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We study the change of the Laughlin states under large deformations of the geometry of the sphere and the plane, associated with Mabuchi geodesics on the space of metrics with Hamiltonian $S^1$-symmetry. For geodesics associated with the square of the symmetry generator, as the geodesic time goes to infinity, the geometry of the sphere becomes that of a thin cigar collapsing to a line and the Laughlin states become concentrated on a discrete set of $S^1$--orbits, corresponding to Bohr-Sommerfeld orbits of geometric quantization. The lifting of the Mabuchi geodesics to the bundle of quantum states, to which the Laughlin states belong, is achieved via generalized coherent state transforms, which correspond to the KZ parallel transport of Chern-Simons theory.

The ‘gasotransmitters’ hydrogen sulfide (H2S), nitric oxide (NO), and carbon monoxide (CO) act as second messengers in human physiology, mediating signal transduction via interaction with or chemical modification of protein targets, thereby regulating processes such as neurotransmission, blood flow, immunomodulation, or energy metabolism. Due to their broad reactivity and potential toxicity, the biosynthesis and breakdown of H2S, NO, and CO are tightly regulated. Growing evidence highlights the active role of gasotransmitters in their mutual cross-regulation. In human physiology, the transsulfuration enzymes cystathionine β-synthase (CBS) and cystathionine γ-lyase (CSE) are prominent H2S enzymatic sources. While CBS is known to be inhibited by NO and CO, little is known about CSE regulation by gasotransmitters. Herein, we investigated the effect of s-nitrosation on CSE catalytic activity. H2S production by recombinant human CSE was found to be inhibited by the physiological nitrosating agent s-nitrosoglutathione (GSNO), while reduced glutathione had no effect. GSNO-induced inhibition was partially reverted by ascorbate and accompanied by the disappearance of one solvent accessible protein thiol. By combining differential derivatization procedures and mass spectrometry-based analysis with functional assays, seven out of the ten protein cysteine residues, namely Cys84, Cys109, Cys137, Cys172, Cys229, Cys307, and Cys310, were identified as targets of s-nitrosation. By generating conservative Cys-to-Ser variants of the identified s-nitrosated cysteines, Cys137 was identified as most significantly contributing to the GSNO-mediated CSE inhibition. These results highlight a new mechanism of crosstalk between gasotransmitters.

This work was supported by Fundação para a Ciência e a Tecnologia (FCT), Portugal, through projects UID/QUI/00100/2019, IF/01091/2013/CP1163/CT0001 and PTDC/QUIQAN/32242/2017 as well as doctoral fellowships SFRH/BD/102846/2014 (to CC) and SFRH/BD/140157/2018 (to JN);joint funding from FCT and the COMPETE Program is also acknowledge through RNEM-LISBOA-01-0145-FEDER-022125-funded postdoctoral fellowship (to JM). Identification of protein covalent modifications (adducts) is a challenging task mainly due to the lack of data processing approaches for adductomics studies. Despite the huge technological advances in mass spectrometry (MS) instrumentation and bioinformatics tools for proteomics studies, these methodologies have very limited success on the identification of low abundant protein adducts. Herein we report a novel strategy inspired on the metabolomics workflows for the identification of covalently-modified peptides that consists on LC-MS data preprocessing followed by statistical analysis. The usefulness of this strategy was evaluated using experimental LC-MS data of histones isolated from HepG2 and THLE2 cells exposed to the chemical carcinogen glycidamide. LC-MS data was preprocessed using the open-source software MZmine and potential adducts were selected based on the m/z increments corresponding to glycidamide incorporation. Then, statistical analysis was applied to reveal the potential adducts as those ions are differently present in cells exposed and not exposed to glycidamide. The results were compared with the ones obtained upon the standard proteomics methodology, which relies on producing comprehensive MS/MS data by data dependent acquisition and analysis with proteomics data search engines. Our novel strategy was able to differentiate HepG2 and THLE2 and to identify adducts that were not detected by the standard methodology of adductomics. Thus, this metabolomics driven approach in adductomics will not only open new opportunities for the identification of protein epigenetic modifications, but also adducts formed by endogenous and exogenous exposure to chemical agents. publishersversion published

Protein covalent adducts formed upon exposure to reactive (mainly electrophilic) chemicals may lead to the development of a wide range of deleterious health outcomes. Therefore, the identification of protein covalent adducts constitutes a huge opportunity for a better understanding of events underlying diseases and for the development of biomarkers which may constitute effective tools for disease diagnosis/prognosis, for the application of personalized medicine approaches and for accurately assessing human exposure to chemical toxicants. The currently available mass spectrometry (MS)-based methodologies, are clearly the most suitable for the analysis of protein covalent modifications, providing accuracy, sensitivity, unbiased identification of the modified residue and conjugates along with quantitative information. However, despite the huge technological advances in MS instrumentation and bioinformatics tools, the identification of low abundant protein covalent adducts is still challenging. This review is aimed at summarizing the MS-based methodologies currently used for the identification of protein covalent adducts and the strategies developed to overcome the analytical challenges, involving not only sample pre-treatment procedures but also distinct MS and data analysis approaches.

