scholarly journals Evolutionary branching in distorted trait spaces

2019 ◽  
Author(s):  
Hiroshi C. Ito ◽  
Akira Sasaki
Keyword(s):  
Covariance Matrix ◽  
Focal Point ◽  
Adaptive Dynamics ◽  
Covariance Matrices ◽  
Evolutionary Branching ◽  
Biological Communities ◽  
Mutational Step ◽  
Significant Magnitude ◽  
Arbitrary Dimensions ◽  
Magnitude Difference

AbstractBiological communities are thought to have been evolving in trait spaces that are not only multi-dimensional, but also distorted in a sense that mutational covariance matrices among traits depend on the parental phenotypes of mutants. Such a distortion may affect diversifying evolution as well as directional evolution. In adaptive dynamics theory, diversifying evolution through ecological interaction is called evolutionary branching. This study analytically develops conditions for evolutionary branching in distorted trait spaces of arbitrary dimensions, by a local nonlinear coordinate transformation so that the mutational covariance matrix becomes locally constant in the neighborhood of a focal point. The developed evolutionary branching conditions can be affected by the distortion when mutational step sizes have significant magnitude difference among directions, i.e., the eigenvalues of the mutational covariance matrix have significant magnitude difference.

Effects of pollution on individual size of a single species

2020 ◽  
pp. 2050079
Author(s):  
Bing Liu ◽  
Le Song ◽  
Xin Wang ◽  
Baolin Kang
Keyword(s):  
Growth Rate ◽  
Evolutionary Dynamics ◽  
Function Analysis ◽  
Fitness Function ◽  
Adaptive Dynamics ◽  
Single Species ◽  
Phenotypic Trait ◽  
Evolutionary Branching ◽  
Critical Function ◽  
Individual Size

In this paper, we develop a single species evolutionary model with a continuous phenotypic trait in a pulsed pollution discharge environment and discuss the effects of pollution on the individual size of the species. The invasion fitness function of a monomorphic species is given, which involves the long-term average exponential growth rate of the species. Then the critical function analysis method is used to obtain the evolutionary dynamics of the system, which is related to interspecific competition intensity between mutant species and resident species and the curvature of the trade-off between individual size and the intrinsic growth rate. We conclude that the pollution affects the evolutionary traits and evolutionary dynamics. The worsening of the pollution can lead to rapid stable evolution toward a smaller individual size, while the opposite is more likely to generate evolutionary branching and promote species diversity. The adaptive dynamics of coevolution of dimorphic species is further analyzed when evolutionary branching occurs.

Trimmed estimators for large dimensional sparse covariance matrices

2018 ◽  
Vol 08 (01) ◽  
pp. 1950003
Author(s):  
Guangren Yang ◽  
Xia Cui
Keyword(s):  
Convergence Rate ◽  
Covariance Matrix ◽  
Covariance Matrices ◽  
Optimal Convergence Rate ◽  
Sample Covariance Matrices ◽  
Optimal Convergence ◽  
Sample Covariance ◽  
Starting Point ◽  
Pairwise Product

In this paper, we will propose two new estimators for sparse covariance matrix. Our starting point is to make the estimator of each element of covariance matrix more robust. More precisely, we will trim the observations for each pairwise product of components of population as a first step. Then we form the sample covariance matrices based on the trimmed data. Finally, we apply the thresholding to the derived sample covariance matrices. These two new estimators will be shown to achieve the optimal convergence rate.

ENCODING STRUCTURAL SIMILARITY BY CROSS-COVARIANCE TENSORS FOR IMAGE CLASSIFICATION

2014 ◽  
Vol 28 (07) ◽  
pp. 1460008
Author(s):  
MARCO SAN BIAGIO ◽  
SAMUELE MARTELLI ◽  
MARCO CROCCO ◽  
MARCO CRISTANI ◽  
VITTORIO MURINO
Keyword(s):  
Computer Vision ◽  
Covariance Matrix ◽  
Image Representation ◽  
Structural Similarity ◽  
Covariance Matrices ◽  
Integral Image ◽  
Computational Burden ◽  
Feature Vectors ◽  
Single Region ◽  
Cross Covariance

In computer vision, an object can be modeled in two main ways: by explicitly measuring its characteristics in terms of feature vectors, and by capturing the relations which link an object with some exemplars, that is, in terms of similarities. In this paper, we propose a new similarity-based descriptor, dubbed structural similarity cross-covariance tensor (SS-CCT), where self-similarities come into play: Here the entity to be measured and the exemplar are regions of the same object, and their similarities are encoded in terms of cross-covariance matrices. These matrices are computed from a set of low-level feature vectors extracted from pairs of regions that cover the entire image. SS-CCT shares some similarities with the widely used covariance matrix descriptor, but extends its power focusing on structural similarities across multiple parts of an image, instead of capturing local similarities in a single region. The effectiveness of SS-CCT is tested on many diverse classification scenarios, considering objects and scenes on widely known benchmarks (Caltech-101, Caltech-256, PASCAL VOC 2007 and SenseCam). In all the cases, the results obtained demonstrate the superiority of our new descriptor against diverse competitors. Furthermore, we also reported an analysis on the reduced computational burden achieved by using and efficient implementation that takes advantage from the integral image representation.

