SwePub - sökning: WFRF:(Bock Wolfgang)

Numrering	Referens	Omslagsbild	Hitta
1.	Bock, Maximilian, et al. (författare) Regular transformation groups based on Fourier-Gauss transforms 2015 Ingår i: Communications on Stochastic Analysis. - : LSU Library. - 0973-9599. ; 9:2, s. 181-203 Tidskriftsartikel (refereegranskat)
2.	Bock, Wolfgang, et al. (författare) Two generalizations of Mehler’s formula in white noise analysis 2023 Ingår i: Stochastics. - : Elsevier. - 1744-2508 .- 1744-2516. ; 95:4, s. 501-520 Tidskriftsartikel (refereegranskat)abstract Mehler's formula is an important tool in Gaussian analysis. In this article, we study two generalizations of Mehler's formula for the Ornstein–Uhlenbeck semigroup, i.e. the semigroup generated by the number operator. The first generalization leads to transformation groups which have as infinitesimal generator a perturbation of the number operator with suitable integral kernel operators, which are well studied in white noise analysis. For the second one, we characterize the complex Hida measures for which a version of Mehler's formula for the Ornstein–Uhlenbeck semigroup can be extended to. We apply this result to the Feynman integrand for a quadratic potential. Here the time independent eigenstates of the considered transformation groups and the time evolution of eigenvalues are provided.
3.	Abdul Salam, Parveena Shamim, et al. (författare) Disease contagion models coupled to crowd motion and mesh-free simulation 2021 Ingår i: Mathematical Models and Methods in Applied Sciences. - : World Scientific. - 0218-2025. ; 31:6, s. 1277-1295 Tidskriftsartikel (refereegranskat)abstract Modeling and simulation of disease spreading in pedestrian crowds have recently become a topic of increasing relevance. In this paper, we consider the influence of the crowd motion in a complex dynamical environment on the course of infection of the pedestrians. To model the pedestrian dynamics, we consider a kinetic equation for multi-group pedestrian flow based on a social force model coupled with an Eikonal equation. This model is coupled with a non-local SEIS contagion model for disease spread, where besides the description of local contacts, the influence of contact times has also been modeled. Hydrodynamic approximations of the coupled system are derived. Finally, simulations of the hydrodynamic model are carried out using a mesh-free particle method. Different numerical test cases are investigated, including uni- and bi-directional flow in a passage with and without obstacles.
4.	Abelev, Betty, et al. (författare) Measurement of prompt J/psi and beauty hadron production cross sections at mid-rapidity in pp collisions at root s=7 TeV 2012 Ingår i: Journal of High Energy Physics. - 1029-8479. ; :11 Tidskriftsartikel (refereegranskat)abstract The ALICE experiment at the LHC has studied J/psi production at mid-rapidity in pp collisions at root s = 7 TeV through its electron pair decay on a data sample corresponding to an integrated luminosity L-int = 5.6 nb(-1). The fraction of J/psi from the decay of long-lived beauty hadrons was determined for J/psi candidates with transverse momentum p(t) > 1,3 GeV/c and rapidity vertical bar y vertical bar < 0.9. The cross section for prompt J/psi mesons, i.e. directly produced J/psi and prompt decays of heavier charmonium states such as the psi(2S) and chi(c) resonances, is sigma(prompt J/psi) (p(t) > 1.3 GeV/c, vertical bar y vertical bar < 0.9) = 8.3 +/- 0.8(stat.) +/- 1.1 (syst.)(-1.4)(+1.5) (syst. pol.) mu b. The cross section for the production of b-hadrons decaying to J/psi with p(t) > 1.3 GeV/c and vertical bar y vertical bar < 0.9 is a sigma(J/psi <- hB) (p(t) > 1.3 GeV/c, vertical bar y vertical bar < 0.9) = 1.46 +/- 0.38 (stat.)(-0.32)(+0.26) (syst.) mu b. The results are compared to QCD model predictions. The shape of the p(t) and y distributions of b-quarks predicted by perturbative QCD model calculations are used to extrapolate the measured cross section to derive the b (b) over bar pair total cross section and d sigma/dy at mid-rapidity.
5.	Abelev, Betty, et al. (författare) Underlying Event measurements in pp collisions at root s=0.9 and 7 TeV with the ALICE experiment at the LHC 2012 Ingår i: Journal of High Energy Physics. - 1029-8479. ; :7 Tidskriftsartikel (refereegranskat)abstract We present measurements of Underlying Event observables in pp collisions at root s = 0 : 9 and 7 TeV. The analysis is performed as a function of the highest charged-particle transverse momentum p(T),L-T in the event. Different regions are defined with respect to the azimuthal direction of the leading (highest transverse momentum) track: Toward, Transverse and Away. The Toward and Away regions collect the fragmentation products of the hardest partonic interaction. The Transverse region is expected to be most sensitive to the Underlying Event activity. The study is performed with charged particles above three different p(T) thresholds: 0.15, 0.5 and 1.0 GeV/c. In the Transverse region we observe an increase in the multiplicity of a factor 2-3 between the lower and higher collision energies, depending on the track p(T) threshold considered. Data are compared to PYTHIA 6.4, PYTHIA 8.1 and PHOJET. On average, all models considered underestimate the multiplicity and summed p(T) in the Transverse region by about 10-30%.
