Association rule mining activity : A general formalism

Mining association rules from a large collection of databases is based on two main tasks. One is generation of large itemsets; and the other is finding associations between the discovered large itemsets. Existing formalism for association rules are based on a single transaction database which is not sufficient to describe the association rules based on multiple database environment. In this paper, we give a general characterization of association rules and also give a framework for knowledge-based mining of multiple databases for association rules.

Partition function for hindered, one-and multi-dimensional rotors

Writing the hindered rotor (hr) partition function as the trace of (rho) over cap = e(-beta(H) over cap hr), we approximate it by the sum of contributions from a set of points in position space. The contribution of the density matrix from each point is approximated by performing a local harmonic expansion around it. The highlight of this method is that it can be easily extended to multidimensional systems. Local harmonic expansion leads to a breakdown of the method a low temperatures. In order to calculate the partition function at low temperatures, we suggest a matrix multiplication procedure. The results obtained using these methods closely agree with the exact partition function at all temperature ranges. Our method bypasses the evaluation of eigenvalues and eigenfunctions and evaluates the density matrix for internal rotation directly. We also suggest a procedure to account for the antisymmetry of the total wavefunction in the same. (C) 2012 Elsevier B.V. All rights reserved.

Zero-Sum Risk-Sensitive Stochastic Differential Games

We study zero-sum risk-sensitive stochastic differential games on the infinite horizon with discounted and ergodic payoff criteria. Under certain assumptions, we establish the existence of values and saddle-point equilibria. We obtain our results by studying the corresponding Hamilton-Jacobi-Isaacs equations. Finally, we show that the value of the ergodic payoff criterion is a constant multiple of the maximal eigenvalue of the generators of the associated nonlinear semigroups.

Two-User Gaussian Interference Channel with Finite Constellation Input and FDMA

In the two-user Gaussian Strong Interference Channel (GSIC) with finite constellation inputs, it is known that relative rotation between the constellations of the two users enlarges the Constellation Constrained (CC) capacity region. In this paper, a metric for finding the approximate angle of rotation to maximally enlarge the CC capacity is presented. It is shown that for some portion of the Strong Interference (SI) regime, with Gaussian input alphabets, the FDMA rate curve touches the capacity curve of the GSIC. Even as the Gaussian alphabet FDMA rate curve touches the capacity curve of the GSIC, at high powers, with both the users using the same finite constellation, we show that the CC FDMA rate curve lies strictly inside the CC capacity curve for the constellations BPSK, QPSK, 8-PSK, 16-QAM and 64-QAM. It is known that, with Gaussian input alphabets, the FDMA inner-bound at the optimum sum-rate point is always better than the simultaneous-decoding inner-bound throughout the Weak Interference (WI) regime. For a portion of the WI regime, it is shown that, with identical finite constellation inputs for both the users, the simultaneous-decoding inner-bound enlarged by relative rotation between the constellations can be strictly better than the FDMA inner-bound.

General-sum stochastic games: Verifiability conditions for Nash equilibria

Unlike zero-sum stochastic games, a difficult problem in general-sum stochastic games is to obtain verifiable conditions for Nash equilibria. We show in this paper that by splitting an associated non-linear optimization problem into several sub-problems, characterization of Nash equilibria in a general-sum discounted stochastic games is possible. Using the aforementioned sub-problems, we in fact derive a set of necessary and sufficient verifiable conditions (termed KKT-SP conditions) for a strategy-pair to result in Nash equilibrium. Also, we show that any algorithm which tracks the zero of the gradient of the Lagrangian of every sub-problem provides a Nash strategy-pair. (c) 2012 Elsevier Ltd. All rights reserved.

