Kernel Estimation of Cumulative Residual Tsallis Entropy and Its Dynamic Version under ρ-Mixing Dependent Data

Tsallis introduced a non-logarithmic generalization of Shannon entropy, namely Tsallis entropy, which is non-extensive. Sati and Gupta proposed cumulative residual information based on this non-extensive entropy measure, namely cumulative residual Tsallis entropy (CRTE), and its dynamic version, namely dynamic cumulative residual Tsallis entropy (DCRTE). In the present paper, we propose non-parametric kernel type estimators for CRTE and DCRTE where the considered observations exhibit an ρ-mixing dependence condition. Asymptotic properties of the estimators were established under suitable regularity conditions. A numerical evaluation of the proposed estimator is exhibited and a Monte Carlo simulation study was carried out.

Envelope Theorems in Economics: Historical Development and Modern Cost-Benefit Applications

This paper reviews some historical development and modern applications of the envelope theorems in economics from a static to a dynamic context. First, we show how the static version of the theorem surfaced in economics, which had eventually lead to the well-known Shephard’s lemma in microeconomics. Second, we present its dynamic version in terms of the classical calculus of variations and optimal control theory via the optimized Hamiltonian function. Third, we show some applications of the theorem for deriving dynamic cost-benefifit rules with special reference to environmental projects involving the green or comprehensive net national product (CNNP). Finally, we illustrate how to extend the cost-benefifit rules to a stochastic economic growth setting.

Topological pumping in acoustic waveguide arrays with hopping modulation

Thouless pumping is the adiabatic transportation of quantized charge, which is regarded as the dynamic version of the quantum Hall effect. Here we propose the design of an acoustic system to demonstrate the topological pumping characterized by transporting acoustic energy from one side to the opposite. The system is composed of coupled acoustic waveguide arrays with modulated coupling along both cross-sections and the propagating direction. We explore multiple topological phases by introducing rich spatial frequency or enlarged range of the hopping modulation. Such distinct topological phases are evidenced by adiabatic evolution of the edge states, where the acoustic system varies continuously and slowly along the state propagating direction. The robustness behavior of the edge states transport is also verified with numerical simulations to imply their topology origin. Our work provides a route to realize topological phases and utilize the corresponding edge states in waveguide arrays that can lead to versatile acoustic wave manipulation applications.

Further Results on the Proportional Vitalities Model

In contrast to many survival models such as proportional hazard rates and proportional mean residual lives, the proportional vitalities model has also been introduced in the literature. In this paper, further stochastic ordering properties of a dynamic version of the model with a random vitality growth parameter are investigated. Examples are presented to illustrate different established properties of the model. Potentials for inference about the parameters in proportional vitalities model with possibly time-varying effects are also argued and discussed.

Learning brain dynamics for decoding and predicting individual differences

Insights from functional Magnetic Resonance Imaging (fMRI), as well as recordings of large numbers of neurons, reveal that many cognitive, emotional, and motor functions depend on the multivariate interactions of brain signals. To decode brain dynamics, we propose an architecture based on recurrent neural networks to uncover distributed spatiotemporal signatures. We demonstrate the potential of the approach using human fMRI data during movie-watching data and a continuous experimental paradigm. The model was able to learn spatiotemporal patterns that supported 15-way movie-clip classification (∼90%) at the level of brain regions, and binary classification of experimental conditions (∼60%) at the level of voxels. The model was also able to learn individual differences in measures of fluid intelligence and verbal IQ at levels comparable to that of existing techniques. We propose a dimensionality reduction approach that uncovers low-dimensional trajectories and captures essential informational (i.e., classification related) properties of brain dynamics. Finally, saliency maps and lesion analysis were employed to characterize brain-region/voxel importance, and uncovered how dynamic but consistent changes in fMRI activation influenced decoding performance. When applied at the level of voxels, our framework implements a dynamic version of multivariate pattern analysis. Our approach provides a framework for visualizing, analyzing, and discovering dynamic spatially distributed brain representations during naturalistic conditions.

Søren Johansen and Katarina Juselius: A Bibliometric Analysis of Citations through Multivariate Bass Models

We showcase the impact of Katarina Juselius and Søren Johansen’s contribution to econometrics using bibliometric data on citations from 1989 to 2017, extracted from the Web of Science (WoS) database. Our purpose is to analyze the impact of KJ and SJ’s ideas on applied and methodological research in econometrics. To this aim, starting from WoS data, we derived two composite indices whose purpose is to disentangle the authors’ impact on applied research from their impact on methodological research. As of 2017, the number of applied citing papers per quarter had not yet reached the peak; conversely, the peak in the methodological literature seem to have been reached around 2000, although the shape of the trajectory is very flat after the peak. We analyzed the data using a multivariate dynamic version of the well known Bass model. Our estimates suggest that the methodological literature is mainly driven by “innovators”, whereas “imitators” are relatively more important in the applied literature: this might explain the different location of the peaks. We also find that, in the literature referring to KJ and SJ, the “cross-fertilization” between methodological and applied research is statistically significant and bi-directional.

How Goals Erase Framing Effects in Risky Decision Making

Evidence has shown that goals systematically change risk preferences in repeated decisions under risk. For instance, decision makers could aim to reach goals in a limited time, such as “making at least $1000 with ten stock investments within a year.” We test whether goal-based risky decisions differ when facing gains as compared to losses. More specifically, we examine the impact of outcome framing (gains vs. losses) and state framing (positive vs. negative resource states) on goal-based risky decisions. Our results (N=100) reveal no framing effects; instead, we find a consistently strong effect of the goal on risk preferences independent of framing. Computational modeling showed that a dynamic version of prospect theory, with a goal-dependent reference point, described 87% of participants best. This model treats outcomes as gains and losses depending on the state-goal distance. Our results show how goals can erase standard framing effects observed in risky choices without goals.