scholarly journals Real-analytic AbC constructions on the torus

2018 ◽  
Vol 39 (10) ◽  
pp. 2643-2688
Author(s):  
SHILPAK BANERJEE ◽  
PHILIPP KUNDE
Keyword(s):  
General Framework ◽  
Smooth Category ◽  
Real Analytic ◽  
Uniquely Ergodic ◽  
Conjugation Method

In this article we demonstrate a way to extend the AbC (approximation by conjugation) method invented by Anosov and Katok from the smooth category to the category of real-analytic diffeomorphisms on the torus. We present a general framework for such constructions and prove several results. In particular, we construct minimal but not uniquely ergodic diffeomorphisms and non-standard real-analytic realizations of toral translations.

scholarly journals Non-standard real-analytic realizations of some rotations of the circle

2015 ◽  
Vol 37 (5) ◽  
pp. 1369-1386 ◽  
Author(s):  
SHILPAK BANERJEE
Keyword(s):  
Two Dimensional ◽  
Dimensional Torus ◽  
Smooth Approximation ◽  
Analytic Set ◽  
Irrational Rotations ◽  
Zero Entropy ◽  
Real Analytic ◽  
Set Up ◽  
Uniquely Ergodic ◽  
Conjugation Method

We extend some aspects of the smooth approximation by conjugation method to the real-analytic set-up, and create examples of zero entropy, uniquely ergodic, real-analytic diffeomorphisms of the two-dimensional torus that are metrically isomorphic to some (Liouvillian) irrational rotations of the circle.

Real-analytic weak mixing diffeomorphisms preserving a measurable Riemannian metric

2016 ◽  
Vol 37 (5) ◽  
pp. 1547-1569 ◽  
Author(s):  
PHILIPP KUNDE
Keyword(s):  
Riemannian Metric ◽  
Weak Mixing ◽  
Real Analytic ◽  
Conjugation Method

On the torus$\mathbb{T}^{m}$of dimension$m\geq 2$we prove the existence of a real-analytic weak mixing diffeomorphism preserving a measurable Riemannian metric. The proof is based on a real-analytic version of the approximation by conjugation method with explicitly defined conjugation maps and partition elements.

scholarly journals Ergodic Properties of Randomly Coloured Point Sets

2013 ◽  
Vol 65 (2) ◽  
pp. 349-402 ◽  
Author(s):  
Peter Müller ◽  
Christoph Richard
Keyword(s):  
General Framework ◽  
Point Sets ◽  
Locally Compact ◽  
Unimodular Group ◽  
Ergodic Properties ◽  
Straightforward Application ◽  
Countable Space ◽  
Local Complexity ◽  
Second Countable Space ◽  
Uniquely Ergodic

AbstractWe provide a framework for studying randomly coloured point sets in a locally compact second-countable space on which a metrizable unimodular group acts continuously and properly. We first construct and describe an appropriate dynamical system for uniformly discrete uncoloured point sets. For point sets of finite local complexity, we characterize ergodicity geometrically in terms of pattern frequencies. The general framework allows us to incorporate a random colouring of the point sets. We derive an ergodic theorem for randomly coloured point sets with finite-range dependencies. Special attention is paid to the exclusion of exceptional instances for uniquely ergodic systems. The setup allows for a straightforward application to randomly coloured graphs

Phonologically conditioned allomorphy in the morphology of Surmiran (Rumantsch)

2008 ◽  
Vol 1 (2) ◽  
pp. 109-134 ◽  
Author(s):  
Stephen R. Anderson
Keyword(s):  
Optimality Theory ◽  
General Framework ◽  
Great Majority ◽  
Historical Change ◽  
Romance Languages ◽  
Morphological Properties ◽  
Entire System ◽  
Verbal System ◽  
Extended Sense ◽  
Phonological Rule

Alternations between allomorphs that are not directly related by phonological rule, but whose selection is governed by phonological properties of the environment, have attracted the sporadic attention of phonologists and morphologists. Such phenomena are commonly limited to rather small corners of a language's structure, however, and as a result have not been a major theoretical focus. This paper examines a set of alternations in Surmiran, a Swiss Rumantsch language, that have this character and that pervade the entire system of the language. It is shown that the alternations in question, best attested in the verbal system, are not conditioned by any coherent set of morphological properties (either straightforwardly or in the extended sense of ‘morphomes’ explored in other Romance languages by Maiden). These alternations are, however, straightforwardly aligned with the location of stress in words, and an analysis is proposed within the general framework of Optimality Theory to express this. The resulting system of phonologically conditioned allomorphy turns out to include the great majority of patterning which one might be tempted to treat as productive phonology, but which has been rendered opaque (and subsequently morphologized) as a result of the working of historical change.

More's usage of Latin verbal predicates: the particular case of fio

Moreana ◽  
2019 ◽  
Vol 56 (Number 211) (1) ◽  
pp. 97-120
Author(s):  
Concepción Cabrillana
Keyword(s):  
General Framework ◽  
Medieval Latin ◽  
Lexical Semantic ◽  
Syntactic Features ◽  
Comparative Review ◽  
Poetic Text

This article addresses Thomas More's use of an especially complex Latin predicate, fio, as a means of examining the degree of classicism in this aspect of his writing. To this end, the main lexical-semantic and syntactic features of the verb in Classical Latin are presented, and a comparative review is made of More's use of the predicate—and also its use in texts contemporaneous to More, as well as in Late and Medieval Latin—in both prose and poetry. The analysis shows that he works within a general framework of classicism, although he introduces some of his own idiosyncrasies, these essentially relating to the meaning of the verb that he employs in a preferential way and to the variety of verbal forms that occur in his poetic text.

