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We present a retrospective joint motion correction and reconstruction scheme for magnetic resonance imaging to reduce the imprint of subject motion on the reconstructed images. In multi-contrast imaging, reconstructions pertaining to distinct acquisition sequences (e.g., T1 or T2 weighted images) might not be equally affected by motion, due to the sequential nature of the data acquisition process or the specific sequence design. To avoid repeating the corrupted scan, we can leverage the uncorrupted reconstructions to post-process the contrasts that are most severely affected by motion, by assuming a shared underlying anatomy. Only rigid motion is considered here, but no further assumptions are required. Classical motion correction schemes are combined with weighted total-variation regularization, whose weight is defined by the structure of the well-resolved contrasts. We will particularly focus on brain imaging with conventional Cartesian sampling. We envision a practical workflow that can easily fit into the existing clinical practice without the need for changing the MRI acquisition protocols.

We generalize the greedy and lazy $\beta$-transformations for a real base $\beta$ to the setting of alternate bases $\boldsymbol{\beta}=(\beta_0,\ldots,\beta_{p-1})$, which were recently introduced by the first and second authors as a particular case of Cantor bases. As in the real base case, these new transformations, denoted $T_\boldsymbol{\beta}$ and $L_\boldsymbol{\beta}$ respectively, can be iterated in order to generate the digits of the greedy and lazy $\boldsymbol{\beta}$-expansions of real numbers. The aim of this paper is to describe the dynamical behaviors of $T_\boldsymbol{\beta}$ and $L_\boldsymbol{\beta}$. We first prove the existence of a unique absolutely continuous (with respect to an extended Lebesgue measure, called the $p$-Lebesgue measure) $T_\boldsymbol{\beta}$-invariant measure. We then show that this unique measure is in fact equivalent to the $p$-Lebesgue measure and that the corresponding dynamical system is ergodic and has entropy $\frac{1}{p}\log(\beta_{p-1}\cdots \beta_0)$. We then express the density of this measure and compute the frequencies of letters in the greedy $\boldsymbol{\beta}$-expansions. We obtain the dynamical properties of $L_\boldsymbol{\beta}$ by showing that the lazy dynamical system is isomorphic to the greedy one. We also provide an isomorphism with a suitable extension of the $\beta$-shift. Finally, we show that the $\boldsymbol{\beta}$-expansions can be seen as $(\beta_{p-1}\cdots \beta_0)$-representations over general digit sets and we compare both frameworks., Comment: 28 pages, 15 figures

INTRODUCTION: The credibility of model-based economic evaluations of Alzheimer's disease (AD) interventions is central to appropriate decision-making in a policy context. We report on the International PharmacoEconomic Collaboration on Alzheimer's Disease (IPECAD) Modeling Workshop Challenge.METHODS: Two common benchmark scenarios, for the hypothetical treatment of AD mild cognitive impairment (MCI) and mild dementia, were developed jointly by 29 participants. Model outcomes were summarized, and cross-comparisons were discussed during a structured workshop.RESULTS: A broad concordance was established among participants. Mean 10-year restricted survival and time in MCI in the control group ranged across 10 MCI models from 6.7 to 9.5 years and 3.4 to 5.6 years, respectively; and across 4 mild dementia models from 5.4 to 7.9 years (survival) and 1.5 to 4.2 years (mild dementia).DISCUSSION: The model comparison increased our understanding of methods, data used, and disease progression. We established a collaboration framework to assess cost-effectiveness outcomes, an important step toward transparent and credible AD models.

In this paper, we show how to modify a compartmental epidemic model, without changing the dimension, such that separable static heterogeneity is taken into account. The derivation is based on the Kermack–McKendrick renewal equation.

Every "x"-adjustment in the so-called xVA financial risk management framework relies on the computation of exposures. Considering thousands of Monte Carlo paths and tens of simulation steps, a financial portfolio needs to be evaluated numerous times during the lifetime of the underlying assets. This is the bottleneck of every simulation of xVA. In this article, we explore numerical techniques for improving the simulation of exposures. We aim to decimate the number of portfolio evaluations, particularly for large portfolios involving multiple, correlated risk factors. The usage of the Stochastic Collocation (SC) method, together with Smolyak's sparse grid extension, allows for a significant reduction in the number of portfolio evaluations, even when dealing with many risk factors. The proposed model can be easily applied to any portfolio and size. We report that for a realistic portfolio comprising linear and non-linear derivatives, the expected reduction in the portfolio evaluations may exceed 6000 times, depending on the dimensionality and the required accuracy. We give illustrative examples and examine the method with realistic multi-currency portfolios consisting of interest rate swaps and swaptions., Comment: 25 pages

