Embedding theorems of funcitional classes, III

In this paper we obtain the necessary and sufficient conditions for embedding results of different function classes. The main result is a criterion for embedding theorems for the so-called generalized Weyl-Nikol'skii class and the generalized Lipschitz class. To define the Weyl-Nikol'skii class, we use the concept of a (λ,β)-derivative, which is a generalization of the derivative in the sense of Weyl. As corollaries, we give estimates of norms and moduli of smoothness of transformed Fourier series.

Embedding theorems of function classes, IV

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Embedding theorems of function classes, II

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Contractive metrics for a Boltzmann equation for granular gases: diffusive equilibriaThe Patterson-Sullivan embedding and minimal volume entropy for outer space

We quantify the long-time behavior of a system of (partially) inelastic particles in a stochastic thermostat by means of the contractivity of a suitable metric in the set of probability measures. Existence, uniqueness, boundedness of moments and regularity of a steady state are derived from this basic property. The solutions of the kinetic model are proved to converge exponentially as t→ ∞ to this diffusive equilibrium in this distance metrizing the weak convergence of measures. Then, we prove a uniform bound in time on Sobolev norms of the solution, provided the initial data has a finite norm in the corresponding Sobolev space. These results are then combined, using interpolation inequalities, to obtain exponential convergence to the diffusive equilibrium in the strong L¹-norm, as well as various Sobolev norms.

The Patterson-Sullivan embedding and minimal volume entropy for outer space

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Embedding theorems of function classes, I

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“Unmixing” Tissue Gene Expression Signatures from Tumor Biopsies

Emergent molecular measurement methods, such as DNA microarray, qRTPCR, andmany others, offer tremendous promise for the personalized treatment of cancer. Thesetechnologies measure the amount of specific proteins, RNA, DNA or other moleculartargets from tumor specimens with the goal of “fingerprinting” individual cancers. Tumorspecimens are heterogeneous; an individual specimen typically contains unknownamounts of multiple tissues types. Thus, the measured molecular concentrations resultfrom an unknown mixture of tissue types, and must be normalized to account for thecomposition of the mixture.For example, a breast tumor biopsy may contain normal, dysplastic and cancerousepithelial cells, as well as stromal components (fatty and connective tissue) and bloodand lymphatic vessels. Our diagnostic interest focuses solely on the dysplastic andcancerous epithelial cells. The remaining tissue components serve to “contaminate”the signal of interest. The proportion of each of the tissue components changes asa function of patient characteristics (e.g., age), and varies spatially across the tumorregion. Because each of the tissue components produces a different molecular signature,and the amount of each tissue type is specimen dependent, we must estimate the tissuecomposition of the specimen, and adjust the molecular signal for this composition.Using the idea of a chemical mass balance, we consider the total measured concentrationsto be a weighted sum of the individual tissue signatures, where weightsare determined by the relative amounts of the different tissue types. We develop acompositional source apportionment model to estimate the relative amounts of tissuecomponents in a tumor specimen. We then use these estimates to infer the tissuespecificconcentrations of key molecular targets for sub-typing individual tumors. Weanticipate these specific measurements will greatly improve our ability to discriminatebetween different classes of tumors, and allow more precise matching of each patient tothe appropriate treatment

Embedding Emotional Context in Recommender Systems

Emotions are crucial for user's decision making in recommendation processes. We first introduce ambient recommender systems, which arise from the analysis of new trends on the exploitation of the emotional context in the next generation of recommender systems. We then explain some results of these new trends in real-world applications through the smart prediction assistant (SPA) platform in an intelligent learning guide with more than three million users. While most approaches to recommending have focused on algorithm performance. SPA makes recommendations to users on the basis of emotional information acquired in an incremental way. This article provides a cross-disciplinary perspective to achieve this goal in such recommender systems through a SPA platform. The methodology applied in SPA is the result of a bunch of technology transfer projects for large real-world rccommender systems

