Robust Cryptography in the Noisy-Quantum-Storage Model

It was shown in [WST08] that cryptographic primitives can be implemented based on the assumption that quantum storage of qubits is noisy. In this work we analyze a protocol for the universal task of oblivious transfer that can be implemented using quantum-key-distribution (QKD) hardware in the practical setting where honest participants are unable to perform noise-free operations. We derive trade-offs between the amount of storage noise, the amount of noise in the operations performed by the honest participants and the security of oblivious transfer which are greatly improved compared to the results in [WST08]. As an example, we show that for the case of depolarizing noise in storage we can obtain secure oblivious transfer as long as the quantum bit-error rate of the channel does not exceed 11% and the noise on the channel is strictly less than the quantum storage noise. This is optimal for the protocol considered. Finally, we show that our analysis easily carries over to quantum protocols for secure identification.Comment: 34 pages, 2 figures. v2: clarified novelty of results, improved security analysis using fidelity-based smooth min-entropy, v3: typos and additivity proof in appendix correcte

Variable Bandwidth Filter for Multibeam Echo-sounding Bottom Detection

The accuracy of a seafloor map derived from multibeam swath bathymetry depends first and foremost on the quality of the bottom detection process that yields estimates of the arrival time and angle of bottom echoes received in each beam. Filtering of each beam with a fixed bandwidth filter, with the bandwidth based on the length of the transmitted pulse, reduces the error associated with the time-angle estimates. However, filters of this type can not be optimal over the wide range of operational environments encountered. Better results are obtained with a processing scheme that varies the filter bandwidth across the swath width using detected time and angle information from the previous ping. This method is evaluated using sonar data obtained with a Reson SeaBat 8111ER and the results compared with those obtained using a fixed bandwidth filter

Hunting French Ducks in a Noisy Environment

We consider the effect of Gaussian white noise on fast-slow dynamical systems with one fast and two slow variables, containing a folded-node singularity. In the absence of noise, these systems are known to display mixed-mode oscillations, consisting of alternating large- and small-amplitude oscillations. We quantify the effect of noise and obtain critical noise intensities above which the small-amplitude oscillations become hidden by fluctuations. Furthermore we prove that the noise can cause sample paths to jump away from so-called canard solutions with high probability before deterministic orbits do. This early-jump mechanism can drastically influence the local and global dynamics of the system by changing the mixed-mode patterns.Comment: 60 pages, 9 figure

Higher Sobolev Regularity of Convex Integration Solutions in Elasticity: The Dirichlet Problem with Affine Data in int(Klc)\text{int}(K^{lc})

In this article we continue our study of higher Sobolev regularity of flexible convex integration solutions to differential inclusions arising from applications in materials sciences. We present a general framework yielding higher Sobolev regularity for Dirichlet problems with affine data in $\text{int}(K^{lc})$. This allows us to simultaneously deal with linear and nonlinear differential inclusion problems. We show that the derived higher integrability and differentiability exponent has a lower bound, which is independent of the position of the Dirichlet boundary data in $\text{int}(K^{lc})$. As applications we discuss the regularity of weak isometric immersions in two and three dimensions as well as the differential inclusion problem for the geometrically linear hexagonal-to-rhombic and the cubic-to-orthorhombic phase transformations occurring in shape memory alloys.Comment: 50 pages, 13 figure

From random Poincar\'e maps to stochastic mixed-mode-oscillation patterns

We quantify the effect of Gaussian white noise on fast--slow dynamical systems with one fast and two slow variables, which display mixed-mode oscillations owing to the presence of a folded-node singularity. The stochastic system can be described by a continuous-space, discrete-time Markov chain, recording the returns of sample paths to a Poincar\'e section. We provide estimates on the kernel of this Markov chain, depending on the system parameters and the noise intensity. These results yield predictions on the observed random mixed-mode oscillation patterns. Our analysis shows that there is an intricate interplay between the number of small-amplitude oscillations and the global return mechanism. In combination with a local saturation phenomenon near the folded node, this interplay can modify the number of small-amplitude oscillations after a large-amplitude oscillation. Finally, sufficient conditions are derived which determine when the noise increases the number of small-amplitude oscillations and when it decreases this number.Comment: 56 pages, 14 figures; revised versio

Polytopes associated to Dihedral Groups

In this note we investigate the convex hull of those $n \times n$-permutation matrices that correspond to symmetries of a regular $n$-gon. We give the complete facet description. As an application, we show that this yields a Gorenstein polytope, and we determine the Ehrhart $h^*$-vector

A three-species model explaining cyclic dominance of pacific salmon

The four-year oscillations of the number of spawning sockeye salmon (Oncorhynchus nerka) that return to their native stream within the Fraser River basin in Canada are a striking example of population oscillations. The period of the oscillation corresponds to the dominant generation time of these fish. Various - not fully convincing - explanations for these oscillations have been proposed, including stochastic influences, depensatory fishing, or genetic effects. Here, we show that the oscillations can be explained as a stable dynamical attractor of the population dynamics, resulting from a strong resonance near a Neimark Sacker bifurcation. This explains not only the long-term persistence of these oscillations, but also reproduces correctly the empirical sequence of salmon abundance within one period of the oscillations. Furthermore, it explains the observation that these oscillations occur only in sockeye stocks originating from large oligotrophic lakes, and that they are usually not observed in salmon species that have a longer generation time.Comment: 7 pages, 5 figure