We investigate two operators on classes of regular languages: polynomial closure ( $$Pol$$ ) and Boolean $$Bool$$ ). apply these to group languages $$\mathcal {G}$$ their well-suited extensions {G} ^+$$ , which is the least algebra containing $$ $$\{\varepsilon \}$$ . This yields $$Bool(Pol(\mathcal {G}))$$ ^+))$$ These form first level in important classifications languages, called concatenati...

It is stressed that the brain/mind complex constitutes a monolithic system that functions with emergent properties at several levels of hierarchical organization. These hierarchical levels are non-reducible to one another; they are at least three (neuronal, functional, and semantic), and they function within an interactional plan. From the epistemological view-point, the brain/mind complex uses...

We consider a semilinear elliptic equation on a smooth bounded domain Ω in R2, assuming that both the domain and the equation are invariant under reflections about one of the coordinate axes, say the y-axis. It is known that nonnegative solutions of the Dirichlet problem for such equations are symmetric about the axis, and, if strictly positive, they are also decreasing in x for x > 0. Our goal...

Internet memes are phenomena that rapidly gain popularity or notoriety on the Internet. Often, modifications or spoofs add to the profile of the original idea thus turning it into a phenomenon that transgresses social and cultural boundaries. It is commonly assumed that Internet memes spread virally but scientific evidence as to this assumption is scarce. In this paper, we address this issue an...

In this paper we study the distributions of number real solutions to power flow equations over varying electrical parameters. We develop a new monodromy and parameter homotopy continuation method for quickly finding all equations. apply find compare these those random polynomials. It is observed that while tend admit many fewer real-valued than bound on total complex solutions, low levels load ...

Since Google Trends and Google Insights for Search were launched, they provide a daily insight into what the world is searching for on Google, by showing the relative volume of search traffic in Google for any search query. An understanding of web search trends can be useful for advertisers, marketers, economists, scholars, and anyone else interested in knowing more about their world and what's...

Logical formalisms such as first-order logic (FO) and fixpoint logic (FP) are well suited to express in a declarative manner fundamental graph functionalities required in distributed systems. We show that these logics constitute good abstractions for programming distributed systems as a whole, since they can be evaluated in a fully distributed manner with reasonable complexity upper-bounds. We ...

A range of solutions to the Monty Hall problem is developed, with the aim of connecting popular (informal) solutions and the formal mathematical solutions of introductory text-books. Under Riemann’s slogan of replacing calculations with ideas, we discover bridges between popular solutions and rigorous (formal) mathematical solutions by using various combinations of symmetry, symmetrization, ind...

We study definability and complexity issues for automatic and ω-automatic structures. These are, in general, infinite structures but they can be finitely presented by a collection of automata. Moreover, they admit effective (in fact automatic) evaluation of all first-order queries. Therefore, automatic structures provide an interesting framework for extending many algorithmic and logical method...

Abstract In this paper we consider spaces of weight square-integrable and harmonic functions L 2 H (Ω, µ ). Weights for which there exists reproducing kernel ) are named ’admissible weights’ such kernels ’harmonic Bergman kernels’. We prove that if only integration is integrable in some negative power, then it admissible. Next construct a on the unit circle non-admissible using Bell-Ligocka the...