scholarly journals Field Theoretical Approach for Signal Detection in Nearly Continuous Positive Spectra I: Matricial Data

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1132
Author(s):  
Vincent Lahoche ◽  
Dine Ousmane Samary ◽  
Mohamed Tamaazousti
Keyword(s):  
Signal Detection ◽  
Covariance Matrix ◽  
Degrees Of Freedom ◽  
Detection Threshold ◽  
Principal Component ◽  
Coarse Graining ◽  
Theoretical Investigations ◽  
Modern Physics ◽  
Highly Correlated ◽  
Nearly Continuous

Renormalization group techniques are widely used in modern physics to describe the relevant low energy aspects of systems involving a large number of degrees of freedom. Those techniques are thus expected to be a powerful tool to address open issues in data analysis when datasets are highly correlated. Signal detection and recognition for a covariance matrix having a nearly continuous spectra is currently one of these opened issues. First, investigations in this direction have been proposed in recent investigations from an analogy between coarse-graining and principal component analysis (PCA), regarding separation of sampling noise modes as a UV cut-off for small eigenvalues of the covariance matrix. The field theoretical framework proposed in this paper is a synthesis of these complementary point of views, aiming to be a general and operational framework, both for theoretical investigations and for experimental detection. Our investigations focus on signal detection. They exhibit numerical investigations in favor of a connection between symmetry breaking and the existence of an intrinsic detection threshold.

scholarly journals Field Theoretical Approach for Signal Detection in Nearly Continuous Positive Spectra II: Tensorial Data

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 795
Author(s):  
Vincent Lahoche ◽  
Mohamed Ouerfelli ◽  
Dine Ousmane Samary ◽  
Mohamed Tamaazousti
Keyword(s):  
Principal Component Analysis ◽  
Renormalization Group ◽  
Signal Detection ◽  
Detection Threshold ◽  
Principal Component ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Component Analysis ◽  
Slight Generalization ◽  
Nearly Continuous

The tensorial principal component analysis is a generalization of ordinary principal component analysis focusing on data which are suitably described by tensors rather than matrices. This paper aims at giving the nonperturbative renormalization group formalism, based on a slight generalization of the covariance matrix, to investigate signal detection for the difficult issue of nearly continuous spectra. Renormalization group allows constructing an effective description keeping only relevant features in the low “energy” (i.e., large eigenvalues) limit and thus providing universal descriptions allowing to associate the presence of the signal with objectives and computable quantities. Among them, in this paper, we focus on the vacuum expectation value. We exhibit experimental evidence in favor of a connection between symmetry breaking and the existence of an intrinsic detection threshold, in agreement with our conclusions for matrices, providing a new step in the direction of a universal statement.

Empirical Orthogonal Functions

2006 ◽  
Author(s):  
Huug van den Dool
Keyword(s):  
Covariance Matrix ◽  
Degrees Of Freedom ◽  
Natural Extension ◽  
Principal Component ◽  
Space Time ◽  
Empirical Orthogonal Functions ◽  
Point Of View ◽  
Empirical Modeling ◽  
Orthogonal Functions ◽  
Set Up

The purpose of this chapter is to discuss Empirical Orthogonal Functions (EOF), both in method and application. When dealing with teleconnections in the previous chapter we came very close to EOF, so it will be a natural extension of that theme. However, EOF opens the way to an alternative point of view about space–time relationships, especially correlation across distant times as in analogues. EOFs have been treated in book-size texts, most recently in Jolliffe (2002), a principal older reference being Preisendorfer (1988). The subject is extremely interdisciplinary, and each field has its own nomenclature, habits and notation. Jolliffe’s book is probably the best attempt to unify various fields. The term EOF appeared first in meteorology in Lorenz (1956). Zwiers and von Storch (1999) and Wilks (1995) devote lengthy single chapters to the topic. Here we will only briefly treat EOF or PCA (Principal Component Analysis) as it is called in most fields. Specifically we discuss how to set up the covariance matrix, how to calculate the EOF, what are their properties, advantages, disadvantages etc. We will do this in both space–time set-ups already alluded to in Equations (2.14) and (2.14a). There are no concrete rules as to how one constructs the covariance matrix. Hence there are in the literature matrices based on correlation, based on covariance, etc. Here we follow the conventions laid out in Chapter 2. The post-processing and display conventions of EOFs can also be quite confusing. Examples will be shown, for both daily and seasonal mean data, for both the Northern and Southern Hemisphere. EOF may or may not look like teleconnections. Therefore, as a diagnostic tool, EOFs may not always allow the interpretation some would wish. This has led to many proposed “simplifications” of the EOFs, which hopefully are more like teleconnections. However, regardless of physical interpretation, since EOFs are maximally efficient in retaining as much of the data set’s information as possible for as few degrees of freedom as possible they are ideally suited for empirical modeling. Indeed EOFs are an extremely popular tool these days.

