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

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 Generalization of Martin's Axiom

We define the $\aleph_{1.5}$ chain condition. The corresponding forcing axiom is a generalization of Martin's Axiom and implies certain uniform failures of club--guessing on $\omega_1$ that don't seem to have been considered in the literature before.Comment: 36 page

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

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 Topology of Parabolic Character Varieties of Free Groups

Let G be a complex affine algebraic reductive group, and let K be a maximal compact subgroup of G. Fix elements h_1,...,h_m in K. For n greater than or equal to 0, let X (respectively, Y) be the space of equivalence classes of representations of the free group of m+n generators in G (respectively, K) such that for each i between 1 and m, the image of the i-th free generator is conjugate to h_i. These spaces are parabolic analogues of character varieties of free groups. We prove that Y is a strong deformation retraction of X. In particular, X and Y are homotopy equivalent. We also describe explicit examples relating X to relative character varieties.Comment: 16 pages, version 2 includes minor revisions and some modified proofs, accepted for publication in Geometriae Dedicat

Worldline Superfield Actions for N=2 Superparticles

We propose doubly supersymmetric actions in terms of n=2(D-2) worldline superfields for N=2 superparticles in D=3,4 and Type IIA D=6 superspaces. These actions are obtained by dimensional reduction of superfield actions for N=1 superparticles in D=4,6 and 10, respectively. We show that in all these models geometrodynamical constraints on target superspace coordinates do not put the theory on the mass shell, so the actions constructed consistently describe the dynamics of the corresponding N=2 superparticles. We also find that in contrast to the IIA D=6 superparticle a chiral IIB D=6 superparticle, which is not obtainable by dimensional reduction from N=1, D=10, is described by superfield constraints which produce dynamical equations. This implies that for the IIB D=6 superparticle the doubly supersymmetric action does not exist in the conventional form.Comment: Latex, 20 pp. Minor corrections, acknowledgements adde

The Universality of Einstein Equations

It is shown that for a wide class of analytic Lagrangians which depend only on the scalar curvature of a metric and a connection, the application of the so--called ``Palatini formalism'', i.e., treating the metric and the connection as independent variables, leads to ``universal'' equations. If the dimension $n$ of space--time is greater than two these universal equations are Einstein equations for a generic Lagrangian and are suitably replaced by other universal equations at bifurcation points. We show that bifurcations take place in particular for conformally invariant Lagrangians $L=R^{n/2} \sqrt g$ and prove that their solutions are conformally equivalent to solutions of Einstein equations. For 2--dimensional space--time we find instead that the universal equation is always the equation of constant scalar curvature; the connection in this case is a Weyl connection, containing the Levi--Civita connection of the metric and an additional vectorfield ensuing from conformal invariance. As an example, we investigate in detail some polynomial Lagrangians and discuss their bifurcations.Comment: 15 pages, LaTeX, (Extended Version), TO-JLL-P1/9

Localisation and colocalisation of KK-theory at sets of primes

Given a set of prime numbers S, we localise equivariant bivariant Kasparov theory at S and compare this localisation with Kasparov theory by an exact sequence. More precisely, we define the localisation at S to be KK^G(A,B) tensored with the ring of S-integers Z[S^-1]. We study the properties of the resulting variants of Kasparov theory.Comment: 16 page