Supervised Gaussian Process Latent Variable Model for Dimensionality Reduction

The Gaussian process latent variable model (GP-LVM) has been identified to be an effective probabilistic approach for dimensionality reduction because it can obtain a low-dimensional manifold of a data set in an unsupervised fashion. Consequently, the GP-LVM is insufficient for supervised learning tasks (e. g., classification and regression) because it ignores the class label information for dimensionality reduction. In this paper, a supervised GP-LVM is developed for supervised learning tasks, and the maximum a posteriori algorithm is introduced to estimate positions of all samples in the latent variable space. We present experimental evidences suggesting that the supervised GP-LVM is able to use the class label information effectively, and thus, it outperforms the GP-LVM and the discriminative extension of the GP-LVM consistently. The comparison with some supervised classification methods, such as Gaussian process classification and support vector machines, is also given to illustrate the advantage of the proposed method.

A Computational Model of Skill Acquisition

This thesis confronts the nature of the process of learning an intellectual skill, the ability to solve problems efficiently in a particular domain of discourse. The investigation is synthetic; a computational performance model, HACKER, is displayed. Hacker is a computer problem-solving system whose performance improves with practice. HACKER maintains performance knowledge as a library of procedures indexed by descriptions of the problem types for which the procedures are appropriate. When applied to a problem, HACKER tries to use a procedure from this "Answer Library". If no procedure is found to be applicable, HACKER writes one using more general knowledge of the problem domain and of programming techniques. This new program may be generalized and added to the Answer Library.

Transformation Based Interpolation with Generalized Representative Values

Z. Huang and Q. Shen. Transformation Based Interpolation with Generalized Representative Values. Proceedings of the 14th International Conference on Fuzzy Systems, pages 821-826.

Fuzzy interpolation with generalized representative values

Z. Huang and Q. Shen. Fuzzy interpolation with generalized representative values. Proceedings of the 2004 UK Workshop on Computational Intelligence, pages 161-171.

Framingham Heart Study 100K project: genome-wide associations for cardiovascular disease outcomes

BACKGROUND:Cardiovascular disease (CVD) and its most common manifestations - including coronary heart disease (CHD), stroke, heart failure (HF), and atrial fibrillation (AF) - are major causes of morbidity and mortality. In many industrialized countries, cardiovascular disease (CVD) claims more lives each year than any other disease. Heart disease and stroke are the first and third leading causes of death in the United States. Prior investigations have reported several single gene variants associated with CHD, stroke, HF, and AF. We report a community-based genome-wide association study of major CVD outcomes.METHODS:In 1345 Framingham Heart Study participants from the largest 310 pedigrees (54% women, mean age 33 years at entry), we analyzed associations of 70,987 qualifying SNPs (Affymetrix 100K GeneChip) to four major CVD outcomes: major atherosclerotic CVD (n = 142; myocardial infarction, stroke, CHD death), major CHD (n = 118; myocardial infarction, CHD death), AF (n = 151), and HF (n = 73). Participants free of the condition at entry were included in proportional hazards models. We analyzed model-based deviance residuals using generalized estimating equations to test associations between SNP genotypes and traits in additive genetic models restricted to autosomal SNPs with minor allele frequency [greater than or equal to]0.10, genotype call rate [greater than or equal to]0.80, and Hardy-Weinberg equilibrium p-value [greater than or equal to] 0.001.RESULTS:Six associations yielded p <10-5. The lowest p-values for each CVD trait were as follows: major CVD, rs499818, p = 6.6 x 10-6; major CHD, rs2549513, p = 9.7 x 10-6; AF, rs958546, p = 4.8 x 10-6; HF: rs740363, p = 8.8 x 10-6. Of note, we found associations of a 13 Kb region on chromosome 9p21 with major CVD (p 1.7 - 1.9 x 10-5) and major CHD (p 2.5 - 3.5 x 10-4) that confirm associations with CHD in two recently reported genome-wide association studies. Also, rs10501920 in CNTN5 was associated with AF (p = 9.4 x 10-6) and HF (p = 1.2 x 10-4). Complete results for these phenotypes can be found at the dbgap website http://www.ncbi.nlm.nih.gov/projects/gap/cgi-bin/study.cgi?id=phs000007.CONCLUSION:No association attained genome-wide significance, but several intriguing findings emerged. Notably, we replicated associations of chromosome 9p21 with major CVD. Additional studies are needed to validate these results. Finding genetic variants associated with CVD may point to novel disease pathways and identify potential targeted preventive therapies.