The COVID-19 pandemic has led to numerous mathematical models for the spread of infection, the majority of which are large compartmental models that implicitly constrain the generation-time distribution. On the other hand, the continuoustime Kermack-McKendrick epidemic model of 1927 (KM27) allows an arbitrary generation-time distribution, but it suffers from the drawback that its numerical implementation is rather cumbersome. Here, we introduce a discrete-time version of KM27 that is as general and flexible, and yet is very easy to implement computationally. Thus, it promises to become a very powerful tool for exploring control scenarios for specific infectious diseases such as COVID-19. To demonstrate this potential, we investigate numerically how the incidence-peak size depends on model ingredients. We find that, with the same reproduction number and the same initial growth rate, compartmental models systematically predict lower peak sizes than models in which the latent and the infectious period have fixed duration.

Detection of unwanted (`foreign') objects within products is a common procedure in many branches of industry for maintaining production quality. X-ray imaging is a fast, non-invasive and widely applicable method for foreign object detection. Deep learning has recently emerged as a powerful approach for recognizing patterns in radiographs (i.e., X-ray images), enabling automated X-ray based foreign object detection. However, these methods require a large number of training examples and manual annotation of these examples is a subjective and laborious task. In this work, we propose a Computed Tomography (CT) based method for producing training data for supervised learning of foreign object detection, with minimal labour requirements. In our approach, a few representative objects are CT scanned and reconstructed in 3D. The radiographs that have been acquired as part of the CT-scan data serve as input for the machine learning method. High-quality ground truth locations of the foreign objects are obtained through accurate 3D reconstructions and segmentations. Using these segmented volumes, corresponding 2D segmentations are obtained by creating virtual projections. We outline the benefits of objectively and reproducibly generating training data in this way compared to conventional radiograph annotation. In addition, we show how the accuracy depends on the number of objects used for the CT reconstructions. The results show that in this workflow generally only a relatively small number of representative objects (i.e., fewer than 10) are needed to achieve adequate detection performance in an industrial setting. Moreover, for real experimental data we show that the workflow leads to higher foreign object detection accuracies than with standard radiograph annotation., Comment: This paper is under consideration at Expert Systems with Applications. 22 pages, 15 figures

In March 2020, the world was thrown into financial distress. This manifested itself in increased uncertainty in the financial markets. Many interest rates collapsed, and funding spreads surged significantly, which increased due to the market turmoil. In light of these events, it is essential to understand and model Wrong-Way Risk (WWR) in a Funding Valuation Adjustment (FVA) context. WWR may currently be absent from FVA calculations in banks' Valuation Adjustment (xVA) engines. However, in this letter, we demonstrate that WWR effects are non-negligible in FVA modelling from a risk-management perspective. We look at the impact of various modelling choices, such as including the default times of the relevant parties, as well as stochastic and deterministic funding spreads. A case study is presented for interest rate derivatives.

Honeybees (Apis mellifera) are important pollinators for wild plants as well as for crops, but honeybee performance is threatened by several stressors including varroa mites, gaps in foraging supply, and pesticides. The consequences of bee colony longtime exposure to multiple stressors are not well understood. The vast number of possible stressor combinations and necessary study duration require research comprising field, laboratory, and simulation experiments. We simulated long‐term exposure of a honeybee colony to the insecticide imidacloprid and to varroa mites carrying the deformed wing virus in landscapes with different temporal gaps in resource availability as single stressors and in combinations. Furthermore, we put a strong emphasis on chronic lethal, acute sublethal, and acute lethal effects of imidacloprid on honeybees. We have chosen conservative published values to parameterize our model (e.g., highest reported imidacloprid contamination). As expected, combinations of stressors had a stronger negative effect on bee performance than each single stressor alone, and effect sizes were larger after 3 years of exposure than after the first year. Imidacloprid‐caused reduction in bee performance was almost exclusively due to chronic lethal effects because the thresholds for acute effects were rarely met in simulations. In addition, honeybee colony extinctions were observed by the last day of the first year but more pronounced on the last days of the second and third simulation year. In conclusion, our study highlights the need for more long‐term studies on chronic lethal effects of pesticides on honeybees. Environ Toxicol Chem 2022;41:2318–2327. © 2022 The Authors. Environmental Toxicology and Chemistry published by Wiley Periodicals LLC on behalf of SETAC., Deutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/501100001659, https://doi.org/10.5281/zenodo.6567312

When Fuat Sezgin came to Istanbul in 1943, he became a student of mathematics and engineering, only changing to Oriental Studies after meeting Hellmut Ritter. We will analyze a paper which Fuat Sezgin published in 1986 and which is a witness of his mathematical abilities. The paper includes an edition of a mathematically difficult text by Ibn al-Haytham which Sezgin reconstructed from a unique Arabic manuscript written with very few diacritical marks. In this treatise, Ibn al-Haytham discusses the theoretical and practical aspects of an instrument which he produced for determining the meridian with utmost accuracy.

