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| 4. |
- Maad Sasane, Sara, et al.
(författare)
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Generators for rings of compactly supported distributions
- 2011
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Ingår i: Integral equations and operator theory. - : Springer Science and Business Media LLC. - 0378-620X .- 1420-8989. ; 69:1, s. 63-71
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Tidskriftsartikel (refereegranskat)abstract
- Let CUnknown control sequence '\tt' denote a closed convex cone in \mathbb RdRd with apex at 0. We denote by E¢(C)Unknown control sequence '\tt' the set of distributions on \mathbb RdRd having compact support contained in CUnknown control sequence '\tt'. Then E¢(C)Unknown control sequence '\tt' is a ring with the usual addition and with convolution. We give a necessary and sufficient analytic condition on [^(f)]1,..., [^(f)]nf1fn for f1,... ,fn Î E¢(C)Unknown control sequence '\tt' to generate the ring E¢(C)Unknown control sequence '\tt'. (Here [^( · )] denotes Fourier-Laplace transformation.) This result is an application of a general result on rings of analytic functions of several variables by Lars Hörmander. En route we answer an open question posed by Yutaka Yamamoto.
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| 5. |
- Sasane, Sara Maad, et al.
(författare)
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A FRIENDLY APPROACH TO COMPLEX ANALYSIS : 2nd edition
- 2023. - 2nd
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Bok (refereegranskat)abstract
- The book constitutes a basic, concise, yet rigorous first course in complex analysis, for undergraduate students who have studied multivariable calculus and linear algebra. The textbook should be particularly useful for students of joint programmes with mathematics, as well as engineering students seeking rigour. The aim of the book is to cover the bare bones of the subject with minimal prerequisites. The core content of the book is the three main pillars of complex analysis: the Cauchy-Riemann equations, the Cauchy Integral Theorem, and Taylor and Laurent series. Each section contains several problems, which are not drill exercises, but are meant to reinforce the fundamental concepts. Detailed solutions to all the 243 exercises appear at the end of the book, making the book ideal for self-study. There are many figures illustrating the text. The second edition corrects errors from the first edition, and includes 89 new exercises, some of which cover auxiliary topics that were omitted in the first edition. Two new appendices have been added, one containing a detailed rigorous proof of the Cauchy Integral Theorem, and another providing background in real analysis needed to make the book self-contained.
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- Agmon, Shmuel, et al.
(författare)
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Persistence of embedded eigenvalues
- 2011
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Ingår i: Journal of Functional Analysis. - : Elsevier BV. - 0022-1236 .- 1096-0783. ; 261:2, s. 451-477
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Tidskriftsartikel (refereegranskat)abstract
- We consider conditions under. which an embedded eigenvalue of a self-adjoint operator remains embedded under small perturbations. In the case of a simple eigenvalue embedded in continuous spectrum of multiplicity m < infinity we show that in favorable situations, the set of small perturbations of a suitable Banach space which do not remove the eigenvalue form a smooth submanifold of codimension in. We also have results regarding the cases when the eigenvalue is degenerate or when the multiplicity of the continuous spectrum is infinite.
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- Aspenberg, Magnus, et al.
(författare)
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Hygiene may attenuate selection for antibiotic resistance by changing microbial community structure
- 2023
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Ingår i: Evolution, Medicine and Public Health. - : Oxford University Press (OUP). - 2050-6201. ; 11:1
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Tidskriftsartikel (refereegranskat)abstract
- Good hygiene, in both health care and the community, is central to containing the rise of antibiotic resistance, as well as to infection control more generally. But despite the well-known importance, the ecological mechanisms by which hygiene (or other transmission control measures) affect the evolution of resistance remain to be elucidated. Using metacommunity ecology theory, we here propose that hygiene attenuates the effect of antibiotic selection pressure. Specifically, we predict that hygiene limits the scope for antibiotics to induce competitive release of resistant bacteria within treated hosts, and that this is due to an effect of hygiene on the distribution of resistant and sensitive strains in the host population. We show this in a mathematical model of bacterial metacommunity dynamics, and test the results against data on antibiotic resistance, antibiotic treatment, and the use of alcohol-based hand rub in long-term care facilities. The data are consistent with hand rub use attenuating the resistance promoting effect of antibiotic treatment. Our results underscore the importance of hygiene, and point to a concrete way to weaken the link between antibiotic use and increasing resistance.
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- Derks, Gianne, et al.
(författare)
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Perturbations of embedded eigenvalues for the planar bilaplacian
- 2011
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Ingår i: Journal of Functional Analysis. - : Elsevier BV. - 0022-1236 .- 1096-0783. ; 260:2, s. 340-398
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Tidskriftsartikel (refereegranskat)abstract
- Operators on unbounded domains may acquire eigenvalues that are embedded in the essential spectrum. Determining the fate of these embedded eigenvalues under small perturbations of the underlying operator is a challenging task, and the persistence properties of such eigenvalues are linked intimately to the multiplicity of the essential spectrum. In this paper, we consider the planar bilaplacian with potential and show that the set of potentials for which an embedded eigenvalue persists is locally an infinite-dimensional manifold with infinite codimension in an appropriate space of potentials.
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- Eriksson, Olivia, et al.