6.	Adamik, Barbara, et al. (författare) Estimation of the Severeness Rate, Death Rate, Household Attack Rate and the Total Number of COVID-19 Cases Based on 16 115 Polish Surveillance Records 2020 Annan publikation (övrigt vetenskapligt/konstnärligt)abstract Background: Estimating the actual number of COVID-19 infections is crucial for steering through the COVID-19 pandemic crisis. It is, however, notoriously difficult, as many cases have no or only mild symptoms. Surveillance data for in-household secondary infections offers unbiased samples for COVID-19 prevalence estimation.Methods: We analyse 16 115 Polish surveillance records to obtain key figures of the COVID-19 pandemic. We propose conservative upper and lower bound estimators for the number of SARS-CoV-2 infections. Further, we estimate age-dependent bounds on the severe case rate, death rate, and the in-household attack rate.Results: By maximum likelihood estimates, the total number of COVID-19 cases in Poland as of July 22nd, 2020, is at most around 13 times larger and at least 1.6 times larger than the recorded number. The lower bound on the severeness rate ranges between 0.2% for the 0–39 year-old to 5.7% for older than 80, while the upper bound is between 2.6% and 34.1%. The lower bound on the death rate is between 0.04% for the age group 40–59 to 1.34% for the oldest. Overall, the severeness and death rates grow exponentially with age. The in-household attack ratio is 8.18% for the youngest group and 16.88% for the oldest.Conclusions: The proposed approach derives highly relevant figures on the COVID-19 pandemic from routine surveillance data, under assumption that household members of detected infected are tested and all severe cases are diagnosed.
7.	Ades, M., et al. (författare) Global Climate : in State of the climate in 2019 2020 Ingår i: Bulletin of The American Meteorological Society - (BAMS). - : American Meteorological Society. - 0003-0007 .- 1520-0477. ; 101:8, s. S17-S127 Tidskriftsartikel (refereegranskat)
8.	Ades, M., et al. (författare) GLOBAL CLIMATE 2020 Ingår i: BULLETIN OF THE AMERICAN METEOROLOGICAL SOCIETY. - 0003-0007 .- 1520-0477. ; 101:8 Tidskriftsartikel (refereegranskat)
9.	Bock, Wolfgang, et al. (författare) A Jordan-Schwinger Variant of the Spectral Theorem for Linear Operators 2024 Ingår i: Journal of Mathematical Analysis and Applications. - : Elsevier. - 0022-247X .- 1096-0813. ; 531:1 Tidskriftsartikel (refereegranskat)abstract In this paper we show variant of the spectral theorem using an algebraic Jordan-Schwinger map. The advantage of this approach is that we don't have restriction of normality on the class of operators we consider.
10.	Bock, Wolfgang, et al. (författare) A Poisson algebra on the Hida test functions and a quantization using the Cuntz algebra 2022 Ingår i: Letters in Mathematical Physics. - : Springer Science and Business Media LLC. - 0377-9017 .- 1573-0530. ; 112:2 Tidskriftsartikel (refereegranskat)abstract In this note, we define one more way of quantization of classical systems. The quantization we consider is an analogue of classical Jordan–Schwinger map which has been known and used for a long time by physicists. The difference, compared to Jordan–Schwinger map, is that we use generators of Cuntz algebra O∞ (i.e. countable family of mutually orthogonal partial isometries of separable Hilbert space) as a “building blocks” instead of creation–annihilation operators. The resulting scheme satisfies properties similar to Van Hove prequantization, i.e. exact conservation of Lie brackets and linearity.
11.	Bock, Wolfgang, et al. (författare) A talented monoid view on Lie bracket algebras over Leavitt path algebras 2023 Ingår i: Journal of Algebra and its Applications. - : World Scientific. - 0219-4988 .- 1793-6829. ; 22:8 Tidskriftsartikel (refereegranskat)abstract In this paper, we study properties such as simplicity, solvability and nilpotency for Lie bracket algebras arising from Leavitt path algebras, based on the talented monoid of the underlying graph. We show that graded simplicity and simplicity of the Leavitt path algebra can be connected via the Lie bracket algebra. Moreover, we use the Gelfand-Kirillov dimension for the Leavitt path algebra for a classification of nilpotency and solvability.
12.	Bock, Wolfgang, et al. (författare) A white noise approach to phase space Feynman path integrals 2012 Ingår i: Theory of Probability and Mathematical Statistics. - : Tara Shevchenko National University Kyiv. - 0094-9000 .- 1547-7363. ; 85, s. 7-22 Tidskriftsartikel (refereegranskat)abstract The concepts of phase space Feynman integrals in White Noise Analysis are established. As an example the harmonic oscillator is treated. The approach perfectly reproduces the right physics. I.e., solutions to the Schrodinger equation are obtained and the canonical commutation relations are satisfied. The later can be shown, since we not only construct the integral but rather the Feynman integrand and the corresponding generating functional.
