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Introduction

## Publications

Publications (239)

Emden-Fowler type equations are nonlinear differential equations that appear in many fields such as mathematical physics, astrophysics and chemistry. In this paper, we perform an asymptotic analysis of a specific Emden-Fowler type equation that emerges in a queuing theory context as an approximation of voltages under a well-known power flow model....

We compare stability regions for different power flow models in the process of charging electric vehicles (EVs) by considering their random arrivals, their stochastic demand for energy at charging stations, and the characteristics of the electricity distribution network. We assume the distribution network is a line with charging stations located on...

In this publication, the Luneberg integrals are revisited and the conditions of the using of such integrals have been recalled. Additivity law of Luneberg’s integrals and the link with the Frenel kernel for the propagation are discussed. By means of the definition of the Luneberg’s integrals, the propagation of a vectorial electromagnetic field (He...

In this paper, we study a single-server polling model with two queues. Customers arrive at the queues according to two independent Poisson processes. The server spends random amounts of time in each queue, regardless of the amounts of work present at the queues. The service speed is not constant; it is assumed that the server works at speed r i x i...

In this publication, the Luneberg integrals are revisited and the conditions of the using of such integrals have been recalled. Additivity law of Luneberg's integrals and the link with the Frenel kernel for the propagation are discussed. By means of the definition of the Luneberg's integrals,the propagation of a vectorial electromagnetic field (Her...

We sharpen the bound n2k on the maximum modulus of the kth radial derivative of the Zernike circle polynomials (disk polynomials) of degree n to n2(n2−12)⋅...⋅(n2−(k−1)2)∕2k(1∕2)k. This bound is obtained from a result of Koornwinder on the non-negativity of connection coefficients of the radial parts of the circle polynomials when expanded into a s...

We sharpen the bound $n^{2k}$ on the maximum modulus of the $k^{{\rm th}}$ radial derivative of the Zernike circle polynomials (disk polynomials) of degree $n$ to $n^2(n^2-1^2)\cdot ... \cdot(n^2-(k-1)^2)/2^k(1/2)_k$. This bound is obtained from a result of Koornwinder on the non-negativity of connection coefficients of the radial parts of the circ...

Scale-free networks contain many small cliques and cycles. We model such networks as inhomogeneous random graphs with regularly varying infinite-variance weights. For these models, the number of cliques and cycles have exact integral expressions amenable to asymptotic analysis. We obtain various asymptotic descriptions for how the average number of...

The fixed-cycle traffic-light (FCTL) queue is the null model for intersections with static signaling, where vehicles arrive, form a queue and depart during cycles controlled by a traffic light. Classical analysis of the FCTL queue based on transform methods requires a computationally challenging step of finding the complex-valued roots of some char...

In this paper we highlight that extreme events such as freak waves are a transient phenomenon in keeping with the old fisherman tale that these extreme events seem to appear out of nowhere. Janssen ( J. Phys. Oceanogr. , vol. 33, 2003, pp. 863–884) obtained an evolution equation for the ensemble average of the excess kurtosis, which is a measure fo...

Scale-free networks contain many small cliques and cycles. We model such networks as inhomogeneous random graphs with regularly varying infinite-variance weights. For these models, the number of cliques and cycles have exact integral expressions amenable to asymptotic analysis. We obtain various asymptotic descriptions for how the average number of...

Arrival processes to service systems are prevalently assumed non-homogeneous
Poisson. Though mathematically convenient, arrival processes are often more
volatile, a phenomenon that is referred to as overdispersion. Motivated by
this, we analyze a class of stochastic models for which we develop performance
approximations that are scalable in the sys...

The enhancement and detection of elongated structures in noisy image data are relevant for many biomedical imaging applications. To handle complex crossing structures in 2D images, 2D orientation scores \(U: {\mathbb {R}} ^ 2\times S ^ 1 \rightarrow {\mathbb {C}}\) were introduced, which already showed their use in a variety of applications. Here w...

In wavefront characterization, often the combination of a Shack-Hartmann sensor and a reconstruction method utilizing the Cartesian derivatives of Zernike circle polynomials (the least-squares method, to be called here Method A) is used, which is known to introduce crosstalk. In [J. Opt. Soc. Am. A31, 1604 (2014)10.1364/JOSAA.31.001604], a crosstal...

It is a well-known problem in Gabor analysis how to construct explicitly given dual frames associated with a given frame. In this paper we will consider a class of window functions for which approximately dual windows can be calculated explicitly. The method makes it possible to get arbitrarily close to perfect reconstruction by allowing the modula...

In wavefront characterization, often the combination of a Shack-Hartmann sensor and a reconstruction method utilizing the Cartesian derivatives of Zernike circle polynomials (the least-squares method, to be called here Method A) is used, which is known to introduce crosstalk. In \citep{janssen2014zernike} a crosstalk-free analytic expression of the...

