Continuous-Discrete Path Integral Filtering

A summary of the relationship between the Langevin equation, Fokker-Planck-Kolmogorov forward equation (FPKfe) and the Feynman path integral descriptions of stochastic processes relevant for the solution of the continuous-discrete filtering problem is provided in this paper. The practical utility of the path integral formula is demonstrated via some nontrivial examples. Specifically, it is shown that the simplest approximation of the path integral formula for the fundamental solution of the FPKfe can be applied to solve nonlinear continuous-discrete filtering problems quite accurately. The Dirac-Feynman path integral filtering algorithm is quite simple, and is suitable for real-time implementation.Comment: 35 pages, 18 figures, JHEP3 clas

Stability of difference schemes in the maximum-norm

AbstractNecessary and sufficient conditions for stability in the maximum-norm of explicity two-level difference schemes with constant coefficients are given. The sufficiency of the conditions has been proved previously by G. Strang

Development of microelectrodes for electrical measurements in a microfluidic system

Transendothelial electrical resistance (TEER) measurements are used to quantitatively monitor cell barrier formation in in vitro models of the blood-brain barrier. TEER measurements in microfluidic in vitro systems are technically problematic and have suffered from poor measurement reproducibility. The aim of this Master’s thesis project was to develop fully integrated electrodes for measuring TEER in a microfluidic blood-brain barrier model. Two patterns of thin film electrodes – one with electrodes placed in the microfluidic channels, and one with electrodes directly above and below the cell culture membrane – were designed, fabricated and embedded in the microfluidic system. Electrodes were fabricated in silver and in platinum, and their reproducibility was evaluated using impedance spectroscopy. Results showed that electrodes fabricated in platinum and placed directly over the membrane could measure impedance with the highest precision. Measurement variation from the electrodes placed in the channels was shown to effectively be reduced by employing a technique of combining six measurements from four electrodes. Based on the reproducibility studies presented in this report, both types of electrodes were believed to have sufficient sensitivity and robustness to be used for TEER measurements. A robust technique to measure TEER enables real-time monitoring of cells in microfluidic systems, and offers a quantitative validation parameter for easy comparison and benchmarking of different system.Sensorer för elektriska mätningar i mikrofluida system Behandling av neurodegenerativa sjukdomar, så som Alzheimers och Parkinsons, är en av vår tids största utmaningar. Med en växande åldrade befolkning förväntas antalet patienter öka, och att hitta effektiva behandlingsmetoder blir alltmer brådskande. Den stora utmaningen ligger i att få läkemedel att nå centrala nervsystemet. På grund av blod-hjärnbarriärer har hjärnan en effektivt skyddande barriär som hindrar substanser från att ta sig in i hjärnan. Inom läkemedelsindustrin läggs enorma resurser på forskning kring hur läkemedel på ett säkert och effektiv sätt ska kunna passera blod-hjärnbarriären. Mycket av denna forskning bedrivs med djurmodeller. Förutom att djurmodeller är etiskt omtvistade, är de kostsamma, arbetsintensiva och på många sätt olika från människokroppen. För att minska användningen av djurmodeller behövs alternativa modeller, där blod-hjärnbarriären kan studeras in vitro. Det senaste årtiondet har en ny klass av in vitro-modeller framträtt, organs-on-chips. Organs-on-chips är mikrofluida system där levande celler kan odlas på ett chip. Dessa modeller har påvisat flera fördelar jämfört med tidigare in vitro-modeller. Genom att utsätta cellkulturen för fluidflöde, kan de bättre efterlikna miljön av blodflöde. I dessa system kan även elektriska sensorer integreras för att studera cellkulturen i realtid. Sensorer kan integreras i en modell av blod-hjärnbarriärer för att mäta den elektriska resistansen över cellbarriären. Dessa mätningar utgör en kvantitativ parameter för hur effektiv barriär cellerna utgör. Mätningarna är dock tekniskt utmanande. På grund av mikrosystemens små dimensioner har de en hög inre resistans som kan vara flera gånger större än resistansen över cellbarriären. Små variationer och mätfel kan därför skapa relativt stor osäkerhet kring resistansen som utgörs av cellbarriären. I detta projekt utvecklades mikrosensorer för resistansmätningar i en modell av blod-hjärnbarriären. Elektrodernas geometri, placering, och material utvärderades med impedans-mätningar för att minimera mätvariation och skapa ett stabilt system. Med de sensorer som presenteras här, kan resistans mätas med god precision. Resistansmätningar av hög kvalitet kan utgöra en parameter för validering, vilket potentiellt kan accelerera utvecklingen av organs-on-chips