13.	Bock, Wolfgang, et al. (författare) Algebraic Entropy of Path Algebras and Leavitt Path Algebras of Finite Graphs 2024 Ingår i: Results in Mathematics. - : Springer. - 1422-6383 .- 1420-9012. ; 79:5 Tidskriftsartikel (refereegranskat)abstract The Gelfand-Kirillov dimension is a well established quantity to classify the growth of infinite dimensional algebras. In this article we introduce the algebraic entropy for path algebras. For the path algebras, Leavitt path algebras and the path algebra of the extended (double) graph, we compare the Gelfand-Kirillov dimension and the entropy. We show that path algebras over finite graphs can be classified to be of finite dimension, finite Gelfand-Kirillov dimension or finite algebraic entropy. We show indeed how these three quantities are dependent on cycles inside the graph. Moreover we show that the algebraic entropy is conserved under Morita equivalence but perhaps for a different filtration. In addition we give several examples of the entropy in path algebras and Leavitt path algebras.
14.	Bock, Wolfgang, et al. (författare) An adjacency matrix perspective of talented monoids and Leavitt path algebras 2023 Ingår i: Linear Algebra and its Applications. - : Elsevier. - 0024-3795 .- 1873-1856. ; 678, s. 295-316 Tidskriftsartikel (refereegranskat)abstract In this article we establish relationships between Leavitt path algebras, talented monoids and the adjacency matrices of the underlying graphs. We show that indeed the adjacency matrix generates in some sense the group action on the generators of the talented monoid. With the help of this, we deduce a form of the aperiodicity index of a graph via the talented monoid. We classify hereditary and saturated subsets via the adjacency matrix. This then translates to a correspondence between the composition series of the talented monoid and the so-called matrix composition series of the adjacency matrix. In addition, we discuss the number of cycles in a graph. In particular, we give an equivalent characterization of acyclic graphs via the adjacency matrix, the talented monoid and the Leavitt path algebra. Finally, we compute the number of linearly independent paths of certain length in the Leavitt path algebra via adjacency matrices.
15.	Bock, Wolfgang, et al. (författare) An analytic method for agent-based modeling of spatially inhomogeneous disease dynamics 2017 Ingår i: Struccture, Function and Dynamics from nm to Gm. - : American Institute of Physics (AIP). - 9780735415515 Konferensbidrag (refereegranskat)abstract In this article we set up a microscopic model for the spread of an infectious disease based on configuration space analysis. Using the so-called Vlasov scaling we obtained the corresponding mesoscopic (kinetic) equations, describing the density of susceptible and infected individuals (particles) in space. The resulting system of equations can be seen as a generalization to a ‘spatial’ SIS-model. The equations showing up in the limiting system are of the type which is know in literature as Fisher–Kolmogorov–Petrovsky–Piscounov type.
16.	Bock, Wolfgang, et al. (författare) Analysis of stochastic quantization for the fractional Edwards measure 2018 Ingår i: Reports on mathematical physics. - : Elsevier. - 0034-4877 .- 1879-0674. ; 82:2, s. 187-202 Tidskriftsartikel (refereegranskat)abstract In [10] the existence of a diffusion process whose invariant measure is the fractional polymer or Edwards measure for fractional Brownian motion in dimension d ∈ ℕ with Hurst parameter H ∈ (0, 1) fulfilling dH < 1 is shown. This Markov process is constructed via Dirichlet form techniques in infinite-dimensional (Gaussian) analysis. This article uses these results as starting point. In particular, we provide a Fukushima decomposition for the stochastic quantization of the fractional Edwards measure and prove that the constructed process solves a stochastic differential equation in infinite dimension for quasi-all starting points in a probabilistically weak sense. Moreover, the solution process is driven by an Ornstein–Uhlenbeck process taking values in an infinite-dimensional distribution space and is unique, in the sense that the underlying Dirichlet form is Markov unique. The equilibrium measure, which is by construction the fractional Edwards measure, is specified to be an extremal Gibbs state and therefore the constructed stochastic dynamics is time ergodic. The studied stochastic differential equation provides in the language of polymer physics the dynamics of the bonds, i.e. stochastically spoken the noise of the process. An integration leads then to polymer paths.
17.	Bock, Wolfgang, et al. (författare) Applied school mathematics : Made in kaiserslautern 2015 Ingår i: Currents in Industrial Mathematics. - Berlin, Heidelberg : Springer. - 9783662482582 - 9783662482575 ; , s. 403-437 Bokkapitel (refereegranskat)abstract The role of mathematics in our society has undergone a dramatic change in recent years. In general, however, mathmatics instruction in schools has not kept pace with this change. Here, we describe the activities and events with which the Felix Klein Center for Mathematics, in Kaiserslautern, has tried to address this deficit. We first look briefly at mathematical modeling and illustrate how it fits into mathematics instruction. We then present examples of various didactic activities.