For each stratum of the space of translation surfaces, we introduce an infinite translation surface containing in an appropriate manner a copy of every translation surface of the stratum. Given a translation surface $(X, \omega)$ in the stratum, a matrix is in its Veech group $\mathrm{SL}(X,\omega)$ if and only if an associated affine automorphism of the infinite surface sends each of a finite set, the ``marked" {\em Voronoi staples}, arising from orientation-paired segments appropriately perpendicular to Voronoi 1-cells, to another pair of orientation-paired ``marked" segments. We prove a result of independent interest. For each real $a\ge \sqrt{2}$ there is an explicit hyperbolic ball such that for any Fuchsian group trivially stabilizing $i$, the Dirichlet domain centered at $i$ of the group already agrees within the ball with the intersection of the hyperbolic half-planes determined by the group elements whose Frobenius norm is at most $a$. %When $\mathrm{SL}(X,\omega)$ is a lattice we use this to give a condition guaranteeing that the full group $\mathrm{SL}(X,\omega)$ has been computed. Together, these results give rise to a new algorithm for computing Veech groups., Comment: 20 pages, 8 figures. New version has more appropriate title, and minor editing

Background In 2016, a study in a Dutch nursing home showed prolonged colonization duration of extended-spectrum β-lactamase-producing (ESBL)-ST131 compared to ESBL-non-ST131. In this study, we assessed the duration of rectal ESBL-producing E. coli (ESBL-EC) colonization in residents in the same nursing home for an extended period of six years. We aimed to estimate the influence of a possible bias when follow up is started during an outbreak. Methods Between 2013 and 2019, repetitive point prevalence surveys were performed by culturing rectal or faecal swabs from all residents. Kaplan–Meier survival analysis was performed to calculate the median time to clearance of ESBL-EC with a log-rank analysis to test for differences between ESBL-ST131 and ESBL-non-ST131. Results The study showed a median time to clearance of 13.0 months (95% CI 0.0–27.9) for ESBL-ST131 compared to 11.2 months (95% CI 4.8–17.6) for ESBL-non-ST131 (p = 0.044). In the subgroup analysis of residents who were ESBL-EC positive in their first survey, the median time to clearance for ST131 was 59.7 months (95% CI 23.7–95.6) compared to 16.2 months (95% CI 2.1–30.4) for ESBL-non-ST131 (p = 0.036). In the subgroup analysis of residents who acquired ESBL-EC, the median time to clearance for ST131 was 7.2 months (95% CI 2.1–12.2) compared to 7.9 months (95% CI 0.0–18.3) for ESBL-non-ST131 (p = 0.718). The median time to clearance in the ESBL-ST131 group was significantly longer in residents who were ESBL-ST131 colonised upon entering the study than in residents who acquired ESBL-ST131 during the study (p = 0.001). Conclusion A prolonged colonization with ESBL-ST131 was only found in the subgroup who was ESBL-EC positive upon entering the study. The prolonged duration with ESBL-ST131 in the previous study was probably biased by factors that occured during (the start of) the outbreak.

The autoxidation of triglyceride (or triacylglycerol, TAG) is a poorly understood complex system. It is known from mass spectrometry measurements that, although initiated by a single molecule, this system involves an abundance of intermediate species and a complex network of reactions. For this reason, the attribution of the mass peaks to exact molecular structures is difficult without additional information about the system. We provide such information using a graph theory-based algorithm. Our algorithm performs an automatic discovery of the chemical reaction network that is responsible for the complexity of the mass spectra in drying oils. This knowledge is then applied to match experimentally measured mass spectra with computationally predicted molecular graphs. We demonstrate this methodology on the autoxidation of triolein as measured by electrospray ionization-mass spectrometry (ESI-MS). Our protocol can be readily applied to investigate other oils and their mixtures.

