Multivariate Gabor frames for operators in matrix-valued signal spaces over locally compact abelian groups

In this paper, we study multivariate Gabor frames in matrix-valued signal spaces over locally compact abelian (LCA) groups, where the lower frame condition depends on a bounded linear operator [Formula: see text] on the underlying matrix-valued signal space. This type of Gabor frame is also known as a multivariate [Formula: see text]-Gabor frame. By extending work of Gǎvruta, we present necessary and sufficient conditions for the existence of [Formula: see text]-Gabor frames of multivariate matrix-valued Gabor systems. Some operators which can transform multivariate matrix-valued Gabor and [Formula: see text]-Gabor frames into [Formula: see text]-Gabor frames in terms of adjointable operators are discussed. Finally, we give a Paley–Wiener-type perturbation result for multivariate matrix-valued [Formula: see text]-Gabor frames.

The Effect of a Goal-Framing Manipulation on Environmentalism

We promoted pro-environmental action as aligned with hedonic, gain and normative goal-frames to test the influence on liberal and conservative environmentalism. Environmentalism was not affected by goal-frame condition, but a main effect of political orientation showed liberals reported greater climate belief and willingness to take action. Overall, frames were equally (in)effective, regardless of political leaning.

The Regularized Weak Functional Matching Pursuit for linear inverse problems

In this work, we present the so-called Regularized Weak Functional Matching Pursuit (RWFMP) algorithm, which is a weak greedy algorithm for linear ill-posed inverse problems. In comparison to the Regularized Functional Matching Pursuit (RFMP), on which it is based, the RWFMP possesses an improved theoretical analysis including the guaranteed existence of the iterates, the convergence of the algorithm for inverse problems in infinite-dimensional Hilbert spaces, and a convergence rate, which is also valid for the particular case of the RFMP. Another improvement is the cancellation of the previously required and difficult to verify semi-frame condition. Furthermore, we provide an a-priori parameter choice rule for the RWFMP, which yields a convergent regularization. Finally, we will give a numerical example, which shows that the “weak” approach is also beneficial from the computational point of view. By applying an improved search strategy in the algorithm, which is motivated by the weak approach, we can save up to 90 of computation time in comparison to the RFMP, whereas the accuracy of the solution does not change as much.

Individual Differences in Risk-Taking Tendency and Framing Effect

I investigated the relationship between framing effect and individuals' level of tendency to take risks. The results showed that the strength of the tendency of individuals to take risks influences the occurrence of framing effect. Frame had relatively less impact on those participants whose tendency to take risks was stronger than that of other people and people in this group tended to pursue risks in both positive and negative frame conditions. Frame had a stronger impact on those participants with a weaker risk-taking tendency, and they tended to avoid risks under positive framing conditions but pursued risks under negative framing. These results explain the preference shift phenomenon, whereby a tendency to take risks under a positive framing condition becomes stronger under a negative framing condition (unidirectional framing effect), that has been found in previous studies. The results also confirmed that framing influenced participants' reaction time, which was shorter in the positive frame condition than in the negative frame condition.

WEIGHTED AND CONTROLLED FRAMES: MUTUAL RELATIONSHIP AND FIRST NUMERICAL PROPERTIES

Weighted and controlled frames have been introduced recently to improve the numerical efficiency of iterative algorithms for inverting the frame operator. In this paper, we develop systematically these notions, including their mutual relationship. We will show that controlled frames are equivalent to standard frames and so this concept gives a generalized way to check the frame condition, while offering a numerical advantage in the sense of preconditioning. Next, we investigate weighted frames, in particular their relation to controlled frames. We consider the special case of semi-normalized weights, where the concepts of weighted frames and standard frames are interchangeable. We also make the connection with frame multipliers. Finally, we analyze weighted frames numerically. First, we investigate three possibilities for finding weights in order to tighten a given frame, i.e. decrease the frame bound ratio. Then, we examine Gabor frames and how well the canonical dual of a weighted frame is approximated by the inversely weighted dual frame.

Infinite matrices, wavelet coefficients and frames

We study the action ofAonf∈L2(ℝ)and on its wavelet coefficients, whereA=(almjk)lmjkis a double infinite matrix. We find the frame condition forA-transform off∈L2(ℝ)whose wavelet series expansion is known.

Dispositional Self-Confidence in Judgment and Framing Bias Susceptibility in a Dynamic Decision Making Environment

Decision-makers demonstrate framing bias when their decision making behavior is a function of the contextual presentation or framing (positive or negative) of the decision problem. Framing effects in simple, static situations (e.g., gambling) have been well documented, but past research on framing has typically ignored both dynamic environments and the effects of predispositional variables like risk-taking tendency and confidence in judgment. We examined the impact of these influences by exposing participants who measured either very high or low in decision making self-confidence to a high workload environment with either an “opportunity for gain” or a “threat of loss” decision frame condition. Participants performed a multi-task, computer-generated flight simulation program (the MAT) for 30 minutes. Results indicated that participants' actual performance on the MAT subtasks could be affected by the framing manipulation, and also that their decision strategies to optimize task performance were influenced by both by the framing manipulation and their self-confidence level.