18.	Bock, Wolfgang, et al. (författare) Are the upper bounds for new SARS-CoV-2 infections in Germany useful? 2021 Ingår i: Computational and Mathematical Biophysis. - : Walter de Gruyter. - 2544-7297. ; 9:1, s. 242-260 Tidskriftsartikel (refereegranskat)abstract At the end of 2019, an outbreak of a new coronavirus, called SARS-CoV-2, was reported in China and later in other parts of the world. First infection reported in Germany by the end of January 2020 and on March 16th, 2020 the federal government announced a partial lockdown in order to mitigate the spread. Since the dynamics of new infections started to slow down, German states started to relax the confinement measures as to May 6th, 2020. As a fall back option, a limit of 50 new infections per 100,000 inhabitants within seven days was introduced for each district in Germany. If a district exceeds this limit, measures to control the spread of the virus should be taken. Based on a multi-patch SEAIRD-type model, we will simulate the effect of choosing a specific upper limit for new infections. We investigate, whether the politically motivated bound is low enough to detect new outbreaks at an early stage. Subsequently, we introduce an optimal control problem to tackle the multi-criteria problem of finding a bound for new infections that is low enough to avoid new outbreaks, which might lead to an overload of the health care system, but is large enough to curb the expected economic losses.
19.	Bock, Wolfgang, et al. (författare) Characterization and analysis of generalized grey incomplete gamma noise 2024 Ingår i: Stochastics. - : Taylor & Francis Group. - 1744-2508 .- 1744-2516. Tidskriftsartikel (refereegranskat)abstract The grey incomplete gamma distributions was established by one of the authors in a previous publication. In this article we use the Kondratiev characterization theorem to identify those via a suitable Laplace transform with holomorphic functions with suitable properties. We establish theorems for the integration and convergence of sequences of these distributions. As direct applications of these analytic tools we give the examples of Donsker's delta function, identify the time-derivative of the process as a suitable distribution and define the Gamma grey Ornstein-Uhlenbeck process.
20.	Bock, Wolfgang, et al. (författare) Convex topological algebras via linear vector fields and Cuntz algebras 2021 Ingår i: Journal of Pure and Applied Algebra. - : Elsevier. - 0022-4049 .- 1873-1376. ; 225:3 Tidskriftsartikel (refereegranskat)abstract A realization by linear vector fields is constructed for any Lie algebra which admits a biorthogonal system and for its any suitable representation. The embedding into Lie algebras of linear vector fields is in analogue to the classical Jordan—Schwinger map. A number of examples of such Lie algebras of linear vector fields is computed. In particular, we obtain examples of the twisted Heisenberg-Virasoro Lie algebra and the Schrödinger-Virasoro Lie algebras among others. More generally, we construct an embedding of an arbitrary locally convex topological algebra into the Cuntz algebra.
21.	Bock, Wolfgang, et al. (författare) Der unmögliche Freistoß 2016 Ingår i: Neue Materialien fuer einen realitaetsbezogenen Mathematikunterricht 3. - Wiesbaden : Springer. - 9783658119010 - 9783658119027 ; , s. 15-24 Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract Die Autoren befassen sich mit der Ableitung und Bearbeitung eines Modellierungsprojektes aus der populären Sportart Fußball: Ein Freistoß wird unter Beachtung der gegebenen physikalischen Effekte mathematisch modelliert und simuliert. Der Fokus liegt auf der möglichen Durchführung dieses Modellierungsprojekts mit Schülerinnen und Schülern der Sekundarstufe II.
22.	Bock, Wolfgang, et al. (författare) Dynamical properties of Gaussian chains and loops with long-range interactions 2021 Ingår i: Reports on mathematical physics. - : Elsevier. - 0034-4877 .- 1879-0674. ; 88:2, s. 233-246 Tidskriftsartikel (refereegranskat)abstract Various authors have invoked discretized fractional Brownian motion (fBm) as a model for chain polymers with long-range interaction of monomers along the chain. We show that for these, in contrast to the Brownian case, linear forces are acting between all pairs of constituents, attractive for small Hurst index H and mostly repulsive when H is larger than 1/2. In the second part of this paper, we extend this study to periodic fBm and related models with a view to ring polymers with long range interactions.
23.	Bock, Wolfgang, et al. (författare) Fractional Brownian motion : Some recent results and generalizations 2020 Ingår i: 9th Jagna International Workshop: Stochastic Analysis – Mathematical Methods and Real-World Models. - : American Institute of Physics (AIP). - 9780735440166 Konferensbidrag (refereegranskat)abstract In this article we present recent results in our ongoing study for weakly self-avoiding fractional processes leading to polymer models. In particular we sketch the results for stars and loops. For fractional random walks we give an explicit formula for the spring constants in the bead-spring model. Furthermore recent findings for the scaling properties of a weakly self-avoiding fractional Brownian motion are presented.
24.	Bock, Wolfgang, et al. (författare) Fractional periodic processes : properties and an application of polymer form factors 2020 Ingår i: Reports on mathematical physics. - : Elsevier. - 0034-4877 .- 1879-0674. ; 85:2, s. 267-280 Tidskriftsartikel (refereegranskat)abstract In this paper we introduce and study three classes of fractional periodic processes. An application to ring polymers is investigated. We obtain closed analytic expressions for the form factors, the Debye functions and their asymptotic decay. The relation between the end-to-halftime and radius of gyration is computed for these classes of periodic processes.
