Relevant bibliographies by topics / Entropic uncertainty

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
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Academic literature on the topic 'Entropic uncertainty'

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Published: 1 April 2023

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Journal articles on the topic "Entropic uncertainty"

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Li, Li-Juan, Fei Ming, Xue-Ke Song, Liu Ye, and Dong Wang. "Review on entropic uncertainty relations." Acta Physica Sinica 71, no. 7 (2022): 070302. http://dx.doi.org/10.7498/aps.71.20212197.

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The Heisenberg uncertainty principle is one of the characteristics of quantum mechanics. With the vigorous development of quantum information theory, uncertain relations have gradually played an important role in it. In particular, in order to solved the shortcomings of the concept in the initial formulation of the uncertainty principle, we brought entropy into the uncertainty relation, after that, the entropic uncertainty relation has exploited the advantages to the full in various applications. As we all know the entropic uncertainty relation has became the core element of the security analysis of almost all quantum cryptographic protocols. This review mainly introduces development history and latest progress of uncertain relations. After Heisenberg's argument that incompatible measurement results are impossible to predict, many scholars, inspired by this viewpoint, have made further relevant investigations. They combined the quantum correlation between the observable object and its environment, and carried out various generalizations of the uncertainty relation to obtain more general formulas. In addition, it also focuses on the entropy uncertainty relationship and quantum-memory-assisted entropic uncertainty relation, and the dynamic characteristics of uncertainty in some physical systems. Finally, various applications of the entropy uncertainty relationship in the field of quantum information are discussed, from randomnesss to wave-particle duality to quantum key distribution.
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Majerník, V., and L. Richterek. "Entropic uncertainty relations." European Journal of Physics 18, no. 2 (March 1, 1997): 79–89. http://dx.doi.org/10.1088/0143-0807/18/2/005.

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Costa, Ana, Roope Uola, and Otfried Gühne. "Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems." Entropy 20, no. 10 (October 5, 2018): 763. http://dx.doi.org/10.3390/e20100763.

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The effect of quantum steering describes a possible action at a distance via local measurements. Whereas many attempts on characterizing steerability have been pursued, answering the question as to whether a given state is steerable or not remains a difficult task. Here, we investigate the applicability of a recently proposed method for building steering criteria from generalized entropic uncertainty relations. This method works for any entropy which satisfy the properties of (i) (pseudo-) additivity for independent distributions; (ii) state independent entropic uncertainty relation (EUR); and (iii) joint convexity of a corresponding relative entropy. Our study extends the former analysis to Tsallis and Rényi entropies on bipartite and tripartite systems. As examples, we investigate the steerability of the three-qubit GHZ and W states.
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Hsu, Li-Yi, Shoichi Kawamoto, and Wen-Yu Wen. "Entropic uncertainty relation based on generalized uncertainty principle." Modern Physics Letters A 32, no. 28 (September 4, 2017): 1750145. http://dx.doi.org/10.1142/s0217732317501450.

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We explore the modification of the entropic formulation of uncertainty principle in quantum mechanics which measures the incompatibility of measurements in terms of Shannon entropy. The deformation in question is the type so-called generalized uncertainty principle that is motivated by thought experiments in quantum gravity and string theory and is characterized by a parameter of Planck scale. The corrections are evaluated for small deformation parameters by use of the Gaussian wave function and numerical calculation. As the generalized uncertainty principle has proven to be useful in the study of the quantum nature of black holes, this study would be a step toward introducing an information theory viewpoint to black hole physics.
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SANTOS, M. A., and I. V. VANCEA. "ENTROPIC LAW OF FORCE, EMERGENT GRAVITY AND THE UNCERTAINTY PRINCIPLE." Modern Physics Letters A 27, no. 02 (January 20, 2012): 1250012. http://dx.doi.org/10.1142/s0217732312500125.

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The entropic formulation of the inertia and the gravity relies on quantum, geometrical and informational arguments. The fact that the results are completely classical is misleading. In this paper, we argue that the entropic formulation provides new insights into the quantum nature of the inertia and the gravity. We use the entropic postulate to determine the quantum uncertainty in the law of inertia and in the law of gravity in the Newtonian Mechanics, the Special Relativity and in the General Relativity. These results are obtained by considering the most general quantum property of the matter represented by the Uncertainty Principle and by postulating an expression for the uncertainty of the entropy such that: (i) it is the simplest quantum generalization of the postulate of the variation of the entropy and (ii) it reduces to the variation of the entropy in the absence of the uncertainty.
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Puchała, Zbigniew, Łukasz Rudnicki, and Karol Życzkowski. "Majorization entropic uncertainty relations." Journal of Physics A: Mathematical and Theoretical 46, no. 27 (June 21, 2013): 272002. http://dx.doi.org/10.1088/1751-8113/46/27/272002.

