scholarly journals Specific Emitter Identification Based on the Natural Measure

Entropy ◽  
2017 ◽  
Vol 19 (3) ◽  
pp. 117 ◽  
Author(s):  
Yongqiang Jia ◽  
Shengli Zhu ◽  
Lu Gan
Keyword(s):  
Natural Measure ◽  
Specific Emitter Identification

scholarly journals Equidistribution Results for Self-Similar Measures

2021 ◽  
Author(s):  
Simon Baker
Keyword(s):  
Sufficient Conditions ◽  
Cantor Set ◽  
Similar Measure ◽  
Natural Measure ◽  
Self Similar

Abstract A well-known theorem due to Koksma states that for Lebesgue almost every $x>1$ the sequence $(x^n)_{n=1}^{\infty }$ is uniformly distributed modulo one. In this paper, we give sufficient conditions for an analogue of this theorem to hold for a self-similar measure. Our approach applies more generally to sequences of the form $(f_{n}(x))_{n=1}^{\infty }$ where $(f_n)_{n=1}^{\infty }$ is a sequence of sufficiently smooth real-valued functions satisfying some nonlinearity conditions. As a corollary of our main result, we show that if $C$ is equal to the middle 3rd Cantor set and $t\geq 1$, then with respect to the natural measure on $C+t,$ for almost every $x$, the sequence $(x^n)_{n=1}^{\infty }$ is uniformly distributed modulo one.

Specific Emitter Identification with Limited Samples: A Model-Agnostic Meta-Learning Approach

2021 ◽  
pp. 1-1
Author(s):  
Ning Yang ◽  
Bangning Zhang ◽  
Guoru Ding ◽  
Yimin Wei ◽  
Guofeng Wei ◽  
...  
Keyword(s):  
Learning Approach ◽  
Meta Learning ◽  
Specific Emitter Identification

Specific Emitter Identification Over Fading Channels

2019 ◽  
Author(s):  
Gagarin Biswal ◽  
Ajay Babu Kambhampati ◽  
Barathram Ramkumar ◽  
M Sabarimalai Manikandan
Keyword(s):  
Fading Channels ◽  
Specific Emitter Identification

scholarly journals The Causal Interaction between Complex Subsystems

Entropy ◽  
2021 ◽  
Vol 24 (1) ◽  
pp. 3
Author(s):  
X. San Liang
Keyword(s):  
Fluid Dynamics ◽  
Maximum Likelihood ◽  
Information Flow ◽  
Maximum Likelihood Estimators ◽  
Climate Science ◽  
Causal Interaction ◽  
Natural Measure ◽  
Analytical Formulas ◽  
Real World Problems

Information flow provides a natural measure for the causal interaction between dynamical events. This study extends our previous rigorous formalism of componentwise information flow to the bulk information flow between two complex subsystems of a large-dimensional parental system. Analytical formulas have been obtained in a closed form. Under a Gaussian assumption, their maximum likelihood estimators have also been obtained. These formulas have been validated using different subsystems with preset relations, and they yield causalities just as expected. On the contrary, the commonly used proxies for the characterization of subsystems, such as averages and principal components, generally do not work correctly. This study can help diagnose the emergence of patterns in complex systems and is expected to have applications in many real world problems in different disciplines such as climate science, fluid dynamics, neuroscience, financial economics, etc.

scholarly journals Quantifying Noninvertibility in Discrete Dynamical Systems

10.37236/9475 ◽  
2020 ◽  
Vol 27 (3) ◽  
Author(s):  
Colin Defant ◽  
James Propp
Keyword(s):  
Dynamical Systems ◽  
Real Number ◽  
Arbitrary Function ◽  
Discrete Dynamical Systems ◽  
Open Problems ◽  
Natural Measure ◽  
Stack Sorting ◽  
Finite Set

Given a finite set $X$ and a function $f:X\to X$, we define the \emph{degree of noninvertibility} of $f$ to be $\displaystyle\deg(f)=\frac{1}{|X|}\sum_{x\in X}|f^{-1}(f(x))|$. This is a natural measure of how far the function $f$ is from being bijective. We compute the degrees of noninvertibility of some specific discrete dynamical systems, including the Carolina solitaire map, iterates of the bubble sort map acting on permutations, bubble sort acting on multiset permutations, and a map that we call "nibble sort." We also obtain estimates for the degrees of noninvertibility of West's stack-sorting map and the Bulgarian solitaire map. We then turn our attention to arbitrary functions and their iterates. In order to compare the degree of noninvertibility of an arbitrary function $f:X\to X$ with that of its iterate $f^k$, we prove that \[\max_{\substack{f:X\to X\\ |X|=n}}\frac{\deg(f^k)}{\deg(f)^\gamma}=\Theta(n^{1-1/2^{k-1}})\] for every real number $\gamma\geq 2-1/2^{k-1}$. We end with several conjectures and open problems.  

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