Why Use Sobolev Metrics on the Space of Curves

We study reparametrization invariant Sobolev metrics on spaces of regular curves. We discuss their completeness properties and the resulting usability for applications in shape analysis. In particular, we will argue, that the development of efficient numerical methods for higher order Sobolev type metrics is an extremely desirable goal

Towards a Lagrange-Newton approach for PDE constrained shape optimization

The novel Riemannian view on shape optimization developed in [Schulz, FoCM, 2014] is extended to a Lagrange-Newton approach for PDE constrained shape optimization problems. The extension is based on optimization on Riemannian vector space bundles and exemplified for a simple numerical example.Comment: 16 pages, 4 figures, 1 tabl

Shape analysis on homogeneous spaces: a generalised SRVT framework

Shape analysis is ubiquitous in problems of pattern and object recognition and has developed considerably in the last decade. The use of shapes is natural in applications where one wants to compare curves independently of their parametrisation. One computationally efficient approach to shape analysis is based on the Square Root Velocity Transform (SRVT). In this paper we propose a generalised SRVT framework for shapes on homogeneous manifolds. The method opens up for a variety of possibilities based on different choices of Lie group action and giving rise to different Riemannian metrics.Comment: 28 pages; 4 figures, 30 subfigures; notes for proceedings of the Abel Symposium 2016: "Computation and Combinatorics in Dynamics, Stochastics and Control". v3: amended the text to improve readability and clarify some points; updated and added some references; added pseudocode for the dynamic programming algorithm used. The main results remain unchange

Magnetic Properties of a Superconductor with no Inversion Symmetry

We study the magnetic properties of a superconductor in a crystal without $z \to -z$ symmetry, in particular how the lack of this symmetry exhibits itself. We show that, though the penetration depth itself shows no such effect, for suitable orientation of magnetic field, there is a magnetic field discontinuity at the interface which shows this absence of symmetry. The magnetic field profile of a vortex in the $x-y$ plane is shown to be identical to that of an ordinary anisotropic superconductor except for a shift in the $-z$ direction by ${\tilde \kappa} \lambda_x$ (see errata). For a vortex along $z$, there is an induced magnetization along the radial direction.Comment: J. Low Temp. Physics, 140, 67 (2005); with Errat

Looking back at superfluid helium

A few years after the discovery of Bose Einstein condensation in several gases, it is interesting to look back at some properties of superfluid helium. After a short historical review, I comment shortly on boiling and evaporation, then on the role of rotons and vortices in the existence of a critical velocity in superfluid helium. I finally discuss the existence of a condensate in a liquid with strong interactions, and the pressure variation of its superfluid transition temperature.Comment: Conference "Bose Einstein Condensation", Institut henri Poincare, Paris, 29 march 200

Supersymmetric Higgs Yukawa Couplings to Bottom Quarks at next-to-next-to-leading Order

The effective bottom Yukawa couplings are analyzed for the minimal supersymmetric extension of the Standard Model at two-loop accuracy within SUSY-QCD. They include the resummation of the dominant corrections for large values of tg(beta). In particular the two-loop SUSY-QCD corrections to the leading SUSY-QCD and top-induced SUSY-electroweak contributions are addressed. The residual theoretical uncertainties range at the per-cent level.Comment: 25 pages, 9 figures, added comments and references, typos corrected, results unchanged, published versio

Improving Key Mismatch Attack on NewHope with Fewer Queries

NewHope is a lattice cryptoscheme based on the Ring Learning With Errors (Ring-LWE) problem, and it has received much attention among the candidates of the NIST post-quantum cryptography standardization project. Recently, there have been key mismatch attacks on NewHope, where the adversary tries to recover the server’s secret key by observing the mismatch of the shared key from chosen queries. At CT-RSA 2019, Bauer et al. first proposed a key mismatch attack on NewHope, and then at ESORICS 2019, Qin et al. proposed an improved version with a success probability of 96.9% using about 880,000 queries. In this paper, we further improve their key mismatch attack on NewHope. First, we reduce the number of queries by adapting the terminating condition to the response from the server using an early abort technique. Next, the success rate of recovering the secret key polynomial is raised by considering the deterministic condition judging its coefficients. Furthermore, the search range of the secret key in Qin et al.’s attack is extended without increasing the number of queries. With the above improvements, to achieve an almost success rate of 97%, about 73% of queries can be reduced compared with Qin et al.’s method. Additionally, the success rate can be improved to 100.0%. In particular, we analyze the trade-off between the cost of queries and the success rate. We show that a lower success rate of 20.9% is available by further reduced queries of 135,000 simultaneously

Fractional Sobolev Metrics on Spaces of Immersed Curves

Motivated by applications in the field of shape analysis, we study reparametrization invariant, fractional order Sobolev-type metrics on the space of smooth regular curves Imm(S1 , R ) and on its Sobolev completions ℐ (S1 , R ). We prove local well-posedness of the geodesic equations both on the Banach manifold ℐ (S1 , R ) and on the Fr´echetmanifold Imm(S1 , R ) provided the order of the metric is greater or equal to one. In addition we show that the -metric induces a strong Riemannian metric on the Banach manifold ℐ (S1 , R ) of the same order , provided > 3 2 . These investigations can be also interpreted as a generalization of the analysis for right invariant metrics on the diffeomorphism group

Study of Zγ events and limits on anomalous ZZγ and Zγγ couplings in pp̄ collisions at s=1.96TeV

We present a measurement of the Zγ production cross section and limits on anomalous ZZγ and Zγγ couplings for form-factor scales of Λ=750 and 1000 GeV. The measurement is based on 138 (152) candidates in the eeγ (μμγ) final state using 320(290)pb-1 of pp̄ collisions at s=1.96TeV. The 95% C.L. limits on real and imaginary parts of individual anomalous couplings are |h10,30Z|<0.23, |h20,40Z|<0.020, |h10,30γ|<0.23, and |h20,40γ|<0.019 for Λ=1000GeV. © 2005 The American Physical Society