scholarly journals Korn and Poincaré-Korn inequalities for functions with a small jump set

2021 ◽  
Author(s):  
Filippo Cagnetti ◽  
Antonin Chambolle ◽  
Lucia Scardia
Keyword(s):  
Higher Dimension ◽  
Approximation Result ◽  
Rigidity Result ◽  
Small Set ◽  
Jump Set

AbstractIn this paper we prove a regularity and rigidity result for displacements in $$GSBD^p$$ G S B D p , for every $$p>1$$ p > 1 and any dimension $$n\ge 2$$ n ≥ 2 . We show that a displacement in $$GSBD^p$$ G S B D p with a small jump set coincides with a $$W^{1,p}$$ W 1 , p function, up to a small set whose perimeter and volume are controlled by the size of the jump. This generalises to higher dimension a result of Conti, Focardi and Iurlano. A consequence of this is that such displacements satisfy, up to a small set, Poincaré-Korn and Korn inequalities. As an application, we deduce an approximation result which implies the existence of the approximate gradient for displacements in $$GSBD^p$$ G S B D p .

Arrangement Of Monomeric Units In Fibrin

1979 ◽  
Author(s):  
Jan Hermans
Keyword(s):  
Fiber Axis ◽  
High Symmetry ◽  
Linear Polymers ◽  
Fiber Volume ◽  
High Fiber ◽  
Rotation Axes ◽  
Small Set ◽  
Helical Turn ◽  
The One ◽  
Kinetics Of

Measurements of light scattering have given much information about formation and properties of fibrin. These studies have determined mass-length ratio of linear polymers (protofibrils) and of fibers, kinetics of polymerization and of lateral association and volume-mass ratio of thick fibers. This ratio is 5 to 1. On the one hand, this high value suggests that the fiber contains channels that allow the diffusion of enzymes such as Factor XHIa and plasmin; on the other hand, the high value appears paradoxical for a stiff fiber made up of elongated units (fibrin monomers) arranged in parallel. Such a high fiber volume is a property of only a small set out of many high-symmetry models of fibrin, which may be constructed from overlapping three-domain monomers which are arranged into strands, are aligned nearly parallel to the fiber axis and make adequate longitudinal and lateral contacts. These models contain helical protofibrils related to each other by rotation axes parallel to the fiber axis. The protofibrils may contain 2, 3 or 4 monomers per helical turn and there are four possible symmetries. A large specific volume is achieved if the ends of each monomer are slightly displaced from the protofibril axis, either by a shift or by a tilt of the monomer. The fiber containing tilted monomers is more highly interconnected; the two ends of a tilted monomer form lateral contacts with different adjacent protofibrils, whereas the two ends of a non-tilted monomer contact the same adjacent protofibril(s).

scholarly journals Neural network aided approximation and parameter inference of non-Markovian models of gene expression

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Qingchao Jiang ◽  
Xiaoming Fu ◽  
Shifu Yan ◽  
Runlai Li ◽  
Wenli Du ◽  
...  
Keyword(s):  
Neural Network ◽  
Stochastic Dynamics ◽  
Stochastic Simulations ◽  
Parameter Inference ◽  
Biochemical Processes ◽  
Markovian Models ◽  
The Neural Network ◽  
Large Numbers ◽  
Small Set ◽  
Noisy Measurements

AbstractNon-Markovian models of stochastic biochemical kinetics often incorporate explicit time delays to effectively model large numbers of intermediate biochemical processes. Analysis and simulation of these models, as well as the inference of their parameters from data, are fraught with difficulties because the dynamics depends on the system’s history. Here we use an artificial neural network to approximate the time-dependent distributions of non-Markovian models by the solutions of much simpler time-inhomogeneous Markovian models; the approximation does not increase the dimensionality of the model and simultaneously leads to inference of the kinetic parameters. The training of the neural network uses a relatively small set of noisy measurements generated by experimental data or stochastic simulations of the non-Markovian model. We show using a variety of models, where the delays stem from transcriptional processes and feedback control, that the Markovian models learnt by the neural network accurately reflect the stochastic dynamics across parameter space.

scholarly journals Cayley Graphs Without a Bounded Eigenbasis

2020 ◽  
Author(s):  
Ashwin Sah ◽  
Mehtaab Sawhney ◽  
Yufei Zhao
Keyword(s):  
Cayley Graph ◽  
Orthonormal Basis ◽  
Cayley Graphs ◽  
The Other ◽  
Transitive Graph ◽  
Classic Result ◽  
Other Hand ◽  
Small Set ◽  
Vertex Transitive ◽  
Vertex Transitive Graph

