A relative double commutant theorem for hereditary sub-C*-algebras

We prove a double commutant theorem for hereditary subalgebras of a large class of C*-algebras, partially resolving a problem posed by Pedersen[8]. Double commutant theorems originated with von Neumann, whose seminal result evolved into an entire field now called von Neumann algebra theory. Voiculescu proved a C*-algebraic double commutant theorem for separable subalgebras of the Calkin algebra. We prove a similar result for hereditary subalgebras which holds for arbitrary corona C*-algebras. (It is not clear how generally Voiculescu's double commutant theorem holds.)

On extending Pollard's theorem for t-representable sums

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Note on a theorem of Bousfield and Friedlander

We examine the proof of a classical localization theorem of Bousfield and Friedlander and we remove the assumption that the underlying model category be right proper. The key to the argument is a lemma about factoring in morphisms in the arrow category of a model category.

Noncooperative Oligopoly in Markets with a Continuum of Traders: A Limit Theorem µa la Cournot

In this paper, we consider an exchange economy µa la Shitovitz (1973), with atoms and an atomless set. We associate with it a strategic market game of the kind first proposed by Lloyd S. Shapley and known as the Shapley window model. We analyze the relationship between the set of the Cournot-Nash equilibrium allocations of the strategic market game and the Walras equilibrium allocations of the exchange economy with which it is associated. We show, with an example, that even when atoms are countably in¯nite, any Cournot-Nash equilibrium allocation of the game is not a Walras equilibrium of the underlying exchange economy. Accordingly, in the original spirit of Cournot (1838), we par- tially replicate the mixed exchange economy by increasing the number of atoms, without a®ecting the atomless part, and ensuring that the measure space of agents remains finite. We show that any sequence of Cournot-Nash equilibrium allocations of the strategic market games associated with the partially replicated exchange economies approximates a Walras equilibrium allocation of the original exchange economy.

A General and Intuitive Envelope Theorem

We present an envelope theorem for establishing first-order conditions in decision problems involving continuous and discrete choices. Our theorem accommodates general dynamic programming problems, even with unbounded marginal utilities. And, unlike classical envelope theorems that focus only on differentiating value functions, we accommodate other endogenous functions such as default probabilities and interest rates. Our main technical ingredient is how we establish the differentiability of a function at a point: we sandwich the function between two differentiable functions from above and below. Our theory is widely applicable. In unsecured credit models, neither interest rates nor continuation values are globally differentiable. Nevertheless, we establish an Euler equation involving marginal prices and values. In adjustment cost models, we show that first-order conditions apply universally, even if optimal policies are not (S,s). Finally, we incorporate indivisible choices into a classic dynamic insurance analysis.

Gehring-Hayman theorem for conformal deformations

We study conformal deformations of a uniform space that satisfies the Ahlfors Q-regularity condition on balls of Whitney type. We verify the Gehring–Hayman Theorem by using a Whitney Covering of the space.

A Schoenflies extension theorem for a class of locally bi-Lipschitz homeomorphisms

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Singular Bott-Chern classes and the arithmetic Grothendieck-Riemann-Roch theorem for closed immersions

We study the singular Bott-Chern classes introduced by Bismut, Gillet and Soulé. Singular Bott-Chern classes are the main ingredient to define direct images for closed immersions in arithmetic K-theory. In this paper we give an axiomatic definition of a theory of singular Bott-Chern classes, study their properties, and classify all possible theories of this kind. We identify the theory defined by Bismut, Gillet and Soulé as the only one that satisfies the additional condition of being homogeneous. We include a proof of the arithmetic Grothendieck-Riemann-Roch theorem for closed immersions that generalizes a result of Bismut, Gillet and Soulé and was already proved by Zha. This result can be combined with the arithmetic Grothendieck-Riemann-Roch theorem for submersions to extend this theorem to arbitrary projective morphisms. As a byproduct of this study we obtain two results of independent interest. First, we prove a Poincaré lemma for the complex of currents with fixed wave front set, and second we prove that certain direct images of Bott-Chern classes are closed.

Recurrence pattern after [(18)F]fluoroethyltyrosine-positron emission tomography-guided radiotherapy for high-grade glioma: a prospective study.

