Phase-Transition in Binary Sequences with Long-Range Correlations

Motivated by novel results in the theory of correlated sequences, we analyze the dynamics of random walks with long-term memory (binary chains with long-range correlations). In our model, the probability for a unit bit in a binary string depends on the fraction of unities preceding it. We show that the system undergoes a dynamical phase-transition from normal diffusion, in which the variance D_L scales as the string's length L, into a super-diffusion phase (D_L ~ L^{1+|alpha|}), when the correlation strength exceeds a critical value. We demonstrate the generality of our results with respect to alternative models, and discuss their applicability to various data, such as coarse-grained DNA sequences, written texts, and financial data.Comment: 4 pages, 4 figure

The structure of economics

In this book we explore the insights that elementary mathematics affords the study of positive economics. We do not explore these issues to their fullest generality of mathematical rigor. Although generality and rigor are important economic goods, their production, because of the above-mentioned law of diminishing returns, entails increasing marginal costs. Thus we are usually content with intuitive, heuristic proofs of many mathematical prpositions. We refer students to standard mathematics texts for rigorous discussions of various theorems we use in this book. We aimed for that unobservable margin where for the bulk of our readers, the marginal benefits of greater rigor and generality equal their respective marginal cost. By example after example we hope to convince the reader that these elementary tools yield interesting and sometimes profound insights into modern economic

ASBĀB AL-NUZŪL: METHODS AND ITS APPLICATION TO VERSES OF THE QUR'AN

The study of asbāb al-nuzūl is an essential instrument in understanding the historical context in the Al-Qur'an. This study aimed to examine the background of the revelation of the verses of the Al-Qur'an. Moreover, it was also very helpful to find out the meaning of the verse to understand the Qur’anfor different times and places. This study employed qualitative research, which referred to library research by examining relevant theories and texts. This study examined the two rules caused by differences of opinion among scholars. The two rules become ibarah (handles); namely, the pronunciation generality is not a specific cause, and a specific cause is not a pronunciation generality.

Trees and Decisions

The traditional model of sequential decision making, for instance, in extensive form games, is a tree. Most texts define a tree as a connected directed graph without loops and a distingueshed node, called the root. But an abstract graph is not a domain for decision theory. Decision theory perceives of acts as function from states to consequences. Sequential decisions, accordingly, get conceptualized by mappings from sets of states to sets of consequences. Thus, the question arises whether a natural definition of a tree can be given, where nodes are sets of states. We show that, indeed, trees can be defined as specific collections of sets. Without loss of generality the elements of these sets can be interpreted as representing plays. Therefore, the elements can serve as states and consequences at the same time.

MENIMBANG KEUMUMAN LAFZH ‘ÂMM DAN MUTHLAQ DALAM MENGUNGKAP MAKNA NASH SYAR’Î

Understanding what is desired by Allah from the texts of the Qur’an that which is essentially many debatable than the immutable have led to a variety of concepts generated by the ushûliyyûn, like ‘âmm and muthlaq. These two concepts are very numerous and often intersect in the texts of the Qur’an, because the sturcture of the words on the legal source are mostly composed of ‘âmm and muthlaq words. Both have the differences and similarities in coverage breadth of its meaning. First, differences can be seen in the ‘âmm word covering the whole meaning of syar'î texts has many forms and varieties. While the muthlaq word consists only of nakirah word both singular and plural form. The other hand, the difference that in generality of ‘âmm is syumûlî and generality of muthlaq is badalî. In addition, the generality of ‘âmm from afrâd side (components), while the generality of muthlaq is from characteristic side. Secondly, the range of ‘âmm word is wider than the muthlaq word, due to the shape and variety of ‘âmm word more than the muthlaq word, ‘âmm word able to spend the amount of units more than the muthlaq word since the generality ‘âmm word on the side of component units, while the generality of the muthlaq word located on the side of characteristic.Copyright (c) 2016 by Al-Ihkam. All right reservedDOI: 10.19105/al-ihkam.v10i2.73

MENIMBANG KEUMUMAN LAFZH ‘ÂMM DAN MUTHLAQ DALAM MENGUNGKAP MAKNA NASH SYAR’Î

Understanding what is desired by Allah from the texts of the Qur’an that which is essentially many debatable than the immutable have led to a variety of concepts generated by the ushûliyyûn, like ‘âmm and muthlaq. These two concepts are very numerous and often intersect in the texts of the Qur’an, because the sturcture of the words on the legal source are mostly composed of ‘âmm and muthlaq words. Both have the differences and similarities in coverage breadth of its meaning. First, differences can be seen in the ‘âmm word covering the whole meaning of syar'î texts has many forms and varieties. While the muthlaq word consists only of nakirah word both singular and plural form. The other hand, the difference that in generality of ‘âmm is syumûlî and generality of muthlaq is badalî. In addition, the generality of ‘âmm from afrâd side (components), while the generality of muthlaq is from characteristic side. Secondly, the range of ‘âmm word is wider than the muthlaq word, due to the shape and variety of ‘âmm word more than the muthlaq word, ‘âmm word able to spend the amount of units more than the muthlaq word since the generality ‘âmm word on the side of component units, while the generality of the muthlaq word located on the side of characteristic.Copyright (c) 2016 by Al-Ihkam. All right reservedDOI: 10.19105/al-ihkam.v10i2.73

Trees and Decisions

The traditional model of sequential decision making, for instance, in extensive form games, is a tree. Most texts de?ne a tree as a connected directed graph without loops and a distinguished node, called the root. But an abstract graph is not a domain for decision theory. Decision theory perceives of acts as functions from states to consequences. Sequential decisions, accordingly, get conceptualized by mappings from sets of states to sets of consequences. Thus, the question arises whether a natural de?nition of a tree can be given, where nodes are sets of states. We show that, indeed, trees can be de?ned as speci?c collections of sets. Without loss of generality the elements of these sets can be interpreted as representing plays. Therefore, the elements can serve as states and consequences at the same time.Decision under uncertainty, Extensive form games, Trees

Artificial Sequences and Complexity Measures

In this paper we exploit concepts of information theory to address the fundamental problem of identifying and defining the most suitable tools to extract, in a automatic and agnostic way, information from a generic string of characters. We introduce in particular a class of methods which use in a crucial way data compression techniques in order to define a measure of remoteness and distance between pairs of sequences of characters (e.g. texts) based on their relative information content. We also discuss in detail how specific features of data compression techniques could be used to introduce the notion of dictionary of a given sequence and of Artificial Text and we show how these new tools can be used for information extraction purposes. We point out the versatility and generality of our method that applies to any kind of corpora of character strings independently of the type of coding behind them. We consider as a case study linguistic motivated problems and we present results for automatic language recognition, authorship attribution and self consistent-classification.Comment: Revised version, with major changes, of previous "Data Compression approach to Information Extraction and Classification" by A. Baronchelli and V. Loreto. 15 pages; 5 figure