Stability of Travelling Waves for Reaction-Diffusion Equations with Multiplicative Noise

We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable travelling wave solutions to the deterministic system retain their orbital stability if the amplitude of the noise is sufficiently small. By applying a stochastic phase-shift together with a time-transform, we obtain a semilinear sPDE that describes the fluctuations from the primary wave. We subsequently develop a semigroup approach to handle the nonlinear stability question in a fashion that is closely related to modern deterministic methods

Superconducting X-ray detectors based on Nb absorbers and Nb/Al tunnel junctions

This thesis describes the research and development of STJs based on Nb/Al\ud technology for application as X-ray detectors in astrophysics conducted by the\ud Low Temperature division of the University of Twente in collaboration with the\ud Stichting Ruimteonderzoek Nederland (SRON). Three topics have been\ud investigated: the spatial inhomogeneous response of STJs which presently\ud limits their performance, the introduction of a thick X-ray absorbing Nb single\ud crystal into the detector design in order to enhance the photon detection\ud efficiency and finally the suitability of Double Relaxation Oscillation\ud Superconducting Quantum Interference Devices (DROSs) as readout amplifiers\ud for cryogenic detectors

Noisy patterns: Bridging the gap between stochastics and dynamics

In this thesis, we study travelling waves in stochastic reaction-diffusion equations. We extend techniques from the deterministic theory for travelling waves to apply to the stochastic version, which allows us to compute the stochastic wave speed and shape, and draw conclusions on the stability of the wave.Analysis and Stochastic

Random Evolutionary Dynamics in Predator-Prey Systems Yields Large, Clustered Ecosystems

We study the effect of speciation, i.e. the introduction of new species through evolution into communities, in the setting of predator-prey systems. Predator-prey dynamics is classically well modeled by Lotka-Volterra equations, also when multiple predator and prey species co-exist. The consequences of the emergence of new species in such systems are much less well understood. We find that introducing random evolving species leads to robust ecosystems in which large numbers of species coexist. Crucially, in these large ecosystems an emergent clustering of species is observed, tying functional differences to phylogenetic history

Random Evolutionary Dynamics in Predator-Prey Systems Yields Large, Clustered Ecosystems

We study the effect of speciation, i.e. the introduction of new species through evolution into communities, in the setting of predator-prey systems. Predator-prey dynamics is classically well modeled by Lotka-Volterra equations, also when multiple predator and prey species co-exist. The consequences of the emergence of new species in such systems are much less well understood. We find that introducing random evolving species leads to robust ecosystems in which large numbers of species coexist. Crucially, in these large ecosystems an emergent clustering of species is observed, tying functional differences to phylogenetic history

Rediscovering Hashed Random Projections for Efficient Quantization of Contextualized Sentence Embeddings

Training and inference on edge devices often requires an efficient setup due to computational limitations. While pre-computing data representations and caching them on a server can mitigate extensive edge device computation, this leads to two challenges. First, the amount of storage required on the server that scales linearly with the number of instances. Second, the bandwidth required to send extensively large amounts of data to an edge device. To reduce the memory footprint of pre-computed data representations, we propose a simple, yet effective approach that uses randomly initialized hyperplane projections. To further reduce their size by up to 98.96%, we quantize the resulting floating-point representations into binary vectors. Despite the greatly reduced size, we show that the embeddings remain effective for training models across various English and German sentence classification tasks that retain 94%--99% of their floating-point

A 1-MHz low noise preamlifier based on Double Relaxation Oscillation SQUIDs

A low noise and wideband preamplifier based on Double Relaxation Oscillation Superconducting Quantum Interference Devices (DROSs) has been realized. A major advantage of a DROS is that it can be operated in a simple flux modulation. So far, biomagnetic measurements performed in our group required only a limited bandwidth smaller than 100 kHz. Other applications, like for instance readout of radiation and particle detectors, demand a larger bandwidth. In this paper, we will discuss our efforts aimed at increasing the operational bandwidth of a DROS in flux locked loop. Presently, a flux locked loop scheme with a -3 dB bandwidth of 1.45 MHz has been built. With this system a white flux noise of 8 ¿¿0/¿Hz was measured with a 1/f-corner frequency of 10 Hz. The slew rate was 2.5·105 ¿0/s. With the mutual input inductance of 6.7 nH, an input current noise of the preamplifier of 2.5 pA/¿Hz was found and a current slew rate of 80 mA/s. We will discuss the suitability of our DROS-based preamplifier for readout of cryogenic particle detectors based on superconducting tunnel junction