Oberwolfach Publications
http://publications.mfo.de:80
The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sun, 05 Feb 2023 05:19:06 GMT2023-02-05T05:19:06ZOberwolfach Publicationshttp://publications.mfo.de/themes/Mirage2/images/apple-touch-icon.png
http://publications.mfo.de:80
Convolution in Dual Cesàro Sequence Spaces
http://publications.mfo.de/handle/mfo/4002
Convolution in Dual Cesàro Sequence Spaces
Curbera, Guillermo P.; Ricker, Werner J.
We investigate convolution operators in the sequence spaces $d_p$, for 1 $\leqslant p<\infty$. These spaces, for $p$ > 1, arise as dual spaces of the Cesàro sequence spaces $ces_p$ thoroughly investigated by G. Bennett. A detailed study is also made of the algebra of those sequences which convolve $d_p$ into $d_p$. It turns out that such multiplier spaces exhibit features which are very different to the classical multiplier spaces of $l^{p}$.
Fri, 16 Dec 2022 00:00:00 GMThttp://publications.mfo.de/handle/mfo/40022022-12-16T00:00:00ZCurbera, Guillermo P.Ricker, Werner J.We investigate convolution operators in the sequence spaces $d_p$, for 1 $\leqslant p<\infty$. These spaces, for $p$ > 1, arise as dual spaces of the Cesàro sequence spaces $ces_p$ thoroughly investigated by G. Bennett. A detailed study is also made of the algebra of those sequences which convolve $d_p$ into $d_p$. It turns out that such multiplier spaces exhibit features which are very different to the classical multiplier spaces of $l^{p}$.Hutchinson's Intervals and Entire Functions from the Laguerre-Pólya Class
http://publications.mfo.de/handle/mfo/4001
Hutchinson's Intervals and Entire Functions from the Laguerre-Pólya Class
Nguyen, Thu Hien; Vishnyakova, Anna
We find the intervals $[\alpha, \beta (\alpha)]$ such that if a univariate real polynomial or entire function $f(z) = a_0 + a_1 z + a_2 z^2 + \cdots $ with positive coefficients satisfy the conditions $ \frac{a_{k-1}^2}{a_{k-2}a_{k}} \in [\alpha, \beta(\alpha)]$ for all $k \geq 2,$ then $f$ belongs to the Laguerre-Pólya class. For instance, from J.I. Hutchinson's theorem, one can observe that $f$ belongs to the Laguerre-Pólya class (has only real zeros) when $q_k(f) \in [4, + \infty).$ We are interested in finding those intervals which are not subsets of $[4, + \infty).$
Mon, 12 Dec 2022 00:00:00 GMThttp://publications.mfo.de/handle/mfo/40012022-12-12T00:00:00ZNguyen, Thu HienVishnyakova, AnnaWe find the intervals $[\alpha, \beta (\alpha)]$ such that if a univariate real polynomial or entire function $f(z) = a_0 + a_1 z + a_2 z^2 + \cdots $ with positive coefficients satisfy the conditions $ \frac{a_{k-1}^2}{a_{k-2}a_{k}} \in [\alpha, \beta(\alpha)]$ for all $k \geq 2,$ then $f$ belongs to the Laguerre-Pólya class. For instance, from J.I. Hutchinson's theorem, one can observe that $f$ belongs to the Laguerre-Pólya class (has only real zeros) when $q_k(f) \in [4, + \infty).$ We are interested in finding those intervals which are not subsets of $[4, + \infty).$Closed geodesics on surfaces
http://publications.mfo.de/handle/mfo/3998
Closed geodesics on surfaces
Dozier, Benjamin
We consider surfaces of three types: the sphere, the torus, and many-holed tori. These surfaces naturally admit geometries of positive, zero, and negative curvature, respectively. It is interesting to study straight line paths, known as geodesics, in these geometries. We discuss the issue of counting closed geodesics; this is particularly rich for hyperbolic (negatively curved) surfaces.