(författare)
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Uncertainty quantification, propagation and characterization by Bayesian analysis combined with global sensitivity analysis applied to dynamical intracellular pathway models
- 2019
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Ingår i: Bioinformatics. - : Oxford University Press (OUP). - 1367-4803 .- 1367-4811. ; 35:2, s. 284-292
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Tidskriftsartikel (refereegranskat)abstract
- Motivation: Dynamical models describing intracellular phenomena are increasing in size and complexity as more information is obtained from experiments. These models are often over-parameterized with respect to the quantitative data used for parameter estimation, resulting in uncertainty in the individual parameter estimates as well as in the predictions made from the model. Here we combine Bayesian analysis with global sensitivity analysis (GSA) in order to give better informed predictions; to point out weaker parts of the model that are important targets for further experiments, as well as to give guidance on parameters that are essential in distinguishing different qualitative output behaviours.Results: We used approximate Bayesian computation (ABC) to estimate the model parameters from experimental data, as well as to quantify the uncertainty in this estimation (inverse uncertainty quantification), resulting in a posterior distribution for the parameters. This parameter uncertainty was next propagated to a corresponding uncertainty in the predictions (forward uncertainty propagation), and a GSA was performed on the predictions using the posterior distribution as the possible values for the parameters. This methodology was applied on a relatively large model relevant for synaptic plasticity, using experimental data from several sources. We could hereby point out those parameters that by themselves have the largest contribution to the uncertainty of the prediction as well as identify parameters important to separate between qualitatively different predictions. This approach is useful both for experimental design as well as model building.
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- Laptev, Ari, et al.
(författare)
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Perturbations of embedded eigenvalues for a magnetic Schrödinger operator on a cylinder
- 2017
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Ingår i: Journal of Mathematical Physics. - : AIP Publishing. - 0022-2488 .- 1089-7658. ; 58:1
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Tidskriftsartikel (refereegranskat)abstract
- Perturbation problems for operators with embedded eigenvalues are generally challenging since the embedded eigenvalues cannot be separated from the rest of the spectrum. In this paper, we study a perturbation problem for embedded eigenvalues for a magnetic Schrödinger operator, when the underlying domain is a cylinder. The magnetic potential is C2 with an algebraic decay rate as the unbounded variable of the cylinder tends to ±∞. In particular, no analyticity of the magnetic potential is assumed. We also assume that the embedded eigenvalue of the unperturbed problem is not the square of an integer, thus avoiding the thresholds of the continuous spectrum of the unperturbed operator. We show that the set of nearby potentials, for which a simple embedded eigenvalue persists, forms a smooth manifold of finite codimension.
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- Lasiecka, Irena, et al.
(författare)
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Existence and exponential decay of solutions to a quasilinear thermoelastic plate system
- 2008
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Ingår i: NoDEA. Nonlinear differential equations and applications (Printed ed.). - Basel : Birkhäuser. - 1021-9722 .- 1420-9004. ; 15:6, s. 689-715
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Tidskriftsartikel (refereegranskat)abstract
- We consider a quasilinear PDE system which models nonlinear vibrations of a thermoelastic plate defined on a bounded domain in , n ≤ 3. Existence of finite energy solutions describing the dynamics of a nonlinear thermoelastic plate is established. In addition asymptotic long time behavior of weak solutions is discussed. It is shown that finite energy solutions decay exponentially to zero with the rate depending only on the (finite energy) size of initial conditions. The proofs are based on methods of weak compactness along with nonlocal partial differential operator multipliers which supply the sought after “recovery” inequalities. Regularity of solutions is also discussed by exploiting the underlying analyticity of the linearized semigroup along with a related maximal parabolic regularity.
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| 12. |
- Maad Sasane, Sara
(författare)
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An age structured cell cycle model with crowding
- 2016
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Ingår i: Journal of Mathematical Analysis and Applications. - : Elsevier BV. - 0022-247X. ; 444:1, s. 768-803
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Tidskriftsartikel (refereegranskat)abstract
- We study a two compartment, nonlinear, age structured model for the cell cycle. The phases of the cell cycle G1, S, G2 and M are grouped into two phases, which we call Phase 1 and Phase 2, where Phase 1 consists of the phase G1 and Phase 2 consists of the phases S, G2 and M. It is assumed that Phase 1 has a variable duration while the duration of Phase 2 is fixed. The model consists of a system of nonlinear PDEs describing the number densities ni(t,τ), i=1,2, of cells in Phase i of age τ (counted from when the cell entered the phase) and time t, together with initial and boundary conditions for ni. We first prove that this initial and boundary value problem is equivalent to solving a system of integral equations. We then prove existence and uniqueness of this system of integral equations, and hence also of the original PDE system. Qualitative behaviour of solutions with small initial and input data is studied, and an application to quorum sensing is discussed. Finally, some simple numerical examples are computed using the derived integral equations.
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| 13. |
- Maad Sasane, Sara
(författare)
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Monotone Smoothing Splines with Bounds
- 2020
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Ingår i: Acta Applicandae Mathematicae. - : Springer Science and Business Media LLC. - 0167-8019 .- 1572-9036. ; 169:1, s. 613-627
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Tidskriftsartikel (refereegranskat)abstract
- The problem of monotone smoothing splines with bounds is formulated as a constrained minimization problem of the calculus of variations. Existence and uniqueness of solutions of this problem is proved, as well as the equivalence of it to a finite dimensional but nonlinear optimization problem. A new algorithm for computing the solution which is a spline curve, using a branch and bound technique, is presented. The method is applied to examples in neuroscience and for fitting cumulative distribution functions from data.
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| 14. |
- Sasane, Sara Maad, et al.
(författare)
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Perturbations of embedded eigenvalues for self-adjoint ODE systems
- 2023
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Ingår i: Arkiv for Matematik. - 0004-2080. ; 61:1, s. 177-202
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Tidskriftsartikel (refereegranskat)abstract
- We consider a perturbation problem for embedded eigenvalues of a self-adjoint differential operator in L2(R;Rn). In particular, we study the set of all small perturbations in an appropriate Banach space for which the embedded eigenvalue remains embedded in the continuous spectrum. We show that this set of small perturbations forms a smooth manifold and we specify its co-dimension. Our methods involve the use of exponential dichotomies, their roughness property and Lyapunov-Schmidt reduction.
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