The Non-Scalability Of The Concept Of Law-A Reply To Thomas Schultz
A hypergraph is Sperner if no hyperedge contains another one. A Sperner hypergraph is equilizable (resp., threshold) if the characteristic vectors of its hyperedges are the (minimal) binary solutions to a linear equation (resp., inequality) with positive coefficients. These combinatorial notions have many applications and are motivated by the theory of Boolean functions and integer programming. We introduce in this paper the class of 1-Sperner hypergraphs, defined by the property that for every two hyperedges the smallest of their two set differences is of size one. We characterize this class of Sperner hypergraphs by a decomposition theorem and derive several consequences from it. In particular, we obtain bounds on the size of 1-Sperner hypergraphs and their transversal hypergraphs, show that the characteristic vectors of the hyperedges are linearly independent over the reals, and prove that 1-Sperner hypergraphs are both threshold and equilizable. The study of 1-Sperner hypergraphs is motivated also by their applications in graph theory, which we present in a companion paper.
We study the following computational problem: for which values of k, the majority of n bits MAJn can be computed with a depth two formula whose each gate computes a majority function of at most k bits? The corresponding computational model is denoted by MAJk ∘ MAJk. We observe that the minimum value of k for which there exists a MAJk ∘ MAJk circuit that has high correlation with the majority of n bits is equal to Θ(n1/2). We then show that for a randomized MAJk ∘ MAJk circuit computing the majority of n input bits with high probability for every input, the minimum value of k is equal to n2/3 + o(1). We show a worst case lower bound: if a MAJk ∘ MAJk circuit computes the majority of n bits correctly on all inputs, then k ≥ n13/19 + o(1).
While many studies have been conducted to test the efficacy and reliability of the Rogerian “Necessary and sufficient conditions” in different settings, the majority of such studies were done from the client or counselor-client perspective. Very few studies have tested the counselor’s subjective perception and experiencing of those conditions. The present pilot qualitative inquiry was conducted to obtain an image of how counselors experience three of these conditions that are often referred to as “core conditions”: empathy, congruence, and unconditional positive regard. The study was performed on a sample of six novice client-centered counselors who had just graduated from a continuous education group in Client-Centered Therapy (CCT). Some of them had previous experience of counseling, some did not, but none of them had previous experience of Client-Centered Therapy. Qualitative methodology was used in the study, including an Interpretative Phenomenological Analysis (IPA). Specifically – the semi-structured interview method was used in order to collect data, and the Meaning Condensation method was used to analyze the data. As a result, the qualitative descriptions of the counselors subjective perception and experiencing of the Rogerian conditions were obtained. They allowed us to draw some conclusions regarding the inner structure of the client-centered conditions themselves.
We study the following computational problem: for which values of k, the majority of n bits MAJn can be computed with a depth two formula whose each gate computes a majority function of at most k bits? The corresponding computational model is denoted by MAJk o MAJk. We observe that the minimum value of k for which there exists a MAJk o MAJk circuit that has high correlation with the majority of n bits is equal to Θ(n1/2). We then show that for a randomized MAJk o MAJk circuit computing the majority of n input bits with high probability for every input, the minimum value of k is equal to n2/3+o(1). We show a worst case lower bound: if a MAJk o MAJk circuit computes the majority of n bits correctly on all inputs, then k ≥ n13/19+o(1). This lower bound exceeds the optimal value for randomized circuits and thus is unreachable for pure randomized techniques. For depth 3 circuits we show that a circuit with k = O(n2/3) can compute MAJn correctly on all inputs.
международное частное право; недвижимость; ; школа бартолистов; бартолисты; теория статутов; статуарная теория/
The article is devoted to a particular form of freedom of assembly — the right to counter-demonstrate. The author underlines the value of this right as an element of democratic society, but also acknowledges the risk of violent actions among participants of opposing demonstrations. Due to this risk, the government may adopt adequate measures restricting the right to counter-demonstrate, certain types of which are analyzed in this paper.
Development of standards of international controllability is reviewed in the article. Institutional approach is applied to development of international legal regime of Energy Charter. Definition of controllability is connected to development of international standards of dispute settlement, which are described in the article in detail. In connection with controllability, Russian interest, defense of investment in European Union and ecological investment encouragement, is reviewed in the article.
мировое управление и управляемость, Мировая экономика, международное экономическое право, энергетическая хартия, International control and controllability, International economics, international economic law, Energy Charter