A finite iteration method for solving systems of (max, min)-linear equations is presented. The systems have variables on both sides of the equations. The algorithm has polynomial complexity and may be extended to wider classes of equations with a similar structure.
The Self Organized Mapping (SOM) is a kind of artificial neural network (ANN) which enables the pattern set self-organization in space with Euclidean metrics. Thus, the traditional SOM consists of two layers; input one with n nodes and output one with H ones. Every output node is characterized by its weight vector Wk G in this case. The absence of pattern coordinates in special cases is a good motivation for self-organization in any metric space (U, d). The learning in the metric space is introduced on the cluster analysis problém and a basic clustering algorithm is obtained. The relationship with the traditional ISODATA method and NP-completeness is proven. The direct generalization comes to SOM learning in the metric space, its algorithm, properties and NP-completeness. The SOM learning is based on an objective function and its batch minimization. Three estimates of the proposed objective function are included. They will help to study the relationship with Kohonen batch learning, the cluster analysis and the convex programming task. The Matlab source code for the SOM in the metric space is available in the appendix. Two numeric examples are oriented at self-organization in the metric space of written words and the metric space of functions.
This paper is a critical appraisal of the most recent attempt from cognitive science in general, developmental and evolutionary biology in particular, to understand the nature and mechanisms underlying consciousness as proposed by Anton J.M. Dijker. The proposal, briefly stated, is to view consciousness as a neural capacity for objec- tivity. What makes the problem of consciousness philosophically and scientifically challenging may be stated as follows: If consciousness has a first-person ontology and our best scientific theories have a third-person ontology, how can we come up with a satisfactory theory? Moreover, if the reduction of one to the other is impossible, what are we supposed to do? By neglecting what Chalmers calls the ''hard problem'' of consciousness, Dijker’s proposal seems unable to respond to the foregoing questions, and these questions, I maintain, are the very motivations that most of us have when we inquire about consciousness., Tento článek je kritickým posouzením posledního pokusu o kognitivní vědu obecně, zejména vývojové a evoluční biologie, pochopit podstatu a mechanismy, které jsou základem vědomí, jak navrhl Anton JM Dijker. Návrh, stručně řečeno, je vnímat vědomí jako neurální schopnost objektivity. Co dělá problém vědomí filozoficky a vědecky náročný, lze říci následovně: Pokud má vědomí první ontologii člověka a naše nejlepší vědecké teorie mají ontologii třetí osoby, jak můžeme přijít s uspokojivou teorií? Pokud je navíc redukce jednoho na druhého nemožná, co máme dělat? Zanedbáním toho, co Chalmers nazývá ,,tvrdým problémem'' vědomí, se zdá, že Dijkerův návrh nedokáže odpovědět na výše uvedené otázky, and John Ian K. Boongaling
We consider Stanley-Reisner rings $k[x_1,\ldots ,x_n]/I(\mathcal {H})$ where $I(\mathcal {H})$ is the edge ideal associated to some particular classes of hypergraphs. For instance, we consider hypergraphs that are natural generalizations of graphs that are lines and cycles, and for these we compute the Betti numbers. We also generalize some known results about chordal graphs and study a weak form of shellability.
For ordered (= partially ordered) sets we introduce certain cardinal characteristics of them (some of those are known). We show that these characteristics—with one exception—coincide.
A closed convex set $Q$ in a local convex topological Hausdorff spaces $X$ is called locally nonconical (LNC) if for every $x, y\in Q$ there exists an open neighbourhood $U$ of $x$ such that $(U\cap Q)+\frac{1}{2}(y-x)\subset Q$. A set $Q$ is local cylindric (LC) if for $x,y\in Q$, $x\ne y$, $z\in (x,y)$ there exists an open neighbourhood $U$ of $z$ such that $U\cap Q$ (equivalently: $\mathrm bd(Q)\cap U$) is a union of open segments parallel to $[x,y]$. In this paper we prove that these two notions are equivalent. The properties LNC and LC were investigated in [3], where the implication ${\mathrm LNC}\Rightarrow {\mathrm LC}$ was proved in general, while the inverse implication was proved in case of Hilbert spaces.
This paper gives some new characterizations of completeness for trellises by introducing the notion of a cycle-complete trellis. One of our results yields, in particular, a characterization of completeness for trellises of finite length due to K. Gladstien (see K. Gladstien: Characterization of completeness for trellises of finite length, Algebra Universalis 3 (1973), 341–344).
The relationship between weighted Lipschitz functions and analytic Bloch spaces has attracted much attention. In this paper, we define harmonic ω-α-Bloch space and characterize it in terms of \omega \left( {{{\left( {1 - {{\left| x \right|}^2}} \right)}^\beta }{{\left( {1 - {{\left| y \right|}^2}} \right)}^{\alpha - \beta }}} \right)\left| {\frac{{f\left( x \right) - f\left( y \right)}}{{x - y}}} \right| and \omega \left( {{{\left( {1 - {{\left| x \right|}^2}} \right)}^\beta }{{\left( {1 - {{\left| y \right|}^2}} \right)}^{\alpha - \beta }}} \right)\left| {\frac{{f\left( x \right) - f\left( y \right)}}{{\left| x \right|y - x'}}} \right| where ω is a majorant. Similar results are extended to harmonic little ω-α-Bloch and Besov spaces. Our results are generalizations of the corresponding ones in G.Ren, U.Kähler (2005)., Xi Fu, Bowen Lu., and Obsahuje seznam literatury