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Surface Deposition of the Enceladus Plume and the Zenith Angle of EmissionsJan 30 2018Aug 22 2018Since the discovery of an ice particle plume erupting from the south polar terrain on Saturn's moon Enceladus, the geophysical mechanisms driving its activity have been the focus of substantial scientific research. The pattern and deposition rate of plume ... More

On Fields with Finite Information DensityApr 15 2004The existence of a natural ultraviolet cutoff at the Planck scale is widely expected. In a previous Letter, it has been proposed to model this cutoff as an information density bound by utilizing suitably generalized methods from the mathematical theory ... More

A Covariant Information-Density Cutoff in Curved Space-TimeOct 07 2003In information theory, the link between continuous information and discrete information is established through well-known sampling theorems. Sampling theory explains, for example, how frequency-filtered music signals are reconstructible perfectly from ... More

On the Vacuum Energy in Expanding Space-TimesOct 23 2002If there is a shortest length in nature, for example at the Planck scale of 10^-35m, then the cosmic expansion should continually create new comoving modes. A priori, each of the new modes comes with its own vacuum energy, which could contribute to the ... More

A Generalized Shannon Sampling Theorem, Fields at the Planck Scale as Bandlimited SignalsMay 16 1999Mar 02 2000It has been shown that space-time coordinates can exhibit only very few types of short-distance structures, if described by linear operators: they can be continuous, discrete or "unsharp" in one of two ways. In the literature, various quantum gravity ... More

Quantum Field Theory with Nonzero Minimal Uncertainties in Positions and MomentaMay 10 1994Oct 05 1994A noncommutative geometric generalisation of the quantum field theoretical framework is developed by generalising the Heisenberg commutation relations. There appear nonzero minimal uncertainties in positions and in momenta. As the main result it is shown ... More

Short-Distance Cutoffs in Curved SpaceMar 30 2004It is shown that space-time may possess the differentiability properties of manifolds as well as the ultraviolet finiteness properties of lattices. Namely, if a field's amplitudes are given on any sufficiently dense set of discrete points this could already ... More

On Symmetric Operators in Noncommutative GeometryNov 28 1998In Noncommutative Geometry, as in quantum theory, classically real variables are assumed to correspond to self-adjoint operators. We consider the relaxation of the requirement of self-adjointness to mere symmetry for operators $X_i$ which encode space-time ... More

On the only three Short Distance Structures which can be described by Linear OperatorsJun 01 1998We point out that if spatial information is encoded through linear operators $X_i$, or `infinite-dimensional matrices' with an involution $X_i^*=X_i$ then these $X_i$ can only describe either continuous, discrete or certain "fuzzy" space-time structures. ... More

Recent results on UV-regularisation through UV-modified uncertainty relationsNov 28 1997Assume that in a fundamental theory of quantum gravity spatial information is encoded through elements x_i of an associative, complex and possibly noncommutative algebra in which the involution acts as x^*_i = x_i. Without further assumptions it can be ... More

On Noncommutative Geometric RegularisationFeb 21 1996Studies in string theory and in quantum gravity suggest the existence of a finite lower bound to the possible resolution of lengths which, quantum theoretically, takes the form of a minimal uncertainty in positions $\Delta x_0$. A finite minimal uncertainty ... More

Simple considerations on the behaviour of bosonic modes with quantum group symmetryAug 06 1993While it is possible to introduce quantum group symmetry into the framework of quantum mechanics, the general problem of how to implement quantum group symmetry into $(3+1)$ dimensional quantum field theory has not yet been solved. Here we try to estimate ... More

Unsharp Degrees of Freedom and the Generating of SymmetriesJul 19 1999In quantum theory, real degrees of freedom are usually described by operators which are self-adjoint. There are, however, exceptions to the rule. This is because, in infinite dimensional Hilbert spaces, an operator is not necessarily self-adjoint even ... More

Instability in invariant theoryJul 08 2018Transcriber's note: In the fall of 1976, my advisor, David Mumford, handed me a short preprint by George Kempf to read. It was the first state of what eventually became his influential Annals paper "Instability in Invariant Theory" (Annals of Mathematics, ... More

