scholarly journals Representation and Characterization of Nonstationary Processes by Dilation Operators and Induced Shape Space Manifolds

Entropy ◽  
2018 ◽  
Vol 20 (9) ◽  
pp. 717 ◽  
Author(s):  
Maël Dugast ◽  
Guillaume Bouleux ◽  
Eric Marcon
Keyword(s):  
Lie Group ◽  
Correlation Coefficients ◽  
Shape Space ◽  
Rotation Matrices ◽  
Dilation Matrix ◽  
Naimark Dilation ◽  
Periodically Correlated Processes ◽  
New Vision

We proposed in this work the introduction of a new vision of stochastic processes through geometry induced by dilation. The dilation matrices of a given process are obtained by a composition of rotation matrices built in with respect to partial correlation coefficients. Particularly interesting is the fact that the obtention of dilation matrices is regardless of the stationarity of the underlying process. When the process is stationary, only one dilation matrix is obtained and it corresponds therefore to Naimark dilation. When the process is nonstationary, a set of dilation matrices is obtained. They correspond to Kolmogorov decomposition. In this work, the nonstationary class of periodically correlated processes was of interest. The underlying periodicity of correlation coefficients is then transmitted to the set of dilation matrices. Because this set lives on the Lie group of rotation matrices, we can see them as points of a closed curve on the Lie group. Geometrical aspects can then be investigated through the shape of the obtained curves, and to give a complete insight into the space of curves, a metric and the derived geodesic equations are provided. The general results are adapted to the more specific case where the base manifold is the Lie group of rotation matrices, and because the metric in the space of curve naturally extends to the space of shapes; this enables a comparison between curves’ shapes and allows then the classification of random processes’ measures.

scholarly journals Representation and Characterization of Nonstationary Processes by Dilation Operators and Induced Shape Space Manifolds

2018 ◽  
Author(s):  
Mael Dugast ◽  
Guillaume Bouleux ◽  
Eric Marcon
Keyword(s):  
Lie Group ◽  
Correlation Coefficients ◽  
Shape Space ◽  
Rotation Matrices ◽  
Dilation Matrix ◽  
Naimark Dilation ◽  
Periodically Correlated Processes ◽  
New Vision

We proposed in this work the introduction of a new vision of stochastic processes through geometry induced by dilation. The dilation matrices of a given process are obtained by a composition of rotation matrices built in with respect to partial correlation coefficients. Particularly interesting is the fact that the obtention of dilation matrices is regardless of the stationarity of the underlying process. When the process is stationary, only one dilation matrix is obtained and it corresponds therefore to Naimark dilation. When the process is nonstationary, a set of dilation matrices is obtained. They correspond to Kolmogorov decomposition. In this work, the nonstationary class of periodically correlated processes was of interest. The underlying periodicity of correlation coefficients is then transmitted to the set of dilation matrices. Because this set lives on the Lie group of rotation matrices, we can see them as points of a closed curve on the Lie group. Geometrical aspects can then be investigated through the shape of the obtained curves, and to give a complete insight into the space of curves, a metric and the derived geodesic equations are provided. The general results are adapted to the more specific case where the base manifold is the Lie group of rotation matrices, and because the metric in the space of curve naturally extends to the space of shapes, this enables a comparison between curves’ shapes and allows then the classification of processes’ measure.

Chemometric Analysis for the Classification of some Groups of Drugs with Divergent Pharmacological Activity on the Basis of some Chromatographic and Molecular Modeling Parameters

2018 ◽  
Vol 21 (2) ◽  
pp. 125-137
Author(s):  
Jolanta Stasiak ◽  
Marcin Koba ◽  
Marcin Gackowski ◽  
Tomasz Baczek
Keyword(s):  
Correlation Analysis ◽  
Pharmacological Activity ◽  
Correlation Coefficients ◽  
Principal Component ◽  
Cardiovascular Drugs ◽  
New Drugs ◽  
Analgesic Drugs ◽  
Starting Point ◽  
Chromatographic Parameters

