scholarly journals Mismatch in the Classification of Linear Subspaces: Sufficient Conditions for Reliable Classification

2016 ◽  
Vol 64 (12) ◽  
pp. 3035-3050 ◽  
Author(s):  
Jure Sokolic ◽  
Francesco Renna ◽  
Robert Calderbank ◽  
Miguel R. D. Rodrigues
Keyword(s):  
Sufficient Conditions ◽  
Linear Subspaces ◽  
Reliable Classification

The λ-classification of continuous-time birth-and-death processes

2003 ◽  
Vol 35 (04) ◽  
pp. 1111-1130 ◽  
Author(s):  
Andrew G. Hart ◽  
Servet Martínez ◽  
Jaime San Martín
Keyword(s):  
Continuous Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Birth And Death Processes ◽  
Positive Recurrent ◽  
Necessary And Sufficient

We study the λ-classification of absorbing birth-and-death processes, giving necessary and sufficient conditions for such processes to be λ-transient, λ-null recurrent and λ-positive recurrent.

scholarly journals An Application of Spherical Geometry to Hyperkähler Slices

2020 ◽  
pp. 1-30
Author(s):  
Peter Crooks ◽  
Maarten van Pruijssen
Keyword(s):  
Sufficient Conditions ◽  
Compact Subgroup ◽  
Spherical Geometry ◽  
Spherical Subgroup ◽  
Cotangent Bundles ◽  
Complex Semisimple ◽  
Reductive Subgroup ◽  
Necessary And Sufficient

Abstract This work is concerned with Bielawski’s hyperkähler slices in the cotangent bundles of homogeneous affine varieties. One can associate such a slice with the data of a complex semisimple Lie group  $G$ , a reductive subgroup $H\subseteq G$ , and a Slodowy slice $S\subseteq \mathfrak{g}:=\text{Lie}(G)$ , defining it to be the hyperkähler quotient of $T^{\ast }(G/H)\times (G\times S)$ by a maximal compact subgroup of  $G$ . This hyperkähler slice is empty in some of the most elementary cases (e.g., when $S$ is regular and $(G,H)=(\text{SL}_{n+1},\text{GL}_{n})$ , $n\geqslant 3$ ), prompting us to seek necessary and sufficient conditions for non-emptiness. We give a spherical-geometric characterization of the non-empty hyperkähler slices that arise when $S=S_{\text{reg}}$ is a regular Slodowy slice, proving that non-emptiness is equivalent to the so-called $\mathfrak{a}$ -regularity of $(G,H)$ . This $\mathfrak{a}$ -regularity condition is formulated in several equivalent ways, one being a concrete condition on the rank and complexity of $G/H$ . We also provide a classification of the $\mathfrak{a}$ -regular pairs $(G,H)$ in which $H$ is a reductive spherical subgroup. Our arguments make essential use of Knop’s results on moment map images and Losev’s algorithm for computing Cartan spaces.

Asymptotic stability of heteroclinic cycles in systems with symmetry. II

2004 ◽  
Vol 134 (6) ◽  
pp. 1177-1197 ◽  
Author(s):  
Martin Krupa ◽  
Ian Melbourne
Keyword(s):  
Asymptotic Stability ◽  
Transition Matrix ◽  
Sufficient Conditions ◽  
Systematic Investigation ◽  
Necessary And Sufficient Conditions ◽  
Sufficient Condition ◽  
Heteroclinic Cycles ◽  
Higher Dimensional ◽  
Necessary And Sufficient

Systems possessing symmetries often admit robust heteroclinic cycles that persist under perturbations that respect the symmetry. In previous work, we began a systematic investigation into the asymptotic stability of such cycles. In particular, we found a sufficient condition for asymptotic stability, and we gave algebraic criteria for deciding when this condition is also necessary. These criteria are satisfied for cycles in R3.Field and Swift, and Hofbauer, considered examples in R4 for which our sufficient condition for stability is not optimal. They obtained necessary and sufficient conditions for asymptotic stability using a transition-matrix technique.In this paper, we combine our previous methods with the transition-matrix technique and obtain necessary and sufficient conditions for asymptotic stability for a larger class of heteroclinic cycles. In particular, we obtain a complete theory for ‘simple’ heteroclinic cycles in R4 (thereby proving and extending results for homoclinic cycles that were stated without proof by Chossat, Krupa, Melbourne and Scheel). A partial classification of simple heteroclinic cycles in R4 is also given. Finally, our stability results generalize naturally to higher dimensions and many of the higher-dimensional examples in the literature are covered by this theory.

