Conformal Change Research Articles

The Chern–Ricci Flow on Oeljeklaus–Toma Manifolds

AbstractWe study the Chern-Ricci flow, an evolution equation of Hermitian metrics, on a family of Oeljeklaus–Toma (OT-) manifolds that are non-Kähler compact complex manifolds with negative Kodaira dimension. We prove that after an initial conformal change, the flow converges in the Gromov–Hausdorff sense to a torus with a flat Riemannianmetric determined by the OT-manifolds themselves.

The simulation for study of von Mises stress sensitiveness to the change of coronal conformity in knee prosthesis

Two-dimensional finite element contact modelling is often conducted to simulate the contact mechanism in knee prosthesis. This is based on the assumption that the contact stresses are more sensitive to change in the coronal plane than in the sagittal plane. Therefore, the simulation is then can be simply conducted only in the coronal plane with neglecting the sagittal dimension. Thus, the model is only a two-dimensional model. Based on this issue, the investigation of the response of contact stress (von Mises) to the coronal and sagittal conformity variation was conducted. For the need of investigation, ten three-dimensional finite element models of knee prosthesis have been created. From the result, the gradient of von Mises stress when the conformity varied in the coronal plane was -12.015, and when the conformity was varied in the sagittal plane, the gradient was −9.774. This meant that the von Mises stress had high sensitiveness to the change of the coronal conformity variation of knee prosthesis than to the change of the sagittal conformity. Therefore, the contact modelling of knee prosthesis can be simply carried out in the coronal plane.

Novel Antibody for the Treatment of Transthyretin Amyloidosis

Familial amyloidotic polyneuropathy (FAP) is a systemic amyloidosis mainly caused by amyloidogenic transthyretin (ATTR). This incurable disease causes death ∼10 years after onset. Although it has been widely accepted that conformational change of the monomeric form of transthyretin (TTR) is very important for amyloid formation and deposition in the organs, no effective therapy targeting this step is available. In this study, we generated a mouse monoclonal antibody, T24, that recognized the cryptic epitope of conformationally changed TTR. T24 inhibited TTR accumulation in FAP model rats, which expressed human ATTR V30M in various tissues and exhibited non-fibrillar deposits of ATTR in the gastrointestinal tracts. Additionally, humanized T24 (RT24) inhibited TTR fibrillation and promoted macrophage phagocytosis of aggregated TTR. This antibody did not recognize normal serum TTR functioning properly in the blood. These results demonstrate that RT24 would be an effective novel therapeutic antibody for FAP.

On conformally related spherically symmetric Finsler metrics

In this paper, we study the projective invariant quantities in Finsler geometry which remain invariant under the conformal change of metrics. In particular, we obtain the necessary and sufficient conditions of a given Douglas and Weyl and generalized Douglas–Weyl (GDW) metric to be invariant under the conformal transformations. Finally, we introduce some explicit examples of these metrics. Also, some of these [Formula: see text]-conformal transformations of Einstein metrics are considered.

Conjugate and conformally conjugate parallelisms on Finsler manifolds

In this paper we study conjugate parallelisms and their conformal changes on Finsler manifolds. We provide sufficient conditions for a Finsler manifold endowed with two conjugate (resp. conformally conjugate) covering parallelisms to become a Berwald (resp. Wagner) manifold. As an application for Lie groups, we give a new proof for a theorem of Latifi and Razavi about bi-invariant Finsler functions being Berwald. By introducing the concept of a conformal change of a parallelism, we also obtain a conceptual proof of a theorem of Hashiguchi and Ichijyō: the class of generalized Berwald manifolds is closed under conformal change.

Planar Shape Interpolation Based On Teichmüller Mapping

AbstractShape interpolation is a classical problem in computer graphics and has been widely investigated in the past two decades. Ideal shape interpolation should be natural and smooth which have good properties such as affine and conformal reproduction, bounded distortion, no fold‐overs, etc. In this paper, we present a new approach for planar shape interpolation based on Teichmüller maps ‐ a special type of maps in the class of quasi‐conformal maps. The algorithm consists of two steps. In the first step, a Teichmüller map is computed from the source shape to the target shape, and then the Beltrami coefficient is interpolated such that the conformal distortion is linear with respect to the time variable. In the second step, the intermediate shape is reconstructed by solving the Beltrami equation locally over each triangle and then stitching the mapped triangles by conformal transformations. The new approach preserves all the good properties mentioned above and produces more natural and more uniform intermediate shapes than the start‐of‐the‐art methods. Especially, the conformal distortion changes linearly with respect to the time variable. Experiment results show that our method can produce appealing results regardless of interpolating between the same or different objects.

