Double fused Lasso regularized regression with both matrix and vector valued predictors

In this note we give a connection between the closure of the range of block Hankel operators acting on the vector-valued Hardy space H2Cn and the left coprime factorization of its symbol. Given a subset F ? H2Cn, we also consider the smallest invariant subspace S*F of the backward shift S* that contains F.

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Operators from H1 into a Banach space and vector valued measures

Geometric Aspects of Banach Spaces ◽

10.1017/cbo9780511662300.007 ◽

1989 ◽

pp. 87-93

Author(s):

Oscar Blasco

Keyword(s):

Banach Space ◽

Vector Valued

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Assessing elderly’s functional balance and mobility via analyzing data from waist-mounted tri-axial wearable accelerometers in timed up and go tests

BMC Medical Informatics and Decision Making ◽

10.1186/s12911-021-01463-4 ◽

2021 ◽

Vol 21 (1) ◽

Author(s):

Lisha Yu ◽

Yang Zhao ◽

Hailiang Wang ◽

Tien-Lung Sun ◽

Terrence E. Murphy ◽

...

Keyword(s):

Predictive Models ◽

Cross Validation ◽

Motor Coordination ◽

Predictive Accuracy ◽

Short Form ◽

Community Dwelling ◽

Regularized Regression ◽

Balance Assessment ◽

Timed Up And Go ◽

Functional Balance

Abstract Background Poor balance has been cited as one of the key causal factors of falls. Timely detection of balance impairment can help identify the elderly prone to falls and also trigger early interventions to prevent them. The goal of this study was to develop a surrogate approach for assessing elderly’s functional balance based on Short Form Berg Balance Scale (SFBBS) score. Methods Data were collected from a waist-mounted tri-axial accelerometer while participants performed a timed up and go test. Clinically relevant variables were extracted from the segmented accelerometer signals for fitting SFBBS predictive models. Regularized regression together with random-shuffle-split cross-validation was used to facilitate the development of the predictive models for automatic balance estimation. Results Eighty-five community-dwelling older adults (72.12 ± 6.99 year) participated in our study. Our results demonstrated that combined clinical and sensor-based variables, together with regularized regression and cross-validation, achieved moderate-high predictive accuracy of SFBBS scores (mean MAE = 2.01 and mean RMSE = 2.55). Step length, gender, gait speed and linear acceleration variables describe the motor coordination were identified as significantly contributed variables of balance estimation. The predictive model also showed moderate-high discriminations in classifying the risk levels in the performance of three balance assessment motions in terms of AUC values of 0.72, 0.79 and 0.76 respectively. Conclusions The study presented a feasible option for quantitatively accurate, objectively measured, and unobtrusively collected functional balance assessment at the point-of-care or home environment. It also provided clinicians and elderly with stable and sensitive biomarkers for long-term monitoring of functional balance.

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Generic rotation sets

Ergodic Theory and Dynamical Systems ◽

10.1017/etds.2020.129 ◽

2020 ◽

pp. 1-13

Author(s):

SEBASTIÁN PAVEZ-MOLINA

Keyword(s):

Dynamical System ◽

Convex Body ◽

Probability Measures ◽

Topological Dynamical System ◽

Continuous Vector ◽

Rotation Set ◽

Vector Valued Function ◽

Vector Valued ◽

Uniquely Ergodic ◽

Dense Set

Abstract Let $(X,T)$ be a topological dynamical system. Given a continuous vector-valued function $F \in C(X, \mathbb {R}^{d})$ called a potential, we define its rotation set $R(F)$ as the set of integrals of F with respect to all T-invariant probability measures, which is a convex body of $\mathbb {R}^{d}$ . In this paper we study the geometry of rotation sets. We prove that if T is a non-uniquely ergodic topological dynamical system with a dense set of periodic measures, then the map $R(\cdot )$ is open with respect to the uniform topologies. As a consequence, we obtain that the rotation set of a generic potential is strictly convex and has $C^{1}$ boundary. Furthermore, we prove that the map $R(\cdot )$ is surjective, extending a result of Kucherenko and Wolf.

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