Search results for "Pointwise"

Combining Real-Time Segmentation and Classification of Rehabilitation Exercises with LSTM Networks and Pointwise Boosting

2020

Autonomous biofeedback tools in support of rehabilitation patients are commonly built as multi-tier pipelines, where a segmentation algorithm is first responsible for isolating motion primitives, and then classification can be performed on each primitive. In this paper, we present a novel segmentation technique that integrates on-the-fly qualitative classification of physical movements in the process. We adopt Long Short-Term Memory (LSTM) networks to model the temporal patterns of a streaming multivariate time series, obtained by sampling acceleration and angular velocity of the limb in motion, and then we aggregate the pointwise predictions of each isolated movement using different boosti…

Pointwise regularity of solutions to nonlinear double obstacle problems

1991

Adjoint-based inversion for porosity in shallow reservoirs using pseudo-transient solvers for non-linear hydro-mechanical processes

2020

Abstract Porous flow is of major importance in the shallow subsurface, since it directly impacts on reservoir-scale processes such as waste fluid sequestration or oil and gas exploration. Coupled and non-linear hydro-mechanical processes describe the motion of a low-viscous fluid interacting with a higher viscous porous rock matrix. This two-phase flow may trigger the initiation of solitary waves of porosity, further developing into vertical high-porosity pipes or chimneys. These preferred fluid escape features may lead to localised and fast vertical flow pathways potentially problematic in the case of for instance CO2 sequestration. Constraining the porosity and the non-linearly related pe…

On the numerical solution of the distributed parameter identification problem

1991

A new error estimate is derived for the numerical identification of a distributed parameter a(x) in a two point boundary value problem, for the case that the finite element method and the fit-to-data output-least-squares technique are used for the identifications. With a special weighted norm, we get a pointwise estimate. Prom the error estimate and also from the numerical tests, we find that if we decrease the mesh size, the maximum error between the identified parameter and the true parameter will increase. In order to improve the accuracy, higher order finite element spaces should be used in the approximations.

Unified halo-independent formalism from convex hulls for direct dark matter searches

2017

Using the Fenchel-Eggleston theorem for convex hulls (an extension of the Caratheodory theorem), we prove that any likelihood can be maximized by either a dark matter 1- speed distribution $F(v)$ in Earth's frame or 2- Galactic velocity distribution $f^{\rm gal}(\vec{u})$, consisting of a sum of delta functions. The former case applies only to time-averaged rate measurements and the maximum number of delta functions is $({\mathcal N}-1)$, where ${\mathcal N}$ is the total number of data entries. The second case applies to any harmonic expansion coefficient of the time-dependent rate and the maximum number of terms is ${\mathcal N}$. Using time-averaged rates, the aforementioned form of $F(v…

Potential construction of the B (1) 1 Π state in KCs based on Fourier-Transform spectroscopy data

2015

Abstract The paper presents an empirical pointwise potential energy curve (PEC) of the extensively perturbed B ( 1 ) 1 Π state of the KCs molecule constructed by applying an Inverted Perturbation Approach routine. The experimental term values in the energy range E ( v ′ , J ′ ) ∈ [ 14071 ; 15502 ] cm − 1 involved in the fit were based on Fourier-Transform spectroscopy data obtained with 0.01 cm−1 accuracy from laser-induced B ( 1 ) 1 Π → X 1 Σ + fluorescence spectra in the present work (654 term values) combined with 520 term values from Birzniece et al. (2012) . The data set included vibrational v ′ ∈ [ 0 , 35 ] and rotational J ′ ∈ [ 7 , 233 ] quantum numbers covering about 85% of the pot…

A pointwise selection principle for metric semigroup valued functions

2008

Abstract Let ∅ ≠ T ⊂ R , ( X , d , + ) be an additive commutative semigroup with metric d satisfying d ( x + z , y + z ) = d ( x , y ) for all x , y , z ∈ X , and X T the set of all functions from T into X . If n ∈ N and f , g ∈ X T , we set ν ( n , f , g , T ) = sup ∑ i = 1 n d ( f ( t i ) + g ( s i ) , g ( t i ) + f ( s i ) ) , where the supremum is taken over all numbers s 1 , … , s n , t 1 , … , t n from T such that s 1 ⩽ t 1 ⩽ s 2 ⩽ t 2 ⩽ ⋯ ⩽ s n ⩽ t n . We prove the following pointwise selection theorem: If a sequence of functions { f j } j ∈ N ⊂ X T is such that the closure in X of the set { f j ( t ) } j ∈ N is compact for each t ∈ T , and lim n → ∞ ( 1 n lim N → ∞ sup j , k ⩾ N , j…

Pointwise k-Pseudo Metric Space

2021

In this paper, the concept of a k-(quasi) pseudo metric is generalized to the L-fuzzy case, called a pointwise k-(quasi) pseudo metric, which is considered to be a map d:J(LX)×J(LX)⟶[0,∞) satisfying some conditions. What is more, it is proved that the category of pointwise k-pseudo metric spaces is isomorphic to the category of symmetric pointwise k-remote neighborhood ball spaces. Besides, some L-topological structures induced by a pointwise k-quasi-pseudo metric are obtained, including an L-quasi neighborhood system, an L-topology, an L-closure operator, an L-interior operator, and a pointwise quasi-uniformity.

Pointwise Hardy inequalities and uniformly fat sets

2008

We prove that it is equivalent for domain in R n \mathbb {R}^n to admit the pointwise p p -Hardy inequality, have uniformly p p -fat complement, or satisfy a uniform inner boundary density condition.

Pointwise Inequalities for Sobolev Functions on Outward Cuspidal Domains

2019

Abstract We show that the 1st-order Sobolev spaces $W^{1,p}(\Omega _\psi ),$$1<p\leq \infty ,$ on cuspidal symmetric domains $\Omega _\psi $ can be characterized via pointwise inequalities. In particular, they coincide with the Hajłasz–Sobolev spaces $M^{1,p}(\Omega _\psi )$.