Sequentially continuous non-linear fundamental systems of solutions of affine equations in locally convex spaces

According to the Mickael's selection theorem any surjective continuous linear operator from one Fr\'echet space onto another has a continuous (not necessarily linear) right inverse. Using this theorem Herzog and Lemmert proved that if $E$ is a Fr\'echet space and $T:E\to E$ is a continuous linear operator such that the Cauchy problem $\dot x=Tx$, $x(0)=x_0$ is solvable in $[0,1]$ for any $x_0\in E$, then for any $f\in C([0,1],E)$, there exists a continuos map $S:[0,1]\times E\to E$, $(t,x)\mapsto S_tx$ such that for any $x_0\in E$, the function $x(t)=S_tx_0$ is a solution of the Cauchy problem $\dot x(t)=Tx(t)+f(t)$, $x(0)=x_0$ (they call $S$ a fundamental system of solutions of the equation $\dot x=Tx+f$). We prove the same theorem, replacing "continuous" by "sequentially continuous" for locally convex spaces from a class which contains strict inductive limits of Fr\'echet spaces and strong duals of Fr\'echet--Schwarz spaces and is closed with respect to finite products and sequentially closed subspaces. The key-point of the proof is an extension of the theorem on existence of a sequentially continuous right inverse of any surjective sequentially continuous linear operator to some class of non-metrizable locally convex spaces.

On effective linearly ordered sets of comparison functions

Both the existence and the non-existence of a linearly ordered (by certain natural order relations) effective set of comparison functions (=dense comparison classes) are compatible with the ZFC axioms of set theory.

Analysis of the effect of finite d.c. blocking capacitance and finite d.c. feed inductance on the performance of inverse class-E amplifiers

The first analysis and synthesis equations for the newly introduced inverse Class-E amplifier when operated with a finite d.c. blocking capacitance and a finite d.c.-feed inductance are presented in the paper. Closed-form design equations are derived in order to establish the circuit component values required for optimum synthesis. Excellent agreement between numerical simulation results and theoretical prediction is obtained. It is shown that drain efficiency approaching 100 at a pre-specified output power level can be achieved as zero-current switching and zero-current derivative conditions are simultaneously satisfied. The proposed analysis offers the prospect for realistic MMIC implementation.

Support vector machine classification for large data sets via minimum enclosing ball clustering

Support vector machine (SVM) is a powerful technique for data classification. Despite of its good theoretic foundations and high classification accuracy, normal SVM is not suitable for classification of large data sets, because the training complexity of SVM is highly dependent on the size of data set. This paper presents a novel SVM classification approach for large data sets by using minimum enclosing ball clustering. After the training data are partitioned by the proposed clustering method, the centers of the clusters are used for the first time SVM classification. Then we use the clusters whose centers are support vectors or those clusters which have different classes to perform the second time SVM classification. In this stage most data are removed. Several experimental results show that the approach proposed in this paper has good classification accuracy compared with classic SVM while the training is significantly faster than several other SVM classifiers.

Reduced-size polarized basis sets for calculations of molecular electric properties. III. Second-row atoms

Reduced-size polarized (ZmPolX) basis sets are developed for the second-row atoms X = Si, P, S, and Cl. The generation of these basis sets follows from a simple physical model of the polarization effect of the external electric field which leads to highly compact polarization functions to be added to the chosen initial basis set. The performance of the ZmPolX sets has been investigated in calculations of molecular dipole moments and polarizabilities. Only a small deterioration of the quality of the calculated molecular electric properties has been found. Simultaneously the size of the present reduced-size ZmPolX basis sets is about one-third smaller than that of the usual polarized (PolX) sets. This reduction considerably widens the range of applications of the ZmPolX sets in calculations of molecular dipole moments, dipole polarizabilities, and related properties.

Self-affine crossover length in a layered silicate deposit

Self-affine dehydrated colloidal deposits on fresh mica surfaces of the synthetic layered silicate 2:1 smectite clay laponite have been studied by means of atomic force microscopy (AFM). AFM images of these prepared assemblies of sol and gel aggregates have been analyzed both by means of standard AFM Fourier software and a wavelet method. The deposited surfaces show a persistence to antipersistent crossover with a clay concentration dependent crossover length. It is concluded that the crossover length is associated with aggregate size, and further that the persistent roughness at small length scales signals near compact clusters of fractal dimension three, whereas the antipersistent roughness at large length scales signals a sedimentation process.

Prediction of Fresh and Hardened Properties of Self-Consolidating Concrete Using Neurofuzzy Approach

Self-consolidating concrete (SCC) developed in Japan in the late 80s has enabled the construction industry to reduce demand on the resources, improve the work conditions and also reduce the impact on the environment by elimination of the need for compaction. This investigation aimed at exploring the potential use of the neurofuzzy (NF) approach to model the fresh and hardened properties of SCC containing pulverised fuel ash (PFA) as based on experimental data investigated in this paper. Twenty six mixes were made with water-to-binder ratio ranging from 0.38 to 0.72, cement content ranging from 183 to 317 kg/m3 , dosage of PFA ranging from 29 to 261 kg/m3 , and percentage of superplasticizer, by mass of powder, ranging from 0 to 1%. Nine properties of SCC mixes modeled by NF were the slump flow, JRing combined to the Orimet, JRing combined to cone, V-funnel, L-box blocking ratio, segregation ratio, and the compressive strength at 7, 28, and 90 days. These properties characterized the filling ability, the passing ability, the segregation resistance of fresh SCC, and the compressive strength. NF model is constructed by training and testing data using the experimental results obtained in this study. The results of NF models were compared with experimental results and were found to be quite accurate. The proposed NF models offers useful modeling approach of the fresh and hardened properties of SCC containing PFA.