On the Casimir Effect in the High Tc CupratesNov 07 2007High temperature superconductors have in common that they consist of parallel planes of copper oxide separated by layers whose composition can vary. Being ceramics, the cuprate superconductors are poor conductors above the transition temperature, T_c. ... More

Approach to Quantum Group deformed Quantum Field TheoryNov 04 1992In quantum field theory the creation and annihilation operators that are located at the points in 3-momentum space have commutation relations that are conserved under the action of a $U({\infty})$ group. Here it is shown how to define an appropriate $U_q({\infty})$ ... More

Quantum Group Symmetric Bargmann Fock ConstructionNov 04 1992Usually in quantum mechanics the Heisenberg algebra is generated by operators of position and momentum. The algebra is then represented on an Hilbert space of square integrable functions. Alternatively one generates the Heisenberg algebra by the raising ... More

Information-theoretic natural ultraviolet cutoff for spacetimeAug 21 2009Feb 04 2010Fields in spacetime could be simultaneously discrete and continuous, in the same way that information can: it has been shown that the amplitudes, \phi(x_n), that a field takes at a generic discrete set of points, x_n, can be sufficient to reconstruct ... More

Minimal Length Uncertainty Relation and Ultraviolet RegularisationDec 08 1996Studies in string theory and quantum gravity suggest the existence of a finite lower limit $\Delta x_0$ to the possible resolution of distances, at the latest on the scale of the Planck length of $10^{-35}m$. Within the framework of the euclidean path ... More

The relativistic quantum channel of communication through field quantaAug 21 2009Sep 07 2009Setups in which a system Alice emits field quanta which a system Bob receives are prototypical for wireless communication and have been extensively studied. In the most basic setup, Alice and Bob are modelled as Unruh-DeWitt detectors for scalar quanta ... More

New methods for creating superoscillationsAug 10 2016Superoscillating functions, i.e., functions that locally oscillate at a rate faster than their highest Fourier component, are of interest for applications from fundamental physics to engineering. Here, we develop a new method which allows one to construct ... More

Group Velocity of Discrete-Time Quantum WalksJan 27 2009We show that certain types of quantum walks can be modeled as waves that propagate in a medium with phase and group velocities that are explicitly calculable. Since the group and phase velocities indicate how fast wave packets can propagate causally, ... More

Towards Spectral Geometric Methods for Euclidean Quantum GravityJan 27 2016Mar 15 2016The unification of general relativity with quantum theory will also require a coming together of the two quite different mathematical languages of general relativity and quantum theory, i.e., of differential geometry and functional analysis respectively. ... More

The Transplanckian Question and the Casimir EffectApr 18 2005It is known that, through inflation, Planck scale phenomena should have left an imprint in the cosmic microwave background. The magnitude of this imprint is expected to be suppressed by a factor $\sigma^n$ where $\sigma\approx 10^{-5}$ is the ratio of ... More

On Information Theory, Spectral Geometry and Quantum GravityAug 01 2007We show that there exists a deep link between the two disciplines of information theory and spectral geometry. This allows us to obtain new results on a well known quantum gravity motivated natural ultraviolet cutoff which describes an upper bound on ... More

Vacuum entanglement enhancement by a weak gravitational fieldAug 29 2010Separate regions in space are generally entangled, even in the vacuum state. It is known that this entanglement can be swapped to separated Unruh-DeWitt detectors, i.e., that the vacuum can serve as a source of entanglement. Here, we demonstrate that, ... More

New methods for creating superoscillationsAug 10 2016Oct 21 2016Superoscillating functions, i.e., functions that locally oscillate at a rate faster than their highest Fourier component, are of interest for applications from fundamental physics to engineering. Here, we develop a new method which allows one to construct ... More

A Convexity Result in the Spectral Geometry of Conformally Equivalent Metrics on SurfacesJul 01 2016We study analytic paths of metrics that induce isospectral Laplace-Beltrami operators over oriented compact surfaces without boundary. Applying perturbation theory, we show that sets of conformally equivalent metrics on such surfaces contain no nontrivial ... More

Analysis of Superoscillatory Wave FunctionsMay 13 2004Surprisingly, differentiable functions are able to oscillate arbitrarily faster than their highest Fourier component would suggest. The phenomenon is called superoscillation. Recently, a practical method for calculating superoscillatory functions was ... More