We consider the imaginary time flow of a quadratic hyperbolic Hamiltonian on the symplectic plane, apply it to the Schrodinger polarization and study the corresponding evolution of polarized sections. The flow is periodic in imaginary time and the evolution of polarized sections has interesting features. On the time intervals for which the polarization is real or Kahler, the half–form corrected time evolution of polarized sections is given by unitary operators which turn out to be equivalent to the classical Segal-Bargmann transforms (which are usually associated to the quadratic elliptic Hamiltonian H = 1 2 p 2 and to the heat operator). At the right endpoint of these intervals, the evolution of polarized sections is given by the Fourier transform from the Schrodinger to the momentum representation. In the complementary intervals of imaginary time, the polarizations are anti–Kahler and the Hilbert space of polarized sections collapses to H = { 0 } . Hyperbolic quadratic Hamiltonians thus give rise to a new factorization of the Segal-Bargmann transform, which is very different from the usual one, where one first applies a bounded contraction operator (the heat kernel operator), mapping L 2 –states to real analytic functions with unique analytic continuation, and then one applies analytic continuation. In the factorization induced by an hyperbolic complexifier, both factors are unbounded operators but their composition is, in the Kahler or real sectors, unitary. In another paper [24] , we explore the application of the above family of unitary transforms to the definition of new holomorphic fractional Fourier transforms.

Herein we report the use of pyridazinediones to functionalise the native solvent accessible interstrand disulfide bonds in trastuzumab with monomethyl auristatin E (MMAE). This method of conjugation delivers serum stable antibody–drug conjugates (ADCs) with a controlled drug loading of 4. Moreover, we demonstrate that the MMAE-bearing ADCs are potent, selective and efficacious against cancer cell lines in both in vitro and in vivo models.

Let $$P$$ be a Delzant polytope. We show that the quantization of the corresponding toric manifold $$X_{P}$$ in toric Kahler polarizations and in the toric real polarization are related by analytic continuation of Hamiltonian flows evaluated at time $$t = {\sqrt{-1}}s$$ . We relate the quantization of $$X_{P}$$ in two different toric Kahler polarizations by taking the time- $${\sqrt{-1}}s$$ Hamiltonian “flow” of strongly convex functions on the moment polytope $$P$$ . By taking $$s$$ to infinity, we obtain the quantization of $$X_{P}$$ in the (singular) real toric polarization. Recall that $$X_{P}$$ has an open dense subset which is biholomorphic to $$({\mathbb {C}}^{*})^{n}$$ . The quantization of $$X_{P}$$ in a toric Kahler polarization can also be described by applying the complexified Hamiltonian flow of the Abreu–Guillemin symplectic potential $$g$$ , at time $$t={\sqrt{-1}}$$ , to an appropriate finite-dimensional subspace of quantum states in the quantization of $$T^{*}{\mathbb {T}}^{n}$$ in the vertical polarization. By taking other imaginary times, $$t= k {\sqrt{-1}}, k\in {\mathbb {R}}$$ , we describe toric Kahler metrics with cone singularities along the toric divisors in $$X_{P}$$ . For convex Hamiltonian functions and sufficiently negative imaginary part of the complex time, we obtain degenerate Kahler structures which are negative definite in some regions of $$X_{P}$$ . We show that the pointwise and $$L^2$$ -norms of quantum states are asymptotically vanishing on negative-definite regions.

Herein we report the use of next generation maleimides (NGMs) for the construction of a potent antibody-drug conjugate (ADC) via functional disulfide bridging. The linker has excellent stability in blood serum and the ADC, armed with monomethyl auristatin E (MMAE), shows excellent potency and cancer cell selectivity in vitro.