Hydrogen Bonding and Dielectric Spectra of Ethylene Glycol-Water Mixtures from Molecular Dynamics Simulations.

Mixtures of ethylene glycol with water are a prominent example of media with variable viscosity. Classical molecular dynamics simulations at room temperature were performed for mixtures of ethylene glycol (EG) and water with EG mole fractions of xE = 0.0, 0.1, 0.2, 0.4, 0.6, 0.9, 1.0. The calculated dielectric loss spectra were in qualitative agreement with experiment. We found a slightly overestimated slowdown of the dynamics with increasing EG concentration compared to experimental data. Statistics of the hydrogen bond network and hydrogen bond lifetimes were derived from suitable time correlation functions and also show a slowdown in the dynamics with increasing xE. A similar picture is predicted for the time scales of EG conformer changes and for molecular reorientation. A slight blue shift was obtained for the power spectra of the molecular center of mass motion. The results were used to give a qualitative interpretation of the origin of three different relaxation times that appear in experimental complex dielectric spectra and of their change with xE.

Substitution Position and Vinylene Bond Geometry Modulating the Fluorescence Solvatochromism and Aggregation-Induced Emission of (9-Anthryl)vinyl(1-pyrenyl)vinylbenzene Isomers

Despite the lack of typical electron donor and acceptor in the molecule structure, a pure aromatic hydrocarbon, trans,trans-1-(9-anthryl)vinyl-4-(1-pyrenyl)vinylbenzene (trans,trans-1,4-AVPVB), shows unusual fluorescence solvatochromism with emission shift over 80 nm. In addition, it displays an aggregation-induced emission (AIE) activity. For comparison, other three isomers, trans,trans-1,2-AVPVB, trans,trans-1,3-AVPVB, and trans,cis-1,4-AVPVB, were also synthesized. The effects of substitution position and vinylene bond geometry on solvatochromism, temperature-induced phase transition and AIE activity were systematically studied. Different from the other isomers, the as-prepared sample of trans,trans-1,2-AVPVB shows an endothermic peak and an exothermic peak before the melting point in the DSC curve. They correspond to a solid-to-gas transition and a solid-to-solid transition, respectively. Theoretical calculation indicates that the fluorescence solvatochromism may be related to the conformational chang...

Inoue surfaces and the Chern–Ricci flow

We investigate the Chern–Ricci flow, an evolution equation of Hermitian metrics, on Inoue surfaces. These are non-Kähler compact complex surfaces of type Class VII. We show that, after an initial conformal change, the flow always collapses the Inoue surface to a circle at infinite time, in the sense of Gromov–Hausdorff.

Minimization of scalar curvature in conformal geometry

Let (M,g_{0}) a smooth compact Riemannian manifold with smooth boundary and dimension nge {3}. We consider a minimization problem for the scalar curvature R after a conformal change. In particular, we seek for minimizers of the ||cdot ||_{infty } functional of R, within a conformal class, under small energy assumptions and natural geometric constraints. We prove that minimizers exist, and have locally constant scalar curvature, outside of a set Gamma with explicit description.

Abstract 1257: A MYC-Aurka protein complex represents an actionable target in p53 altered liver cancer

Abstract Myc oncoproteins are causally involved in the genesis of a large fraction of human tumors. Three closely related Myc proteins, c-myc, N-myc and L-myc, have been implicated in cancer, whereas c-myc was identified as an important oncogenic driver in frequent solid tumors.Applying transposon-based mosaic liver cancer mouse models and direct in vivo shRNA screening technology, we found that bypassing a latent p19Arf- and Aurka mediated G2/M cell cycle arrest is required for development of p53 altered liver carcinomas with activated Ras/MAPK signalling. The resulting tumors depend on high MYC levels for survival. A direct interaction of Aurka and MYC was identified in p53 altered liver cancer cells, which could be efficiently disrupted by conformation changing Aurka inhibitors, resulting in MYC degradation and cell death specifically of p53 altered human and murine hepatoma cells. Treatment studies in mouse models of p53 deficient therapy resistant liver cancer revealed marked therapeutic efficacy of conformation changing Aurka inhibitors, thus suggesting a new therapeutic strategy against this major lethal cancer. Citation Format: Dauch Daniel, Ramona Rudalska, Giacomo Cossa, Jean Charles Nault, Sandrine Imbeaud, Nisar P. Malek, Thomas Longerich, Stefan Laufer, Antti Poso, Jessica Zucman-Rossi, Martin Eilers, Lars Zender. A MYC-Aurka protein complex represents an actionable target in p53 altered liver cancer. [abstract]. In: Proceedings of the 107th Annual Meeting of the American Association for Cancer Research; 2016 Apr 16-20; New Orleans, LA. Philadelphia (PA): AACR; Cancer Res 2016;76(14 Suppl):Abstract nr 1257.

