scholarly journals Modular Interpretation of a Non-Reductive Chow Quotient

2018 ◽  
Vol 61 (2) ◽  
pp. 457-477 ◽  
Author(s):  
Patricio Gallardo ◽  
Noah Giansiracusa
Keyword(s):  
Parameter Space ◽  
Rooted Tree ◽  
Configuration Spaces ◽  
Diagonal Action ◽  
Rational Varieties ◽  
Special Case

AbstractThe space of n distinct points and adisjoint parametrized hyperplane in projective d-space up to projectivity – equivalently, configurations of n distinct points in affine d-space up to translation and homothety – has a beautiful compactification introduced by Chen, Gibney and Krashen. This variety, constructed inductively using the apparatus of Fulton–MacPherson configuration spaces, is a parameter space of certain pointed rational varieties whose dual intersection complex is a rooted tree. This generalizes $\overline M _{0,n}$ and shares many properties with it. In this paper, we prove that the normalization of the Chow quotient of (ℙd)n by the diagonal action of the subgroup of projectivities fixing a hyperplane, pointwise, is isomorphic to this Chen–Gibney–Krashen space Td, n. This is a non-reductive analogue of Kapranov's famous quotient construction of $\overline M _{0,n}$, and indeed as a special case we show that $\overline M _{0,n}$ is the Chow quotient of (ℙ1)n−1 by an action of 𝔾m ⋊ 𝔾a.

Finite-core hetons: stability and interactions

2000 ◽  
Vol 423 ◽  
pp. 127-154 ◽  
Author(s):  
M. A. SOKOLOVSKIY ◽  
J. VERRON
Keyword(s):  
Parameter Space ◽  
The Other ◽  
Geometrical Parameters ◽  
Stationary States ◽  
Contour Dynamics ◽  
Surgery Technique ◽  
Special Case ◽  
Dynamics Method

The dynamics of vertically compensated two-layer vortices (hetons) with finite cores are examined within the context of the quasi-geostrophic approximation on the f-plane. The two-layer version of the contour dynamics method is used, and complemented by the so-called contour surgery technique. Special attention is paid to two-heton interactions when the initial locations of the vortex patches are symmetrical. A classification of the different regimes observed is made according to external parameters, namely geometrical parameters and stratification. In this parameter space, novel quasi-stationary states resulting from collisions between two hetons may be observed: (i) formation of a configuration consisting of two-layer vortices moving in opposite directions and, as a special case, a configuration analogous to the ‘klapstoss’ billiard shot, (ii) absorption of one heton by the other and subsequent movement of a new dipole, (iii) formation of two-layer dipoles, larger than the original hetons, associated with rotating peripheral satellite eddies in their wakes. Some of these results may have implications for the analysis of mesoscale vortices in the ocean.

Relativistic thermal electron scale instabilities in sheared flow plasma

2016 ◽  
Vol 82 (2) ◽  
Author(s):  
Evan D. Miller ◽  
Barrett N. Rogers
Keyword(s):  
Parameter Space ◽  
Flow Instability ◽  
Skin Depth ◽  
Unstable Region ◽  
Linear Dispersion ◽  
Thermal Electron ◽  
Sheared Flow ◽  
Depth Scale ◽  
Special Case ◽  
Two Fluid

The linear dispersion relation obeyed by finite-temperature, non-magnetized, relativistic two-fluid plasmas is presented, in the special case of a discontinuous bulk velocity profile and parallel wave vectors. It is found that such flows become universally unstable at the collisionless electron skin-depth scale. Further analyses are performed in the limits of either free-streaming ions or ultra-hot plasmas. In these limits, the system is highly unstable in the parameter regimes associated with either the electron scale Kelvin–Helmholtz instability (ESKHI) or the relativistic electron scale sheared flow instability (RESI) recently highlighted by Gruzinov. Coupling between these modes provides further instability throughout the remaining parameter space, provided both shear flow and temperature are finite. An explicit parameter space bound on the highly unstable region is found.

scholarly journals A polynomial expression for the Hilbert series of the quotient ring of diagonal coinvariants (condensed version)

