TRENTOOL : an open source toolbox to estimate neural directed interactions with transfer entropy

To investigate directed interactions in neural networks we often use Norbert Wiener's famous definition of observational causality. Wiener’s definition states that an improvement of the prediction of the future of a time series X from its own past by the incorporation of information from the past of a second time series Y is seen as an indication of a causal interaction from Y to X. Early implementations of Wiener's principle – such as Granger causality – modelled interacting systems by linear autoregressive processes and the interactions themselves were also assumed to be linear. However, in complex systems – such as the brain – nonlinear behaviour of its parts and nonlinear interactions between them have to be expected. In fact nonlinear power-to-power or phase-to-power interactions between frequencies are reported frequently. To cover all types of non-linear interactions in the brain, and thereby to fully chart the neural networks of interest, it is useful to implement Wiener's principle in a way that is free of a model of the interaction [1]. Indeed, it is possible to reformulate Wiener's principle based on information theoretic quantities to obtain the desired model-freeness. The resulting measure was originally formulated by Schreiber [2] and termed transfer entropy (TE). Shortly after its publication transfer entropy found applications to neurophysiological data. With the introduction of new, data efficient estimators (e.g. [3]) TE has experienced a rapid surge of interest (e.g. [4]). Applications of TE in neuroscience range from recordings in cultured neuronal populations to functional magnetic resonanace imaging (fMRI) signals. Despite widespread interest in TE, no publicly available toolbox exists that guides the user through the difficulties of this powerful technique. TRENTOOL (the TRansfer ENtropy TOOLbox) fills this gap for the neurosciences by bundling data efficient estimation algorithms with the necessary parameter estimation routines and nonparametric statistical testing procedures for comparison to surrogate data or between experimental conditions. TRENTOOL is an open source MATLAB toolbox based on the Fieldtrip data format. ..

Consistency test of neutrinoless double beta decay with one isotope

We discuss a consistency test which makes it possible to discriminate unknown nuclear background lines from neutrinoless double beta decay with only one isotope. By considering both the transition to the ground state and to the first excited $0^+$ state, a sufficiently large detector can reveal if neutrinoless double beta decay or some other nuclear physics process is at work. Such a detector could therefore simultaneously provide a consistency test for a certain range of Majorana masses and be sensitive to lower values of the effective Majorana mass.Comment: 1+12 pages, 4 figures; v2: discussion enhanced, figures improved, matches journal versio

Left-Right Symmetric Theory with Light Sterile Neutrinos

A simple theoretical framework for the spontaneous breaking of parity, baryon and lepton numbers is proposed. In this context, the baryon and lepton numbers are independent local gauge symmetries, while parity is defined making use of the left-right symmetry. We show that in the minimal model the new leptoquark fields needed to define an anomaly-free theory also generate neutrino masses through the type III seesaw mechanism. The spectrum of neutrinos and some phenomenological aspects are discussed. This theory predicts the possible existence of two light sterile neutrinos.Comment: minor corrections, published in Physical Review D as a Rapid Communicatio

Running Neutrino Mass Parameters in See-Saw Scenarios

We systematically analyze quantum corrections in see-saw scenarios, including effects from above the see-saw scales. We derive approximate renormalization group equations for neutrino masses, lepton mixings and CP phases, yielding an analytic understanding and a simple estimate of the size of the effects. Even for hierarchical masses, they often exceed the precision of future experiments. Furthermore, we provide a software package allowing for a convenient numerical renormalization group analysis, with heavy singlets being integrated out successively at their mass thresholds. We also discuss applications to model building and related topics.Comment: 49 pages, 9 figures; minor corrections in Sec. 6.5.1; the accompanying software packages REAP/MPT can be downloaded from http://www.ph.tum.de/~rg

The LMA Solution from Bimaximal Lepton Mixing at the GUT Scale by Renormalization Group Running

We show that in see-saw models with bimaximal lepton mixing at the GUT scale and with zero CP phases, the solar mixing angle theta_{12} generically evolves towards sizably smaller values due to Renormalization Group effects, whereas the evolution of theta_{13} and theta_{23} is comparatively small. The currently favored LMA solution of the solar neutrino problem can thus be obtained in a natural way from bimaximal mixing at the GUT scale. We present numerical examples for the evolution of the leptonic mixing angles in the Standard Model and the MSSM, in which the current best-fit values of the LMA mixing angles are produced. These include a case where the mass eigenstates corresponding to the solar mass squared difference have opposite CP parity.Comment: 14 pages, 10 figures; references and a subsection containing an example with odd CP parities added; results and conclusions unchange