25.	Bock, Wolfgang, et al. (författare) Generalized Mittag-Leffler kernels and generalized scaling operators in Mittag-Leffler analysis 2021 Ingår i: Methods of Functional Analysis and Topology. - : Institute of Mathematics. - 2415-7503. ; 27:4, s. 308-319 Tidskriftsartikel (refereegranskat)abstract Generalized scaling operators and generalized Gauss kernels are fundamental concepts in Gaussian analysis with application to path integrals and PDEs via the Feynman-Kac formula. In non-Gaussian analysis, particularly in Mittag-Leffler analysis, i.e., in the case when compared to a Gaussian characteristic function the exponential is replaced by a Mittag-Leffler function, these concepts are unknown. In view of this, we elaborate in this article the generalized scaling and generalized Mittag-Leffler kernels and prove a form of a Wick-type product formula. We give some first examples for generalized scaling.
26.	Bock, Wolfgang (författare) Generalized scaling operators in white noise analysis and applications to Hamiltonian path integrals with quadratic action 2016 Ingår i: Stochastic and Infinite Dimensional Analysis. - Cham : Springer. - 9783319072449 - 9783319072456 ; , s. 51-73 Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract We give an outlook, how to realize the ideas of complex scaling from [15–17] to phase space path integrals in the framework of White Noise Analysis. The idea of this scaling method goes back to [9]. Therefore we extend the concept complex scaling to scaling with suitable bounded operators.
27.	Bock, Wolfgang (författare) Hamiltonian path integrals in momentum space representation via white noise techniques 2014 Ingår i: Reports on mathematical physics. - : Elsevier. - 0034-4877 .- 1879-0674. ; 73:1, s. 91-107 Tidskriftsartikel (refereegranskat)abstract The concepts of Feynman integrals in white noise analysis are used to construct the Feynman integrand for the harmonic oscillator in momentum space representation as a Hida distribution. Moreover it is shown that in a limit sense, the potential free case fulfills the conservation of momentum.
28.	Bock, Wolfgang (författare) How to use white noise analysis to make Feynman integrals mathematically rigorous 2017 Ingår i: Let us use white noise. - : World Scientific. - 9789813220942 - 9789813220959 ; , s. 67-115 Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract In this chapter we summarize applications of White Noise Analysis within the framework of Feynman Path Integrals. With more than 30 years of intensive study this field can be seen as one of the most important applications. Of course this chapter cannot give an exhaustive summary of all approaches to different path integrals in White Noise Analysis. Here we give a slice through different attemtps to path integrals in the White Noise framework.
29.	Bock, Wolfgang, et al. (författare) Integral representation of generalized grey Brownian motion 2020 Ingår i: Stochastics. - : Taylor & Francis. - 1744-2508 .- 1744-2516. ; 92:4, s. 552-565 Tidskriftsartikel (refereegranskat)abstract In this paper, we investigate the representation of a class of non-Gaussian processes, namely generalized grey Brownian motion, in terms of a weighted integral of a stochastic process which is a solution of a certain stochastic differential equation. In particular, the underlying process can be seen as a non-Gaussian extension of the Ornstein–Uhlenbeck process, hence generalizing the representation results of Muravlev, Russian Math. Surveys 66 (2), 2011 as well as Harms and Stefanovits, Stochastic Process. Appl. 129, 2019 to the non-Gaussian case.
30.	Bock, Wolfgang, et al. (författare) Local times for multifractional Brownian motion in higher dimensions : a white noise approach 2016 Ingår i: Infinite Dimensional Analysis Quantum Probability and Related Topics. - : World Scientific. - 0219-0257. ; 19:4 Tidskriftsartikel (refereegranskat)abstract We present the expansion of the multifractional Brownian motion (mBm) local time in higher dimensions, in terms of Wick powers of white noises (or multiple Wiener integrals). If a suitable number of kernels is subtracted, they exist in the sense of generalized white noise functionals. Moreover, we show the convergence of the regularized truncated local times for mBm in the sense of Hida distributions.
31.	Bock, Wolfgang, et al. (författare) Modellierung und Simulation von Krankheitsausbreitungen 2018 Ingår i: Digitale Werkzeuge, Simulationen und mathematisches Modellieren. - Wiesbaden : Springer. - 9783658219390 - 9783658219406 ; , s. 121-136 Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract In diesem Artikel zeigen wir auf, wie eine räumliche und zeitliche Krankheitsdynamik in der Sekundarstufe 2 behandelt werden kann. Wir beschränken uns hier auf Krankheiten, die von Mensch zu Mensch übertragbar sind, wie etwa Grippe und Ebola. Dabei spielt die Simulation am Computer eine zentrale Rolle. Die benutzten Methoden hierbei sind zelluläre Automaten und explizite Euler-Algorithmen zur Lösung von Differentialgleichungen.