Interaction between tangeretin and ovalbumin to reduce the allergic effects of ovalbumin

Food allergy has become a worldwide problem. To find an effective way to reduce the allergic effect of allergen is an interesting topic. In this work, the interaction between ovalbumin(OVA) and tangeretin was studied by means of spectroscopy, molecular docking calculation and animal experiment. As the results show, static quenching of fluorescence intensity happened due to the interaction between OVA and tangeretin. Binding constants, binding sites, and thermometric parameters were obtained. The conformation changing of OVA occurred due to the interaction between it and tangeretin. The molecular docking calculation results show that the epitopes Arginine 84(ARG84), Leucine 87(LEU87), Asparagine 88(ASN88), Serine 103(SER103), Arginine 104(ARG104), Leucine 124(LEU124), Arginine 126(ARG126), Glycine 127(GLY127), Glycine 128(GLY128) and Tryptohan 148(TRP148) of OVA were occupied by tangeretin after the docking, which means tangeretin may have some inhibition effects. As the results of animal experiments, the amount of IgE and lung tissue sections of female BALB/c mice in different groups show that tangeretin with different concentrations has better effects than dexamethasone. In conclusion, the tangeretin may have the effects to reduce the allergic effects of OVA via occupying the IgE-binding epitopes of OVA.

Conformal Ricci solitons and related integrability conditions

Abstract We introduce, in the Riemannian setting, the notion of conformal Ricci soliton, which includes as particular cases Einstein manifolds, conformal Einstein manifolds and (generic and gradient) Ricci solitons. We provide necessary integrability conditions for the existence of these structures that also recover, in the corresponding contexts, those already known in the literature for conformally Einstein manifolds and for gradient Ricci solitons. A crucial tool in our analysis is the construction of (0, 3)-tensors related to the geometric structures, that in the special case of gradient Ricci solitons become the celebrated tensor D recently introduced by Cao and Chen. We derive commutation rules for covariant derivatives (of functions and tensors) and of transformation laws of some geometric objects under a conformal change of the underlying metric.

Book-Tax Conformity and Reporting Behavior A Quasi-Experiment

We examine how a comprehensive change in book-tax conformity affects firms’ reporting behavior. To this end, we exploit a Reform Act as a quasi-natural experiment which implied a decrease in book-tax conformity in Germany in 2010. In particular, this reform allows firms to exercise tax accounting options independently from financial accounting. Our study builds on a unique dataset of linked individual financial statements and actual tax return data. It covers roughly 150 incorporated firms for the years 2008 to 2012. Exploiting the exceptional change in conformity, we contribute to the ongoing debate on the impact of booktax conformity. Our results show that profitable companies, which have a clear tax sheltering incentive, actually use the newly introduced reporting leeway to manage taxable income downwards. This is especially attributable to companies exploiting favorable tax depreciation rules. Moreover, we find larger opportunistic tax reporting responses for small companies with less complex and predominantly domestic group structures. In addition, we observe that a decrease in book-tax conformity induces a decrease in the general persistence of taxable income, but at the same time gives rise to higher financial earnings persistence. This corroborates our finding of increased tax sheltering activity in post reform years.

Fractional-Parabolic Deformations with Sinh-Acceleration

We develop a general simple methodology for very fast and accurate evaluation of integrals of functions that admit analytic continuation into wide regions of the complex plane or into appropriate Riemann surfaces. We use a family of fractional-parabolic deformations of the contours of integration to appropriate Riemann surfaces, make the corresponding conformal changes of variables and use the simplified trapezoid rule. An additional change variables leads to numerical schemes of complexity of the order of $A\pi^{-2}E^2$, where $E=\ln(1/\eps)$, $\eps$ is the error tolerance, and $A$ is, typically, in the range $[0.5,3]$, or even $A\pi^{-2}E \ln E$ (the Laplace and Fourier inversion, the Laplace transform and other integrals with exponentially decreasing or oscillating factors). Simple efficient error bounds make adaptive procedures unnecessary. As applications, we consider special functions of several classes, and outline applications to the Wiener-Hopf factorization, calculation of various probability distributions and pricing vanillas and exotics in the L'evy models, Heston model, and more general stochastic volatility models and affine models. The method can be applied to various boundary problems for partial differential and pseudo-differential equations, and in essentially all situations when the saddle point method or reduction to a cut are applied. Simple approximate recommendations for the choice of parameters of the scheme lead to programs that are accurate and competitive with Mathematica and Python, even without parallelization. In a number of situations, for the error tolerance $10^{-15}$, the resulting programs are dozens, hundreds and even thousands times faster than functions implemented in MATLAB, 8-15 times faster than SymPy. For $ _1F_1$ and $ _2F_1$, in some regions in the parameter space, the new programs are faster than functions implemented in Mathematica. Pricing of vanillas in the Heston model requires the summation of 6-15 terms for options of maturities T ≥ 0.004, in a wide region of strikes; the number of terms is a decreasing function of $T$.

