242 research outputs found
On the word problem for SP-categories, and the properties of two-way communication
International audienceThe word problem for categories with free products and coproducts (sums), SP-categories, is directly related to the problem of determining the equivalence of certain processes. Indeed, the maps in these categories may be directly interpreted as processes which communicate by two-way channels. The maps of an SP-category may also be viewed as a proof theory for a simple logic with a game theoretic intepretation. The cut-elimination procedure for this logic determines equality only up to certain permuting conversions. As the equality classes under these permuting conversions are finite, it is easy to see that equality between cut-free terms (even in the presence of the additive units) is decidable. Unfortunately, this does not yield a tractable decision algorithm as these equivalence classes can contain exponentially many terms. However, the rather special properties of these free categories -- and, thus, of two-way communication -- allow one to devise a tractable algorithm for equality. We show that, restricted to cut-free terms s,t : X --> A, the decision procedure runs in time polynomial on |X||A|, the product of the sizes of the domain and codomain type
Comparison of high-specific-activity ultratrace 123/131I-MIBG and carrier-added 123/131I-MIBG on efficacy, pharmacokinetics, and tissue distribution
Metaiodobenzylguanidine (MIBG) is an enzymatically stable synthetic analog of norepinephrine that when radiolabled with diagnostic ((123)I) or therapeutic ((131)I) isotopes has been shown to concentrate highly in sympathetically innervated tissues such as the heart and neuroendocrine tumors that possesses high levels of norepinephrine transporter (NET). As the transport of MIBG by NET is a saturable event, the specific activity of the preparation may have dramatic effects on both the efficacy and safety of the radiodiagnostic/radiotherapeutic. Using a solid labeling approach (Ultratrace), noncarrier-added radiolabeled MIBG can be efficiently produced. In this study, specific activities of >1200 mCi/micromol for (123)I and >1600 mCi/micromol for (131)I have been achieved. A series of studies were performed to assess the impact of cold carrier MIBG on the tissue distribution of (123/131)I-MIBG in the conscious rat and on cardiovascular parameters in the conscious instrumented dog. The present series of studies demonstrated that the carrier-free Ultratrace MIBG radiolabeled with either (123)I or (131)I exhibited similar tissue distribution to the carrier-added radiolabeled MIBG in all nontarget tissues. In tissues that express NETs, the higher the specific activity of the preparation the greater will be the radiopharmaceutical uptake. This was reflected by greater efficacy in the mouse neuroblastoma SK-N-BE(2c) xenograft model and less appreciable cardiovascular side-effects in dogs when the high-specific-activity radiopharmaceutical was used. The increased uptake and retention of Ultratrace (123/131)I-MIBG may translate into a superior diagnostic and therapeutic potential. Lastly, care must be taken when administering therapeutic doses of the current carrier-added (131)I-MIBG because of its potential to cause adverse cardiovascular side-effects, nausea, and vomiting
A Physicist's Proof of the Lagrange-Good Multivariable Inversion Formula
We provide yet another proof of the classical Lagrange-Good multivariable
inversion formula using techniques of quantum field theory.Comment: 9 pages, 3 diagram
Combinatorial Hopf algebras and Towers of Algebras
Bergeron and Li have introduced a set of axioms which guarantee that the
Grothendieck groups of a tower of algebras can be
endowed with the structure of graded dual Hopf algebras. Hivert and Nzeutzhap,
and independently Lam and Shimozono constructed dual graded graphs from
primitive elements in Hopf algebras. In this paper we apply the composition of
these constructions to towers of algebras. We show that if a tower
gives rise to graded dual Hopf algebras then we must
have where .Comment: 7 page
Reproducibility of the heat/capsaicin skin sensitization model in healthy volunteers
INTRODUCTION: Heat/capsaicin skin sensitization is a well-characterized human experimental model to induce hyperalgesia and allodynia. Using this model, gabapentin, among other drugs, was shown to significantly reduce cutaneous hyperalgesia compared to placebo. Since the larger thermal probes used in the original studies to produce heat sensitization are now commercially unavailable, we decided to assess whether previous findings could be replicated with a currently available smaller probe (heated area 9 cm(2) versus 12.5–15.7 cm(2)). STUDY DESIGN AND METHODS: After Institutional Review Board approval, 15 adult healthy volunteers participated in two study sessions, scheduled 1 week apart (Part A). In both sessions, subjects were exposed to the heat/capsaicin cutaneous sensitization model. Areas of hypersensitivity to brush stroke and von Frey (VF) filament stimulation were measured at baseline and after rekindling of skin sensitization. Another group of 15 volunteers was exposed to an identical schedule and set of sensitization procedures, but, in each session, received either gabapentin or placebo (Part B). RESULTS: Unlike previous reports, a similar reduction of areas of hyperalgesia was observed in all groups/sessions. Fading of areas of hyperalgesia over time was observed in Part A. In Part B, there was no difference in area reduction after gabapentin compared to placebo. CONCLUSION: When using smaller thermal probes than originally proposed, modifications of other parameters of sensitization and/or rekindling process may be needed to allow the heat/capsaicin sensitization protocol to be used as initially intended. Standardization and validation of experimental pain models is critical to the advancement of translational pain research