On the Implementation of Constraints through Projection OperatorsSep 19 2000Quantum constraints of the type Q \psi = 0 can be straightforwardly implemented in cases where Q is a self-adjoint operator for which zero is an eigenvalue. In that case, the physical Hilbert space is obtained by projecting onto the kernel of Q, i.e. ... More

Corrections to the Emergent Canonical Commutation Relations Arising in the Statistical Mechanics of Matrix ModelsSep 15 1997Sep 18 1997We study the leading corrections to the emergent canonical commutation relations arising in the statistical mechanics of matrix models, by deriving several related Ward identities, and give conditions for these corrections to be small. We show that emergent ... More

The Virial Relation and Intrinsic Shape of Early-Type GalaxiesSep 22 2016Sep 26 2016Early-type galaxies (ETGs) are supposed to follow the virial relation $M = k_e \sigma_*^2 R_e / G$, with $M$ being the mass, $\sigma_*$ being the stellar velocity dispersion, $R_e$ being the effective radius, $G$ being Newton's constant, and $k_e$ being ... More

Generalized roll-call model for the Shapley-Shubik indexFeb 13 2016In 1996 Dan Felsenthal and Mosh\'e Machover considered the following model. An assembly consisting of $n$ voters exercises roll-call. All $n!$ possible orders in which the voters may be called are assumed to be equiprobable. The votes of each voter are ... More

On minimum sum representations for weighted voting gamesMar 08 2011A proposal in a weighted voting game is accepted if the sum of the (non-negative) weights of the "yea" voters is at least as large as a given quota. Several authors have considered representations of weighted voting games with minimum sum, where the weights ... More

A note on limit results for the Penrose-Banzhaf indexAug 09 2018It is well known that the Penrose-Banzhaf index of a weighted game can differ starkly from corresponding weights. Limit results are quite the opposite, i.e., under certain conditions the power distribution approaches the weight distribution. Here we provide ... More

The quasi-Assouad dimension for stochastically self-similar setsSep 08 2017The class of stochastically self-similar sets contains many famous examples of random sets, e.g. Mandelbrot percolation and general fractal percolation. Under the assumption of the uniform open set condition and some mild assumptions on the iterated function ... More

Semiglobal Numerical Calculations of Asymptotically Minkowski SpacetimesDec 06 2001This talk reports on recent progress toward the semiglobal study of asymptotically flat spacetimes within numerical relativity. The development of a 3D solver for asymptotically Minkowski-like hyperboloidal initial data has rendered possible the application ... More

Additional Information on Heavy Quark Parameters from Charged Lepton Forward-Backward AsymmetryFeb 08 2016The determination of $|V_{cb}|$ using inclusive and exclusive (semi-)leptonic decays exhibits a long-standing tension of varying ${\cal O}(3 \sigma)$ significance. For the inclusive determination the decay rate is expanded in $1/m_b$ using heavy quark ... More

A Survey on Reproducibility in Parallel ComputingNov 13 2015We summarize the results of a survey on reproducibility in parallel computing, which was conducted during the Euro-Par conference in August 2015. The survey form was handed out to all participants of the conference and the workshops. The questionnaire, ... More

Spectral synthesis provides 2-D videos on a 1-D screen with 360°-visibility and mirror-immunityFeb 07 2014Spatial-light-modulator (SLM)-based tunable sources have complex setups. A simpler setup, comprising an SLM-projector and a dispersive element, synthesizes light as effectively, based on a Superposition of Newtonian Spectra (SNS). As a generalization ... More

The "Missing Mass Problem" in Astronomy and the Need for a Modified Law of GravityJan 23 2014Since the 1930s, astronomical observations have accumulated evidence that our understanding of the dynamics of galaxies and groups of galaxies is grossly incomplete: assuming the validity of Newton's law of gravity on astronomical scales, the observed ... More

A Simplified Treatment of Gravitational Interaction on Galactic ScalesNov 20 2012Jan 31 2013I present a simple scheme for the treatment of gravitational interactions on galactic scales. In analogy to known mechanisms of quantum field theory, I assume ad hoc that gravitation is mediated by virtual exchange particles - gravitons - with very small ... More

