity measurements, spectral (u.v.-vis., i.r., 1D n.m.r., 2D hetcor and e.p.r.) and thermal studies. The formation of 1,2-dihydroquinazolin-4(3H)-one rather than hydrazone, in the reaction of aromatic aldehyde and o-aminobenzoylhydrazide is proved by single crystal X-ray diffraction and 2D hetcor n.m.r. studies. On the basis of elemental analysis, u.v.-vis.spectroscopy and magnetic moment studies, six coordinate geometry for all the complexes was proposed. The i.r. spectral studies reveal the bidentate behaviour of the ligand.

Wave propagation analysis in carbon nanotube embedded composite using wavelet based spectral finite elements

In this paper, elastic wave propagation is studied in a nanocomposite reinforced with multiwall carbon nanotubes (CNTs). Analysis is performed on a representative volume element of square cross section. The frequency content of the exciting signal is at the terahertz level. Here, the composite is modeled as a higher order shear deformable beam using layerwise theory, to account for partial shear stress transfer between the CNTs and the matrix. The walls of the multiwall CNTs are considered to be connected throughout their length by distributed springs, whose stiffness is governed by the van der Waals force acting between the walls of nanotubes. The analyses in both the frequency and time domains are done using the wavelet-based spectral finite element method (WSFEM). The method uses the Daubechies wavelet basis approximation in time to reduce the governing PDE to a set of ODEs. These transformed ODEs are solved using a finite element (FE) technique by deriving an exact interpolating function in the transformed domain to obtain the exact dynamic stiffness matrix. Numerical analyses are performed to study the spectrum and dispersion relations for different matrix materials and also for different beam models. The effects of partial shear stress transfer between CNTs and matrix on the frequency response function (FRF) and the time response due to broadband impulse loading are investigated for different matrix materials. The simultaneous existence of four coupled propagating modes in a double-walled CNT-composite is also captured using modulated sinusoidal excitation.

Structural and spectral perspectives of a novel thiosemicarbazone synthesized from di-2-pyridyl ketone and 4-phenyl-3-thiosemicarbazide

A new thiosemicarbazone, HL is synthesized from di-2-pyridyl ketone and 4-phenyl-3-thiosemicarbazide and structurally and spectrochemically characterized. H-1 NMR, C-13 NMR, COSY, HMQC and IR spectra of the compound are studied and the proton magnetic resonance spectrum reveals some unprecedented observations. The thione form is predominant in the solid state, as supported by the crystal structure and IR data, while a thiol-thione equilibrium is proposed in the solution state by NMR studies. The compound crystallizes into a monoclinic lattice with space group C2/c and the ZE conformation is exhibited by the thiosemicarbazone. Intra- and intermolecular hydrogen-bonding interactions give rise to a two-dimensional packing in the crystal lattice

Optimal Sleep-Wake Policies for an Energy Harvesting Sensor Node

We study a sensor node with an energy harvesting source. In any slot,the sensor node is in one of two modes: Wake or Sleep. The generated energy is stored in a buffer. The sensor node senses a random field and generates a packet when it is awake. These packets are stored in a queue and transmitted in the wake mode using the energy available in the energy buffer. We obtain energy management policies which minimize a linear combination of the mean queue length and the mean data loss rate. Then, we obtain two easily implementable suboptimal policies and compare their performance to that of the optimal policy. Next, we extend the Throughput Optimal policy developed in our previous work to sensors with two modes. Via this policy, we can increase the through put substantially and stabilize the data queue by allowing the node to sleep in some slots and to drop some generated packets. This policy requires minimal statistical knowledge of the system. We also modify this policy to decrease the switching costs.