scholarly journals Suitability Analysis of 17 Probiotic Type Strains of Lactic Acid Bacteria as Starter for Kimchi Fermentation

Foods ◽  
2021 ◽  
Vol 10 (6) ◽  
pp. 1435
Author(s):  
Hee Seo ◽  
Jae-Han Bae ◽  
Gayun Kim ◽  
Seul-Ah Kim ◽  
Byung Hee Ryu ◽  
...  
Keyword(s):  
Lactic Acid ◽  
Lactic Acid Bacteria ◽  
Growth Rates ◽  
Principal Component ◽  
Fermented Foods ◽  
Suitability Analysis ◽  
Moderate Growth ◽  
Health Promoting ◽  
Highly Correlated ◽  
Type Strains

The use of probiotic starters can improve the sensory and health-promoting properties of fermented foods. This study aimed to evaluate the suitability of probiotic lactic acid bacteria (LAB) as a starter for kimchi fermentation. Seventeen probiotic type strains were tested for their growth rates, volatile aroma compounds, metabolites, and sensory characteristics of kimchi, and their characteristics were compared to those of Leuconostoc (Le.) mesenteroides DRC 1506, a commercial kimchi starter. Among the tested strains, Limosilactobacillus fermentum, Limosilactobacillus reuteri, Lacticaseibacillus rhamnosus, Lacticaseibacillus paracasei, and Ligilactobacillus salivarius exhibited high or moderate growth rates in simulated kimchi juice (SKJ) at 37 °C and 15 °C. When these five strains were inoculated in kimchi and metabolite profiles were analyzed during fermentation using GC/MS and 1H-NMR, data from the principal component analysis (PCA) showed that L. fermentum and L. reuteri were highly correlated with Le. mesenteroides in concentrations of sugar, mannitol, lactate, acetate, and total volatile compounds. Sensory test results also indicated that these three strains showed similar sensory preferences. In conclusion, L. fermentum and L. reuteri can be considered potential candidates as probiotic starters or cocultures to develop health-promoting kimchi products.

Experimental and theoretical investigations of quadrupole collective degrees of freedom in 104Ru

2006 ◽  
Vol 766 ◽  
pp. 25-51 ◽  
Author(s):  
J. Srebrny ◽  
T. Czosnyka ◽  
Ch. Droste ◽  
S.G. Rohoziński ◽  
L. Próchniak ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Theoretical Investigations

scholarly journals Are children’s judgments of another’s accuracy linked to their metacognitive confidence judgments?

2021 ◽  
Author(s):  
Carolyn Baer ◽  
Puja Malik ◽  
Darko Odic
Keyword(s):  
Signal Detection ◽  
Signal Detection Theory ◽  
Learning Task ◽  
Detection Theory ◽  
Simulation Theory ◽  
Reasoning Task ◽  
Decision Accuracy ◽  
Self And Other ◽  
Highly Correlated ◽  
Tight Correlation

AbstractThe world can be a confusing place, which leads to a significant challenge: how do we figure out what is true? To accomplish this, children possess two relevant skills: reasoning about the likelihood of their own accuracy (metacognitive confidence) and reasoning about the likelihood of others’ accuracy (mindreading). Guided by Signal Detection Theory and Simulation Theory, we examine whether these two self- and other-oriented skills are one in the same, relying on a single cognitive process. Specifically, Signal Detection Theory proposes that confidence in a decision is purely derived from the imprecision of that decision, predicting a tight correlation between decision accuracy and confidence. Simulation Theory further proposes that children attribute their own cognitive experience to others when reasoning socially. Together, these theories predict that children’s self and other reasoning should be highly correlated and dependent on decision accuracy. In four studies (N = 374), children aged 4–7 completed a confidence reasoning task and selective social learning task each designed to eliminate confounding language and response biases, enabling us to isolate the unique correlation between self and other reasoning. However, in three of the four studies, we did not find that individual differences on the two tasks correlated, nor that decision accuracy explained performance. These findings suggest self and other reasoning are either independent in childhood, or the result of a single process that operates differently for self and others.

