Cubic Sieve Congruence of the Discrete Logarithm Problem, and fractional part sequences

The Cubic Sieve Method for solving the Discrete Logarithm Problem in prime fields requires a nontrivial solution to the Cubic Sieve Congruence (CSC) x(3) equivalent to y(2)z (mod p), where p is a given prime number. A nontrivial solution must also satisfy x(3) not equal y(2)z and 1 <= x, y, z < p(alpha), where alpha is a given real number such that 1/3 < alpha <= 1/2. The CSC problem is to find an efficient algorithm to obtain a nontrivial solution to CSC. CSC can be parametrized as x equivalent to v(2)z (mod p) and y equivalent to v(3)z (mod p). In this paper, we give a deterministic polynomial-time (O(ln(3) p) bit-operations) algorithm to determine, for a given v, a nontrivial solution to CSC, if one exists. Previously it took (O) over tilde (p(alpha)) time in the worst case to determine this. We relate the CSC problem to the gap problem of fractional part sequences, where we need to determine the non-negative integers N satisfying the fractional part inequality {theta N} < phi (theta and phi are given real numbers). The correspondence between the CSC problem and the gap problem is that determining the parameter z in the former problem corresponds to determining N in the latter problem. We also show in the alpha = 1/2 case of CSC that for a certain class of primes the CSC problem can be solved deterministically in <(O)over tilde>(p(1/3)) time compared to the previous best of (O) over tilde (p(1/2)). It is empirically observed that about one out of three primes is covered by the above class. (C) 2013 Elsevier B.V. All rights reserved.

Discrete time second order sliding mode observer for uncertain linear multi-output system

This paper presents a second order sliding mode observer (SOSMO) design for discrete time uncertain linear multi-output system. The design procedure is effective for both matched and unmatched bounded uncertainties and/or disturbances. A second order sliding function and corresponding sliding manifold for discrete time system are defined similar to the lines of continuous time counterpart. A boundary layer concept is employed to avoid switching across the defined sliding manifold and the sliding trajectory is confined to a boundary layer once it converges to it. The condition for existence of convergent quasi-sliding mode (QSM) is derived. The observer estimation errors satisfying given stability conditions converge to an ultimate finite bound (within the specified boundary layer) with thickness O(T-2) where T is the sampling period. A relation between sliding mode gain and boundary layer is established for the existence of second order discrete sliding motion. The design strategy is very simple to apply and is demonstrated for three examples with different class of disturbances (matched and unmatched) to show the effectiveness of the design. Simulation results to show the robustness with respect to the measurement noise are given for SOSMO and the performance is compared with pseudo-linear Kalman filter (PLKF). (C) 2013 Published by Elsevier Ltd. on behalf of The Franklin Institute

Multi Label Classification of Discrete Data

The paper describes an algorithm for multi-label classification. Since a pattern can belong to more than one class, the task of classifying a test pattern is a challenging one. We propose a new algorithm to carry out multi-label classification which works for discrete data. We have implemented the algorithm and presented the results for different multi-label data sets. The results have been compared with the algorithm multi-label KNN or ML-KNN and found to give good results.

Kinetically stabilized C-60-toluene solvate nanostructures with a discrete absorption edge enabling supramolecular topotactic molecular exchange

Nanosized fullerene solvates have attracted widespread research attention due to recent interesting discoveries. A particular type of solvate is limited to a fixed number of solvents and designing new solvates within the same family is a fundamental challenge. Here we demonstrate that the hexagonal closed packed (HCP) phase of C-60 solvates, formed with m-xylene, can also be stabilized using toluene. Contrary to the notion on their instability, these can be stabilized from minutes up to months by tuning the occupancy of solvent molecules. Due to high stability, we could record their absorption edge, and measure excitonic life-time, which has not been reported for any C-60 solvate. Despite being solid, absorbance spectrum of the solvates is similar in appearance to that of C-60 in solution. A new absorption band appears at 673 nm. The fluorescence lifetime at 760 nm is similar to 1.2 ns, suggesting an excited state unaffected by solvent-C-60 interaction. Finally, we utilized the unstable set of HCP solvates to exchange with a second solvent by a topotactic exchange mechanism, which rendered near permanent stability to the otherwise few minutes stable solvates. This is also the first example of topotactic exchange in supramolecular crystal, which is widely known in ionic solids. (C) 2014 Elsevier Ltd. All rights reserved.

