| 1. |
- Lamers, Jules, 1986
(författare)
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The Functional Method for the Domain-Wall Partition Function
- 2018
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Ingår i: Symmetry, Integrability and Geometry - Methods and Applications. - 1815-0659. ; 14
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Forskningsöversikt (refereegranskat)abstract
- We review the (algebraic-)functional method devised by Galleas and further developed by Galleas and the author. We first explain the method using the simplest example: the computation of the partition function for the six-vertex model with domain-wall boundary conditions. At the heart of the method lies a linear functional equation for the partition function. After deriving this equation we outline its analysis. The result is a closed expression in the form of a symmetrized sum - or, equivalently, multiple-integral formula - that can be rewritten to recover Izergin's determinant. Special attention is paid to the relation with other approaches. In particular we show that the Korepin-Izergin approach can be recovered within the functional method. We comment on the functional method's range of applicability, and review how it is adapted to the technically more involved example of the elliptic solid-on-solid model with domain walls and a reflecting end. We present a new formula for the partition function of the latter, which was expressed as a determinant by Tsuchiya-Filali-Kitanine. Our result takes the form of a 'crossing-symmetrized' sum with 2(L) terms featuring the elliptic domain-wall partition function, which appears to be new also in the limiting case of the six-vertex model. Further taking the rational limit we recover the expression obtained by Frassek using the boundary perimeter Bethe ansatz.
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| 2. |
- Athanasopoulos, George, et al.
(författare)
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Forecast reconciliation : A review
- 2024
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Ingår i: International Journal of Forecasting. - : Elsevier. - 0169-2070 .- 1872-8200. ; 40:2, s. 430-456
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Forskningsöversikt (refereegranskat)abstract
- Collections of time series formed via aggregation are prevalent in many fields. These are commonly referred to as hierarchical time series and may be constructed cross-sectionally across different variables, temporally by aggregating a single series at different frequencies, or even generalised beyond aggregation as time series that respect linear constraints. When forecasting such time series, a desirable condition is for forecasts to be coherent: to respect the constraints. The past decades have seen substantial growth in this field with the development of reconciliation methods that ensure coherent forecasts and improve forecast accuracy. This paper serves as a comprehensive review of forecast reconciliation and an entry point for researchers and practitioners dealing with hierarchical time series. The scope of the article includes perspectives on forecast reconciliation from machine learning, Bayesian statistics and probabilistic forecasting, as well as applications in economics, energy, tourism, retail demand and demography.
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| 3. |
- Ames, Ellery, 1984, et al.
(författare)
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Stationary solutions of the axially symmetric Einstein-Vlasov system: present status and open problems
- 2024
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Ingår i: Classical and Quantum Gravity. - 0264-9381 .- 1361-6382. ; 41:7
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Forskningsöversikt (refereegranskat)abstract
- The purpose of this work is to review the status about stationary solutions of the axially symmetric Einstein-Vlasov system with a focus on open problems of both analytical and numerical nature. For the latter we emphasize that the code used to construct stationary solutions in Ames et al (2016 Class. Quantum Grav. 33 155008; 2019 Phys. Rev. D 99 024012) is open source, see Ames and Logg (2023 J. Open Source Softw. 8 5979). In the analytical setting the open problems include establishing methods for proving existence of axisymmetric stationary solutions which are far from spherically symmetric, both in the general case and for certain special classes of solutions pointed out in the text. In the numerical setting there are intriguing properties of highly relativistic solutions that demand further attention, such as whether a sequence of such stationary solutions can approach a Kerr black hole, or if they necessarily approach the thin ring limit reminiscent of cosmic strings. The question of whether stationary solutions include states with thin-disk like morphologies as seen in many galaxies is also open. Finally, there are opportunities to extend this research to new settings such as the case of massless particles and coupled black hole-matter systems. We believe that some of the open problems highlighted here are of central importance for the understanding of nature.
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| 4. |
- Ames, Ellery, 1984, et al.
(författare)
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Stationary solutions of the axially symmetric Einstein-Vlasov system: present status and open problems
- 2024
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Ingår i: CLASSICAL AND QUANTUM GRAVITY. - 0264-9381 .- 1361-6382. ; 41:7
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Forskningsöversikt (refereegranskat)abstract
- The purpose of this work is to review the status about stationary solutions of the axially symmetric Einstein-Vlasov system with a focus on open problems of both analytical and numerical nature. For the latter we emphasize that the code used to construct stationary solutions in Ames et al (2016 Class. Quantum Grav. 33 155008; 2019 Phys. Rev. D 99 024012) is open source, see Ames and Logg (2023 J. Open Source Softw. 8 5979). In the analytical setting the open problems include establishing methods for proving existence of axisymmetric stationary solutions which are far from spherically symmetric, both in the general case and for certain special classes of solutions pointed out in the text. In the numerical setting there are intriguing properties of highly relativistic solutions that demand further attention, such as whether a sequence of such stationary solutions can approach a Kerr black hole, or if they necessarily approach the thin ring limit reminiscent of cosmic strings. The question of whether stationary solutions include states with thin-disk like morphologies as seen in many galaxies is also open. Finally, there are opportunities to extend this research to new settings such as the case of massless particles and coupled black hole-matter systems. We believe that some of the open problems highlighted here are of central importance for the understanding of nature.
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| 5. |
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| 6. |
- Borén, Jan, 1963, et al.
(författare)
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Kinetic Studies to Investigate Lipoprotein Metabolism.
