We show that Kirchhoff ’s law of conservation holds for non-commutative graph flows if and only if the graph is planar. We generalize the theory of (Euclidean) lattices to infinite dimension and... Show moreWe show that Kirchhoff ’s law of conservation holds for non-commutative graph flows if and only if the graph is planar. We generalize the theory of (Euclidean) lattices to infinite dimension and consider the ring of algebraic integers as such a lattice. We compute some invariants using capacity theory and obtain a partial solution to the (algorithmic) closest vector problem. We generalize the results on (universally) graded rings by Lenstra and Silverberg. We study the special case of group rings, and show that under similar assumptions rings can be uniquely decomposed into a group ring in a maximal way. We give a functorial algorithm to compute roots of fractional ideals of orders in number rings. Show less
The emergence of complex diseases resulting from abnormal cell-cell signaling and the spread of infectious diseases caused by pathogens are significant threats to humanity. Unraveling the dynamic... Show moreThe emergence of complex diseases resulting from abnormal cell-cell signaling and the spread of infectious diseases caused by pathogens are significant threats to humanity. Unraveling the dynamic mechanisms underlying cell-cell signaling and infectious disease spreading is crucial for effective disease prevention and treatment. As science and technology advance, the availability and diversity of observational and experimental data related to these biological processes continue to grow. In this thesis, we integrate multisource data with dynamic modeling to investigate the biological mechanisms of Notch signaling in biological development and to develop prevention and control strategies for infectious diseases. Show less
Gomon, D.; Putter, H.; Fiocco, M.; Signorelli, M. 2024
The classical paradigm in appointment scheduling is to rely on ‘a priori schedules’, determined by minimizing the given cost function; the corresponding arrival times are then announced to the... Show moreThe classical paradigm in appointment scheduling is to rely on ‘a priori schedules’, determined by minimizing the given cost function; the corresponding arrival times are then announced to the clients, and not adjusted while serving them. The idea of the present paper is to reduce the cost by periodically updating the schedule (and notifying the clients about this), based on the current state of the system. Evaluation of the objective function is done highly efficiently and accurately by approximating the service times by their phase-type counterparts. The resulting method is computationally inexpensive, thus facilitating frequent evaluation and periodic adaptation of schedules ‘on the fly’. A computational study illustrates the performance of the method, including an assessment of the impact of the rescheduling frequency and the variability of the service times. The most prominent conclusion is that typically, even with relatively few updates, costs can be reduced drastically. Our experiments, however, also reveal that one can construct instances for which increasing the rescheduling frequency does not guarantee a cost reduction; we provide an in-depth analysis of the remarkable phenomenon. The work has broad application potential, e.g., in healthcare and for delivery companies. Show less
For the sake of computational efficiency and for theoretical purposes, in mathematical modelling, the DiracDelta distributions are often utilized as a replacement for cells or vesicles, since the... Show moreFor the sake of computational efficiency and for theoretical purposes, in mathematical modelling, the DiracDelta distributions are often utilized as a replacement for cells or vesicles, since the size of cells or vesicles is much smaller than the size of the surrounding tissues. Here, we consider the scenario that the cell or the vesicle releases the diffusive compounds to the immediate environment, which is modelled by the diffusion equation. Typically, one separates the intracellular and extracellular environment and uses homogeneous Neumann boundary condition for the cell boundary (so-called spatial exclusion model), while the point source model neglects the intracellular environment. We show that extra conditions are needed such that the solutions to the two models are consistent. We prove a necessary and sufficient condition for the consistency. Suggested by the numerical results, we conclude that an initial condition in the form of Gaussian kernel in the point source model compensates for a time-delay discrepancy between the solutions to the two models in the numerical solutions. Various approaches determining optimal amplitude and variance of the Gaussian kernel have been discussed. Show less
Zhou, H.; Dorsman, J.L.; Mandjes, M.; Snelder, M. 2023
Mobility as a Service (MaaS) and new mobility concepts mutually inspire each other, provide alternatives for the private car-oriented transport system as we know it, and will offer more mobility... Show moreMobility as a Service (MaaS) and new mobility concepts mutually inspire each other, provide alternatives for the private car-oriented transport system as we know it, and will offer more mobility choices in a single journey than ever. This multitude of mobility choices however poses challenges in modeling the travelers’ mode choices in travel demand prediction models. To address these challenges, this paper develops a multimodal tour-based mode choice model as part of an activity-based demand model. By explicitly modeling access and egress modes, this choice model creates multimodal mode chain sets on a tour level based on restrictions with respect to personal vehicle ownership, MaaS subscription ownership and vehicle states, and subsequently makes mode choices for every traveler. For the creation of these mode chain sets, we introduce the concept of mode categorization. Seven mode categories are proposed, which include both private and shared mobility concepts. This categorization makes sure that modes are mutually sufficiently different in nature, so that reasonably unbiased mode chain choices can be made. Furthermore, the reduction to seven categories enables the study of large scenarios, while the introduced categories still represent new and already existing modes well. The potential of the model is illustrated by simulating travel demand in the Metropolitan region Rotterdam-The Hague. The results show that our model is capable of making plausible mode choices in the presence of MaaS and new mobility concepts, and can be used to assess the impact of mobility hubs where access and egress mode choice is important. Show less