Interaction of additive and quantization noises in digital PLLs

Phase-locked loops (PLLs) are a crucial component in modern communications systems. Comprising of a phase-detector, linear filter, and controllable oscillator, they are widely used in radio receivers to retrieve the information content from remote signals. As such, they are capable of signal demodulation, phase and carrier recovery, frequency synthesis, and clock synchronization. Continuous-time PLLs are a mature area of study, and have been covered in the literature since the early classical work by Viterbi [1] in the 1950s. With the rise of computing in recent decades, discrete-time digital PLLs (DPLLs) are a more recent discipline; most of the literature published dates from the 1990s onwards. Gardner [2] is a pioneer in this area. It is our aim in this work to address the difficulties encountered by Gardner [3] in his investigation of the DPLL output phase-jitter where additive noise to the input signal is combined with frequency quantization in the local oscillator. The model we use in our novel analysis of the system is also applicable to another of the cases looked at by Gardner, that is the DPLL with a delay element integrated in the loop. This gives us the opportunity to look at this system in more detail, our analysis providing some unique insights into the variance `dip' seen by Gardner in [3]. We initially provide background on the probability theory and stochastic processes. These branches of mathematics are the basis for the study of noisy analogue and digital PLLs. We give an overview of the classical analogue PLL theory as well as the background on both the digital PLL and circle map, referencing the model proposed by Teplinsky et al. [4, 5]. For our novel work, the case of the combined frequency quantization and noisy input from [3] is investigated first numerically, and then analytically as a Markov chain via its Chapman-Kolmogorov equation. The resulting delay equation for the steady-state jitter distribution is treated using two separate asymptotic analyses to obtain approximate solutions. It is shown how the variance obtained in each case matches well to the numerical results. Other properties of the output jitter, such as the mean, are also investigated. In this way, we arrive at a more complete understanding of the interaction between quantization and input noise in the first order DPLL than is possible using simulation alone. We also do an asymptotic analysis of a particular case of the noisy first-order DPLL with delay, previously investigated by Gardner [3]. We show a unique feature of the simulation results, namely the variance `dip' seen for certain levels of input noise, is explained by this analysis. Finally, we look at the second-order DPLL with additive noise, using numerical simulations to see the effects of low levels of noise on the limit cycles. We show how these effects are similar to those seen in the noise-free loop with non-zero initial conditions.

A multivariate generalized ARCH approach to modeling risk premia in forward foreign exchange rate markets

Assuming that daily spot exchange rates follow a martingale process, we derive the implied time series process for the vector of 30-day forward rate forecast errors from using weekly data. The conditional second moment matrix of this vector is modelled as a multivariate generalized ARCH process. The estimated model is used to test the hypothesis that the risk premium is a linear function of the conditional variances and covariances as suggested by the standard asset pricing theory literature. Little supportt is found for this theory; instead lagged changes in the forward rate appear to be correlated with the 'risk premium.'. © 1990.

Generalized sampling using a compound-eye imaging system for multi-dimensional object acquisition.

In this paper, we propose generalized sampling approaches for measuring a multi-dimensional object using a compact compound-eye imaging system called thin observation module by bound optics (TOMBO). This paper shows the proposed system model, physical examples, and simulations to verify TOMBO imaging using generalized sampling. In the system, an object is modulated and multiplied by a weight distribution with physical coding, and the coded optical signal is integrated on to a detector array. A numerical estimation algorithm employing a sparsity constraint is used for object reconstruction.