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Maassen, Hans, and J. B. M. Uffink. "Generalized entropic uncertainty relations." Physical Review Letters 60, no. 12 (March 21, 1988): 1103–6. http://dx.doi.org/10.1103/physrevlett.60.1103.

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Adamczak, Radosław, Rafał Latała, Zbigniew Puchała, and Karol Życzkowski. "Asymptotic entropic uncertainty relations." Journal of Mathematical Physics 57, no. 3 (March 2016): 032204. http://dx.doi.org/10.1063/1.4944425.

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Khedr, Ahmad N., Abdel-Baset A. Mohamed, Abdel-Haleem Abdel-Aty, Mahmoud Tammam, Mahmoud Abdel-Aty, and Hichem Eleuch. "Entropic Uncertainty for Two Coupled Dipole Spins Using Quantum Memory under the Dzyaloshinskii–Moriya Interaction." Entropy 23, no. 12 (November 28, 2021): 1595. http://dx.doi.org/10.3390/e23121595.

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In the thermodynamic equilibrium of dipolar-coupled spin systems under the influence of a Dzyaloshinskii–Moriya (D–M) interaction along the z-axis, the current study explores the quantum-memory-assisted entropic uncertainty relation (QMA-EUR), entropy mixedness and the concurrence two-spin entanglement. Quantum entanglement is reduced at increased temperature values, but inflation uncertainty and mixedness are enhanced. The considered quantum effects are stabilized to their stationary values at high temperatures. The two-spin entanglement is entirely repressed if the D–M interaction is disregarded, and the entropic uncertainty and entropy mixedness reach their maximum values for equal coupling rates. Rather than the concurrence, the entropy mixedness can be a proper indicator of the nature of the entropic uncertainty. The effect of model parameters (D–M coupling and dipole–dipole spin) on the quantum dynamic effects in thermal environment temperature is explored. The results reveal that the model parameters cause significant variations in the predicted QMA-EUR.
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Rudnicki, Łukasz. "Uncertainty-reality complementarity and entropic uncertainty relations." Journal of Physics A: Mathematical and Theoretical 51, no. 50 (November 20, 2018): 504001. http://dx.doi.org/10.1088/1751-8121/aaecf5.

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Dissertations / Theses on the topic "Entropic uncertainty"

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Hertz, Anaëlle. "Exploring continuous-variable entropic uncertainty relations and separability criteria in quantum phase space." Doctoral thesis, Universite Libre de Bruxelles, 2018. https://dipot.ulb.ac.be/dspace/bitstream/2013/267632/5/ContratAH.pdf.