32.	Bock, Wolfgang, et al. (författare) Numerical simulation of agent-based modeling of spatially inhomogeneous disease dynamics 2017 Ingår i: Structure, Function and Dynamics from NM to GM. - : American Institute of Physics (AIP). - 9780735415515 Konferensbidrag (refereegranskat)abstract In recent years much about the modeling and understanding of various types of disease spreading and epidemic behavior have been studied. In principle one can distinguish two types of models for disease spread. On the one hand there is the classical SIR-model from Kermack and McKendrick [1] which describes the time evolution of the number of susceptible (S), infected (I) and recovered (R) individuals by a system of ordinary differential equations. This model has been developed and extended exhaustively in the last 90 years. Among those extensions are the introduction of new compartments to model vector-bourne diseases, see e.g. [2], delay equations to model incubation time, e.g. [3], models considering the age and wealth structure etc. Recently, models with fractional derivatives have also been considered[4]. Unfortunately, we are unable to provide a detailed account concerning this subject and refer the interested reader to [5]. A main drawback of the models described above is that they do not provide any information about the spatial spread of a disease. Nevertheless, there have been various approaches to link many different SIR-areas to obtain spatial behavior. In the SIR-model case, an advection-diffusion equation has been identified as the limiting equation,see e.g. [6]. Another approach in incorporating spatial information for the SIR-model may also be found in [7]. Although the SIR-model and all its extensions are very flexible in describing the different aspects of disease dynamics, the modeling assumptions of the disease spread is purely on the macroscopic level. However, for many different diseases the infection mechanism is only known on the microscopic, i.e., particle-to-particle or individ uumto-individuum level. One way to consider both microscopical modeling and spatial resolution is to describe of the disease dynamics by means of an interacting particle system with suitable interaction potentials. Fundamental in this area are dynamics in so-called marked configuration spaces [8]. These techniques together with a proper scaling of the microscopic system,the so-called Vlasov scaling, have been recently used to model the dynamics of cancer cells [9]. In our approach the components of particle configurations consist of susceptible and infected/infective particles that interact with one another. One may also easily incorporate other types of particles to model recovery or short time immunity. Themicroscopic dynamics then results from suitable ”spin-flip”-processes (particle changes the type).This article shows first numerical results for the SIS-system without movement. The SIS-system allows infective/infected particles to recover and become susceptible again. The numerical methods are based on the analysis provided in [10].
33.	Bock, Wolfgang, et al. (författare) On Solvable Lie Algebras of White Noise Operators 2022 Ingår i: Symmetry. - : MDPI. - 2073-8994. ; 14:11 Tidskriftsartikel (refereegranskat)abstract We characterize the dimension of Lie algebras of white noise operators containing the quantum white noise derivatives of the conservation operator. We establish isomorphisms to filiform Lie algebras, Engel-type algebras, and solvable Lie algebras with Heisenberg nilradical and Abelian nilradical. A new class of solvable Lie algebras is proposed, those having an Engel-type algebra as nilradical. This arises in white noise analysis as a (Formula presented.) -dimensional Lie algebra containing the identity operator, annihilation operators, creation operators (Heisenberg algebra), number operator, and Gross Laplacian.
34.	Bock, Wolfgang, et al. (författare) On the potential in non-Gaussian chain polymer models 2019 Ingår i: Mathematical methods in the applied sciences. - : John Wiley & Sons. - 0170-4214 .- 1099-1476. ; 42:18, s. 7452-7460 Tidskriftsartikel (refereegranskat)abstract In this paper, we investigate the potential for a class of non-Gaussian processes so-called generalized grey Brownian motion. We obtain a closed analytic form for the potential as an integral of the M-Wright functions and the Green function. In particular, we recover the special cases of Brownian motion and fractional Brownian motion. In addition, we give the connection to a fractional partial differential equation and its the fundamental solution.
35.	Bock, Wolfgang, et al. (författare) Optimal control and basic reproduction numbers for a compartmental spatial multipatch dengue model 2018 Ingår i: Mathematical methods in the applied sciences. - : Elsevier. - 0170-4214 .- 1099-1476. ; 41:9, s. 3231-3245 Tidskriftsartikel (refereegranskat)abstract Dengue is a vector-borne viral disease increasing dramatically over the past years due to improvement in human mobility. In this work, a multipatch model for dengue transmission dynamics is studied, and by that, the control efforts to minimize the disease spread by host and vector control are investigated. For this model, the basic reproduction number is derived, giving a choice for parameters in the endemic case. The multipatch system models the host movement within the patches, which coupled via a residence-time budgeting matrix P. Numerical results confirm that the control mechanism embedded in incidence rates of the disease transmission effectively reduces the spread of the disease.
36.	Bock, Wolfgang, et al. (författare) Optimal control of a multi-patch dengue model under the influence of Wolbachia bacterium 2019 Ingår i: Mathematical Biosciences. - : Elsevier. - 0025-5564 .- 1879-3134. ; 315 Tidskriftsartikel (refereegranskat)abstract In this work, a multi-patch model for dengue transmission dynamics including the bacterium Wolbachia is studied and by that the control efforts to minimize the disease spread by host and vector control are investigated. The multi-patch system models the host movement within the patches which coupled via a residence-time budgeting matrix P. Numerical results confirm that the control mechanism embedded in incidence rates of the disease transmission, effectively reduce the spread of the disease.