Contrasting geochemical signatures on land from the Middle and Late Permian extinction events

The end of the Palaeozoic is marked by two mass-extinction events during the Middle Permian (Capitanian) and the Late Permian (Changhsingian). Given similarities between the two events in geochemical signatures, such as large magnitude negative C-13 anomalies, sedimentological signatures such as claystone breccias, and the approximate contemporaneous emplacement of large igneous provinces, many authors have sought a common causal mechanism. Here, a new high-resolution continental record of the Capitanian event from Portal Mountain, Antarctica, is compared with previously published Changhsingian records of geochemical signatures of weathering intensity and palaeoclimatic change. Geochemical means of discriminating sedimentary provenance (Ti/Al, U/Th and La/Ce ratios) all indicate a common provenance for the Portal Mountain sediments and associated palaeosols, so changes spanning the Capitanian extinction represent changes in weathering intensity rather than sediment source. Proxies for weathering intensity chemical index of alteration, W and rare earth element accumulation all decline across the Capitanian extinction event at Portal Mountain, which is in contrast to the increased weathering recorded globally at the Late Permian extinction. Furthermore, palaeoclimatic proxies are consistent with unchanging or cooler climatic conditions throughout the Capitanian event, which contrasts with Changhsingian records that all indicate a significant syn-extinction and post-extinction series of greenhouse warming events. Although both the Capitanian and Changhsingian event records indicate significant redox shifts, palaeosol geochemistry of the Changhsingian event indicates more reducing conditions, whereas the new Capitanian record of reduced trace metal abundances (Cr, Cu, Ni and Ce) indicates more oxidizing conditions. Taken together, the differences in weathering intensity, redox and the lack of evidence for significant climatic change in the new record suggest that the Capitanian mass extinction was not triggered by dyke injection of coal-beds, as in the Changhsingian extinction, and may instead have been triggered directly by the Emeishan large igneous province or by the interaction of Emeishan basalts with platform carbonates.

Discrete Vortex Method-Based Model for Ground-Effect Studies

A discrete vortex method-based model has been proposed for two-dimensional/three-dimensional ground-effect prediction. The model merely requires two-dimensional sectional aerodynamics in free flight. This free-flight data can be obtained either from experiments or a high-fidelity computational fluid dynamics solver. The first step of this two-step model involves a constrained optimization procedure that modifies the vortex distribution on the camber line as obtained from a discrete vortex method to match the free-flight data from experiments/computational fluid dynamics. In the second step, the vortex distribution thus obtained is further modified to account for the presence of the ground plane within a discrete vortex method-based framework. Whereas the predictability of the lift appears as a natural extension, the drag predictability within a potential flow framework is achieved through the introduction of what are referred to as drag panels. The need for the use of the generalized Kutta-Joukowski theorem is emphasized. The extension of the model to three dimensions is by the way of using the numerical lifting-line theory that allows for wing sweep. The model is extensively validated for both two-dimensional and three-dimensional ground-effect studies. The work also demonstrates the ability of the model to predict lift and drag coefficients of a high-lift wing in ground effect to about 2 and 8% accuracy, respectively, as compared to the results obtained using a Reynolds-averaged Navier-Stokes solver involving grids with several million volumes. The model shows a lot of promise in design, particularly during the early phase.

Linear Index Coding and Representable Discrete Polymatroids

Discrete polymatroids are the multi-set analogue of matroids. In this paper, we explore the connections between linear index coding and representable discrete polymatroids. The index coding problem involves a sender which generates a set of messages X = {x(1), x(2), ... x(k)} and a set of receivers R which demand messages. A receiver R is an element of R is specified by the tuple (x, H) where x. X is the message demanded by R and H subset of X \textbackslash {x} is the side information possessed by R. It is first shown that a linear solution to an index coding problem exists if and only if there exists a representable discrete polymatroid satisfying certain conditions which are determined by the index coding problem considered. El Rouayheb et. al. showed that the problem of finding a multi-linear representation for a matroid can be reduced to finding a perfect linear index coding solution for an index coding problem obtained from that matroid. Multi-linear representation of a matroid can be viewed as a special case of representation of an appropriate discrete polymatroid. We generalize the result of El Rouayheb et. al. by showing that the problem of finding a representation for a discrete polymatroid can be reduced to finding a perfect linear index coding solution for an index coding problem obtained from that discrete polymatroid.

Discrete-Rate Adaptation and Selection in Energy Harvesting Wireless Systems

In a system with energy harvesting (EH) nodes, the design focus shifts from minimizing energy consumption by infrequently transmitting less information to making the best use of available energy to efficiently deliver data while adhering to the fundamental energy neutrality constraint. We address the problem of maximizing the throughput of a system consisting of rate-adaptive EH nodes that transmit to a destination. Unlike related literature, we focus on the practically important discrete-rate adaptation model. First, for a single EH node, we propose a discrete-rate adaptation rule and prove its optimality for a general class of stationary and ergodic EH and fading processes. We then study a general system with multiple EH nodes in which one is opportunistically selected to transmit. We first derive a novel and throughput-optimal joint selection and rate adaptation rule (TOJSRA) when the nodes are subject to a weaker average power constraint. We then propose a novel rule for a multi-EH node system that is based on TOJSRA, and we prove its optimality for stationary and ergodic EH and fading processes. We also model the various energy overheads of the EH nodes and characterize their effect on the adaptation policy and the system throughput.