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The uncertainty principle lies at the heart of quantum physics. It exhibits one of the key divergences between a classical and a quantum system: it is impossible to define a quantum state for which the values of two observables that do not commute are simultaneously specified with infinite precision. A paradigmatic example is given by Heisenberg’s original formulation of the uncertainty principle expressed in terms of variances of two canonically-conjugate variables, such as position x and momentum p, which was later generalized to a symplectic-invariant form by Schrödinger and Robertson. A different kind of uncertainty relations, originated by Białynicki-Birula and Mycielski, again for canonically-conjugate variables, relies on Shannon entropy instead of variances as a measure of uncertainty. In this thesis, we suggest several improvements of these entropic uncertainty relations and highlight the fact that they are better formulated in terms of entropy power, a notion borrowed from the information theory of real-valued signals. Our first novel entropic uncertainty relation takes x-p correlations into account and is consequently saturated by all pure Gaussian states in an arbitrary number of modes, improving on the original formulation by Białynicki-Birula and Mycielski. Our second main result is the derivation of an entropic uncertainty relation that holds for any n-tuples of not-necessarily canonically conjugate variables based on the matrix of their commutators. We then define a general form of the entropic uncertainty principle that combines both previous results. It expresses the incompatibility between two arbitrary variable n-uples and is saturated by all pure Gaussian states. Interestingly, we can also deduce from it the most general form of the Robertson uncertainty relation based on the covariance matrix of n variables.This line of research underlines the interest of defining an entropic uncertainty relation that is intrinsically invariant under symplectic transformations. Then, as a first attempt to reach this goal, we conjecture a symplectic-invariant uncertainty relation that is based on the joint differential entropy of the Wigner function. This conjecture is, however, only legitimate for states with a non-negative Wigner function. We also suggest a complex extension of this so-called Wigner entropy, which could provide the way towards an extension (and proof) of the above conjecture for all states. As a second attempt, we introduce the notion of multi-copy uncertainty observables, exploiting a connection with the algebra of angular momenta. Expressing the positivity of the variance of our multi-copy observable coincides with the Schrödinger-Robertson uncertainty relation, which suggests that the discrete Shannon entropy of such an uncertainty observable provides a new symplectic-invariant measure of uncertainty.Currently available separability criteria for continuous-variable systems imply a necessary and sufficient condition for a two-mode Gaussian state to be separable, but leave many entangled non-Gaussian states undetected. In this thesis, we introduce two improved separability criteria that enable a stronger entanglement detection. The first improved condition is based on the knowledge of an additional parameter, namely the degree of Gaussianity, and exploits a connection with Gaussianity-bounded uncertainty relations by Mandilara and Cerf. We exhibit families of non- Gaussian entangled states whose entanglement remains undetected by the Duan- Simon criterion. The second improved separability criterion is based on our improved entropic uncertainty relation that takes x-p correlations into account, and has the main advantage over the one proposed by Walborn et al. that it does not require any optimization procedure.
Le principe d’incertitude se situe au cœur de la physique quantique. Il représente l’une des différences majeures entre des systèmes classiques et quantiques, soit qu’il est impossible de définir un état quantique pour lequel deux observables qui ne commutent pas auraient des valeurs spécifiées simultanément et avec une précision infinie. La formulation originale du principe d’incertitude est due à Heisenberg et est exprimée en termes des variances de deux variables canoniquement conjuguées, telles que la position x et l’impulsion p. Cela fut par la suite généralisé par Schrödinger et Robertson qui ont donné au principe d’incertitude une forme invariante sous transformations symplectiques. Si l’incertitude est mesurée à l’aide de l’entropie différentielle de Shannon plutôt que des variances, il est alors possible de définir d’autres types de relations d’incertitude. Originellement introduites par Białynicki-Birula et Mycielski, elles expriment également l’incompatibilité entre deux variables canoniquement conjuguées. Dans cette thèse, nous proposons différentes améliorations de ces relations d’incertitude entropiques et mettons particulièrement l’accent sur le fait qu’elles s’expriment mieux sous forme de puissances entropiques, une notion empruntée à la théorie de l’information. En premier lieu, nous introduisons une nouvelle relation d’incertitude entropique qui tient compte des corrélations x-p et qui est par conséquent saturée par tous les états purs Gaussiens, ce qui représente une amélioration par rapport à la formulation originale de Białynicki- Birula et Mycielski. En second lieu, nous dérivons une relation d’incertitude entropique valide pour tous les n-uplets de variables non nécessairement canoniquement conjuguées et basée sur la matrice de leurs commutateurs. Nous définissons ensuite une forme plus générale du principe d’incertitude entropique qui combine les deux résultats précédents. Il exprime l’incompatibilité entre deux n-uplets arbitraires de variables et est saturé par tous les états purs Gaussiens. Notons que de ce principe d’incertitude entropique, nous pouvons déduire la forme la plus générale de la relation d’incertitude de Robertson, basée sur la matrice de covariance de n variables. Les résultats précédents soulignent un des points essentiels de notre axe de recherche: définir une relation d’incertitude entropique intrinsèquement invariante sous trans- formations symplectiques. Afin d’atteindre cet objectif, notre première tentative est de conjecturer une relation d’incertitude — invariante sous transformations symplectiques — basée sur l’entropie différentielle jointe de la fonction de Wigner. Cette conjecture n’est cependant légitime que pour des états décrits par une fonction de Wigner non-négative. Nous proposons aussi une extension complexe de cette en- tropie dite entropie de Wigner, qui pourrait ouvrir la voie vers une extension (et une preuve) de la conjecture proposée ci-dessus qui serait alors valide pour tous les états quantiques. Comme seconde tentative, en exploitant une connexion avec l’algèbre des moments angulaires, nous introduisons la notion d’observables d’incertitude agissant sur plusieurs copies d’un état. Exprimer la positivité de la variance de notre observable coïncide avec la relation d’incertitude de Schrödinger-Robertson, ce qui suggère que l’entropie discrète de Shannon d’une telle observable fournit une nouvelle mesure de l’incertitude. Cette relation d’incertitude est invariante sous transformations symplectiques.Les critères de séparabilité actuellement disponibles pour les variables continues donnent une condition nécessaire et suffisante afin qu’un état Gaussien bimodal soit séparable, mais laissent de nombreux états intriqués non-Gaussiens non détectés. Dans cette thèse, nous introduisons deux nouveaux critères de séparabilité qui permettent une meilleure détection de l’intrication. La première nouvelle condition est basée sur la connaissance d’un paramètre supplémentaire, à savoir le degré de Gaussianité de l’état, et exploite une connexion avec les relations d’incertitude de Mandilara et Cerf bornées par ce degré de Gaussianité. En particulier, nous donnons l’exemple de familles d’états intriqués non Gaussiens dont l’intrication est détectée par notre critère, mais pas par celui de Duan-Simon. Le second critère de séparabil- ité entropique que nous proposons est basé sur notre nouvelle relation d’incertitude entropique qui tient compte des corrélations x-p. Son principal avantage par rapport au critère de Walborn et al. est de ne nécessiter aucune procédure d’optimisation.
Doctorat en Sciences de l'ingénieur et technologie
info:eu-repo/semantics/nonPublished
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Rybokas, Mindaugas. "The information analysis and the research on entropy for measurement data." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2006. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2006~D_20060928_151951-20485.

