Charge order and Mott insulating ground states in small-angle twisted bilayer graphene

In this work, we determine states of electronic order of small-angle twisted bilayer graphene. Ground states are determined for weak and strong couplings which are representatives for varying distances of the twist-angle from its magic value. In the weak-coupling regime, charge density waves emerge which break translational and $C_{3}$-rotational symmetry. In the strong coupling-regime, we find rotational and translational symmetry breaking Mott insulating states for all commensurate moir\'e band fillings. Depending on the local occupation of superlattice sites hosting up to four electrons, global spin-(ferromagnetic) and valley symmetries are also broken which may give rise to a reduced Landau level degeneracy as observed in experiments for commensurate band fillings. The formation of those particular electron orders is traced back to the important role of characteristic non-local interactions which connect all localized states belonging to one hexagon formed by the AB- and BA-stacked regions of the superlattice

Dynamics and order in graphene-based systems

The dynamics of out-of-time order correlators is studied in strongly correlated electron systems. This certain type of correlation function is a measure for the process of quantum information scrambling which is linked to the fundamental processes of entanglement growth and thermalization in quantum systems. Particularly interesting are quantum chaotic systems where the scrambling rate specifies the exponential growth of out-of-time order correlators. Whereas the scrambling rate is well defined theoretically, its interpretation in a physical context is still under debate. Furthermore, its role for physical effects and quantities which can be measured in experiments is little understood and deserves further investigation. In the first part of this work, scrambling rates are determined analytically and are analyzed for interacting electrons in graphene and electrons in a disordered metal coupled to a dissipative bath of phonons. A resemblance between the scrambling rate and the single-particle scattering rates is observed. In addition, a proposed link between quantum chaotic dynamics of out-of-time order correlators and the dynamics of fluctuations of observables is investigated. This principle could be used to determine scrambling rates in experiments. Subsequently, possible electron orders are investigated in the system of small-angle twisted-bilayer graphene in the second part of this work. Here, the interplay between the moiré interference pattern and the interlayer hybridization due to a finite interlayer tunneling of electrons causes the bandwidth of the so-called moiré bands to depend on the twist-angle. For twist-angles in the vicinity of the magic-angle, interaction effects are strongly enhanced and a series of strong correlation effects is expected. A minimal low-energy model of interacting electrons is derived where relevant electron-electron interaction processes are identified. This model is analyzed with respect to possible electronic ground states as a function of the twist-angle. A tendency towards a formation of nematic states is observed in a weak-coupling regime, whereas various Mott-insulating states are found for strong couplings

Does Laziness Pay Off? - A Lazy-Constraint Approach to Timetabling

Timetabling is a classical and complex task for public transport operators as well as for railway undertakings. The general question is: Which vehicle is taking which route through the transportation network in which order? In this paper, we consider the special setting to find optimal timetables for railway systems under a moving block regime. We directly set up on our work of [T. Schlechte et al., 2022], i.e., we consider the same model formulation and real-world instances of a moving block headway system. In this paper, we present a repair heuristic and a lazy-constraint approach utilizing the callback features of Gurobi, see [Gurobi Optimization, 2022]. We provide an experimental study of the different algorithmic approaches for a railway network with 100 and up to 300 train requests. The computational results show that the lazy-constraint approach together with the repair heuristic significantly improves our previous approaches

Metabolic, mental and immunological effects of normoxic and hypoxic training in multiple sclerosis patients: a pilot study

