scholarly journals Generalized Mutual Information

Stats ◽  
2020 ◽  
Vol 3 (2) ◽  
pp. 158-165
Author(s):  
Zhiyi Zhang
Keyword(s):  
Information Theory ◽  
Positive Integer ◽  
Mutual Information ◽  
General Class ◽  
Building Blocks ◽  
Potential Utility ◽  
First Order ◽  
The Family ◽  
Random Elements

Mutual information is one of the essential building blocks of information theory. It is however only finitely defined for distributions in a subclass of the general class of all distributions on a joint alphabet. The unboundedness of mutual information prevents its potential utility from being extended to the general class. This is in fact a void in the foundation of information theory that needs to be filled. This article proposes a family of generalized mutual information whose members are indexed by a positive integer n, with the nth member being the mutual information of nth order. The mutual information of the first order coincides with Shannon’s, which may or may not be finite. It is however established (a) that each mutual information of an order greater than 1 is finitely defined for all distributions of two random elements on a joint countable alphabet, and (b) that each and every member of the family enjoys all the utilities of a finite Shannon’s mutual information.

scholarly journals Allometric Scaling of Mutual Information in Complex Networks: A Conceptual Framework and Empirical Approach

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 206
Author(s):  
Eduardo Viegas ◽  
Hayato Goto ◽  
Yuh Kobayashi ◽  
Misako Takayasu ◽  
Hideki Takayasu ◽  
...  
Keyword(s):  
Information Theory ◽  
Mutual Information ◽  
Scaling Laws ◽  
Allometric Scaling ◽  
Free Market ◽  
Preferential Attachment ◽  
Building Blocks ◽  
Structural Features ◽  
Network Activity ◽  
Analysis Tool

Complexity and information theory are two very valuable but distinct fields of research, yet sharing the same roots. Here, we develop a complexity framework inspired by the allometric scaling laws of living biological systems in order to evaluate the structural features of networks. This is done by aligning the fundamental building blocks of information theory (entropy and mutual information) with the core concepts in network science such as the preferential attachment and degree correlations. In doing so, we are able to articulate the meaning and significance of mutual information as a comparative analysis tool for network activity. When adapting and applying the framework to the specific context of the business ecosystem of Japanese firms, we are able to highlight the key structural differences and efficiency levels of the economic activities within each prefecture in Japan. Moreover, we propose a method to quantify the distance of an economic system to its efficient free market configuration by distinguishing and quantifying two particular types of mutual information, total and structural.

Thienopyrrolocarbazoles: New Building Blocks for Functional Organic Materials

2019 ◽  
Author(s):  
Dorian Bader ◽  
Johannes Fröhlich ◽  
Paul Kautny
Keyword(s):  
Building Block ◽  
Organic Materials ◽  
Building Blocks ◽  
Molecular Properties ◽  
The Family ◽  
Facile Preparation

The facile preparation of three regioisomeric thienopyrrolocarbazoles applying a convenient C-H activation approach is presented. Derived from indolo[3,2,1-<i>jk</i>]carbazole, the incorporation of thiophene into the triarylamine framework significantly impacted the molecular properties of the parent scaffold. The developed thienopyrrolocarbazoles enrich the family of triarylamine donors and constitute a novel building block for functional organic materials.

Thienopyrrolocarbazoles: New Building Blocks for Functional Organic Materials

2019 ◽  
Author(s):  
Dorian Bader ◽  
Johannes Fröhlich ◽  
Paul Kautny
Keyword(s):  
Building Block ◽  
Organic Materials ◽  
Building Blocks ◽  
Molecular Properties ◽  
The Family ◽  
Facile Preparation

The facile preparation of three regioisomeric thienopyrrolocarbazoles applying a convenient C-H activation approach is presented. Derived from indolo[3,2,1-<i>jk</i>]carbazole, the incorporation of thiophene into the triarylamine framework significantly impacted the molecular properties of the parent scaffold. The developed thienopyrrolocarbazoles enrich the family of triarylamine donors and constitute a novel building block for functional organic materials.

