Holomorphic families of nonequivalent embeddings and of holomorphic group actions on affine space

We construct holomorphic families of proper holomorphic embeddings of \mathbb {C}^{k} into \mathbb {C}^{n} (0\textless k\textless n-1), so that for any two different parameters in the family, no holomorphic automorphism of \mathbb {C}^{n} can map the image of the corresponding two embeddings onto each other. As an application to the study of the group of holomorphic automorphisms of \mathbb {C}^{n}, we derive the existence of families of holomorphic \mathbb {C}^{*}-actions on \mathbb {C}^{n} (n\ge5) so that different actions in the family are not conjugate. This result is surprising in view of the long-standing holomorphic linearization problem, which, in particular, asked whether there would be more than one conjugacy class of \mathbb {C}^{*}-actions on \mathbb {C}^{n} (with prescribed linear part at a fixed point).

Infinite Transitivity on Affine Varieties

In this note we survey recent results on automorphisms of affine algebraic varieties, infinitely transitive group actions and flexibility. We present related constructions and examples, and discuss geometric applications and open problems.

Uniqueness of the Embedding Continuous Convolution Semigroup of a Gaussian Probability Measure on the Affine Group and an Application in Mathematical Finance

Let {μ(i)t}t≥0 ( i=1,2 ) be continuous convolution semigroups (c.c.s.) of probability measures on Aff(1) (the affine group on the real line). Suppose that μ(1)1=μ(2)1 . Assume furthermore that {μ(1)t}t≥0 is a Gaussian c.c.s. (in the sense that its generating distribution is a sum of a primitive distribution and a second-order differential operator). Then μ(1)t=μ(2)t for all t≥0 . We end up with a possible application in mathematical finance.

Up, down, strange and charm quark masses with Nf = 2+1+1 twisted mass lattice QCD

We present a lattice QCD calculation of the up, down, strange and charm quark masses performed using the gauge configurations produced by the European Twisted Mass Collaboration with Nf=2+1+1 dynamical quarks, which include in the sea, besides two light mass degenerate quarks, also the strange and charm quarks with masses close to their physical values. The simulations are based on a unitary setup for the two light quarks and on a mixed action approach for the strange and charm quarks. The analysis uses data at three values of the lattice spacing and pion masses in the range 210–450 MeV, allowing for accurate continuum limit and controlled chiral extrapolation. The quark mass renormalization is carried out non-perturbatively using the RI′-MOM method. The results for the quark masses converted to the scheme are: mud(2 GeV)=3.70(17) MeV, ms(2 GeV)=99.6(4.3) MeV and mc(mc)=1.348(46) GeV. We obtain also the quark mass ratios ms/mud=26.66(32) and mc/ms=11.62(16). By studying the mass splitting between the neutral and charged kaons and using available lattice results for the electromagnetic contributions, we evaluate mu/md=0.470(56), leading to mu=2.36(24) MeV and md=5.03(26) MeV.

A first look at maximally twisted mass lattice QCD calculations at the physical point

In this contribution, a first look at simulations using maximally twisted mass Wilson fermions at the physical point is presented. A lattice action including clover and twisted mass terms is presented and the Monte Carlo histories of one run with two mass-degenerate flavours at a single lattice spacing are shown. Measurements from the light and heavy-light pseudoscalar sectors are compared to previous Nf = 2 results and their phenomenological values. Finally, the strategy for extending simulations to Nf = 2+1+1 is outlined.

Flexibility Properties in Complex Analysis and Affine Algebraic Geometry

In the last decades affine algebraic varieties and Stein manifolds with big (infinite-dimensional) automorphism groups have been intensively studied. Several notions expressing that the automorphisms group is big have been proposed. All of them imply that the manifold in question is an Oka–Forstnerič manifold. This important notion has also recently merged from the intensive studies around the homotopy principle in Complex Analysis. This homotopy principle, which goes back to the 1930s, has had an enormous impact on the development of the area of Several Complex Variables and the number of its applications is constantly growing. In this overview chapter we present three classes of properties: (1) density property, (2) flexibility, and (3) Oka–Forstnerič. For each class we give the relevant definitions, its most significant features and explain the known implications between all these properties. Many difficult mathematical problems could be solved by applying the developed theory, we indicate some of the most spectacular ones.

Progress in Simulations with Twisted Mass Fermions at the Physical Point

In this contribution, results from Nf = 2 lattice QCD simulations at one lattice spacing using twisted mass fermions with a clover term at the physical pion mass are presented. The mass splitting between charged and neutral pions (including the disconnected contribution) is shown to be around 20(20) MeV. Further, a first measurement using the clover twisted mass action of the average momentum fraction of the pion is given. Finally, an analysis of pseudoscalar meson masses and decay constants is presented involving linear interpolations in strange and charm quark masses. Matching to meson mass ratios allows the calculation of quark mass ratios: ms=ml = 27:63(13), mc=ml = 339:6(2:2) and mc=ms = 12:29(10). From this mass matching the quantities fK = 153:9(7:5) MeV, fD = 219(11) MeV, fDs = 255(12) MeV and MDs = 1894(93) MeV are determined without the application of finite volume or discretization artefact corrections and with errors dominated by a preliminary estimate of the lattice spacing.