Integral point sets over finite fieldsApr 08 2008We consider point sets in the affine plane $\mathbb{F}_q^2$ where each Euclidean distance of two points is an element of $\mathbb{F}_q$. These sets are called integral point sets and were originally defined in $m$-dimensional Euclidean spaces $\mathbb{E}^m$. ... More

Ground states of dipolar gases in quasi-1D ring trapsNov 25 2011Dec 15 2011We compute the ground state of dipoles in a quasi-one-dimensional ring trap using few-body techniques combined with analytic arguments. The effective interaction between two dipoles depends on their center-of-mass coordinate and can be tuned by varying ... More

Generalized roll-call model for the Shapley-Shubik indexFeb 13 2016Aug 08 2018In 1996 Dan Felsenthal and Mosh\'e Machover considered the following model. An assembly consisting of $n$ voters exercises roll-call. All $n!$ possible orders in which the voters may be called are assumed to be equiprobable. The votes of each voter are ... More

The box dimension of random box-like self-affine setsDec 22 2015May 19 2017In this paper we study two random analogues of the box-like self-affine attractors introduced by Fraser, itself an extension of Sierpi\'nski carpets. We determine the almost sure box-counting dimension for the homogeneous random case ($1$-variable random), ... More

Exponential Stability for Linear Evolutionary EquationsFeb 28 2013Jun 14 2013We give an approach to exponential stability within the framework of evolutionary equations due to [R. Picard. A structural observation for linear material laws in classical mathematical physics. Math. Methods Appl. Sci., 32(14):1768-1803,2009]. We derive ... More

Squaring the square with integer linear programmingJan 24 2014We consider so-called squaring the square-puzzles where a given square (or rectangle) should be dissected into smaller squares. For a specific instance of such problems we demonstrate that a mathematically rigorous solution can be quite involved. As an ... More

Equivariant vector bundles on Drinfeld's upper half spaceJun 15 2006Jun 24 2007Let X be Drinfeld's upper half space of dimension d over a finite extension K of Q_p. We construct for every homogeneous vector bundle F on the projective space P^d a GL_{d+1}(K)-equivariant filtration by closed K-Frechet spaces on F(X). This gives rise ... More

The box dimension of random box-like self-affine setsDec 22 2015In this paper we study two random analogues of the box-like self-affine attractors introduced by Fraser, itself an extension of Sierpi\'nski carpets. We determine the almost sure box-counting dimension for the homogeneous random case ($1$-variable random), ... More

Exponential Stability and Initial Value Problems for Evolutionary EquationsJul 03 2017Jul 07 2017In this thesis we consider so-called linear evolutionary problems, a class of linear partial differential equations covering classical elliptic, parabolic and hyperbolic equations from mathematical physics as well as classes of integro-differenital equations, ... More

Searches and electroweak measurements at HERANov 10 2004The H1 and ZEUS collaborations have used the HERA I data to search for physics beyond the SM and to test electroweak physics in electron-proton collisions. The new period of data taking (HERA II) has started and first HERA II analyses become available. ... More

A Technical Report on PLS-Completeness of Single-Swap for Unweighted Metric Facility Location and $K$-MeansApr 19 2017Recently, [Bra17] showed that the single-swap heuristic for weighted metric uncapacitated facility location and $K$-Means is tightly PLS-complete. We build upon this work and present a stronger reduction, which proves tight PLS-completeness for the unweighted ... More

Trip-Based Public Transit Routing Using Condensed Search TreesJul 05 2016Sep 15 2016We study the problem of planning Pareto-optimal journeys in public transit networks. Most existing algorithms and speed-up techniques work by computing subjourneys to intermediary stops until the destination is reached. In contrast, the trip-based model ... More

The "Graviton Picture": a Bohr Model for Gravitation on Galactic Scales?May 06 2014Modified Newtonian Dynamics (MOND) provides a successful description of stellar and galactic dynamics on almost all astronomical scales. A key feature of MOND is the transition function from Newtonian to modified dynamics which corresponds to the empirical ... More

