Upper bounds on quantum uncertainty products and complexity measures

2011 ◽  
Vol 84 (4) ◽  
Author(s):  
Ángel Guerrero ◽  
Pablo Sánchez-Moreno ◽  
Jesús S. Dehesa
2019 ◽  
Vol 30 (06n07) ◽  
pp. 921-957
Author(s):  
Janusz A. Brzozowski ◽  
Sylvie Davies

A regular language [Formula: see text] is non-returning if in the minimal deterministic finite automaton accepting it there are no transitions into the initial state. Eom, Han and Jirásková derived upper bounds on the state complexity of boolean operations and Kleene star, and proved that these bounds are tight using two different binary witnesses. They derived tight upper bounds for concatenation and reversal using three different ternary witnesses. These five witnesses use a total of six different transformations. We show that for each [Formula: see text], there exists a ternary witness of state complexity [Formula: see text] that meets the bound for reversal, and restrictions of this witness to binary alphabets meet the bounds for star, product, and boolean operations. Hence all of these operations can be handled simultaneously with a single witness, using only three different transformations. We also derive tight upper bounds on the state complexity of binary operations that take arguments with different alphabets. We prove that the maximal syntactic semigroup of a non-returning language has [Formula: see text] elements and requires at least [Formula: see text] generators. We find the maximal state complexities of atoms of non-returning languages. We show that there exists a most complex sequence of non-returning languages that meet the bounds for all of these complexity measures. Furthermore, we prove there is a most complex sequence that meets all the bounds using alphabets of minimal size.


Author(s):  
Slavcho Shtrakov

In this paper, we study two classes of complexity measures induced by new data structures (abstract reduction systems) for representing [Formula: see text]-valued functions (operations), namely subfunction and minor reductions. When assigning values to some variables in a function, the resulting functions are called subfunctions, and when identifying some variables, the resulting functions are called minors. The number of the distinct objects obtained under these reductions of a function [Formula: see text] is a well-defined measure of complexity denoted by [Formula: see text] and [Formula: see text], respectively. We examine the maximums of these complexities and construct functions which reach these upper bounds.


2010 ◽  
Vol 24 (2) ◽  
pp. 131-135 ◽  
Author(s):  
Włodzimierz Klonowski ◽  
Pawel Stepien ◽  
Robert Stepien

Over 20 years ago, Watt and Hameroff (1987 ) suggested that consciousness may be described as a manifestation of deterministic chaos in the brain/mind. To analyze EEG-signal complexity, we used Higuchi’s fractal dimension in time domain and symbolic analysis methods. Our results of analysis of EEG-signals under anesthesia, during physiological sleep, and during epileptic seizures lead to a conclusion similar to that of Watt and Hameroff: Brain activity, measured by complexity of the EEG-signal, diminishes (becomes less chaotic) when consciousness is being “switched off”. So, consciousness may be described as a manifestation of deterministic chaos in the brain/mind.


Author(s):  
Liliane Campos

By decentring our reading of Hamlet, Stoppard’s tragicomedy questions the legitimacy of centres and of stable frames of reference. So Liliane Campos examines how Stoppard plays with the physical and cosmological models he finds in Hamlet, particularly those of the wheel and the compass, and gives a new scientific depth to the fear that time is ‘out of joint’. In both his play and his own film adaptation, Stoppard’s rewriting gives a 20th-century twist to these metaphors, through references to relativity, indeterminacy, and the role of the observer. When they refer to the uncontrollable wheels of their fate, his characters no longer describe the destruction of order, but uncertainty about which order is at work, whether heliocentric or geocentric, random or tragic. When they express their loss of bearings, they do so through the thought experiments of modern physics, from Galilean relativity to quantum uncertainty, drawing our attention to shifting frames of reference. Much like Schrödinger’s cat, Stoppard’s Rosencrantz and Guildenstern are both dead and alive. As we observe their predicament, Campos argues, we are placed in the paradoxical position of the observer in 20th-century physics, and constantly reminded that our time-specific relation to the canon inevitably determines our interpretation.


1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.


Author(s):  
S. Yahya Mohamed ◽  
A. Mohamed Ali

In this paper, the notion of energy extended to spherical fuzzy graph. The adjacency matrix of a spherical fuzzy graph is defined and we compute the energy of a spherical fuzzy graph as the sum of absolute values of eigenvalues of the adjacency matrix of the spherical fuzzy graph. Also, the lower and upper bounds for the energy of spherical fuzzy graphs are obtained.


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