Generalized Markov branching processes

A generalized Markov Brnching Process (GMBP) is a Markov branching model where the infinitesimal branching rates are modified with an interaction index. It is proved that there always exists only one GMBP. An associated differential-integral equation is derived. The extinction probalility and the mean and conditional mean extinction times are obtained. Ergodicity and stability of GMBP with resurrection are also considered. Easy checking criteria are established for ordinary and strong ergodicty. The equilibrium distribution is given in an elegant closed form. The probability meaning of our results is clear and thus explained.

Analytically continued generalized continuum distorted waves

The continuum distorted-wave eikonal-initial-state (CDW-EIS) theory of Crothers and McCann (Crothers DSF and McCann JF, 1983 J. Phys. B: At. Mol. Opt. Phys. 16 3229 ) used to describe ionization in ion-atom collisions is generalized (G) to GCDW-EIS, to incorporate the azimuthal ange dependence into the final-state wavefunction. This is accomplished by the analytic continuation of hydrogenic-like wavefunctions from below to above threshold, using parabolic coordinates and quantum numbers including magnetic quantum numbers, thus providing a more complete set of states. At impact energies lower than 25 ke V u^{-1}, the total CDW-EIS ionization cross section falls off, with decreasing energy, too quickly in comparison with experimental data by Crothers and McCann. The idea behind and motivation for the GCDW-EIS model is to improve the theory with respect to experiment, by including contributions from non-zero magnetic quantum numbers. We also therefore incidentally provide a new derivation of the theory of continuum distorted waves for zero magnetic quantum numbers while simultaneously generalizing it.

Boundary conditions in the simplest model of linear and second harmonic magneto-optical effects

This paper is concerned with linear and nonlinear magneto- optical effects in multilayered magnetic systems when treated by the simplest phenomenological model that allows their response to be represented in terms of electric polarization, The problem is addressed by formulating a set of boundary conditions at infinitely thin interfaces, taking into account the existence of surface polarizations. Essential details are given that describe how the formalism of distributions (generalized functions) allows these conditions to be derived directly from the differential form of Maxwell's equations. Using the same formalism we show the origin of alternative boundary conditions that exist in the literature. The boundary value problem for the wave equation is formulated, with an emphasis on the analysis of second harmonic magneto-optical effects in ferromagnetically ordered multilayers. An associated problem of conventions in setting up relationships between the nonlinear surface polarization and the fundamental electric field at the interfaces separating anisotropic layers through surface susceptibility tensors is discussed. A problem of self- consistency of the model is highlighted, relating to the existence of resealing procedures connecting the different conventions. The linear approximation with respect to magnetization is pursued, allowing rotational anisotropy of magneto-optical effects to be easily analyzed owing to the invariance of the corresponding polar and axial tensors under ordinary point groups. Required representations of the tensors are given for the groups infinitym, 4mm, mm2, and 3m, With regard to centrosymmetric multilayers, nonlinear volume polarization is also considered. A concise expression is given for its magnetic part, governed by an axial fifth-rank susceptibility tensor being invariant under the Curie group infinityinfinitym.

Generalized compound transport of charged particles in turbulent magnetized plasmas

The transport of charged particles in partially turbulent magnetic systems is investigated from first principles. A generalized compound transport model is proposed, providing an explicit relation between the mean-square deviation of the particle parallel and perpendicular to a magnetic mean field, and the mean-square deviation which characterizes the stochastic field-line topology. The model is applied in various cases of study, and the relation to previous models is discussed.