Against Absolute Actualization: Three "Non-Localities" and Failure of Model-External Randomness made easy with Many-Worlds Models including Stronger Bell-Violation and Correct QM ProbabilityNov 20 2013Jun 05 2014Experimental violation of Bell-inequalities proves actualization of many futures (~ many-worlds); I show that this is not mere interpretation. To show this self-contained pedagogically, I resolve the EPR paradox by starting with a visually intuitive non-quantum ... More

Exploring Inequality Violations by Classical Hidden Variables NumericallyAug 29 2013There are increasingly suggestions for computer simulations of quantum statistics which try to violate Bell type inequalities via classical, common cause correlations. The Clauser-Horne-Shimony-Holt (CHSH) inequality is very robust. However, we argue ... More

The de Rham cohomology of Drinfeld's half spaceApr 10 2013Aug 07 2014Let X be Drinfeld's half space over a p-adic field K. The de Rham cohomology of X was first computed by Schneider and Stuhler. Afterwards there were given different proofs by Alon, de Shalit, Iovita and Spiess. This paper presents yet another approach ... More

Many Worlds Model resolving the Einstein Podolsky Rosen paradox via a Direct Realism to Modal Realism Transition that preserves Einstein LocalityAug 08 2011The violation of Bell inequalities by quantum physical experiments disproves all relativistic micro causal, classically real models, short Local Realistic Models (LRM). Non-locality, the infamous "spooky interaction at a distance" (A. Einstein), is already ... More

Model-independent analysis of Tau -> lll' decaysDec 19 2008Many models for physics beyond the Standard Model predict lepton-flavour violating decays of charged leptons at a level which may become observable very soon. We investigate the decays of a Tau-lepton into three charged leptons (Tau -> lll', l(') = e,\mu ... More

Prospects for standard SUSY searches at the LHCOct 20 2008We present the recent prospects and strategies of the ATLAS and CMS experiments in the search for signatures of Supersymmetry. The emphasis is placed on standard signatures with missing transverse energy and on the initial data taking periods.

Helium Clusters Capture of Heliophobes, Strong Depletion and Spin dependent Pick-up StatisticsFeb 07 2010This much revised and shortened PhD thesis contains many ideas that I could not follow up on, like self destructing beams in scattering cells, the depletion enhancing Wittig tube, ionic seeding via beta-decay foil or Langmuir-Taylor filaments, analysis ... More

Convex hulls of polyominoesFeb 26 2007In this article we prove a conjecture of Bezdek, Brass, and Harborth concerning the maximum volume of the convex hull of any facet-to-facet connected system of n unit hypercubes in the d-dimensional Euclidean space. For d=2 we enumerate the extremal polyominoes ... More

Well-posedness for a general class of differential inclusionsAug 01 2018We consider an abstract class of differential inclusions, which covers differential-algebraic and non-autonomous problems as well as problems with delay. Under weak assumptions on the operators involved, we prove the well-posedness of those differential ... More

Importance in systems with interval decisionsMar 12 2018Aug 06 2018Given a system where the real-valued states of the agents are aggregated by a function to a real-valued state of the entire system, we are interested in the influence or importance of the different agents for that function. This generalizes the notion ... More

Measuring voting power in convex policy spacesDec 20 2013Classical power index analysis considers the individual's ability to influence the aggregated group decision by changing its own vote, where all decisions and votes are assumed to be binary. In many practical applications we have more options than either ... More

A characterization of boundary conditions yielding maximal monotone operatorsOct 18 2013Aug 13 2014We provide a characterization for maximal monotone realizations for a certain class of (nonlinear) operators in terms of their corresponding boundary data spaces. The operators under consideration naturally arise in the study of evolutionary problems ... More

Counting polyominoes with minimum perimeterJun 21 2005Nov 02 2015The number of essentially different square polyominoes of order n and minimum perimeter p(n) is enumerated.

