Factorizing τ-spectra of mappings

AbstractIn this paper by a spectrum of mappings we mean a morphism of spectra of spaces. However, using the notion of a mapping of mappings, we give the definition of a spectrum of mappings similar to that of a spectrum of spaces. In this case, the formulations of the given results are also similar to the formulations of the corresponding results concerning the spectra of spaces.For the spectra of mappings we define the notion of a τ-spectrum of mappings factorizing in a special sense and prove a version of the Spectral Theorem for such spectra. Furthermore, to a given indexed collection F of mapping we associate a τ-spectrum factorizing in the above special sense whose mappings are Containing Mappings for F constructed in Iliadis (2005) [4]. These associated τ-spectra and the corresponding version of the Spectral Theorem imply that for a given indexed collection F of mappings any so-called “natural” τ-spectrum for F factorizing in the special sense contains a cofinal and τ-closed subspectrum whose mappings are Containing Mapping for F. Thus, Containing Mappigs for F appear here without any concrete construction. The associated τ-spectra are used also in order to define and characterize the so-called second-type saturated classes of mappings (which are “saturated” by universal elements)

Some properties of the containing spaces and saturated classes of spaces

[EN] Subjects of this paper are: (a) containing spaces constructed in [2] for an indexed collection S of subsets, (b) classes consisting of ordered pairs (Q,X), where Q is a subset of a space X, which are called classes of subsets, and (c) the notion of universality in such classes. We show that if T is a containing space constructed for an indexed collection S of spaces and for every X ϵ S, QX is a subset of X, then the corresponding containing space TIQ constructed for the indexed collection Q ={QX : X ϵ S} of spaces, under a simple condition, can be considered as a specific subset of T. We prove some “commutative” properties of these specific subsets. For classes of subsets we introduce the notion of a (properly) universal element and define the notion of a (complete) saturated class of subsets. Such a class is “saturated” by (properly) universal elements. We prove that the intersection of (complete) saturated classes of subsets is also a (complete) saturated class. We consider the following classes of subsets: (a) IP(Cl), (b) IP(Op), and (c) IP(n.dense) consisting of all pairs (Q;X) such that: (a) Q is a closed subset of X, (b) Q is an open subset of X, and (c) Q is a never dense subset of X, respectively. We prove that the classes IP(Cl) and IP(Op) are complete saturated and the class IP(n.dense) is saturated. Saturated classes of subsets are convenient to use for the construction of new saturated classes by the given ones.Iliadis, S. (2003). Some properties of the containing spaces and saturated classes of spaces. Applied General Topology. 4(2):487-507. doi:10.4995/agt.2003.2047.SWORD48750742R. Engelking, W. Holsztynski and R. Sikorski, Some examples of Borel sets, Colloq. Math. 15 (1966), 271-274.Iliadis, S. (2000). A construction of containing spaces. Topology and its Applications, 107(1-2), 97-116. doi:10.1016/s0166-8641(00)90095-6R. Sikorski, Some examples of Borel sets, Colloq. Math. 5 (1958), 170-171

Predicting Wood Thermal Conductivity Using Artificial Neural Networks

An artificial neural network model that estimates wood thermal conductivity under a wide range of conditions of moisture content, temperature and apparent density was developed and tested with literature-obtained experimental data. The optimal network was determined to consist of an input layer, three hidden layers, and one output layer following the feed forward network structure and more specifically the back-propagation algorithm. Each of the three hidden layers of the ANN consisted of eleven neurons. The Neuralworks software package was used for the determination of the network structure and architecture, and for the training and testing phase. The evaluation produced an R2 value equal to 0.9994 and a RMS Error equal to 0.0123, thus proving that the developed ANN model is a reliable approach with powerful predictive capacity towards the estimation of thermal conductivity and it can be used by researchers under a wide range of conditions

Does combined training of biofeedback and neurofeedback affect smoking status, behavior, and longitudinal brain plasticity?

Introduction: Investigations of biofeedback (BF) and neurofeedback (NF) training for nicotine addiction have been long documented to lead to positive gains in smoking status, behavior and to changes in brain activity. We aimed to: (a) evaluate a multi-visit combined BF/NF intervention as an alternative smoking cessation approach, (b) validate training-induced feedback learning, and (c) document effects on resting-state functional connectivity networks (rsFCN); considering gender and degree of nicotine dependence in a longitudinal design.Methods: We analyzed clinical, behavioral, and electrophysiological data from 17 smokers who completed five BF and 20 NF sessions and three evaluation stages. Possible neuroplastic effects were explored comparing whole-brain rsFCN by phase-lag index (PLI) for different brain rhythms. PLI connections with significant change across time were investigated according to different resting-state networks (RSNs).Results: Improvements in smoking status were observed as exhaled carbon monoxide levels, Total Oxidative Stress, and Fageström scores decreased while Vitamin E levels increased across time. BF/NF promoted gains in anxiety, self-esteem, and several aspects of cognitive performance. BF learning in temperature enhancement was observed within sessions. NF learning in theta/alpha ratio increase was achieved across baselines and within sessions. PLI network connections significantly changed across time mainly between or within visual, default mode and frontoparietal networks in theta and alpha rhythms, while beta band RSNs mostly changed significantly after BF sessions.Discussion: Combined BF/NF training positively affects the clinical and behavioral status of smokers, displays benefit in smoking harm reduction, plays a neuroprotective role, leads to learning effects and to positive reorganization of RSNs across time.Clinical Trial Registration:https://clinicaltrials.gov/ct2/show/NCT02991781

Search for dark matter produced in association with bottom or top quarks in √s = 13 TeV pp collisions with the ATLAS detector

A search for weakly interacting massive particle dark matter produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and miss- ing transverse momentum are considered. The analysis uses 36.1 fb−1 of proton–proton collision data recorded by the ATLAS experiment at √s = 13 TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are in- terpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour- neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50 GeV are excluded assuming a dark-matter candidate mass of 1 GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross- section of 300 times the predicted rate for mediators with masses between 10 and 50 GeV and assuming a dark-matter mass of 1 GeV and unitary coupling. Constraints on colour- charged scalar simplified models are also presented. Assuming a dark-matter particle mass of 35 GeV, mediator particles with mass below 1.1 TeV are excluded for couplings yielding a dark-matter relic density consistent with measurements