Entropy and conditional entropy

Author(s):  
Meir Smorodinsky
Keyword(s):  
Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 286
Author(s):  
Soheil Keshmiri

Recent decades have witnessed a substantial progress in the utilization of brain activity for the identification of stress digital markers. In particular, the success of entropic measures for this purpose is very appealing, considering (1) their suitability for capturing both linear and non-linear characteristics of brain activity recordings and (2) their direct association with the brain signal variability. These findings rely on external stimuli to induce the brain stress response. On the other hand, research suggests that the use of different types of experimentally induced psychological and physical stressors could potentially yield differential impacts on the brain response to stress and therefore should be dissociated from more general patterns. The present study takes a step toward addressing this issue by introducing conditional entropy (CE) as a potential electroencephalography (EEG)-based resting-state digital marker of stress. For this purpose, we use the resting-state multi-channel EEG recordings of 20 individuals whose responses to stress-related questionnaires show significantly higher and lower level of stress. Through the application of representational similarity analysis (RSA) and K-nearest-neighbor (KNN) classification, we verify the potential that the use of CE can offer to the solution concept of finding an effective digital marker for stress.


Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 378
Author(s):  
Taeyong Kwon ◽  
Seongsim Yoon ◽  
Sanghoo Yoon

Uncertainty in the rainfall network can lead to mistakes in dam operation. Sudden increases in dam water levels due to rainfall uncertainty are a high disaster risk. In order to prevent these losses, it is necessary to configure an appropriate rainfall network that can effectively reflect the characteristics of the watershed. In this study, conditional entropy was used to calculate the uncertainty of the watershed using rainfall and radar data observed from 2018 to 2019 in the Goesan Dam and Hwacheon Dam watersheds. The results identified radar data suitable for the characteristics of the watershed and proposed a site for an additional rainfall gauge. It is also necessary to select the location of the additional rainfall gauged by limiting the points where smooth movement and installation, for example crossing national borders, are difficult. The proposed site emphasized accessibility and usability by leveraging road information and selecting a radar grid near the road. As a practice result, the uncertainty of precipitation in the Goesan and Hwacheon Dam watersheds could be decreased by 70.0% and 67.9%, respectively, when four and three additional gauge sites were installed without any restriction. When these were installed near to the road, with five and four additional gauge sites, the uncertainty in the Goesan Dam and Hwacheon Dam watersheds were reduced by up to 71.1%. Therefore, due to the high degree of uncertainty, it is necessary to measure precipitation. The operation of the rainfall gauge can provide a smooth site and configure an appropriate monitoring network.


2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Peter Brown ◽  
Hamza Fawzi ◽  
Omar Fawzi

AbstractThe rates of quantum cryptographic protocols are usually expressed in terms of a conditional entropy minimized over a certain set of quantum states. In particular, in the device-independent setting, the minimization is over all the quantum states jointly held by the adversary and the parties that are consistent with the statistics that are seen by the parties. Here, we introduce a method to approximate such entropic quantities. Applied to the setting of device-independent randomness generation and quantum key distribution, we obtain improvements on protocol rates in various settings. In particular, we find new upper bounds on the minimal global detection efficiency required to perform device-independent quantum key distribution without additional preprocessing. Furthermore, we show that our construction can be readily combined with the entropy accumulation theorem in order to establish full finite-key security proofs for these protocols.


2014 ◽  
Vol 269 ◽  
pp. 94-102 ◽  
Author(s):  
Anton M. Unakafov ◽  
Karsten Keller

Optik ◽  
2014 ◽  
Vol 125 (15) ◽  
pp. 3946-3953 ◽  
Author(s):  
Fei Hao ◽  
Jinfei Shi ◽  
Zhisheng Zhang ◽  
Ruwen Chen ◽  
Songqing Zhu

2014 ◽  
Vol 17 (03n04) ◽  
pp. 1450016 ◽  
Author(s):  
V. I. YUKALOV ◽  
D. SORNETTE

The idea is advanced that self-organization in complex systems can be treated as decision making (as it is performed by humans) and, vice versa, decision making is nothing but a kind of self-organization in the decision maker nervous systems. A mathematical formulation is suggested based on the definition of probabilities of system states, whose particular cases characterize the probabilities of structures, patterns, scenarios, or prospects. In this general framework, it is shown that the mathematical structures of self-organization and of decision making are identical. This makes it clear how self-organization can be seen as an endogenous decision making process and, reciprocally, decision making occurs via an endogenous self-organization. The approach is illustrated by phase transitions in large statistical systems, crossovers in small statistical systems, evolutions and revolutions in social and biological systems, structural self-organization in dynamical systems, and by the probabilistic formulation of classical and behavioral decision theories. In all these cases, self-organization is described as the process of evaluating the probabilities of macroscopic states or prospects in the search for a state with the largest probability. The general way of deriving the probability measure for classical systems is the principle of minimal information, that is, the conditional entropy maximization under given constraints. Behavioral biases of decision makers can be characterized in the same way as analogous to quantum fluctuations in natural systems.


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