Time-Dependent Effects of Acute Exercise-Induced Arousal on Long-Term Memory for Emotional and Neutral Stimuli

Psychological research has strongly documented the memory-enhancing effects of emotional arousal, while the effects of acute aerobic exercise on memory are not well understood. Manipulation of arousal has been shown to enhance long-term memory for emotional stimuli in a time-dependent fashion. This presents an opportunity to investigate the role of acute exercise in memory modulation. The purpose of this study was to determine the time-dependent relationship between acute exercise-induced arousal and long-term emotional memory. Participants viewed pleasant, neutral, and unpleasant images before or after completing a high-intensity session of cycling exercise. Salivary alpha-amylase, a biomarker of central norepinephrine, was measured as an indicator of arousal. No effects of exercise on recognition memory were revealed, however; a single session of high-intensity cycling increased salivary alpha-amylase. Our results also indicate that the influence of exercise on emotional responsiveness should be considered in further exploration of the memory-enhancing potential of acute exercise.

Quantitative Derivation of Effective Evolution Equations for the Dynamics of Bose-Einstein Condensates

This thesis proves certain results concerning an important question in non-equilibrium quantum statistical mechanics which is the derivation of effective evolution equations approximating the dynamics of a system of large number of bosons initially at equilibrium (ground state at very low temperatures). The dynamics of such systems are governed by the time-dependent linear many-body Schroedinger equation from which it is typically difficult to extract useful information due to the number of particles being large. We will study quantitatively (i.e. with explicit bounds on the error) how a suitable one particle non-linear Schroedinger equation arises in the mean field limit as number of particles N → ∞ and how the appropriate corrections to the mean field will provide better approximations of the exact dynamics. In the first part of this thesis we consider the evolution of N bosons, where N is large, with two-body interactions of the form N³ᵝv(Nᵝ⋅), 0≤β≤1. The parameter β measures the strength and the range of interactions. We compare the exact evolution with an approximation which considers the evolution of a mean field coupled with an appropriate description of pair excitations, see [18,19] by Grillakis-Machedon-Margetis. We extend the results for 0 ≤ β < 1/3 in [19, 20] to the case of β < 1/2 and obtain an error bound of the form p(t)/Nᵅ, where α>0 and p(t) is a polynomial, which implies a specific rate of convergence as N → ∞. In the second part, utilizing estimates of the type discussed in the first part, we compare the exact evolution with the mean field approximation in the sense of marginals. We prove that the exact evolution is close to the approximate in trace norm for times of the order o(1)√N compared to log(o(1)N) as obtained in Chen-Lee-Schlein [6] for the Hartree evolution. Estimates of similar type are obtained for stronger interactions as well.