Coherence of the posterior predictive p-value based on the posterior odds.

^aIt is well-known that classical p-values sometimes behave incoherently for testing hypotheses in the sense that, when $\Theta_{0} \subset \Theta_{0}{'}$, the support given to $\Theta_{0}$ is greater than or equal to the support given to $\Theta_{0}^{'}$ . This problem is also found for posterior predictive p-values (a Bayesian-motivated alternative to classical p-values). In this paper, it is proved that, under some conditions, the posterior predictive p-value based on the posterior odds is coherent, showing that the choice of a suitable discrepancy variable is crucial

Combined grazing incidence RBS and TEM analysis of luminescent nano-SiGe/SiO2 multilayers.

Multilayer structures with five periods of amorphous SiGe nanoparticles/SiO2 layers with different thickness were deposited by Low Pressure Chemical Vapor Deposition and annealed to crystallize the SiGe nanoparticles. The use of grazing incidence RBS was necessary to obtain sufficient depth resolution to separate the signals arising from the individual layers only a few nm thick. The average size and areal density of the embedded SiGe nanoparticles as well as the oxide interlayer thickness were determined from the RBS spectra. Details of eventual composition changes and diffusion processes caused by the annealing processes were also studied. Transmission Electron Microscopy was used to obtain complementary information on the structural parameters of the samples in order to check the information yielded by RBS. The study revealed that annealing at 900 °C for 60 s, enough to crystallize the SiGe nanoparticles, leaves the structure unaltered if the interlayer thickness is around 15 nm or higher

Probing equilibrium glass flow up to exapoise viscosities

Glasses are out-of-equilibrium systems aging under the crystallization threat. During ordinary glass formation, the atomic diffusion slows down rendering its experimental investigation impractically long, to the extent that a timescale divergence is taken for granted by many. We circumvent here these limitations, taking advantage of a wide family of glasses rapidly obtained by physical vapor deposition directly into the solid state, endowed with different "ages" rivaling those reached by standard cooling and waiting for millennia. Isothermally probing the mechanical response of each of these glasses, we infer a correspondence with viscosity along the equilibrium line, up to exapoise values. We find a dependence of the elastic modulus on the glass age, which, traced back to temperature steepness index of the viscosity, tears down one of the cornerstones of several glass transition theories: the dynamical divergence. Critically, our results suggest that the conventional wisdom picture of a glass ceasing to flow at finite temperature could be wrong.Comment: 4 figures and 1 supplementary figur

Physical consequences of P≠\neqNP and the DMRG-annealing conjecture

Computational complexity theory contains a corpus of theorems and conjectures regarding the time a Turing machine will need to solve certain types of problems as a function of the input size. Nature {\em need not} be a Turing machine and, thus, these theorems do not apply directly to it. But {\em classical simulations} of physical processes are programs running on Turing machines and, as such, are subject to them. In this work, computational complexity theory is applied to classical simulations of systems performing an adiabatic quantum computation (AQC), based on an annealed extension of the density matrix renormalization group (DMRG). We conjecture that the computational time required for those classical simulations is controlled solely by the {\em maximal entanglement} found during the process. Thus, lower bounds on the growth of entanglement with the system size can be provided. In some cases, quantum phase transitions can be predicted to take place in certain inhomogeneous systems. Concretely, physical conclusions are drawn from the assumption that the complexity classes {\bf P} and {\bf NP} differ. As a by-product, an alternative measure of entanglement is proposed which, via Chebyshev's inequality, allows to establish strict bounds on the required computational time.Comment: Accepted for publication in JSTA

Matrix Big Brunch

Following the holographic description of linear dilaton null Cosmologies with a Big Bang in terms of Matrix String Theory put forward by Craps, Sethi and Verlinde, we propose an extended background describing a Universe including both Big Bang and Big Crunch singularities. This belongs to a class of exact string backgrounds and is perturbative in the string coupling far away from the singularities, both of which can be resolved using Matrix String Theory. We provide a simple theory capable of describing the complete evolution of this closed Universe.Comment: 15 pages, no figures. References adde

Ab Initio Treatment of Collective Correlations and the Neutrinoless Double Beta Decay of 48^{48}Ca

Working with Hamiltonians from chiral effective field theory, we develop a novel framework for describing arbitrary deformed medium-mass nuclei by combining the in-medium similarity renormalization group with the generator coordinate method. The approach leverages the ability of the first method to capture dynamic correlations and the second to include collective correlations without violating symmetries. We use our scheme to compute the matrix element that governs the neutrinoless double beta decay of $^{48}$Ca to $^{48}$Ti, and find it to have the value $0.61$, near or below the predictions of most phenomenological methods. The result opens the door to ab initio calculations of the matrix elements for the decay of heavier nuclei such as $^{76}$Ge, $^{130}$Te, and $^{136}$Xe.Comment: 6 pages, 4 figures and 1 table. supplementary material included. version to be publishe