scholarly journals Branching and extinction in evolutionary public goods games

2020 ◽  
Author(s):  
Brian Johnson ◽  
Philipp M. Altrock ◽  
Gregory J. Kimmel
Keyword(s):  
Public Goods ◽  
Public Good ◽  
Population Size ◽  
Adaptive Dynamics ◽  
Small Population ◽  
Neighborhood Size ◽  
Evolutionary Branching ◽  
Final State ◽  
Evolutionary Origins ◽  
Public Goods Games

AbstractPublic goods games (PGGs) describe situations in which individuals contribute to a good at a private cost, but others can free-ride by receiving their share of the public benefit at no cost. PGGs can be nonlinear, as often observed in nature, whereby either benefit, cost, or both are nonlinear functions of the available public good (PG): at low levels of PG there can be synergy whereas at high levels, the added benefit of additional PG diminishes. PGGs can be local such that the benefits and costs are relevant only in a local neighborhood or subset of the larger population in which producers (cooperators) and free-riders (defectors) co-evolve. Cooperation and defection can be seen as two extremes of a continuous spectrum of traits. The level of public good production, and similarly, the neighborhood size can vary across individuals. To better understand how distinct strategies in the nonlinear public goods game emerge and persist, we study the adaptive dynamics of production rate and neighborhood size. We explain how an initially monomorphic population, in which individuals have the same trait values, could evolve into a dimorphic population by evolutionary branching, in which we see distinct cooperators and defectors emerge, respectively characterized by high production and low neighborhood sizes, and low production and high neighborhood sizes. We find that population size plays a crucial role in determining the final state of the population, as smaller populations may not branch, or may observe extinction of a subpopulation after branching. Our work elucidates the evolutionary origins of cooperation and defection in nonlinear local public goods games, and highlights the importance of small population size effects on the process and outcome of evolutionary branching.

scholarly journals The cost function of the data fusion process and its application

2019 ◽  
Vol 12 (5) ◽  
pp. 2967-2977 ◽  
Author(s):  
Simone Ceccherini ◽  
Nicola Zoppetti ◽  
Bruno Carli ◽  
Ugo Cortesi ◽  
Samuele Del Bianco ◽  
...  
Keyword(s):  
Data Fusion ◽  
Cost Function ◽  
Covariance Matrix ◽  
Expected Value ◽  
Covariance Matrices ◽  
Complete Data ◽  
Sufficient Statistics ◽  
The Cost ◽  
Analytical Expressions

Abstract. When the complete data fusion method is used to fuse inconsistent measurements, it is necessary to add to the measurement covariance matrix of each fusing profile a covariance matrix that takes into account the inconsistencies. A realistic estimate of these inconsistency covariance matrices is required for effectual fused products. We evaluate the possibility of assisting the estimate of the inconsistency covariance matrices using the value of the cost function minimized in the complete data fusion. The analytical expressions of expected value and variance of the cost function are derived. Modelling the inconsistency covariance matrix with one parameter, we determine the value of the parameter that makes the reduced cost function equal to its expected value and use the variance to assign an error to this determination. The quality of the inconsistency covariance matrix determined in this way is tested for simulated measurements of ozone profiles obtained in the thermal infrared in the framework of the Sentinel-4 mission of the Copernicus programme. As expected, the method requires sufficient statistics and poor results are obtained when a small number of profiles are being fused together, but very good results are obtained when the fusion involves a large number of profiles.

Lassoing eigenvalues

Biometrika ◽  
2020 ◽  
Vol 107 (2) ◽  
pp. 397-414 ◽  
Author(s):  
David E Tyler ◽  
Mengxi Yi
Keyword(s):  
Covariance Matrix ◽  
Penalty Function ◽  
Covariance Matrices ◽  
Penalty Functions ◽  
Sample Covariance Matrix ◽  
Sample Covariance Matrices ◽  
Sample Covariance ◽  
Nonsmooth Penalty

Summary The properties of penalized sample covariance matrices depend on the choice of the penalty function. In this paper, we introduce a class of nonsmooth penalty functions for the sample covariance matrix and demonstrate how their use results in a grouping of the estimated eigenvalues. We refer to the proposed method as lassoing eigenvalues, or the elasso.

scholarly journals An Improved SINS Alignment Method Based on Adaptive Cubature Kalman Filter

