### Refine

#### Has Fulltext

- yes (448) (remove)

#### Year of publication

#### Document Type

- Preprint (448) (remove)

#### Language

- English (428)
- German (17)
- Multiple languages (2)
- French (1)

#### Keywords

- index (11)
- boundary value problems (9)
- elliptic operators (9)
- Fredholm property (8)
- K-theory (7)
- manifolds with singularities (6)
- pseudodifferential operators (6)
- relative index (6)
- Atiyah-Patodi-Singer theory (5)
- index theory (5)

#### Institute

- Institut für Mathematik (374)
- Interdisziplinäres Zentrum für Dynamik komplexer Systeme (52)
- Institut für Physik und Astronomie (36)
- Institut für Anglistik und Amerikanistik (18)
- Extern (7)
- Wirtschaftswissenschaften (3)
- Institut für Psychologie (2)
- Hasso-Plattner-Institut für Digital Engineering gGmbH (1)
- Institut für Informatik und Computational Science (1)
- Institut für Religionswissenschaft (1)

The Collatz conjecture is a number theoretical problem, which has puzzled countless researchers using myriad approaches. Presently, there are scarcely any methodologies to describe and treat the problem from the perspective of the Algebraic Theory of Automata. Such an approach is promising with respect to facilitating the comprehension of the Collatz sequences "mechanics". The systematic technique of a state machine is both simpler and can fully be described by the use of algebraic means.
The current gap in research forms the motivation behind the present contribution. The present authors are convinced that exploring the Collatz conjecture in an algebraic manner, relying on findings and fundamentals of Graph Theory and Automata Theory, will simplify the problem as a whole.

The present work will introduce a Finite State Machine (FSM) that processes any Collatz Sequence; further, we will endeavor to investigate its behavior in relationship to transformations of a special infinite input. Moreover, we will prove that the machine’s word transformation is equivalent to the standard Collatz number transformation and subsequently discuss the possibilities for use of this approach at solving similar problems. The benefit of this approach is that the investigation of the word transformation performed by the Finite State Machine is less complicated than the traditional number-theoretical transformation.

In a bounded domain with smooth boundary in R^3 we consider the stationary Maxwell equations
for a function u with values in R^3 subject to a nonhomogeneous condition
(u,v)_x = u_0 on
the boundary, where v is a given vector field and u_0 a function on the boundary. We specify this problem within the framework of the Riemann-Hilbert boundary value problems for the Moisil-Teodorescu system. This latter is proved to satisfy the Shapiro-Lopaniskij condition if an only if the vector v is at no point tangent to the boundary. The Riemann-Hilbert problem for the Moisil-Teodorescu system fails to possess an adjoint boundary value problem with respect to the Green formula, which satisfies the Shapiro-Lopatinskij condition. We develop the construction of Green formula to get a proper concept of adjoint boundary value problem.

Luhmann in da Contact Zone
(2016)

Our aim in this contribution is to productively engage with the abstractions and complexities of Luhmann’s conceptions of society from a postcolonial perspective, with a particular focus on the explanatory powers of his sociological systems theory when it leaves the realms of Europe and ventures to describe regions of the global South. In view of its more recent global reception beyond Europe, our aim is to thus – following the lead of Dipesh Chakrabarty – provincialize Luhmann’s system theory especially with regard to its underlying assumptions about a global “world society”. For these purposes, we intend to revisit Luhmann in the post/colonial contact zone: We wish to reread Luhmann in the context of spaces of transcultural encounter where “global designs and local histories” (Mignolo), where inclusion into and exclusion from “world society” (Luhmann) clash and interact in intricate ways. The title of our contribution, ‘Luhmann in da Contact Zone’ is deliberately ambiguous: On the one hand, we of course use ‘Luhmann’ metonymically, as representative of a highly complex theoretical design. We shall cursorily outline this design with a special focus on the notion of a singular, modern “world society”, only to confront it with the epistemic challenges of the contact zone. On the other hand, this critique will also involve the close observation of Niklas Luhman as a human observer (a category which within the logic of systems theory actually does not exist) who increasingly transpires in his late writings on exclusion in the global South. By following this dual strategy, we wish to trace an increasing fracture between one Luhmann and the other, between abstract theoretical design and personalized testimony. It is by exploring and measuring this fracture that we hope to eventually be able to map out the potential of a possibly more productive encounter between systems theory and specific strands of postcolonial theory for a pluritopic reading of global modernity.

This essay reads Sam Selvon’s novel The Lonely Londoners (1956) as a milestone in the decolonisation of British fiction. After an introduction to Selvon and the core composition of the novel, it discusses the ways in which the narrative takes on issues of race and racism, how it in the tradition of the Trinidadian carnival confronts audiences with sexual profanation and black masculine swagger, and not least how the novel, especially through its elaborate use of creole Englishes, reimagines London as a West Indian metropolis. The essay then turns more systematically to the ways in which Selvon translates Western literary models and their isolated subject positions into collective modes of narrative performance taken from Caribbean orature and the calypsonian tradition. The Lonely Londoners breathes entirely new life into the ossified conventions of the English novel, and imbues it with unforeseen aesthetic, ethical, political and epistemological possibilities.