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Information entropy parameter has been applied for an expression of the result of data assessment and it is supplemented by an index of sample of data that was evaluated out of set of information. A modelling system and software have been developed that can be used and are used for practical processing of measurement data for circular raster scales.
Duomenų įverčiui išreikšti pritaikytas informacinės entropijos parametras pateiktoje rezultato išraiškoje yra papildytas rodikliu apie duomenų imtį, kuri buvo įvertinta iš visos šį objektą charakterizuojančių duomenų aibės. Sukurta modeliavimo sistema ir programinė įranga gali būti naudojama didelio skaičiaus nežinomųjų lygtims spręsti, o praktikoje naudojama rastrinių skalių matavimo duomenims apdoroti.
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Vanslette, Kevin M. "Theoretical Study of Variable Measurement Uncertainty h_I and Infinite Unobservable Entropy." Digital WPI, 2013. https://digitalcommons.wpi.edu/etd-theses/289.

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This paper examines the statistical mechanical and thermodynamical consequences of variable phase-space volume element $h_I=?igtriangleup x_i?igtriangleup p_i$. Varying $h_I$ leads to variations in the amount of measured entropy of a system but the maximum entropy remains constant due to the uncertainty principle. By taking $h_u ightarrow 0^+$ an infinite unobservable entropy is attained leading to an infinite unobservable energy per particle and an unobservable chemical equilibrium between all particles. The amount of heat fluxing though measurement apparatus is formulated as a function of $h_I$ for systems in steady state equilibrium as well as the number of measured particles or sub-particles so any system can be described as unitary or composite in number. Some example systems are given using variable $h_I$.
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Kane, Thomas Brett. "Reasoning with uncertainty using Nilsson's probabilistic logic and the maximum entropy formalism." Thesis, Heriot-Watt University, 1992. http://hdl.handle.net/10399/789.

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Yassin-Kassab, Abdullah. "Entropy-based inference and calibration methods for civil engineering system models under uncertainty." Thesis, University of Liverpool, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.367272.

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Mujumdar, Anusha Pradeep. "Cross entropy-based analysis of spacecraft control systems." Thesis, University of Exeter, 2016. http://hdl.handle.net/10871/28006.

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Space missions increasingly require sophisticated guidance, navigation and control algorithms, the development of which is reliant on verification and validation (V&V) techniques to ensure mission safety and success. A crucial element of V&V is the assessment of control system robust performance in the presence of uncertainty. In addition to estimating average performance under uncertainty, it is critical to determine the worst case performance. Industrial V&V approaches typically employ mu-analysis in the early control design stages, and Monte Carlo simulations on high-fidelity full engineering simulators at advanced stages of the design cycle. While highly capable, such techniques present a critical gap between pessimistic worst case estimates found using analytical methods, and the optimistic outlook often presented by Monte Carlo runs. Conservative worst case estimates are problematic because they can demand a controller redesign procedure, which is not justified if the poor performance is unlikely to occur. Gaining insight into the probability associated with the worst case performance is valuable in bridging this gap. It should be noted that due to the complexity of industrial-scale systems, V&V techniques are required to be capable of efficiently analysing non-linear models in the presence of significant uncertainty. As well, they must be computationally tractable. It is desirable that such techniques demand little engineering effort before each analysis, to be applied widely in industrial systems. Motivated by these factors, this thesis proposes and develops an efficient algorithm, based on the cross entropy simulation method. The proposed algorithm efficiently estimates the probabilities associated with various performance levels, from nominal performance up to degraded performance values, resulting in a curve of probabilities associated with various performance values. Such a curve is termed the probability profile of performance (PPoP), and is introduced as a tool that offers insight into a control system's performance, principally the probability associated with the worst case performance. The cross entropy-based robust performance analysis is implemented here on various industrial systems in European Space Agency-funded research projects. The implementation on autonomous rendezvous and docking models for the Mars Sample Return mission constitutes the core of the thesis. The proposed technique is implemented on high-fidelity models of the Vega launcher, as well as on a generic long coasting launcher upper stage. In summary, this thesis (a) develops an algorithm based on the cross entropy simulation method to estimate the probability associated with the worst case, (b) proposes the cross entropy-based PPoP tool to gain insight into system performance, (c) presents results of the robust performance analysis of three space industry systems using the proposed technique in conjunction with existing methods, and (d) proposes an integrated template for conducting robust performance analysis of linearised aerospace systems.
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Lamba, Amrita. "The Effects of Uncertainty on Cooperation: using Bayesian Cognition and Entropy to Model Cooperative Heuristics." W&M ScholarWorks, 2017. https://scholarworks.wm.edu/etd/1516639680.