- 2012
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Ingår i: Journal of internal medicine. - : Wiley. - 1365-2796 .- 0954-6820. ; 271:2, s. 166-173
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Forskningsöversikt (refereegranskat)abstract
- To develop novel strategies for prevention and treatment of dyslipidaemia, it is essential to understand the pathophysiology of dyslipoproteinaemia in humans. Lipoprotein metabolism is a complex system in which abnormal concentrations of various lipoprotein particles can result from alterations in their rates of production, conversion and/or catabolism. Traditional methods that measure plasma lipoprotein concentrations only provide static estimates of lipoprotein metabolism and hence limited mechanistic information. By contrast, the use of tracers labelled with stable isotopes and mathematical modelling provides a powerful tool for probing lipid and lipoprotein kinetics in vivo and furthering understanding of the pathogenesis of dyslipoproteinaemia.
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| 7. |
- Cregg, P. J., et al.
(författare)
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Inclusion of interactions in mathematical modelling of implant assisted magnetic drug targeting
- 2012
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Ingår i: Applied Mathematical Modelling. - : Elsevier BV. - 0307-904X. ; 36:1, s. 1-34
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Forskningsöversikt (refereegranskat)abstract
- Drug delivery technologies are an important area within biomedicine. Targeted drug delivery aims to reduce the undesired side effects of drug usage by directing or capturing the active agents near a desired site within the body. This is particularly beneficial in, for instance, cancer chemotherapy, where the side effects of general (systemic) drug administration can be severe. One approach to targeted drug delivery uses magnetic nanoparticles as the constituents of carriers for the desired active agent. Once injected into the body, the behaviour of these magnetic carriers can be influenced and controlled by magnetic fields. In implant assisted magnetic drug targeting systems a magnetic implant, typically a stent, wire or spherical seed can be used to target sites deep within the body as the implant acts as a focus for the resulting magnetic force. This can be easily understood as the force depends on the gradient of the magnetic field and the gradient near the implant is large. In designing such a system many factors need to be considered including physical factors such as the size and nature of the implants and carriers, and the fields required. Moreover, the range of applicability of these systems in terms of the regions of the vasculature system, from low blood velocity environments, such as capillary beds to higher velocity arteries, must be considered. Furthermore, assessment criteria for these systems are needed. Mathematical modelling and simulation has a valuable role to play in informing in vitro and in vivo experiments, leading to practical system design. Specifically, the implant assisted magnetic drug targeting systems of Aviles. Ebner and Ritter are considered within this review, and two dimensional mathematical modelling is performed using the open source C++ finite volume library OpenFOAM. In the first system treated, a large ferromagnetic particle is implanted into a capillary bed as a seed to aid collection of single domain nanoparticles (radius 20-100 nm). The Langevin function is used to calculate the magnetic moment of the particles, and the model is further adapted to treat the agglomeration of particles known to occur in these systems. This agglomeration can be attributed to interparticle interactions and here the magnetic dipole-dipole and hydrodynamic interactions for two mutually interacting nanoparticles are modelled, following Mikkelsen et al. who treated two particle interactions in microfluidic systems, with low magnetic field (0.05 T). The resulting predicted performance is found to both increase and decrease significantly depending on initial positions of the particles. Secondly, a ferromagnetic, coiled wire stent is implanted in a large arterial vessel. The magnetic dipole-dipole and hydrodynamic interactions for multiple particles are included. Different initial positions are considered and the system performance is assessed. Inclusion of these interactions yields predictions that are in closer agreement with the experimental results of Aviles et al. We conclude that the discrepancies between the non interacting theoretical predictions and the corresponding experimental results can (as suggested by Aviles et al.) be largely attributed to interparticle interactions and the consequent agglomeration.
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| 8. |
- de Graaf, Albert A, et al.
(författare)
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Nutritional systems biology modeling: from molecular mechanisms to physiology.
- 2009
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Ingår i: PLoS computational biology. - : Public Library of Science (PLoS). - 1553-7358 .- 1553-734X. ; 5:11
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Forskningsöversikt (refereegranskat)abstract
- The use of computational modeling and simulation has increased in many biological fields, but despite their potential these techniques are only marginally applied in nutritional sciences. Nevertheless, recent applications of modeling have been instrumental in answering important nutritional questions from the cellular up to the physiological levels. Capturing the complexity of today's important nutritional research questions poses a challenge for modeling to become truly integrative in the consideration and interpretation of experimental data at widely differing scales of space and time. In this review, we discuss a selection of available modeling approaches and applications relevant for nutrition. We then put these models into perspective by categorizing them according to their space and time domain. Through this categorization process, we identified a dearth of models that consider processes occurring between the microscopic and macroscopic scale. We propose a "middle-out" strategy to develop the required full-scale, multilevel computational models. Exhaustive and accurate phenotyping, the use of the virtual patient concept, and the development of biomarkers from "-omics" signatures are identified as key elements of a successful systems biology modeling approach in nutrition research--one that integrates physiological mechanisms and data at multiple space and time scales.
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| 9. |
- de Prenter, Frits, et al.
(författare)
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Stability and conditioning of immersed finite element methods : analysis and remedies
- 2023
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Ingår i: Archives of Computational Methods in Engineering. - : Springer Nature. - 1134-3060 .- 1886-1784. ; 30, s. 3617-3656
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Forskningsöversikt (refereegranskat)abstract
- This review paper discusses the developments in immersed or unfitted finite element methods over the past decade. The main focus is the analysis and the treatment of the adverse effects of small cut elements. We distinguish between adverse effects regarding the stability and adverse effects regarding the conditioning of the system, and we present an overview of the developed remedies. In particular, we provide a detailed explanation of Schwarz preconditioning, element aggregation, and the ghost penalty formulation. Furthermore, we outline the methodologies developed for quadrature and weak enforcement of Dirichlet conditions, and we discuss open questions and future research directions.
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| 10. |
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