Finite dimensional irreducible representations and the uniqueness of the Lebesgue decomposition of positive functionals

We prove for an arbitrary complex $^*$-algebra $A$ that every topologically irreducible $^*$-representation of $A$ on a Hilbert space is finite dimensional precisely when the Lebesgue decomposition of representable positive functionals over $A$ is unique. In particular, the uniqueness of the Lebesgue decomposition of positive functionals over the $L^1$-algebras of locally compact groups provides a new characterization of Moore groups.Comment: To appear in: Journal of Operator Theor

Reducing Consumption Of Food With High Level Of Fat, Sugar And/Or Salt Among Young Generation

The young generation is the most influenced and vulnerable segment of the market. Food with high level of fat, sugar and/or salt are popularised for this segment. At the same time nearly 7 people die of obesity or from complications of obesity in Hungary each hour – one every 9 minutes. Less than 10% of youth are of the belief of eating healthy and more then one third of youth don’t take care about healthy eating. The young generation can be especially influenced by use of well-known persons, prize games and free gifts. The idea of fat tax’s introduction could be an obvious proposal

Designing Homes for Function and Safety

4 pp., 3 illustrationsThe principle of universal design is that homes should be as usable as possible by people of all ages and physical ablities. This might be accomplished by widening doors, making floor levels flush, placing electrical outlets within reach of a person in a wheelchair, or installing handrails on both sides of stairs. These and many other tips are included in this publication

Self-Adaptive, Dynamic, Integrated Statistical and Information Theory Learning

The paper analyses and serves with a positioning of various error measures applied in neural network training and identifies that there is no best of measure, although there is a set of measures with changing superiorities in different learning situations. An outstanding, remarkable measure called $E_{Exp}$ published by Silva and his research partners represents a research direction to combine more measures successfully with fixed importance weighting during learning. The main idea of the paper is to go far beyond and to integrate this relative importance into the neural network training algorithm(s) realized through a novel error measure called $E_{ExpAbs}$. This approach is included into the Levenberg-Marquardt training algorithm, so, a novel version of it is also introduced, resulting a self-adaptive, dynamic learning algorithm. This dynamism does not has positive effects on the resulted model accuracy only, but also on the training process itself. The described comprehensive algorithm tests proved that the proposed, novel algorithm integrates dynamically the two big worlds of statistics and information theory that is the key novelty of the paper.Comment: 62 pages, 30 figures, original articl

Characterization of the Dynamic Transcriptome of a Herpesvirus with Long-read Single Molecule Real-Time Sequencing

Herpesvirus gene expression is co-ordinately regulated and sequentially ordered during productive infection. The viral genes can be classified into three distinct kinetic groups: immediate-early, early, and late classes. In this study, a massively parallel sequencing technique that is based on PacBio Single Molecule Real-time sequencing platform, was used for quantifying the poly(A) fraction of the lytic transcriptome of pseudorabies virus (PRV) throughout a 12- hour interval of productive infection on PK-15 cells. Other approaches, including microarray, real-time RT-PCR and Illumina sequencing are capable of detecting only the aggregate transcriptional activity of particular genomic regions, but not individual herpesvirus transcripts. However, SMRT sequencing allows for a distinction between transcript isoforms, including length- and splice variants, as well as between overlapping polycistronic RNA molecules. The non-amplified Isoform Sequencing (Iso-Seq) method was used to analyse the kinetic properties of the lytic PRV transcripts and to then classify them accordingly. Additionally, the present study demonstrates the general utility of long-read sequencing for the time-course analysis of global gene expression in practically any organism