Spectral moment sum rules for the retarded Green's function and self-energy of the inhomogeneous Bose-Hubbard model in equilibrium and nonequilibrium

We derive exact expressions for the zeroth and the first three spectral moment sum rules for the retarded Green's function and for the zeroth and the first spectral moment sum rules for the retarded self-energy of the inhomogeneous Bose-Hubbard model in nonequilibrium, when the local on-site repulsion and the chemical potential are time-dependent, and in the presence of an external time-dependent electromagnetic field. We also evaluate these expressions for the homogeneous case in equilibrium, where all time dependence and external fields vanish. Unlike similar sum rules for the Fermi-Hubbard model, in the Bose-Hubbard model case, the sum rules often depend on expectation values that cannot be determined simply from parameters in the Hamiltonian like the interaction strength and chemical potential but require knowledge of equal-time many-body expectation values from some other source. We show how one can approximately evaluate these expectation values for the Mott-insulating phase in a systematic strong-coupling expansion in powers of the hopping divided by the interaction. We compare the exact moment relations to the calculated moments of spectral functions determined from a variety of different numerical approximations and use them to benchmark their accuracy. DOI: 10.1103/PhysRevA.87.013628

A Calcium-Dependent Plasticity Rule for HCN Channels Maintains Activity Homeostasis and Stable Synaptic Learning

Theoretical and computational frameworks for synaptic plasticity and learning have a long and cherished history, with few parallels within the well-established literature for plasticity of voltage-gated ion channels. In this study, we derive rules for plasticity in the hyperpolarization-activated cyclic nucleotide-gated (HCN) channels, and assess the synergy between synaptic and HCN channel plasticity in establishing stability during synaptic learning. To do this, we employ a conductance-based model for the hippocampal pyramidal neuron, and incorporate synaptic plasticity through the well-established Bienenstock-Cooper-Munro (BCM)-like rule for synaptic plasticity, wherein the direction and strength of the plasticity is dependent on the concentration of calcium influx. Under this framework, we derive a rule for HCN channel plasticity to establish homeostasis in synaptically-driven firing rate, and incorporate such plasticity into our model. In demonstrating that this rule for HCN channel plasticity helps maintain firing rate homeostasis after bidirectional synaptic plasticity, we observe a linear relationship between synaptic plasticity and HCN channel plasticity for maintaining firing rate homeostasis. Motivated by this linear relationship, we derive a calcium-dependent rule for HCN-channel plasticity, and demonstrate that firing rate homeostasis is maintained in the face of synaptic plasticity when moderate and high levels of cytosolic calcium influx induced depression and potentiation of the HCN-channel conductance, respectively. Additionally, we show that such synergy between synaptic and HCN-channel plasticity enhances the stability of synaptic learning through metaplasticity in the BCM-like synaptic plasticity profile. Finally, we demonstrate that the synergistic interaction between synaptic and HCN-channel plasticity preserves robustness of information transfer across the neuron under a rate-coding schema. Our results establish specific physiological roles for experimentally observed plasticity in HCN channels accompanying synaptic plasticity in hippocampal neurons, and uncover potential links between HCN-channel plasticity and calcium influx, dynamic gain control and stable synaptic learning.

Antenna Selection in Interference-Constrained Underlay Cognitive Radios: SEP-Optimal Rule and Performance Benchmarking

In the underlay mode of cognitive radio, secondary users are allowed to transmit when the primary is transmitting, but under tight interference constraints that protect the primary. However, these constraints limit the secondary system performance. Antenna selection (AS)-based multiple antenna techniques, which exploit spatial diversity with less hardware, help improve secondary system performance. We develop a novel and optimal transmit AS rule that minimizes the symbol error probability (SEP) of an average interference-constrained multiple-input-single-output secondary system that operates in the underlay mode. We show that the optimal rule is a non-linear function of the power gain of the channel from the secondary transmit antenna to the primary receiver and from the secondary transmit antenna to the secondary receive antenna. We also propose a simpler, tractable variant of the optimal rule that performs as well as the optimal rule. We then analyze its SEP with L transmit antennas, and extensively benchmark it with several heuristic selection rules proposed in the literature. We also enhance these rules in order to provide a fair comparison, and derive new expressions for their SEPs. The results bring out new inter-relationships between the various rules, and show that the optimal rule can significantly reduce the SEP.