2011 ◽  
Vol DMTCS Proceedings vol. AO,... (Proceedings) ◽  
Author(s):  
J. Haglund
Keyword(s):  
Hilbert Series ◽  
Quotient Ring ◽  
Rational Functions ◽  
Constant Term ◽  
Diagonal Action ◽  
Integer Coefficients ◽  
Polynomial Expression ◽  
International Audience ◽  
Special Case ◽  
Invent Math

International audience A special case of Haiman's identity [Invent. Math. 149 (2002), pp. 371–407] for the character of the quotient ring of diagonal coinvariants under the diagonal action of the symmetric group yields a formula for the bigraded Hilbert series as a sum of rational functions in $q,t$. In this paper we show how a summation identity of Garsia and Zabrocki for Macdonald polynomial Pieri coefficients can be used to transform Haiman's formula for the Hilbert series into an explicit polynomial in $q,t$ with integer coefficients. We also provide an equivalent formula for the Hilbert series as the constant term in a multivariate Laurent series. Un cas spécial de l'identité de Haiman [Invent. Math. \textbf149 (2002), pp. 371–407] pour le caractère de l'anneau quotient des coinvariants diagonaux sous l'action du groupe symétrique fournit une formule pour la série de Hilbert bigraduée comme somme de fonctions rationnelles en q,t. Dans cet article nous montrons comment une identité de sommation de Garsia et Zabrocki pour les coefficients de Pieri des polynômes de Macdonald peut être utilisée pour transformer la formule de Haiman pour la série de Hilbert en un polynôme explicite en q,t à coefficients entiers. Nous présentons également une formule équivalente pour la série de Hilbert comme terme constant d'une série de Laurent multivariée.

scholarly journals Reconstruction Thresholds on Regular Trees

2003 ◽  
Vol DMTCS Proceedings vol. AC,... (Proceedings) ◽  
Author(s):  
James B. Martin
Keyword(s):  
Statistical Physics ◽  
Gibbs Measures ◽  
Rooted Tree ◽  
Hard Core ◽  
Core Model ◽  
A Value ◽  
Binary State ◽  
International Audience ◽  
Hard Core Model ◽  
Special Case

International audience We consider themodel of broadcasting on a tree, with binary state space, on theinfinite rooted tree $T^k$ in which each node has $k$ children. The root of the tree takesa random value $0$ or $1$, and then each node passes a value independently to each of its children according to a $2x2$ transition matrix $\mathbf{P}$. We say that reconstruction is possible if the values at the dth level of the tree contain non-vanishing information about the value at the root as $d→∞$. Extending a method of Brightwell and Winkler, we obtain new conditions under which reconstruction is impossible, both in the general case and in the special case $p_11=0$. The latter case is closely related to the hard-core model from statistical physics; a corollary of our results is that, for the hard-core model on the $(k+1)$-regular tree with activity $λ =1$, the unique simple invariant Gibbs measure is extremal in the set of Gibbs measures, for any $k ≥ 2$.

scholarly journals Sex, fitness decline and recombination – Muller’s ratchet vs. Ohta’s ratchet

2020 ◽  
Author(s):  
Yongsen Ruan ◽  
Haiyu Wang ◽  
Lingjie Zhang ◽  
Haijun Wen ◽  
Chung-I Wu
Keyword(s):  
Parameter Space ◽  
Asexual Population ◽  
Main Hypothesis ◽  
Muller's Ratchet ◽  
Restricted Parameter Space ◽  
Biological Phenomena ◽  
Muller’S Ratchet ◽  
Selection For ◽  
Driving Fitness ◽  
Special Case

AbstractIt is generally accepted that the absence of recombination reduces the efficacy of natural selection for, or against, mutations. A special case is Muller’s Ratchet (MR) whereby non-recombining genomes experience irreversible fitness decline due to the accumulation of deleterious mutations. MR has been a main hypothesis for sexual reproduction as well as many other biological phenomena. We now ask whether the fitness decline can indeed be stopped if an asexual population turns sexual to become recombining. The possible fitness decline under recombination is referred to as Ohta’s Ratchet (OR). In comparison, MR is more effective in driving fitness reduction than OR, but only in a restricted parameter space of mutation rate, population size and selection. Outside of this space, the two ratchets are equally effective or, alternatively, neither is sufficiently powerful. Furthermore, beneficial mutations can affect the population fitness, which may diverge between the two ratchets, but only in a small parameter space. Since recombination plays a limited role in driving fitness decline, the operation of MR could be far less common in nature than believed. A companion report (see Supplement) surveying the biological phenomena attributed to MR indeed suggests the alternative explanations to be generally more compelling.

