Search results for " Analysis"

Hölder regularity for the gradient of the inhomogeneous parabolic normalized p-Laplacian

2018

In this paper, we study an evolution equation involving the normalized [Formula: see text]-Laplacian and a bounded continuous source term. The normalized [Formula: see text]-Laplacian is in non-divergence form and arises for example from stochastic tug-of-war games with noise. We prove local [Formula: see text] regularity for the spatial gradient of the viscosity solutions. The proof is based on an improvement of flatness and proceeds by iteration.

Regularity for nonlinear stochastic games

2015

We establish regularity for functions satisfying a dynamic programming equation, which may arise for example from stochastic games or discretization schemes. Our results can also be utilized in obtaining regularity and existence results for the corresponding partial differential equations. peerReviewed

Remarks on regularity for p-Laplacian type equations in non-divergence form

2018

We study a singular or degenerate equation in non-divergence form modeled by the $p$-Laplacian, $$-|Du|^\gamma\left(\Delta u+(p-2)\Delta_\infty^N u\right)=f\ \ \ \ \text{in}\ \ \ \Omega.$$ We investigate local $C^{1,\alpha}$ regularity of viscosity solutions in the full range $\gamma>-1$ and $p>1$, and provide local $W^{2,2}$ estimates in the restricted cases where $p$ is close to 2 and $\gamma$ is close to 0.

Passive Control of Linear Structures Equipped with non-Linear Viscous Dampers and Amplification Mechanism

2008

Fluid damper devices in civil structures such as buildings or bridges are commonly used as energy absorbers for seismic protection. The problem in the response analysis of structures with filled dampers mainly consists in the fact that, due to the strongly nonlinear behavior of such equipments, the response spectrum technique fails. Moreover, in order to enhance the damping effect various toggle brace configurations have been recently proposed. In this paper by using the concept of power spectral density function compatible with the elastic response spectrum and the stochastic linearization technique, the equivalent damping ratio is obtained. It is shown that once the system is linearized r…

Fractional Hardy inequalities and visibility of the boundary

2013

We prove fractional order Hardy inequalities on open sets under a combined fatness and visibility condition on the boundary. We demonstrate by counterexamples that fatness conditions alone are not sufficient for such Hardy inequalities to hold. In addition, we give a short exposition of various fatness conditions related to our main result, and apply fractional Hardy inequalities in connection to the boundedness of extension operators for fractional Sobolev spaces.

Visual Contrast Modulates Operant Learning Responses in Larval Zebrafish.

2018

The larval zebrafish is a promising vertebrate model organism to study neural mechanisms underlying learning and memory due to its small brain and rich behavioral repertoire. Here, we report on a high-throughput operant conditioning system for zebrafish larvae, which can simultaneously train 12 fish to associate a visual conditioned pattern with electroshocks. We find that the learning responses can be enhanced by the visual contrast, not the spatial features of the conditioned patterns, highlighted by several behavioral metrics. By further characterizing the learning curves as well as memory extinction, we demonstrate that the percentage of learners and the memory length increase as the co…

Toimijuus korkeakoulutettujen suomen oppijoiden visuaalisissa narratiiveissa

2018

This socioculturally informed study explores how highly educated Finnish language learners represent their agency in visual narratives. Learners (n=59) were asked to draw two pictures of themselves as Finnish language users and provide verbal interpretations of the drawings. The aim of using visual narratives is to reach aspects such as feelings and beliefs which might be difficult to express verbally. The data were analyzed first by using visual grammar set out by Kress and van Leeuwen (2006) and secondly by content analysis. The findings suggest that learners saw Finnish language as a tool for oral communication. However, difficulties with speaking and listening appeared to restrict learn…

I look but do I see? : the application of visual design grammar in an introductory image analysis discussion course

2004

Development and characterisation of polymer composite materials with bio-inspired functions

2018

Promocijas darbs ir izstrādāts disertācijas veidā fizikas nozarē materiālu fizikas apakšnozarē. Pētījums tika veikts LU Materiālu mehānikas institūtā. Darbs saistīts ar aktuālu un jaunu pētījumu virzienu: bioinspirēto funkciju tālāku attīstīšanu slodzi nesošos kompozītos. Tās ir mehānisku triecienu vizuālās indikācijas un polimēru matricas vaskulārās pašdziedināšanas funkcijas. Šīs funkcijas tika nodrošinātas, izveidojot viedus slāņus un iebūvējot tos kompozītā. Pētījumā tika noskaidrotas piemērotās pārbaužu secības, attīstītas kvantitatīvas metodes un mehānisks modelis, lai novērtētu jauno funkciju efektivitāti kompozītos. Ir pierādīta funkciju augstā efektivitāte un spēja uzlabot slodzi n…

AnatomySketch : An Extensible Open-Source Software Platform for Medical Image Analysis Algorithm Development

2021

AbstractThe development of medical image analysis algorithm is a complex process including the multiple sub-steps of model training, data visualization, human–computer interaction and graphical user interface (GUI) construction. To accelerate the development process, algorithm developers need a software tool to assist with all the sub-steps so that they can focus on the core function implementation. Especially, for the development of deep learning (DL) algorithms, a software tool supporting training data annotation and GUI construction is highly desired. In this work, we constructed AnatomySketch, an extensible open-source software platform with a friendly GUI and a flexible plugin interfac…