557 research outputs found
Vickrey Auctions for Irregular Distributions
The classic result of Bulow and Klemperer \cite{BK96} says that in a
single-item auction recruiting one more bidder and running the Vickrey auction
achieves a higher revenue than the optimal auction's revenue on the original
set of bidders, when values are drawn i.i.d. from a regular distribution. We
give a version of Bulow and Klemperer's result in settings where bidders'
values are drawn from non-i.i.d. irregular distributions. We do this by
modeling irregular distributions as some convex combination of regular
distributions. The regular distributions that constitute the irregular
distribution correspond to different population groups in the bidder
population. Drawing a bidder from this collection of population groups is
equivalent to drawing from some convex combination of these regular
distributions. We show that recruiting one extra bidder from each underlying
population group and running the Vickrey auction gives at least half of the
optimal auction's revenue on the original set of bidders
A universal characterization of higher algebraic K-theory
In this paper we establish a universal characterization of higher algebraic
K-theory in the setting of small stable infinity categories. Specifically, we
prove that connective algebraic K-theory is the universal additive invariant,
i.e., the universal functor with values in spectra which inverts Morita
equivalences, preserves filtered colimits, and satisfies Waldhausen's
additivity theorem. Similarly, we prove that non-connective algebraic K-theory
is the universal localizing invariant, i.e., the universal functor that
moreover satisfies the "Thomason-Trobaugh-Neeman" localization theorem.
To prove these results, we construct and study two stable infinity categories
of "noncommutative motives"; one associated to additivity and another to
localization. In these stable infinity categories, Waldhausen's S. construction
corresponds to the suspension functor and connective and non-connective
algebraic K-theory spectra become corepresentable by the noncommutative motive
of the sphere spectrum. In particular, the algebraic K-theory of every scheme,
stack, and ring spectrum can be recovered from these categories of
noncommutative motives.
In order to work with these categories of noncommutative motives, we
establish comparison theorems between the category of spectral categories
localized at the Morita equivalences and the category of small
idempotent-complete stable infinity categories. We also explain in detail the
comparison between the infinity categorical version of Waldhausen K-theory and
the classical definition.
As an application of our theory, we obtain a complete classification of the
natural transformations from higher algebraic K-theory to topological
Hochschild homology (THH) and topological cyclic homology (TC). Notably, we
obtain an elegant conceptual description of the cyclotomic trace map.Comment: Various revisions and correction
A Generalization of Martin's Axiom
We define the chain condition. The corresponding forcing axiom
is a generalization of Martin's Axiom and implies certain uniform failures of
club--guessing on that don't seem to have been considered in the
literature before.Comment: 36 page
The Baum-Connes Conjecture via Localisation of Categories
We redefine the Baum-Connes assembly map using simplicial approximation in
the equivariant Kasparov category. This new interpretation is ideal for
studying functorial properties and gives analogues of the assembly maps for all
equivariant homology theories, not just for the K-theory of the crossed
product. We extend many of the known techniques for proving the Baum-Connes
conjecture to this more general setting
The derived category of quasi-coherent sheaves and axiomatic stable homotopy
We prove in this paper that for a quasi-compact and semi-separated (non
necessarily noetherian) scheme X, the derived category of quasi-coherent
sheaves over X, D(A_qc(X)), is a stable homotopy category in the sense of
Hovey, Palmieri and Strickland, answering a question posed by Strickland.
Moreover we show that it is unital and algebraic. We also prove that for a
noetherian semi-separated formal scheme X, its derived category of sheaves of
modules with quasi-coherent torsion homologies D_qct(X) is a stable homotopy
category. It is algebraic but if the formal scheme is not a usual scheme, it is
not unital, therefore its abstract nature differs essentially from that of the
derived category of a usual scheme.Comment: v2: 31 pages, some improvements in exposition; v3 updated
bibliography, to appear Adv. Mat
Simple, optimal and efficient auctions
Proceedings of the 7th International Workshop, WINE 2011, Singapore, December 11-14, 2011.We study the extent to which simple auctions can simultaneously achieve good revenue and efficiency guarantees in single-item settings. Motivated by the optimality of the second price auction with monopoly reserves when the bidders’ values are drawn i.i.d. from regular distributions [12], and its approximate optimality when they are drawn from independent regular distributions [11], we focus our attention to the second price auction with general (not necessarily monopoly) reserve prices, arguably one of the simplest and most intuitive auction formats. As our main result, we show that for a carefully chosen set of reserve prices this auction guarantees at least 20% of both the optimal welfare and the optimal revenue, when the bidders’ values are distributed according to independent, not necessarily identical, regular distributions. We also prove a similar guarantee, when the values are drawn i.i.d. from a—possibly irregular—distribution.National Science Foundation (U.S.) (award CCF-0953960)National Science Foundation (U.S.) (CCF-1101491
The relationship of femoral neck shaft angle and adiposity to greater trochanteric pain syndrome in women. A case control morphology and anthropometric study
OBJECTIVE To evaluate if pelvic or hip width predisposed women to developing greater trochanteric pain syndrome (GTPS). DESIGN Prospective case control study. PARTICIPANTS Four groups were included in the study: those gluteal tendon reconstructions (n=31, GTR), those with conservatively managed GTPS (n=29), those with hip osteoarthritis (n=20, OA) and 22 asymptomatic participants (ASC). METHODS Anterior-posterior pelvic x-rays were evaluated for femoral neck shaft angle; acetabular index, and width at the lateral acetabulum, and the superior and lateral aspects of the greater trochanter. Body mass index, and waist, hip and greater trochanter girth were measured. Data were analysed using a one-way analysis of variance (ANOVA; posthoc Scheffe analysis), then multivariate analysis. RESULTS The GTR group had a lower femoral neck shaft angle than the other groups (p=0.007). The OR (95% CI) of having a neck shaft angle of less than 134°, relative to the ASC group: GTR=3.33 (1.26 to 8.85); GTPS=1.4 (0.52 to 3.75); OA=0.85 (0.28 to 2.61). The OR of GTR relative to GTPS was 2.4 (1.01 to 5.6). No group difference was found for acetabular or greater trochanter width. Greater trochanter girth produced the only anthropometric group difference (mean (95% CI) in cm) GTR=103.8 (100.3 to 107.3), GTPS=105.9 (100.2 to 111.6), OA=100.3 (97.7 to 103.9), ASC=99.1 (94.7 to 103.5), (ANOVA: p=0.036). Multivariate analysis confirmed adiposity is associated with GTPS. CONCLUSION A lower neck shaft angle is a risk factor for, and adiposity is associated with, GTPS in women
Gorenstein homological algebra and universal coefficient theorems
We study criteria for a ring—or more generally, for a small category—to be Gorenstein and for a module over it to be of finite projective dimension. The goal is to unify the universal coefficient theorems found in the literature and to develop machinery for proving new ones. Among the universal coefficient theorems covered by our methods we find, besides all the classic examples, several exotic examples arising from the KK-theory of C*-algebras and also Neeman’s Brown–Adams representability theorem for compactly generated categories
Derived categories of cubic fourfolds
We discuss the structure of the derived category of coherent sheaves on cubic
fourfolds of three types: Pfaffian cubics, cubics containing a plane and
singular cubics, and discuss its relation to the rationality of these cubics.Comment: 18 page
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