37.	Bock, Wolfgang, et al. (författare) Parameter estimation from occupation times : a white noise approach 2014 Ingår i: Communcations on Stocastic Analysis. - : LSU Library. - 2688-6669 .- 0973-9599. ; 8:4 Tidskriftsartikel (refereegranskat)abstract We derive an equation to compute directly the expected occupation time of the centered Ornstein–Uhlenbeck process. This allows us toidentify the parameters of the Ornstein–Uhlenbeck process for available occupation times via a standard least squares minimization. To test the method,we generate occupation times via Monte–Carlo simulations and recover theparameters with the above mentioned procedure.
38.	Bock, Wolfgang, et al. (författare) Parameter estimation of fiber lay-down in nonwoven production : an occupation time approach 2018 Ingår i: International Journal of Advances in Engineering Sciences and Applied Mathematics. - : Springer. - 0975-0770 .- 0975-5616. ; 10:1, s. 2-8 Tidskriftsartikel (refereegranskat)abstract In this paper we investigate the parameter estimation of the fiber lay-down process in the production of nonwovens. The parameter estimation is based on the mass per unit area data, which is available at least on an industrial scale. We introduce a stochastic model to represent the fiber lay-down and through the model’s parameters we characterize this fiber lay-down. Based on the occupation time, which is the equivalent quantity for the mass per unit area in the context of stochastic dynamical systems, an optimization procedure is formulated that estimates the parameters of the model. The optimization procedure is tested using occupation time data given by Monte–Carlo simulations. The feasibility of the optimization procedure on an industrial level is tested using the fiber paths simulated by the industrial software FYDIST.
39.	Bock, Wolfgang, et al. (författare) Polymer measure : Varadhan’s renormalization revisited 2015 Ingår i: Reviews in Mathematical Physics. - : World Scientific. - 0129-055X. ; 27:3 Tidskriftsartikel (refereegranskat)abstract Through chaos decomposition, we improve the Varadhan estimate for the rate of convergence of the centered approximate self-intersection local time of planar Brownian motion.
40.	Bock, Wolfgang, et al. (författare) Scaling properties of weakly self-avoiding fractional Brownian motion in one dimension 2015 Ingår i: Journal of statistical physics. - : Springer. - 0022-4715 .- 1572-9613. ; 161:5, s. 1155-1162 Tidskriftsartikel (refereegranskat)abstract We use an off-lattice discretization of fractional Brownian motion (fBm) and a Metropolis algorithm to determine the asymptotic scaling of this discretized fBm under the influence of an excluded volume as in the Edwards and Domb–Joyce models. We find a good agreement between the Flory index describing the scaling of end-to-end length with a mean field formula proposed earlier for this class of models.
41.	Bock, Wolfgang, et al. (författare) Self-intersection local times for multifractional Brownian motion in higher dimensions : a white noise approach 2020 Ingår i: Infinite Dimensional Analysis Quantum Probability and Related Topics. - : World Scientific. - 0219-0257. ; 23:1 Tidskriftsartikel (refereegranskat)abstract In this paper, we study the self-intersection local times of multifractional Brownian motion (mBm) in higher dimensions in the framework of white noise analysis. We show that when a suitable number of kernel functions of self-intersection local times of mBm are truncated then we obtain a Hida distribution. In addition, we present the expansion of the self-intersection local times in terms of Wick powers of white noises. Moreover, we obtain the convergence of the regularized truncated self-intersection local times in the sense of Hida distributions.
42.	Bock, Wolfgang, et al. (författare) Stochastic analysis for vector-valued generalized grey Brownian motion 2023 Ingår i: Theory Probability and Mathematical Statistics. - : American Mathematical Society (AMS). - 0094-9000 .- 1547-7363. ; :108, s. 1-27 Tidskriftsartikel (refereegranskat)abstract In this article, we show that the standard vector-valued generalization of a generalized grey Brownian motion (ggBm) has independent components if and only if it is a fractional Brownian motion. In order to extend ggBm with independent components, we introduce a vector-valued generalized grey Brownian motion (vggBm). The characteristic function of the corresponding measure is introduced as the product of the characteristic functions of the one-dimensional case. We show that for this measure, the Appell system and a calculus of generalized functions or distributions are accessible. We characterize these distributions with suitable transformations and give a d-dimensional Donsker’s delta function as an example for such distributions. From there, we show the existence of local times and self-intersection local times of vggBm as distributions under some constraints, and compute their corresponding generalized expectations. At the end, we solve a system of linear SDEs driven by a vggBm noise in d dimensions.
43.	Bock, Wolfgang, et al. (författare) Stochastic quantization for the fractional Edwards measure 2017 Ingår i: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications. - : Springer. - 0167-8019 .- 1572-9036. ; 151, s. 81-88 Tidskriftsartikel (refereegranskat)abstract We prove that there exists a diffusion process whose invariant measure is the fractional polymer or Edwards measure for fractional Brownian motion, μg , H, H∈ (0 , 1) for dH< 1. The diffusion is constructed in the framework of Dirichlet forms in infinite dimensional (Gaussian) analysis. Moreover, the process is invariant under time translations.