Spitzer's identity describes the position of a reflected random walk over time in terms of a bivariate transform. Among its many applications in probability theory are congestion levels in queues and random walkers in physics. We present a new derivation of Spitzer's identity under the assumption that the increments of the random walk have bounded...

Real-world networks often have power-law degrees and scale-free properties, such as ultrasmall distances and ultrafast information spreading. In this paper, we study a third universal property: three-point correlations that suppress the creation of triangles and signal the presence of hierarchy. We quantify this property in terms of c¯(k), the prob...

The enhancement and detection of elongated structures in noisy image data is relevant for many biomedical imaging applications. To handle complex crossing structures in 2D images, 2D orientation scores $U: \mathbb{R} ^ 2\times S ^ 1 \rightarrow \mathbb{R}$ were introduced, which already showed their use in a variety of applications. Here we extend...

Real-world networks often have power-law degrees and scale-free properties such as ultra-small distances and ultra-fast information spreading. We provide evidence of a third universal property: three-point correlations that suppress the creation of triangles and signal the presence of hierarchy. We quantify this property in terms of $\bar c(k)$, th...

The dominant pole approximation (DPA) is a classical analytic method to
obtain from a generating function asymptotic estimates for its underlying
coefficients. We apply DPA to a discrete queue in a critical many-sources
regime, in order to obtain tail asymptotics for the stationary queue length. As
it turns out, this regime leads to a clustering of...

The Struve functions H n ( z ) , n = 0 , 1 , ... are approximated in a simple, accurate form that is valid for all z ≥ 0. The authors previously treated the case n = 1 that arises in impedance calculations for the rigid-piston circular radiator mounted in an infinite planar baffle [Aarts and Janssen, J. Acoust. Soc. Am. 113, 2635–2637 (2003)]. The...

We investigate the presence of triangles in a class of correlated random graphs in which hidden variables determine the pairwise connections between vertices. The class rules out self-loops and multiple edges and allows for negative degree correlations (disassortative mixing) due to infinite-variance degrees controlled by a structural cutoff $h_s$...

Scale-free networks arise from power-law degree distributions. Due to the
finite size of real-world networks, the power law inevitably has a cutoff at
some maximum degree $\Delta$. We investigate the relative size of the giant
component $S$ in the large-network limit. We show that $S$ as a function of
$\Delta$ increases fast when $\Delta$ is just l...

The Quality-and-Efficiency-Driven (QED) regime provides a basis for solving
asymptotic dimensioning problems that trade off revenue, costs and service
quality. We derive bounds for the optimality gaps that capture the differences
between the true optimum and the asymptotic optimum based on the QED
approximations. Our bounds generalize earlier resul...

We study an M/G/1-type queueing model with the following additional feature.
The server works continuously, at fixed speed, even if there are no service
requirements. In the latter case, it is building up inventory, which can be
interpreted as negative workload. At random times, with an intensity
{\omega}(x) when the inventory is at level x > 0, th...

We consider 3D versions of the Zernike polynomials that are commonly used in
2D in optics and lithography. We generalize the 3D Zernike polynomials to
functions that vanish to a prescribed degree $\alpha\geq0$ at the rim of their
supporting ball $\rho\leq1$. The analytic theory of the 3D generalized Zernike
functions is developed, with attention fo...

The three-dimensional frequency transfer function for optical imaging systems was introduced by Frieden in the 1960s. The analysis of this function and its partly back-transformed functions (two-dimensional and one-dimensional optical transfer functions) in the case of an ideal or aberrated imaging system has received relatively little attention in...

We introduce a family of heavy-traffic regimes for large scale service
systems, presenting a range of scalings that include both moderate and extreme
heavy traffic, as compared to classical heavy traffic. The heavy-traffic
regimes can be translated into capacity sizing rules that lead to
Economies-of-Scales, so that the system utilization approache...

In this publication, the modelisation of an air bubble as inclusion in a droplet is treated from scalar theory point of view (Fresnel’s theory). 50 nm nanoparticles are detected from the numerical reconstruction of air bubbles created by heating of the nanoparticles in the bubble (section 3.1, pages 6,7,8). The elaborated model is compared with Lor...

We consider Markovian many-server systems with admission control operating in
a QED regime, where the relative utilization approaches unity while the number
of servers grows large, providing natural Economies-of-Scale. In order to
determine the optimal admission control policy, we adopt a revenue maximization
framework, and suppose that the revenue...

Wireless networks equipped with the CSMA protocol are subject to collisions due to interference. For a given interference range, we investigate the tradeoff between collisions (hidden nodes) and unused capacity (exposed nodes). We show that the sensing range that maximizes throughput critically depends on the activation rate of nodes. For infinite...