Aim and Objective: In this study, chemometric methods as correlation analysis, cluster analysis (CA), principal component analysis (PCA), and factor analysis (FA) have been used to reduce the number of chromatographic parameters (logk/logkw) and various (e.g., 0D, 1D, 2D, 3D) structural descriptors for three different groups of drugs, such as 12 analgesic drugs, 11 cardiovascular drugs and 36 “other” compounds and especially to choose the most important data of them. Material and Methods: All chemometric analyses have been carried out, graphically presented and also discussed for each group of drugs. At first, compounds’ structural and chromatographic parameters were correlated. The best results of correlation analysis were as follows: correlation coefficients like R = 0.93, R = 0.88, R = 0.91 for cardiac medications, analgesic drugs, and 36 “other” compounds, respectively. Next, part of molecular and HPLC experimental data from each group of drugs were submitted to FA/PCA and CA techniques. Results: Almost all results obtained by FA or PCA, and total data variance, from all analyzed parameters (experimental and calculated) were explained by first two/three factors: 84.28%, 76.38 %, 69.71% for cardiovascular drugs, for analgesic drugs and for 36 “other” compounds, respectively. Compounds clustering by CA method had similar characteristic as those obtained by FA/PCA. In our paper, statistical classification of mentioned drugs performed has been widely characterized and discussed in case of their molecular structure and pharmacological activity. Conclusion: Proposed QSAR strategy of reduced number of parameters could be useful starting point for further statistical analysis as well as support for designing new drugs and predicting their possible activity.

scholarly journals Morphological and Ultrastructural Characterization of Hemocytes in an Insect Model, the Hematophagous Dipetalogaster maxima (Hemiptera: Reduviidae)

Insects ◽  
2021 ◽  
Vol 12 (7) ◽  
pp. 640
Author(s):  
Natalia R. Moyetta ◽  
Fabián O. Ramos ◽  
Jimena Leyria ◽  
Lilián E. Canavoso ◽  
Leonardo L. Fruttero
Keyword(s):  
Cell Biology ◽  
Cell Types ◽  
Transmission Electron ◽  
Ultrastructural Characterization ◽  
Current Classification ◽  
Contrast Microscopy ◽  
First Time ◽  
Controversial Aspect

Hemocytes, the cells present in the hemolymph of insects and other invertebrates, perform several physiological functions, including innate immunity. The current classification of hemocyte types is based mostly on morphological features; however, divergences have emerged among specialists in triatomines, the insect vectors of Chagas’ disease (Hemiptera: Reduviidae). Here, we have combined technical approaches in order to characterize the hemocytes from fifth instar nymphs of the triatomine Dipetalogaster maxima. Moreover, in this work we describe, for the first time, the ultrastructural features of D. maxima hemocytes. Using phase contrast microscopy of fresh preparations, five hemocyte populations were identified and further characterized by immunofluorescence, flow cytometry and transmission electron microscopy. The plasmatocytes and the granulocytes were the most abundant cell types, although prohemocytes, adipohemocytes and oenocytes were also found. This work sheds light on a controversial aspect of triatomine cell biology and physiology setting the basis for future in-depth studies directed to address hemocyte classification using non-microscopy-based markers.

scholarly journals Semi-automated regional classification of the style of activity of slow rock-slope deformations using PS InSAR and SqueeSAR velocity data

Landslides ◽  
2021 ◽  
Author(s):  
Chiara Crippa ◽  
Elena Valbuzzi ◽  
Paolo Frattini ◽  
Giovanni B. Crosta ◽  
Margherita C. Spreafico ◽  
...  
Keyword(s):  
Rock Slope ◽  
Progressive Failure ◽  
Principal Component ◽  
Cost Effective ◽  
Displacement Rate ◽  
Machine Learning Classification ◽  
Management Perspective ◽  
Alpine Environments

AbstractLarge slow rock-slope deformations, including deep-seated gravitational slope deformations and large landslides, are widespread in alpine environments. They develop over thousands of years by progressive failure, resulting in slow movements that impact infrastructures and can eventually evolve into catastrophic rockslides. A robust characterization of their style of activity is thus required in a risk management perspective. We combine an original inventory of slow rock-slope deformations with different PS-InSAR and SqueeSAR datasets to develop a novel, semi-automated approach to characterize and classify 208 slow rock-slope deformations in Lombardia (Italian Central Alps) based on their displacement rate, kinematics, heterogeneity and morphometric expression. Through a peak analysis of displacement rate distributions, we characterize the segmentation of mapped landslides and highlight the occurrence of nested sectors with differential activity and displacement rates. Combining 2D decomposition of InSAR velocity vectors and machine learning classification, we develop an automatic approach to characterize the kinematics of each landslide. Then, we sequentially combine principal component and K-medoids cluster analyses to identify groups of slow rock-slope deformations with consistent styles of activity. Our methodology is readily applicable to different landslide datasets and provides an objective and cost-effective support to land planning and the prioritization of local-scale studies aimed at granting safety and infrastructure integrity.

