Sense Of Brown Research Articles

Exotic groupoid $C^*$-algebras associated to double groupoids

We consider a class of partial action groupoids called double groupoids which are constructed from pairs of subgroups satisfying similar conditions to those of a matched pair of groups. If the double groupoid is étale, then we show that whenever the partially acting group admit exotic ideal completions in the sense of Brown and Guentner, the corresponding double groupoid also admit exotic $C^*$-completions.

A note on ideal C$$^*$$-completions and amenability

AbstractFor a discrete group G, we consider certain ideals $$\mathcal {I}\subset c_0(G)$$ I ⊂ c 0 ( G ) of sequences with prescribed rate of convergence to zero. We show that the equality between the full group C$$^*$$ ∗ -algebra of G and the C$$^*$$ ∗ -completion $$\textrm{C}^*_{\mathcal {I}}(G)$$ C I ∗ ( G ) in the sense of Brown and Guentner (Bull. London Math. Soc. 45:1181–1193, 2013) implies that G is amenable.

The squeegee man

SummaryIn this “hundreds” honoring Kathleen Stewart, I evoke a scene from my childhood to dwell on misrecognition and the intensities of what José Estaban Muñoz (2020) describes as a “sense of Brown,” that plural yet particular relatedness that emerges out of the displacements and intimacies of coloniality.

Brownness Is Here, Queerness Is Not Yet (T)Here

Brownness Is Here, Queerness Is Not Yet (T)Here

Mediated Identifications

Mediated Identifications

The Brown Commons in the Time of Pandemic

The Brown Commons in the Time of Pandemic

The Sense of Brown. By José Esteban Muñoz. Edited and with an introduction by Joshua Chambers-Letson and Tavia Nyong'o. Durham, NC: Duke University Press, 2020. Pp. xxxiii + 185 + 14 illus. $25.95 Pb.

The Sense of Brown. By José Esteban Muñoz. Edited and with an introduction by Joshua Chambers-Letson and Tavia Nyong'o. Durham, NC: Duke University Press, 2020. Pp. xxxiii + 185 + 14 illus. $25.95 Pb. - Volume 47 Issue 1

The Sense of Brown. By José Esteban Muñoz. Edited by Joshua Chambers-Letson and Tavia Nyong’o. Durham, NC: Duke University Press, 2020; 224 pp.; illustrations. $99.95 cloth, $29.95 paper, e-book available.

The Sense of Brown. By José Esteban Muñoz. Edited by Joshua Chambers-Letson and Tavia Nyong’o. Durham, NC: Duke University Press, 2020; 224 pp.; illustrations. 29.95 paper, e-book available. - Volume 65 Issue 3

Why does invasion imply substitution? Beyond the paradigm of invasion fitness.

Adaptive dynamics combines deterministic population dynamics of groups having different trait values and random process describing mutation and tries to predict the course of evolution of a species of interest. One of basic interests is to know which group survives, residents or mutants. By using invasion fitness as the primary tool, "invasion implies substitution" principle, IIS principle for short, has been established under the existence of a generating function in the sense of Brown and Vincent (Theor Popul Biol 31(1):140-166, 1987) and Vincent and Brown (Evolutionary game theory, natural selection, and darwinian dynamics. Cambridge University Press, Cambridge, 2005). This principle essentially says that the local gradient of invasion fitness ultimately determines the outcome of the competition. However, as we will see in this paper, even if a system is within the scope of IIS principle, its neighborhood always contains systems which are beyond this scope. In this paper, in order to overcome such a limitation, we establish a wider class of systems which is still reasonable as a model of evolution of a species. For our wider class, the notion of raw invasion fitness is introduced. In terms of raw invasion fitness, an explicit criterion for the existence of generating function and a counterpart of IIS principle are obtained. This enables us to discuss small perturbations of a system within or without the scope of generating functions/IIS principle. Eventually, we understand why invasion implies substitution, i.e. why the method using invasion fitness works well with the existence of generating function, from our broader point of view.

Semiclassical limits of quantum affine spaces

AbstractSemiclassical limits of generic multi-parameter quantized coordinate rings A=$\mathcal{O}$q(kn) of affine spaces are constructed and related to A, for k an algebraically closed field of characteristic zero and q a multiplicatively antisymmetric matrix whose entries generate a torsion-free subgroup of k×. A semiclassical limit of A is a Poisson algebra structure on the corresponding classical coordinate ring R=$\mathcal{O}$(kn), and results of Oh, Park, Shin and the authors are used to construct homeomorphisms from the Poisson-prime and Poisson-primitive spectra of R onto the prime and primitive spectra of~A. The Poisson-primitive spectrum of R is then identified with the space of symplectic cores in kn in the sense of Brown and Gordon, and an example is presented (over ℂ) for which the Poisson-primitive spectrum of R is not homeomorphic to the space of symplectic leaves in kn. Finally, these results are extended from quantum affine spaces to quantum affine toric varieties.