Prostate cancer (PCa) diagnosis and treatment is still limited due to the lack of reliable imaging methods for cancer localization. Based on the fundamental role played by angiogenesis in cancer growth and development, several dynamic contrast enhanced (DCE) imaging methods have been developed to probe tumor angiogenic vasculature. In DCE magnetic...

The advanced ENZ-theory of diffraction integrals, as published recently in J.
Europ. Opt. Soc. Rap. Public. 8, 13044 (2013), presents the diffraction
integrals per Zernike term in the form of doubly infinite series. These double
series involve, aside from an overall azimuthal factor, the products of Jinc
functions for the radial dependence and stru...

We propose using the circle polynomials to describe a particle's transmission function in a digital holography setup. This allows both opaque and phase particles to be determined. By means of this description, we demonstrate that it is possible to estimate the digital in-line hologram produced by a spherical particle. The experimental intensity dis...

In this paper, a new methodology is presented to derive the aberration state of a lithographic projection system from wafer metrology data. For this purpose, new types of phase-shift gratings (PSGs) are introduced, with special features that give rise to a simple linear relation between the PSG image displacement and the phase aberration function o...

The partial derivatives and Laplacians of the Zernike circle polynomials
occur in various places in the literature on computational optics. In a number
of cases, the expansion of these derivatives and Laplacians in the circle
polynomials are required. For the first-order partial derivatives, analytic
results are scattered in the literature, startin...

Consider the all-time maximum of a Brownian motion with negative drift. Assume that this process is sampled at certain points in time, where the time between two consecutive points is rendered by an Erlang distribution with mean 1/ω1/ω. The family of Erlang distributions covers the range between deterministic and exponential distributions. We show...

The computational methods for the diffraction integrals that occur in the Extended Nijboer-Zernike (ENZ-) approach to circular, aberrated, defocused optical systems are reviewed and updated. In the ENZ-approach, the Debye approximation of Rayleigh's integral for the through-focus, complex, point-spread function is evaluated in semi-analytic form. T...

We develop many-server asymptotics in the QED regime for models with
admission control. The admission control, designed to reduce the incoming
traffic in periods of congestion, scales with the size of the system. For a
class of Markovian models with this scaled control, we identify the QED limits
for two stationary performance measures. We also der...

Various authors have presented the aberration function of an optical system as a power series expansion with respect to the ray coordinates in the exit pupil and the coordinates of the intersection point with the image field of the optical system. In practical applications, for reasons of efficiency and accuracy, an expansion with the aid of orthog...

The Halfin–Whitt regime, or the quality-and-efficiency-driven (QED) regime, for multiserver systems refers to a situation with many servers, a critical load, and yet favorable system performance. We apply this regime to the classical multiserver loss system with slow retrials. We derive nondegenerate limiting expressions for the main steady-state p...

In many-server systems it is crucial to staff the right number of servers so
that targeted service levels are met. These staffing problems typically lead to
constraint satisfaction problems that are hard to solve. During the last
decade, a powerful many-server asymptotic theory has been developed to solve
such problems and optimal staffing rules ar...

Ultrashort X-ray pulses from free-electron laser X-ray sources make it feasible to conduct small- and wide-angle scattering experiments on biomolecular samples in solution at sub-picosecond timescales. During these so-called fluctuation scattering experiments, the absence of rotational averaging, typically induced by Brownian motion in classic solu...

Loudspeakers are often modelled as a rigid piston in an infinite baffle. As a model for real loudspeakers, this approach is limited in two ways. One issue is that a loudspeaker cone is not rigid, and a second issue is that a loudspeaker is mostly used in a cabinet. Both issues are addressed here by developing the velocity of the radiator in terms o...

Random-access networks may exhibit severe unfairness in throughput, in the sense that some nodes receive consistently higher throughput than others. Recent studies show that this unfairness is due to local differences in the neighborhood structure: nodes with fewer neighbors receive better access. We study the unfairness in saturated linear network...

It has been suggested by Morse and Ingard that the sound radiation of a loudspeaker in a box is comparable to that of a spherical cap on a rigid sphere. This has been established recently by the present authors, who developed a computation scheme for the forward and inverse calculation of the pressure due to a harmonically excited, flexible cap on...

We propose in this paper an analytical solution to the problem of scalar diffraction of a partially coherent beam by an opaque disk. This analytical solution is applied in digital in-line holography of particles.

The integrals occurring in optical diffraction theory under conditions
of partial coherence have the form of an incomplete autocorrelation
integral of the pupil function of the optical system. The incompleteness
is embodied by a spatial coherence function of limited extent. In the
case of circular optical systems and coherence functions supported b...

We apply a new corrected diffusion approximation for the Erlang C formula to determine staffing levels in cost minimization and constraint satisfaction problems. These problems are motivated by large customer contact centers that are modeled as an M/M/s queue with s the number of servers or agents. The proposed staffing levels are refinements of th...

