14 papers · ranked by Valyu relevance
Mahsa Soheil Shamaee, Sajad Fathi Hafshejani
This paper introduces a novel approach to enhance the performance of the stochastic gradient descent (SGD) algorithm by incorporating a modified decay step size based on √ 1 t . The proposed step size integrates a logarithmic term, leading to the selection of smaller values in the final iterations. Our analysis…
Michael Hintermüller, Kostas Papafitsoros, Carlos N. Rautenberg
> Abstract. We consider a mollifying operator with variable step that, in contrast to the standard mollification, is able to preserve the boundary values of functions. We prove boundedness of the operator in all basic Lebesgue, Sobolev and BV spaces as well as corresponding approximation results. The results are then…
Natalia de Castro, María A. Garrido-Vizuete, Rafael Robles, María Trinidad Villar-Liñán
'María Trinidad Villar-Liñán'] In this work we present the notion of greyscale of a graph as a colouring of its vertices that uses colours from the real interval [0,1]. Any greyscale induces another colouring by assigning to each edge the non-negative difference between the colours of its vertices. These edge colours…
Aline C. Soterroni, Roberto L. Galski, Marluce C. Scarabello, Fernando M. Ramos
'Fernando M. Ramos'] In this work, the q-Gradient (q-G) method, a q-version of the Steepest Descent method, is presented. The main idea behind the q-G method is the use of the negative of the q-gradient vector of the objective function as the search direction. The q-gradient vector, or simply the q-gradient, is a…
Seyed-Saleh Hosseini-Yazdi
Uneven terrain presents significant challenges for walkers, resulting in increased energy expenditures. Given that Center of Mass (COM) work reflects this energy demand, it's reasonable to assume that individuals also seek strategies to minimize mechanical work. One such strategy involves deciding between extending…
Andreas Mayr, Benjamin Hofner, Elisabeth Waldmann, Tobias Hepp + 2 more
'Sebastian Meyer' 'Olaf Gefeller'] Statistical boosting algorithms have triggered a lot of research during the last decade. They combine a powerful machine learning approach with classical statistical modelling, offering various practical advantages like automated variable selection and implicit regularization of…
Adam B. Grimmitt, Maeve E. Whelan, Douglas N. Martini, Wouter Hoogkamer
Older adults and neurological populations tend to walk with slower speeds, more gait variability, and a higher metabolic cost. This higher metabolic cost could be related to their increased gait variability, but this relationship is still unclear. The purpose of this study was to determine how increased step length…
Kévin Duarte, Jean-Marie Monnez, Eliane Albuisson, Chenping Hou
The present study addresses the problem of sequential least square multidimensional linear regression, particularly in the case of a data stream, using a stochastic approximation process. To avoid the phenomenon of numerical explosion which can be encountered and to reduce the computing time in order to take into…
Eisuke Chikayama
Whereas the Dirac delta function introduced by P. A. M. Dirac in 1930 to develop his theory of quantum mechanics has been well studied, a not famous formula related to the delta function using the Heaviside step function in a single-variable form, also given by Dirac, has been poorly studied. Following Dirac’s method…
John Fieberg, Johannes Signer, Brian Smith, Tal Avgar
Resource-selection and step-selection analyses allow researchers to link animals to their environment and are commonly used to address questions related to wildlife management and conservation efforts. Step-selection analyses that incorporate movement characteristics, referred to as integrated step-selection analyses…
Zhaoyi Li, Hong-lin Liao
We prove that the two-step backward differentiation formula (BDF2) method is stable on arbitrary time grids; while the variable-step BDF3 scheme is stable if almost all adjacent step ratios are less than 2.553. These results relax the severe mesh restrictions in the literature and provide a new understanding of…
L. Erikstad, V. Bakkestuen
The paper present a streamlined workflow, using multivariate analyses of environmental variables in combinations with GIS overlay analyses that provide methods to extract and analyse major environmental and climatic gradients by using fishnet polygons as sample units. The method opens for illustrating multivariate…
Jiawei Zhang
In this paper, we aim at providing an introduction to the gradient descent based optimization algorithms for learning deep neural network models. Deep learning models involving multiple nonlinear projection layers are very challenging to train. Nowadays, most of the deep learning model training still relies on the back…
Corey J. Scholes, Michael D. McDonald, Anthony W. Parker
The validity of fatigue protocols involving multi-joint movements, such as stepping, has yet to be clearly defined. Although surface electromyography can monitor the fatigue state of individual muscles, the effects of joint angle and velocity variation on signal parameters are well established. Therefore, the aims of…