StaRMAP - A second order staggered grid method for spherical harmonics moment equations of radiative transfer

We present a simple method to solve spherical harmonics moment systems, such as the the time-dependent $P_N$ and $SP_N$ equations, of radiative transfer. The method, which works for arbitrary moment order $N$, makes use of the specific coupling between the moments in the $P_N$ equations. This coupling naturally induces staggered grids in space and time, which in turn give rise to a canonical, second-order accurate finite difference scheme. While the scheme does not possess TVD or realizability limiters, its simplicity allows for a very efficient implementation in Matlab. We present several test cases, some of which demonstrate that the code solves problems with ten million degrees of freedom in space, angle, and time within a few seconds. The code for the numerical scheme, called StaRMAP (Staggered grid Radiation Moment Approximation), along with files for all presented test cases, can be downloaded so that all results can be reproduced by the reader.Comment: 28 pages, 7 figures; StaRMAP code available at http://www.math.temple.edu/~seibold/research/starma

Towards reconstructing the quantum effective action of gravity

Starting from a parameterisation of the quantum effective action for gravity we calculate correlation functions for observable quantities. The resulting templates allow to reverse-engineer the couplings describing the effective dynamics from the correlation functions. Applying this new formalism to the autocorrelation function of spatial volume fluctuations measured within the Causal Dynamical Triangulations program suggests that the corresponding quantum effective action consists of the Einstein-Hilbert action supplemented by a non-local interaction term. We expect that our matching-template formalism can be adapted to a wide range of quantum gravity programs allowing to bridge the gap between the fundamental formulation and observable low-energy physics.Comment: 6 pages, 1 figure; v2: reference update+clarification; v3: matches published versio

Efficient Bayesian estimation of Markov model transition matrices with given stationary distribution

Direct simulation of biomolecular dynamics in thermal equilibrium is challenging due to the metastable nature of conformation dynamics and the computational cost of molecular dynamics. Biased or enhanced sampling methods may improve the convergence of expectation values of equilibrium probabilities and expectation values of stationary quantities significantly. Unfortunately the convergence of dynamic observables such as correlation functions or timescales of conformational transitions relies on direct equilibrium simulations. Markov state models are well suited to describe both, stationary properties and properties of slow dynamical processes of a molecular system, in terms of a transition matrix for a jump process on a suitable discretiza- tion of continuous conformation space. Here, we introduce statistical estimation methods that allow a priori knowledge of equilibrium probabilities to be incorporated into the estimation of dynamical observables. Both, maximum likelihood methods and an improved Monte Carlo sampling method for reversible transition ma- trices with fixed stationary distribution are given. The sampling approach is applied to a toy example as well as to simulations of the MR121-GSGS-W peptide, and is demonstrated to converge much more rapidly than a previous approach in [F. Noe, J. Chem. Phys. 128, 244103 (2008)]Comment: 15 pages, 8 figure

On The Dimension of The Virtually Cyclic Classifying Space of a Crystallographic Group

In this paper we construct a model for the classifying space, BVCG, of a crystallographic group G of rank n relative to the family VC of virtually-cyclic subgroups of G. The model is used to show that there exists no other model for the virtually-cyclic classifying space of G with dimension less than vcd(G)+1, where vcd(G) denotes the virtual cohomological dimension of G. In addition, the dimension of our construction realizes this limit.Comment: 10 page

Resolving Spacetime Singularities within Asymptotic Safety

A key incentive of quantum gravity is the removal of spacetime singularities plaguing the classical theory. We compute the non-perturbative momentum-dependence of a specific structure function within the gravitational asymptotic safety program which encodes the quantum corrections to the graviton propagator for momenta above the Planck scale. The resulting quantum corrected Newtonian potential approaches a constant negative value as the distance between the two point masses goes to zero, thereby removing the classical singularity. The generic nature of the underlying mechanism suggests that it will remain operative in the context of black hole and cosmic singularities.Comment: v2: some improvements and clarifications; version accepted for publication in PR

Differentiating U(1)′U(1)^\prime supersymmetric models with right sneutrino and neutralino dark matter

We perform a detailed analysis of dark matter signals of supersymmetric models containing an extra $U(1)^\prime$ gauge group. We investigate scenarios in which either the right sneutrino or the lightest neutralino are phenomenologically acceptable dark matter candidates and we explore the parameter spaces of different supersymmetric realisations featuring an extra $U(1)^\prime$. We impose consistency with low energy observables, with known mass limits for the superpartners and $Z^\prime$ bosons, as well as with Higgs boson signal strengths, and we moreover verify that predictions for the anomalous magnetic moment of the muon agree with the experimental value and require that the dark matter candidate satisfies the observed relic density and direct and indirect dark matter detection constraints. For the case where the sneutrino is the dark matter candidate, we find distinguishing characteristics among different $U(1)^\prime$ mixing angles. If the neutralino is the lightest supersymmetric particle, its mass is heavier than that of the light sneutrino in scenarios where the latter is a dark matter candidate, the parameter space is less restricted and differentiation between models is more difficult. We finally comment on the possible collider tests of these models.Comment: 21 pages, 11 figures, version accepted by PR

Real-Time Recommendation of Streamed Data

This tutorial addressed two trending topics in the field of recommender systems research, namely A/B testing and real-time recommendations of streamed data. Focusing on the news domain, participants learned how to benchmark the performance of stream-based recommendation algorithms in a live recommender system and in a simulated environment

The Gravitational Two-Loop Counterterm is Asymptotically Safe

Weinberg's asymptotic safety scenario provides an elegant mechanism to construct a quantum theory of gravity within the framework of quantum field theory based on a non-Gau{\ss}ian fixed point of the renormalization group flow. In this work we report novel evidence for the validity of this scenario, using functional renormalization group techniques to determine the renormalization group flow of the Einstein-Hilbert action supplemented by the two-loop counterterm found by Goroff and Sagnotti. The resulting system of beta functions comprises three scale-dependent coupling constants and exhibits a non-Gau{\ss}ian fixed point which constitutes the natural extension of the one found at the level of the Einstein-Hilbert action. The fixed point exhibits two ultraviolet attractive and one repulsive direction supporting a low-dimensional UV-critical hypersurface. Our result vanquishes the longstanding criticism that asymptotic safety will not survive once a "proper perturbative counterterm" is included in the projection space.Comment: 7 pages, 1 figur