scholarly journals The weak and the strong equivalence relation and the asymptotic inversion

Filomat ◽  
2011 ◽  
Vol 25 (4) ◽  
pp. 29-36
Author(s):  
Dragan Djurcic ◽  
Ivan Mitrovic ◽  
Mladen Janjic
Keyword(s):  
Equivalence Relation ◽  
Functional Class ◽  
Asymptotic Equivalence ◽  
Measurable Functions ◽  
Functional Classes ◽  
Half Axis ◽  
The Relationship ◽  
Rapidly Varying Functions

In this paper we discuss the relationship between the weak and the strong asymptotic equivalence relation and the asymptotic inversion, for positive and measurable functions defined on a half-axis [a,+?) (a > 0). As the main results, we prove a certain characterizations of the functional class of all rapidly varying functions, as well as some other functional classes.

scholarly journals Aggregation of Indistinguishability Fuzzy Relations Revisited

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1441
Author(s):  
Juan-De-Dios González-Hedström ◽  
Juan-José Miñana ◽  
Oscar Valero
Keyword(s):  
Equivalence Relation ◽  
Fuzzy Relations ◽  
Measure Of Similarity ◽  
Dual Notion ◽  
The Relationship

Indistinguishability fuzzy relations were introduced with the aim of providing a fuzzy notion of equivalence relation. Many works have explored their relation to metrics, since they can be interpreted as a kind of measure of similarity and this is, in fact, a dual notion to dissimilarity. Moreover, the problem of how to construct new indistinguishability fuzzy relations by means of aggregation has been explored in the literature. In this paper, we provide new characterizations of those functions that allow us to merge a collection of indistinguishability fuzzy relations into a new one in terms of triangular triplets and, in addition, we explore the relationship between such functions and those that aggregate extended pseudo-metrics, which are the natural distances associated to indistinguishability fuzzy relations. Our new results extend some already known characterizations which involve only bounded pseudo-metrics. In addition, we provide a completely new description of those indistinguishability fuzzy relations that separate points, and we show that both differ a lot.

scholarly journals The TL region gene 37 encodes a Qa-1 antigen.

1990 ◽  
Vol 172 (6) ◽  
pp. 1795-1804 ◽  
Author(s):  
P R Wolf ◽  
R G Cook
Keyword(s):  
Mhc Class I ◽  
Strain Distribution ◽  
Polyacrylamide Gel Electrophoresis ◽  
Functional Class ◽  
Class I ◽  
Mouse Strains ◽  
Gamma Delta T Cells ◽  
Gamma Delta ◽  
Region Gene ◽  
The Relationship

Of all the biochemically defined mouse MHC class I molecules, the Qa-1 antigens are the only ones for which a gene has not been identified. Recent evidence has suggested that Qa-1 antigens are functional class I molecules and can function as restriction elements for gamma/delta T cells. We have examined the relationship between Qa-1 and the product of gene 37, a presumed novel class I antigen encoded within the TL region. Immunoprecipitation and polyacrylamide gel electrophoresis analysis of the molecules reactive with anti-Qa-1 and anti-37 sera show that the Qa-1 molecule of Qa-1b (Qa-1.2) mouse strains is identical to the product of gene 37 on the basis of molecular weight, pI, and strain distribution. Immunodepletion, biosynthetic labeling, and tunicamycin treatment confirm that the protein encoded by gene 37 in Qa-1b mice is Qa-1.2. In contrast, the anti-37 serum was unable to recognize the Qa-1 molecule in Qa-1a strains. Given the fact that the only allele to gene 37 thus far identified in a Qa-1a strain (A/J) has a termination codon in the alpha 3 domain, our data lead us to conclude that the Qa-1 molecule expressed in Qa-1a mice is not a true allelic product of the gene 37 encoded antigen of Qa-1b mouse strains.

Toward a Generalization of Rough Sets Based on Active and Passive Relations

2006 ◽  
Vol 10 (6) ◽  
pp. 939-945
Author(s):  
Masashi Emoto ◽  
◽  
Rolly Intan ◽  
Masao Mukaidono ◽  
Keyword(s):  
Conditional Probability ◽  
Equivalence Relation ◽  
Rough Sets ◽  
Probability Relation ◽  
Data Elements ◽  
The Relationship

In the generalization of rough sets, many concepts use a relation weaker than the equivalence relation usually used in classical rough sets, e.g., induced by a conditional probability relation. The conditional probability relation is binary and assumes that the relationship between two data (elements or objects) resembles a relationship between two events in conditional probability. We use the asymmetric property of the conditional probability relation to propose active and passive relations, then discuss a generalization and properties of rough sets based on active and passive relations.

scholarly journals Cardinality of sets of closed functional classes in weak 3-valued logics