Drug bioactivation to reactive metabolites capable of covalent adduct formation with bionucleophiles is a major cause of drug-induced adverse reactions. Therefore, elucidation of reactive metabolites is essential to unravel the toxicity mechanisms induced by drugs and thereby identify patient subgroups at higher risk. Etravirine (ETR) was the first second-generation Non-Nucleoside Reverse Transcriptase Inhibitor (NNRTI) to be approved, as a therapeutic option for HIV-infected patients who developed resistance to the first-generation NNRTIs. Additionally, ETR came into market aiming to overcome some adverse effects associated with the previously used efavirenz (neurotoxicity) and nevirapine (hepatotoxicity) therapies. Nonetheless, post-marketing reports of severe ETR-induced skin rash and hypersensitivity reactions have prompted the U.S. FDA to issue a safety alert on ETR. Taking into consideration that ETR usage may increase in the near future, due to the possible use of the drug for coinfection with malaria and HIV, the development of reliable prognostic tools for early risk/benefit estimations is urgent. In the current study, high resolution mass spectrometry-based methodologies were integrated with MS3 experiments for the identification of reactive ETR metabolites/adducts: 1) in vitro incubation of the drug with human and rat liver S9 fractions in the presence of Phase I and II co-factors, including glutathione, as a trapping bionucleophile; and 2) in vivo, using urine samples from HIV-infected patients on ETR therapy. We obtained evidence for multiple bioactivation pathways leading to the formation of covalent adducts with glutathione and N-acetyl-L-cysteine. These results suggest that similar reactions may occur with cysteine residues of proteins, supporting a role for ETR bioactivation in the onset of the toxic effects elicited by the drug. Additionally, ETR metabolites stemming from amine oxidation, with potential toxicological significance, were identified in vitro and in vivo. Also noteworthy is the fact that new metabolic conjugation pathways of glucuronide metabolites were demonstrated for the first time, raising questions about their potential toxicological implications. In conclusion, these results represent not only a contribution towards the elucidation of new metabolic pathways of drugs in general but also an important step towards the elucidation of potentially toxic ETR pathways, whose understanding may be crucial for reliable risk/benefit estimations of ETR-based regimens.

This study analyzed the effects of a 12-week resistance training (RT) program without dietary interventions on metabolic syndrome (MetS) components and inflammatory biomarkers in older women.Fifty-three older women (mean [±SD] age 70.4 ± 5.7 years; mean body mass index 26.7 ± 4.0 kg/mAfter the 12-week period, there were significantly reductions (P 0.05) in glucose levels (-20.4% vs -0.3%), waist circumference (-1.5% vs +2.0%), and systolic BP (-6.2% vs +0.9%), and complete normalization of MetS prevalence (18% at baseline vs. 0% after 12-weeks RT) in the TG. Moreover, C-reactive protein and tumor necrosis factor-α concentrations decreased in the TG (-28.6% and -21.6%, respectively), but increased in the CG (+34.5% and +13.3%, respectively). In addition there were positive improvements in the MetS Z-score in the TG but not CG (-21.6% vs +13.3%, respectively).The results suggest that a 12-week RT program seems to effectively reduce MetS components and inflammatory biomarkers in older women, regardless of dietary intervention. The RT-induced adaptations in body composition and inflammatory biomarkers appear to be related to healthy adaptations in risk factors for MetS.

Highly homogeneous ADCs are generated by the efficient bridging of interchain disulfide bonds in trastuzumab, using next generation maleimides., The advent of Adcetris™ and Kadcyla™, two recently FDA-approved antibody–drug conjugates (ADCs), in the clinic has had a major impact on the treatment of lymphoma and breast cancer patients, respectively, worldwide. Despite these successes many new ADCs fail at various stages of development, often due to shortcomings in the methods used for their assembly. To address this problem we have developed next generation maleimides (NGMs), which specifically re-bridge reduced interchain disulfide bonds and allow the efficient conjugation of small molecules to antibodies, without the need for engineering of the target antibody. The method is site-specific and generates near homogeneous products in good yields. Moreover, adjustment of the reaction conditions allows control of the conjugation in terms of stoichiometry (drug-loading) and site selectivity. Using this method we prepared a series of ADCs from trastuzumab and doxorubicin (DOX) with a controlled drug-to-antibody ratio (DAR) of 1, 2, 3 and 4. All of these constructs were fully active by ELISA and had more than 90% of re-bridged disulfide bonds by CE-SDS when compared to clinical grade antibody. Furthermore, digest experiments of the DAR 2 material revealed that almost all of the drug had been targeted to the Fab arms of the antibody. Thus, NGMs offer a flexible and simple platform for the controlled assembly of ADCs from an antibody.

