Some individuals have very specific and differentiated emotional experiences, such as anger, shame, excitement, and happiness, whereas others have more general affective experiences of pleasure or discomfort that are not as highly differentiated. Considering that individuals with major depressive disorder (MDD) have cognitive deficits for negative information, we predicted that people with MDD would have less differentiated negative emotional experiences than would healthy people. To test this hypothesis, we assessed participants' emotional experiences using a 7-day experience-sampling protocol. Depression was assessed using structured clinical interviews and the Beck Depression Inventory-II. As predicted, individuals with MDD had less differentiated emotional experiences than did healthy participants, but only for negative emotions. These differences were above and beyond the effects of emotional intensity and variability.

An optimally controlled quantum system possesses a search landscape defined by the physical objective as a functional of the control field. This paper particularly explores the topological structure of quantum mechanical transition probability landscapes. The quantum system is assumed to be controllable and the analysis is based on the Euler-Lagrange variational equations derived from a cost function only requiring extremizing the transition probability. It is shown that the latter variational equations are automatically satisfied as a mathematical identity for control fields that either produce transition probabilities of zero or unit value. Similarly, the variational equations are shown to be inconsistent ͑i.e., they have no solution͒ for any control field that produces a transition probability different from either of these two extreme values. An upper bound is shown to exist on the norm of the functional derivative of the transition probability with respect to the control field anywhere over the landscape. The trace of the Hessian, evaluated for a control field producing a transition probability of a unit value, is shown to be bounded from below. Furthermore, the Hessian at a transition probability of unit value is shown to have an extensive null space and only a finite number of negative eigenvalues. Collectively, these findings show that ͑a͒ the transition probability landscape extrema consists of values corresponding to no control or full control, ͑b͒ approaching full control involves climbing a gentle slope with no false traps in the control space and ͑c͒ an inherent degree of robustness exists around any full control solution. Although full controllability may not exist in some applications, the analysis provides a basis to understand the evident ease of finding controls that produce excellent yields in simulations and in the laboratory. P i→f , ͑1͒and this paper is concerned with analyzing the structure of the control landscapewhich is a functional of the control field ͓30͔. In the laboratory other factors can enter, but an ultimate common goal is the clean performance of state-to-state transfer in Eq. ͑1͒.Knowledge of the general topology of this landscape, including its extrema values, slopes, and curvature, is fundamental to understanding the ability of finding good quality robust controls in the laboratory and in simulations. This paper will carry out an analysis of the control landscape in Eq. ͑2͒, treating ͑t͒ as an arbitrary continuous temporal function. As a result, the search to maximize P i→f is formally over an infinite dimensional space. However, in PHYSICAL REVIEW A 74, 012721 ͑2006͒

High-dimensional model representation (HDMR) is a general set of quantitative model assessment and analysis tools for improving the efficiency of deducing high dimensional input-output system behavior. RS-HDMR is a particular form of HDMR based on random sampling (RS) of the input variables. The component functions in an HDMR expansion are optimal choices tailored to the n-variate function f(x) being represented over the desired domain of the n-dimensional vector x. The high-order terms (usually larger than second order, or equivalently beyond cooperativity between pairs of variables) in the expansion are often negligible. When it is necessary to go beyond the first and the second order RS-HDMR, this article introduces a modified low-order term product (lp)-RS-HDMR method to approximately represent the high-order RS-HDMR component functions as products of low-order functions. Using this method the high-order truncated RS-HDMR expansions may be constructed without directly computing the original high-order terms. The mathematical foundations of lp-RS-HDMR are presented along with an illustration of its utility in an atmospheric chemical kinetics model.

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