Existence and non existence results for the singular Nirenberg problem

In this paper we study the problem, posed by Troyanov (Trans AMS 324: 793–821, 1991), of prescribing the Gaussian curvature under a conformal change of the metric on surfaces with conical singularities. Such geometrical problem can be reduced to the solvability of a nonlinear PDE with exponential type non-linearity admitting a variational structure. In particular, we are concerned with the case where the prescribed function K changes sign. When the surface is the standard sphere, namely for the singular Nirenberg problem, we give sufficient conditions on K, concerning mainly the regularity of its nodal line and the topology of its positive nodal region, to be the Gaussian curvature of a conformal metric with assigned conical singularities. Besides, we find a class of functions on \(\mathbb {S}^2\) which do not verify our conditions and which can not be realized as the Gaussian curvature of any conformal metric with one conical singularity. This shows that our result is somehow sharp.

A notion of the weighted σk-curvature for manifolds with density

We propose a natural definition of the weighted σk-curvature for a manifold with density; i.e. a triple (Mn,g,e−ϕdvol). This definition is intended to capture the key properties of the σk-curvatures in conformal geometry with the role of pointwise conformal changes of the metric replaced by pointwise changes of the measure. We justify our definition through three main results. First, we show that shrinking gradient Ricci solitons are local extrema of the total weighted σk-curvature functionals when the weighted σk-curvature is variational. Second, we characterize the shrinking Gaussians as measures on Euclidean space in terms of the total weighted σk-curvature functionals. Third, we characterize when the weighted σk-curvature is variational. These results are all analogues of their conformal counterparts, and in the case k=1 recover some of the well-known properties of Perelman's W-functional.

A Class of Locally Conformal Almost Cosymplectic Manifolds

In this paper, we study a class of almost contact manifolds, namely locally conformal almost manifolds. We investigate subclasses of such manifolds and prove that some of them contain the class of bundle-like metric structures. Under some conditions, we prove that the class of conformal changes of almost cosymplectic structures is a subclass of (almost)-cosymplectic structures. Examples are also obtained.

Conformational Changes in Antigen-Antibody Binding: Molecular Dynamics Study

Proline cis-trans isomerization have emerged as an effective regulatory mechanism in a wide range of biological processes related to Alzheimer disease and cancer. However, the details of the mechanism still remain to be clarified. The cis-trans isomerization has been observed in an antigen-antibody system, epiregulin (EPR) and its antibody by X-ray crystallography. Anti EPR antibody, 9E5 has a proline at the residue 103 in the third complementarity-determining region of the heavy chain (CDR-H3), which is in the cis conformation for EPR free 9E5 (apo 9E5) and the trans one for the complex of EPR-9E5 obtained from X-ray crystallography (we refer this complex as “trans-Complex”). Because the cis-trans isomerization is known to occur slowly, with the duration ranging from several minutes to hours, we investigated whether EPR forms a stable complex with apo 9E5 before the isomerization occurs. To identify a stable EPR-binding structure with apo 9E5, we conducted extensive binding molecular dynamics (MD) simulations and additional long MD simulations. An EPR-9E5 complex of which the bound structure is highly similar to that of the trans-Complex was found. We refer this complex as “cis-Complex”. We then investigated the structural stability and conformational changes of the cis-Complex. The cis-Complex is stable for at least 4 μs. It is found that the CDR-H3 loop plays important role for the EPR binding process in which the CDR-H3 loop interacts with EPR strongly. The interaction energy between the EPR and 9E5 is lower than that for the trans-Complex by more than 100 kJ/mol. From 10 μs-MD simulations of the cis-Complex, it is also found that the slight conformal changes of the Pro103 occur slowly during 10 μs.

Conformal Pseudo-Asymptotics and Special Functions

We develop a general simple methodology for very fast and accurate evaluation of special functions of several classes. We use a family of fractional-parabolic deformations of the contours of integration to appropriate Riemann surfaces, make the corresponding conformal changes of variables and use the simplified trapezoid rule. Simple approximate recommendations for the choice of parameters of the scheme lead to programs that are competitive with Mathematica and Python. In a number of situations, for the error tolerance E-15, the programs are dozens, hundreds and even thousands times faster than functions implemented in MATLAB.