Iterative methods for shifted positive definite linear systems and time discretization of the heat equation

In earlier work we have studied a method for discretization in time of a parabolic problem which consists in representing the exact solution as an integral in the complex plane and then applying a quadrature formula to this integral. In application to a spatially semidiscrete finite element version of the parabolic problem, at each quadrature point one then needs to solve a linear algebraic system having a positive definite matrix with a complex shift, and in this paper we study iterative methods for such systems. We first consider the basic and a preconditioned version of the Richardson algorithm, and then a conjugate gradient method as well as a preconditioned version thereof

Computer use and stress, sleep disturbances, and symptoms of depression among young adults – a prospective cohort study

BACKGROUND: We have previously studied prospective associations between computer use and mental health symptoms in a selected young adult population. The purpose of this study was to investigate if high computer use is a prospective risk factor for developing mental health symptoms in a population-based sample of young adults. METHODS: The study group was a cohort of young adults (n = 4163), 20–24 years old, who responded to a questionnaire at baseline and 1-year follow-up. Exposure variables included time spent on computer use (CU) in general, email/chat use, computer gaming, CU without breaks, and CU at night causing lost sleep. Mental health outcomes included perceived stress, sleep disturbances, symptoms of depression, and reduced performance due to stress, depressed mood, or tiredness. Prevalence ratios (PRs) were calculated for prospective associations between exposure variables at baseline and mental health outcomes (new cases) at 1-year follow-up for the men and women separately. RESULTS: Both high and medium computer use compared to low computer use at baseline were associated with sleep disturbances in the men at follow-up. High email/chat use was negatively associated with perceived stress, but positively associated with reported sleep disturbances for the men. For the women, high email/chat use was (positively) associated with several mental health outcomes, while medium computer gaming was associated with symptoms of depression, and CU without breaks with most mental health outcomes. CU causing lost sleep was associated with mental health outcomes for both men and women. CONCLUSIONS: Time spent on general computer use was prospectively associated with sleep disturbances and reduced performance for the men. For the women, using the computer without breaks was a risk factor for several mental health outcomes. Some associations were enhanced in interaction with mobile phone use. Using the computer at night and consequently losing sleep was associated with most mental health outcomes for both men and women. Further studies should focus on mechanisms relating information and communication technology (ICT) use to sleep disturbances

A picture is worth a thousand words : content-based image retrieval techniques

In my dissertation I investigate techniques for improving the state of the art in content-based image retrieval. To place my work into context, I highlight the current trends and challenges in my field by analyzing over 200 recent articles. Next, I propose a novel paradigm called __artificial imagination__, which gives the retrieval system the power to imagine and think along with the user in terms of what she is looking for. I then introduce a new user interface for visualizing and exploring image collections, empowering the user to navigate large collections based on her own needs and preferences, while simultaneously providing her with an accurate sense of what the database has to offer. In the later chapters I present work dealing with millions of images and focus in particular on high-performance techniques that minimize memory and computational use for both near-duplicate image detection and web search. Finally, I show early work on a scene completion-based image retrieval engine, which synthesizes realistic imagery that matches what the user has in mind.LEI Universiteit LeidenNWOImagin

Numerical methods for hyperbolic and parabolic integro-differential equations

An analysis by energy methods is given for fully discrete numerical methods for time-dependent partial integro-differential equations. Stability and error estimates are derived in H1 and L2. The methods considered pay attention to the storage needs during time-stepping

Galerkin FEM for fractional order parabolic equations with initial data in H−s, 0<s≤1H^{-s},~0 < s \le 1

We investigate semi-discrete numerical schemes based on the standard Galerkin and lumped mass Galerkin finite element methods for an initial-boundary value problem for homogeneous fractional diffusion problems with non-smooth initial data. We assume that $\Omega\subset \mathbb{R}^d$, $d=1,2,3$ is a convex polygonal (polyhedral) domain. We theoretically justify optimal order error estimates in $L_2$- and $H^1$-norms for initial data in $H^{-s}(\Omega),~0\le s \le 1$. We confirm our theoretical findings with a number of numerical tests that include initial data $v$ being a Dirac $\delta$-function supported on a $(d-1)$-dimensional manifold.Comment: 13 pages, 3 figure