Soil Compaction results from compressive forces applied to compressible soil by machinery wheels, combined with tillage operations. Draft animal‐pulled equipment may also cause soil compaction, but a huge gap exists on experimental data to adequately assess their impacts and, actually, animal traction is an option seen with increasing potential to contribute to sustainable agriculture, especially in mountain areas. This study was conducted to assess the impacts on soil compaction of tillage operations with motor tractor and draft animals. In a farm plot (Vale de Frades, NE Portugal) treatments were applied in sub‐plots (30 m x 3 m), consisting in a two way tillage with tractor (T), a pair of cows (C) and a pair of donkeys (D). Undisturbed soil samples (120) were taken before and after operations for bulk density (BD) and saturated hydraulic conductivity (Ks). The relative changes in BD observed after tillage in the 0-0.05 m soil depth increased after operations in all treatments. The increase was higher in the tractor sub-plot (15%) than in those where animal traction was used (8%). Before operation Ks class was rapid and fast in all samples, and after operation this value was reduced to 33% in T, whereas it reached 83% in C. Electrical Resistivity Tomography (ERT) was useful as a tool to identify the alterations caused by tillage operations on soil physical status. These preliminary results confirm the potential of animal traction as an option for mountain agri‐environments, yet it requires much wider research to soundly ground its assets. Authors wish to acknowledge the most relevant contribution of the farmers of Vale de Frades involved in the experiment, for their enthusiasm and refined performance in the field, accepting to freely provide their time, their work and their draft animals to carry out the required operations. info:eu-repo/semantics/publishedVersion

We address quantization of the natural symplectic structure on a moduli space of parabolic vector bundles of parabolic degree zero over CP 1 with four parabolic points and parabolic weights in {0,1/2}. Identifying such parabolic bundles as vector bundles on an elliptic curve, we obtain explicit expressions for the corresponding non-abelian theta func- tions. These non-abelian theta functions are described in terms of certain naturally defined distributions on the compact group SU(2).

Leukocytes rely on dynamic actin-dependent changes in cell shape to pass through blood vessels, which is fundamental to immune surveillance. Wiskott-Aldrich Syndrome protein (WASp) is a hematopoietic cell–restricted cytoskeletal regulator important for modulating cell shape through Arp2/3-mediated actin polymerization. A recently identified WASpI294T mutation was shown to render WASp constitutively active in vivo, causing increased filamentous (F)–actin polymerization, high podosome turnover in macrophages, and myelodysplasia. The aim of this study was to determine the effect of WASpI294T expression in lymphocytes. Here, we report that lymphocytes isolated from a patient with WASpI294T, and in a cellular model of WASpI294T, displayed abnormal microvillar architecture, associated with an increase in total cellular F-actin. Microvillus function was additionally altered as lymphocytes bearing the WASpI294T mutation failed to roll normally on L-selectin ligand under flow. This was not because of defects in L-selectin expression, shedding, cytoskeletal anchorage, or membranal positioning; however, under static conditions of adhesion, WASpI294T-expressing lymphocytes exhibited altered dynamic interaction with L-selectin ligand, with a significantly reduced rate of adhesion turnover. Together, our results demonstrate that WASpI294T significantly affects lymphocyte membrane topography and L-selectin–dependent adhesion, which may be linked to defective hematopoiesis and leukocyte function in affected patients.

We study the dependence of geometric quantization of the standard symplectic torus on the choice of invariant polarization. Real and mixed polarizations are interpreted as degenerate complex structures. Using a weak version of the equations of covariant constancy, and the Weil-Brezin expansion to describe distributional sections, we give a unified analytical description of the quantization spaces for all nonnegative polarizations. The Blattner-Kostant-Sternberg (BKS) pairing maps between half-form corrected quantization spaces for different polarizations are shown to be transitive and related to an action of $Sp(2g,\R)$. Moreover, these maps are shown to be unitary., 24 pages; revised version, to appear in JFA