Sensors ◽  
2019 ◽  
Vol 19 (24) ◽  
pp. 5509 ◽  
Author(s):  
Yonggang Zhang ◽  
Geng Xu ◽  
Xin Liu
Keyword(s):  
Kalman Filter ◽  
Covariance Matrix ◽  
Real Life ◽  
Covariance Matrices ◽  
The Body ◽  
Alignment Method ◽  
Initial Alignment ◽  
Noise Covariance Matrix ◽  
Cubature Kalman Filter ◽  
Noise Covariance

Initial alignment is critical and indispensable for the inertial navigation system (INS), which determines the initial attitude matrix between the reference navigation frame and the body frame. The conventional initial alignment methods based on the Kalman-like filter require an accurate noise covariance matrix of state and measurement to guarantee the high estimation accuracy. However, in a real-life practical environment, the uncertain noise covariance matrices are often induced by the motion of the carrier and external disturbance. To solve the problem of initial alignment with uncertain noise covariance matrices and a large initial misalignment angle in practical environment, an improved initial alignment method based on an adaptive cubature Kalman filter (ACKF) is proposed in this paper. By virtue of the idea of the variational Bayesian (VB) method, the system state, one step predicted error covariance matrix, and measurement noise covariance matrix of initial alignment are adaptively estimated together. Simulation and vehicle experiment results demonstrate that the proposed method can improve the accuracy of initial alignment compared with existing methods.

scholarly journals The cost function of the data fusion process and its application

2019 ◽  
Author(s):  
Simone Ceccherini ◽  
Nicola Zoppetti ◽  
Bruno Carli ◽  
Ugo Cortesi ◽  
Samuele Del Bianco ◽  
...  
Keyword(s):  
Data Fusion ◽  
Cost Function ◽  
Covariance Matrix ◽  
Expected Value ◽  
Covariance Matrices ◽  
Complete Data ◽  
Sufficient Statistics ◽  
The Cost ◽  
Analytical Expressions

Abstract. When the complete data fusion method is used to fuse inconsistent measurements, it is necessary to add to the measurement covariance matrix of each fusing profile a covariance matrix that takes into account the inconsistencies. A realistic estimate of these inconsistency covariance matrices is required for effectual fused products. We evaluate the possibility of assisting the estimate of the inconsistency covariance matrices using the value of the cost function minimized in the complete data fusion. The analytical expressions of expected value and variance of the cost function are derived. Modelling the inconsistency covariance matrix with one parameter, we determine the value of the parameter that makes the reduced cost function equal to its expected value and use the variance to assign an error to this determination. The quality of the inconsistency covariance matrix determined in this way is tested for simulated measurements of ozone profiles obtained in the thermal infrared in the framework of the Sentinel 4 mission of the Copernicus programme. As expected, the method requires a sufficient statistics and poor results are obtained when a small numbers of profiles are being fused together, but very good results are obtained when the fusion involves a large number of profiles.

scholarly journals Retrieval of ash properties from IASI measurements

2016 ◽  
Author(s):  
Lucy J. Ventress ◽  
Don Grainger ◽  
Gregory McGarragh ◽  
Elisa Carboni ◽  
Andrew J. Smith
Keyword(s):  
Covariance Matrix ◽  
Optical Depth ◽  
Sensitivity Study ◽  
Covariance Matrices ◽  
Effective Radius ◽  
Radiative Transfer Model ◽  
Retrieval Algorithm ◽  
Transfer Model ◽  
Ancillary Data ◽  
Clear Sky

Abstract. A new optimal estimation algorithm for the retrieval of volcanic ash properties has been developed for use with hyperspectral satellite instruments such as the Infrared Atmospheric Sounding Interferometer (IASI). The retrieval method uses the wavenumber range 680–1200 cm−1, which contains window channels, the CO2 ν2 band (used for the height retrieval), and the O3 ν3 band. Assuming a single infinitely (geometrically) thin ash plume and combining this with the output from the radiative transfer model RTTOV, the retrieval algorithm produces the most probable values for the ash optical depth (AOD), particle effective radius, plume top height and surface temperature. A comprehensive uncertainty budget is obtained for each pixel. Improvements to the algorithm through the use of different measurement error covariance matrices is explored, comparing the results from a sensitivity study of the retrieval process using covariance matrices trained on either clear-sky or cloudy scenes. The result exhibited that, due to the smaller variance contained within it, the clear-sky covariance matrix is preferable. However, if the retrieval fails to pass the quality control tests, the cloudy covariance matrix is implemented. The retrieval algorithm is applied to scenes from the Eyjafjallajökull eruption in 2010 and the retrieved parameters are compared to ancillary data sources. The ash optical depth gives an RMS difference of 0.46 when compared to retrievals from the MODIS instrument for all pixels and an improved RMS of 0.2 for low optical depths. Measurements from the FAAM and DLR flight campaigns are used to verify the retrieved particle effective radius, with the retrieved distribution of sizes for the scene showing excellent consistency. Further, the plume top altitudes are compared to derived cloud-top altitudes from the CALIOP instrument and show agreement with RMS values of less than 1 km.

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