Persistence of fractional Brownian motion with moving boundaries and applications

We consider various problems related to the persistence probability of fractional Brownian motion (FBM), which is the probability that the FBM $X$ stays below a certain level until time $T$. Recently, Oshanin et al. study a physical model where persistence properties of FBM are shown to be related to scaling properties of a quantity $J_N$, called steady-state current. It turns out that for this analysis it is important to determine persistence probabilities of FBM with a moving boundary. We show that one can add a boundary of logarithmic order to a FBM without changing the polynomial rate of decay of the corresponding persistence probability which proves a result needed in Oshanin et al. Moreover, we complement their findings by considering the continuous-time version of $J_N$. Finally, we use the results for moving boundaries in order to improve estimates by Molchan concerning the persistence properties of other quantities of interest, such as the time when a FBM reaches its maximum on the time interval $(0,1)$ or the last zero in the interval $(0,1)$.Comment: 13 page

A note on the regularity of matrices with uniform polynomial entries

In this text we study the regularity of matrices with special polynomial entries. Barring some mild conditions we show that these matrices are regular if a natural limit size is not exceeded. The proof draws connections to generalized Vandermonde matrices and Schur polynomials that are discussed in detail

Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics

Inspired by the success of deep learning techniques in the physical and chemical sciences, we apply a modification of an autoencoder type deep neural network to the task of dimension reduction of molecular dynamics data. We can show that our time-lagged autoencoder reliably finds low-dimensional embeddings for high-dimensional feature spaces which capture the slow dynamics of the underlying stochastic processes - beyond the capabilities of linear dimension reduction techniques

On Gravity, Torsion and the Spectral Action Principle

We consider compact Riemannian spin manifolds without boundary equipped with orthogonal connections. We investigate the induced Dirac operators and the associated commutative spectral triples. In case of dimension four and totally anti-symmetric torsion we compute the Chamseddine-Connes spectral action, deduce the equations of motions and discuss critical points.Comment: minor modifications, some further typos fixe

Chess players' performance beyond 64 squares: A case study on the limitations of cognitive abilities transfer

In a beauty contest experiment with over 6,000 chess players, ranked from amateur to world class, we found that Grandmasters act very similar to other humans. This even holds true when they play exclusively against players of approximately their own strength. In line with psychological research on chess players' thinking, we argue that they are not more rational in a game theoretic sense per se. Their skills are rather specific for their game.chess, beauty contest, cognitive transfer

git2net - Mining Time-Stamped Co-Editing Networks from Large git Repositories

Data from software repositories have become an important foundation for the empirical study of software engineering processes. A recurring theme in the repository mining literature is the inference of developer networks capturing e.g. collaboration, coordination, or communication from the commit history of projects. Most of the studied networks are based on the co-authorship of software artefacts defined at the level of files, modules, or packages. While this approach has led to insights into the social aspects of software development, it neglects detailed information on code changes and code ownership, e.g. which exact lines of code have been authored by which developers, that is contained in the commit log of software projects. Addressing this issue, we introduce git2net, a scalable python software that facilitates the extraction of fine-grained co-editing networks in large git repositories. It uses text mining techniques to analyse the detailed history of textual modifications within files. This information allows us to construct directed, weighted, and time-stamped networks, where a link signifies that one developer has edited a block of source code originally written by another developer. Our tool is applied in case studies of an Open Source and a commercial software project. We argue that it opens up a massive new source of high-resolution data on human collaboration patterns.Comment: MSR 2019, 12 pages, 10 figure