(1824) Proposal to Reject the Name Ulmus campestris (Ulmaceae)

It is proposed here that the name Glycine coccinea (and thus also Kennedia coccinea) be conserved in the sense of Ventenat, with his plate (Tabula) 105 from Jard. Malmaison. (1805) as the conserved type, and that Kennedia prostrata be conserved in the sense of Brown, with a Brown specimen in BM as the conserved type (note that other specimens exist in BM, CANB and K which appear to be duplicates of the specimen nominated as conserved type, and these may be considered isotypes if the proposal is accepted). Acceptance of this proposal will preserve the traditional application of the names Kennedia coccinea and K. prostrata and effectively formalise the circumscriptions of Robert Brown (l.c., 1812) followed by all workers in the following two centuries. A failure of the proposal will mean that the plant known for 200 years as Kennedia prostrata R. Br. will need a name change to K. coccinea (Curtis) Vent., and the plant that has been known since 1805 as K. coccinea will require a new name. For two such well-known species such a reversal of names would be most confusing and disruptive.

Compact homotopy functors and the equivariant Sullivan profinite completion

A study is made of compact homotopy functors, i.e. set-valued homotopy functors in the sense of E.H. Brown, defined on an abstract homotopy category C in the sense of Brown, and admitting factorizations through the category of compact Hausdorff spaces. A Sullivan type completion is defined in this abstract context, and it is shown that this gives rise to a completion for ‘topologized objects’ in C . Finally, the equivariant Sullivan profinite completion is obtained by taking C to be the homotopy category of based G-CW complexes, where G is a compact Lie group.

Some Extensions of the Idea of Bias

Laplace ([13], p. 44, lines 5 and 6), in his statement concerning the "milieu de probabilite", seems to have referred to a probability distribution of the true value of a certain quantity ("le veritable instant du phenomene"), or, as we would say at present, to a probability distribution of a certain parameter. Thereby he differs from the attitude adopted in most of the work discussed in the present paper. Yet, one might hold that he possessed the idea of median-unbiased estimators. At any rate, when applying his notions to what Todhunter ([26] p. 469, art. 875) calls a case of no practical value, Laplace ([13], p. 48, lines 11 and 12 from the bottom) virtually rejected the use of arithmetic means of observations. Judging from innumerable texts, one finds that after him emphasis has long been mainly on mean-unbiasedness (see, however, Pitman (]20], bottom of p. 215), who mentions the existence of bias in the sense that the probability that a certain mean-unbiased estimator is less than the parameter in question is $>\frac{1}{2}$). Yet it is hard to find the requirement of mean-unbiasedness justified in print (cf., Brown ([3], lines 6-8 of Section 3): the average of independent mean-unbiased estimates is consistent; Lehmann ([14], lines 4-10 from bottom of p. 588): mean-unbiasedness flows from his general concept in the case of a quadratic loss function; Birnbaum ([2], p. 32): mean-unbiasedness is merely a technically useful property of the classical estimators in the linear estimation problem, which, at least in the case of normal errors, could equally well or preferably be justified on the basis of median-unbiasedness), much harder, in fact, than to find warnings against the hope that much is gained if an estimator be mean-unbiased (cf., Kendall ([12], Vol. 2, Section 17.9); the examples provided by Girshick, Mosteller and Savage ([9], middle of p. 20), Halmos ([10], the end of p. 43), Savage ([23], bottom of p. 244); lack of invariance under certain transformations being stressed by Halmos ([10], bottom of p. 42), Brown ([3], lines 13-16 of Section 3), Fisher ([7], p. 143, line 13 from bottom)). All the same, much interesting work has been devoted to mean-unbiased estimators, some of it investigating the conversion of biased estimators into unbiased ones (e.g., Quenouille [21], Olkin and Pratt [17]), or deriving unbiased estimators ab initio (e.g. Tate [25]). It is not the purpose of this paper to provide a bibliography that is at all near completeness, but it is interesting that the last two references illustrate a statement, made by Schmetterer ([24], middle of p. 215), to the effect that a close connection exists between integral equations and linear operators on the one hand, and the theory of mean-unbiased estimators on the other. This suggests that part of the motivation for the research in this field is of a mathematical, rather than a statistical nature. This view seems to be corroborated by Fraser's statement ([8], lines 12-14 from bottom of p. 49) to the effect that median-unbiasedness does not seem to lend itself to the mathematical analysis needed to find minimum risk estimates, and hence has found little application. The present paper seeks to extend the notion of unbiasedness (and the notion of bias) in a direction different from Lehmann [14] (who gave a definition within the framework of general decision theory), and from Brown [3] (who was primarily concerned with types of unbiasedness, among them median-unbiasedness, that are invariant "under simultaneous one-to-one transformations of the parameter and (its) estimate", or rather under simultaneous strictly monotone transformations of the parameter and its estimate), and from Peterson's [19] density-unbiasedness. It originated in work by the author [29], [30], on the estimation of the latent roots of certain matrices occurring in response surface theory. It had become clear that in this case it was of primary interest whether or not the frequency of obtaining too small (or too large, respectively) estimates would be unduly large. The present paper will make this notion more precise. Several types of bias (or of unbiasedness, respectively) will emerge, all of them clearly invariant in the sense of Brown. Median-unbiasedness will turn out to be a special case of this larger concept. Finally, certain seemingly unfamiliar properties of the sample median, of the product-moment correlation coefficient, and of Olkin and Pratt's function of the latter [17] will be proved and used to illustrate some of the concepts discussed.

Grey in sense of Brown

Grey in sense of Brown

Gery in sense of Brown

Gery in sense of Brown

Grey in Sense of Brown

Grey in Sense of Brown