Asymmetric wave transmission through one dimensional lattices with cubic-quintic nonlinearity

One dimensional lattice with an on-site cubic-quintic nonlinear response described by a cubic-quintic discrete nonlinear Schr\"odinger equation is tested for asymmetric wave propagation. The lattice is connected to linear side chains. Asymmetry is introduced by breaking the mirror symmetry of the lattice with respect to the center of the nonlinear region. Three cases corresponding to dimer, trimer and quadrimer are discussed with focus on the corresponding diode-like effect. Transmission coefficients are analytically calculated for left and right moving waves via backward transfer map. The different transmission coefficients for the left and right moving waves impinging the lattice give rise to a diode-like effect which is tested for different variations in asymmetry and site dependent coefficients. We show that there is a higher transmission for incoming waves with lower wavenumbers as compared to the waves with comparatively larger wavenumbers and a diode-like effect improves by increasing the nonlinear layers. We also show that in the context of transport through such lattices, the cooperation between cubic and quintic nonlinear response is not "additive". Finally, we numerically analyse Gaussian wave packet dynamics impinging on the CQDNLS lattice for all three cases.Comment: 10 pages, 17 figure

Two particle entanglement and its geometric duals

We show that for a system of two entangled particles, there is a dual description to the particle equations in terms of classical theory of conformally stretched spacetime. We also connect these entangled particle equations with Finsler geometry. We show that this duality translates strongly coupled quantum equations in the pilot-wave limit to weakly coupled geometric equations.Comment: 10pp, Typos corrected, Accepted versio

Vagal nerve stimulation; current and future Interventions

Vagus Nerve is the 10th and the largest cranial nerve of the parasympathetic system, consist of approximately 20% efferent and 80% afferent. It is a big nerve, providing autonomous, cardiovascular, respiratory, gastrointestinal, immune and endocrine systems

NEUROLOGICAL INVOLVEMENT IN COVID-19 INFECTIONS; PATHOPHYSIOLOGY, PRESENTATION AND OUTCOME.

Severe acute respiratory syndrome corona virus 2 (SARS CoV 2) seems to display an increasing affinity for the nervous system. The ongoing pandemic has made evident that diverse neurological manifestations may occur with COVID 19. Headache and dizziness remain the most common symptoms however stroke, seizures, encephalopathy, neuropathy and skeletal muscle injury may be seen. An increasing number of patients report initial anosmia and ageusia. Tendency for serious illness is believed to be in the elderly or people with a history of diabetes, high blood pressure and heart disease. Many patients on immunosuppressive therapies such as multiple sclerosis, myasthenia gravis or sarcoidosis are additionally high risk. Angiotensin-converting enzyme 2 (ACE 2) has been identified as the cellular receptor for SARS CoV 2 present in both neurons and glial tissue. The pathophysiology of neurotoxicity at best remains elusive with dysregulation of homeostasis and pro inflammatory cytokine production causing direct, indirect and post infectious neurological complications. Vigilant observation for neurological involvement is important not only to prevent spread of this highly contagious disease but also for appropriate, timely management. A directed neurological examination limiting exposure of medical personnel to potentially infected patients is mandatory. Appropriate constrained investigations should be considered only if there is a likelihood of changing management. Tele neurology consultations, whenever possible is the need of the hour. Outcomes of COVID 19 patients with severe illness and neurological complications remains grave. Pharmaceutical research needs to change directions to expedite the development of a possible vaccine and also accelerate in the quest for newer antiviral agents

A descriptive study to find possible correlation between MRI findings of pituitary gland and serum prolactin level

Objective: To explore equation, if any, between findings of magnetic resonance imaging of pituitary gland and serum prolactin level. Methods: The retrospective, descriptive study was conducted at the Department of Radiology, Aga Khan University Hospital, Karachi, and related to patients\\u27 records from April 19, 2006 to April 23, 2009. Seventy patients underwent magnetic resonance imaging of brain for pituitary gland. Inclusion criteria were all patients referred with relevant clinical symptoms or deranged serum prolactin level. Patients who were claustrophobic or had a pacemaker, aneurysm clip, metallic foreign body in the orbit or with no laboratory investigation were excluded from the study. SPSS 19 was used for statistical analysis. Results: Of the 70 patients, normal imaging was noted in 29 (41.4 %) patients. Out of these, 18 (62.06%) patients had normal and 11 (37.93%) had raised serum prolactin levels. Microadenoma was found in 23 (32.8%) patients. Out of these, 10 (42.47%) had normal and 13 (56.52%) had raised prolactin levels. Macroadenoma was found in 16 (22.8 %). Out of these, 8 (50%) had normal and 8 (50%) had raised prolactin levels. Pituitary cyst was located in 2 (2.8 %) patients. Out of these, 1 (50%) had normal and 1 (50%) had raised serum prolactin levels. Conclusion: Magnetic resonance imaging of pituitary gland was not associated with serum prolactin levels in patients with clinical suspicion of pituitary abnormality. Therefore, regular monitoring of serum prolactin is suggested

Role of ADC values and ratios of MRI scan in differentiating typical from atypical/anaplastic meningiomas

Atypical/anaplastic meningiomas are prone to aggressive behaviour which affects treatment planning and prognostication. Our aim was to assess the role of Apparent Diffusion Coefficient (ADC) values of MRI brain in differentiating typical from atypical/anaplastic meningioma. We reviewed 84 typical and 37 atypical/anaplastic meningiomas and compared mean ADC values and ADC ratios of their preoperative MRI brain. At 3 Tesla, mean ADC value for typical meningioma was1.03±0.10x10-3 and 0.63±0.05x10-3 for atypical/anaplastic meningioma. At 1.5 Tesla, mean ADC value for typical meningioma was 1.05±0.11x10-3 and atypical/ anaplastic meningioma was 0.70 ± 0.04x10-3. The mean ADC ratios were 1.08 ± 0.17 and 0.85 ± 0.15 for typical and atypical/anaplastic meningomas respectively. Mean ADC ratios and the mean ADC values of typical and atypical/anaplastic meningiomas were significantly different (p\u3c 0.001). ADC values and ADC ratios have important role in differentiating typical from atypical/anaplastic meningioma and it must be part of the routine preoperative MRI reportin