Signal detection using multi-channel seismic data

1996 ◽  
Vol 86 (1A) ◽  
pp. 221-231 ◽  
Author(s):  
Gregory S. Wagner ◽  
Thomas J. Owens
Keyword(s):  
Signal Detection ◽  
Seismic Data ◽  
Spatial Coherence ◽  
Vertical Component ◽  
Principal Component ◽  
Minimum Variance ◽  
Data Detection ◽  
Array Data ◽  
Detection Approach ◽  
Sample Covariance

Abstract We outline a simple signal detection approach for multi-channel seismic data. Our approach is based on the premise that the wave-field spatial coherence increases when a signal is present. A measure of spatial coherence is provided by the largest eigenvalue of the multi-channel data's sample covariance matrix. The primary advantages of this approach are its speed and simplicity. For three-component data, this approach provides a more robust statistic than particle motion polarization. For array data, this approach provides beamforming-like signal detection results without the need to form beams. This approach allows several options for the use of three-component array data. Detection statistics for three-component, vertical-component array, and three different three-component array approaches are compared to conventional and minimum-variance vertical-component beamforming. Problems inherent in principal-component analysis (PCA) in general and PCA of high-frequency seismic data in particular are also discussed. Multi-channel beamforming and the differences between principal component and factor analysis are discussed in the appendix.

scholarly journals Optimizing the structure and movement of a robotic bat with biological kinematic synergies

2018 ◽  
Vol 37 (10) ◽  
pp. 1233-1252 ◽  
Author(s):  
Jonathan Hoff ◽  
Alireza Ramezani ◽  
Soon-Jo Chung ◽  
Seth Hutchinson
Keyword(s):  
Principal Component Analysis ◽  
Topological Structure ◽  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Principal Component ◽  
Biologically Inspired ◽  
Wing Kinematics ◽  
Wing Motion ◽  
Kinematic Synergies ◽  
Low Dimensional

In this article, we present methods to optimize the design and flight characteristics of a biologically inspired bat-like robot. In previous, work we have designed the topological structure for the wing kinematics of this robot; here we present methods to optimize the geometry of this structure, and to compute actuator trajectories such that its wingbeat pattern closely matches biological counterparts. Our approach is motivated by recent studies on biological bat flight that have shown that the salient aspects of wing motion can be accurately represented in a low-dimensional space. Although bats have over 40 degrees of freedom (DoFs), our robot possesses several biologically meaningful morphing specializations. We use principal component analysis (PCA) to characterize the two most dominant modes of biological bat flight kinematics, and we optimize our robot’s parametric kinematics to mimic these. The method yields a robot that is reduced from five degrees of actuation (DoAs) to just three, and that actively folds its wings within a wingbeat period. As a result of mimicking synergies, the robot produces an average net lift improvesment of 89% over the same robot when its wings cannot fold.

Abnormalities Detection of IMU Based on PCA in Motion Monitoring

2012 ◽  
Vol 224 ◽  
pp. 533-538 ◽  
Author(s):  
Jing Zhou ◽  
Steven Su ◽  
Ai Huang Guo ◽  
Wei Dong Chen
Keyword(s):  
Measurement Method ◽  
Degrees Of Freedom ◽  
Inertial Sensors ◽  
Principal Component ◽  
Body Sensor Networks ◽  
Remote Measurement ◽  
Micro Electro Mechanical Systems ◽  
Inertial Measurement ◽  
Multiple Degrees Of Freedom ◽  
Measurement Units

Inertial measurement units (IMU) are used as an affordable and effective remote measurement method for health monitoring in body sensor networks (BSNs) based on tracking people’s daily motions and activities. These inertial sensors are mostly micro-electro-mechanical systems with a combination of multi-axis combinations of precision gyroscopes, accelerometers, and magnetometers to sense multiple degrees of freedom (DoF).Unfortunately in the process of motion monitoring actual sensor outputs may contain some abnormalities, which might result in the misinterpretations of activities. In this paper, we use Principal component analysis (PCA) combined with Hotelling’s T2 and SPE statistic to detect abnormal data in the process of motion monitoring with IMU to ensure the reliability and accuracy in application. The simulated results prove this method is effective and feasible.

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