Abstract Does every $n$-vertex Cayley graph have an orthonormal eigenbasis all of whose coordinates are $O(1/\sqrt{n})$? While the answer is yes for abelian groups, we show that it is no in general. On the other hand, we show that every $n$-vertex Cayley graph (and more generally, vertex-transitive graph) has an orthonormal basis whose coordinates are all $O(\sqrt{\log n / n})$, and that this bound is nearly best possible. Our investigation is motivated by a question of Assaf Naor, who proved that random abelian Cayley graphs are small-set expanders, extending a classic result of Alon–Roichman. His proof relies on the existence of a bounded eigenbasis for abelian Cayley graphs, which we now know cannot hold for general groups. On the other hand, we navigate around this obstruction and extend Naor’s result to nonabelian groups.

Nominal and pronominal gender: Putting Greenberg’s Universal 43 to the test

2020 ◽  
Vol 73 (4) ◽  
pp. 525-574
Author(s):  
Thomas Berg
Keyword(s):  
Strong Correlation ◽  
Time Frame ◽  
Grammatical Gender ◽  
Personal Pronouns ◽  
Small Set ◽  
Pronominal Gender ◽  
Processing Difficulty

AbstractThe aim of this study is to scrutinize Greenberg’s Universal 43, which predicts pronominal gender in the presence of nominal gender. On the basis of a sample of 500 gendered and ungendered languages, gender marking is examined in nouns, personal pronouns, possessors and possessums. Ungendered languages outnumber gendered languages. Eight out of 12 logically possible gender constellations are attested in the database. In keeping with Greenberg, languages with nominal gender show a strong bias towards gendered pronouns. There is a strong correlation between gendered personal pronouns and gendered possessors. Gendered possessums are cross-linguistically uncommon. The empirical patterns are brought about by a small set of theoretical principles. Gender is independently specified for each category. Gender marking is an effort. The strength of the correlation depends on the “distance” between two given gender sites. Coding gender twice in the same time frame creates a processing difficulty. Natural and grammatical gender conspire to generate the gender sensitivity of individual categories.

scholarly journals A Korn-type inequality in SBD for functions with small jump sets

2017 ◽  
Vol 27 (13) ◽  
pp. 2461-2484 ◽  
Author(s):  
Manuel Friedrich
Keyword(s):  
Bounded Variation ◽  
Elastic Strain ◽  
Special Functions ◽  
Type Inequality ◽  
Rigid Motion ◽  
Exceptional Set ◽  
Finite Perimeter ◽  
Functions Of Bounded Deformation ◽  
Jump Set

We present a Korn-type inequality in a planar setting for special functions of bounded deformation. We prove that for each function in [Formula: see text] with a sufficiently small jump set the distance of the function and its derivative from an infinitesimal rigid motion can be controlled in terms of the linearized elastic strain outside of a small exceptional set of finite perimeter. Particularly, the result shows that each function in [Formula: see text] has bounded variation away from an arbitrarily small part of the domain.

scholarly journals Visual response of ventrolateral prefrontal neurons and their behavior-related modulation

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Stefano Rozzi ◽  
Marco Bimbi ◽  
Alfonso Gravante ◽  
Luciano Simone ◽  
Leonardo Fogassi
Keyword(s):  
Visual Cues ◽  
Visual Stimuli ◽  
Visual Response ◽  
Visual Responses ◽  
Action Execution ◽  
Natural Behavior ◽  
Large Sector ◽  
Small Set ◽  
Early Passive ◽  
Task Conditions

AbstractThe ventral part of lateral prefrontal cortex (VLPF) of the monkey receives strong visual input, mainly from inferotemporal cortex. It has been shown that VLPF neurons can show visual responses during paradigms requiring to associate arbitrary visual cues to behavioral reactions. Further studies showed that there are also VLPF neurons responding to the presentation of specific visual stimuli, such as objects and faces. However, it is largely unknown whether VLPF neurons respond and differentiate between stimuli belonging to different categories, also in absence of a specific requirement to actively categorize or to exploit these stimuli for choosing a given behavior. The first aim of the present study is to evaluate and map the responses of neurons of a large sector of VLPF to a wide set of visual stimuli when monkeys simply observe them. Recent studies showed that visual responses to objects are also present in VLPF neurons coding action execution, when they are the target of the action. Thus, the second aim of the present study is to compare the visual responses of VLPF neurons when the same objects are simply observed or when they become the target of a grasping action. Our results indicate that: (1) part of VLPF visually responsive neurons respond specifically to one stimulus or to a small set of stimuli, but there is no indication of a “passive” categorical coding; (2) VLPF neuronal visual responses to objects are often modulated by the task conditions in which the object is observed, with the strongest response when the object is target of an action. These data indicate that VLPF performs an early passive description of several types of visual stimuli, that can then be used for organizing and planning behavior. This could explain the modulation of visual response both in associative learning and in natural behavior.