scholarly journals Oscillation Conditions for Difference Equations with a Monotone or Nonmonotone Argument

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
G. M. Moremedi ◽  
I. P. Stavroulakis
Keyword(s):  
Positive Integer ◽  
Difference Equation ◽  
Difference Equations ◽  
Delay Difference Equation ◽  
Real Numbers ◽  
First Order ◽  
All Solutions ◽  
Delay Difference ◽  
Constant Argument

Consider the first-order delay difference equation with a constant argument Δxn+pnxn-k=0,  n=0,1,2,…, and the delay difference equation with a variable argument Δxn+pnxτn=0,  n=0,1,2,…, where p(n) is a sequence of nonnegative real numbers, k is a positive integer, Δx(n)=x(n+1)-x(n), and τ(n) is a sequence of integers such that τ(n)≤n-1 for all n≥0 and limn→∞τ(n)=∞. A survey on the oscillation of all solutions to these equations is presented. Examples illustrating the results are given.

scholarly journals Cost-effectiveness of the Family Nurse Partnership (FNP) programme in England: Evidence from the building blocks trial

2017 ◽  
Vol 23 (6) ◽  
pp. 1367-1374 ◽  
Author(s):  
Belen Corbacho ◽  
Kerry Bell ◽  
Eugena Stamuli ◽  
Gerry Richardson ◽  
Sarah Ronaldson ◽  
...  
Keyword(s):  
Cost Effectiveness ◽  
Building Blocks ◽  
The Family ◽  
Family Nurse Partnership

scholarly journals Costs and consequences of the Family Nurse Partnership (FNP) programme in England: evidence from the Building Blocks trial

F1000Research ◽  
2019 ◽  
Vol 8 ◽  
pp. 1640 ◽  
Author(s):  
Kerry Bell ◽  
Belen Corbacho ◽  
Sarah Ronaldson ◽  
Gerry Richardson ◽  
Kerry Hood ◽  
...  
Keyword(s):  
Home Visiting ◽  
Controlled Trial ◽  
Full Range ◽  
Building Blocks ◽  
Public Health Services ◽  
Intervention Programme ◽  
The Family ◽  
Cost Consequence ◽  
Implementation Costs ◽  
Family Nurse Partnership

Background: The Family Nurse Partnership (FNP) is a licensed intensive home visiting intervention programme delivered to teenage mothers which was originally introduced in England in 2006 by the Department of Health and is now provided through local commissioning of public health services and supported by a national unit led by a consortium of partners. The Building Blocks (BB) trial aimed to explore the effectiveness and cost-effectiveness of this programme. This paper reports the results of an economic evaluation of the Building Blocks randomised controlled trial (RCT) based on a cost-consequence approach. Methods: A large sample of 1618 families was followed-up at various intervals during pregnancy and for two years after birth. A cost-consequence approach was taken to appraise the full range of costs arising from the intervention including both health and social measures of cost alongside the consequences of the trial, specifically, the primary outcomes. Results: A large number of potential factors were identified that are likely to attract additional costs beyond the implementation costs of the intervention including both health and non-health outcomes. Conclusion: Given the extensive costs and only small beneficial consequences observed within the two year follow-up period, the cost-consequence model suggests that the FNP intervention is unlikely to be worth the substantial costs and policy makers may wish to consider other options for investment. Trial registration: ISRCTN23019866 (20/04/2009)

scholarly journals Reasoning with Time Intervals: A Logical and Computational Perspective

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Guido Sciavicco
Keyword(s):  
Temporal Reasoning ◽  
Point Of View ◽  
Time Intervals ◽  
First Order ◽  
Modal Interval ◽  
The Family ◽  
First Results ◽  
Comprehensive Survey ◽  
Classical Point

