443 research outputs found
Generalised Moore spectra in a triangulated category
In this paper we consider a construction in an arbitrary triangulated
category T which resembles the notion of a Moore spectrum in algebraic
topology. Namely, given a compact object C of T satisfying some finite tilting
assumptions, we obtain a functor which "approximates" objects of the module
category of the endomorphism algebra of C in T. This generalises and extends a
construction of Jorgensen in connection with lifts of certain homological
functors of derived categories. We show that this new functor is well-behaved
with respect to short exact sequences and distinguished triangles, and as a
consequence we obtain a new way of embedding the module category in a
triangulated category. As an example of the theory, we recover Keller's
canonical embedding of the module category of a path algebra of a quiver with
no oriented cycles into its u-cluster category for u>1.Comment: 26 pages, improvement to exposition of the proof of Theorem 3.
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
MR imaging–derived oxygen-hemoglobin dissociation curves and fetal-placental oxygen-hemoglobin affinities
PURPOSE: To generate magnetic resonance (MR) imaging–derived, oxygen-hemoglobin dissociation curves and to map fetal-placental oxygen-hemoglobin affinity in pregnant mice noninvasively by combining blood oxygen level–dependent (BOLD) T2* and oxygen-weighted T1 contrast mechanisms under different respiration challenges. MATERIALS AND METHODS: All procedures were approved by the Weizmann Institutional Animal Care and Use Committee. Pregnant mice were analyzed with MR imaging at 9.4 T on embryonic days 14.5 (eight dams and 58 fetuses; imprinting control region ICR strain) and 17.5 (21 dams and 158 fetuses) under respiration challenges ranging from hyperoxia to hypoxia (10 levels of oxygenation, 100%–10%; total imaging time, 100 minutes). A shorter protocol with normoxia to hyperoxia was also performed (five levels of oxygenation, 20%–100%; total imaging time, 60 minutes). Fast spin-echo anatomic images were obtained, followed by sequential acquisition of three-dimensional gradient-echo T2*- and T1-weighted images. Automated registration was applied to align regions of interest of the entire placenta, fetal liver, and maternal liver. Results were compared by using a two-tailed unpaired Student t test. R1 and R2* values were derived for each tissue. MR imaging–based oxygen-hemoglobin dissociation curves were constructed by nonlinear least square fitting of 1 minus the change in R2*divided by R2*at baseline as a function of R1 to a sigmoid-shaped curve. The apparent P50 (oxygen tension at which hemoglobin is 50% saturated) value was derived from the curves, calculated as the R1 scaled value (x) at which the change in R2* divided by R2*at baseline scaled (y) equals 0.5. RESULTS: The apparent P50 values were significantly lower in fetal liver than in maternal liver for both gestation stages (day 14.5: 21% ± 5 [P = .04] and day 17.5: 41% ± 7 [P < .0001]). The placenta showed a reduction of 18% ± 4 in mean apparent P50 values from day 14.5 to day 17.5 (P = .003). Reproduction of the MR imaging–based oxygen-hemoglobin dissociation curves with a shorter protocol that excluded the hypoxic periods was demonstrated. CONCLUSION: MR imaging–based oxygen-hemoglobin dissociation curves and oxygen-hemoglobin affinity information were derived for pregnant mice by using 9.4-T MR imaging, which suggests a potential to overcome the need for direct sampling of fetal or maternal blood. Online supplemental material is available for this article
Bounded derived categories of very simple manifolds
An unrepresentable cohomological functor of finite type of the bounded
derived category of coherent sheaves of a compact complex manifold of dimension
greater than one with no proper closed subvariety is given explicitly in
categorical terms. This is a partial generalization of an impressive result due
to Bondal and Van den Bergh.Comment: 11 pages one important references is added, proof of lemma 2.1 (2)
and many typos are correcte
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
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
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
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