Bounds on the sum-rate capacity of the Gaussian MIMO X channel

We consider the MIMO X channel (XC), a system consisting of two transmit-receive pairs, where each transmitter communicates with both the receivers. Both the transmitters and receivers are equipped with multiple antennas. First, we derive an upper bound on the sum-rate capacity of the MIMO XC under individual power constraint at each transmitter. The sum-rate capacity of the two-user multiple access channel (MAC) that results when receiver cooperation is assumed forms an upper bound on the sum-rate capacity of the MIMO XC. We tighten this bound by considering noise correlation between the receivers and deriving the worst noise covariance matrix. It is shown that the worst noise covariance matrix is a saddle-point of a zero-sum, two-player convex-concave game, which is solved through a primal-dual interior point method that solves the maximization and the minimization parts of the problem simultaneously. Next, we propose an achievable scheme which employs dirty paper coding at the transmitters and successive decoding at the receivers. We show that the derived upper bound is close to the achievable region of the proposed scheme at low to medium SNRs.

On Uniform Approximate Solutions in Bending of Symmetric Laminated Plates

A layer-wise theory with the analysis of face ply independent of lamination is used in the bending of symmetric laminates with anisotropic plies. More realistic and practical edge conditions as in Kirchhoff's theory are considered. An iterative procedure based on point-wise equilibrium equations is adapted. The necessity of a solution of an auxiliary problem in the interior plies is explained and used in the generation of proper sequence of two dimensional problems. Displacements are expanded in terms of polynomials in thickness coordinate such that continuity of transverse stresses across interfaces is assured. Solution of a fourth order system of a supplementary problem in the face ply is necessary to ensure the continuity of in-plane displacements across interfaces and to rectify inadequacies of these polynomial expansions in the interior distribution of approximate solutions. Vertical deflection does not play any role in obtaining all six stress components and two in-plane displacements. In overcoming lacuna in Kirchhoff's theory, widely used first order shear deformation theory and other sixth and higher order theories based on energy principles at laminate level in smeared laminate theories and at ply level in layer-wise theories are not useful in the generation of a proper sequence of 2-D problems converging to 3-D problems. Relevance of present analysis is demonstrated through solutions in a simple text book problem of simply supported square plate under doubly sinusoidal load.

Optimal synthesis of adjustable planar four-bar crank-rocker type mechanisms for approximate multi-path generation

This paper deals with an optimization based method for synthesis of adjustable planar four-bar, crank-rocker mechanisms. For multiple different and desired paths to be traced by a point on the coupler, a two stage method first determines the parameters of the possible driving dyads. Then the remaining mechanism parameters are determined in the second stage where a least-squares based circle-fitting procedure is used. Compared to existing formulations, the optimization method uses less number of design variables. Two numerical examples demonstrate the effectiveness of the proposed synthesis method. (C) 2013 Elsevier Ltd. All rights reserved.

Nucleation of a Stable Solid from Melt in the Presence of Multiple Metastable Intermediate Phases: Wetting, Ostwald's Step Rule, and Vanishing Polymorphs