Thu, 08 Dec 2022 00:00:00 GMThttp://publications.mfo.de/handle/mfo/39982022-12-08T00:00:00ZDozier, BenjaminWe consider surfaces of three types: the sphere, the torus, and many-holed tori. These surfaces naturally admit geometries of positive, zero, and negative curvature, respectively. It is interesting to study straight line paths, known as geodesics, in these geometries. We discuss the issue of counting closed geodesics; this is particularly rich for hyperbolic (negatively curved) surfaces.Route planning for bacteria
http://publications.mfo.de/handle/mfo/3997
Route planning for bacteria
Hellmuth, Kathrin; Klingenberg, Christian
Bacteria have been fascinating biologists since their discovery in the late 17th century. By analysing their movements, mathematical models have been developed as a tool to understand their behaviour. However, adapting these models to real situations can be challenging, because the model coefficients cannot be observed directly. In this snapshot, we study this question mathematically and explain how the idea of “route planning” can be used to determine these model coefficients.
Thu, 08 Dec 2022 00:00:00 GMThttp://publications.mfo.de/handle/mfo/39972022-12-08T00:00:00ZHellmuth, KathrinKlingenberg, ChristianBacteria have been fascinating biologists since their discovery in the late 17th century. By analysing their movements, mathematical models have been developed as a tool to understand their behaviour. However, adapting these models to real situations can be challenging, because the model coefficients cannot be observed directly. In this snapshot, we study this question mathematically and explain how the idea of “route planning” can be used to determine these model coefficients.Characterizations of intrinsic volumes on convex bodies and convex functions
http://publications.mfo.de/handle/mfo/3996
Characterizations of intrinsic volumes on convex bodies and convex functions
Mussnig, Fabian
If we want to express the size of a two-dimensional shape with a number, then we usually think about its area or circumference. But what makes these quantities so special? We give an answer to this question in terms of classical mathematical results. We also take a look at applications and new generalizations to the setting of functions.
Thu, 08 Dec 2022 00:00:00 GMThttp://publications.mfo.de/handle/mfo/39962022-12-08T00:00:00ZMussnig, FabianIf we want to express the size of a two-dimensional shape with a number, then we usually think about its area or circumference. But what makes these quantities so special? We give an answer to this question in terms of classical mathematical results. We also take a look at applications and new generalizations to the setting of functions.Quasi-Equilibria and Click Times for a Variant of Muller's Ratchet
http://publications.mfo.de/handle/mfo/3993
Quasi-Equilibria and Click Times for a Variant of Muller's Ratchet
González Casanova, Adrian; Smadi, Charline; Wakolbinger, Anton
Consider a population of $N$ individuals, each of them carrying a type in $\mathbb N_0$. The population evolves according to a Moran dynamics with selection and mutation, where an individual of type $k$ has the same selective advantage over all individuals with type $k' > k$, and type $k$ mutates to type
$k+1$ at a constant rate. This model is thus a variation of the classical Muller's ratchet: there the selective advantage is proportional to $k' - k$. For a regime of selection strength and mutation rates which is between the regimes of weak and strong selection/mutation, we obtain the asymptotic rate of the click times of the ratchet (i.e. the times at which the hitherto minimal ('best') type in the population is lost), and reveal the quasi-stationary type frequency profile between clicks. The large population limit of this profile is characterized as the normalized attractor of a "dual" hierarchical multitype logistic system, and also via the distribution of the final minimal
displacement in a branching random walk with one-sided steps. An important role in the proofs is played by a graphical representation of the model, both forward and backward in time, and a central tool is the ancestral selection graph decorated by mutations.