2013 ◽  
Vol 19 ◽  
pp. 334-343
Author(s):  
Н.Н. Преловский
Keyword(s):  
Functional Class ◽  
Functional Classes

This paper proves that sets of closed functional classes in 3-valued logics of Bochvar $B_3$ and Hallden $H_3$ contains a continuum of different closed classes. It is also proven that both of these logics contain a closed functional class which has no basis.

scholarly journals Genome plasticity, a key factor of evolution in prokaryotes

2018 ◽  
Author(s):  
Itamar Sela ◽  
Yuri I. Wolf ◽  
Eugene V. Koonin
Keyword(s):  
Scaling Laws ◽  
Statistical Tests ◽  
Prokaryotic Genome ◽  
Functional Class ◽  
Gene Gain ◽  
Genome Plasticity ◽  
Microbial Genomes ◽  
Number Of Genes ◽  
Key Factor ◽  
Functional Classes

In prokaryotic genomes, the number of genes that belong to distinct functional classes shows apparent universal scaling with the total number of genes [1–5] (Fig. 1). This scaling can be approximated with a power law, where the scaling power can be sublinear, near-linear or super-linear. Scaling laws are robust under various statistical tests [4], across different databases and for different gene classifications [1–5]. Several models aimed at explaining the observed scaling laws have been proposed, primarily, based on the specifics of the respective biological functions [1, 5–8]. However, a coherent theory to explain the emergence of scaling within the framework of population genetics is lacking. We employ a simple mathematical model for prokaryotic genome evolution [9] which, together with the analysis of 34 clusters of closely related microbial genomes [10], allows us to identify the underlying forces that dictate genome content evolution. In addition to the scaling of the number of genes in different functional classes, we explore gene contents divergence to characterize the evolutionary processes acting upon genomes [11]. We find that evolution of the gene content is dominated by two factors that are specific to a functional class, namely, selection landscape and genome plasticity. Selection landscape quantifies the fitness cost that is associated with deletion of a gene in a given functional class or the advantage of successful incorporation of an additional gene. Genome plasticity, that can be considered a measure of evolvability, reflects both the availability of the genes of a given functional class in the external gene pool that is accessible to the evolving microbial population, and the ability of microbial genomes to accommodate these genes. The selection landscape determines the gene loss rate, and genome plasticity is the principal determinant of the gene gain rate.

scholarly journals Description vs. Interpretation: The Attitudes of Traditional and Current Archaeology Towards the Problem of Impresso-Barbotine in the Early Neolithic

2016 ◽  
Vol 8 (3) ◽  
pp. 657
Author(s):  
Jasna Vuković
Keyword(s):  
Material Culture ◽  
Surface Treatment ◽  
Ceramic Ware ◽  
Future Research ◽  
Early Neolithic ◽  
Historical Method ◽  
Functional Classes ◽  
Chronological Sequence ◽  
Complex Forms ◽  
The Relationship

The problem of the relationship impresso-barbotine has been chosen here, as an excellent example to illustrate the tendencies and shortcomings of the Yugoslav/Serbian archaeology during the major part of the 20th century, as well as the results forming the base for future research and new conclusions. The impresso-barbotine problem has been recognized as one of the important aspects of research into the Early Neolithic as early as in the 1950s, and formed the base for the formation of several relative chronological system. However, although the culture-historical approach is based upon detailed description and stylistic-typological analyses, these phenomena are defined and described in a number of different ways (if at all), causing great confusion. The highly simplified notion about the production and usage of ceramic ware, as well as the negligence for the functional and technological aspects, resulted in the absence of a clear statement if these techniques are in fact a form of decoration or surface treatment. On the other hand, paradoxically, these "elusive" phenomena have been taken as very precise chronological markers. The conclusions are not questionable even today, since the recent research has proven the chronological primacy of impresso over barbotine. Here, however, the shortcomings of the culture- historical method are most obvious: after the establishment of the relative chronological sequence and the identification of a change in the material culture, the reasons that induced the changes are not considered – interpretation is completely absent. However, the current archaeological trends focus upon the processes leading to changes in the material culture, the ones that cannot be explained without considering technology – from forming techniques to modes of usage. Bearing in mind that impresso, and afterwards barbotine appear on the same functional classes of pottery (storage, transportation), it may seem that the same idea motivated both manners of surface treatment – roughening so as to facilitate handling. In order to explain the reasons for the changes it is necessary to consider the forming techniques, with the most reliable indication in the chronological sequence impresso – relief impresso (plastic wheat-grain motif) – barbotine. The production of pottery with uneven surfaces rendered by impressing an instrument (impresso) and applying plastic bands, additionally fastened by impressing sharp instruments (relief impresso), is a time-consuming technique, requiring a lot of attention. It is therefore no wonder that the technique takes over of applying a layer of clay over a semi-dry surface and then arranging it with fingers – barbotine, since it is simpler and requires less work for the same effect. Current archaeological analyses of technology prove that the process of improvement of pottery forming techniques (leading to craft specialization) above all leads to simplification of procedure, in order to increase the number of vessels produced. Thus the typical assumption of traditional archaeology needs to be questioned, that the "development of culture" may be seen through the "evolution" of shapes and modes of decoration (treatment of surface), inevitably leading from simpler to more complex forms.