44.	Bock, Wolfgang, et al. (författare) Teamcycling : Optimales Teamtraining im Radsport 2014 Ingår i: Neue Materialien fuer einen realitätsbezogenen Mathematikunterricht 2. - Wiesbaden : Springer. ; , s. 1-9 Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract Das Gruppentraining im Radsport ermöglicht es, dass viele Fahrer nahe ihres optimalen Pulsbereichs trainieren und trotzdem in hohem Tempo fahren können. Hierbei wird der Trainingspuls mittels Führungswechseln gesteuert. In diesem Beitrag wird aufgezeigt, wie dieses Thema als Modellierungsprojekt, welches interdisziplinäre Fragestellungen aus den Gebieten Mathematik, Physik, Biologie, Sport und Informatik beinhaltet, für die Sekundarstufe II genutzt werden kann. Weiterhin werden Erweiterungen und Vereinfachungen zur Umsetzung skizziert.
45.	Bock, Wolfgang, et al. (författare) Testing, social distancing and age specific quarantine for COVID-19 : Case studies in Iligan City and Cagayan de Oro City, Philippines 2020 Ingår i: 9th Jagna International Workshop Stochastic Analysis – Mathematical Methods and Real-World Models, 8–18 January 2020, Bohol, Philippines. - : American Institute of Physics (AIP). - 9780735440166 Konferensbidrag (refereegranskat)abstract The world today grapples with the health crisis caused by the novel COVID-19. Unfortunately, the Philippines, which was spared from the previous epidemics like Ebola and SARS, is now facing this major obstacle. The local government units of the country responded by issuing guidelines to mitigate the spread of infection. Two neighboring cities in the Philippines, namely, Iligan and Cagayan de Oro have been the focus of this study. Simulations have been undertaken to investigate the prevalence of the disease and the health care systems capacity to accommodate critically ill patients over time. The effects of mitigating strategies like social distancing, age specific quarantine and testing were considered. The model used for the spread of COVID-19 is an individual-based SIR model. The results indicated that social distancing and age specific quarantine can effectively slow down the progression of the disease. Moreover, social distancing combined with an effective testing strategy can keep the epidemic subcritical.
46.	Bock, Wolfgang, et al. (författare) The Edwards model for fractional Brownian loops and starbursts 2021 Ingår i: Journal of Stochastic Analysis. - : Louisiana State University Libraries. - 2689-6931. ; 2:2 Tidskriftsartikel (refereegranskat)abstract We extend Varadhan’s construction of the Edwards model forpolymers to fractional Brownian loops and fractional Brownian starbursts.We show that, as in the fBm case, the Edwards density under a renormalizaionis an integrable function for the case Hd ≤ 1.
47.	Bock, Wolfgang, et al. (författare) The Feynman integrand for the charged particle in a constant magnetic field as white noise distribution 2012 Ingår i: Communcations on Stocastic Analysis. - : LSU Library. - 2688-6669 .- 0973-9599. ; 6:4 Tidskriftsartikel (refereegranskat)abstract The concepts of Feynman integrals in white noise analysis areused to realize the Feynman integrand for a charged particle in a constantmagnetic field as a Hida distribution. For this purpose the velocity dependentpotential gives rise to a generalized Gauss kernel.
48.	Bock, Wolfgang, et al. (författare) The Hamiltonian path integral for potentials of the Albeverio Hø egh-Krohn class : a white noise approach 2017 Ingår i: Reports on mathematical physics. - : Elsevier. - 0034-4877 .- 1879-0674. ; 79:1, s. 89-109 Tidskriftsartikel (refereegranskat)abstract We identify the integrand for the Hamiltonian path integral in space representation as a Kondratiev distribution. For this purpose we use methods from white noise analysis to compute also the Green's function of the underlying Schrödinger equation. We show that its generalized expectation solves the Schrödinger equation and that a functional form of the canonical commutation realtions is fulfilled.
49.	Bock, Wolfgang, et al. (författare) The Hamiltonian path integrand for the charged particle in a constant magnetic field as white noise distribution 2015 Ingår i: Infinite Dimensional Analysis Quantum Probability and Related Topics. - : World Scientific. - 0219-0257. ; 18:2 Tidskriftsartikel (refereegranskat)abstract The concepts of Hamiltonian Feynman integrals in white noise analysis are used to realize as the first velocity-dependent potential of the Hamiltonian Feynman integrand for a charged particle in a constant magnetic field in coordinate space as a Hida distribution. For this purpose the velocity-dependent potential gives rise to a generalized Gauss kernel. Besides the propagators, the generating functionals are obtained.
50.	Bock, Wolfgang, et al. (författare) Wick type SDEs driven by grey Brownian motion 2017 Ingår i: Structure, Function and Dynamics from nm to Gm. - : American Institute of Physics (AIP). - 9780735415515 Konferensbidrag (refereegranskat)abstract We derive solutions of the Ornstein-Uhlenbeck and of a linear Wick-type stochastic differential equation (SDE) driven by grey Brownian motion. The solutions are characterized to be in a suitable distribution space.

Skapa referenser, mejla, bekava och länka

Länka till träfflistan

Träfflista för sökning "WFRF:(Bock Wolfgang) "

Avgränsa träffmängd

År