Quasi-trivial Quandles and Biquandles, Cocycle Enhancements and Link-Homotopy of Pretzel links

We investigate some algebraic structures called quasi-trivial quandles and we use them to study link-homotopy of pretzel links. Precisely, a necessary and sufficient condition for a pretzel link with at least two components being trivial under link-homotopy is given. We also generalize the quasi-trivial quandle idea to the case of biquandles and consider enhancement of the quasi-trivial biquandle cocycle counting invariant by quasi-trivial biquandle cocycles, obtaining invariants of link-homotopy type of links analogous to the quasi-trivial quandle cocycle invariants in Ayumu Inoue's article arXiv:1205.5891.Comment: 14 pages. Version 3 includes some corrections and typo fixe

Fitting ARMA Time Series Models without Identification: A Proximal Approach

Fitting autoregressive moving average (ARMA) time series models requires model identification before parameter estimation. Model identification involves determining the order of the autoregressive and moving average components which is generally performed by inspection of the autocorrelation and partial autocorrelation functions or other offline methods. In this work, we regularize the parameter estimation optimization problem with a nonsmooth hierarchical sparsity-inducing penalty based on two path graphs that allows performing model identification and parameter estimation simultaneously. A proximal block coordinate descent algorithm is then proposed to solve the underlying optimization problem efficiently. The resulting model satisfies the required stationarity and invertibility conditions for ARMA models. Numerical studies supporting the performance of the proposed method and comparing it with other schemes are presented

Stochastic Optimization Algorithms for Problems with Controllable Biased Oracles

Motivated by multiple emerging applications in machine learning, we consider an optimization problem in a general form where the gradient of the objective is available through a biased stochastic oracle. We assume the bias magnitude can be reduced by a bias-control parameter, however, a lower bias requires more computation/samples. For instance, for two applications on stochastic composition optimization and policy optimization for infinite-horizon Markov decision processes, we show that the bias follows a power law and exponential decay, respectively, as functions of their corresponding bias control parameters. For problems with such gradient oracles, the paper proposes stochastic algorithms that adjust the bias-control parameter throughout the iterations. We analyze the nonasymptotic performance of the proposed algorithms in the nonconvex regime and establish their sample or bias-control computation complexities to obtain a stationary point. Finally, we numerically evaluate the performance of the proposed algorithms over the two applications

Stochastic Composition Optimization of Functions without Lipschitz Continuous Gradient

In this paper, we study the stochastic optimization of two-level composition of functions without Lipschitz continuous gradient. The smoothness property is generalized by the notion of relative smoothness which provokes the Bregman gradient method. We propose three Stochastic Compositional Bregman Gradient algorithms for the three possible nonsmooth compositional scenarios and provide their sample complexities to achieve an $\epsilon$-approximate stationary point. For the smooth of relative smooth composition, the first algorithm requires $O(\epsilon^{-2})$ calls to the stochastic oracles of the inner function value and gradient as well as the outer function gradient. When both functions are relatively smooth, the second algorithm requires $O(\epsilon^{-3})$ calls to the inner function stochastic oracle and $O(\epsilon^{-2})$ calls to the inner and outer function stochastic gradient oracles. We further improve the second algorithm by variance reduction for the setting where just the inner function is smooth. The resulting algorithm requires $O(\epsilon^{-5/2})$ calls to the stochastic inner function value and $O(\epsilon^{-3/2})$ calls to the inner stochastic gradient and $O(\epsilon^{-2})$ calls to the outer function stochastic gradient. Finally, we numerically evaluate the performance of these algorithms over two examples

The Role of Tumor Microenvironment in Mycosis Fungoides and Sézary Syndrome.

Mycosis fungoides (MF) and Sézary syndrome (SS) are the most common subtypes of cutaneous T-cell lymphomas (CTCLs). Most cases of MF display an indolent course during its early stage. However, in some patients, it can progress to the tumor stage with potential systematic involvement and a poor prognosis. SS is defined as an erythrodermic CTCL with leukemic involvements. The pathogenesis of MF and SS is still not fully understood, but recent data have found that the development of MF and SS is related to genetic alterations and possibly to environmental influences. In CTCL, many components interacting with tumor cells, such as tumor-associated macrophages, fibroblasts, dendritic cells, mast cells, and myeloid-derived suppressor cells, as well as with chemokines, cytokines and other key players, establish the tumor microenvironment (TME). In turn, the TME regulates tumor cell migration and proliferation directly and indirectly and may play a critical role in the progression of MF and SS. The TME of MF and SS appear to show features of a Th2 phenotype, thus dampening tumor-related immune responses. Recently, several studies have been published on the immunological characteristics of MF and SS, but a full understanding of the CTCL-related TME remains to be determined. This review focuses on the role of the TME in MF and SS, aiming to further demonstrate the pathogenesis of the disease and to provide new ideas for potential treatments targeted at the microenvironment components of the tumor

Is Algorithm Aversion WEIRD? A Cross-Country Comparison of Individual-Differences and Algorithm Aversion

Although algorithms offer superior performance over humans across many tasks, individuals often exhibit algorithm aversion, resisting algorithmic advice in favour of human recommendations. However, most algorithm aversion studies rely on American samples, potentially limiting the generalisability of the findings. Given the increasing adoption of algorithms globally, we explore if the impact of two crucial factors driving algorithm aversion, uniqueness neglect and familiarity, differ between culturally different countries. Drawing on the individualism-collectivism cultural dimension, we conducted two online studies comparing algorithm aversion between people in India and the United States in medical and financial services scenarios. While our results suggest that there is no difference in the degree of algorithm aversion between Indians and Americans at an aggregate level, we find important cross-cultural differences: Uniqueness neglect strengthens algorithm aversion for Americans more than Indians, while familiarity weakens algorithm aversion more for Indians than Americans. Thus, our results reveal generalisability issues within the algorithm aversion literature, as factors influencing algorithm aversion can be culturally dependent

The Validity and Reliability of the Mi Band Wearable Device for Measuring Steps and Heart Rate

International Journal of Exercise Science 13(4): 689-701, 2020. The study objectives were to 1) evaluate the criterion validity and reliability of the Mi Band 2 wearable activity monitor to measure steps during a six-minute walk test (6MWT), a treadmill walking test at various speed (1.28 km/h, 1.92 km/h, and 2.88 km/h) and a stair climbing test; 2) assess the validity and reliability of the monitor to measure heart rate during rest and exercise. Fourteen participants (females: n = 8; mean age ± SD: 23 ± 4.2) completed the study. The mean body mass index was 22 ± 3.6. The majority (~92%) of the Mi Band met the standard of 5% absolute percent error for measuring steps during the 6MWT. However, the Mi Band underestimated steps at slower walking speeds (\u3c 2.88 km/h). Mi Band showed good internal consistency during the six-minute walk test and stairs climb (ICC: 0.83). The validity and reliability of the Mi Band to measure heart rate may not be suited for clinical or research use. The Mi Band significantly underestimated heart rate during exercise. Overall, caution is required when interpreting the steps recorded (at slower speeds) and heart rate measurements