Coframe teleparallel models of gravity. Exact solutions

The superstring and superbrane theories which include gravity as a necessary and fundamental part renew an interest to alternative representations of general relativity as well as the alternative models of gravity. We study the coframe teleparallel theory of gravity with a most general quadratic Lagrangian. The coframe field on a differentiable manifold is a basic dynamical variable. A metric tensor as well as a metric compatible connection is generated by a coframe in a unique manner. The Lagrangian is a general linear combination of Weitzenb\"{o}ck's quadratic invariants with free dimensionless parameters \r_1,\r_2,\r_3. Every independent term of the Lagrangian is a global SO(1,3)-invariant 4-form. For a special choice of parameters which confirms with the local SO(1,3) invariance this theory gives an alternative description of Einsteinian gravity - teleparallel equivalent of GR. We prove that the sign of the scalar curvature of a metric generated by a static spherical-symmetric solution depends only on a relation between the free parameters. The scalar curvature vanishes only for a subclass of models with \r_1=0. This subclass includes the teleparallel equivalent of GR. We obtain the explicit form of all spherically symmetric static solutions of the ``diagonal'' type to the field equations for an arbitrary choice of free parameters. We prove that the unique asymptotic-flat solution with Newtonian limit is the Schwarzschild solution that holds for a subclass of teleparallel models with \r_1=0. Thus the Yang-Mills-type term of the general quadratic coframe Lagrangian should be rejected.Comment: 28 pages, Latex error is fixe

Spreading, Nonergodicity, and Selftrapping: a puzzle of interacting disordered lattice waves

Localization of waves by disorder is a fundamental physical problem encompassing a diverse spectrum of theoretical, experimental and numerical studies in the context of metal-insulator transitions, the quantum Hall effect, light propagation in photonic crystals, and dynamics of ultra-cold atoms in optical arrays, to name just a few examples. Large intensity light can induce nonlinear response, ultracold atomic gases can be tuned into an interacting regime, which leads again to nonlinear wave equations on a mean field level. The interplay between disorder and nonlinearity, their localizing and delocalizing effects is currently an intriguing and challenging issue in the field of lattice waves. In particular it leads to the prediction and observation of two different regimes of destruction of Anderson localization - asymptotic weak chaos, and intermediate strong chaos, separated by a crossover condition on densities. On the other side approximate full quantum interacting many body treatments were recently used to predict and obtain a novel many body localization transition, and two distinct phases - a localization phase, and a delocalization phase, both again separated by some typical density scale. We will discuss selftrapping, nonergodicity and nonGibbsean phases which are typical for such discrete models with particle number conservation and their relation to the above crossover and transition physics. We will also discuss potential connections to quantum many body theories.Comment: 13 pages in Springer International Publishing Switzerland 2016 1 M. Tlidi and M. G. Clerc (eds.), Nonlinear Dynamics: Materials, Theory and Experiment, Springer Proceedings in Physics 173. arXiv admin note: text overlap with arXiv:1405.112

Cross-frequency phase-amplitude coupling in repetitive movements in patients with Parkinson’s disease

Bradykinesia is a cardinal motor symptom in Parkinson's disease (PD), the pathophysiology of which is not fully understood. We analyzed the role of cross-frequency coupling of oscillatory cortical activity in motor impairment in patients with PD and healthy controls. High-density EEG signals were recorded during various motor activities and at rest. Patients performed a repetitive finger-pressing task normally, but were slower than controls during tapping. Phase-amplitude coupling (PAC) between β (13-30 Hz) and broadband γ (50-150 Hz) was computed from individual EEG source signals in the premotor, primary motor, and primary somatosensory cortices, and the primary somatosensory complex. In all four regions, averaging the entire movement period resulted in higher PAC in patients than in controls for the resting condition and the pressing task (similar performance between groups). However, this was not the case for the tapping tasks where patients performed slower. This suggests the strength of state-related β-γ PAC does not determine Parkinsonian bradykinesia. Examination of the dynamics of oscillatory EEG signals during motor transitions revealed a distinctive motif of PAC rise and decay around press onset. This pattern was also present at press offset and slow tapping onset, linking such idiosyncratic PAC changes to transitions between different movement states. The transition-related PAC modulation in patients was similar to controls in the pressing task but flattened during slow tapping, which related to normal and abnormal performance, respectively. These findings suggest that the dysfunctional evolution of neuronal population dynamics during movement execution is an important component of the pathophysiology of Parkinsonian bradykinesia.NEW & NOTEWORTHY Our findings using noninvasive EEG recordings provide evidence that PAC dynamics might play a role in the physiological cortical control of movement execution and may encode transitions between movement states. Results in patients with Parkinson's disease suggest that bradykinesia is related to a deficit of the dynamic regulation of PAC during movement execution rather than its absolute strength. Our findings may contribute to the development of a new concept of the pathophysiology of bradykinesia