On Extensions of generalized Steinberg RepresentationsFeb 04 2004Let F be a local non-archimedean field and let G be the group of F-valued points of a reductive algebraic group over F. In this paper we compute the Ext-groups of generalized Steinberg representations in the category of smooth G-representations with coefficients ... More

Exponential stability for second order evolutionary problemsAug 01 2014Apr 13 2015We study the exponential stability of evolutionary equations. The focus is laid on second order problems and we provide a way to rewrite them as a suitable first order evolutionary equation, for which the stability can be proved by using frequency domain ... More

Autonomous Evolutionary Inclusions with Applications to Problems with Nonlinear Boundary ConditionsDec 10 2012We study an abstract class of autonomous differential inclusions in Hilbert spaces and show the well-posedness and causality, by establishing the operators involved as maximal monotone operators in time and space. Then the proof of the well-posedness ... More

Milgrom's Law and Lambda's Shadow: How Massive Gravity Connects Galactic and Cosmic DynamicsJun 02 2015Massive gravity provides a natural solution for the dark energy problem of cosmology and is also a candidate for resolving the dark matter problem. I demonstrate that, assuming reasonable scaling relations, massive gravity can provide for Milgrom's law ... More

Does the Jet Production Efficiency of Radio Galaxies Control Their Optical AGN Types?Aug 25 2014The jet production efficiency of radio galaxies can be quantified by comparison of their kinetic jet powers P_jet and Bondi accretion powers P_B. These two parameters are known to be related linearly, with the jet power resulting from the Bondi power ... More

How long does it take to consensus in the Hegselmann-Krause model?May 22 2014Hegselmann and Krause introduced a discrete-time model of opinion dynamics with agents having limit confidence. It is well known that the dynamics reaches a stable state in a polynomial number of time steps. However, the gap between the known lower and ... More

Quantum Randi ChallengeJul 23 2012Dec 24 2012Observed violations of Bell type inequalities exclude all relativistic micro causal ("local"), counterfactual definite ("real") hidden variable models of nature. This further relativization of our concept of reality triggers a growing pseudoscientific ... More

Can Massive Gravity Explain the Mass Discrepancy - Acceleration Relation of Disk Galaxies?May 28 2013The empirical mass discrepancy-acceleration (MDA) relation of disk galaxies provides a key test for models of galactic dynamics. In terms of modified laws of gravity and/or inertia, the MDA relation quantifies the transition from Newtonian to modified ... More

A Derivation of Modified Newtonian DynamicsMar 28 2013Modified Newtonian Dynamics (MOND) is a possible solution for the missing mass problem in galactic dynamics; its predictions are in good agreement with observations in the limit of weak accelerations. However, MOND does not derive from a physical mechanism ... More

Historical Parallels between, and Modal Realism underlying Einstein and Everett RelativitiesJan 09 2013A century ago, "past" and "future", previously strictly apart, mixed up and merged. Temporal terminology improved. Today, not actualized quantum states, that is merely "possible" alternatives, objectively "exist" (are real) when they interfere. Again, ... More

Supporting Abstract Relational Space-Time as Fundamental without Doctrinism against EmergenceDec 16 2009Oct 02 2011Modern physics, via the standard model with Higgs mechanism and string theory for example, has supplied ether-like models and emergent general relativity scenarios that substantially weaken the usual defense of orthodox relativity and abstract, relational ... More

Numerical modeling of black holes as sources of gravitational waves in a nutshellDec 23 2008These notes summarize basic concepts underlying numerical relativity and in particular the numerical modeling of black hole dynamics as a source of gravitational waves. Main topics are the 3+1 decomposition of general relativity, the concept of a well-posed ... More

Approximating power by weightsFeb 01 2018Aug 08 2018Determining the power distribution of the members of a shareholder meeting or a legislative committee is a well-known problem for many applications. In some cases it turns out that power is nearly proportional to relative voting weights, which is very ... More

Complexity of Single-Swap Heuristics for Metric Facility Location and Related ProblemDec 06 2016Jan 30 2017Metric facility location and $K$-means are well-known problems of combinatorial optimization. Both admit a fairly simple heuristic called single-swap, which adds, drops or swaps open facilities until it reaches a local optimum. For both problems, it is ... More

Problems and Successes in the Numerical Approach to the Conformal Field EquationsApr 12 2002This talk reports on the status of an approach to the numerical study of isolated systems with the conformal field equations. We first describe the algorithms used in a code which has been developed at AEI in the last years, and discuss a milestone result ... More

Asymptotically Flat Initial Data for Gravitational Wave Spacetimes, Conformal Compactification and Conformal SymmetryNov 02 1998We study the utilization of conformal compactification within the conformal approach to solving the constraints of general relativity for asymptotically flat initial data. After a general discussion of the framework, particular attention is paid to simplifications ... More

