Existence of superposition solutions for pulse propagation in nonlinear resonant media

Existence of self-similar, superposed pulse-train solutions of the nonlinear, coupled Maxwell-Schr\"odinger equations, with the frequencies controlled by the oscillator strengths of the transitions, is established. Some of these excitations are specific to the resonant media, with energy levels in the configurations of $\Lambda$ and $N$ and arise because of the interference effects of cnoidal waves, as evidenced from some recently discovered identities involving the Jacobian elliptic functions. Interestingly, these excitations also admit a dual interpretation as single pulse-trains, with widely different amplitudes, which can lead to substantially different field intensities and population densities in different atomic levels.Comment: 11 Pages, 6 Figures, presentation changed and 3 figures adde

Quantum superchemistry: Role of trapping profile and quantum statistics

The process of Raman photoassociation of a trapped atomic condensate to form condensed molecules has been labeled superchemistry because it can occur at 0 K and experiences coherent bosonic stimulation. We show here that the differences from ordinary chemical processes go even deeper, with the conversion rates depending on the quantum state of the reactants, as expressed by the Wigner function. We consider different initial quantum states of the trapped atomic condensate and different forms of the confining potentials, demonstrating the importance of the quantum statistics and the extra degrees of freedom which massive particles and trapping potentials make available over the analogous optical process of second-harmonic generation. We show that both mean-field analyses and quantum calculations using an inappropriate initial condition can make inaccurate predictions for a given system. This is possible whether using a spatially dependent analysis or a zero-dimensional approach as commonly used in quantum optics

Specifically neuropathic Gaucher's mutations accelerate cognitive decline in Parkinson's

Objective: We hypothesized that specific mutations in the β‐glucocerebrosidase gene (GBA) causing neuropathic Gaucher's disease (GD) in homozygotes lead to aggressive cognitive decline in heterozygous Parkinson's disease (PD) patients, whereas non‐neuropathic GD mutations confer intermediate progression rates. Methods: A total of 2,304 patients with PD and 20,868 longitudinal visits for up to 12.8 years (median, 4.1) from seven cohorts were analyzed. Differential effects of four types of genetic variation in GBA on longitudinal cognitive decline were evaluated using mixed random and fixed effects and Cox proportional hazards models. Results: Overall, 10.3% of patients with PD and GBA sequencing carried a mutation. Carriers of neuropathic GD mutations (1.4% of patients) had hazard ratios (HRs) for global cognitive impairment of 3.17 (95% confidence interval [CI], 1.60–6.25) and a hastened decline in Mini–Mental State Exam scores compared to noncarriers (p = 0.0009). Carriers of complex GBA alleles (0.7%) had an HR of 3.22 (95% CI, 1.18–8.73; p = 0.022). By contrast, the common, non‐neuropathic N370S mutation (1.5% of patients; HR, 1.96; 95% CI, 0.92–4.18) or nonpathogenic risk variants (6.6% of patients; HR, 1.36; 95% CI, 0.89–2.05) did not reach significance. Interpretation Mutations in the GBA gene pathogenic for neuropathic GD and complex alleles shift longitudinal cognitive decline in PD into “high gear.” These findings suggest a relationship between specific types of GBA mutations and aggressive cognitive decline and have direct implications for improving the design of clinical trials. Ann Neurol 2016;80:674–68

Specifically neuropathic Gaucher's mutations accelerate cognitive decline in Parkinson's

Objective: We hypothesized that specific mutations in the β-glucocerebrosidase gene (GBA) causing neuropathic Gaucher's disease (GD) in homozygotes lead to aggressive cognitive decline in heterozygous Parkinson's disease (PD) patients, whereas non-neuropathic GD mutations confer intermediate progression rates. Methods: A total of 2,304 patients with PD and 20,868 longitudinal visits for up to 12.8 years (median, 4.1) from seven cohorts were analyzed. Differential effects of four types of genetic variation in GBA on longitudinal cognitive decline were evaluated using mixed random and fixed effects and Cox proportional hazards models. Results: Overall, 10.3% of patients with PD and GBA sequencing carried a mutation. Carriers of neuropathic GD mutations (1.4% of patients) had hazard ratios (HRs) for global cognitive impairment of 3.17 (95% confidence interval [CI], 1.60–6.25) and a hastened decline in Mini–Mental State Exam scores compared to noncarriers (p = 0.0009). Carriers of complex GBA alleles (0.7%) had an HR of 3.22 (95% CI, 1.18–8.73; p = 0.022). By contrast, the common, non-neuropathic N370S mutation (1.5% of patients; HR, 1.96; 95% CI, 0.92–4.18) or nonpathogenic risk variants (6.6% of patients; HR, 1.36; 95% CI, 0.89–2.05) did not reach significance. Interpretation: Mutations in the GBA gene pathogenic for neuropathic GD and complex alleles shift longitudinal cognitive decline in PD into “high gear.” These findings suggest a relationship between specific types of GBA mutations and aggressive cognitive decline and have direct implications for improving the design of clinical trials. Ann Neurol 2016;80:674–685