Constructions of Almost Optimal Resilient Boolean Functions on Large Even Number of Variables

In this paper, a technique on constructing nonlinear resilient Boolean functions is described. By using several sets of disjoint spectra functions on a small number of variables, an almost optimal resilient function on a large even number of variables can be constructed. It is shown that given any $m$, one can construct infinitely many $n$-variable ($n$ even), $m$-resilient functions with nonlinearity $>2^{n-1}-2^{n/2}$. A large class of highly nonlinear resilient functions which were not known are obtained. Then one method to optimize the degree of the constructed functions is proposed. Last, an improved version of the main construction is given.Comment: 14 pages, 2 table

Phase retrieval via regularization in self-diffraction based spectral interferometry

A novel variant of spectral phase interferometry for direct electric-field reconstruction (SPIDER) is introduced and experimentally demonstrated. Other than most previously demonstrated variants of SPIDER, our method is based on a third-order nonlinear optical effect, namely self-diffraction, rather than the second-order effect of sum-frequency generation. On one hand, self-diffraction (SD) substantially simplifies phase-matching capabilities for multi-octave spectra that cannot be hosted by second-order processes, given manufacturing limitations of crystal lengths in the few-micrometer range. On the other hand, however, SD SPIDER imposes an additional constraint as it effectively measures the spectral phase of a self-convolved spectrum rather than immediately measuring the fundamental phase. Reconstruction of the latter from the measured phase and the spectral amplitude of the fundamental turns out to be an ill-posed problem, which we address by a regularization approach. We discuss the numerical implementation in detail and apply it to measured data from a Ti:sapphire amplifier system. Our experimental demonstration used 40-fs pulses and a 500 $\mu$m thick BaF${}_2$ crystal to show that the SD SPIDER signal is sufficiently strong to be separable from stray light. Extrapolating these measurements to the thinnest conceivable nonlinear media, we predict that bandwidths well above two optical octaves can be measured by a suitably adapted SD SPIDER apparatus, enabling the direct characterization of pulses down to single-femtosecond pulse durations. Such characteristics appear out of range for any currently established pulse measurement technique

A metaproteomic approach to study human-microbial ecosystems at the mucosal luminal interface

Aberrant interactions between the host and the intestinal bacteria are thought to contribute to the pathogenesis of many digestive diseases. However, studying the complex ecosystem at the human mucosal-luminal interface (MLI) is challenging and requires an integrative systems biology approach. Therefore, we developed a novel method integrating lavage sampling of the human mucosal surface, high-throughput proteomics, and a unique suite of bioinformatic and statistical analyses. Shotgun proteomic analysis of secreted proteins recovered from the MLI confirmed the presence of both human and bacterial components. To profile the MLI metaproteome, we collected 205 mucosal lavage samples from 38 healthy subjects, and subjected them to high-throughput proteomics. The spectral data were subjected to a rigorous data processing pipeline to optimize suitability for quantitation and analysis, and then were evaluated using a set of biostatistical tools. Compared to the mucosal transcriptome, the MLI metaproteome was enriched for extracellular proteins involved in response to stimulus and immune system processes. Analysis of the metaproteome revealed significant individual-related as well as anatomic region-related (biogeographic) features. Quantitative shotgun proteomics established the identity and confirmed the biogeographic association of 49 proteins (including 3 functional protein networks) demarcating the proximal and distal colon. This robust and integrated proteomic approach is thus effective for identifying functional features of the human mucosal ecosystem, and a fresh understanding of the basic biology and disease processes at the MLI. © 2011 Li et al

Integrative analysis of the inter-tumoral heterogeneity of triple-negative breast cancer.

Triple-negative breast cancers (TNBC) lack estrogen and progesterone receptors and HER2 amplification, and are resistant to therapies that target these receptors. Tumors from TNBC patients are heterogeneous based on genetic variations, tumor histology, and clinical outcomes. We used high throughput genomic data for TNBC patients (n = 137) from TCGA to characterize inter-tumor heterogeneity. Similarity network fusion (SNF)-based integrative clustering combining gene expression, miRNA expression, and copy number variation, revealed three distinct patient clusters. Integrating multiple types of data resulted in more distinct clusters than analyses with a single datatype. Whereas most TNBCs are classified by PAM50 as basal subtype, one of the clusters was enriched in the non-basal PAM50 subtypes, exhibited more aggressive clinical features and had a distinctive signature of oncogenic mutations, miRNAs and expressed genes. Our analyses provide a new classification scheme for TNBC based on multiple omics datasets and provide insight into molecular features that underlie TNBC heterogeneity