The role of time in artificial intelligence is extremely important. Interval-based temporal reasoning can be seen as a generalization of the classical point-based one, and the first results in this field date back to Hamblin (1972) and Benhtem (1991) from the philosophical point of view, to Allen (1983) from the algebraic and first-order one, and to Halpern and Shoham (1991) from the modal logic one. Without purporting to provide a comprehensive survey of the field, we take the reader to a journey through the main developments in modal and first-order interval temporal reasoning over the past ten years and outline some landmark results on expressiveness and (un)decidability of the satisfiability problem for the family of modal interval logics.

scholarly journals FAMILY IN TALENT AND CREATIVITY DEVELOPMENT

2020 ◽  
Vol 5 (35) ◽  
pp. 215-224
Author(s):  
Ahmad Abd Mustafa Smadi ◽  
Bsaer Ahmad Mustafa al-Qudah ◽  
Najihah Abd Wahid
Keyword(s):  
Building Blocks ◽  
Family Counseling ◽  
Family Factors ◽  
Gifted Children ◽  
Academic Problems ◽  
Descriptive Research ◽  
Creativity Development ◽  
The Family ◽  
Qualitative Descriptive

Talent and creativity development require extraordinary counseling from the members of the family, and as such, it is necessary to highlight the crucial role of family counseling towards developing talent and creativity. The article aims to examine the contributory role of the family in talent and creativity growth. The study shall serve as a reference for families to eliminate challenges growing with talent and creativity maturation. If the family has no awareness of how to deal with their gifted son, it may cause psychological stress and academic problems, thus undoubtedly affect the child’s talent. Hence the importance of this study is to demonstrate the role of family counseling in developing the talent and creativity of the gifted child by providing support and awareness to the family on how to deal with this talent to preserve and develop this talent because the gifted individuals are the basic building blocks in the progress and development of societies. Therefore, the article attempts to analyze the talent and creativity of gifted children and counseling of gifted family. The article includes a quick overview of talent origins, components and techniques, the role of the family in talent and creativity development, family factors influencing talent, creativity, gifted children, and family counseling. The study is qualitative descriptive research since the approach is considered suitable for determining the particular role expected from the family towards developing talent and creativity. The approach used in this study is appropriate for pinpointing the responsibilities of families in the process of growing children’s talent and creativity.

Universal Building Blocks

2020 ◽  
pp. 65-92
Author(s):  
Ron Harris
Keyword(s):  
Simple Structure ◽  
Building Blocks ◽  
Clear Pattern ◽  
Historical Evidence ◽  
Long Distance ◽  
The Family ◽  
Endogenous Institutions ◽  
Historical Origin ◽  
Basic Functions ◽  
Organic As

This chapter argues that a number of precursor institutions of the long-distance trade organization developed locally, independently, and endemically in many different places along the Eurasian landmass. It shows that there is often no direct and clear evidence for the endogenous origins of institutions. The chapter also discusses the endemic appearance of an institution that does not have a clear pattern of migration but, together with its relatively simple structure, supports the identification of an endogenous institution. Endogenous institutions are often organic, as is the case with the itinerant trader or the family, or simple institutions that address basic functions, such as the loan, agency, or ship. They are to be found throughout Eurasia, and there is no historical evidence of a single historical origin for any of them or of a clear route of their migration.

From the Outside In

2015 ◽  
Author(s):  
Derek Smith
Keyword(s):  
Positive Integer ◽  
Infinite Family ◽  
Open Problems ◽  
The Family

This chapter discusses Slothouber–Graatsma–Conway puzzle, which asks one to assemble six 1 × 2 × 2 pieces and three 1 × 1 × 1 pieces into the shape of a 3 × 3 × 3 cube. The puzzle has been generalized to larger cubes, and there is an infinite family of such puzzles. The chapter's primary argument is that, for any odd positive integer n = 2k + 1, there is exactly one way, up to symmetry, to make an n × n × n cube out of n tiny 1 × 1 × 1 cubes and six of each of a set of rectangular blocks. The chapter describes a way to solve each puzzle in the family and explains why there are no other solutions. It then presents several related open problems.

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