Finite volume effects in chiral perturbation theory with twisted boundary conditions

We study the effects of a finite cubic volume with twisted boundary conditions on pseudoscalar mesons. We apply Chiral Perturbation Theory in the p-regime and introduce the twist by means of a constant vector field. The corrections of masses, decay constants, pseudoscalar coupling constants and form factors are calculated at next-to-leading order. We detail the derivations and compare with results available in the literature. In some case there is disagreement due to a different treatment of new extra terms generated from the breaking of the cubic invariance. We advocate to treat such terms as renormalization terms of the twisting angles and reabsorb them in the on-shell conditions. We confirm that the corrections of masses, decay constants, pseudoscalar coupling constants are related by means of chiral Ward identities. Furthermore, we show that the matrix elements of the scalar (resp. vector) form factor satisfies the Feynman–Hellman Theorem (resp. the Ward–Takahashi identity). To show the Ward–Takahashi identity we construct an effective field theory for charged pions which is invariant under electromagnetic gauge transformations and which reproduces the results obtained with Chiral Perturbation Theory at a vanishing momentum transfer. This generalizes considerations previously published for periodic boundary conditions to twisted boundary conditions. Another method to estimate the corrections in finite volume are asymptotic formulae. Asymptotic formulae were introduced by Lüscher and relate the corrections of a given physical quantity to an integral of a specific amplitude, evaluated in infinite volume. Here, we revise the original derivation of Lüscher and generalize it to finite volume with twisted boundary conditions. In some cases, the derivation involves complications due to extra terms generated from the breaking of the cubic invariance. We isolate such terms and treat them as renormalization terms just as done before. In that way, we derive asymptotic formulae for masses, decay constants, pseudoscalar coupling constants and scalar form factors. At the same time, we derive also asymptotic formulae for renormalization terms. We apply all these formulae in combination with Chiral Perturbation Theory and estimate the corrections beyond next-to-leading order. We show that asymptotic formulae for masses, decay constants, pseudoscalar coupling constants are related by means of chiral Ward identities. A similar relation connects in an independent way asymptotic formulae for renormalization terms. We check these relations for charged pions through a direct calculation. To conclude, a numerical analysis quantifies the importance of finite volume corrections at next-to-leading order and beyond. We perform a generic Analysis and illustrate two possible applications to real simulations.

The algebraic density property for affine toric varieties

In this paper we generalize the algebraic density property to not necessarily smooth affine varieties relative to some closed subvariety containing the singular locus. This property implies the remarkable approximation results for holomorphic automorphisms of the Andersén–Lempert theory. We show that an affine toric variety X satisfies this algebraic density property relative to a closed T-invariant subvariety Y if and only if X∖Y≠TX∖Y≠T. For toric surfaces we are able to classify those which possess a strong version of the algebraic density property (relative to the singular locus). The main ingredient in this classification is our proof of an equivariant version of Brunella's famous classification of complete algebraic vector fields in the affine plane.

On the Closure of the Tame Automorphism Group of Affine Three-Space

We provide explicit families of tame automorphisms of the complex affine three-space which degenerate to wild automorphisms. This shows that the tame subgroup of the group of polynomial automorphisms of C3 is not closed, when the latter is seen as an infinite-dimensional algebraic group.

Absence of somatostatin SST(2) receptor internalization in vivo after intravenous SOM230 application in the AR42J animal tumor model

Among clinically relevant somatostatin functions, agonist-induced somatostatin receptor subtype 2 (sst(2)) internalization is a potent mechanism for tumor targeting with sst(2) affine radioligands such as octreotide. Since, as opposed to octreotide, the second generation multi-somatostatin analog SOM230 (pasireotide) exhibits strong functional selectivity, it appeared of interest to evaluate its ability to affect sst(2) internalization in vivo. Rats bearing AR42J tumors endogenously expressing somatostatin sst(2) receptors were injected intravenously with SOM230 or with the [Tyr(3), Thr(8)]-octreotide (TATE) analog; they were euthanized at various time points; tumors and pancreas were analyzed by immunohistochemistry for the cellular localization of somatostatin sst(2) receptors. SOM230-induced sst(2) internalization was also evaluated in vitro by immunofluorescence microscopy in AR42J cells. At difference to the efficient in vivo sst(2) internalization triggered by intravenous [Tyr(3), Thr(8)]-octreotide, intravenous SOM230 did not elicit sst(2) internalization: immunohistochemically stained sst(2) in AR42J tumor cells and pancreatic cells were detectable at the cell surface at 2.5min, 10min, 1h, 6h, or 24h after SOM230 injection while sst(2) were found intracellularly after [Tyr(3), Thr(8)]-octreotide injection. The inability of stimulating sst(2) internalization by SOM230 was confirmed in vitro in AR42J cells by immunofluorescence microscopy. Furthermore, SOM230 was unable to antagonize agonist-induced sst(2) internalization, neither in vivo, nor in vitro. Therefore, SOM230 does not induce sst(2) internalization in vivo or in vitro in AR42J cells and pancreas, at difference to octreotide derivatives with comparable sst(2) binding affinities. These characteristics may point towards different tumor targeting but also to different desensitization properties of clinically applied SOM230.

