On $ n $-tuplewise IP-sensitivity and thick sensitivity

<p style='text-indent:20px;'>Let <inline-formula><tex-math id="M2">\begin{document}$ (X,T) $\end{document}</tex-math></inline-formula> be a topological dynamical system and <inline-formula><tex-math id="M3">\begin{document}$ n\geq 2 $\end{document}</tex-math></inline-formula>. We say that <inline-formula><tex-math id="M4">\begin{document}$ (X,T) $\end{document}</tex-math></inline-formula> is <inline-formula><tex-math id="M5">\begin{document}$ n $\end{document}</tex-math></inline-formula>-tuplewise IP-sensitive (resp. <inline-formula><tex-math id="M6">\begin{document}$ n $\end{document}</tex-math></inline-formula>-tuplewise thickly sensitive) if there exists a constant <inline-formula><tex-math id="M7">\begin{document}$ \delta&gt;0 $\end{document}</tex-math></inline-formula> with the property that for each non-empty open subset <inline-formula><tex-math id="M8">\begin{document}$ U $\end{document}</tex-math></inline-formula> of <inline-formula><tex-math id="M9">\begin{document}$ X $\end{document}</tex-math></inline-formula>, there exist <inline-formula><tex-math id="M10">\begin{document}$ x_1,x_2,\dotsc,x_n\in U $\end{document}</tex-math></inline-formula> such that</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \Bigl\{k\in \mathbb{N}\colon \min\limits_{1\le i&lt;j\le n}d(T^k x_i,T^k x_j)&gt;\delta\Bigr\} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>is an IP-set (resp. a thick set).</p><p style='text-indent:20px;'>We obtain several sufficient and necessary conditions of a dynamical system to be <inline-formula><tex-math id="M11">\begin{document}$ n $\end{document}</tex-math></inline-formula>-tuplewise IP-sensitive or <inline-formula><tex-math id="M12">\begin{document}$ n $\end{document}</tex-math></inline-formula>-tuplewise thickly sensitive and show that any non-trivial weakly mixing system is <inline-formula><tex-math id="M13">\begin{document}$ n $\end{document}</tex-math></inline-formula>-tuplewise IP-sensitive for all <inline-formula><tex-math id="M14">\begin{document}$ n\geq 2 $\end{document}</tex-math></inline-formula>, while it is <inline-formula><tex-math id="M15">\begin{document}$ n $\end{document}</tex-math></inline-formula>-tuplewise thickly sensitive if and only if it has at least <inline-formula><tex-math id="M16">\begin{document}$ n $\end{document}</tex-math></inline-formula> minimal points. We characterize two kinds of sensitivity by considering some kind of factor maps. We introduce the opposite side of pairwise IP-sensitivity and pairwise thick sensitivity, named (almost) pairwise IP<inline-formula><tex-math id="M17">\begin{document}$ ^* $\end{document}</tex-math></inline-formula>-equicontinuity and (almost) pairwise syndetic equicontinuity, and obtain dichotomies results for them. In particular, we show that a minimal system is distal if and only if it is pairwise IP<inline-formula><tex-math id="M18">\begin{document}$ ^* $\end{document}</tex-math></inline-formula>-equicontinuous. We show that every minimal system admits a maximal almost pairwise IP<inline-formula><tex-math id="M19">\begin{document}$ ^* $\end{document}</tex-math></inline-formula>-equicontinuous factor and admits a maximal pairwise syndetic equicontinuous factor, and characterize them by the factor maps to their maximal distal factors.</p>

The activity of enzymes can be modified by homeopathic dilutions of their effectors

Introduction: The fungal and bacterial materials are very useful for testing the influence of low and very low doses of low molecular phenolic effectors on enzymatic system of phenoloxidases when they are incubated together in the reaction space. Aim: Searching for the model useful biological systems to study the action of diluted low molecular substances on living organisms, which is based on common physical and biochemical analytical procedures. Methods: The fungal and actinomycetal bacterial materials from laboratory cultures as a source of common phenoloxidases, laccase, peroxidase and O-demethylase as well as the pure plant peroxidase were used in experiments described earlier [1-5]. Subsequent dilutions of low molecular phenolic metabolites, appropriate for studied enzymatic systems, prepared in 75% ethanol in the proportion of 1:100 (centesimal) and dynamized by shaking in accordance with homeopathic procedures were prepared in our laboratory. During experiments with bacterial and fungal materials and a pure plant peroxidase, which were incubated together with subsequent dilutions of proper phenolic effector, different analytic methods were used including a gel (PAGE) [4] and capillary (MEKCE) electrophoresis [5], spectral and colorimetric methods [1,2,3] as well as the electron microscopy [5]. Results: In the light of presented data [1-5], the incubation of biological material with diluted phenolic effectors induces various effects on tested enzyme activity. It changed in sinusoidal manner with an gradual growth of dilution rate of tested effectors, which was distinctly visible on the diagram when the number of dilutions was localized on abscissa and biological activity on the ordinate. Exemplary results of the chosen experiments will be presented. For tested enzymes: laccase, peroxidase and O-demethylase, the distance between maximal points of enzymatic activity, shown on a sine curve, repeats more often every 10 subsequent centesimal dilutions. Along with the extension of incubation period the displacement of maximal and minimal points on curve were noticed, which revealed a dynamic aspect of studied phenomenon. Conclusions: Fungal and bacterial cells seem to be a very convenient material for studying the action of diluted metabolites on enzymatic systems because their popular presence in environment. Results of all experiments confirmed the same nature of the mentioned observations. Because other authors had similar conclusion concerning human [6,7] and plant materials [8,9], the described relations seem to be common in natural world. It could also be stressed that the therapeutic effect of homeopathic remedies could be based on the mechanism described above and it is highly probable that it leads to a normalisation of disturbed enzyme systems in the living organisms.