Self-Assembled Discrete Molecules for Sensing Nitroaromatics

Efficient sensing of trace amount nitroaromatic (NAC) explosives has become a major research focus in recent time due to concerns over national security as well as their role as environment pollutants. NO2-containing electron-deficient aromatic compounds, such as picric acid (PA), trinitrotoluene (TNT), and dinitrotoluene (DNT), are the common constituents of many commercially available chemical explosives. In this article, we have summarized our recent developments on the rational design of electron-rich self-assembled discrete molecular sensors and their efficacy in sensing nitroaromatics both in solution as well as in vapor phase. Several p-electron-rich fluorescent metallacycles (squares, rectangles, and tweezers/pincers) and metallacages (trigonal and tetragonal prisms) have been synthesized by means of metal-ligand coordination-bonding interactions, with enough internal space to accommodate electron-deficient nitroaromatics at the molecular level by multiple supramolecular interactions. Such interactions subsequently result in the detectable fluorescence quenching of sensors even in the presence of trace quantities of nitroaromatics. The fascinating sensing characteristics of molecular architectures discussed in this article may enable future development of improved sensors for nitroaromatic explosives.

Voice source characterization using pitch synchronous discrete cosine transform for speaker identification

A characterization of the voice source (VS) signal by the pitch synchronous (PS) discrete cosine transform (DCT) is proposed. With the integrated linear prediction residual (ILPR) as the VS estimate, the PS DCT of the ILPR is evaluated as a feature vector for speaker identification (SID). On TIMIT and YOHO databases, using a Gaussian mixture model (GMM)-based classifier, it performs on par with existing VS-based features. On the NIST 2003 database, fusion with a GMM-based classifier using MFCC features improves the identification accuracy by 12% in absolute terms, proving that the proposed characterization has good promise as a feature for SID studies. (C) 2015 Acoustical Society of America

Alternative Formulation of the Discrete Linear Quadratic Regulator (DLQR)

In this paper, an alternative apriori and aposteriori formulation has been derived for the discrete linear quadratic regulator (DLQR) in a manner analogous to that used in the discrete Kalman filter. It has been shown that the formulation seamlessly fits into the available formulation of the DLQR and the equivalent terms in the existing formulation and the proposed formulation have been identified. Thereafter, the significance of this alternative formulation has been interpreted in terms of the sensitivity of the controller performances to any changes in the states or to changes in the control inputs. The implications of this alternative formulation to adaptive controller tuning have also been discussed.

Template-free coordination-driven self-assembly of discrete hexanuclear prismatic cages employing half-sandwich octahedral Ru-2(II) acceptors and triimidazole donors

Coordination-driven self-assembly of dinuclear half-sandwich p-cymene ruthenium(II) complexes Ru-2(mu-eta(4)-C2O4)(CH3OH)(2)(eta(6)-p-cymene)(2)](O3SCF3)(2) (1a) and Ru-2(mu-eta(4)-C6H2O4)(CH3OH)(2)(eta(6)-p-cymene)(2)](O3SCF3)(2) (1b) separately with imidazole-based tritopic donors (L-1-L-2) in methanol yielded a series of hexanuclear 3+2] trigonal prismatic cages (2-5), respectively L-1 = 1,3,5-tris(imidazole-1-yl) benzene; L-2 = 4,4',4 `'-tris(imidazole-1-yl) triphenylamine]. All the self-assembled cages 2-5 were characterized by various spectroscopic techniques (multinuclear NMR, Infra-red and ESI-MS) and their sizes, shapes were obtained through geometry optimization using molecular mechanics universal force field (MMUFF) computation. Despite the possibility due to the free rotation of donor sites of imidazole ligands, of two different atropoisomeric prismatic cages (C-3h or C-s) and polymeric product, the self-selection of single (C(3)h) conformational isomeric cages as the only product is a noteworthy observation. (C) 2015 Elsevier B.V. All rights reserved.

Influence of the upwelling events on the delta C-13 and delta O-18 of the benthic bivalve shells of the South Western Continental Margin of India

In this study, the influence of the spatial and temporal variability of upwelling intensity and the associated biological productivity observed during different phases of summer monsoon along the southwestern continental margin of India (SWCMI) on the delta C-13 and delta O-18 of the inorganic biogenic carbonate shells was investigated. Multispecies benthic bivalve shells (1-5 mm) separated from ten surface sediment samples of SWCMI (off 12 degrees N, 10 degrees N and 9 degrees N) collected during the onset (OSM) and peak (PSM) phase of the summer monsoon of 2009 were analysed for delta C-13 and delta O-18. Sea surface temperature along the study region indicates prominent upwelling in PSM than in OSM. A comparison of analytical and predicted values for delta O-18 in the bivalve shells confirmed their in situ origin during both the sampling periods. During PSM, the delta C-13 values in the benthic bivalve shells were more depleted in C-13 than during OSM which recorded lower values of delta C-13 in dissolved inorganic carbon of bottom waters expected in the study region in PSM due to the upwelled waters, high surface productivity and the associated high degradation of the organic matter in the subsurface and bottom waters. However, this depletion of delta C-13 was not observed in benthic bivalve shells obtained from 10 degrees N, since it is influenced by high export fluxes of carbon from the Cochin estuary since early monsoon months.