Notch signalling is critical for the development of the nervous system. In the zebrafish mind-bomb mutants, disruption of E3 ubiquitin ligase activity inhibits Notch signalling. In these utant embryos, precocious development of primary neurons leading to depletion of neural progenitor cells results in a neurogenic phenotype characterized by defects in neural patterning and brain development. Cyclin-dependent kinase 5 (Cdk5), a predominant neuronal kinase, is involved in a variety of essential functions of the nervous system. Most recently, mammalian studies on Notch and Cdk5 regulating each other’s function have been emerging. The status of Cdk5 in the mindbomb mutant embryos with excessive primary neurons is not known. In situ hybridization of the zebrafish mindbomb mutant embryos uncovered a robust upregulation in Cdk5 expression but with a reduced Cdk5 activity. The implications of these findings in both the mammalian system and zebrafish are discussed in this mini-review to provide a glimpse into the relationship between Notch and Cdk5 that may explain certain neurodevelopmental defects associated with either mutations in ubiquitin ligase or altered expression of Cdk5. and Corresponding author: Jyotshna Kanungo
In this note, we point out that Theorem 3.1 as well as Theorem 3.5 in G. D. Çaylı and F. Karaçal (Kybernetika 53 (2017), 394-417) contains a superfluous condition. We have also generalized them by using closure (interior, resp.) operators.
The paper discusses basics of calculus of backward fractional differences and sums. We state their definitions, basic properties and consider a special two-term linear fractional difference equation. We construct a family of functions to obtain its solution.
In this note we study fields $F$ with the property that the simple transcendental extension $F(u)$ of $F$ is isomorphic to some subfield of $F$ but not isomorphic to $F$. Such a field provides one type of solution of the Schröder-Bernstein problem for fields.
We study the stability of average optimal control of general discrete-time Markov processes. Under certain ergodicity and Lipschitz conditions the stability index is bounded by a constant times the Prokhorov distance between distributions of random vectors determinating the "original and the perturbated" control processes.
King and Korf \cite{KingKorf01} introduced, in the framework of a discrete-time dynamic market model on a general probability space, a new concept of arbitrage called \emph{free lunch in the limit} which is slightly weaker than the common free lunch. The definition was motivated by the attempt at proposing the pricing theory based on the theory of conjugate duality in optimization. We show that this concept of arbitrage fails to have a basic property of other common concepts used in pricing theory - it depends on the underlying probability measure more than through its null sets. However, we show that the interesting pricing results obtained by conjugate duality are still valid if it is only assumed that the market admits no free lunch rather than no free lunch in the limit.
A topological duality for monadic n-valued Luk asiewicz algebras introduced by M. Abad (Abad, M.: Estructuras cíclica y monádica de un álgebra de L ukasiewicz nvalente. Notas de Lógica Matemática 36. Instituto de Matemática. Universidad Nacional del Sur, 1988) is determined. When restricted to the category of Q-distributive lattices and Q-homomorphims, it coincides with the duality obtained by R. Cignoli in 1991. A new characterization of congruences by means of certain closed and involutive subsets of the associated space is also obtained. This allowed us to describe subdirectly irreducible algebras in this variety, arriving by a different method at the results established by Abad.
We provide a necessary and sufficient condition under which a generalized ordered topological product (GOTP) of two GO-spaces is monotonically Lindelöf.
The paper gives an overview of feature selection techniques in statistical pattern recognition with particular emphasis on methods developed within the Institute of Information Theory and Automation research team throughout recent years. Besides discussing the advances in methodology since times of Perez's pioneering work the paper attempts to put the methods into a taxonomical framework. The methods discussed include the latest variants of the optimal algorithms, enhanced sub-optimal techniques and the simultaneous semi-parametric probability density function modelling and feature space selection method. Some related issues are illustrated on real data by means of the Feature Selection Toolbox software.