There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

CoSaMP: Iterative signal recovery from incomplete and inaccurate samples

Compressive sampling (CoSa) is a new paradigm for developing data sampling technologies It is based on the principle that many types of vector-space data are compressible, which is a term of art in mathematical signal processing The key ideas are that randomized dimension reduction preserves the information in a compressible signal and that it is possible to develop hardware devices that implement this dimension reduction efficiently The main computational challenge in CoSa is to reconstruct a compressible signal from the reduced representation acquired by the sampling device This extended abstract describes a recent algorithm, called, CoSaMP, that accomplishes the data recovery task It was the first known method to offer near-optimal guarantees on resource usage

/pdf/cosamp-iterative-signal-recovery-from-incomplete-and-36ikti059u.pdf

CoSaMP: iterative signal recovery from incomplete and inaccurate samples

We describe the landscape of somatic genomic alterations based on multidimensional and comprehensive characterization of more than 500 glioblastoma tumors (GBMs). We identify several novel mutated genes as well as complex rearrangements of signature receptors, including EGFR and PDGFRA. TERT promoter mutations are shown to correlate with elevated mRNA expression, supporting a role in telomerase reactivation. Correlative analyses confirm that the survival advantage of the proneural subtype is conferred by the G-CIMP phenotype, and MGMT DNA methylation may be a predictive biomarker for treatment response only in classical subtype GBM. Integrative analysis of genomic and proteomic profiles challenges the notion of therapeutic inhibition of a pathway as an alternative to inhibition of the target itself. These data will facilitate the discovery of therapeutic and diagnostic target candidates, the validation of research and clinical observations and the generation of unanticipated hypotheses that can advance our molecular understanding of this lethal cancer.

The somatic genomic landscape of glioblastoma

We propose a new method for reconstruction of sparse signals with and without noisy perturbations, termed the subspace pursuit algorithm. The algorithm has two important characteristics: low computational complexity, comparable to that of orthogonal matching pursuit techniques when applied to very sparse signals, and reconstruction accuracy of the same order as that of linear programming (LP) optimization methods. The presented analysis shows that in the noiseless setting, the proposed algorithm can exactly reconstruct arbitrary sparse signals provided that the sensing matrix satisfies the restricted isometry property with a constant parameter. In the noisy setting and in the case that the signal is not exactly sparse, it can be shown that the mean-squared error of the reconstruction is upper-bounded by constant multiples of the measurement and signal perturbation energies.

Subspace Pursuit for Compressive Sensing Signal Reconstruction

We propose a new method for reconstruction of sparse signals with and without noisy perturbations, termed the subspace pursuit algorithm. The algorithm has two important characteristics: low computational complexity, comparable to that of orthogonal matching pursuit techniques when applied to very sparse signals, and reconstruction accuracy of the same order as that of LP optimization methods. The presented analysis shows that in the noiseless setting, the proposed algorithm can exactly reconstruct arbitrary sparse signals provided that the sensing matrix satisfies the restricted isometry property with a constant parameter. In the noisy setting and in the case that the signal is not exactly sparse, it can be shown that the mean squared error of the reconstruction is upper bounded by constant multiples of the measurement and signal perturbation energies.

This paper introduces several new combinatorial constructions of low-density parity-check (LDPC) codes, in contrast to the prevalent practice of using long, random-like codes. The proposed codes are well structured, and unlike random codes can lend themselves to a very low-complexity implementation. Constructions of regular Gallager codes based on cyclic difference families, cycle-invariant difference sets, and affine 1-configurations are introduced. Several constructions of difference families used for code design are presented, as well as bounds on the minimal distance of the codes based on the concept of a generalized Pasch configuration.

/pdf/combinatorial-constructions-of-low-density-parity-check-2s2udqjoep.pdf

Combinatorial constructions of low-density parity check codes for iterative decoding

We describe the first DNA-based storage architecture that enables random access to data blocks and rewriting of information stored at arbitrary locations within the blocks. The newly developed architecture overcomes drawbacks of existing read-only methods that require decoding the whole file in order to read one data fragment. Our system is based on new constrained coding techniques and accompanying DNA editing methods that ensure data reliability, specificity and sensitivity of access, and at the same time provide exceptionally high data storage capacity. As a proof of concept, we encoded parts of the Wikipedia pages of six universities in the USA, and selected and edited parts of the text written in DNA corresponding to three of these schools. The results suggest that DNA is a versatile media suitable for both ultrahigh density archival and rewritable storage applications.

/pdf/a-rewritable-random-access-dna-based-storage-system-16mx0ijijg.pdf

A Rewritable, Random-Access DNA-Based Storage System.

: We propose a new method for reconstruction of sparse signals with and without noisy perturbations, termed the subspace pursuit algorithm. The algorithm has two important characteristics: low computational complexity, comparable to that of orthogonal matching pursuit techniques, and reconstruction accuracy of the same order as that of LP optimization methods. The presented analysis shows that in the noiseless setting, the proposed algorithm can exactly reconstruct arbitrary sparse signals provided that the sensing matrix satisfies the restricted isometry property with a constant parameter. In the noisy setting and in the case that the signal is not exactly sparse it can be shown that the mean squared error of the reconstruction is upper bounded by constant multiples of the measurement and signal perturbation energies.

https://apps.dtic.mil/sti/pdfs/ADA528357.pdf

Olgica Milenkovic

Papers

Subspace Pursuit for Compressive Sensing Signal Reconstruction

Subspace Pursuit for Compressive Sensing Signal Reconstruction

Combinatorial constructions of low-density parity check codes for iterative decoding

A Rewritable, Random-Access DNA-Based Storage System.

Subspace Pursuit for Compressive Sensing: Closing the Gap Between Performance and Complexity