We study a transform, inspired by coherent state transforms, from the Hilbert space of Clifford algebra valued square integrable functions $L^2({\mathbb R}^m,dx)\otimes {\mathbb C}_{m}$ to a Hilbert space of solutions of the Weyl equation on ${\mathbb R}^{m+1}= {\mathbb R} \times {\mathbb R}^m$, namely to the Hilbert space ${\mathcal M}L^2({\mathbb R}^{m+1},d\mu)$ of ${\mathbb C}_m$-valued monogenic functions on ${\mathbb R}^{m+1}$ which are $L^2$ with respect to an appropriate measure $d\mu$. We prove that this transform is a unitary isomorphism of Hilbert spaces and that it is therefore an analog of the Segal-Bargmann transform for Clifford analysis. As a corollary we obtain an orthonormal basis of monogenic functions on ${\mathbb R}^{m+1}$. We also study the case when ${\mathbb R}^m$ is replaced by the $m$-torus ${\mathbb T}^m.$ Quantum mechanically, this extension establishes the unitary equivalence of the Schr\"odinger representation on $M$, for $M={\mathbb R}^m$ and $M={\mathbb T}^m$, with a representation on the Hilbert space ${\mathcal M}L^2({\mathbb R} \times M,d\mu)$ of solutions of the Weyl equation on the space-time ${\mathbb R}\times M$.

We introduce a one-parameter family of transforms, $U^t_{(m)}$, $t>0$, from the Hilbert space of Clifford algebra valued square integrable functions on the $m$--dimensional sphere, $L^2(S^{m},d\sigma_{m})\otimes \mathbb{C}_{m+1}$, to the Hilbert spaces, ${\mathcal M}L^2(\mathbb{R}^{m+1} \setminus \{0\},d\mu_t)$, of monogenic functions on $\mathbb{R}^{m+1}\setminus \{0\}$ which are square integrable with respect to appropriate measures, $d\mu_t$. We prove that these transforms are unitary isomorphisms of the Hilbert spaces and are extensions of the Segal-Bargman coherent state transform, $U_{(1)} : L^2(S^{1},d\sigma_{1}) \longrightarrow {\mathcal H}L^2({\mathbb{C} \setminus \{0\}},d\mu)$, to higher dimensional spheres in the context of Clifford analysis. In Clifford analysis it is natural to replace the analytic continuation from $S^m$ to $S^m_{\mathbb{C}}$ as in \cite{Ha1, St, HM} by the Cauchy--Kowalewski extension from $S^m$ to $\mathbb{R}^{m+1}\setminus \{0\}$. One then obtains a unitary isomorphism from an $L^2$--Hilbert space to an Hilbert space of solutions of the Dirac equation, that is to a Hilbert space of monogenic functions., Comment: 13 pages

Thiol-stable albumin biologics are enabled by controlled, quantitative hydrolysis of maleimide–albumin conjugates, i.e. with no retro-Michael., Herein we report the use of bromomaleimides for the construction of stable albumin conjugates via conjugation to its native, single accessible, cysteine followed by hydrolysis. Advantages over the classical maleimide approach are highlighted in terms of quantitative hydrolysis and absence of undesirable retro-Michael deconjugation.

We extend the coherent state transform (CST) of Hall to the context of the moduli spaces of semistable holomorphic vector bundles with fixed determinant over elliptic curves. We show that by applying the CST to appropriate distributions, we obtain the space of level k, rank n and genus one non-abelian theta functions with the unitarity of the CST transform being preserved. Furthermore, the shift k -> k+n appears in a natural way in this finite-dimensional framework., small misprints corrected

We extend the coherent state transform (CST) of Hall to the context of abelian varieties by considering them as quotients of the complexification of the abelian group K=U(1)g. We show that this transform, applied to appropriate distributions on K, gives all classical theta functions, and that, by defining on this space of theta functions an inner product related to the K-averaged heat kernel, the unitarity of the CST transform is still preserved.

P2X receptors are trimeric membrane ion channels activated by extracellular ATP. Elucidation of their physiological roles has been handicapped by a lack of specific tools. In the present work, the P2X2 receptor was engineered to open and close with different wavelengths of light. We synthesized a photoswitchable crosslinker, bis(maleimido)azobenzene, of molecular dimensions appropriate to bridge cysteines introduced at different subunits at the outer pore (P329C). This produced a P2X2 receptor that was opened within milliseconds at 440 nm light and closed rapidly at 360 nm light, as measured by the ionic currents. When the P329C mutation was combined with the ATP-binding site mutation, K69A, ATP had no effect while light-induced currents were still present. The light-gated receptor displayed similar unitary currents, inward rectification and calcium permeability (PCa/PNa = 2.6), as the P2X2 receptors activated by ATP. P2X3 receptors with an equivalent mutation (P320C) could be controlled with light, displaying typical rapid desensitization. P2X3[P320C] subunits also co-assembled with native P2X2 subunits in pheochromocytoma 12 cells to form light-gated heteromeric P2X2/3 receptors. We extended this approach to acid-sensing ion channels (ASICs), which are also trimers but are unrelated in sequence to P2X receptors. The structurally equivalent mutation in human ASIC1 (G430C) was readily opened and closed by brief applications of light following modification with bis(maleimido)azobenzene. This provides functional evidence that P2X receptors and ASICs can open by a similar mechanism at the level of the pore. The generation of these engineered receptors should facilitate investigation of the functional roles of P2X receptors and ASICs in the cell, tissue and intact organism.