scholarly journals The Underlying Order Induced by Orthogonality and the Quantum Speed Limit

2021 ◽  
Vol 3 (3) ◽  
pp. 376-388
Author(s):  
Francisco J. Sevilla ◽  
Andrea Valdés-Hernández ◽  
Alan J. Barrios
Keyword(s):  
Energy Spectrum ◽  
Energy Distribution ◽  
Finite Time ◽  
Complete Characterization ◽  
Comprehensive Analysis ◽  
Orthogonality Condition ◽  
Speed Limit ◽  
Physical Quantities

We perform a comprehensive analysis of the set of parameters {ri} that provide the energy distribution of pure qutrits that evolve towards a distinguishable state at a finite time τ, when evolving under an arbitrary and time-independent Hamiltonian. The orthogonality condition is exactly solved, revealing a non-trivial interrelation between τ and the energy spectrum and allowing the classification of {ri} into families organized in a 2-simplex, δ2. Furthermore, the states determined by {ri} are likewise analyzed according to their quantum-speed limit. Namely, we construct a map that distinguishes those ris in δ2 correspondent to states whose orthogonality time is limited by the Mandelstam–Tamm bound from those restricted by the Margolus–Levitin one. Our results offer a complete characterization of the physical quantities that become relevant in both the preparation and study of the dynamics of three-level states evolving towards orthogonality.

scholarly journals Molecular Classification and Tumor Microenvironment Characterization of Gallbladder Cancer by Comprehensive Genomic and Transcriptomic Analysis

Cancers ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 733
Author(s):  
Nobutaka Ebata ◽  
Masashi Fujita ◽  
Shota Sasagawa ◽  
Kazuhiro Maejima ◽  
Yuki Okawa ◽  
...  
Keyword(s):  
Tumor Microenvironment ◽  
Gallbladder Cancer ◽  
Epithelial To Mesenchymal Transition ◽  
Molecular Classification ◽  
Mesenchymal Transition ◽  
Elevated Expression ◽  
Fresh Frozen ◽  
Therapeutic Decision Making

Gallbladder cancer (GBC), a rare but lethal disease, is often diagnosed at advanced stages. So far, molecular characterization of GBC is insufficient, and a comprehensive molecular portrait is warranted to uncover new targets and classify GBC. We performed a transcriptome analysis of both coding and non-coding RNAs from 36 GBC fresh-frozen samples. The results were integrated with those of comprehensive mutation profiling based on whole-genome or exome sequencing. The clustering analysis of RNA-seq data facilitated the classification of GBCs into two subclasses, characterized by high or low expression levels of TME (tumor microenvironment) genes. A correlation was observed between gene expression and pathological immunostaining. TME-rich tumors showed significantly poor prognosis and higher recurrence rate than TME-poor tumors. TME-rich tumors showed overexpression of genes involved in epithelial-to-mesenchymal transition (EMT) and inflammation or immune suppression, which was validated by immunostaining. One non-coding RNA, miR125B1, exhibited elevated expression in stroma-rich tumors, and miR125B1 knockout in GBC cell lines decreased its invasion ability and altered the EMT pathway. Mutation profiles revealed TP53 (47%) as the most commonly mutated gene, followed by ELF3 (13%) and ARID1A (11%). Mutations of ARID1A, ERBB3, and the genes related to the TGF-β signaling pathway were enriched in TME-rich tumors. This comprehensive analysis demonstrated that TME, EMT, and TGF-β pathway alterations are the main drivers of GBC and provides a new classification of GBCs that may be useful for therapeutic decision-making.

scholarly journals Construction and Characterization of Representations of SU(7) for GUT Model Builders

