Birecurrent sets

2018 ◽  
Vol 28 (04) ◽  
pp. 613-652 ◽  
Author(s):  
Francesco Dolce ◽  
Dominique Perrin ◽  
Antonio Restivo ◽  
Christophe Reutenauer ◽  
Giuseppina Rindone
Keyword(s):  
Minimal Representation ◽  
Linear Combinations ◽  
Strongly Connected ◽  
Completely Reducible

A set is called recurrent if its minimal automaton is strongly connected and birecurrent if it is recurrent as well as reversal. We prove a series of results concerning birecurrent sets. It is already known that any birecurrent set is completely reducible (that is, such that the minimal representation of its characteristic series is completely reducible). The main result of this paper characterizes completely reducible sets as linear combinations of birecurrent sets

Descriptive statistics

2017 ◽  
Author(s):  
Andrew Gelman ◽  
Deborah Nolan
Keyword(s):  
Descriptive Statistics ◽  
Metabolic Rates ◽  
World Record ◽  
Linear Combinations ◽  
Record Times ◽  
Starting Point ◽  
Statistics Course ◽  
Scatter Plots ◽  
Economic Indexes ◽  
The Mean

Descriptive statistics is the typical starting point for a statistics course, and it can be tricky to teach because the material is more difficult than it first appears. The activities in this chapter focus more on the topics of data displays and transformations, rather than the mean, median, and standard deviation, which are covered easily in a textbook and on homework assignments. Specific topics include: distributions and handedness scores; extrapolation of time series and world record times for the mile run; linear combinations and economic indexes; scatter plots and exam scores; and logarithmic transformations and metabolic rates.

Intimation

2017 ◽  
Author(s):  
G. R. F. Ferrari
Keyword(s):  
Social Life ◽  
Relevance Theory ◽  
Self Presentation ◽  
Erving Goffman ◽  
Strongly Connected ◽  
Dan Sperber ◽  
Paul Grice

The communicative scale is introduced. What is fundamental to communication is the intention of the communicator rather than the codes that languages employ. Following the model first proposed by Paul Grice and developed in Dan Sperber and Deirdre Wilson’s ‘relevance theory’, the structure of communicative intentionality is understood to be recursive: its underlying form is ‘I want you to know that I want you to know’. This leaves room for a simpler kind of transmission, to be called ‘intimation’, whose underlying form would be ‘I want you to know’. If communication is a transmission at the ‘full-on’ position of the scale, and if the switch is off when no communication is intended, then intimation would be at the intermediate, ‘half-on’ position. Intimation is particularly useful in contexts where discretion, suggestiveness, or plausible deniability are needed. It is strongly connected to self-presentation in social life (as studied by Erving Goffman).

scholarly journals Some inequalities of linear combinations of independent random variables: II

Bernoulli ◽  
2013 ◽  
Vol 19 (5A) ◽  
pp. 1776-1789 ◽  
Author(s):  
Xiaoqing Pan ◽  
Maochao Xu ◽  
Taizhong Hu
Keyword(s):  
Random Variables ◽  
Independent Random Variables ◽  
Linear Combinations

scholarly journals Reconstruction of Relative Phase of Self-Transmitting Devices by Using Multiprobe Solutions and Non-Convex Optimization

Sensors ◽  
2021 ◽  
Vol 21 (7) ◽  
pp. 2459
Author(s):  
Rubén Tena Sánchez ◽  
Fernando Rodríguez Varela ◽  
Lars J. Foged ◽  
Manuel Sierra Castañer
Keyword(s):  
Iterative Algorithm ◽  
Degrees Of Freedom ◽  
Relative Phase ◽  
Low Cost ◽  
Initial Guess ◽  
Noise Model ◽  
Medium Size ◽  
Phase Reconstruction ◽  
Linear Combinations ◽  
Iterative Optimization Algorithm