scholarly journals The Influence of Varying Fluorination Patterns on the Thermodynamics and Kinetics of Benzenesulfonamide Binding to Human Carbonic Anhydrase II

Biomolecules ◽  
2020 ◽  
Vol 10 (4) ◽  
pp. 509 ◽  
Author(s):  
Steffen Glöckner ◽  
Khang Ngo ◽  
Björn Wagner ◽  
Andreas Heine ◽  
Gerhard Klebe
Keyword(s):  
Carbonic Anhydrase ◽  
Carbonic Anhydrase Ii ◽  
The Novel ◽  
Binding Modes ◽  
X Ray ◽  
Structure Activity ◽  
Small Set ◽  
Novel Method ◽  
Human Carbonic Anhydrase ◽  
Kinetics Of

The fluorination of lead-like compounds is a common tool in medicinal chemistry to alter molecular properties in various ways and with different goals. We herein present a detailed study of the binding of fluorinated benzenesulfonamides to human Carbonic Anhydrase II by complementing macromolecular X-ray crystallographic observations with thermodynamic and kinetic data collected with the novel method of kinITC. Our findings comprise so far unknown alternative binding modes in the crystalline state for some of the investigated compounds as well as complex thermodynamic and kinetic structure-activity relationships. They suggest that fluorination of the benzenesulfonamide core is especially advantageous in one position with respect to the kinetic signatures of binding and that a higher degree of fluorination does not necessarily provide for a higher affinity or more favorable kinetic binding profiles. Lastly, we propose a relationship between the kinetics of binding and ligand acidity based on a small set of compounds with similar substitution patterns.

Conservation or change? Exploring trends in Modern Hebrew in light of new spoken corpora of the first two generations of speakers

2020 ◽  
Vol 54 (s41) ◽  
pp. 89-115
Author(s):  
Einat Gonen
Keyword(s):  
Early Modern ◽  
First Generation ◽  
Linguistic Features ◽  
The Feminine ◽  
Two Generations ◽  
Modern Hebrew ◽  
Small Set ◽  
Diachronic Study ◽  
The 1950S

Abstract This paper presents a diachronic study of Modern Hebrew agreement between numerals and their quantified nouns. This research is possible thanks to the discovery of two rare collections of recordings from the 1950s and 1960s, which document four generations of speakers and have become important sources of spoken Early Modern Hebrew. On the basis of these two corpora, I compare numeral agreement in the first two generations of speakers with present-day usage and analyze trends of change and conversation in Modern Hebrew. The study shows that the first generation of speakers (“Gen1”) largely acquired the gender distinction of cardinals. However, in contrast to other agreement issues that educated Gen1 speakers realized fully, numeral use showed variation and absence of agreement in a small set of cases. Moreover, some linguistic features of Gen1 Hebrew found in this study no longer characterize Present-Day Hebrew; among these features is prosodic conditioning, which led to a Gen1 tendency to use the feminine form of the numeral ‘four’ with masculine nouns more frequently than was the case with other numerals.

scholarly journals A note on moduli spaces of conformal classes for flat tori of higher dimension and on their conformal multiplication

2021 ◽  
Author(s):  
Anna Gori ◽  
Alberto Verjovsky ◽  
Fabio Vlacci
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Abelian Varieties ◽  
Complex Multiplication ◽  
Higher Dimension ◽  
Geometric Constructions ◽  
Flat Torus ◽  
Flat Tori

AbstractMotivated by the theory of complex multiplication of abelian varieties, in this paper we study the conformality classes of flat tori in $${\mathbb {R}}^{n}$$ R n and investigate criteria to determine whether a n-dimensional flat torus has non trivial (i.e. bigger than $${\mathbb {Z}}^{*}={\mathbb {Z}}{\setminus }\{0\}$$ Z ∗ = Z \ { 0 } ) semigroup of conformal endomorphisms (the analogs of isogenies for abelian varieties). We then exhibit several geometric constructions of tori with this property and study the class of conformally equivalent lattices in order to describe the moduli space of the corresponding tori.

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