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Cooperative heuristics have traditionally been researched through the lens of standard dual-process models of cognition and from the perspective of evolutionary psychology. Despite the popularity of these approaches, research on intuitive versus extensional processing falls short in its endeavor to methodologically quantify heuristic processing and to empirically validate existing theories of social evaluation. Furthermore, several conceptualizations of the term heuristic have been proposed in the social psychology literature, leading to a lack of consensus on how cooperative heuristics function. to address these issues, the current study proposes a novel method for quantifying heuristic cognition. We propose a Bayesian cognition model of heuristics based on the free energy principle and present a framework for defining heuristics as Bayesian priors. to test our model, we ran an experiment on Amazon Mechanical Turk and used a modified version of the Prisoner’s Dilemma game. Overall, the results of experiment supported our theoretical predictions and our quantitative model of cooperative heuristics. Additionally, we found evidence to suggest that men and women respond differently to social uncertainty in cooperative exchanges.
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Johansson, Mathias. "Resource Allocation under Uncertainty : Applications in Mobile Communications." Doctoral thesis, Uppsala University, Signals and Systems Group, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-4559.

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This thesis is concerned with scheduling the use of resources, or allocating resources, so as to meet future demands for the entities produced by the resources. We consider applications in mobile communications such as scheduling users' transmissions so that the amount of transmitted information is maximized, and scenarios in the manufacturing industry where the task is to distribute work among production units so as to minimize the number of missed orders.

The allocation decisions are complicated by a lack of information concerning the future demand and possibly also about the capacities of the available resources. We therefore resort to using probability theory and the maximum entropy principle as a means for making rational decisions under uncertainty.

By using probabilities interpreted as a reasonable degree of belief, we find optimum decision rules for the manufacturing problem, bidding under uncertainty in a certain type of auctions, scheduling users in communications with uncertain channel qualities and uncertain arrival rates, quantization of channel information, partitioning bandwidth between interfering and non-interfering areas in cellular networks, hand-overs and admission control. Moreover, a new method for making optimum approximate Bayesian inference is introduced.

We further discuss reasonable optimization criteria for the mentioned applications, and provide an introduction to the topic of probability theory as an extension to two-valued logic. It is argued that this view unifies a wide range of resource-allocation problems, and we discuss various directions for further research.

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Boidol, Jonathan [Verfasser], and Volker [Akademischer Betreuer] Tresp. "Monitoring data streams : Classification under uncertainty and entropy-based dependency-detection on streaming data / Jonathan Boidol ; Betreuer: Volker Tresp." München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2017. http://d-nb.info/1139977768/34.

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Xie, Li Information Technology &amp Electrical Engineering Australian Defence Force Academy UNSW. "Finite horizon robust state estimation for uncertain finite-alphabet hidden Markov models." Awarded by:University of New South Wales - Australian Defence Force Academy. School of Information Technology and Electrical Engineering, 2004. http://handle.unsw.edu.au/1959.4/38664.

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In this thesis, we consider a robust state estimation problem for discrete-time, homogeneous, first-order, finite-state finite-alphabet hidden Markov models (HMMs). Based on Kolmogorov's Theorem on the existence of a process, we first present the Kolmogorov model for the HMMs under consideration. A new change of measure is introduced. The statistical properties of the Kolmogorov representation of an HMM are discussed on the canonical probability space. A special Kolmogorov measure is constructed. Meanwhile, the ergodicity of two expanded Markov chains is investigated. In order to describe the uncertainty of HMMs, we study probability distance problems based on the Kolmogorov model of HMMs. Using a change of measure technique, the relative entropy and the relative entropy rate as probability distances between HMMs, are given in terms of the HMM parameters. Also, we obtain a new expression for a probability distance considered in the existing literature such that we can use an information state method to calculate it. Furthermore, we introduce regular conditional relative entropy as an a posteriori probability distance to measure the discrepancy between HMMs when a realized observation sequence is given. A representation of the regular conditional relative entropy is derived based on the Radon-Nikodym derivative. Then a recursion for the regular conditional relative entropy is obtained using an information state method. Meanwhile, the well-known duality relationship between free energy and relative entropy is extended to the case of regular conditional relative entropy given a sub-[special character]-algebra. Finally, regular conditional relative entropy constraints are defined based on the study of the probability distance problem. Using a Lagrange multiplier technique and the duality relationship for regular conditional relative entropy, a finite horizon robust state estimator for HMMs with regular conditional relative entropy constraints is derived. A complete characterization of the solution to the robust state estimation problem is also presented.
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Books on the topic "Entropic uncertainty"

