Double symbolic joint entropy in nonlinear dynamic complexity analysis

Symbolizations, the base of symbolic dynamic analysis, are classified as global static and local dynamic approaches which are combined by joint entropy in our works for nonlinear dynamic complexity analysis. Two global static methods, symbolic transformations of Wessel N. symbolic entropy and base-scale entropy, and two local ones, namely symbolizations of permutation and differential entropy, constitute four double symbolic joint entropies that have accurate complexity detections in chaotic models, logistic and Henon map series. In nonlinear dynamical analysis of different kinds of heart rate variability, heartbeats of healthy young have higher complexity than those of the healthy elderly, and congestive heart failure (CHF) patients are lowest in heartbeats' joint entropy values. Each individual symbolic entropy is improved by double symbolic joint entropy among which the combination of base-scale and differential symbolizations have best complexity analysis. Test results prove that double symbolic joint entropy is feasible in nonlinear dynamic complexity analysis.Comment: 7 pages, 4 figure

forall x: Calgary. An Introduction to Formal Logic

forall x: Calgary is a full-featured textbook on formal logic. It covers key notions of logic such as consequence and validity of arguments, the syntax of truth-functional propositional logic TFL and truth-table semantics, the syntax of first-order (predicate) logic FOL with identity (first-order interpretations), translating (formalizing) English in TFL and FOL, and Fitch-style natural deduction proof systems for both TFL and FOL. It also deals with some advanced topics such as truth-functional completeness and modal logic. Exercises with solutions are available. It is provided in PDF (for screen reading, printing, and a special version for dyslexics) and in LaTeX source code

Between Action and Power: A Perspective on Symbolization and Ritual Efficacy

The purpose of this paper is to clarify the notion of symbolization and relate it to that of ritual efficacy. It is demonstrated that terms such as “symbolization” and “symbol” are used rather loosely by prominent anthropologists and therefore require closer scrutiny. The first half of the paper explorers the notion of symbolizing in Geertz and Turner’s respective theories toward the end of erecting three criteria for an adequate theory of symbolization. The criteria are, in turn, deduced from Jarvie and Sperber’s respective critique. The second half of the paper regards the relationship between symbolization and power through Tambiah’s account of ritual efficacy, which is articulated and assessed against the background of the three criteria. Consecutively, Tambiah’s theory is specified by merging it with Searle’s conceptual apparatus, rendering it analytically superior to the predecessor. It is discovered that specificity is an important virtue for a theory of symbolization. Upon conclusion, the applicability of Tambiah’s specified theory is investigated by considering some of Holbraad’s ethnographical material on the ritual invocation of power.The purpose of this paper is to clarify the notion of symbolization and relate it to that of ritual efficacy. It is demonstrated that terms such as “symbolization” and “symbol” are used rather loosely by prominent anthropologists and therefore require closer scrutiny. The first half of the paper explorers the notion of symbolizing in Geertz and Turner’s respective theories toward the end of erecting three criteria for an adequate theory of symbolization. The criteria are, in turn, deduced from Jarvie and Sperber’s respective critique. The second half of the paper regards the relationship between symbolization and power through Tambiah’s account of ritual efficacy, which is articulated and assessed against the background of the three criteria. Consecutively, Tambiah’s theory is specified by merging it with Searle’s conceptual apparatus, rendering it analytically superior to the predecessor. It is discovered that specificity is an important virtue for a theory of symbolization. Upon conclusion, the applicability of Tambiah’s specified theory is investigated by considering some of Holbraad’s ethnographical material on the ritual invocation of power

A parasitological view of non-constructible sets

The genetic code, the primary manifestation of life, and, on the other hand, language, the universal endowment of humanity and its momentous leap from genetics to civilization, are the two fundamental stores of information transmissible from the ancestry to the progeny, the molecular succession, which ensures the transfer of hereditary messages from the cells of one generation to the next generation, and the verbal legacy as a necessary prerequisite of cultural tradition. Divergent terminologies direct attention to different pattemings; and finding a logically convincing test, acceptable all around, that can determine whether one such system of terms is superior to its rivals, is often impossible. Yet the slow processes of evolution presumably apply to human societies and their symbolic systems as much as to human bodies, so that when logic cannot decide, survival eventually will

Time series irreversibility: a visibility graph approach

We propose a method to measure real-valued time series irreversibility which combines two differ- ent tools: the horizontal visibility algorithm and the Kullback-Leibler divergence. This method maps a time series to a directed network according to a geometric criterion. The degree of irreversibility of the series is then estimated by the Kullback-Leibler divergence (i.e. the distinguishability) between the in and out degree distributions of the associated graph. The method is computationally effi- cient, does not require any ad hoc symbolization process, and naturally takes into account multiple scales. We find that the method correctly distinguishes between reversible and irreversible station- ary time series, including analytical and numerical studies of its performance for: (i) reversible stochastic processes (uncorrelated and Gaussian linearly correlated), (ii) irreversible stochastic pro- cesses (a discrete flashing ratchet in an asymmetric potential), (iii) reversible (conservative) and irreversible (dissipative) chaotic maps, and (iv) dissipative chaotic maps in the presence of noise. Two alternative graph functionals, the degree and the degree-degree distributions, can be used as the Kullback-Leibler divergence argument. The former is simpler and more intuitive and can be used as a benchmark, but in the case of an irreversible process with null net current, the degree-degree distribution has to be considered to identifiy the irreversible nature of the series.Comment: submitted for publicatio

On the acquisition of the german plural markings

In the following, we will discuss the acquisition of plural forms in German from the unified perspective of the two, in our opinion compatible, approaches, on the basis of a longitudinal data sample of eight children. There are at least six recordings of each child, all of whom are girls. Together, the data cover the acquisition period from 1;11 to 2;10. One may thus anticipate that the data sample under investigation reflects the transition from purely lexical memorization to the acquisition of regularities or patterns