Fourier transform convolution integrals applied to generalized Born molecular volume.

Generalized Born methods are currently among the solvation models most commonly used for biological applications. We reformulate the generalized Born molecular volume method initially described by (Lee et al, 2003, J Phys Chem, 116, 10606; Lee et al, 2003, J Comp Chem, 24, 1348) using fast Fourier transform convolution integrals. Changes in the initial method are discussed and analyzed. Finally, the method is extensively checked with snapshots from common molecular modeling applications: binding free energy computations and docking. Biologically relevant test systems are chosen, including 855-36091 atoms. It is clearly demonstrated that, precision-wise, the proposed method performs as good as the original, and could better benefit from hardware accelerated boards.

Study of the impact of tissue density heterogeneities on 3-dimensional abdominal dosimetry: comparison between dose kernel convolution and direct monte carlo methods.

Dose kernel convolution (DK) methods have been proposed to speed up absorbed dose calculations in molecular radionuclide therapy. Our aim was to evaluate the impact of tissue density heterogeneities (TDH) on dosimetry when using a DK method and to propose a simple density-correction method. METHODS: This study has been conducted on 3 clinical cases: case 1, non-Hodgkin lymphoma treated with (131)I-tositumomab; case 2, a neuroendocrine tumor treatment simulated with (177)Lu-peptides; and case 3, hepatocellular carcinoma treated with (90)Y-microspheres. Absorbed dose calculations were performed using a direct Monte Carlo approach accounting for TDH (3D-RD), and a DK approach (VoxelDose, or VD). For each individual voxel, the VD absorbed dose, D(VD), calculated assuming uniform density, was corrected for density, giving D(VDd). The average 3D-RD absorbed dose values, D(3DRD), were compared with D(VD) and D(VDd), using the relative difference Δ(VD/3DRD). At the voxel level, density-binned Δ(VD/3DRD) and Δ(VDd/3DRD) were plotted against ρ and fitted with a linear regression. RESULTS: The D(VD) calculations showed a good agreement with D(3DRD). Δ(VD/3DRD) was less than 3.5%, except for the tumor of case 1 (5.9%) and the renal cortex of case 2 (5.6%). At the voxel level, the Δ(VD/3DRD) range was 0%-14% for cases 1 and 2, and -3% to 7% for case 3. All 3 cases showed a linear relationship between voxel bin-averaged Δ(VD/3DRD) and density, ρ: case 1 (Δ = -0.56ρ + 0.62, R(2) = 0.93), case 2 (Δ = -0.91ρ + 0.96, R(2) = 0.99), and case 3 (Δ = -0.69ρ + 0.72, R(2) = 0.91). The density correction improved the agreement of the DK method with the Monte Carlo approach (Δ(VDd/3DRD) < 1.1%), but with a lesser extent for the tumor of case 1 (3.1%). At the voxel level, the Δ(VDd/3DRD) range decreased for the 3 clinical cases (case 1, -1% to 4%; case 2, -0.5% to 1.5%, and -1.5% to 2%). No more linear regression existed for cases 2 and 3, contrary to case 1 (Δ = 0.41ρ - 0.38, R(2) = 0.88) although the slope in case 1 was less pronounced. CONCLUSION: This study shows a small influence of TDH in the abdominal region for 3 representative clinical cases. A simple density-correction method was proposed and improved the comparison in the absorbed dose calculations when using our voxel S value implementation.

The Gaussian assumption in second-order estimation problems in digital communications

This paper deals with the goodness of the Gaussian assumption when designing second-order blind estimationmethods in the context of digital communications. The low- andhigh-signal-to-noise ratio (SNR) asymptotic performance of the maximum likelihood estimator—derived assuming Gaussiantransmitted symbols—is compared with the performance of the optimal second-order estimator, which exploits the actualdistribution of the discrete constellation. The asymptotic study concludes that the Gaussian assumption leads to the optimalsecond-order solution if the SNR is very low or if the symbols belong to a multilevel constellation such as quadrature-amplitudemodulation (QAM) or amplitude-phase-shift keying (APSK). On the other hand, the Gaussian assumption can yield importantlosses at high SNR if the transmitted symbols are drawn from a constant modulus constellation such as phase-shift keying (PSK)or continuous-phase modulations (CPM). These conclusions are illustrated for the problem of direction-of-arrival (DOA) estimation of multiple digitally-modulated signals.

Joint array combining and MLSE for single-user receivers in multipath Gaussian multiuser channels

The well-known structure of an array combiner along with a maximum likelihood sequence estimator (MLSE) receiveris the basis for the derivation of a space-time processor presentinggood properties in terms of co-channel and intersymbol interferencerejection. The use of spatial diversity at the receiver front-endtogether with a scalar MLSE implies a joint design of the spatialcombiner and the impulse response for the sequence detector. Thisis faced using the MMSE criterion under the constraint that thedesired user signal power is not cancelled, yielding an impulse responsefor the sequence detector that is matched to the channel andcombiner response. The procedure maximizes the signal-to-noiseratio at the input of the detector and exhibits excellent performancein realistic multipath channels.

Derivation of an observer model adapted to irregular signals based on convolution channels.