scholarly journals An Automated Method for the Quantification and Fractal Analysis of Immunostaining

2004 ◽  
Vol 26 (3) ◽  
pp. 125-134
Author(s):  
Armin Gerger ◽  
Patrick Bergthaler ◽  
Josef Smolle
Keyword(s):  
Fractal Analysis ◽  
Quantitative Description ◽  
Fractal Dimensionality ◽  
Texture Features ◽  
Second Step ◽  
Digital Information ◽  
Automated Method ◽  
Reliable Classification ◽  
The One

Aims. In tissue counter analysis (TCA) digital images of complex histologic sections are dissected into elements of equal size and shape, and digital information comprising grey level, colour and texture features is calculated for each element. In this study we assessed the feasibility of TCA for the quantitative description of amount and also of distribution of immunostained material. Methods. In a first step, our system was trained for differentiating between background and tissue on the one hand and between immunopositive and so‐called other tissue on the other. In a second step, immunostained slides were automatically screened and the procedure was tested for the quantitative description of amount of cytokeratin (CK) and leukocyte common antigen (LCA) immunopositive structures. Additionally, fractal analysis was applied to all cases describing the architectural distribution of immunostained material. Results. The procedure yielded reproducible assessments of the relative amounts of immunopositive tissue components when the number and percentage of CK and LCA stained structures was assessed. Furthermore, a reliable classification of immunopositive patterns was found by means of fractal dimensionality. Conclusions. Tissue counter analysis combined with classification trees and fractal analysis is a fully automated and reproducible approach for the quantitative description in immunohistology.

scholarly journals Classification of rough transformations of a circle from a modern point of view

2018 ◽  
Vol 20 (4) ◽  
pp. 408-418
Author(s):  
A. E. Kolobyanina ◽  
E. V. Nozdrinova ◽  
O. V. Pochinka
Keyword(s):  
Invariant Manifolds ◽  
Sufficient Conditions ◽  
Periodic Points ◽  
Point Of View ◽  
Topological Classification ◽  
Topological Invariants ◽  
Modern Theory ◽  
Ambient Manifold ◽  
Periodic Data

In this paper the authors use modern methods and approaches to present a solution to the problem of the topological classification of circle’s rough transformations in canonical formulation. In the modern theory of dynamical systems such problems are understood as the complete topological classification: finding topological invariants, proving the completeness of the set of invariants found and constructing a standard representative from a given set of topological invariants. Namely, in the first theorem of this paper the type of periodic data of circle’s rough transformations is established. In the second theorem necessary and sufficient conditions of their conjugacy are proved. These conditions mean coincidence of periodic data and rotation numbers. In the third theorem the admissible set of parameters is implemented by a rough transformation of a circle. While proving the theorems, we assume that the results on the local topological classification of hyperbolic periodic points, as well as the results on the global representation of the ambient manifold as a union of invariant manifolds of periodic points, are known.

scholarly journals Analysis of the Strong and Weak Monotonic External Stability of the Resonance in a Perturbed Dynamical System

2021 ◽  
Vol 16 ◽  
pp. 180-191
Author(s):  
Vladislav V. Lyubimov
Keyword(s):  
Dynamical System ◽  
Sufficient Conditions ◽  
Strong Stability ◽  
New Classification ◽  
External Stability ◽  
Fast Phase ◽  
Stability And Instability ◽  
Long Time ◽  
Independent Variable

