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 $\bigoplus_{n\ge0}A_n$ 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 $\bigoplus_{n\ge0}A_n$ gives rise to graded dual Hopf algebras then we must have $\dim(A_n)=r^nn!$ where $r = \dim(A_1)$.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 $X$ makes $T_X[-1]$ into a Lie algebra object in $D^+(X)$, the bounded below derived category of coherent sheaves on $X$. Furthermore Kapranov proved that, for a K\"ahler manifold $X$, the Dolbeault resolution $\Omega^{\bullet-1}(T_X^{1,0})$ of $T_X[-1]$ is an $L_\infty$ 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 $(L,A)$, i.e. a Lie algebroid $L$ together with a Lie subalgebroid $A$, we define the Atiyah class $\alpha_E$ of an $A$-module $E$ (relative to $L$) as the obstruction to the existence of an $A$-compatible $L$-connection on $E$. We prove that the Atiyah classes $\alpha_{L/A}$ and $\alpha_E$ respectively make $L/A[-1]$ and $E[-1]$ into a Lie algebra and a Lie algebra module in the bounded below derived category $D^+(\mathcal{A})$, where $\mathcal{A}$ is the abelian category of left $\mathcal{U}(A)$-modules and $\mathcal{U}(A)$ is the universal enveloping algebra of $A$. Moreover, we produce a homotopy Leibniz algebra and a homotopy Leibniz module stemming from the Atiyah classes of $L/A$ and $E$, and inducing the aforesaid Lie structures in $D^+(\mathcal{A})$.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

Physics, Topology, Logic and Computation: A Rosetta Stone

In physics, Feynman diagrams are used to reason about quantum processes. In the 1980s, it became clear that underlying these diagrams is a powerful analogy between quantum physics and topology: namely, a linear operator behaves very much like a "cobordism". Similar diagrams can be used to reason about logic, where they represent proofs, and computation, where they represent programs. With the rise of interest in quantum cryptography and quantum computation, it became clear that there is extensive network of analogies between physics, topology, logic and computation. In this expository paper, we make some of these analogies precise using the concept of "closed symmetric monoidal category". We assume no prior knowledge of category theory, proof theory or computer science.Comment: 73 pages, 8 encapsulated postscript figure

Forms of Structuralism: Bourbaki and the Philosophers

In this paper, we argue that, contrary to the view held by most philosophers of mathematics, Bourbaki’s technical conception of mathematical structuralism is relevant to philosophy of mathematics. In fact, we believe that Bourbaki has captured the core of any mathematical structuralism