Anthropomorphic model observers are mathe- matical algorithms which are applied to images with the ultimate goal of predicting human signal detection and classification accuracy across varieties of backgrounds, image acquisitions and display conditions. A limitation of current channelized model observers is their inability to handle irregularly-shaped signals, which are common in clinical images, without a high number of directional channels. Here, we derive a new linear model observer based on convolution channels which we refer to as the "Filtered Channel observer" (FCO), as an extension of the channelized Hotelling observer (CHO) and the nonprewhitening with an eye filter (NPWE) observer. In analogy to the CHO, this linear model observer can take the form of a single template with an external noise term. To compare with human observers, we tested signals with irregular and asymmetrical shapes spanning the size of lesions down to those of microcalfications in 4-AFC breast tomosynthesis detection tasks, with three different contrasts for each case. Whereas humans uniformly outperformed conventional CHOs, the FCO observer outperformed humans for every signal with only one exception. Additive internal noise in the models allowed us to degrade model performance and match human performance. We could not match all the human performances with a model with a single internal noise component for all signal shape, size and contrast conditions. This suggests that either the internal noise might vary across signals or that the model cannot entirely capture the human detection strategy. However, the FCO model offers an efficient way to apprehend human observer performance for a non-symmetric signal.

Testing Mean-Variance Efficiency in CAPM with Possibly Non-Gaussian Errors : An Exact Simulation-Based Approach

In this paper we propose exact likelihood-based mean-variance efficiency tests of the market portfolio in the context of Capital Asset Pricing Model (CAPM), allowing for a wide class of error distributions which include normality as a special case. These tests are developed in the frame-work of multivariate linear regressions (MLR). It is well known however that despite their simple statistical structure, standard asymptotically justified MLR-based tests are unreliable. In financial econometrics, exact tests have been proposed for a few specific hypotheses [Jobson and Korkie (Journal of Financial Economics, 1982), MacKinlay (Journal of Financial Economics, 1987), Gib-bons, Ross and Shanken (Econometrica, 1989), Zhou (Journal of Finance 1993)], most of which depend on normality. For the gaussian model, our tests correspond to Gibbons, Ross and Shanken’s mean-variance efficiency tests. In non-gaussian contexts, we reconsider mean-variance efficiency tests allowing for multivariate Student-t and gaussian mixture errors. Our framework allows to cast more evidence on whether the normality assumption is too restrictive when testing the CAPM. We also propose exact multivariate diagnostic checks (including tests for multivariate GARCH and mul-tivariate generalization of the well known variance ratio tests) and goodness of fit tests as well as a set estimate for the intervening nuisance parameters. Our results [over five-year subperiods] show the following: (i) multivariate normality is rejected in most subperiods, (ii) residual checks reveal no significant departures from the multivariate i.i.d. assumption, and (iii) mean-variance efficiency tests of the market portfolio is not rejected as frequently once it is allowed for the possibility of non-normal errors.

Propriétés algébriques d'une algèbre de convolution

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal

Essays on numerically efficient inference in nonlinear and non-Gaussian state space models, and commodity market analysis.

The first two articles build procedures to simulate vector of univariate states and estimate parameters in nonlinear and non Gaussian state space models. We propose state space speci fications that offer more flexibility in modeling dynamic relationship with latent variables. Our procedures are extension of the HESSIAN method of McCausland[2012]. Thus, they use approximation of the posterior density of the vector of states that allow to : simulate directly from the state vector posterior distribution, to simulate the states vector in one bloc and jointly with the vector of parameters, and to not allow data augmentation. These properties allow to build posterior simulators with very high relative numerical efficiency. Generic, they open a new path in nonlinear and non Gaussian state space analysis with limited contribution of the modeler. The third article is an essay in commodity market analysis. Private firms coexist with farmers' cooperatives in commodity markets in subsaharan african countries. The private firms have the biggest market share while some theoretical models predict they disappearance once confronted to farmers cooperatives. Elsewhere, some empirical studies and observations link cooperative incidence in a region with interpersonal trust, and thus to farmers trust toward cooperatives. We propose a model that sustain these empirical facts. A model where the cooperative reputation is a leading factor determining the market equilibrium of a price competition between a cooperative and a private firm

Finite-size scaling analysis of the avalanches in the three-dimensional Gaussian random-field Ising model with metastable dynamics

A numerical study is presented of the third-dimensional Gaussian random-field Ising model at T=0 driven by an external field. Standard synchronous relaxation dynamics is employed to obtain the magnetization versus field hysteresis loops. The focus is on the analysis of the number and size distribution of the magnetization avalanches. They are classified as being nonspanning, one-dimensional-spanning, two-dimensional-spanning, or three-dimensional-spanning depending on whether or not they span the whole lattice in different space directions. Moreover, finite-size scaling analysis enables identification of two different types of nonspanning avalanches (critical and noncritical) and two different types of three-dimensional-spanning avalanches (critical and subcritical), whose numbers increase with L as a power law with different exponents. We conclude by giving a scenario for avalanche behavior in the thermodynamic limit.

Spanning avalanches in the three-dimensional Gaussian random-field Ising model with metastable dynamics: Field dependence and geometrical properties

Spanning avalanches in the 3D Gaussian Random Field Ising Model (3D-GRFIM) with metastable dynamics at T=0 have been studied. Statistical analysis of the field values for which avalanches occur has enabled a Finite-Size Scaling (FSS) study of the avalanche density to be performed. Furthermore, a direct measurement of the geometrical properties of the avalanches has confirmed an earlier hypothesis that several types of spanning avalanches with two different fractal dimensions coexist at the critical point. We finally compare the phase diagram of the 3D-GRFIM with metastable dynamics with the same model in equilibrium at T=0.