Estimation of time delay by coherence analysis

Using coherence analysis (which is an extensively used method to study the correlations in frequency domain, between two simultaneously measured signals) we estimate the time delay between two signals. This method is suitable for time delay estimation of narrow band coherence signals for which the conventional methods cannot be reliably applied. We show by analysing coupled R\"ossler attractors with a known delay, that the method yields satisfactory results. Then, we apply this method to human pathologic tremor. The delay between simultaneously measured traces of Electroencephalogram (EEG) and Electromyogram (EMG) data of subjects with essential hand tremor is calculated. We find that there is a delay of 11-27 milli-seconds ($ms$) between the tremor correlated parts (cortex) of the brain (EEG) and the trembling hand (EMG) which is in agreement with the experimentally observed delay value of 15 $ms$ for the cortico-muscular conduction time. By surrogate analysis we calculate error-bars of the estimated delay.Comment: 21 pages, 8 figures, elstart.cls file included. Accepted for publication in Physica

Energy efficient engine: Low-pressure turbine subsonic cascade component development and integration program

A subsonic cascade test program was conducted to provide technical data for optimizing the blade and vane airfoil designs for the Energy Efficient Engine Low-Pressure Turbine component. The program consisted of three parts. The first involved an evaluation of the low-chamber inlet guide vane. The second, was an evaluation of two candidate aerodynamic loading philosophies for the fourth blade root section. The third part consisted of an evaluation of three candidate airfoil geometries for the fourth blade mean section. The performance of each candidate airfoil was evaluated in a linear cascade configuration. The overall results of this study indicate that the aft-loaded airfoil designs resulted in lower losses which substantiated Pratt & Whitney Aircraft's design philosophy for the Energy Efficient Engine low-pressure turbine component

Cortical involvement in the generation of essential tremor

Conflicting results on the existence of tremor-related cortical activity in essential tremor (ET) have raised questions on the role of the cortex in tremor generation. Here we attempt to address these issues. We recorded 64 channel surface EEGs and EMGs from forearm muscles in 15 patients with definite ET. EEG and EMG power spectra, relative power of the rhythmic EMG activity, relative EEG power at the tremor frequency, and EEG–EMG and EEG–EEG coherence were calculated and their dynamics over time explored. Corticomuscular delay was studied using a new method for narrow-band coherent signals. Corticomuscular coherence in the contralateral central region at the tremor frequency was present in all patients in recordings with a relative tremor EMG power exceeding a certain level. However, the coherence was lost intermittently even with tremors far above this level. Physiological 15- to 30-Hz coherence was found consistently in 11 patients with significantly weaker EMG activity in this frequency range. A more frontal (mesial) hot spot was also intermittently coupled with the tremor and the central hot spot in five patients. Corticomuscular delays were compatible with transmission in fast corticospinal pathways and feedback of the tremor signal. Thus the tremor rhythm is intermittently relayed only in different cortical motor areas. We hypothesize that tremor oscillations build up in different subcortical and subcortico-cortical circuits only temporarily entraining each other

Cortical correlates of the basic and first harmonic frequency of Parkinsonian tremor

Objective It has been hypothesized that the basic and first harmonic frequency of Parkinsonian tremor are somewhat independent oscillations the biological basis of which remains unclear. Methods We recorded 64-channel EEG in parallel with EMG of the forearm muscles most affected by rest tremor in 21 PD patients. EMG power spectrum, corticomuscular coherence spectra and EEG power spectra for each EEG electrode were calculated. The dynamics of the coherence and relative EMG and EEG power at the basic (tremor) frequency were calculated by a sliding, overlapping window analysis. Corticomuscular delays and direction of interaction were analysed by the maximizing coherence method for narrow band signals. Results The contralateral EEG electrodes with maximal coherence were different for the basic and first harmonic frequency. The dynamical coherence curves showed non-parallel time courses for the two frequencies. The mean EEG-EMG and EMG-EEG delays were all around 15–20 ms but significantly longer for the first harmonic than for the basic frequency. Conclusions Our data indicate different cortical representations and corticomuscular interaction of the basic and first harmonic frequencies of Parkinsonian tremor. Significance Separate central generators seem to contribute to the tremor via different pathways. Further studies on this complex tremor network are warranted

Predictive Screening of M1 and M2 Macrophages Reveals the Immunomodulatory Effectiveness of Post Spinal Cord Injury Azithromycin Treatment