Confounds in pictorial sets: The role of complexity and familiarity in basic-level picture processing

Complexity is conventionally defined as the level of detail or intricacy contained within a picture. The study of complexity has received relatively little attention-in part, because of the absence of an acceptable metric. Traditionally, normative ratings of complexity have been based on human judgments. However, this study demonstrates that published norms for visual complexity are biased. Familiarity and learning influence the subjective complexity scores for nonsense shapes, with a significant training x familiarity interaction [F(1,52) = 17.53, p <.05]. Several image-processing techniques were explored as alternative measures of picture and image complexity. A perimeter detection measure correlates strongly with human judgments of the complexity of line drawings of real-world objects and nonsense shapes and captures some of the processes important in judgments of subjective complexity, while removing the bias due to familiarity effects.

USP17 Regulates Ras Activation and Cell Proliferation by Blocking RCE1 Activity

The proto-oncogene Ras undergoes a series of post-translational modifications at its carboxyl-terminal CAAX motif that are essential for its proper membrane localization and function. One step in this process is the cleavage of the CAAX motif by the enzyme Ras-converting enzyme 1 (RCE1). Here we show that the deubiquitinating enzyme USP17 negatively regulates the activity of RCE1. We demonstrate that USP17 expression blocks Ras membrane localization and activation, thereby inhibiting phosphorylation of the downstream kinases MEK and ERK. Furthermore, we show that this effect is caused by the loss of RCE1 catalytic activity as a result of its deubiquitination by USP17. We also show that USP17 and RCE1 co-localize at the endoplasmic reticulum and that USP17 cannot block proliferation or Ras membrane localization in RCE1 null cells. These studies demonstrate that USP17 modulates Ras processing and activation, at least in part, by regulating RCE1 activity.

Unite and conquer: univariate and multivariate approaches for finding differentially expressed gene sets

Motivation: Recently, many univariate and several multivariate approaches have been suggested for testing differential expression of gene sets between different phenotypes. However, despite a wealth of literature studying their performance on simulated and real biological data, still there is a need to quantify their relative performance when they are testing different null hypotheses.

Results: In this article, we compare the performance of univariate and multivariate tests on both simulated and biological data. In the simulation study we demonstrate that high correlations equally affect the power of both, univariate as well as multivariate tests. In addition, for most of them the power is similarly affected by the dimensionality of the gene set and by the percentage of genes in the set, for which expression is changing between two phenotypes. The application of different test statistics to biological data reveals that three statistics (sum of squared t-tests, Hotelling's T2, N-statistic), testing different null hypotheses, find some common but also some complementing differentially expressed gene sets under specific settings. This demonstrates that due to complementing null hypotheses each test projects on different aspects of the data and for the analysis of biological data it is beneficial to use all three tests simultaneously instead of focusing exclusively on just one.

A general framework for measuring inconsistency through minimal inconsistent sets

Hunter and Konieczny explored the relationships between measures of inconsistency for a belief base and the minimal inconsistent subsets of that belief base in several of their papers. In particular, an inconsistency value termed MIVC, defined from minimal inconsistent subsets, can be considered as a Shapley Inconsistency Value. Moreover, it can be axiomatized completely in terms of five simple axioms. MinInc, one of the five axioms, states that each minimal inconsistent set has the same amount of conflict. However, it conflicts with the intuition illustrated by the lottery paradox, which states that as the size of a minimal inconsistent belief base increases, the degree of inconsistency of that belief base becomes smaller. To address this, we present two kinds of revised inconsistency measures for a belief base from its minimal inconsistent subsets. Each of these measures considers the size of each minimal inconsistent subset as well as the number of minimal inconsistent subsets of a belief base. More specifically, we first present a vectorial measure to capture the inconsistency for a belief base, which is more discriminative than MIVC. Then we present a family of weighted inconsistency measures based on the vectorial inconsistency measure, which allow us to capture the inconsistency for a belief base in terms of a single numerical value as usual. We also show that each of the two kinds of revised inconsistency measures can be considered as a particular Shapley Inconsistency Value, and can be axiomatically characterized by the corresponding revised axioms presented in this paper.

On the derived category of a regular toric scheme

Let X be a quasi-compact scheme, equipped with an open covering by affine schemes U s = Spec A s . A quasi-coherent sheaf on X gives rise, by taking sections over the U s , to a diagram of modules over the coordinate rings A s , indexed by the intersection poset S of the covering. If X is a regular toric scheme over an arbitrary commutative ring, we prove that the unbounded derived category of quasi-coherent sheaves on X can be obtained from a category of Sop-diagrams of chain complexes of modules by inverting maps which induce homology isomorphisms on hyper-derived inverse limits. Moreover, we show that there is a finite set of weak generators, one for each cone in the fan S. The approach taken uses the machinery of Bousfield–Hirschhorn colocalisation of model categories. The first step is to characterise colocal objects; these turn out to be homotopy sheaves in the sense that chain complexes over different open sets U s agree on intersections up to quasi-isomorphism. In a second step it is shown that the homotopy category of homotopy sheaves is equivalent to the derived category of X.