PURPOSE: To assess the failure pattern observed after (18)F fluoroethyltyrosine (FET) planning after chemo- and radiotherapy (RT) for high-grade glioma. METHODS: All patients underwent prospectively RT planning using morphological gross tumour volumes (GTVs) and biological tumour volumes (BTVs). The post-treatment recurrence tumour volumes (RTVs) of 10 patients were transferred on their CT planning. First, failure patterns were defined in terms of percentage of RTV located outside the GTV and BTV. Second, the location of the RTV with respect to the delivered dose distribution was assessed using the RTV's DVHs. Recurrences with >95% of their volume within 95% isodose line were considered as central recurrences. Finally, the relationship between survival and GTV/BTV mismatches was assessed. RESULTS: The median percentages of RTV outside the GTV and BTV were 41.8% (range, 10.5-92.4) and 62.8% (range, 34.2-81.1), respectively. The majority of recurrences (90%) were centrally located. Using a composite target volume planning formalism, the degree of GTV and BTV mismatch did not correlate with survivorship. CONCLUSIONS: The observed failure pattern after FET-PET planning and chemo-RT is primarily central. The target mismatch-survival data suggest that using FET-PET planning may counteract the possibility of BTV-related progression, which may have a detrimental effect on survival.

A Many-to-many 'rural hospital theorem'

We show that the full version of the so-called 'rural hospital theorem' (Roth, 1986) generalizes to many-to-many matching where agents on both sides of the market have separable and substitutable preferences.

A non-possibility theorem for joint-stability in interindustry models

Joint-stability in interindustry models relates to the mutual simultaneous consistency of the demand-driven and supply-driven models of Leontief and Ghosh, respectively. Previous work has claimed joint-stability to be an acceptable assumption from the empirical viewpoint, provided only small changes in exogenous variables are considered. We show in this note, however, that the issue has deeper theoretical roots and offer an analytical demonstration that shows the impossibility of consistency between demand-driven and supply-driven models.

A lower bound in Nehari's theorem on the polydisc

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A Folk Theorem for Games when Frequent Monitoring Decreases Noise

This paper studies frequent monitoring in an infinitely repeated game with imperfect public information and discounting, where players observe the state of a continuous time Brownian process at moments in time of length _. It shows that a limit folk theorem can be achieved with imperfect public monitoring when players monitor each other at the highest frequency, i.e., _. The approach assumes that the expected joint output depends exclusively on the action profile simultaneously and privately decided by the players at the beginning of each period of the game, but not on _. The strong decreasing effect on the expected immediate gains from deviation when the interval between actions shrinks, and the associated increase precision of the public signals, make the result possible in the limit. JEL: C72/73, D82, L20. KEYWORDS: Repeated Games, Frequent Monitoring, Public Monitoring, Brownian Motion.

A novel tool to analyze MRI recurrence patterns in glioblastoma.

At least 10% of glioblastoma relapses occur at distant and even contralateral locations. This disseminated growth limits surgical intervention and contributes to neurological morbidity. Preclinical data pointed toward a role for temozolomide (TMZ) in reducing radiotherapy-induced glioma cell invasiveness. Our objective was to develop and validate a new analysis tool of MRI data to examine the clinical recurrence pattern of glioblastomas. MRIcro software was used to map the location and extent of initial preoperative and recurrent tumors on MRI of 63 patients in the European Organisation for Research and Treatment of Cancer (EORTC) 26981/22981/National Cancer Institute of Canada (NCIC) CE.3 study into the same stereotaxic space. This allowed us to examine changes of site and distance between the initial and the recurrent tumor on the group level. Thirty of the 63 patients were treated using radiotherapy, while the other patients completed a radiotherapy-plus-TMZ treatment. Baseline characteristics (median age, KPS) and outcome data (progression-free survival, overall survival) of the patients included in this analysis resemble those of the general study cohort. The patient groups did not differ in the promoter methylation status of methyl guanine methyltransferase (MGMT). Overall frequency of distant recurrences was 20%. Analysis of recurrence patterns revealed no difference between the groups in the size of the recurrent tumor or in the differential effect on the distance of the recurrences from the preoperative tumor location. The data show the feasibility of groupwise recurrence pattern analysis. An effect of TMZ treatment on the recurrence pattern in the EORTC 26981/22981/NCIC CE.3 study could not be demonstrated.