Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group

We study Sobolev-type metrics of fractional order $s\geq0$ on the group \Diff_c(M) of compactly supported diffeomorphisms of a manifold $M$. We show that for the important special case $M=S^1$ the geodesic distance on \Diff_c(S^1) vanishes if and only if $s\leq\frac12$. For other manifolds we obtain a partial characterization: the geodesic distance on \Diff_c(M) vanishes for $M=\R\times N, s<\frac12$ and for $M=S^1\times N, s\leq\frac12$, with $N$ being a compact Riemannian manifold. On the other hand the geodesic distance on \Diff_c(M) is positive for $\dim(M)=1, s>\frac12$ and $\dim(M)\geq2, s\geq1$. For $M=\R^n$ we discuss the geodesic equations for these metrics. For $n=1$ we obtain some well known PDEs of hydrodynamics: Burgers' equation for $s=0$, the modified Constantin-Lax-Majda equation for $s=\frac 12$ and the Camassa-Holm equation for $s=1$.Comment: 16 pages. Final versio

Design of small-molecule active-site inhibitors of the S1A family proteases as procoagulant and anticoagulant drugs

Vitamin K antagonists (VKA) have long been the default drugs for anticoagulant management in venous thrombosis. While efficacious, they are difficult to use due to interpatient dose–response variability and the risks of bleeding. The approval of fondaparinux, a heparin-derived factor Xa (fXa) inhibitor, provided validation for the development of direct oral anticoagulants (DOAC), and currently such inhibitors of thrombin and fXa are in clinical use. These agents can be used without regular coagulation monitoring, but the inherent risk of bleeding complications associated with blocking the common coagulation pathway remains. Efforts are now underway to develop DOACs that inhibit components of the intrinsic and extrinsic coagulation cascades upstream of thrombin and fX. Evidence from humans and from transgenic animal models suggests that this strategy may provide a better therapeutic margin between antithrombotic and antihemostatic effects. Here the design of active-site inhibitors of S1A proteases involved in coagulation and fibrinolysis is summarized

Ecological disturbance in tropical peatlands prior to marine Permian-Triassic mass extinction

The Permian-Triassic mass extinction is widely attributed to the global environmental changes caused by the eruption of the Siberian Traps. However, the precise temporal link between marine and terrestrial crises and volcanism is unclear. Here, we report anomalously high mercury (Hg) concentrations in terrestrial strata from southwestern China, synchronous with Hg anomalies in the marine Permian-Triassic type section. The terrestrial sediments also record increased abundance of fossil charcoal coincident with the onset of a negative carbon isotope excursion and the loss of tropical rainforest vegetation, both of which occurred immediately before the peak of Hg concentrations. The organic carbon isotope data show an ∼5‰–6‰ negative excursion in terrestrial organic matter (bulk organic, cuticles, and charcoal), reflecting change in atmospheric CO2 carbon-isotope composition coincident with enhanced wildfire indicated by increased charcoal. Hg spikes provide a correlative tool between terrestrial and marine records along with carbon isotope trends. These data demonstrate that ecological deterioration occurred in tropical peatlands prior to the main marine mass extinction

Insecurity for compact surfaces of positive genus

A pair of points in a riemannian manifold $M$ is secure if the geodesics between the points can be blocked by a finite number of point obstacles; otherwise the pair of points is insecure. A manifold is secure if all pairs of points in $M$ are secure. A manifold is insecure if there exists an insecure point pair, and totally insecure if all point pairs are insecure. Compact, flat manifolds are secure. A standing conjecture says that these are the only secure, compact riemannian manifolds. We prove this for surfaces of genus greater than zero. We also prove that a closed surface of genus greater than one with any riemannian metric and a closed surface of genus one with generic metric are totally insecure.Comment: 37 pages, 11 figure

Quantum to Classical Transition from the Cosmic Background Radiation

We have revisited the Ghirardi-Rimini-Weber-Pearle (GRWP) approach for continuous dynamical evolution of the state vector for a macroscopic object. Our main concern is to recover the decoupling of the state vector dynamics for the center-of-mass (CM) and internal motion, as in the GRWP model, but within the framework of the standard cosmology. In this connection we have taken the opposite direction of the GRWP argument, that the cosmic background radiation (CBR) has originated from a fundamental stochastic hitting process. We assume the CBR as a clue of the Big Bang, playing a main role in the decoupling of the state vector dynamics of the CM and internal motion. In our model, instead of describing a continuous spontaneous localization (CSL) of a system of massive particles as proposed by Ghirardi, Pearle and Rimini, the It\^{o} stochastic equation accounts for the intervention of the CBR on the system of particles. Essentially, this approach leads to a pre-master equation for both the CBR and particles degrees of freedom. The violation of the principle of energy conservation characteristic of the CSL model is avoided as well as the additional assumption on the size of the GRWP's localization width necessary to reach the decoupling between the collective and internal motions. Moreover, realistic estimation for the decoherence time, exhibiting an interesting dependence on the CBR temperature, is obtained. From the formula for the decoherence time it is possible to analyze the transition from micro to macro dynamics in both the early hot Universe and the nowadays cold one. The entropy of the system under decoherence is analyzed and the emergent `pointer basis' is discussed. In spite of not having imposed a privileged basis, in our model the position still emerges as the preferred observable as in the CSL model.Comment: 14 pages, no figure. To appear in Phys. Rev.

Automated Classification of Airborne Laser Scanning Point Clouds

Making sense of the physical world has always been at the core of mapping. Up until recently, this has always dependent on using the human eye. Using airborne lasers, it has become possible to quickly "see" more of the world in many more dimensions. The resulting enormous point clouds serve as data sources for applications far beyond the original mapping purposes ranging from flooding protection and forestry to threat mitigation. In order to process these large quantities of data, novel methods are required. In this contribution, we develop models to automatically classify ground cover and soil types. Using the logic of machine learning, we critically review the advantages of supervised and unsupervised methods. Focusing on decision trees, we improve accuracy by including beam vector components and using a genetic algorithm. We find that our approach delivers consistently high quality classifications, surpassing classical methods

Characterizing normal crossing hypersurfaces

The objective of this article is to give an effective algebraic characterization of normal crossing hypersurfaces in complex manifolds. It is shown that a hypersurface has normal crossings if and only if it is a free divisor, has a radical Jacobian ideal and a smooth normalization. Using K. Saito's theory of free divisors, also a characterization in terms of logarithmic differential forms and vector fields is found and and finally another one in terms of the logarithmic residue using recent results of M. Granger and M. Schulze.Comment: v2: typos fixed, final version to appear in Math. Ann.; 24 pages, 2 figure

Constraints on radiative decay of the 17-keV neutrino from COBE Measurements

It is shown that, for a nontrivial radiative decay channel of the 17-keV neutrino, the photons would distort the microwave background radiation through ionization of the universe. The constraint on the branching ratio of such decays from COBE measurements is found to be more stringent than that from other considerations. The limit on the branching ratio in terms of the Compton $y$ parameter is $B_\gamma < 1.5 \times 10^{-7} ({\tau_\nu \over 10^{11} sec})^{0.45} ({y \over 10^{-3}})^{1.11} h^{-1}$ for an $\Omega=1, \Omega_b=0.1$ universe.Comment: 7 pages. (figures will be sent on request) (To appear in Phys. Rev. D.