Periods for Continuous Self-Maps of the Figure-Eight Space

2003 ◽  
Vol 13 (07) ◽  
pp. 1743-1754 ◽  
Author(s):  
Jaume Llibre ◽  
José Paraños ◽  
J. Ángel Rodríguez
Keyword(s):  
Euler Characteristic ◽  
Connected Graph ◽  
Complete Classification ◽  
Branching Points ◽  
Branching Point

Let 8 be the graph shaped like the number 8. This paper contains a characterization of all possible sets of periods for all continuous self-maps of 8 with the branching point fixed. We remark that this characterization is the first complete classification of the sets of periods for all continuous self-maps on a connected graph with negative Euler characteristic with fixed branching points.

ON THE EXTENSION OF SHARKOVSKIĬ'S THEOREM TO CONNECTED GRAPHS WITH NON-POSITIVE EULER CHARACTERISTIC

1995 ◽  
Vol 05 (05) ◽  
pp. 1395-1405 ◽  
Author(s):  
J. LLIBRE ◽  
J. PARAÑOS ◽  
J. A. RODRIGUEZ
Keyword(s):  
Euler Characteristic ◽  
Topological Graph ◽  
Topological Graphs ◽  
Connected Graphs ◽  
Linear Orderings ◽  
Branching Points ◽  
Branching Point

This paper contains a characterization of all possible sets of periods for all continuous self-maps on a connected topological graph with zero Euler characteristic having all branching points fixed. A characterization in terms of linear orderings is given for the simplest connected topological graph with zero Euler characteristic that has a branching point, the topological graph shaped like the letter σ. In this case a proof follows by lifting the continuous self-map on σ. We show the difficulties that arise in the simplest connected topological graphs with negative Euler characteristic, like for instance the topological graph shaped like the figure 8.

On independent permutation separability criteria

2006 ◽  
Vol 6 (3) ◽  
pp. 277-288
Author(s):  
L. Clarisse ◽  
P. Wocjan
Keyword(s):  
Complete Classification ◽  
Necessary Condition ◽  
Numerical Verification ◽  
Separability Criteria

Recently, P.\ Wocjan and M.\ Horodecki [Open Syst.\ Inf.\ Dyn.\ 12, 331 (2005)] gave a characterization of combinatorially independent permutation separability criteria. Combinatorial independence is a necessary condition for permutations to yield truly independent criteria meaning that no criterion is strictly stronger that any other. In this paper we observe that some of these criteria are still dependent and analyze why these dependencies occur. To remove them we introduce an improved necessary condition and give a complete classification of the remaining permutations. We conjecture that the remaining class of criteria only contains truly independent permutation separability criteria. Our conjecture is based on the proof that for two, three and four parties all these criteria are truly independent and on numerical verification of their independence for up to 8 parties. It was commonly believed that for three parties there were 9 independent criteria, here we prove that there are exactly 6 independent criteria for three parties and 22 for four parties.

scholarly journals Phase retrieval in frame theory

2020 ◽  
Author(s):  
◽  
Dorsa Ghoreishi
Keyword(s):  
Phase Retrieval ◽  
Complete Classification ◽  
Frame Theory ◽  
Weak Phase ◽  
The Relationship

This dissertation is the study of phase retrieval in frame theory. The first part is concerned with the analysis of phase retrieval and the complete classification of norm retrieval. Norm retrieval is essential to transfer the properties of phase retrieval to the complement space. The first section includes the results regarding projections and also the characterization of phase retrieval and norm retrieval for subspaces. The second part is the study of weak phase retrieval which was motivated by the idea of reducing the number of vectors satisfying the properties close to phase retrieval. The last section provides the correlation between weak phase retrieval and phase retrieval properties along with the examples illustrating the relationship between weak phase retrieval and the related concepts.

scholarly journals Geometric Classification of Graph C*-algebras over Finite Graphs

2018 ◽  
Vol 70 (2) ◽  
pp. 294-353 ◽  
Author(s):  
Søren Eilers ◽  
Gunnar Restorff ◽  
Efren Ruiz ◽  
Adam P.W. Sørensen
Keyword(s):  
Standard Condition ◽  
Classification Problem ◽  
Complete Classification ◽  
Type I ◽  
Simple Graphs ◽  
Finite Graphs ◽  
C Algebras ◽  
Special Case

AbstractWe address the classification problem for graph C*-algebras of finite graphs (finitely many edges and vertices), containing the class of Cuntz-Krieger algebras as a prominent special case. Contrasting earlier work, we do not assume that the graphs satisfy the standard condition (K), so that the graph C*-algebras may come with uncountably many ideals.We find that in this generality, stable isomorphism of graph C*-algebras does not coincide with the geometric notion of Cuntz move equivalence. However, adding a modest condition on the graphs, the two notions are proved to be mutually equivalent and equivalent to the C*-algebras having isomorphicK-theories. This proves in turn that under this condition, the graph C*-algebras are in fact classifiable byK-theory, providing, in particular, complete classification when the C* - algebras in question are either of real rank zero or type I/postliminal. The key ingredient in obtaining these results is a characterization of Cuntz move equivalence using the adjacency matrices of the graphs.Our results are applied to discuss the classification problem for the quantumlens spaces defined by Hong and Szymański, and to complete the classification of graph C*-algebras associated with all simple graphs with four vertices or less.

scholarly journals Multiplicative automatic sequences

2021 ◽  
Author(s):  
Jakub Konieczny ◽  
Mariusz Lemańczyk ◽  
Clemens Müllner
Keyword(s):  
Complete Classification ◽  
Automatic Sequences ◽  
Complex Valued

AbstractWe obtain a complete classification of complex-valued sequences which are both multiplicative and automatic.

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 Characteristic cohomology and observables in higher spin gravity

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Alexey Sharapov ◽  
Evgeny Skvortsov
Keyword(s):  
Higher Spin Gravity ◽  
Complete Classification ◽  
Gravity Models ◽  
Simons Theory ◽  
Surface Charges ◽  
Higher Spin ◽  
Dynamical Invariants ◽  
Chern Simons ◽  
Conserved Currents

Abstract We give a complete classification of dynamical invariants in 3d and 4d Higher Spin Gravity models, with some comments on arbitrary d. These include holographic correlation functions, interaction vertices, on-shell actions, conserved currents, surface charges, and some others. Surprisingly, there are a good many conserved p-form currents with various p. The last fact, being in tension with ‘no nontrivial conserved currents in quantum gravity’ and similar statements, gives an indication of hidden integrability of the models. Our results rely on a systematic computation of Hochschild, cyclic, and Chevalley-Eilenberg cohomology for the corresponding higher spin algebras. A new invariant in Chern-Simons theory with the Weyl algebra as gauge algebra is also presented.

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