The path integral computation of field strength correlation functions for two-dimensional Yang–Mills theories over Riemann surfaces is studied. The calculation is carried out by Abelianization, which leads to correlators that are topological. They are nontrivial as a result of the topological obstructions to the Abelianization. It is shown in the large N limit on the sphere that the correlators undergo second order phase transitions at the critical point. Our results are applied to a computation of contractible Wilson loops.

A new method to obtain the Picard-Fuchs equations of effective, N=2 supersymmetric gauge theories with massive matter hypermultiplets in the fundamental representation is presented. It generalises a previously described method to derive the Picard-Fuchs equations of both pure super Yang-Mills and supersymmetric gauge theories with massless matter hypermultiplets. The techniques developed are well suited to symbolic computer calculations., Comment: 29 pages, uses phyzzx.tex

A new method to obtain the Picard-Fuchs equations of effective $N = 2$ supersymmetric gauge theories in 4 dimensions is developed. It includes both pure super Yang-Mills and supersymmetric gauge theories with massless matter hypermultiplets. It applies to all classical gauge groups, and directly produces a decoupled set of second-order, partial differential equations satisfied by the period integrals of the Seiberg-Witten differential along the 1-cycles of the algebraic curves describing the vacuum structure of the corresponding $N = 2$ theory., Latex version, 43 pages, a few cosmetic changes and some references added

P2X receptors are trimeric membrane proteins that function as ion channels gated by extracellular ATP. We have engineered a P2X2 receptor that opens within milliseconds by irradiation at 440 nm, and rapidly closes at 360 nm. This requires bridging receptor subunits via covalent attachment of 4,4'-bis(maleimido)azobenzene to a cysteine residue (P329C) introduced into each second transmembrane domain. The cis-trans isomerization of the azobenzene pushes apart the outer ends of the transmembrane helices and opens the channel in a light-dependent manner. Light-activated channels exhibited similar unitary currents, rectification, calcium permeability, and dye uptake as P2X2 receptors activated by ATP. P2X3 receptors with an equivalent mutation (P320C) were also light sensitive after chemical modification. They showed typical rapid desensitization, and they could coassemble with native P2X2 subunits in pheochromocytoma cells to form light-activated heteromeric P2X2/3 receptors. A similar approach was used to open and close human acid-sensing ion channels (ASICs), which are also trimers but are unrelated in sequence to P2X receptors. The experiments indicate that the opening of the permeation pathway requires similar and substantial movements of the transmembrane helices in both P2X receptors and ASICs, and the method will allow precise optical control of P2X receptors or ASICs in intact tissues.

In the case of a compact real analytic symplectic manifold M we describe an approach to the complexification of Hamiltonian flows [Se, Do1, Th1] and corresponding geodesics on the space of Kahler metrics. In this approach, motivated by recent work on quantization, the complexified Hamiltonian flows act, through the Grobner theory of Lie series, on the sheaf of complex valued real analytic functions, changing the sheaves of holomorphic functions. This defines an action on the space of (equivalent) complex structures on M and also a direct action on M. This description is related to the approach of [BLU] where one has an action on a complexification M_C of M followed by projection to M. Our approach allows for the study of some Hamiltonian functions which are not real analytic. It also leads naturally to the consideration of continuous degenerations of diffeomorphisms and of Kahler structures of M. Hence, one can link continuously (geometric quantization) real, and more general non-Kahler, polarizations with Kahler polarizations. This corresponds to the extension of the geodesics to the boundary of the space of Kahler metrics. Three illustrative examples are considered. We find an explicit formula for the complex time evolution of the Kahler potential under the flow. For integral symplectic forms, this formula corresponds to the complexification of the prequantization of Hamiltonian symplectomorphisms. We verify that certain families of Kahler structures, which have been studied in geometric quantization, are geodesic families., final version