Extreme self-sacrifice beyond fusion: Moral expansiveness and the special case of allyship

2018 ◽  
Vol 41 ◽  
Author(s):  
Daniel Crimston ◽  
Matthew J. Hornsey
Keyword(s):  
General Theory ◽  
Biological Markers ◽  
Natural Environment ◽  
Relevant Dimension ◽  
Special Case

AbstractAs a general theory of extreme self-sacrifice, Whitehouse's article misses one relevant dimension: people's willingness to fight and die in support of entities not bound by biological markers or ancestral kinship (allyship). We discuss research on moral expansiveness, which highlights individuals’ capacity to self-sacrifice for targets that lie outside traditional in-group markers, including racial out-groups, animals, and the natural environment.

Determination of the phase structure of polymerblends by electron microscopy

1978 ◽  
Vol 36 (1) ◽  
pp. 492-493
Author(s):  
Dr. G. Kaemof
Keyword(s):  
Screw Extruder ◽  
Electron Microscopic ◽  
Thin Sections ◽  
Single Screw Extruder ◽  
Transmission Electron ◽  
The Matrix ◽  
Twin Screw ◽  
Special Case ◽  
Microscopic Investigations

A mixture of polycarbonate (PC) and styrene-acrylonitrile-copolymer (SAN) represents a very good example for the efficiency of electron microscopic investigations concerning the determination of optimum production procedures for high grade product properties.The following parameters have been varied:components of charge (PC : SAN 50 : 50, 60 : 40, 70 : 30), kind of compounding machine (single screw extruder, twin screw extruder, discontinuous kneader), mass-temperature (lowest and highest possible temperature).The transmission electron microscopic investigations (TEM) were carried out on ultra thin sections, the PC-phase of which was selectively etched by triethylamine.The phase transition (matrix to disperse phase) does not occur - as might be expected - at a PC to SAN ratio of 50 : 50, but at a ratio of 65 : 35. Our results show that the matrix is preferably formed by the components with the lower melting viscosity (in this special case SAN), even at concentrations of less than 50 %.

Test Validation Without Measurement

2016 ◽  
Vol 32 (3) ◽  
pp. 204-214 ◽  
Author(s):  
Emilie Lacot ◽  
Mohammad H. Afzali ◽  
Stéphane Vautier
Keyword(s):  
Test Data ◽  
Test Scores ◽  
Scientific Explanation ◽  
Test Validation ◽  
Clinical Tests ◽  
Ethical Perspective ◽  
Power Of Test ◽  
Memory Accuracy ◽  
Social Uses ◽  
Special Case

Abstract. Test validation based on usual statistical analyses is paradoxical, as, from a falsificationist perspective, they do not test that test data are ordinal measurements, and, from the ethical perspective, they do not justify the use of test scores. This paper (i) proposes some basic definitions, where measurement is a special case of scientific explanation; starting from the examples of memory accuracy and suicidality as scored by two widely used clinical tests/questionnaires. Moreover, it shows (ii) how to elicit the logic of the observable test events underlying the test scores, and (iii) how the measurability of the target theoretical quantities – memory accuracy and suicidality – can and should be tested at the respondent scale as opposed to the scale of aggregates of respondents. (iv) Criterion-related validity is revisited to stress that invoking the explanative power of test data should draw attention on counterexamples instead of statistical summarization. (v) Finally, it is argued that the justification of the use of test scores in specific settings should be part of the test validation task, because, as tests specialists, psychologists are responsible for proposing their tests for social uses.

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