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Jessop, Alan. Informed assessments: An introduction to information, entropy, and statistics. New York: Ellis Horwood, 1995.

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Jessop, A. Informed assessments: An introduction to information, entropy and statistics. New York: Ellis Horwood, 1995.

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Watts, Barry D. Clausewitzian friction and future war. Washington, D.C: Institute for National Strategic Studies, National Defense University, 1996.

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Watts, Barry D. Clausewitzian friction and future war. Washington, D.C: Institute for National Strategic Studies, National Defense University, 1996.

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Watts, Barry D. Clausewitzian friction and future war. Washington, D.C: Institute for National Strategic Studies, National Defense University, 2004.

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Entropic Tokyo: Metropolis of Uncertainty, Multiplicity and Flexibility. LetteraVentidue Edizioni, 2021.

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Golan, Amos. The Metrics of Info-Metrics. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780199349524.003.0003.

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In this chapter I present the key ideas and develop the essential quantitative metrics needed for modeling and inference with limited information. I provide the necessary tools to study the traditional maximum-entropy principle, which is the cornerstone for info-metrics. The chapter starts by defining the primary notions of information and entropy as they are related to probabilities and uncertainty. The unique properties of the entropy are explained. The derivations and discussion are extended to multivariable entropies and informational quantities. For completeness, I also discuss the complete list of the Shannon-Khinchin axioms behind the entropy measure. An additional derivation of information and entropy, due to the independently developed work of Wiener, is provided as well.
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Nizami, Iftikhar R. *. Uncertainty in psychophysics: evidence for the entropy theory of perception. 1988.

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Hackworth, John. Essay Concerning the History of Entropy and the Rise of Uncertainty. BookBaby, 2016.

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Rajagopal. Market Entropy: How to Manage Chaos and Uncertainty for Improved Organizational Performance. Business Expert Press, 2020.

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Book chapters on the topic "Entropic uncertainty"

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Ohya, Masanori, and Dénes Petz. "Entropic Uncertainty Relations." In Quantum Entropy and Its Use, 283–94. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-642-57997-4_17.

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Maassen, H. "A discrete entropic uncertainty relation." In Quantum Probability and Applications V, 263–66. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/bfb0085519.

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Blankenbecler, R., and M. H. Partovi. "Quantum Density Matrix and Entropic Uncertainty." In Maximum-Entropy and Bayesian Methods in Science and Engineering, 235–44. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-3049-0_11.

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Bialynicki-Birula, Iwo, and Łukasz Rudnicki. "Entropic Uncertainty Relations in Quantum Physics." In Statistical Complexity, 1–34. Dordrecht: Springer Netherlands, 2011. http://dx.doi.org/10.1007/978-90-481-3890-6_1.

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Bialynicki-Birula, Iwo. "Entropic uncertainty relations in quantum mechanics." In Quantum Probability and Applications II, 90–103. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/bfb0074463.

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Damgård, Ivan B., Serge Fehr, Renato Renner, Louis Salvail, and Christian Schaffner. "A Tight High-Order Entropic Quantum Uncertainty Relation with Applications." In Advances in Cryptology - CRYPTO 2007, 360–78. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-74143-5_20.

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Dias, José G. "Latent Class Models of Time Series Data: An Entropic-Based Uncertainty Measure." In Algorithms from and for Nature and Life, 205–14. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-00035-0_20.

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Bouman, Niek J., Serge Fehr, Carlos González-Guillén, and Christian Schaffner. "An All-But-One Entropic Uncertainty Relation, and Application to Password-Based Identification." In Theory of Quantum Computation, Communication, and Cryptography, 29–44. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-35656-8_3.

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Seidenfeld, Teddy. "Entropy and Uncertainty." In Advances in the Statistical Sciences: Foundations of Statistical Inference, 259–87. Dordrecht: Springer Netherlands, 1987. http://dx.doi.org/10.1007/978-94-009-4788-7_23.

