Control Theoretic Approach To Sampling And Approximation Problems

Thesis (Ph.D.) University of Alaska Fairbanks, 2009We present applications of some methods of control theory to problems of signal processing and optimal quadrature problems. The following problems are considered: construction of sampling and interpolating sequences for multi-band signals; spectral estimation of signals modeled by a finite sum of exponentials modulated by polynomials; construction of optimal quadrature formulae for integrands determined by solutions of initial boundary value problems. A multi-band signal is a function whose Fourier transform is supported on a finite union of intervals. The approach used in Chapter I is based on connections between the sampling and interpolation problem and the problem of the controllability of a dynamical system. We prove that there exist infinitely many sampling and interpolating sequences for signals whose spectra are supported on a union of two disjoint intervals, and provide an algorithm for construction of such sequences. There exist numerous methods for solving the spectral estimation problem. In Chapter II we introduce a new approach to this problem based on the Boundary Control method, which uses the connection between inverse problems of mathematical physics and control theory for partial differential equations. Using samples of the signal at integer moments of time we construct a convolution operator regarded as an input-output map of a linear discrete dynamical system. This system can be identified, and the exponents and amplitudes of the signal can be found from the parameters of the system. We show that the coefficients of the signal can be recovered by solving a generalized eigenvalue problem as in the Matrix Pencil method. Our method allows to consider signals with polynomial amplitudes, and we obtain an exact formula for these amplitudes. In the third chapter we consider an optimal quadrature problem for solutions of initial boundary value problems. The problem of optimization of an error functional over the set of solutions and quadrature weights is a problem of optimal control of partial differential equations. We obtain estimates for the error in quadrature formulae and an optimality condition for quadrature weights

Solving dynamical systems in neuromorphic hardware: simulation studies using balanced spiking networks

International audienc

The classification of the patients with pulmonary diseases using breath air samples spectral analysis

Technique of exhaled breath sampling is discussed. The procedure of wavelength auto-calibration is proposed and tested. Comparison of the experimental data with the model absorption spectra of 5% CO2 is conducted. The classification results of three study groups obtained by using support vector machine and principal component analysis methods are presented

Breath air measurement using wide-band frequency tuning IR laser photo-acoustic spectroscopy

The results of measuring of biomarkers in breath air of patients with broncho-pulmonary diseases using wide-band frequency tuning IR laser photo-acoustic spectroscopy and the methods of data mining are presented. We will discuss experimental equipment and various methods of intellectual analysis of the experimental spectra in context of above task

Response to : The GPRC5A frameshift variant c.183del is not associated with increased breast cancer risk in BRCA1 mutation carriers

Non peer reviewe

BRCA1-deficient breast cancer cell lines are resistant to MEK inhibitors and show distinct sensitivities to 6-thioguanine

Germ-line or somatic inactivation of BRCA1 is a defining feature for a portion of human breast cancers. Here we evaluated the anti-proliferative activity of 198 FDA-approved and experimental drugs against four BRCA1-mutant (HCC1937, MDA-MB-436, SUM1315MO2, and SUM149PT) and four BRCA1-wild-type (MDA-MB-231, SUM229PE, MCF10A, and MCF7) breast cancer cell lines. We found that all BRCA1-mutant cell lines were insensitive to inhibitors of mitogen-activated protein kinase kinase 1 and 2 (MEK1/2) Selumetinib and Pimasertib in contrast to BRCA1-wildtype control cell lines. However, unexpectedly, only two BRCA1-mutant cell lines, HCC1937 and MDA-MB-436, were hypersensitive to a nucleotide analogue 6-thioguanine (6-TG). SUM149PT cells readily formed radiation-induced RAD51-positive nuclear foci indicating a functional homologous recombination, which may explain their resistance to 6-TG. However, the reason underlying 6-TG resistance of SUM1315MO2 cells remains unclear. Our data reveal a remarkable heterogeneity among BRCA1-mutant cell lines and provide a reference for future studies.Peer reviewe

Network-guided identification of cancer-selective combinatorial therapies in ovarian cancer

Each patient's cancer consists of multiple cell subpopulations that are inherently heterogeneous and may develop differing phenotypes such as drug sensitivity or resistance. A personalized treatment regimen should therefore target multiple oncoproteins in the cancer cell populations that are driving the treatment resistance or disease progression in a given patient to provide maximal therapeutic effect, while avoiding severe co-inhibition of non-malignant cells that would lead to toxic side effects. To address the intra- and inter-tumoral heterogeneity when designing combinatorial treatment regimens for cancer patients, we have implemented a machine learning-based platform to guide identification of safe and effective combinatorial treatments that selectively inhibit cancer-related dysfunctions or resistance mechanisms in individual patients. In this case study, we show how the platform enables prediction of cancer-selective drug combinations for patients with high-grade serous ovarian cancer using single-cell imaging cytometry drug response assay, combined with genome-wide transcriptomic and genetic profiles. The platform makes use of drug-target interaction networks to prioritize those combinations that warrant further preclinical testing in scarce patient-derived primary cells. During the case study in ovarian cancer patients, we investigated (i) the relative performance of various ensemble learning algorithms for drug response prediction, (ii) the use of matched single-cell RNA-sequencing data to deconvolute cell population-specific transcriptome profiles from bulk RNA-seq data, (iii) and whether multi-patient or patient-specific predictive models lead to better predictive accuracy. The general platform and the comparison results are expected to become useful for future studies that use similar predictive approaches also in other cancer types.</p