One-Step (18)F-Labeling of Carbohydrate-Conjugated Octreotate-Derivatives Containing a Silicon-Fluoride-Acceptor (SiFA): In Vitro and in Vivo Evaluation as Tumor Imaging Agents for Positron Emission Tomography (PET)

The synthesis, radiolabeling, and initial evaluation of new silicon-fluoride acceptor (SiFA) derivatized octreotate derivatives is reported. So far, the main drawback of the SiFA technology for the synthesis of PET-radiotracers is the high lipophilicity of the resulting radiopharmaceutical. Consequently, we synthesized new SiFA-octreotate analogues derivatized with Fmoc-NH-PEG-COOH, Fmoc-Asn(Ac?AcNH-?-Glc)-OH, and SiFA-aldehyde (SIFA-A). The substances could be labeled in high yields (38 ± 4%) and specific activities between 29 and 56 GBq/?mol in short synthesis times of less than 30 min (e.o.b.). The in vitro evaluation of the synthesized conjugates displayed a sst2 receptor affinity (IC?? = 3.3 ± 0.3 nM) comparable to that of somatostatin-28. As a measure of lipophilicity of the conjugates, the log P(ow) was determined and found to be 0.96 for SiFA-Asn(AcNH-?-Glc)-PEG-Tyr³-octreotate and 1.23 for SiFA-Asn(AcNH-?-Glc)-Tyr³-octreotate, which is considerably lower than for SiFA-Tyr³-octreotate (log P(ow) = 1.59). The initial in vivo evaluation of [¹?F]SiFA-Asn(AcNH-?-Glc)-PEG-Tyr³-octreotate revealed a significant uptake of radiotracer in the tumor tissue of AR42J tumor-bearing nude mice of 7.7% ID/g tissue weight. These results show that the high lipophilicity of the SiFA moiety can be compensated by applying hydrophilic moieties. Using this approach, a tumor-affine SiFA-containing peptide could successfully be used for receptor imaging for the first time in this proof of concept study.

Femur Specific Polyaffine Model to Regularize the Log-Domain Demons Registration

Osteoarticular allograft transplantation is a popular treatment method in wide surgical resections with large defects. For this reason hospitals are building bone data banks. Performing the optimal allograft selection on bone banks is crucial to the surgical outcome and patient recovery. However, current approaches are very time consuming hindering an efficient selection. We present an automatic method based on registration of femur bones to overcome this limitation. We introduce a new regularization term for the log-domain demons algorithm. This term replaces the standard Gaussian smoothing with a femur specific polyaffine model. The polyaffine femur model is constructed with two affine (femoral head and condyles) and one rigid (shaft) transformation. Our main contribution in this paper is to show that the demons algorithm can be improved in specific cases with an appropriate model. We are not trying to find the most optimal polyaffine model of the femur, but the simplest model with a minimal number of parameters. There is no need to optimize for different number of regions, boundaries and choice of weights, since this fine tuning will be done automatically by a final demons relaxation step with Gaussian smoothing. The newly developed synthesis approach provides a clear anatomically motivated modeling contribution through the specific three component transformation model, and clearly shows a performance improvement (in terms of anatomical meaningful correspondences) on 146 CT images of femurs compared to a standard multiresolution demons. In addition, this simple model improves the robustness of the demons while preserving its accuracy. The ground truth are manual measurements performed by medical experts.

Geometry-Aware Multiscale Image Registration via OBBTree-Based Polyaffine Log-Demons

Non-linear image registration is an important tool in many areas of image analysis. For instance, in morphometric studies of a population of brains, free-form deformations between images are analyzed to describe the structural anatomical variability. Such a simple deformation model is justified by the absence of an easy expressible prior about the shape changes. Applying the same algorithms used in brain imaging to orthopedic images might not be optimal due to the difference in the underlying prior on the inter-subject deformations. In particular, using an un-informed deformation prior often leads to local minima far from the expected solution. To improve robustness and promote anatomically meaningful deformations, we propose a locally affine and geometry-aware registration algorithm that automatically adapts to the data. We build upon the log-domain demons algorithm and introduce a new type of OBBTree-based regularization in the registration with a natural multiscale structure. The regularization model is composed of a hierarchy of locally affine transformations via their logarithms. Experiments on mandibles show improved accuracy and robustness when used to initialize the demons, and even similar performance by direct comparison to the demons, with a significantly lower degree of freedom. This closes the gap between polyaffine and non-rigid registration and opens new ways to statistically analyze the registration results.