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Bouchon-Meunier, Bernadette. "Uncertainty Management: Probability, Possibility, Entropy, and Other Paradigms." In Uncertainty Modeling, 53–60. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-51052-1_4.

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Conference papers on the topic "Entropic uncertainty"

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Man'ko, Margarita A., Guillaume Adenier, Andrei Yu Khrennikov, Pekka Lahti, Vladimir I. Man'ko, and Theo M. Nieuwenhuizen. "Tomographic Entropy and New Entropic Uncertainty Relations." In Quantum Theory. AIP, 2007. http://dx.doi.org/10.1063/1.2827295.

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Zozor, Steeve, Mariela Portesi, and Mariela Portesi. "Some entropic extensions of the uncertainty principle." In 2008 IEEE International Symposium on Information Theory Conference. IEEE, 2008. http://dx.doi.org/10.1109/isit.2008.4595273.

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Sen, Chiradeep, Farhad Ameri, and Joshua D. Summers. "Entropic Method for Sequencing Discrete Design Decisions." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-87600.

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Early stages of engineering design processes are characterized by high levels of uncertainty due to incomplete knowledge. As the design progresses, additional information is externally added or internally generated within the design process. As a result, the design solution becomes increasingly well-defined and the uncertainty of the problem reduces, diminishing to zero at the end of the process when the design is fully defined. In this research a measure of uncertainty is proposed for a class of engineering design problems called discrete design problems. Previously, three components of complexity in engineering design, namely, size, coupling and solvability, were identified. In this research uncertainty is measured in terms of the number of design variables (size) and the dependency between the variables (coupling). The solvability of each variable is assumed to be uniform for the sake of simplicity. The dependency between two variables is measured as the effect of a decision made on one variable on the solution options available to the other variable. A measure of uncertainty is developed based on this premise, and applied to an example problem to monitor uncertainty reduction through the design process. Results are used to identify and compare three task-sequencing strategies in engineering design.
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Krawec, Walter O. "A New High-Dimensional Quantum Entropic Uncertainty Relation with Applications." In 2020 IEEE International Symposium on Information Theory (ISIT). IEEE, 2020. http://dx.doi.org/10.1109/isit44484.2020.9174330.

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Nawaz, Shahid, and Ariel Caticha. "Momentum and uncertainty relations in the entropic approach to quantum theory." In BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING: 31st International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering. AIP, 2012. http://dx.doi.org/10.1063/1.3703627.

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Zozor, Steeve, and Christophe Vignat. "Non-Gaussian asymptotic minimizers in entropic uncertainty principles and the dimensional effect." In 2006 IEEE International Symposium on Information Theory. IEEE, 2006. http://dx.doi.org/10.1109/isit.2006.261918.

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Krawec, Walter O. "Key-Rate Bound of a Semi-Quantum Protocol Using an Entropic Uncertainty Relation." In 2018 IEEE International Symposium on Information Theory (ISIT). IEEE, 2018. http://dx.doi.org/10.1109/isit.2018.8437303.

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Li, M., N. Williams, and S. Azarm. "Interval Uncertainty Reduction and Single-Disciplinary Sensitivity Analysis With Multi-Objective Optimization." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86282.

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Sensitivity analysis has received significant attention in engineering design. While sensitivity analysis methods can be global, taking into account all variations, or local, taking into account small variations, they generally identify which uncertain parameters are most important and to what extent their effect might be on design performance. The extant methods do not, in general, tackle the question of which ranges of parameter uncertainty are most important or how to best allocate investments to partial uncertainty reduction in parameters under a limited budget. More specifically, no previous approach has been reported that can handle single-disciplinary multi-output global sensitivity analysis for both a single design and multiple designs under interval uncertainty. Two new global uncertainty metrics, i.e., radius of output sensitivity region and multi-output entropy performance, are presented. With these metrics, a multi-objective optimization model is developed and solved to obtain fractional levels of parameter uncertainty reduction that provide the greatest payoff in system performance for the least amount of “investment”. Two case studies of varying difficulty are presented to demonstrate the applicability of the proposed approach.
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Bialynicki-Birula, Iwo. "Rényi Entropy and the Uncertainty Relations." In FOUNDATIONS OF PROBABILITY AND PHYSICS - 4. AIP, 2007. http://dx.doi.org/10.1063/1.2713446.

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Timashev, S. A., and A. N. Tyrsin. "Entropy Approach to Risk-Analysis of Critical Infrastructures Systems." In First International Symposium on Uncertainty Modeling and Analysis and Management (ICVRAM 2011); and Fifth International Symposium on Uncertainty Modeling and Anaylsis (ISUMA). Reston, VA: American Society of Civil Engineers, 2011. http://dx.doi.org/10.1061/41170(400)18.

