scholarly journals A Mathematical Analysis of the Card Game of Betweenies through Kelly's Criterion

2010 ◽  
Vol 2010 ◽  
pp. 1-19
Author(s):  
Konstantinos Drakakis
Keyword(s):  
Mathematical Analysis ◽  
Direct Approach ◽  
Card Game ◽  
Information Theoretic ◽  
The Third ◽  
Theoretic Technique

In the game of Betweenies, the player is dealt two cards out of a deck and bets on the probability that the third card to be dealt will have a numerical value in between the values of the first two cards. In this work, we present the exact rules of the two main versions of the game, and we study the optimal betting strategies. After discussing the shortcomings of the direct approach, we introduce an information-theoretic technique, Kelly's criterion, which basically maximizes the expected log-return of the bet: we offer an overview, discuss feasibility issues, and analyze the strategies it suggests. We also provide some gameplay simulations.

scholarly journals Entrack: Probabilistic Spherical Regression with Entropy Regularization for Fiber Tractography

2020 ◽  
Author(s):  
Viktor Wegmayr ◽  
Joachim M. Buhmann
Keyword(s):  
Brain Connectivity ◽  
Magnetic Resonance Images ◽  
Probabilistic Methods ◽  
Fiber Tractography ◽  
Information Theoretic ◽  
Spherical Regression ◽  
Theoretic Technique ◽  
White Matter Tractography ◽  
Von Mises

Abstract White matter tractography, based on diffusion-weighted magnetic resonance images, is currently the only available in vivo method to gather information on the structural brain connectivity. The low resolution of diffusion MRI data suggests to employ probabilistic methods for streamline reconstruction, i.e., for fiber crossings. We propose a general probabilistic model for spherical regression based on the Fisher-von-Mises distribution, which efficiently estimates maximum entropy posteriors of local streamline directions with machine learning methods. The optimal precision of posteriors for streamlines is determined by an information-theoretic technique, the expected log-posterior agreement concept. It relies on the requirement that the posterior distributions of streamlines, inferred on retest measurements of the same subject, should yield stable results within the precision determined by the noise level of the data source.

An information theoretic technique to design belief network based expert systems

1996 ◽  
Vol 17 (1) ◽  
pp. 13-30 ◽  
Author(s):  
Sumit Sarkar ◽  
Ram S. Sriram ◽  
Shibu Joykutty ◽  
Ishwar Murthy
Keyword(s):  
Expert Systems ◽  
Information Theoretic ◽  
Belief Network ◽  
Theoretic Technique

Questions of generality as probes into nineteenth-century mathematical analysis

2017 ◽  
Author(s):  
Renaud Chorlay
Keyword(s):  
Nineteenth Century ◽  
Set Theory ◽  
Mathematical Analysis ◽  
Analytic Functions ◽  
Function Theory ◽  
The Third ◽  
Point Set

This article examines ways of expressing generality and epistemic configurations in which generality issues became intertwined with epistemological topics, such as rigor, or mathematical topics, such as point-set theory. In this regard, three very specific configurations are discussed: the first evolving from Niels Henrik Abel to Karl Weierstrass, the second in Joseph-Louis Lagrange’s treatises on analytic functions, and the third in Emile Borel. Using questions of generality, the article first compares two major treatises on function theory, one by Lagrange and one by Augustin Louis Cauchy. It then explores how some mathematicians adopted the sophisticated point-set theoretic tools provided for by the advocates of rigor to show that, in some way, Lagrange and Cauchy had been right all along. It also introduces the concept of embedded generality for capturing an approach to generality issues that is specific to mathematics.

scholarly journals The Demonstration of Antibodies in the Intestinal Mucus of Sheep Infected with Oesophagostomum Columbianum by Means of the Percutaneous Anaphylaxis Test

1966 ◽  
Vol 19 (2) ◽  
pp. 339 ◽  
Author(s):  
C Dobson
Keyword(s):  
Immune Response ◽  
Direct Evidence ◽  
Direct Approach ◽  
The Third ◽  
Intestinal Mucus ◽  
Helminth Infections ◽  
Oesophagostomum Columbianum ◽  
Third Stage

There is little evidence in the literature that a direct approach has been made to the demonstration of antibodies against helminth infections in mucus (Pierce 1959; Soulsby 1960). Soulsby attempted to detect these antibodies in intestinal mucus with haemagglutinating techniques but had no success. Less direct evidence is available, however, for the existence of immune substances in the intestinal mucus of infected animals, because Douvres (1962) has reported the existence of in vitro precipitin reactions against the third-stage and third-moult phase larvae of Oesophagostomum radiatum using intestinal extracts from infected calves. Similarly the hypertrophy of lymphoid (Soulsby 1962) and mucin (Wells 1963) cells within the intestinal tissues during nematode infections is indicative of an immune response.

scholarly journals Impossibility of blind quantum sampling for classical client

2019 ◽  
Vol 19 (9&10) ◽  
pp. 793-806
Author(s):  
Tomoyuki Morimae ◽  
Harumichi Nishimura ◽  
Yuki Takeuch ◽  
Seiichiro Tani
Keyword(s):  
Quantum Computing ◽  
Polynomial Time ◽  
Open Problem ◽  
Input Output ◽  
Information Theoretic ◽  
Single Qubit ◽  
The Third ◽  
The One ◽  
Qubit States ◽  
Polynomial Time Hierarchy

Blind quantum computing enables a client, who can only generate or measure single-qubit states, to delegate quantum computing to a remote quantum server in such a way that the input, output, and program are hidden from the server. It is an open problem whether a completely classical client can delegate quantum computing blindly (in the information theoretic sense). In this paper, we show that if a completely classical client can blindly delegate sampling of subuniversal models, such as the DQC1 model and the IQP model, then the polynomial-time hierarchy collapses to the third level. Our delegation protocol is the one where the client first sends a polynomial-length bit string to the server and then the server returns a single bit to the client. Generalizing the no-go result to more general setups is an open problem.

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