Optimal Weighted Antenna Selection For Imperfect Channel Knowledge From Training

Receive antenna selection (AS) reduces the hardware complexity of multi-antenna receivers by dynamically connecting an instantaneously best antenna element to the available radio frequency (RF) chain. Due to the hardware constraints, the channels at various antenna elements have to be sounded sequentially to obtain estimates that are required for selecting the ``best'' antenna and for coherently demodulating data. Consequently, the channel state information at different antennas is outdated by different amounts. We show that, for this reason, simply selecting the antenna with the highest estimated channel gain is not optimum. Rather, the channel estimates of different antennas should be weighted differently, depending on the training scheme. We derive closed-form expressions for the symbol error probability (SEP) of AS for MPSK and MQAM in time-varying Rayleigh fading channels for arbitrary selection weights, and validate them with simulations. We then derive an explicit formula for the optimal selection weights that minimize the SEP. We find that when selection weights are not used, the SEP need not improve as the number of antenna elements increases, which is in contrast to the ideal channel estimation case. However, the optimal selection weights remedy this situation and significantly improve performance.

Air Fleet and Facility Planning via Optimal Control Models

A study is presented which is aimed at developing techniques suitable for effective planning and efficient operation of fleets of aircraft typical of the air force of a developing country. An important aspect of fleet management, the problem of resource allocation for achieving prescribed operational effectiveness of the fleet, is considered. For analysis purposes, it is assumed that the planes operate in a single flying-base repair-depot environment. The perennial problem of resource allocation for fleet and facility buildup that faces planners is modeled and solved as an optimal control problem. These models contain two "policy" variables representing investments in aircraft and repair facilities. The feasibility of decentralized control is explored by assuming the two policy variables are under the control of two independent decisionmakers guided by different and not often well coordinated objectives.

Air Fleet and Facility Planning via Optimal Control Models

A study is presented which is aimed at developing techniques suitable for effective planning and efficient operation of fleets of aircraft typical of the air force of a developing country. An important aspect of fleet management, the problem of resource allocation for achieving prescribed operational effectiveness of the fleet, is considered. For analysis purposes, it is assumed that the planes operate in a single flying-base repair-depot environment. The perennial problem of resource allocation for fleet and facility buildup that faces planners is modeled and solved as an optimal control problem. These models contain two "policy" variables representing investments in aircraft and repair facilities. The feasibility of decentralized control is explored by assuming the two policy variables are under the control of two independent decisionmakers guided by different and not often well coordinated objectives.

Optimal infinite-horizon feedback laws for a general class of constrained discrete-time systems: stability and moving-horizon approximations

Stability results are given for a class of feedback systems arising from the regulation of time-varying discrete-time systems using optimal infinite-horizon and moving-horizon feedback laws. The class is characterized by joint constraints on the state and the control, a general nonlinear cost function and nonlinear equations of motion possessing two special properties. It is shown that weak conditions on the cost function and the constraints are sufficient to guarantee uniform asymptotic stability of both the optimal infinite-horizon and movinghorizon feedback systems. The infinite-horizon cost associated with the moving-horizon feedback law approaches the optimal infinite-horizon cost as the moving horizon is extended.

Spectral assignments based on the 13C NMR spectra of mixed liquid crystals of opposite diamagnetic anisotropies

The proton-decoupled 13C NMR spectra of mixtures of liquid crystals with opposite diamagnetic anisotropies have been studied in the natural abundance of 13C. A new method to assign the spectral lines to specific carbons in the liquid crystalline phase has been developed. For this purpose, the assignments of lines in the isotropic media are required, and they were obtained from two-dimensional hetero-COSY experiments. From the spectra in the �critical� mixtures where both the orientations of the liquid crystal directors, with the alignments along and perpendicular to the direction of the magnetic field, �coexist,� the 13C chemical-shift anisotropies have been determined, assuming uniaxial symmetry.

Spectral studies on pyridinium hexafluorotitanate(IV)

Pure samples of pyridinium hexafluorotitanate(IV) [(C5H5N+H)2TiF=6] were prepared by the reaction of pyridinium poly(hydrogen fluoride) and titanium tetrachloride. The i.r. spectral data in the range 4000–200 cm−1 and 1H, 19F, and 13CNMR spectra for this compound are reported.