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Reports on the topic "Entropic uncertainty"

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Clark, Todd E., Gergely Ganics, and Elmar Mertens. What is the predictive value of SPF point and density forecasts? Federal Reserve Bank of Cleveland, November 2022. http://dx.doi.org/10.26509/frbc-wp-202237.

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This paper presents a new approach to combining the information in point and density forecasts from the Survey of Professional Forecasters (SPF) and assesses the incremental value of the density forecasts. Our starting point is a model, developed in companion work, that constructs quarterly term structures of expectations and uncertainty from SPF point forecasts for quarterly fixed horizons and annual fixed events. We then employ entropic tilting to bring the density forecast information contained in the SPF’s probability bins to bear on the model estimates. In a novel application of entropic tilting, we let the resulting predictive densities exactly replicate the SPF’s probability bins. Our empirical analysis of SPF forecasts of GDP growth and inflation shows that tilting to the SPF’s probability bins can visibly affect our model-based predictive distributions. Yet in historical evaluations, tilting does not offer consistent benefits to forecast accuracy relative to the model-based densities that are centered on the SPF’s point forecasts and reflect the historical behavior of SPF forecast errors. That said, there can be periods in which tilting to the bin information helps forecast accuracy. Replication files are available at https://github.com/elmarmertens/ClarkGanicsMertensSPFfancharts
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Bielinskyi, Andriy, Serhiy Semerikov, Oleksandr Serdiuk, Victoria Solovieva, Vladimir Soloviev, and Lukáš Pichl. Econophysics of sustainability indices. [б. в.], October 2020. http://dx.doi.org/10.31812/123456789/4118.

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In this paper, the possibility of using some econophysical methods for quantitative assessment of complexity measures: entropy (Shannon, Approximate and Permutation entropies), fractal (Multifractal detrended fluctuation analysis – MF-DFA), and quantum (Heisenberg uncertainty principle) is investigated. Comparing the capability of both entropies, it is obtained that both measures are presented to be computationally efficient, robust, and useful. Each of them detects patterns that are general for crisis states. The similar results are for other measures. MF-DFA approach gives evidence that Dow Jones Sustainability Index is multifractal, and the degree of it changes significantly at different periods. Moreover, we demonstrate that the quantum apparatus of econophysics has reliable models for the identification of instability periods. We conclude that these measures make it possible to establish that the socially responsive exhibits characteristic patterns of complexity, and the proposed measures of complexity allow us to build indicators-precursors of critical and crisis phenomena.
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Danylchuk, H., V. Derbentsev, Володимир Миколайович Соловйов, and A. Sharapov. Entropy analysis of dynamic properties of regional stock markets. Society for Cultural and Scientific Progress in Central and Eastern Europe, 2016. http://dx.doi.org/10.31812/0564/1154.

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This paper examines entropy analysis of regional stock markets. We propose and empirically demonstrate the effectiveness of using such entropy as sample entropy, wavelet and Tsallis entropy as a measure of uncertainty and instability of such complex systems as regional stock markets. Our results show that these entropy measures can be effectively used as crisis prediction indicators.
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Soloviev, Vladimir, Andrii Bielinskyi, and Viktoria Solovieva. Entropy Analysis of Crisis Phenomena for DJIA Index. [б. в.], June 2019. http://dx.doi.org/10.31812/123456789/3179.

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The Dow Jones Industrial Average (DJIA) index for the 125-year-old (since 1896) history has experienced many crises of different nature and, reflecting the dynamics of the world stock market, is an ideal model object for the study of quantitative indicators and precursors of crisis phenomena. In this paper, the classification and periodization of crisis events for the DJIA index have been carried out; crashes and critical events have been highlighted. Based on the modern paradigm of the theory of complexity, a spectrum of entropy indicators and precursors of crisis phenomena have been proposed. The entropy of a complex system is not only a measure of uncertainty (like Shannon's entropy) but also a measure of complexity (like the permutation and Tsallis entropy). The complexity of the system in a crisis changes significantly. This fact can be used as an indicator, and in the case of a proactive change as a precursor of a crisis. Complex systems also have the property of scale invariance, which can be taken into account by calculating the Multiscale entropy. The calculations were carried out within the framework of the sliding window algorithm with the subsequent comparison of the entropy measures of complexity with the dynamics of the DJIA index itself. It is shown that Shannon's entropy is an indicator, and the permutation and Tsallis entropy are the precursors of crisis phenomena to the same extent for both crashes and critical events.
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