Spinal cord injury (SCI) triggers a heterogeneous macrophage response that when experimentally polarized toward alternative forms of activation (M2 macrophages) promotes tissue and functional recovery. There are limited pharmacological therapies that can drive this reparative inflammatory state. In the current study, we used in vitrosystems to comprehensively defined markers of macrophages with known pathological (M1) and reparative (M2) properties in SCI. We then used these markers to objectively define the macrophage activation states after SCI in response to delayed azithromycin treatment. Mice were subjected to moderate-severe thoracic contusion SCI. Azithromycin or vehicle was administered beginning 30 minutes post-SCI and then daily for 3 or 7 days post injury (dpi). We detected a dose-dependent polarization toward purportedly protective M2 macrophages with daily AZM treatment. Specifically, AZM doses of 10, 40, or 160 mg/kg decreased M1 macrophage gene expression at 3 dpi while the lowest (10 mg/kg) and highest (160 mg/kg) doses increased M2 macrophage gene expression at 7 dpi. Azithromycin has documented immunomodulatory properties and is commonly prescribed to treat infections in SCI individuals. This work demonstrates the utility of objective, comprehensive macrophage gene profiling for evaluating immunomodulatory SCI therapies and highlights azithromycin as a promising agent for SCI treatment

Azithromycin Drives Alternative Macrophage Activation and Improves Recovery and Tissue Sparing in Contusion Spinal Cord Injury

BACKGROUND: Macrophages persist indefinitely at sites of spinal cord injury (SCI) and contribute to both pathological and reparative processes. While the alternative, anti-inflammatory (M2) phenotype is believed to promote cell protection, regeneration, and plasticity, pro-inflammatory (M1) macrophages persist after SCI and contribute to protracted cell and tissue loss. Thus, identifying non-invasive, clinically viable, pharmacological therapies for altering macrophage phenotype is a challenging, yet promising, approach for treating SCI. Azithromycin (AZM), a commonly used macrolide antibiotic, drives anti-inflammatory macrophage activation in rodent models of inflammation and in humans with cystic fibrosis. METHODS: We hypothesized that AZM treatment can alter the macrophage response to SCI and reduce progressive tissue pathology. To test this hypothesis, mice (C57BL/6J, 3-month-old) received daily doses of AZM (160 mg/kg) or vehicle treatment via oral gavage for 3 days prior and up to 7 days after a moderate-severe thoracic contusion SCI (75-kdyn force injury). Fluorescent-activated cell sorting was used in combination with real-time PCR (rtPCR) to evaluate the disposition and activation status of microglia, monocytes, and neutrophils, as well as macrophage phenotype in response to AZM treatment. An open-field locomotor rating scale (Basso Mouse Scale) and gridwalk task were used to determine the effects of AZM treatment on SCI recovery. Bone marrow-derived macrophages (BMDMs) were used to determine the effect of AZM treatment on macrophage phenotype in vitro. RESULTS: In accordance with our hypothesis, SCI mice exhibited significantly increased anti-inflammatory and decreased pro-inflammatory macrophage activation in response to AZM treatment. In addition, AZM treatment led to improved tissue sparing and recovery of gross and coordinated locomotor function. Furthermore, AZM treatment altered macrophage phenotype in vitro and lowered the neurotoxic potential of pro-inflammatory, M1 macrophages. CONCLUSIONS: Taken together, these data suggest that pharmacologically intervening with AZM can alter SCI macrophage polarization toward a beneficial phenotype that, in turn, may potentially limit secondary injury processes. Given that pro-inflammatory macrophage activation is a hallmark of many neurological pathologies and that AZM is non-invasive and clinically viable, these data highlight a novel approach for treating SCI and other maladaptive neuroinflammatory conditions

Gap generation in the BCS model with finite range temporal interaction

In the [BCS] paper the theory of superconductivity was developed for the BCS model, in which the (instantaneous) interaction is only between fermions of opposite momentum and spin. Such model was analyzed by variational methods, finding that a superconducting behavior is energetically favorable. Subsequently it was claimed that in the thermodynamic limit the BCS model is equivalent to the (exactly solvable) quadratic mean field BCS model; a rigorous proof of this claim is however still lacking. In this paper we consider the BCS model with a finite range temporal interaction, and we prove rigorously its equivalence with the mean field BCS model in the thermodinamic limit if the range is long enough, by a (uniformly convergent) perturbation expansion about mean field theory.Comment: 14 page

Constructive Field Theory and Applications: Perspectives and Open Problems

In this paper we review many interesting open problems in mathematical physics which may be attacked with the help of tools from constructive field theory. They could give work for future mathematical physicists trained with the constructive methods well within the 21st century