A Novel Breast Tissue Density Classification Methodology

It has been shown that the accuracy of mammographic abnormality detection methods is strongly dependent on the breast tissue characteristics, where a dense breast drastically reduces detection sensitivity. In addition, breast tissue density is widely accepted to be an important risk indicator for the development of breast cancer. Here, we describe the development of an automatic breast tissue classification methodology, which can be summarized in a number of distinct steps: 1) the segmentation of the breast area into fatty versus dense mammographic tissue; 2) the extraction of morphological and texture features from the segmented breast areas; and 3) the use of a Bayesian combination of a number of classifiers. The evaluation, based on a large number of cases from two different mammographic data sets, shows a strong correlation ( and 0.67 for the two data sets) between automatic and expert-based Breast Imaging Reporting and Data System mammographic density assessment

Embedding objects into Matlab/Simulink for process supervision

This paper introduces how artificial intelligence technologies can be integrated into a known computer aided control system design (CACSD) framework, Matlab/Simulink, using an object oriented approach. The aim is to build a framework to aid supervisory systems analysis, design and implementation. The idea is to take advantage of an existing CACSD framework, Matlab/Simulink, so that engineers can proceed: first to design a control system, and then to design a straightforward supervisory system of the control system in the same framework. Thus, expert systems and qualitative reasoning tools are incorporated into this popular CACSD framework to develop a computer aided supervisory system design (CASSD) framework. Object-variables an introduced into Matlab/Simulink for sharing information between tools

Galois representations, embedding problems and modular forms

To an odd irreducible 2-dimensional complex linear representation of the absolute Galois group of the field Q of rational numbers, a modular form of weight 1 is associated (modulo Artin's conjecture on the L-series of the representation in the icosahedral case). In addition, linear liftings of 2-dimensional projective Galois representations are related to solutions of certain Galois embedding problems. In this paper we present some recent results on the existence of liftings of projective representations and on the explicit resolution of embedding problems associated to orthogonal Galois representations, and explain how these results can be used to construct modular forms.

p38/MKP-1-regulated AKT coordinates macrophage transitions and resolution of inflammation during tissue repair

Repair of damaged tissue requires the coordinated action of inflammatory and tissue-specific cells to restore homeostasis, but the underlying regulatory mechanisms are poorly understood. In this paper, we report new roles for MKP-1 (mitogen-activated protein kinase [MAPK] phosphatase-1) in controlling macrophage phenotypic transitions necessary for appropriate muscle stem cell¿dependent tissue repair. By restricting p38 MAPK activation, MKP-1 allows the early pro- to antiinflammatory macrophage transition and the later progression into a macrophage exhaustion-like state characterized by cytokine silencing, thereby permitting resolution of inflammation as tissue fully recovers. p38 hyperactivation in macrophages lacking MKP-1 induced the expression of microRNA-21 (miR-21), which in turn reduced PTEN (phosphatase and tensin homologue) levels, thereby extending AKT activation. In the absence of MKP-1, p38-induced AKT activity anticipated the acquisition of the antiinflammatory gene program and final cytokine silencing in macrophages, resulting in impaired tissue healing. Such defects were reversed by temporally controlled p38 inhibition. Conversely, miR-21¿AKT interference altered homeostasis during tissue repair. This novel regulatory mechanism involving the appropriate balance of p38, MKP-1, miR-21, and AKT activities may have implications in chronic inflammatory degenerative diseases.

Tumor necrosis factor-alpha mediates changes in tissue protein turnover in a rat cancer cachexia model.

Rats bearing the Yoshida AH-130 ascites hepatoma showed enhanced fractional rates of protein degradation in gastrocnemius muscle, heart, and liver, while fractional synthesis rates were similar to those in non-tumor bearing rats. This hypercatabolic pattern was associated with marked perturbations of the hormonal homeostasis and presence of tumor necrosis factor in the circulation. The daily administration of a goat anti-murine TNF IgG to tumor-bearing rats decreased protein degradation rates in skeletal muscle, heart, and liver as compared with tumor-bearing rats receiving a nonimmune goat IgG. The anti-TNF treatment was also effective in attenuating early perturbations in insulin and corticosterone homeostasis. Although these results suggest that tumor necrosis factor plays a significant role in mediating the changes in protein turnover and hormone levels elicited by tumor growth, the inability of such treatment to prevent a reduction in body weight implies that other mediators or tumor-related events were also involved.