Homotopy Type Theory in Lean

We discuss the homotopy type theory library in the Lean proof assistant. The library is especially geared toward synthetic homotopy theory. Of particular interest is the use of just a few primitive notions of higher inductive types, namely quotients and truncations, and the use of cubical methods.Comment: 17 pages, accepted for ITP 201

Comparison of the Extended Kalman Filter and the Unscented Kalman Filter for Magnetocardiography activation time imaging

The non-invasive and radiation-free imaging of the electrical activity of the heart with Electrocardiography (ECG) or Magnetocardiography (MCG) can be helpful for physicians for instance in the localization of the origin of cardiac arrhythmia. In this paper we compare two Kalman Filter algorithms for the solution of a nonlinear state-space model and for the subsequent imaging of the activation/depolarization times of the heart muscle: the Extended Kalman Filter (EKF) and the Unscented Kalman Filter (UKF). The algorithms are compared for simulations of a (6×6) magnetometer array, a torso model with piecewise homogeneous conductivities, 946 current dipoles located in a small part of the heart (apex), and several noise levels. It is found that for all tested noise levels the convergence of the activation times is faster for the UKF

Equation of state of forsterite

Shock wave data for pure forsterite with initial bulk densities of 2.6 and 3.1 g/cm^3 are obtained to 0.370 Mb by impacting series of specimens with tungsten alloy plates that are launched at speeds of up to 2.3 km/sec with a high-performance propellant gun. The onset of a shock-induced phase change, probably corresponding to the forsterite-‘post spinel’ phase change is observed at 0.280±0.025 Mb. Because of the low shock temperatures, the transition is believed to be limited by the reaction rate and this pressure value should be taken only as an upper limit. Adiabats derived from the Hugoniot data for the forsterite phase are fit to the two-parameter finite strain Birch-Murnaghan equation and to two simple ionic equations of state. The Birch-Murnaghan form of the equation of state gives a zero-pressure bulk modulus (1.29 Mb) that agrees more closely with the ultrasonic data than the modulus obtained from the ionic equations of state. An unusual relaxation effect, in which the elastic shock precursor velocity varies from 5.8 to 9.5 km/sec, is also observed. The characteristic time of the relaxation process appears to be less than 1 μsec

From AMANDA to IceCube

The first string of the neoteric high energy neutrino telescope IceCube successfully began operating in January 2005. It is anticipated that upon completion the new detector will vastly increase the sensitivity and extend the reach of AMANDA to higher energies. A discussion of the IceCube's discovery potential for extra-terrestrial neutrinos, together with the prospects of new physics derived from the ongoing AMANDA research will be the focus of this paper. Preliminary results of the first antarctic high energy neutrino telescope AMANDA searching in the muon neutrino channel for localized and diffuse excess of extra-terrestrial neutrinos will be reviewed using data collected between 2000 and 2003. Neutrino flux limits obtained with the all-flavor dedicated UHE and cascade analyses will be described. A first neutrino spectrum above one TeV in agreement with atmospheric neutrino flux expectations and no extra-terrestrial contribution will be presented, followed by a discussion of a limit for neutralino CDM candidates annihilating in the center of the Sun.Comment: 15 pages, 8 figures Invited talk contribution at 5th International Conference on Non-accelerator New Physics (NANP 05), Dubna, Russia, 20-25 Jun 200

Spin dynamics in the Kapitza-Dirac effect

Electron spin dynamics in Kapitza-Dirac scattering from a standing laser wave of high frequency and high intensity is studied. We develop a fully relativistic quantum theory of the electron motion based on the time-dependent Dirac equation. Distinct spin dynamics, with Rabi oscillations and complete spin-flip transitions, is demonstrated for Kapitza-Dirac scattering involving three photons in a parameter regime accessible to future high-power X-ray laser sources. The Rabi frequency and, thus, the diffraction pattern is shown to depend crucially on the spin degree of freedom

SU(3)_LxU(1)_N Model for Right-Handed Neutrino Neutral Currents

A model based on the \mbox{SU(3)}_L\otimes \mbox{U(1)}_N gauge group, in which neutrinos have right-handed neutral currents is considered. We argue that in order to have a result consistent with low-energy one, the right-handed neutrino component must be treated as correction instead of an equivalent spin state.Comment: 6 pages, Latex, no figures, Accepted for publication in Phys. Rev.

Post-operative effects on silver coated tumor endoprosthesis and biofilm prophylaxis systems

Despite the high state of the art in limp replacement and the reconstructive tumor surgery, failures cannot be excluded. Investigations on post-operative effects on explanted silver coated modules of MUTARS® prostheses have disclosed changes in the silver surface. Both, the silver coatings and the perioperative lavage with antiseptics reduce efficiently the risks of infections

Polarization of Tau Leptons Produced in Quasielastic Neutrino--Nucleon Scattering

A numerical analysis of the polarization vector of tau leptons produced through quasielastic neutrino and antineutrino interactions with free nucleons is given with two models for vector electromagnetic form factors of proton and neutron. The impact of G parity violating axial and vector second-class currents is investigated by applying a simple heuristic model for the induced scalar and tensor form factors.Comment: Thesis of a talk given at the 8th Scientific Conference (SCYSS-04), Dubna, Russia, 2 - 6 Feb 2004. 11 pages, 6 figures; added references, figures and discussion; conclusions unchange

Capture rate and neutron helicity asymmetry for ordinary muon capture on hydrogen

Applying heavy-baryon chiral perturbation theory to ordinary muon capture (OMC) on a proton, we calculate the capture rate and neutron helicity asymmetry up to next-to-next-to-leading order. For the singlet hyperfine state, we obtain the capture rate Gamma_0 = 695 sec^{-1} while, for the triplet hyperfine state, we obtain the capture rate Gamma_1 = 11.9 sec^{-1} and the neutron asymmetry alpha_1 = 0.93. If the existing formalism is used to relate these atomic capture rates to Gamma_{liq}, the OMC rate in liquid hydrogen, then Gamma_{liq} corresponding to our improved values of Gamma_0 and Gamma_1 is found to be significantly larger than the experimental value, primarily due to the updated larger value of g_A. We argue that this apparent difficulity may be correlated to the specious anomaly recently reported for mu^- + p to n + nu_mu + gamma, and we suggest a possibility to remove these two "problems" simply and simultaneously by reexamining the molecular physics input that underlies the conventional analysis of Gamma_{liq}.Comment: 14 pages, 1 figur