Phase reconstruction is in general a non-trivial problem when it comes to devices where the reference is not accessible. A non-convex iterative optimization algorithm is proposed in this paper in order to reconstruct the phase in reference-less spherical multiprobe measurement systems based on a rotating arch of probes. The algorithm is based on the reconstruction of the phases of self-transmitting devices in multiprobe systems by taking advantage of the on-axis top probe of the arch. One of the limitations of the top probe solution is that when rotating the measurement system arch, the relative phase between probes is lost. This paper proposes a solution to this problem by developing an optimization iterative algorithm that uses partial knowledge of relative phase between probes. The iterative algorithm is based on linear combinations of signals when the relative phase is known. Phase substitution and modal filtering are implemented in order to avoid local minima and make the algorithm converge. Several noise-free examples are presented and the results of the iterative algorithm analyzed. The number of linear combinations used is far below the square of the degrees of freedom of the non-linear problem, which is compensated by a proper initial guess. With respect to noisy measurements, the top probe method will introduce uncertainties for different azimuth and elevation positions of the arch. This is modelled by considering the real noise model of a low-cost receiver and the results demonstrate the good accuracy of the method. Numerical results on antenna measurements are also presented. Due to the numerical complexity of the algorithm, it is limited to electrically small- or medium-size problems.

scholarly journals The Nexus of Sophisticated Digital Assets with Economic Policy Uncertainty: A Survey of Empirical Findings and an Empirical Investigation

2021 ◽  
Vol 13 (10) ◽  
pp. 5383
Author(s):  
Nikolaos A. Kyriazis
Keyword(s):  
Economic Policy ◽  
Empirical Investigation ◽  
Econometric Analysis ◽  
Policy Uncertainty ◽  
Negative Effects ◽  
Economic Policy Uncertainty ◽  
Strongly Connected ◽  
Threshold Arch ◽  
Best Fit ◽  
Digital Assets

This paper sets out to explore the nexus between economic policy uncertainty (EPU) and digital currencies. An integrated survey takes place based on eleven primary studies. Furthermore, an econometric analysis is conducted by the threshold ARCH, simple asymmetric ARCH and non-linear ARCH specifications covering the bull and the bear markets as well as the highly volatile period up to the present. Threshold ARCH is found to provide the best fit for estimations. Outcomes reveal that Bitcoin is strongly connected with EPU while Ethereum and Litecoin are not but are strongly linked with Bitcoin performance. Moreover, weak negative effects of the VIX on both cryptocurrencies are detected while oil exerts weak positive impacts on Ethereum. Overall, Ethereum and Litecoin could serve for diversifiers against Bitcoin or hedgers against traditional assets during highly stressed periods with the advantage of not being affected by economic policy uncertainty news.

scholarly journals New ideas for handling of loop and angular integrals in D-dimensions in QCD

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Valery E. Lyubovitskij ◽  
Fabian Wunder ◽  
Alexey S. Zhevlakov
Keyword(s):  
Computer Algebra ◽  
Cross Sections ◽  
Orthogonal Basis ◽  
Computer Algebra Systems ◽  
Covariant Formalism ◽  
Linear Combinations ◽  
Recursion Relations ◽  
New Ideas ◽  
Rotational Invariant ◽  
Geometric Picture

Abstract We discuss new ideas for consideration of loop diagrams and angular integrals in D-dimensions in QCD. In case of loop diagrams, we propose the covariant formalism of expansion of tensorial loop integrals into the orthogonal basis of linear combinations of external momenta. It gives a very simple representation for the final results and is more convenient for calculations on computer algebra systems. In case of angular integrals we demonstrate how to simplify the integration of differential cross sections over polar angles. Also we derive the recursion relations, which allow to reduce all occurring angular integrals to a short set of basic scalar integrals. All order ε-expansion is given for all angular integrals with up to two denominators based on the expansion of the basic integrals and using recursion relations. A geometric picture for partial fractioning is developed which provides a new rotational invariant algorithm to reduce the number of denominators.

scholarly journals Linear Combinations of the Complex Degrees of Coherence

Photonics ◽  
2021 ◽  
Vol 8 (5) ◽  
pp. 146
Author(s):  
Zhangrong Mei ◽  
Olga Korotkova
Keyword(s):  
Spatial Coherence ◽  
Light Fields ◽  
Linear Combinations

We propose a method for structuring the spatial coherence state of light via mixed linear combinations of N complex degrees of coherence (CDC) and specify the conditions under which such combinations represent a valid CDC. Several examples demonstrate that this method opens previously unknown avenues for modeling random sources, radiating to light fields with unique features.

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