Developmental time is a key life-history trait with large effects on Darwinian fitness. In many insects, developmental time is currently under strong selection to minimize ecological mismatches in... Show moreDevelopmental time is a key life-history trait with large effects on Darwinian fitness. In many insects, developmental time is currently under strong selection to minimize ecological mismatches in seasonal timing induced by climate change. The genetic basis of responses to such selection, however, is poorly understood. To address this problem, we set up a long-term evolve-and-resequence experiment in the beetle Tribolium castaneum and selected replicate, outbred populations for fast or slow embryonic development. The response to this selection was substantial and embryonic developmental timing of the selection lines started to diverge during dorsal closure. Pooled whole-genome resequencing, gene expression analysis and an RNAi screen pinpoint a 222 bp deletion containing binding sites for Broad and Tramtrack upstream of the ecdysone degrading enzyme Cyp18a1 as a main target of selection. Using CRISPR/Cas9 to reconstruct this allele in the homogenous genetic background of a laboratory strain, we unravel how this single deletion advances the embryonic ecdysone peak inducing dorsal closure and show that this allele accelerates larval development but causes a trade-off with fecundity. Our study uncovers a life-history allele of large effect and reveals the evolvability of developmental time in a natural insect population. Show less
Brown, C.; Derks, G.; Heijster, P. van; Lloyd, D.J.B. 2023
Analytically tracking patterns emerging from a small amplitude Turing instability to large amplitude remains a challenge as no general theory exists. In this paper, we consider a three component... Show moreAnalytically tracking patterns emerging from a small amplitude Turing instability to large amplitude remains a challenge as no general theory exists. In this paper, we consider a three component reaction-diffusion system with one of its components singularly perturbed, this component is known as the fast variable. We develop an analytical theory describing the periodic patterns emerging from a Turing instability using geometric singular perturbation theory. We show analytically that after the initial Turing instability, spatially periodic patterns evolve into a small amplitude spike in the fast variable whose amplitude grows as one moves away from onset. This is followed by a secondary transition where the spike in the fast variable widens, its periodic pattern develops two sharp transitions between two flat states and the amplitudes of the other variables grow. The final type of transition we uncover analytically is where the flat states of the fast variable develop structure in the periodic pattern. The analysis is illustrated and motivated by a numerical investigation. We conclude with a preliminary numerical investigation where we uncover more complicated periodic patterns and snaking-like behaviour that are driven by the three transitions analysed in this paper. This paper provides a crucial step towards understanding how periodic patterns transition from a Turing instability to large amplitude. Show less
During the past 14 years, a clinical audit has been used in the Netherlands to provide hospitals with data on their performance in colorectal cancer care. Continuous feedback on the quality of care... Show moreDuring the past 14 years, a clinical audit has been used in the Netherlands to provide hospitals with data on their performance in colorectal cancer care. Continuous feedback on the quality of care provided at each hospital is essential to improve patient outcomes. It is unclear which methods should be used to generate most informative output for the identification of potential quality issues. Our aim is to compare the commonly employed funnel plot with existing cumulative sum (CUSUM) methodology for the evaluation of postoperative survival and hospital stay outcomes of patients who underwent colorectal surgery in the Netherlands. Data from the Dutch ColoRectal Audit on 25367 patients in the Netherlands who underwent surgical resection for colorectal cancer in 71 hospitals between 2019 and 2021 is used to compare four methods for the detection of deviations in the quality of care. Two methods based on binary outcomes (funnel plot, binary CUSUM) and two CUSUM charts based on survival outcomes (BK-CUSUM and CGR-CUSUM) are considered. A novel approach for determining hospital specific control limits for CUSUM charts is proposed. The ability to detect deviations as well as the time until detection are compared for the four methods. Charts were constructed for the inspection of both postoperative survival and hospital stay. Methods using survival outcomes always yielded faster detection times compared to approaches employing binary outcomes. Detections between methods mostly coincided for postoperative survival. For hospital stay detections varied strongly, with methods based on survival outcomes signalling over half the hospitals. Further pros and cons as well as pitfalls of all methods under consideration are discussed. Methodology for the continuous inspection of the quality of care should be tailored to the specific outcome. Properly understanding how the mechanism of a control chart functions is crucial for the correct interpretation of results. This is particularly true for CUSUM charts, which require the choice of a parameter that greatly influences the results. When applying CUSUM charts, consideration of these issues is strongly recommended. Show less
Classifying elements of the Brauer group of a variety X over a p-adic field by the p-adic accuracy needed to evaluate them gives a filtration on Br X. We relate this filtration to that defined by... Show moreClassifying elements of the Brauer group of a variety X over a p-adic field by the p-adic accuracy needed to evaluate them gives a filtration on Br X. We relate this filtration to that defined by Kato’s Swan conductor. The refined Swan conductor controls how the evaluation maps vary on p-adic discs: this provides a geometric characterisation of the refined Swan conductor. We give applications to rational points on varieties over number fields, including failure of weak approximation for varieties admitting a non-zero global 2-form. Show less