Development and destruction of the liberal prison system in Spain: a general framework for studying the topic

2019 ◽  
Vol 5 (10) ◽  
pp. 424
Author(s):  
Luis Gargallo Vaamonde
Keyword(s):  
Civil War ◽  
20Th Century ◽  
General Framework ◽  
Belief System ◽  
Prison System ◽  
Early Years ◽  
Second Republic ◽  
Social Harmony ◽  
The Government ◽  
The Individual

During the Restoration and the Second Republic, up until the outbreak of the Civil War, the prison system that was developed in Spain had a markedly liberal character. This system had begun to acquire robustness and institutional credibility from the first dec- ade of the 20th Century onwards, reaching a peak in the early years of the government of the Second Republic. This process resulted in the establishment of a penitentiary sys- tem based on the widespread and predominant values of liberalism. That liberal belief system espoused the defence of social harmony, property and the individual, and penal practices were constructed on the basis of those principles. Subsequently, the Civil War and the accompanying militarist culture altered the prison system, transforming it into an instrument at the service of the conflict, thereby wiping out the liberal agenda that had been nurtured since the mid-19th Century.

Target-Templated de novo Design of Macrocyclic D-/L-Peptides: Inhibitors of the PD-1/PD-L1 Interaction

2020 ◽  
Author(s):  
Salvador Guardiola ◽  
Monica Varese ◽  
Xavier Roig ◽  
Jesús Garcia ◽  
Ernest Giralt
Keyword(s):  
Protein Interactions ◽  
Cyclic Peptides ◽  
General Framework ◽  
Large Scale ◽  
De Novo ◽  
Inhibitory Effect ◽  
Original Text ◽  
Protein Protein Interactions ◽  
Retraction Notice ◽  
Pharmaceutical Properties

<p>NOTE: This preprint has been retracted by consensus from all authors. See the retraction notice in place above; the original text can be found under "Version 1", accessible from the version selector above.</p><p><br></p><p>------------------------------------------------------------------------</p><p><br></p><p>Peptides, together with antibodies, are among the most potent biochemical tools to modulate challenging protein-protein interactions. However, current structure-based methods are largely limited to natural peptides and are not suitable for designing target-specific binders with improved pharmaceutical properties, such as macrocyclic peptides. Here we report a general framework that leverages the computational power of Rosetta for large-scale backbone sampling and energy scoring, followed by side-chain composition, to design heterochiral cyclic peptides that bind to a protein surface of interest. To showcase the applicability of our approach, we identified two peptides (PD-<i>i</i>3 and PD-<i>i</i>6) that target PD-1, a key immune checkpoint, and work as protein ligand decoys. A comprehensive biophysical evaluation confirmed their binding mechanism to PD-1 and their inhibitory effect on the PD-1/PD-L1 interaction. Finally, elucidation of their solution structures by NMR served as validation of our <i>de novo </i>design approach. We anticipate that our results will provide a general framework for designing target-specific drug-like peptides.<i></i></p>

A Target-Based Method for Designing Heterochiral Cyclic Peptide Binders: De Novo Inhibitors of the PD-1/PD-L1 Interaction

2020 ◽  
Author(s):  
Salvador Guardiola ◽  
Monica Varese ◽  
Xavier Roig ◽  
Jesús Garcia ◽  
Ernest Giralt
Keyword(s):  
Protein Interactions ◽  
Cyclic Peptides ◽  
General Framework ◽  
Large Scale ◽  
Cyclic Peptide ◽  
De Novo ◽  
Inhibitory Effect ◽  
Original Text ◽  
Retraction Notice ◽  
Pharmaceutical Properties

<p>NOTE: This preprint has been retracted by consensus from all authors. See the retraction notice in place above; the original text can be found under "Version 1", accessible from the version selector above.</p><p><br></p><p>------------------------------------------------------------------------</p><p><br></p><p>Peptides, together with antibodies, are among the most potent biochemical tools to modulate challenging protein-protein interactions. However, current structure-based methods are largely limited to natural peptides and are not suitable for designing target-specific binders with improved pharmaceutical properties, such as macrocyclic peptides. Here we report a general framework that leverages the computational power of Rosetta for large-scale backbone sampling and energy scoring, followed by side-chain composition, to design heterochiral cyclic peptides that bind to a protein surface of interest. To showcase the applicability of our approach, we identified two peptides (PD-<i>i</i>3 and PD-<i>i</i>6) that target PD-1, a key immune checkpoint, and work as protein ligand decoys. A comprehensive biophysical evaluation confirmed their binding mechanism to PD-1 and their inhibitory effect on the PD-1/PD-L1 interaction. Finally, elucidation of their solution structures by NMR served as validation of our <i>de novo </i>design approach. We anticipate that our results will provide a general framework for designing target-specific drug-like peptides.<i></i></p>

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