When in parliamentary debate there is no debate

On the 1st October 2017 an independence referendum was organised in Catalonia. The aim of this paper is to analyse the nature of the political debate going on in the Catalan Parliament during the whole process by focusing on the kind of argumentation strategies that were used by each of the leanings to legitimise their political decisions. We do that relying on a methodological distinction that differentiates between sound argumentation and fallacious argumentation. By using a Critical Discourse Analysis approach, this study offers a wide picture of the kind of argumentation used by the main political actors involved in the process of decision making in Catalonia. The results show that there is more emphasis in antagonising with the others, than engaging in sound argument exchange that could facilitate minimal points of consensus. Such results may help explain why the Catalan conflict is still unsolved at the political level.

Degree requirements of physiology undergraduate programs in the Physiology Majors Interest Group

Physiology undergraduate degree programs operate in isolation relative to other biological science programs, with little to no understanding of how other institutions structure their course requirements and other degree requirements. The purpose of this report is to preliminarily describe the collective curriculum of physiology programs represented at the Physiology Majors Interest Group (P-MIG) annual meetings from 2018 to 2019. A short preconference survey was sent to attendees that inquired about degree requirements of their respective physiology programs. The requirement for Physiology I (69.2%) with laboratory (66.7%) and Anatomy I (57.1%) with laboratory (42.9%), or combined Anatomy and Physiology I (16.7%) and laboratory (18.2%), were common requirements, but many programs did not require Physiology II (27.3%) or Anatomy II (11.1%). There was nearly consensus on required prerequisites such as Biology (2 semesters with laboratories, 85.7%), Chemistry (2 semesters with laboratory, 88.9%), Physics (2 semesters with laboratory, 75%), Calculus I (61.1%), and Statistics (Biostatistics 42.9%; General Statistics 13.3%). There was less agreement among programs in regards to Calculus II (20.0%), Organic Chemistry (2 semesters, 55.6%), and Biochemistry I (47%), which may be reflective of individual department focus. There was considerable heterogeneity among physiology program course requirements for disciplinary core courses and upper division electives. This report is meant to generate discussion on physiology program curricula in efforts to improve physiology education for majors and assist P-MIG in determining minimal points of consensus as they write the first set of national curricular guidelines for degree programs.

Null systems in the non-minimal case

In this paper, it is shown that if a dynamical system is null and distal, then it is equicontinuous. It turns out that a null system with closed proximal relation is mean equicontinuous. As a direct application, it follows that a null dynamical system with dense minimal points is also mean equicontinuous. Meanwhile, a distal system with trivial $\text{Ind}_{\text{fip}}$-pairs and a non-trivial regionally proximal relation of order $\infty$ are constructed.

Limiting proper minimal points of nonconvex sets in finite-dimensional spaces

In this paper, limiting proper minimal points of nonconvex sets in Euclidean finite-dimensional spaces are investigated. The relationships between these minimal points and Borwein, Benson, and Henig proper minimal points, under appropriate assumptions, are established. Furthermore, a density property is derived and a linear characterization of limiting proper minimal points is provided.

Collaborative Strategy for Grey Wolf Optimization Algorithm

Grey wolf Optimizer (GWO) is one of the well known meta-heuristic algorithm for determining the minimum value among a set of values. In this paper, we proposed a novel optimization algorithm called collaborative strategy for grey wolf optimizer (CSGWO). This algorithm enhances the behaviour of GWO that enhances the search feature to search for more points in the search space, whereas more groups will search for the global minimal points. The algorithm has been tested on 23 well-known benchmark functions and the results are verified by comparing them with state of the art algorithms: Polar particle swarm optimizer, sine cosine Algorithm (SCA), multi-verse optimizer (MVO), supernova optimizer as well as particle swarm optimizer (PSO). The results show that the proposed algorithm enhanced GWO behaviour for reaching the best solution and showed competitive results that outperformed the compared meta-heuristics over the tested benchmarked functions.

A Branch-and-bound algorithm for concave minimization problem with upper bounded variables

This paper presents a branch-and-bound algorithm for solving the concave minimization problems with upper bounded variables. The algorithm uses simplex to construct the branching and the bounding procedure. The linear convex envelope (the objective function of the subproblem) is uniquely determined on the candidate simplex which contains the subset of the local minimal points. The optimal solution of the subproblem is a local optimum of the original concave problem and used in reducing the list of active subproblems. The branching process splits the candidate simplex into two subsimplices by fixing the selected branching variable at value 0 or upper bound. Then the subsimplices are one less dimensional than the candidate. It means that the size of the subproblems gradually decreases. Further research needs to be focused on the efficient determination method of the simplex. The algorithm of this paper can be applied to solving the concave minimization problems under knapsack type constraints.