A perturbed dynamical system involving two ordinary differential equations is under review. Whereupon, the differential equation for determining the fast phase contains the ratio of the two frequencies. When these frequencies coincide for a long time, a resonance is implemented in this system. The aim of this paper is to obtain the conditions of monotonic external stability and instability of this resonance. The sufficient conditions for the external stability and instability of the resonance defined in this paper assume that the signs of the analyzed derivatives remain unchanged in the non-resonant section of the change in the independent variable. This paper gives a new classification of the phenomenon of external stability of resonance, which includes weak, linear, and strong stability. It should be noted that the conditions of monotonic external stability and instability of the resonance presented in this paper can be used in various scientific and technological problems, in which resonances are observed. Particularly, the concluding part of the paper considers the application of the results obtained within the framework of the problem of the perturbed motion of a rigid body relative to a fixed point.

scholarly journals Alignment and Proficiency of Virgin Olive Oil Sensory Panels: The OLEUM Approach

Foods ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 355 ◽  
Author(s):  
Sara Barbieri ◽  
Karolina Brkić Bubola ◽  
Alessandra Bendini ◽  
Milena Bučar-Miklavčič ◽  
Florence Lacoste ◽  
...  
Keyword(s):  
Quality Control ◽  
Decision Tree ◽  
Olive Oil ◽  
Reference Materials ◽  
Virgin Olive Oil ◽  
Sensory Data ◽  
Physical Chemical ◽  
Control Procedures ◽  
Reliable Classification

A set of 334 commercial virgin olive oil (VOO) samples were evaluated by six sensory panels during the H2020 OLEUM project. Sensory data were elaborated with two main objectives: (i) to classify and characterize samples in order to use them for possible correlations with physical–chemical data and (ii) to monitor and improve the performance of panels. After revision of the IOC guidelines in 2018, this work represents the first published attempt to verify some of the recommended quality control tools to increase harmonization among panels. Specifically, a new “decision tree” scheme was developed, and some IOC quality control procedures were applied. The adoption of these tools allowed for reliable classification of 289 of 334 VOOs; for the remaining 45, misalignments between panels of first (on the category, 21 cases) or second type (on the main perceived defect, 24 cases) occurred. In these cases, a “formative reassessment” was necessary. At the end, 329 of 334 VOOs (98.5%) were classified, thus confirming the effectiveness of this approach to achieve a better proficiency. The panels showed good performance, but the need to adopt new reference materials that are stable and reproducible to improve the panel’s skills and agreement also emerged.

scholarly journals Clumpiness: time-domain classification of red giant evolutionary states

2020 ◽  
Vol 497 (4) ◽  
pp. 4843-4856 ◽  
Author(s):  
James S Kuszlewicz ◽  
Saskia Hekker ◽  
Keaton J Bell
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Series Data ◽  
Red Giants ◽  
Distance Information ◽  
Evolutionary State ◽  
State Classification ◽  
Red Giant ◽  
Reliable Classification

ABSTRACT Long, high-quality time-series data provided by previous space missions such as CoRoT and Kepler have made it possible to derive the evolutionary state of red giant stars, i.e. whether the stars are hydrogen-shell burning around an inert helium core or helium-core burning, from their individual oscillation modes. We utilize data from the Kepler mission to develop a tool to classify the evolutionary state for the large number of stars being observed in the current era of K2, TESS, and for the future PLATO mission. These missions provide new challenges for evolutionary state classification given the large number of stars being observed and the shorter observing duration of the data. We propose a new method, Clumpiness, based upon a supervised classification scheme that uses ‘summary statistics’ of the time series, combined with distance information from the Gaia mission to predict the evolutionary state. Applying this to red giants in the APOKASC catalogue, we obtain a classification accuracy of $\sim 91{{\ \rm per\ cent}}$ for the full 4 yr of Kepler data, for those stars that are either only hydrogen-shell burning or also helium-core burning. We also applied the method to shorter Kepler data sets, mimicking CoRoT, K2, and TESS achieving an accuracy $\gt 91{{\ \rm per\ cent}}$ even for the 27 d time series. This work paves the way towards fast, reliable classification of vast amounts of relatively short-time-span data with a few, well-engineered features.

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