Wed, 30 Nov 2022 00:00:00 GMThttp://publications.mfo.de/handle/mfo/39932022-11-30T00:00:00ZGonzález Casanova, AdrianSmadi, CharlineWakolbinger, AntonConsider a population of $N$ individuals, each of them carrying a type in $\mathbb N_0$. The population evolves according to a Moran dynamics with selection and mutation, where an individual of type $k$ has the same selective advantage over all individuals with type $k' > k$, and type $k$ mutates to type
$k+1$ at a constant rate. This model is thus a variation of the classical Muller's ratchet: there the selective advantage is proportional to $k' - k$. For a regime of selection strength and mutation rates which is between the regimes of weak and strong selection/mutation, we obtain the asymptotic rate of the click times of the ratchet (i.e. the times at which the hitherto minimal ('best') type in the population is lost), and reveal the quasi-stationary type frequency profile between clicks. The large population limit of this profile is characterized as the normalized attractor of a "dual" hierarchical multitype logistic system, and also via the distribution of the final minimal
displacement in a branching random walk with one-sided steps. An important role in the proofs is played by a graphical representation of the model, both forward and backward in time, and a central tool is the ancestral selection graph decorated by mutations.Jahresbericht | Annual Report - 2021
http://publications.mfo.de/handle/mfo/3991
Jahresbericht | Annual Report - 2021
Mathematisches Forschungsinstitut Oberwolfach
Sat, 01 Jan 2022 00:00:00 GMThttp://publications.mfo.de/handle/mfo/39912022-01-01T00:00:00ZMathematisches Forschungsinstitut OberwolfachA tale of three curves
http://publications.mfo.de/handle/mfo/3986
A tale of three curves
Balakrishnan, Jennifer S.
In this snapshot, we give a survey of some problems in the study of rational points on higher genus curves, discussing questions ranging from the era of the ancient Greeks to a few posed by mathematicians of the 20th century. To answer these questions, we describe a selection of techniques in modern number theory that can be used to determine the set of rational points on a curve.
Thu, 27 Oct 2022 00:00:00 GMThttp://publications.mfo.de/handle/mfo/39862022-10-27T00:00:00ZBalakrishnan, Jennifer S.In this snapshot, we give a survey of some problems in the study of rational points on higher genus curves, discussing questions ranging from the era of the ancient Greeks to a few posed by mathematicians of the 20th century. To answer these questions, we describe a selection of techniques in modern number theory that can be used to determine the set of rational points on a curve.What is pattern?
http://publications.mfo.de/handle/mfo/3983
What is pattern?
Baake, Michael; Grimm, Uwe; Moody, Robert V.
Pattern is ubiquitous and seems totally familiar. Yet if we ask what it is, we find a bewildering collection of answers. Here we suggest that there is a common thread, and it revolves around dynamics.
Tue, 25 Oct 2022 00:00:00 GMThttp://publications.mfo.de/handle/mfo/39832022-10-25T00:00:00ZBaake, MichaelGrimm, UweMoody, Robert V.Pattern is ubiquitous and seems totally familiar. Yet if we ask what it is, we find a bewildering collection of answers. Here we suggest that there is a common thread, and it revolves around dynamics.Biological shape analysis with geometric statistics and learning
http://publications.mfo.de/handle/mfo/3985
Biological shape analysis with geometric statistics and learning
Utpala, Saiteja; Miolane, Nina
The advances in biomedical imaging techniques have enabled us to access the 3D shapes of a variety of structures: organs, cells, proteins. Since biological shapes are related to physiological functions, shape data may hold the key to unlocking outstanding mysteries in biomedicine. This snapshot introduces the mathematical framework of geometric statistics and learning and its applications to biomedicine.
Tue, 25 Oct 2022 00:00:00 GMThttp://publications.mfo.de/handle/mfo/39852022-10-25T00:00:00ZUtpala, SaitejaMiolane, NinaThe advances in biomedical imaging techniques have enabled us to access the 3D shapes of a variety of structures: organs, cells, proteins. Since biological shapes are related to physiological functions, shape data may hold the key to unlocking outstanding mysteries in biomedicine. This snapshot introduces the mathematical framework of geometric statistics and learning and its applications to biomedicine.