On the characteristic of integral point sets in $\mathbb{E}^m$Nov 29 2005We generalise the definition of the characteristic of an integral triangle to integral simplices and prove that each simplex in an integral point set has the same characteristic. This theorem is used for an efficient construction algorithm for integral ... More

The power of the largest playerMar 13 2018Apr 26 2018Decisions in a shareholder meeting or a legislative committee are often modeled as a weighted game. Influence of a member is then measured by a power index. A large variety of different indices has been introduced in the literature. This paper analyzes ... More

Ready for the design of voting rules?May 05 2014The design of fair voting rules has been addressed quite often in the literature. Still, the so-called inverse problem is not entirely resolved. We summarize some achievements in this direction and formulate explicit open questions and conjectures.

Computing the Power Distribution in the IMFMar 04 2016The International Monetary Fund is one of the largest international organizations using a weighted voting system. The weights of its 188 members are determined by a fixed amount of basic votes plus some extra votes for so-called Special Drawing Rights ... More

On the inverse power index problemNov 27 2012Weighted voting games are frequently used in decision making. Each voter has a weight and a proposal is accepted if the weight sum of the supporting voters exceeds a quota. One line of research is the efficient computation of so-called power indices measuring ... More

On a class of block operator matrices in system theoryFeb 19 2015We consider a class of block operator matrices arising in the study of scattering passive systems, especially in the context of boundary control problems. We prove that these block operator matrices are indeed a subclass of block operator matrices considered ... More

No finite $5$-regular matchstick graph existsJan 08 2014A graph $G=(V,E)$ is called a unit-distance graph in the plane if there is an injective embedding of $V$ in the plane such that every pair of adjacent vertices are at unit distance apart. If additionally the corresponding edges are non-crossing and all ... More

On the dimensions of attractors of random self-similar graph directed iterated function systemsNov 11 2015May 19 2017In this paper we propose a new model of random graph directed fractals that extends the current well-known model of random graph directed iterated function systems, $V$-variable attractors, and fractal and Mandelbrot percolation. We study its dimensional ... More

Well-posedness of Linear Integro-Differential Equations with Operator-valued KernelsOct 05 2012Apr 04 2016We study linear integro-differential equations in Hilbert spaces with operator-valued kernels and give sufficient conditions for the well-posedness. We show that several types of integro-differential equations are covered by the class of evolutionary ... More

Concentration for Poisson functionals: component counts in random geometric graphsJun 26 2015Jan 13 2016Upper bounds for the probabilities $\mathbb{P}(F\geq \mathbb{E} F + r)$ and $\mathbb{P}(F\leq \mathbb{E} F - r)$ are proved, where $F$ is a certain component count associated with a random geometric graph built over a Poisson point process on $\mathbb{R}^d$. ... More

Fast regocnition of planar non unit distance graphsJan 17 2014We study criteria attesting that a given graph can not be embedded in the plane so that neighboring vertices are at unit distance apart and the straight line edges do not cross.

Well-posedness for a general class of differential inclusionsAug 01 2018May 02 2019We consider an abstract class of differential inclusions, which covers differential-algebraic and non-autonomous problems as well as problems with delay. Under weak assumptions on the operators involved, we prove the well-posedness of those differential ... More

On the dimensions of attractors of random self-similar graph directed iterated function systemsNov 11 2015In this paper we propose a new model of random graph directed fractals that extends the current well-known model of random graph directed iterated function systems, $V$-variable attractors, and fractal and Mandelbrot percolation. We study its dimensional ... More

Exact Hausdorff and packing measures for random self-similar code-trees with necksOct 19 2017Random code-trees with necks were introduced recently to generalise the notion of $V$-variable and random homogeneous sets. While it is known that the Hausdorff and packing dimensions coincide irrespective of overlaps, their exact Hausdorff and packing ... More

Seeing lens imaging as a superposition of multiple viewsOct 12 2015In the conventional approach to lens imaging, rays are used to map object points to image points. However, many students have a need to think of the image as a whole. To answer this need, lens imaging is reinterpreted as a superposition of sharp images ... More