An Asymptotic Second-Order Lower Bound for the Bayes Risk of a Sequential Procedure

2004 ◽  
Vol 23 (3) ◽  
pp. 451-464 ◽  
Author(s):  
Kamel Rekab ◽  
Mohamed Tahir
Keyword(s):  
Lower Bound ◽  
Second Order ◽  
Sequential Procedure ◽  
Bayes Risk

scholarly journals Entropic upper bound for Bayes risk in the quantum case

2018 ◽  
Vol 38 (2) ◽  
pp. 429-440
Author(s):  
Rafał Wieczorek ◽  
Hanna Podsędkowska
Keyword(s):  
Lower Bound ◽  
Loss Function ◽  
Upper Bound ◽  
Von Neumann Algebra ◽  
General Setting ◽  
Probability Of Detection ◽  
Bayes Risk ◽  
Quantum Case ◽  
Von Neumann ◽  
Finite Von Neumann Algebra

The entropic upper bound for Bayes risk in a general quantum case is presented. We obtained generalization of the entropic lower bound for probability of detection. Our result indicates upper bound for Bayes risk in a particular case of loss function – for probability of detection in a pretty general setting of an arbitrary finite von Neumann algebra. It is also shown under which condition the indicated upper bound is achieved.

scholarly journals The lower bound of number of solutions for the second order nonlinear boundary value problem via the root functions method

2007 ◽  
Vol 57 (2) ◽  
Author(s):  
Peter Somora
Keyword(s):  
Lower Bound ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Second Order ◽  
Dirichlet Boundary Conditions ◽  
Number Of Solutions ◽  
Root Functions ◽  
Number Of Zeros ◽  
Variational Solutions ◽  
Homogeneous Dirichlet Boundary Conditions

AbstractWe consider a second order nonlinear differential equation with homogeneous Dirichlet boundary conditions. Using the root functions method we prove a relation between the number of zeros of some variational solutions and the number of solutions of our boundary value problem which follows into a lower bound of the number of its solutions.

scholarly journals On local convexity of nonlinear mappings between Banach spaces

2012 ◽  
Vol 10 (6) ◽  
Author(s):  
Iryna Banakh ◽  
Taras Banakh ◽  
Anatolij Plichko ◽  
Anatoliy Prykarpatsky
Keyword(s):  
Banach Space ◽  
Lower Bound ◽  
Banach Spaces ◽  
Lipschitz Constant ◽  
Second Order ◽  
Local Convexity ◽  
Convexity Number ◽  
Locally Convex ◽  
Nonlinear Mappings

AbstractWe find conditions for a smooth nonlinear map f: U → V between open subsets of Hilbert or Banach spaces to be locally convex in the sense that for some c and each positive ɛ < c the image f(B ɛ(x)) of each ɛ-ball B ɛ(x) ⊂ U is convex. We give a lower bound on c via the second order Lipschitz constant Lip2(f), the Lipschitz-open constant Lipo(f) of f, and the 2-convexity number conv2(X) of the Banach space X.

scholarly journals Positive Periodic Solution for Second-Order Singular Semipositone Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Xiumei Xing
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Lower Bound ◽  
Differential Equations ◽  
Positive Periodic Solution ◽  
Second Order ◽  
Nonlinear Alternative ◽  
Alternative Principle

We study the existence of a positive periodic solution for second-order singular semipositone differential equation by a nonlinear alternative principle of Leray-Schauder. Truncation plays an important role in the analysis of the uniform positive lower bound for all the solutions of the equation. Recent results in the literature (Chu et al., 2010) are generalized.

scholarly journals Sharp Second-Order Pointwise Asymptotics for Lossless Compression with Side Information

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 705
Author(s):  
Lampros Gavalakis ◽  
Ioannis Kontoyiannis
Keyword(s):  
Lower Bound ◽  
Side Information ◽  
Conditional Entropy ◽  
Lossless Compression ◽  
Second Order ◽  
Arbitrary Sequence ◽  
Mixing Conditions ◽  
Compression Algorithms ◽  
Information Density ◽  
Conditional Information

The problem of determining the best achievable performance of arbitrary lossless compression algorithms is examined, when correlated side information is available at both the encoder and decoder. For arbitrary source-side information pairs, the conditional information density is shown to provide a sharp asymptotic lower bound for the description lengths achieved by an arbitrary sequence of compressors. This implies that for ergodic source-side information pairs, the conditional entropy rate is the best achievable asymptotic lower bound to the rate, not just in expectation but with probability one. Under appropriate mixing conditions, a central limit theorem and a law of the iterated logarithm are proved, describing the inevitable fluctuations of the second-order asymptotically best possible rate. An idealised version of Lempel-Ziv coding with side information is shown to be universally first- and second-order asymptotically optimal, under the same conditions. These results are in part based on a new almost-sure invariance principle for the conditional information density, which may be of independent interest.

The Lower Bound on the Second-Order Nonlinearity for a Class of Bent Functions

2012 ◽  
Vol 35 (8) ◽  
pp. 1588 ◽  
Author(s):  
Chun-Lei LI ◽  
Huan-Guo ZHANG ◽  
Xiang-Yong ZENG ◽  
Lei HU
Keyword(s):  
Lower Bound ◽  
Second Order ◽  
Bent Functions ◽  
Second Order Nonlinearity
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