scholarly journals Prognostic role of metabolic risk factors (hyperhomocysteinemia) in the development of chronic heart failure

2015 ◽  
Vol 18 (1) ◽  
pp. 20
Author(s):  
Ye. N. Berezikova ◽  
M. G. Pustovetova ◽  
S. N. Shilov ◽  
A. V. Yefremov ◽  
A. T. Teplyakov ◽  
...  
Keyword(s):  
Heart Failure ◽  
Chronic Heart Failure ◽  
Blood Serum ◽  
Homocysteine Level ◽  
Functional Class ◽  
Enzyme Linked Immunosorbent Assay ◽  
Control Group ◽  
Relationship Of ◽  
The Relationship

The aim of the study was to assess the relationship of homocysteine levels in the blood serum with the severity and nature of chronic heart failure (CHF) in patients with coronary heart disease. 94 patients with CHF were examined. The control group included 32 patients without cardiovascular disorders. At baseline and after 12 months of observation the homocysteine levels in the blood serum were determined by enzyme-linked immunosorbent assay. Correlative relationship of hyperhomocysteinemia with ischemic myocardial remodeling and with reduced inotropic function in CHF patients was observed. The homocysteine level in the blood serum of CHF patients significantly exceeded that of the control group and moderately increased with the progression of the disease severity of functional class. In the group with an unfavorable course of CHF the baseline homocysteine level proved to have the greatest value as compared to that in the group with a favorable course. In patients with a favorable course of CHF the homocysteinemia level tended to decrease towards the end of prospective study, whereas in patients with an unfavorable course, on the contrary, hyperhomocysteinemia persisted (p<0.01). In case the hyperhomocysteinemia baseline exceeds 18.5 mkmol/L (ROC-AreaSE = 0.860.04, sensitivity 71 %, specificity 90%), the severity and characteristics of the ischemic CHF could be most likely predicted. Thus, hyperhomocysteinemia is related with the severity and nature of CHF. Determining the level of homocysteine in the blood serum can be recommended for early prediction of the severity and nature of CHF.

scholarly journals Spatiospectral brain networks reflective of improvisational experience

2021 ◽  
Author(s):  
Josef Faller ◽  
Andrew Goldman ◽  
Yida Lin ◽  
James R. McIntosh ◽  
Paul Sajda
Keyword(s):  
Large Scale ◽  
Time Window ◽  
Network Connectivity ◽  
Functional Class ◽  
Network Activity ◽  
Oddball Paradigm ◽  
Auditory Oddball ◽  
Scalp Eeg ◽  
Musical Structures ◽  
Functional Classes

AbstractMusical improvisers are trained to categorize certain musical structures into functional classes, which is thought to facilitate improvisation. Using a novel auditory oddball paradigm (Goldman et al., 2020) which enables us to disassociate a deviant (i.e. musical cord inversion) from a consistent functional class, we recorded scalp EEG from a group of musicians who spanned a range of improvisational and classically trained experience. Using a spatiospectral based inter and intra network connectivity analysis, we found that improvisers showed a variety of differences in connectivity within and between large-scale cortical networks compared to classically trained musicians, as a function of deviant type. Inter-network connectivity in the alpha band, for a time window leading up to the behavioural response, was strongly linked to improvisation experience, with the default mode network acting as a hub. Spatiospectral networks post response were substantially different between improvisers and classically trained musicians, with greater inter-network connectivity (specific to the alpha and beta bands) seen in improvisers whereas those with more classical training had largely reduced inter-network activity (mostly in the gamma band). More generally, we interpret our findings in the context of network-level correlates of expectation violation as a function of subject expertise, and we discuss how these may generalize to other and more ecologically valid scenarios.

scholarly journals Asymptotic -Algebras from -Actions on Higher Rank Graphs

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Inhyeop Yi
Keyword(s):  
Dynamical System ◽  
Semidirect Product ◽  
Equivalence Relation ◽  
Asymptotic Equivalence ◽  
Vertex Set ◽  
Higher Rank

For a dynamical system arising from -action on a higher rank graph with finite vertex set, we show that the semidirect product of the asymptotic equivalence relation groupoid is essentially principal if and only if the -graph satisfies the aperiodic condition. Then we show that the corresponding asymptotic Ruelle algebra is simple if the graph is primitive with the aperiodic condition.

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