The exponential cost optimality for finite horizon semi-Markov decision processes

summary:This paper considers an exponential cost optimality problem for finite horizon semi-Markov decision processes (SMDPs). The objective is to calculate an optimal policy with minimal exponential costs over the full set of policies in a finite horizon. First, under the standard regular and compact-continuity conditions, we establish the optimality equation, prove that the value function is the unique solution of the optimality equation and the existence of an optimal policy by using the minimum nonnegative solution approach. Second, we establish a new value iteration algorithm to calculate both the value function and the $\epsilon$-optimal policy. Finally, we give a computable machine maintenance system to illustrate the convergence of the algorithm

AirFL-Mem: Improving Communication-Learning Trade-Off by Long-Term Memory

Addressing the communication bottleneck inherent in federated learning (FL), over-the-air FL (AirFL) has emerged as a promising solution, which is, however, hampered by deep fading conditions. In this paper, we propose AirFL-Mem, a novel scheme designed to mitigate the impact of deep fading by implementing a \emph{long-term} memory mechanism. Convergence bounds are provided that account for long-term memory, as well as for existing AirFL variants with short-term memory, for general non-convex objectives. The theory demonstrates that AirFL-Mem exhibits the same convergence rate of federated averaging (FedAvg) with ideal communication, while the performance of existing schemes is generally limited by error floors. The theoretical results are also leveraged to propose a novel convex optimization strategy for the truncation threshold used for power control in the presence of Rayleigh fading channels. Experimental results validate the analysis, confirming the advantages of a long-term memory mechanism for the mitigation of deep fading.Comment: 8 pages, 3 figures, submitted for possible publicatio

Tensor Completion via Tensor Train Based Low-Rank Quotient Geometry under a Preconditioned Metric

This paper investigates the low-rank tensor completion problem, which is about recovering a tensor from partially observed entries. We consider this problem in the tensor train format and extend the preconditioned metric from the matrix case to the tensor case. The first-order and second-order quotient geometry of the manifold of fixed tensor train rank tensors under this metric is studied in detail. Algorithms, including Riemannian gradient descent, Riemannian conjugate gradient, and Riemannian Gauss-Newton, have been proposed for the tensor completion problem based on the quotient geometry. It has also been shown that the Riemannian Gauss-Newton method on the quotient geometry is equivalent to the Riemannian Gauss-Newton method on the embedded geometry with a specific retraction. Empirical evaluations on random instances as well as on function-related tensors show that the proposed algorithms are competitive with other existing algorithms in terms of recovery ability, convergence performance, and reconstruction quality.Comment: The manuscript has been adjusted in several place

Understanding tourists’ dining behaviors at traditional Chinese nutraceutical restaurants

Nutraceutical restaurants providing medical and/or health benefits have become an emerging market; however, the underlying factors and the mechanism explaining dining behaviours in nutraceutical restaurants remain unknown. This study utilized a mixed-methods approach to bridge this research gap. An exploratory qualitative interview was conducted to identify the determinants of patronage behaviour at nutraceutical restaurants. We further conducted a quantitative study utilizing an extended value-attitude-behaviour model to provide quantitative evidence. The results showed that health, cultural values, and social norms significantly influenced customers’ attitudes, thus leading to their revisit intentions. Furthermore, we found a significant role of social norms in determining nutraceutical consumption. Additionally, age was found to moderate the effects of health values and social norms on revisit intention

Designing Enhanced Multi-dimensional Constellations for Code-Domain NOMA

This paper presents an enhanced design of multi-dimensional (MD) constellations which play a pivotal role in many communication systems such as code-domain non-orthogonal multiple access (CD-NOMA). MD constellations are attractive as their structural properties, if properly designed, lead to signal space diversity and hence improved error rate performance. Unlike the existing works which mostly focus on MD constellations with large minimum Euclidean distance (MED), we look for new MD constellations with additional feature that the minimum product distance (MPD) is also large. To this end, a non-convex optimization problem is formulated and then solved by the convex-concave procedure (CCCP). Compared with the state-of-the-art literature, our proposed MD constellations lead to significant error performance enhancement over Rayleigh fading channels whilst maintaining almost the same performance over the Gaussian channels. To demonstrate their application, we also show that these MD constellations give rise to good codebooks in sparse code multiple access systems. All the obtained MD constellations can be found in https://github.com/Aureliano1/Multi-dimensional-constellation

A Search for Spectral Galaxy Pairs of Overlapping Galaxies based on Fuzzy Recognition

The Spectral Galaxy Pairs (SGPs) are defined as the composite galaxy spectra which contain two independent redshift systems. These spectra are useful for studying dust properties of the foreground galaxies. In this paper, a total of 165 spectra of SGPs are mined out from Sloan Digital Sky Survey (SDSS) Data Release 9 (DR9) using the concept of membership degree from the fuzzy set theory particularly defined to be suitable for fuzzily identifying emission lines. The spectra and images of this sample are classified according to the membership degree and their image features, respectively. Many of these 2nd redshift systems are too small or too dim to select from the SDSS images alone, making the sample a potentially unique source of information on dust effects in low-luminosity or low-surface-brightness galaxies that are underrepresented in morphological pair samples. The dust extinction of the objects with high membership degree is also estimated by Balmer decrement. Additionally, analyses for a series of spectroscopic observations of one SGP from 165 systems indicate that a newly star-forming region of our Milky Way might occur.Comment: 16pages, 6figure