Higher Algebraic Structures and Quantization
We derive (quasi-)quantum groups in 2+1 dimensional topological field theory
directly from the classical action and the path integral. Detailed computations
are carried out for the Chern-Simons theory with finite gauge group. The
principles behind our computations are presumably more general. We extend the
classical action in a d+1 dimensional topological theory to manifolds of
dimension less than d+1. We then ``construct'' a generalized path integral
which in d+1 dimensions reduces to the standard one and in d dimensions
reproduces the quantum Hilbert space. In a 2+1 dimensional topological theory
the path integral over the circle is the category of representations of a
quasi-quantum group. In this paper we only consider finite theories, in which
the generalized path integral reduces to a finite sum. New ideas are needed to
extend beyond the finite theories treated here.Comment: 62 pages + 16 figures (revised version). In this revision we make
some small corrections and clarification
Picturing classical and quantum Bayesian inference
We introduce a graphical framework for Bayesian inference that is
sufficiently general to accommodate not just the standard case but also recent
proposals for a theory of quantum Bayesian inference wherein one considers
density operators rather than probability distributions as representative of
degrees of belief. The diagrammatic framework is stated in the graphical
language of symmetric monoidal categories and of compact structures and
Frobenius structures therein, in which Bayesian inversion boils down to
transposition with respect to an appropriate compact structure. We characterize
classical Bayesian inference in terms of a graphical property and demonstrate
that our approach eliminates some purely conventional elements that appear in
common representations thereof, such as whether degrees of belief are
represented by probabilities or entropic quantities. We also introduce a
quantum-like calculus wherein the Frobenius structure is noncommutative and
show that it can accommodate Leifer's calculus of `conditional density
operators'. The notion of conditional independence is also generalized to our
graphical setting and we make some preliminary connections to the theory of
Bayesian networks. Finally, we demonstrate how to construct a graphical
Bayesian calculus within any dagger compact category.Comment: 38 pages, lots of picture
From Atiyah Classes to Homotopy Leibniz Algebras
A celebrated theorem of Kapranov states that the Atiyah class of the tangent
bundle of a complex manifold makes into a Lie algebra object in
, the bounded below derived category of coherent sheaves on .
Furthermore Kapranov proved that, for a K\"ahler manifold , the Dolbeault
resolution of is an
algebra. In this paper, we prove that Kapranov's theorem holds in much wider
generality for vector bundles over Lie pairs. Given a Lie pair , i.e. a
Lie algebroid together with a Lie subalgebroid , we define the Atiyah
class of an -module (relative to ) as the obstruction to
the existence of an -compatible -connection on . We prove that the
Atiyah classes and respectively make and
into a Lie algebra and a Lie algebra module in the bounded below
derived category , where is the abelian
category of left -modules and is the universal
enveloping algebra of . Moreover, we produce a homotopy Leibniz algebra and
a homotopy Leibniz module stemming from the Atiyah classes of and ,
and inducing the aforesaid Lie structures in .Comment: 36 page
Multivariate Lagrange inversion formula and the cycle lemma
International audienceWe give a multitype extension of the cycle lemma of (Dvoretzky and Motzkin 1947). This allows us to obtain a combinatorial proof of the multivariate Lagrange inversion formula that generalizes the celebrated proof of (Raney 1963) in the univariate case, and its extension in (Chottin 1981) to the two variable case. Until now, only the alternative approach of (Joyal 1981) and (Labelle 1981) via labelled arborescences and endofunctions had been successfully extended to the multivariate case in (Gessel 1983), (Goulden and Kulkarni 1996), (Bousquet et al. 2003), and the extension of the cycle lemma to more than 2 variables was elusive. The cycle lemma has found a lot of applications in combinatorics, so we expect our multivariate extension to be quite fruitful: as a first application we mention economical linear time exact random sampling for multispecies trees
Categorical formulation of quantum algebras
We describe how dagger-Frobenius monoids give the correct categorical
description of certain kinds of finite-dimensional 'quantum algebras'. We
develop the concept of an involution monoid, and use it to construct a
correspondence between finite-dimensional C*-algebras and certain types of
dagger-Frobenius monoids in the category of Hilbert spaces. Using this
technology, we recast the spectral theorems for commutative C*-algebras and for
normal operators into an explicitly categorical language, and we examine the
case that the results of measurements do not form finite sets, but rather
objects in a finite Boolean topos. We describe the relevance of these results
for topological quantum field theory.Comment: 34 pages, to appear in Communications in Mathematical Physic
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