Background: Physical activity might attenuate inflammation and neurodegeneration in multiple sclerosis (MS). Erythropoietin, which is produced upon exposure to hypoxia, is thought to act as a neuroprotective agent in MS. Therefore, we studied the effects of intermittent hypoxic training on activity energy expenditure, maximal workload, serum erythropoietin, and immunophenotype focusing on regulatory and IL-17A-producing T cells. Methods: We assigned 34 relapsing-remitting MS patients within a randomized, single blind, parallel-group study to either normoxic (NO) or hypoxic (HO) treadmill training, both 3 times/week for 1 h over 4 weeks (Clinicaltrials.gov identifier: NCT02509897). Before and after training, activity energy expenditure (metabolic chamber), maximal workload (incremental treadmill test), walking ability, depressive symptoms (Beck Depression Inventory I), serum erythropoietin concentrations, and immunophenotype of peripheral blood mononuclear cells (PBMCs) were assessed. Results: Energy expenditure did not change due to training in both groups, but was rather fueled by fat than by carbohydrate oxidation after HO training (P = 0.002). Maximal workload increased by 40 Watt and 42 Watt in the NO and HO group, respectively (both P < 0.0001). Distance patients walked in 6 min increased by 25 m and 27 m in the NO and HO group, respectively (NO P = 0.02; HO P = 0.01). Beck Depression Inventory score markedly decreased in both groups (NO P = 0.03; HO P = 0.0003). NO training shifted Treg subpopulations by increasing and decreasing the frequency of CD39(+) and CD31(+) Tregs, respectively, and decreased IL-17A-producing CD4(+) cells. HO training provoked none of these immunological changes. Erythropoietin concentrations were within normal range and did not significantly change in either group. Conclusion: 4 weeks of moderate treadmill training had considerable effects on fitness level and mood in MS patients, both under normoxic and hypoxic conditions. Additionally, NO training improved Th17/Treg profile and HO training improved fatty acid oxidation during exercise. These effects could not be attributed to an increase of erythropoietin

Peroxisomal β-oxidation acts as a sensor for intracellular fatty acids and regulates lipolysis

To liberate fatty acids (FAs) from intracellular stores, lipolysis is regulated by the activity of the lipases adipose triglyceride lipase (ATGL), hormone-sensitive lipase and monoacylglycerol lipase. Excessive FA release as a result of uncontrolled lipolysis results in lipotoxicity, which can in turn promote the progression of metabolic disorders. However, whether cells can directly sense FAs to maintain cellular lipid homeostasis is unknown. Here we report a sensing mechanism for cellular FAs based on peroxisomal degradation of FAs and coupled with reactive oxygen species (ROS) production, which in turn regulates FA release by modulating lipolysis. Changes in ROS levels are sensed by PEX2, which modulates ATGL levels through post-translational ubiquitination. We demonstrate the importance of this pathway for non-alcoholic fatty liver disease progression using genetic and pharmacological approaches to alter ROS levels in vivo, which can be utilized to increase hepatic ATGL levels and ameliorate hepatic steatosis. The discovery of this peroxisomal β-oxidation-mediated feedback mechanism, which is conserved in multiple organs, couples the functions of peroxisomes and lipid droplets and might serve as a new way to manipulate lipolysis to treat metabolic disorders

Metabolic reconstitution of germ-free mice by a gnotobiotic microbiota varies over the circadian cycle.

The capacity of the intestinal microbiota to degrade otherwise indigestible diet components is known to greatly improve the recovery of energy from food. This has led to the hypothesis that increased digestive efficiency may underlie the contribution of the microbiota to obesity. OligoMM12-colonized gnotobiotic mice have a consistently higher fat mass than germ-free (GF) or fully colonized counterparts. We therefore investigated their food intake, digestion efficiency, energy expenditure, and respiratory quotient using a novel isolator-housed metabolic cage system, which allows long-term measurements without contamination risk. This demonstrated that microbiota-released calories are perfectly balanced by decreased food intake in fully colonized versus gnotobiotic OligoMM12 and GF mice fed a standard chow diet, i.e., microbiota-released calories can in fact be well integrated into appetite control. We also observed no significant difference in energy expenditure after normalization by lean mass between the different microbiota groups, suggesting that cumulative small differences in energy balance, or altered energy storage, must underlie fat accumulation in OligoMM12 mice. Consistent with altered energy storage, major differences were observed in the type of respiratory substrates used in metabolism over the circadian cycle: In GF mice, the respiratory exchange ratio (RER) was consistently lower than that of fully colonized mice at all times of day, indicative of more reliance on fat and less on glucose metabolism. Intriguingly, the RER of OligoMM12-colonized gnotobiotic mice phenocopied fully colonized mice during the dark (active/eating) phase but phenocopied GF mice during the light (fasting/resting) phase. Further, OligoMM12-colonized mice showed a GF-like drop in liver glycogen storage during the light phase and both liver and plasma metabolomes of OligoMM12 mice clustered closely with GF mice. This implies the existence of microbiota functions that are required to maintain normal host metabolism during the resting/fasting phase of circadian cycle and which are absent in the OligoMM12 consortium