We study the half-form Kähler quantization of a smooth symplectic toric manifold $(X,\omega)$, such that $[ \omega/ 2\pi]- c_{1}(X)/2 \in H^{2}(X,{\mathbb{Z}} )$ and is non-negative. We define the half-form corrected quantization of $(X,\omega)$ to be given by holomorphic sections of a certain Hermitian line bundle $L\to X$ with Chern class $[ \omega/ 2\pi]- c_{1}(X)/2$. These sections then correspond to integral points of a "corrected" polytope $P_{L}$ with integral vertices. For a suitably translated moment polytope $P_{X}$ for $(X,\omega)$, we have that $P_{L}\subset P_{X}$ is obtained from $P_{X}$ by a one-half inward-pointing normal shift along the boundary. ¶ We use our results on the half-form corrected Kähler quantization to motivate a definition of half-form corrected quantization in the singular real toric polarization. Using families of complex structures studied in Baier-Florentino-Mourão-Nunes, which include the degeneration of Kähler polarizations to the vertical polarization, we show that, under this degeneration, the half-form corrected $L^{2}$-normalized monomial holomorphic sections converge to Dirac-delta-distributional sections supported on the fibers over the integral points of $P_{L}$, which correspond to corrected Bohr-Sommerfeld fibers. This result and the limit of the corrected connection, with curvature singularities along the boundary of $P_X$, justifies the direct definition we give for the corrected quantization in the singular real toric polarization. We show that the space of quantum states for this definition coincides with the space obtained via degeneration of the Kähler quantization. ¶ We also show that the BKS pairing between Kähler polarizations is not unitary in general. On the other hand, the unitary connection induced by this pairing is flat.

Segal-Bargmann coherent state transforms can be viewed as unitary maps from L2 spaces of functions (or sections of an appropriate line bundle) on a manifold X to spaces of square integrable holomorphic functions (or sections) on Xℂ. It is natural to consider higher dimensional extensions of X based on Clifford algebras as they could be useful in studying quantum systems with internal, discrete, degrees of freedom corresponding to nonzero spins. Notice that the extensions of X based on the Grassmann algebra appear naturally in the study of supersymmetric quantum mechanics. In Clifford analysis, the zero mass Dirac equation provides a natural generalization of the Cauchy-Riemann conditions of complex analysis and leads to monogenic functions. For the simplest but already quite interesting case of X = ℝ, we introduce two extensions of the Segal-Bargmann coherent state transform from L2(ℝ, dx) ⊗ ℝm to Hilbert spaces of slice monogenic and axial monogenic functions and study their properties. These two transfo...

A cutoff version of the λϕ4 O(N) model is considered to leading order in 1/N with particular attention paid to the effective potential, which is surprisingly rich in structure. With suitable restriction on a background classical field, one finds a phenomenologically viable model with spontaneously broken symmetry, a potential bounded below, and amplitudes free of tachyons. The model has an O(N − 1) singlet resonance in both weak and strong couplings, which can be interpreted as the Higgs meson in applications. Further, an unphysical resonance, which can be used to define a triviality scale for the model, appears at a mass above the cutoff mass Λ. The phenomenological aspects of our discussion are consistent with previous studies, whose results are obtained by somewhat different methods. The question of the double-scaling limit for the cutoff model is considered as an application of the effective potential. It is shown that the double-scaling limit is not possible.

Graphical abstract, Bromomaleimides are useful building blocks in synthesis and powerful reagents for the selective chemical modification of proteins. A mild new synthesis of these reagents is described, along with the convenient transferability of the approach to dithiomaleimides and bromopyridazinediones.

For the cotangent bundle $T^{*}K$ of a compact Lie group $K$, we study the complex-time evolution of the vertical tangent bundle and the associated geometric quantization Hilbert space $L^{2}(K)$ under an infinite-dimensional family of Hamiltonian flows. For each such flow, we construct a generalized coherent state transform (CST), which is a unitary isomorphism between $L^{2}(K)$ and a certain weighted $L^{2}$-space of holomorphic functions. For a particular set of choices, we show that this isomorphism is naturally decomposed as a product of a Heisenberg-type evolution (for complex time $-\tau$) within $L^{2}(K)$, followed by a polarization--changing geometric quantization evolution (for complex time $+\tau$). In this case, our construction yields the usual generalized Segal--Bargmann transform of Hall. We show that the infinite-dimensional family of Hamiltonian flows can also be understood in terms of Thiemann's "complexifier" method (which generalizes the construction of adapted complex structures). We will also investigate some properties of the generalized CSTs, and discuss how their existence can be understood in terms of Mackey's generalization of the Stone-von Neumann theorem., Comment: 28 pages

