University of Luxembourg

About: University of Luxembourg is a education organization based out in Luxembourg, Luxembourg. It is known for research contribution in the topics: Context (language use) & Computer science. The organization has 4744 authors who have published 22175 publications receiving 381824 citations.

Non-Abelian parafermions in time-reversal invariant interacting helical systems

Abstract: The interplay between bulk spin-orbit coupling and electron-electron interactions produces umklapp scattering in the helical edge states of a two-dimensional topological insulator. If the chemical potential is at the Dirac point, umklapp scattering can open a gap in the edge state spectrum even if the system is time-reversal invariant. We determine the zero-energy bound states at the interfaces between a section of a helical liquid which is gapped out by the superconducting proximity effect and a section gapped out by umklapp scattering. We show that these interfaces pin charges which are multiples of $e/2$, giving rise to a Josephson current with $8\ensuremath{\pi}$ periodicity. Moreover, the bound states, which are protected by time-reversal symmetry, are fourfold degenerate and can be described as ${\mathbb{Z}}_{4}$ parafermions. We determine their braiding statistics and show how braiding can be implemented in topological insulator systems.

Transcriptional and metabolic adaptation of human neurons to the mitochondrial toxicant MPP(

Abstract: Assessment of the network of toxicity pathways by Omics technologies and bioinformatic data processing paves the road toward a new toxicology for the twenty-first century. Especially, the upstream network of responses, taking place in toxicant-treated cells before a point of no return is reached, is still little explored. We studied the effects of the model neurotoxicant 1-methyl-4-phenylpyridinium (MPP+) by a combined metabolomics (mass spectrometry) and transcriptomics (microarrays and deep sequencing) approach to provide unbiased data on earliest cellular adaptations to stress. Neural precursor cells (LUHMES) were differentiated to homogeneous cultures of fully postmitotic human dopaminergic neurons, and then exposed to the mitochondrial respiratory chain inhibitor MPP+ (5 μM). At 18–24 h after treatment, intracellular ATP and mitochondrial integrity were still close to control levels, but pronounced transcriptome and metabolome changes were seen. Data on altered glucose flux, depletion of phosphocreatine and oxidative stress (e.g., methionine sulfoxide formation) confirmed the validity of the approach. New findings were related to nuclear paraspeckle depletion, as well as an early activation of branches of the transsulfuration pathway to increase glutathione. Bioinformatic analysis of our data identified the transcription factor ATF-4 as an upstream regulator of early responses. Findings on this signaling pathway and on adaptive increases of glutathione production were confirmed biochemically. Metabolic and transcriptional profiling contributed complementary information on multiple primary and secondary changes that contribute to the cellular response to MPP+. Thus, combined ‘Omics’ analysis is a new unbiased approach to unravel earliest metabolic changes, whose balance decides on the final cell fate.

Many-Body Descriptors for Predicting Molecular Properties with Machine Learning: Analysis of Pairwise and Three-Body Interactions in Molecules

Abstract: Machine learning (ML) based prediction of molecular properties across chemical compound space is an important and alternative approach to efficiently estimate the solutions of highly complex many-electron problems in chemistry and physics. Statistical methods represent molecules as descriptors that should encode molecular symmetries and interactions between atoms. Many such descriptors have been proposed; all of them have advantages and limitations. Here, we propose a set of general two-body and three-body interaction descriptors which are invariant to translation, rotation, and atomic indexing. By adapting the successfully used kernel ridge regression methods of machine learning, we evaluate our descriptors on predicting several properties of small organic molecules calculated using density-functional theory. We use two data sets. The GDB-7 set contains 6868 molecules with up to 7 heavy atoms of type CNO. The GDB-9 set is composed of 131722 molecules with up to 9 heavy atoms containing CNO. When trained ...

Stochastic thermodynamics in the strong coupling regime: An unambiguous approach based on coarse graining

Abstract: We consider a classical and possibly driven composite system $X\ensuremath{\bigotimes}Y$ weakly coupled to a Markovian thermal reservoir $R$ so that an unambiguous stochastic thermodynamics ensues for $X\ensuremath{\bigotimes}Y$. This setup can be equivalently seen as a system $X$ strongly coupled to a non-Markovian reservoir $Y\ensuremath{\bigotimes}R$. We demonstrate that only in the limit where the dynamics of $Y$ is much faster than $X$, our unambiguous expressions for thermodynamic quantities, such as heat, entropy, or internal energy, are equivalent to the strong coupling expressions recently obtained in the literature using the Hamiltonian of mean force. By doing so, we also significantly extend these results by formulating them at the level of instantaneous rates and by allowing for time-dependent couplings between $X$ and its environment. Away from the limit where $Y$ evolves much faster than $X$, previous approaches fail to reproduce the correct results from the original unambiguous formulation, as we illustrate numerically for an underdamped Brownian particle coupled strongly to a non-Markovian reservoir.

Wigner chaos and the fourth moment

Abstract: We prove that a normalized sequence of multiple Wigner integrals (in a fixed order of free Wigner chaos) converges in law to the standard semicircular distribution if and only if the corresponding sequence of fourth moments converges to 2, the fourth moment of the semicircular law. This extends to the free probabilistic, setting some recent results by Nualart and Peccati on characterizations of central limit theorems in a fixed order of Gaussian Wiener chaos. Our proof is combinatorial, analyzing the relevant noncrossing partitions that control the moments of the integrals. We can also use these techniques to distinguish the first order of chaos from all others in terms of distributions; we then use tools from the free Malliavin calculus to give quantitative bounds on a distance between different orders of chaos. When applied to highly symmetric kernels, our results yield a new transfer principle, connecting central limit theorems in free Wigner chaos to those in Gaussian Wiener chaos. We use this to prove a new free version of an important classical theorem, the Breuer–Major theorem.