In many systems, nucleation of a stable solid may occur in the presence of other (often more than one) metastable phases. These may be polymorphic solids or even liquid phases. Sometimes, the metastable phase might have a lower free energy minimum than the liquid but higher than the stable-solid-phase minimum and have characteristics in between the parent liquid and the globally stable solid phase. In such cases, nucleation of the solid phase from the melt may be facilitated by the metastable phase because the latter can ``wet'' the interface between the parent and the daughter phases, even though there may be no signature of the existence of metastable phase in the thermodynamic properties of the parent liquid and the stable solid phase. Straightforward application of classical nucleation theory (CNT) is flawed here as it overestimates the nucleation barrier because surface tension is overestimated (by neglecting the metastable phases of intermediate order) while the thermodynamic free energy gap between daughter and parent phases remains unchanged. In this work, we discuss a density functional theory (DFT)-based statistical mechanical approach to explore and quantify such facilitation. We construct a simple order-parameter-dependent free energy surface that we then use in DFT to calculate (i) the order parameter profile, (ii) the overall nucleation free energy barrier, and (iii) the surface tension between the parent liquid and the metastable solid and also parent liquid and stable solid phases. The theory indeed finds that the nucleation free energy barrier can decrease significantly in the presence of wetting. This approach can provide a microscopic explanation of the Ostwald step rule and the well-known phenomenon of ``disappearing polymorphs'' that depends on temperature and other thermodynamic conditions. Theory reveals a diverse scenario for phase transformation kinetics, some of which may be explored via modem nanoscopic synthetic methods.

Power-Controlled Reverse Channel Training in a Multiuser TDD-MIMO Spatial Multiplexing System With CSIR

This paper considers the design of a power-controlled reverse channel training (RCT) scheme for spatial multiplexing (SM)-based data transmission along the dominant modes of the channel in a time-division duplex (TDD) multiple-input and multiple-output (MIMO) system, when channel knowledge is available at the receiver. A channel-dependent power-controlled RCT scheme is proposed, using which the transmitter estimates the beamforming (BF) vectors required for the forward-link SM data transmission. Tight approximate expressions for 1) the mean square error (MSE) in the estimate of the BF vectors, and 2) a capacity lower bound (CLB) for an SM system, are derived and used to optimize the parameters of the training sequence. Moreover, an extension of the channel-dependent training scheme and the data rate analysis to a multiuser scenario with M user terminals is presented. For the single-mode BF system, a closed-form expression for an upper bound on the average sum data rate is derived, which is shown to scale as ((L-c - L-B,L- tau)/L-c) log logM asymptotically in M, where L-c and L-B,L- tau are the channel coherence time and training duration, respectively. The significant performance gain offered by the proposed training sequence over the conventional constant-power orthogonal RCT sequence is demonstrated using Monte Carlo simulations.

Achievable secrecy sum-rate in a fading MAC-WT with power control and without CSI of eavesdropper

We consider a two user fading Multiple Access Channel with a wire-tapper (MAC-WT) where the transmitter has the channel state information (CSI) to the intended receiver but not to the eavesdropper (eve). We provide an achievable secrecy sum-rate with optimal power control. We next provide a secrecy sum-rate with optimal power control and cooperative jamming (CJ). We then study an achievable secrecy sum rate by employing an ON/OFF power control scheme which is more easily computable. We also employ CJ over this power control scheme. Results show that CJ boosts the secrecy sum-rate significantly even if we do not know the CSI of the eve's channel. At high SNR, the secrecy sum-rate (with CJ) without CSI of the eve exceeds the secrecy sum-rate (without CJ) with full CSI of the eve.

A scaled unscented transformation based directed Gaussian sum filter for nonlinear dynamic system identification

Impoverishment of particles, i.e. the discretely simulated sample paths of the process dynamics, poses a major obstacle in employing the particle filters for large dimensional nonlinear system identification. A known route of alleviating this impoverishment, i.e. of using an exponentially increasing ensemble size vis-a-vis the system dimension, remains computationally infeasible in most cases of practical importance. In this work, we explore the possibility of unscented transformation on Gaussian random variables, as incorporated within a scaled Gaussian sum stochastic filter, as a means of applying the nonlinear stochastic filtering theory to higher dimensional structural system identification problems. As an additional strategy to reconcile the evolving process dynamics with the observation history, the proposed filtering scheme also modifies the process model via the incorporation of gain-weighted innovation terms. The reported numerical work on the identification of structural dynamic models of dimension up to 100 is indicative of the potential of the proposed filter in realizing the stated aim of successfully treating relatively larger dimensional filtering problems. (C) 2013 Elsevier Ltd. All rights reserved.