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1044
Author(s):  
Daniel Jones ◽  
Jeffery A. Secrest
Keyword(s):  
Gauge Symmetry ◽  
Symmetry Group ◽  
Lie Group ◽  
Cartan Subalgebra ◽  
Natural Extension ◽  
Grand Unification ◽  
Raising And Lowering Operators ◽  
Higher Dimensional ◽  
Lowering Operators

The natural extension to the SU(5) Georgi-Glashow grand unification model is to enlarge the gauge symmetry group. In this work, the SU(7) symmetry group is examined. The Cartan subalgebra is determined along with their commutation relations. The associated roots and weights of the SU(7) algebra are derived and discussed. The raising and lowering operators are explicitly constructed and presented. Higher dimensional representations are developed by graphical as well as tensorial methods. Applications of the SU(7) Lie group to supersymmetric grand unification as well as applications are discussed.

scholarly journals On equicontinuous factors of flows on locally path-connected compact spaces

2020 ◽  
pp. 1-18
Author(s):  
NIKOLAI EDEKO
Keyword(s):  
Lie Group ◽  
Metric Space ◽  
Betti Number ◽  
Alternative Proof ◽  
Simple Consequence ◽  
Compact Metric Space ◽  
Invariant Functions ◽  
Compact Spaces ◽  
Path Connected

Abstract We consider a locally path-connected compact metric space K with finite first Betti number $\textrm {b}_1(K)$ and a flow $(K, G)$ on K such that G is abelian and all G-invariant functions $f\,{\in}\, \text{\rm C}(K)$ are constant. We prove that every equicontinuous factor of the flow $(K, G)$ is isomorphic to a flow on a compact abelian Lie group of dimension less than ${\textrm {b}_1(K)}/{\textrm {b}_0(K)}$ . For this purpose, we use and provide a new proof for Theorem 2.12 of Hauser and Jäger [Monotonicity of maximal equicontinuous factors and an application to toral flows. Proc. Amer. Math. Soc.147 (2019), 4539–4554], which states that for a flow on a locally connected compact space the quotient map onto the maximal equicontinuous factor is monotone, i.e., has connected fibers. Our alternative proof is a simple consequence of a new characterization of the monotonicity of a quotient map $p\colon K\to L$ between locally connected compact spaces K and L that we obtain by characterizing the local connectedness of K in terms of the Banach lattice $\textrm {C}(K)$ .

scholarly journals Practical classification of triple-negative breast cancer: intratumoral heterogeneity, mechanisms of drug resistance, and novel therapies

2020 ◽  
Vol 6 (1) ◽  
Author(s):  
Antonio Marra ◽  
Dario Trapani ◽  
Giulia Viale ◽  
Carmen Criscitiello ◽  
Giuseppe Curigliano
Keyword(s):  
Breast Cancer ◽  
Triple Negative Breast Cancer ◽  
Triple Negative ◽  
Residual Disease ◽  
Therapeutic Approaches ◽  
Minimal Residual Disease Monitoring ◽  
Anticancer Treatment ◽  
Immune Contexture

Abstract Triple-negative breast cancer (TNBC) is not a unique disease, encompassing multiple entities with marked histopathological, transcriptomic and genomic heterogeneity. Despite several efforts, transcriptomic and genomic classifications have remained merely theoretic and most of the patients are being treated with chemotherapy. Driver alterations in potentially targetable genes, including PIK3CA and AKT, have been identified across TNBC subtypes, prompting the implementation of biomarker-driven therapeutic approaches. However, biomarker-based treatments as well as immune checkpoint inhibitor-based immunotherapy have provided contrasting and limited results so far. Accordingly, a better characterization of the genomic and immune contexture underpinning TNBC, as well as the translation of the lessons learnt in the metastatic disease to the early setting would improve patients’ outcomes. The application of multi-omics technologies, biocomputational algorithms, assays for minimal residual disease monitoring and novel clinical trial designs are strongly warranted to pave the way toward personalized anticancer treatment for patients with TNBC.

Lie group classification of the N-th-order nonlinear evolution equations

2011 ◽  
Vol 54 (12) ◽  
pp. 2553-2572 ◽  
Author(s):  
ShouFeng Shen ◽  
ChangZheng Qu ◽  
Qing Huang ◽  
YongYang Jin
Keyword(s):  
Lie Group ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Group Classification ◽  
Nonlinear Evolution Equations ◽  
Lie Group Classification
Sign in / Sign up

Export Citation Format

Share Document