Detecting Generalized Synchronization Between Chaotic Signals: A Kernel-based Approach

A unified framework for analyzing generalized synchronization in coupled chaotic systems from data is proposed. The key of the proposed approach is the use of the kernel methods recently developed in the field of machine learning. Several successful applications are presented, which show the capability of the kernel-based approach for detecting generalized synchronization. It is also shown that the dynamical change of the coupling coefficient between two chaotic systems can be captured by the proposed approach.Comment: 20 pages, 15 figures. massively revised as a full paper; issues on the choice of parameters by cross validation, tests by surrogated data, etc. are added as well as additional examples and figure

Analysis of thermal-hydraulic transients for the Miniature Neutron Source Reactor (MNSR) in Ghana

Abstract: A mathematical model is presented that permits to simulate the effect of the cooling coils of the pool upper section on the reactor thermal-hydraulic behaviour of Ghana research reactor-1. The model is based on a lumped parameter description solved numerically using Matlab/Simulink tool which is a commercial software package with the capability of modelling dynamical and control systems. The model incorporates fuel grids and cooling coil models as well as radiating energy from the clad. In this model, the reactor tank and the pool is divided into three sections. The model predictions are qualified by comparing the results with experimental data. The effect of cooling the upper section of the pool on reactor thermal-hydraulic parameters using the cooling coil is presented and discussed. It was observed that all maximum values of the reactor thermalhydraulic parameters decrease when the cooling coil power is increased. Good agreement is found between the model predictions and the experimental results

SYZ mirror symmetry for hypertoric varieties

We construct a Lagrangian torus fibration on a smooth hypertoric variety and a corresponding SYZ mirror variety using $T$-duality and generating functions of open Gromov-Witten invariants. The variety is singular in general. We construct a resolution using the wall and chamber structure of the SYZ base.Comment: v_2: 31 pages, 5 figures, minor revision. To appear in Communications in Mathematical Physic

Safety and feasibility of switching from phenytoin to levetiracetam monotherapy for glioma-related seizure control following craniotomy: a randomized phase II pilot study

Seizures are common in patients with gliomas, and phenytoin (PHT) is frequently used to control tumor-related seizures. PHT, however, has many undesirable side effects (SEs) and drug interactions with glioma chemotherapy. Levetiracetam (LEV) is a newer antiepileptic drug (AED) with fewer SEs and essentially no drug interactions. We performed a pilot study testing the safety and feasibility of switching patients from PHT to LEV monotherapy for postoperative control of glioma-related seizures. Over a 13-month period, 29 patients were randomized in a 2:1 ratio to initiate LEV therapy within 24 h of surgery or to continue PHT therapy. 6 month follow-up data were available for 15 patients taking LEV and for 8 patients taking PHT. In the LEV group, 13 patients (87%) were seizure-free. In the PHT group, 6 patients (75%) were seizure-free. Reported SEs at 6 months was as follows (%LEV/%PHT group): dizziness (0/14), difficulty with coordination (0/29), depression (7/14) lack of energy or strength (20/43), insomnia (40/43), mood instability (7/0). The pilot data presented here suggest that it is safe to switch patients from PHT to LEV monotherapy following craniotomy for supratentorial glioma. A large-scale, double-blinded, randomized control trial of LEV versus PHT is required to determine seizure control equivalence and better assess differences in SEs

Integrative analysis of gene expression and copy number alterations using canonical correlation analysis

Supplementary Figure 1. Representation of the samples from the tuning set by their coordinates in the first two pairs of features (extracted from the tuning set) using regularized dual CCA, with regularization parameters tx = 0.9, ty = 0.3 (left panel), and PCA+CCA (right panel). We show the representations with respect to both the copy number features and the gene expression features in a superimposed way, where each sample is represented by two markers. The filled markers represent the coordinates in the features extracted from the copy number variables, and the open markers represent coordinates in the features extracted from the gene expression variables. Samples with different leukemia subtypes are shown with different colors. The first feature pair distinguishes the HD50 group from the rest, while the second feature pair represents the characteristics of the samples from the E2A/PBX1 subtype. The high canonical correlation obtained for the tuning samples with regularized dual CCA is apparent in the left panel, where the two points for each sample coincide. Nevertheless, the extracted features have a high generalization ability, as can be seen in the left panel of Figure 5, showing the representation of the validation samples. 1 Supplementary Figure 2. Representation of the samples from the tuning set by their coordinates in the first two pairs of features (extracted from the tuning set) using regularized dual CCA, with regularization parameters tx = 0, ty = 0 (left panel), and tx = 1, ty = 1 (right panel). We show the representations with respect to both the copy number features and the gene expression features in a superimposed way, where each sample is represented by tw

A Kernel Method For Canonical Correlation Analysis

roduce a quadratic regularization term #(a + b )/2 into the cost function of CCA. By the quadratic regularization, it follows that a can be written by a weighted sum of # x (x i ) where x i is the i-th sample, and b can be written by a weighted sum of # y (y i ). Therefore, a # x (x) = # i # i # x (x i ) # x (x). This fact enables us to use a "kernel trick": Let k(z, w) be a kernel function which is symmetric and positive definite, then there exists # z (z) and k(z, w) = # z (z) # z (w). Using a kernel, we can calculate # x (x i ) # x (x) directly without knowing #. This means the complexity problem of calculation is solved as well, because we do not need to calculate # anymore. 6. Consequently, we obtain KCCA: 1. Calculate matrices of kernels K x = (k x (x i , x j )) and K y = (k y (y i , y j )), where k x and k y are kernels. 2. Solve the generalized eigen problem, M# = #L# and M # = #N#, where M = (1/n)K x JK y , L = (1/n)K x JK x + (#/#)K x , N = (1/n)K

The em Algorithm for Kernel Matrix Completion with Auxiliary Data

In biological data, it is often the case that observed data are available only for a subset of samples. When akernel matrix is derived from such data, we have to leave the entries for unavailable samples as missing. Inthis paper, the missing entries are completed by exploiting an auxiliary kernel matrix derived from anotherinformation source. The parametric model of kernel matrices is created as a set of spectral variants of theauxiliary kernel matrix, and the missing entries are estimated by fitting this model to the existing entries. Formodel fitting, we adopt theemalgorithm (distinguished from the EM algorithm of Dempster et al., 1977)based on the information geometry of positive definite matrices. We will report promising results on bacteriaclustering experiments using two marker sequences: 16S and gyrB