Mackey showed that for a compact Lie group $K$, the pair $(K,C^{0}(K))$ has a unique non-trivial irreducible covariant pair of representations. We study the relevance of this result to the unitary equivalence of quantizations for an infinite-dimensional family of $K\times K$ invariant polarizations on $T^{\ast}K$. The K\"{a}hler polarizations in the family are generated by (complex) time-$\tau$ Hamiltonian flows applied to the (Schr\"{o}dinger) vertical real polarization. The unitary equivalence of the corresponding quantizations of $T^{\ast}K$ is then studied by considering covariant pairs of representations of $K$ defined by geometric prequantization and of representations of $C^0(K)$ defined via Heisenberg time-$(-\tau)$ evolution followed by time-$(+\tau)$ geometric-quantization-induced evolution. We show that in the semiclassical and large imaginary time limits, the unitary transform whose existence is guaranteed by Mackey's theorem can be approximated by composition of the time-$(+\tau)$ geometric-quantization-induced evolution with the time-$(-\tau)$ evolution associated with the momentum space [W. D. Kirwin and S. Wu, Momentum space for compact Lie groups and the Peter-Weyl theorem, to appear] quantization of the Hamiltonian function generating the flow. In the case of quadratic Hamiltonians, this asymptotic result is exact and unitary equivalence between quantizations is achieved by identifying the Heisenberg imaginary time evolution with heat operator evolution, in accordance with the coherent state transform of Hall.

We study the Maslov correction to semiclassical states by using a Kahler regularized BKS pairing map from the energy representation to the Schrodinger representation. For general semiclassical states, the existence of this regularization is based on recently found families of Kahler polarizations degenerating to singular real polarizations and corresponding to special geodesic rays in the space of Kahler metrics. In the case of the one-dimensional harmonic oscillator, we show that the correct phases associated with caustic points of the projection of the Lagrangian curves to the configuration space are correctly reproduced.

We review some aspects of the construction of self-dual gravity and the associated field theory of ${\cal N}=2$ strings in terms of two-dimensional sigma models at large $N$. The theory is defined through a large $N$ Wess-Zumino-Witten model in a nontrivial background and in a particular double scaling limit. We examine the canonical structure of the theory and describe an infinite-dimensional Poisson algebra of currents., To appear in the special issue of the Journ. of Chaos, Solitons and Fractals, 24 pages

We explore the quantum properties of self-dual gravity formulated as a large $N$ two-dimensional WZW sigma model. Using a non-trivial classical background, we show that a $(2,2)$ space-time is generated. The theory contains an infinite series of higher point vertices. At tree level we show that, in spite of the presence of higher than cubic vertices, the on-shell 4 and higher point functions vanish, indicating that this model is related with the field theory of closed N=2 strings. We examine the one-loop on-shell 3-point amplitude and show that it is ultra-violet finite., This is the final version. By editorial mistake at Phys.Lett.B an older version was published in print

Herein we report a new approach to the synthesis of 2,4-bifunctionalised cyclopentenones via one-pot conversion of 2-furaldehyde with morpholine followed by concomitant 1,4 addition and elimination. This protocol has also been extended to afford 2-hydroxy, 2-amino and 2-phenyl cyclopentenones.

We continue our analysis of the field strength correlation functions of two-dimensional QCD on Riemann surfaces by studying the large $N$ limit of these correlation functions on the sphere for gauge group $U(N)$. Our results allow us to exhibit an explicit master field for the field strength $F_{\mu\nu}$ in a ``topological gauge'', given by a single master matrix in the Lie algebra of the maximal torus of the gauge group. Field correlators are obtained from traces of products of the master field. We also obtain a master field for the gauge potential $A_{\mu}$ on the sphere, consistent with the master field for the field strength., Comment: 14 pages, latex file, no macros, 1 reference added

It is known that the partition function and correlators of the two-dimensional topological field theory $G_K(N)/ G_K(N)$ on the Riemann surface $\Sigma_{g,s}$ is given by Verlinde numbers, dim($V_{g,s,K}$) and that the large $K$ limit of dim($V_{g,s,K}$) gives Vol(${\cal M}_s$), the volume of the moduli space of flat connections of gauge group $G(N)$ on $\Sigma_{g,s}$, up to a power of $K$. Given this relationship, we complete the computation of Vol(${\cal M}_s$) using only algebraic results from conformal field theory. The group-level duality of $G(N)_K$ is used to show that if $G(N)$ is a classical group, then $\displaystyle \lim_{N\rightarrow \infty} G_K(N) / G_K(N)$ is a BF theory with gauge group $G(K)$. Therefore this limit computes Vol(${\cal M}^\prime_s$), the volume of the moduli space of flat connections of gauge group $G(K)$.