Recollecting Bones
(2016)

In the same “guarded, roundabout and reticent way” which Lindsay Barrett invokes for Australian conversations about imperial injustice, Germans, too, must begin to more systematically explore, in Paul Gilroy’s words, “the connections and the differences between anti-semitism and anti-black and other racisms and asses[s] the issues that arise when it can no longer be denied that they interacted over a long time in what might be seen as Fascism’s intellectual, ethical and scientific pre-history” (Gilroy 1996: 26). In the meantime, we need to care for the dead. We need to return them, first, from the status of scientific objects to the status of ancestral human beings, and then progressively, and proactively, as close as possible to the care of those communities from whom they were stolen.

Kleine Kosmopolitismen
(2016)

Postcolonial Justice
(2016)

Postcolonial Piracy
(2016)

Media piracy is a contested term in the academic as much as the public debate. It is used by the corporate industries as a synonym for the theft of protected media content with disastrous economic consequences. It is celebrated by technophile elites as an expression of freedom that ensures creativity as much as free market competition. Marxist critics and activists promote flapiracy as a subversive practice that undermines the capitalist world system and its structural injustices. Artists and entrepreneurs across the globe curse it as a threat to their existence, while many use pirate infrastructures and networks fundamentally for the production and dissemination of their art. For large sections of the population across the global South, piracy is simply the only means of accessing the medial flows of a progressively globalising planet.

Reflections of Lusáni Cissé
(2016)

This is a brief survey of a constructive technique of analytic continuation related to an explicit integral formula of Golusin and Krylov (1933). It goes far beyond complex analysis and applies to the Cauchy problem for elliptic partial differential equations as well. As started in the classical papers, the technique is elaborated in generalised Hardy spaces also called Hardy-Smirnov spaces.

In order to evade detection by network-traffic analysis, a growing proportion of malware uses the encrypted HTTPS protocol. We explore the problem of detecting malware on client computers based on HTTPS traffic analysis. In this setting, malware has to be detected based on the host IP address, ports, timestamp, and data volume information of TCP/IP packets that are sent and received by all the applications on the client. We develop a scalable protocol that allows us to collect network flows of known malicious and benign applications as training data and derive a malware-detection method based on a neural networks and sequence classification. We study the method's ability to detect known and new, unknown malware in a large-scale empirical study.

We consider the Navier-Stokes equations in the layer R^n x [0,T] over R^n with finite T > 0. Using the standard fundamental solutions of the Laplace operator and the heat operator, we reduce the Navier-Stokes equations to a nonlinear Fredholm equation of the form (I+K) u = f, where K is a compact continuous operator in anisotropic normed Hölder spaces weighted at the point at infinity with respect to the space variables. Actually, the weight function is included to provide a finite energy estimate for solutions to the Navier-Stokes equations for all t in [0,T]. On using the particular properties of the de Rham complex we conclude that the Fréchet derivative (I+K)' is continuously invertible at each point of the Banach space under consideration and the map I+K is open and injective in the space. In this way the Navier-Stokes equations prove to induce an open one-to-one mapping in the scale of Hölder spaces.

Convoluted Brownian motion
(2016)

In this paper we analyse semimartingale properties of a class of Gaussian periodic processes, called convoluted Brownian motions, obtained by convolution between a deterministic function and a Brownian motion. A classical
example in this class is the periodic Ornstein-Uhlenbeck process. We compute their characteristics and show that in general, they are neither
Markovian nor satisfy a time-Markov field property. Nevertheless, by enlargement
of filtration and/or addition of a one-dimensional component, one can in some case recover the Markovianity. We treat exhaustively the case of the bidimensional trigonometric convoluted Brownian motion and the higher-dimensional monomial convoluted Brownian motion.

We prove statistical rates of convergence for kernel-based least squares regression from i.i.d. data using a conjugate gradient algorithm, where regularization against overfitting is obtained by early stopping. This method is related to Kernel Partial Least Squares, a regression method that combines supervised dimensionality reduction with least squares projection. Following the setting introduced in earlier related literature, we study so-called "fast convergence rates" depending on the regularity of the target regression function (measured by a source condition in terms of the kernel integral operator) and on the effective dimensionality of the data mapped into the kernel space. We obtain upper bounds, essentially matching known minimax lower bounds, for the L^2 (prediction) norm as well as for the stronger Hilbert norm, if the true
regression function belongs to the reproducing kernel Hilbert space. If the latter assumption is not fulfilled, we obtain similar convergence rates for appropriate norms, provided additional unlabeled data are available.

Using an algorithm based on a retrospective rejection sampling scheme, we propose an exact simulation of a Brownian diffusion whose drift admits several jumps. We treat explicitly and extensively the case of two jumps, providing numerical simulations. Our main contribution is to manage the technical difficulty due to the presence of two jumps thanks to a new explicit expression of the transition density of the skew Brownian motion with two semipermeable barriers and a constant drift.

When trying to extend the Hodge theory for elliptic complexes on compact closed manifolds to the case of compact manifolds with boundary one is led to a boundary value problem for
the Laplacian of the complex which is usually referred to as Neumann problem. We study the Neumann problem for a larger class of sequences of differential operators on
a compact manifold with boundary. These are sequences of small curvature, i.e., bearing the property that the composition of any two neighbouring operators has order less than two.