Random-access algorithms such as CSMA provide a popular mechanism for distributed medium access control in large-scale wireless networks. In recent years, tractable stochastic models have been shown to yield accurate throughput estimates for CSMA networks. We consider a saturated random-access network on a general conflict graph, and prove that for...

A generalization of the Zernike circle polynomials for expansion of functions
vanishing outside the unit disk is given. These generalized Zernike functions
have the form Zm,{\alpha} n ({\rho}, \vartheta) = Rm,{\alpha} n ({\rho})
exp(im\vartheta), 0 \leq {\rho} < 1, 0 \leq \vartheta < 2{\pi}, and vanish for
{\rho} > 1, where n and m are integers suc...

Consider a queueing system in which arriving customers are placed on a circle and wait for service. A traveling server moves at constant speed on the circle, stopping at the location of the customers until service completion. The server is greedy: ...

We present a Fourier Transform Infrared spectrometer for use with a frequency comb laser as source. The spectrometer can completely resolve the modes of the frequency comb at 100 MHz.

One of the main features of wavelet and Gabor theories is that they aim at decomposing signals into elementary ones localized
to a certain extent in the time-frequency plane. One way of making this notion of localization more precise is to use time-frequency
distributions. During the last 15 years there has been an interest in the signal analysis c...

Several quantities related to the Zernike circle polynomials admit an
expression, via the basic identity in the diffraction theory of Nijboer
and Zernike, as an infinite integral involving the product of two or
three Bessel functions. In this paper these integrals are identified and
evaluated explicitly for the cases of (a)~the expansion coefficien...

The invention of the femtosecond frequency comb (FC) laser has revolutionized the field of high-resolution spectroscopy, by providing very accurate reference frequencies in the optical domain, acting as a frequency ruler. Similarly, a frequency comb can be viewed as a ruler for distance measurement, which is based on the fact that the vacuum distan...

The theory of orthogonal polynomial (Zernike) expansions of functions on a disk, as used in the diffraction theory of optical aberrations, is applied to obtain (semi-) analytical expressions for the spatial impulse responses arising from a non-uniformly moving, baffled, circular piston. These expressions are in terms of the expansion coefficients o...

It has been suggested by Morse and Ingard that the sound radiation of a loudspeaker in a box is comparable to that of a spherical cap on a rigid sphere. This has been established recently by the present authors, who developed a computation scheme for the forward and inverse calculation of the pressure due to a harmonically excited, flexible cap on...

We investigate general properties of the interferograms from a frequency comb laser in a non-linear dispersive medium. The focus is on interferograms at large delay distances and in particular on their broadening, the fringe formation and shape. It is observed that at large delay distances the interferograms spread linearly and that its shape is de...

Random-access algorithms such as CSMA provide a popular mechanism for distributed medium access control in large-scale wireless networks. In recent years, tractable stochastic models have been shown to yield accurate throughput estimates for CSMA networks. We consider a saturated random-access network on a general conflict graph, and prove that for...

Loudspeakers are often modelled as a rigid piston in an infinite baffle. As a model for real loudspeakers, this
approach is limited in two ways. One issue is that a loudspeaker cone is not rigid and a second issue is that a
loudspeaker is mostly used in a cabinet. Both issues are addressed here by developing the velocity of the
radiator in terms of...

We investigate the final size distribution of the SIR (susceptible-infected-recovered) epidemic model in the critical regime. Using the integral representation of Martin-Löf (1998) for the hitting time of a Brownian motion with parabolic drift, we derive asymptotic expressions for the final size distribution that capture the effect of the initial n...

We investigate the final size distribution of the SIR (susceptible-infected-recovered) epidemic model in the critical regime. Using the integral representation of Martin-Löf (1998) for the hitting time of a Brownian motion with parabolic drift, we derive asymptotic expressions for the final size distribution that capture the effect of the initial n...

Random-access algorithms such as CSMA provide a popular mechanism for distributed medium access control in largescale wireless networks. In recent years, tractable models have been shown to yield accurate throughput estimates for CSMA networks. We consider the saturated model on a general conflict graph, and prove that for each graph, there exists...

We have investigated correlation patterns generated by a frequency-comb laser in a dispersive unbalanced Michelson interferometer and apply the developed formalism to the case of distance metrology. Due to group velocity dispersion, the position of the brightest fringe of the correlation pattern, which is used for distance determination, cannot be...

Several quantities related to the Zernike circle polynomials admit an expression as an infinite integral involving the product of two or three Bessel functions. In this paper these integrals are identified and evaluated explicitly for the cases of (a) the expansion coefficients of scaled-and-shifted circle polynomials, (b) the expansion coefficient...