Introduction to wavelet analysis over IR Discretizing and periodizing the half-plane Multi-resolution Fractal transforms Group theory as unifying language.

The authors present a rigorous treatment of the first principles algebraic and analytic core quantum field theory. Their aim is to correlate modern mathematical theory with explanation observed process particle production particle-wave duality that heuristic provides. Many topics are treated here in book form for time, from origins complex structures quantization tachyons domains dependence quantized wave equations. This work begins comprehensive analysis, universal format, structure...

Protecting biodiversity involves preserving the maximum number and abundance of species while giving special attention to with unique genetic or morphological characteristics. In balancing different priorities, conservation policymakers may consider quantitative measures that compare diversity across ecological communities. To serve this purpose, a measure should increase decrease changes in community composition way reflects what is valued, including richness, evenness, distinctness....

We report results of a study utilizing recently developed tissue diagnostic method, based on label-free spectral techniques, for the classification lung cancer histopathological samples from microarray. The method allows reproducible and objective diagnosis unstained sections. This is accomplished by acquiring infrared hyperspectral data sets containing thousands spectra, each collected pixels about 6 μm edge; these pixel spectra contain an encoded snapshot entire biochemical composition...

Molecular markers based on gene expression profiles have been used in experimental and clinical settings to distinguish cancerous tumors stage, grade, survival time, metastasis, drug sensitivity. However, most significant are unstable (not reproducible) among data sets. We introduce a standardized method for representing cancer as 2-level hierarchical feature vectors, with basic level well second of (more stable) pathway markers, the purpose discriminating subtypes. This extends standard...

The widely used k top scoring pair (k-TSP) algorithm is a simple yet powerful parameter-free classifier. It owes its success in many cancer microarray datasets to an effective feature selection that based on relative expression ordering of gene pairs. However, general robustness does not extend some difficult datasets, such as those involving outcome prediction, which may be due the relatively voting scheme by We believe performance can enhanced separating component and combining it with...

Microbes affect each other's growth in multiple, often elusive, ways. The ensuing interdependencies form complex networks, believed to reflect taxonomic composition as well community-level functional properties and dynamics. elucidation of these networks is pursued by measuring pairwise interactions coculture experiments. However, the combinatorial complexity precludes an exhaustive experimental analysis interactions, even for moderately sized microbial communities. Here, we used a machine...

We study Schrödinger semigroups in the scale of Sobolev spaces, and show that, for Kato class potentials, range such L p has exactly two more derivatives than potential; this proves a conjecture B. Simon. that eigenfunctions operators are generically smoother by (in given spaces) their potentials. give applications to relation between potential's smoothness particle kinetic energy context quantum mechanics, characterize energies Coulomb systems. The techniques proof involve Leibniz chain...

Wavelets provide a new class of orthogonal expansions in L2(Rd) with good time/frequency localization and regularity/approximation properties. They have been successfully applied to signal processing, numerical analysis, quantum mechanics. We study pointwise convergence properties wavelet show that such (and more generally, multiscale expansions) Lp functions (1 ≤ p ∞) converge almost everywhere, precisely everywhere on the Lebesgue set function being expanded. is partially insensitive order...

In this note we announce that under general hypotheses, wavelet-type expansions (of functions in <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L Superscript p"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>p</mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding="application/x-tex">{L^p}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, alttext="1...

We still do not know how the brain and its computations are affected by nerve cell deaths their compensatory learning processes, as these develop in neurodegenerative diseases (ND). Compensatory processes ND symptoms usually observed at a point when disease has already large parts of brain. can register such motor and/or mental disorders (dementias) even provide symptomatic relief, though structural effects most cases yet understood. It is very important to obtain early diagnosis, which...

This paper is concerned with the oscillatory behavior of first-order delay differential equations form \begin{eqnarray} x' (t)+p(t)x({\tau }(t))=0, \quad t\geq t_{0}, \end{eqnarray} where $p, {\tau } \in C([t_{0}, \infty ), \mathbb {R}^+), {R}^+=[0, \tau (t)$ non-decreasing, $\tau (t) <t$ for $t \geq t_{0}$ and $\lim _{t{\rightarrow }{\infty }} = \infty$. Let numbers $k$ $L$ be defined by \[ k=\liminf \int _{\tau (t)}^{t}p(s)ds \mbox {and} L=\limsup (t)}^{t}p(s)ds. \] It proved here that...

We report results on a statistical analysis of an infrared spectral dataset comprising total 388 lung biopsies from 374 patients.

We present a coupled variational autoencoder (VAE) method, which improves the accuracy and robustness of model representation handwritten numeral images. The improvement is measured in both increasing likelihood reconstructed images reducing divergence between posterior prior latent distribution. new method weighs outlier samples with higher penalty by generalizing original evidence lower bound function using entropy based on principles nonlinear statistical coupling. evaluated performance...

This paper studies the question of lower bounds on number neurons and examples necessary to program a given task into feedforward neural networks. We introduce notion information complexity network complement that complexity. Neural deals with for resources (numbers neurons) needed by perform within tolerance. Information measures (i.e. examples) about desired input–output function. study interaction two complexities, so building then programming feed-forward nets tasks. show something...

High throughput technologies, including array-based chromatin immunoprecipitation, have rapidly increased our knowledge of transcriptional maps—the identity and location regulatory binding sites within genomes. Still, the full identification sites, even in lower eukaryotes, remains largely incomplete. In this paper we develop a supervised learning approach to site using support vector machines (SVMs) combine 26 different data types. A comparison with standard position specific scoring...

Glioblastoma multiforme (GBM) tends to occur between the ages of 45 and 70. This relatively early onset its poor prognosis make impact GBM on public health far greater than would be suggested by low frequency. Tissue blood samples have now been collected for a number populations, predisposing alleles sought several different genome-wide association (GWA) studies. The Cancer Genome Atlas (TCGA) at NIH has also considerable amount data. Because concordance results obtained using only 14 single...