A hierarchical physical model-based approach to predictive control of a thermal power plant for efficient plant-wide disturbance rejection

Extending the work presented in Prasad et al. (IEEE Proceedings on Control Theory and Applications, 147, 523-37, 2000), this paper reports a hierarchical nonlinear physical model-based control strategy to account for the problems arising due to complex dynamics of drum level and governor valve, and demonstrates its effectiveness in plant-wide disturbance handling. The strategy incorporates a two-level control structure consisting of lower-level conventional PI regulators and a higher-level nonlinear physical model predictive controller (NPMPC) for mainly set-point manoeuvring. The lower-level PI loops help stabilise the unstable drum-boiler dynamics and allow faster governor valve action for power and grid-frequency regulation. The higher-level NPMPC provides an optimal load demand (or set-point) transition by effective handling of plant-wide interactions and system disturbances. The strategy has been tested in a simulation of a 200-MW oil-fired power plant at Ballylumford in Northern Ireland. A novel approach is devized to test the disturbance rejection capability in severe operating conditions. Low frequency disturbances were created by making random changes in radiation heat flow on the boiler-side, while condenser vacuum was fluctuating in a random fashion on the turbine side. In order to simulate high-frequency disturbances, pulse-type load disturbances were made to strike at instants which are not an integral multiple of the NPMPC sampling period. Impressive results have been obtained during both types of system disturbances and extremely high rates of load changes, right across the operating range, These results compared favourably with those from a conventional state-space generalized predictive control (GPC) method designed under similar conditions.

A novel shrinkage technique based on the normal inverse Gaussian density model

This paper proposes a novel image denoising technique based on the normal inverse Gaussian (NIG) density model using an extended non-negative sparse coding (NNSC) algorithm proposed by us. This algorithm can converge to feature basis vectors, which behave in the locality and orientation in spatial and frequency domain. Here, we demonstrate that the NIG density provides a very good fitness to the non-negative sparse data. In the denoising process, by exploiting a NIG-based maximum a posteriori estimator (MAP) of an image corrupted by additive Gaussian noise, the noise can be reduced successfully. This shrinkage technique, also referred to as the NNSC shrinkage technique, is self-adaptive to the statistical properties of image data. This denoising method is evaluated by values of the normalized signal to noise rate (SNR). Experimental results show that the NNSC shrinkage approach is indeed efficient and effective in denoising. Otherwise, we also compare the effectiveness of the NNSC shrinkage method with methods of standard sparse coding shrinkage, wavelet-based shrinkage and the Wiener filter. The simulation results show that our method outperforms the three kinds of denoising approaches mentioned above.

Quasi-classical model of non-destructive wavepacket manipulation by intense ultrashort nonresonant laser pulses

A quasi-classical model (QCM) of nuclear wavepacket generation, modification and imaging by three intense ultrafast near-infrared laser pulses has been developed. Intensities in excess of 10(13) W cm(-2) are studied, the laser radiation is non-resonant and pulse durations are in the few-cycle regime, hence significantly removed from the conditions typical of coherent control and femtochemistry. The 1s sigma ground state of the D-2 precursor is projected onto the available electronic states in D-2(+) (1s sigma(g) ground and 2p sigma(u) dissociative) and D+ + D+ (Coulomb explosion) by tunnel ionization by an ultrashort 'pump' pulse, and relative populations are found numerically. A generalized non-adiabatic treatment allows the dependence of the initial vibrational population distribution on laser intensity to be calculated. The wavepacket is approximated as a classical ensemble of particles moving on the 1s sigma(g) potential energy surface (PES), and hence follow trajectories of different amplitudes and frequencies depending on the initial vibrational state. The 'control' pulse introduces a time-dependent polarization of the molecular orbital, causing the PES to be modified according to the dynamic Stark effect and the transition dipole. The trajectories adjust in amplitude, frequency and phase-offset as work is done on or by the resulting force; comparing the perturbed and unperturbed trajectories allows the final vibrational state populations and phases to be determined. The action of the 'probe' pulse is represented by a discrete internuclear boundary, such that elements of the ensemble at a larger internuclear separation are assumed to be photodissociated. The vibrational populations predicted by the QCM are compared to recent quantum simulations (Niederhausen and Thumm 2008 Phys. Rev. A 77 013404), and a remarkable agreement has been found. The applicability of this model to femtosecond and attosecond time-scale experiments is discussed and the relation to established femtochemistry and coherent control techniques are explored.