Cross-frequency phase-amplitude coupling in repetitive movements in patients with Parkinson’s disease

Bradykinesia is a cardinal motor symptom in Parkinson’s disease whose pathophysiology is incompletely understood. When signals are recorded from the cortex or scalp at rest, affected patients display enhanced phase-amplitude coupling between β (13-30Hz) and broadband γ (50-150Hz) oscillatory activities. However, it remains unclear whether and how abnormal phase-amplitude coupling is involved in slowing Parkinsonian movements during their execution. To address these questions, we analyzed high-density EEG signals recorded simultaneously with various motor activities and at rest in 19 patients with Parkinson’s disease and 20 healthy controls. The motor tasks consisted of repetitive index finger pressing, and slow and fast tapping movements. Individual EEG source signals were computed for the premotor cortex, primary motor cortex, primary somatosensory cortex, and primary somatosensory complex. For the resting condition and the pressing task, phase-amplitude coupling averaged over the 4 motor regions and the entire movement period was larger in patients than in controls. In contrast, in all tapping tasks, state-related phase-amplitude coupling was similar between patients and controls. These findings were not aligned with motor performance and EMG data, which showed abnormalities in patients for tapping but not for pressing, suggesting that the strength of β-broadband γ phase-amplitude coupling during the movement period does not directly relate to Parkinsonian bradykinesia. Subsequently, we examined the dynamics of oscillatory EEG signals during motor transitions. When healthy controls performed the pressing task, dynamic phase-amplitude coupling increased shortly before pressing onset and decreased subsequently. A strikingly similar motif of coupling rise and decay was observed around the offset of pressing and around the onset of slow tapping, suggesting that such transient phase-amplitude coupling changes may be linked to transitions between different movement states – akin to preparatory states in dynamical systems theory of motor control. In patients, the modulation of phase-amplitude coupling was similar in (normally executed) pressing, but flattened in slow (abnormally executed) tapping compared to the controls. These deviations in phase-amplitude coupling around motor action transients may indicate dysfunctional evolution of neuronal population dynamics from the preparatory state to movement generation in Parkinson’s disease. These findings may indicate that cross-frequency coupling is involved in the pathophysiology of bradykinesia in Parkinson’s disease through its abnormal dynamic modulation

Selective Sirt2 inhibition by ligand-induced rearrangement of the active site.

Sirtuins are a highly conserved class of NAD(+)-dependent lysine deacylases. The human isotype Sirt2 has been implicated in the pathogenesis of cancer, inflammation and neurodegeneration, which makes the modulation of Sirt2 activity a promising strategy for pharmaceutical intervention. A rational basis for the development of optimized Sirt2 inhibitors is lacking so far. Here we present high-resolution structures of human Sirt2 in complex with highly selective drug-like inhibitors that show a unique inhibitory mechanism. Potency and the unprecedented Sirt2 selectivity are based on a ligand-induced structural rearrangement of the active site unveiling a yet-unexploited binding pocket. Application of the most potent Sirtuin-rearranging ligand, termed SirReal2, leads to tubulin hyperacetylation in HeLa cells and induces destabilization of the checkpoint protein BubR1, consistent with Sirt2 inhibition in vivo. Our structural insights into this unique mechanism of selective sirtuin inhibition provide the basis for further inhibitor development and selective tools for sirtuin biology

Compaction and dilation rate dependence of stresses in gas-fluidized beds

A particle dynamics-based hybrid model, consisting of monodisperse spherical solid particles and volume-averaged gas hydrodynamics, is used to study traveling planar waves (one-dimensional traveling waves) of voids formed in gas-fluidized beds of narrow cross sectional areas. Through ensemble-averaging in a co-traveling frame, we compute solid phase continuum variables (local volume fraction, average velocity, stress tensor, and granular temperature) across the waves, and examine the relations among them. We probe the consistency between such computationally obtained relations and constitutive models in the kinetic theory for granular materials which are widely used in the two-fluid modeling approach to fluidized beds. We demonstrate that solid phase continuum variables exhibit appreciable ``path dependence'', which is not captured by the commonly used kinetic theory-based models. We show that this path dependence is associated with the large rates of dilation and compaction that occur in the wave. We also examine the relations among solid phase continuum variables in beds of cohesive particles, which yield the same path dependence. Our results both for beds of cohesive and non-cohesive particles suggest that path-dependent constitutive models need to be developed.Comment: accepted for publication in Physics of Fluids (Burnett-order effect analysis added

Axial-Vector Torsion and the Teleparallel Kerr Spacetime

In the context of the teleparallel equivalent of general relativity, we obtain the tetrad and the torsion fields of the stationary axisymmetric Kerr spacetime. It is shown that, in the slow rotation and weak field approximations, the axial-vector torsion plays the role of the gravitomagnetic component of the gravitational field, and is thus the responsible for the Lense-Thirring effect.Comment: 9 pages, no figures, to appear in Class. Quant. Gra