Relative information of type s, Csisz�r's f-divergence, and information inequalities*1

2004 ◽  
Vol 166 (1-4) ◽  
pp. 105-125 ◽  
Author(s):  
I TANEJA
Keyword(s):  
Information Inequalities ◽  
Relative Information

scholarly journals New Inequalities between Information Measures of Network Information Content

2013 ◽  
Vol 2013 ◽  
pp. 1-3 ◽  
Author(s):  
Pantelimon-George Popescu ◽  
Florin Pop ◽  
Alexandru Herişanu ◽  
Nicolae Ţăpuş
Keyword(s):  
Information Processing ◽  
Complex Systems ◽  
Complex Networks ◽  
Information Content ◽  
Discrete Case ◽  
Network Information ◽  
Information Inequalities ◽  
Information Measures ◽  
New Inequalities

We refine a classical logarithmic inequality using a discrete case of Bernoulli inequality, and then we refine furthermore two information inequalities between information measures for graphs, based on information functionals, presented by Dehmer and Mowshowitz in (2010) as Theorems 4.7 and 4.8. The inequalities refer to entropy-based measures of network information content and have a great impact for information processing in complex networks (a subarea of research in modeling of complex systems).

Individual categorisation of glucose profiles using compositional data analysis

2018 ◽  
Vol 28 (12) ◽  
pp. 3550-3567 ◽  
Author(s):  
Lyvia Biagi ◽  
Arthur Bertachi ◽  
Marga Giménez ◽  
Ignacio Conget ◽  
Jorge Bondia ◽  
...  
Keyword(s):  
Data Analysis ◽  
Compositional Data ◽  
Glucose Monitoring ◽  
Glucose Variability ◽  
Compositional Data Analysis ◽  
Relative Information ◽  
Glucose Profiles ◽  
Patient Groups ◽  
The Times

The aim of this study was to apply a methodology based on compositional data analysis (CoDA) to categorise glucose profiles obtained from continuous glucose monitoring systems. The methodology proposed considers complete daily glucose profiles obtained from six patients with type 1 diabetes (T1D) who had their glucose monitored for eight weeks. The glucose profiles were distributed into the time spent in six different ranges. The time in one day is finite and limited to 24 h, and the times spent in each of these different ranges are co-dependent and carry only relative information; therefore, CoDA is applied to these profiles. A K-means algorithm was applied to the coordinates obtained from the CoDA to obtain different patterns of days for each patient. Groups of days with relatively high time in the hypo and/or hyperglycaemic ranges and with different glucose variability were observed. Using CoDA of time in different ranges, individual glucose profiles were categorised into groups of days, which can be used by physicians to detect the different conditions of patients and personalise patient's insulin therapy according to each group. This approach can be useful to assist physicians and patients in managing the day-to-day variability that hinders glycaemic control.

scholarly journals Representation Lost: The Case for a Relational Interpretation of Quantum Mechanics

Entropy ◽  
2018 ◽  
Vol 20 (12) ◽  
pp. 975 ◽  
Author(s):  
Raffael Krismer
Keyword(s):  
Thought Experiment ◽  
Dynamical Evolution ◽  
Bayesian Probability ◽  
Special Focus ◽  
Probability Models ◽  
Classical Probability ◽  
Unitary Evolution ◽  
Relative Information ◽  
Mechanical Analogue ◽  
Argument Proceeds

Contemporary non-representationalist interpretations of the quantum state (especially QBism, neo-Copenhagen views, and the relational interpretation) maintain that quantum states codify observer-relative information. This paper provides an extensive defense of such views, while emphasizing the advantages of, specifically, the relational interpretation. The argument proceeds in three steps: (1) I present a classical example (which exemplifies the spirit of the relational interpretation) to illustrate why some of the most persistent charges against non-representationalism have been misguided. (2) The special focus is placed on dynamical evolution. Non-representationalists often motivate their views by interpreting the collapse postulate as the quantum mechanical analogue of Bayesian probability updating. However, it is not clear whether one can also interpret the Schrödinger equation as a form of rational opinion updating. Using results due to Hughes & van Fraassen as well as Lisi, I argue that unitary evolution has a counterpart in classical probability theory: in both cases (quantum and classical) probabilities relative to a non-participating observer evolve according to an entropy maximizing principle (and can be interpreted as rational opinion updating). (3) Relying on a thought-experiment by Frauchiger and Renner, I discuss the differences between quantum and classical probability models.

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