In this paper we explore special values of Gaussian hypergeometric functions in terms of products of Euler $$\Gamma $$ Γ -functions and exponential functions of linear functions of the hypergeometric parameters. They include some classical evaluations, but the main inspiration is from the contiguity method recently applied by Akihito Ebisu.

Background Quantification of acquisition routes of antibiotic resistant bacteria (ARB) is pivotal for understanding transmission dynamics and designing cost-effective interventions. Different methods have been used to quantify the importance of transmission routes, such as relative risks, odds ratios (OR), genomic comparisons and basic reproduction numbers. We systematically reviewed reported estimates on acquisition routes’ contributions of ARB in humans, animals, water and the environment and assessed the methods used to quantify the importance of transmission routes. Methods PubMed and EMBASE were searched, resulting in 6054 articles published up until January 1st, 2019. Full text screening was performed on 525 articles and 277 are included. Results We extracted 718 estimates with S. aureus (n = 273), E. coli (n = 157) and Enterobacteriaceae (n = 99) being studied most frequently. Most estimates were derived from statistical methods (n = 560), mainly expressed as risks (n = 246) and ORs (n = 239), followed by genetic comparisons (n = 85), modelling (n = 62) and dosage of ARB ingested (n = 17). Transmission routes analysed most frequently were occupational exposure (n = 157), travelling (n = 110) and contacts with carriers (n = 83). Studies were mostly performed in the United States (n = 142), the Netherlands (n = 87) and Germany (n = 60). Comparison of methods was not possible as studies using different methods to estimate the same route were lacking. Due to study heterogeneity not all estimates by the same method could be pooled. Conclusion Despite an abundance of published data the relative importance of transmission routes of ARB has not been accurately quantified. Links between exposure and acquisition are often present, but the frequency of exposure is missing, which disables estimation of transmission routes’ importance. To create effective policies reducing ARB, estimates of transmission should be weighed by the frequency of exposure occurrence.

Background Hospital outbreaks of multidrug resistant Pseudomonas aeruginosa are often caused by Pseudomonas aeruginosa clones which produce metallo-β-lactamases, such as Verona Integron-encoded Metallo-β-lactamase (VIM). Although different sources have been identified, the exact transmission routes often remain unknown. However, quantifying the role of different transmission routes of VIM-PA is important for tailoring infection prevention and control measures. The aim of this study is to quantify the relative importance of different transmission routes by applying a mathematical transmission model using admission and discharge dates as well as surveillance culture data of patients. Methods We analyzed VIM-PA surveillance data collected between 2010 and 2018 of two intensive-care unit (ICU) wards for adult patients of the Erasmus University Medical Center Rotterdam using a mathematical transmission model. We distinguished two transmission routes: direct cross-transmission and a persistent environmental route. Based on admission, discharge dates, and surveillance cultures, we estimated the proportion of transmissions assigned to each of the routes. Results Our study shows that only 13.7% (95% CI 1.4%, 29%) of the transmissions that occurred in these two ICU wards were likely caused by cross-transmission, leaving the vast majority of transmissions (86.3%, 95% CI 71%, 98.6%) due to persistent environmental contamination. Conclusions Our results emphasize that persistent contamination of the environment may be an important driver of nosocomial transmissions of VIM-PA in ICUs. To minimize the transmission risk from the environment, potential reservoirs should be regularly and thoroughly cleaned and disinfected, or redesigned.

Infections caused by antibiotic-resistant bacteria have become more prevalent during past decades. Yet, it is unknown whether such infections occur in addition to infections with antibiotic-susceptible bacteria, thereby increasing the incidence of infections, or whether they replace such infections, leaving the total incidence unaffected. Observational longitudinal studies cannot separate both mechanisms. Using plasmid-based beta-lactam resistant E. coli as example we applied mathematical modelling to investigate whether seven biological mechanisms would lead to replacement or addition of infections. We use a mathematical neutral null model of individuals colonized with susceptible and/or resistant E. coli, with two mechanisms implying a fitness cost, i.e., increased clearance and decreased growth of resistant strains, and five mechanisms benefitting resistance, i.e., 1) increased virulence, 2) increased transmission, 3) decreased clearance of resistant strains, 4) increased rate of horizontal plasmid transfer, and 5) increased clearance of susceptible E. coli due to antibiotics. Each mechanism is modelled separately to estimate addition to or replacement of antibiotic-susceptible infections. Fitness costs cause resistant strains to die out if other strain characteristics are maintained equal. Under the assumptions tested, increased virulence is the only mechanism that increases the total number of infections. Other benefits of resistance lead to replacement of susceptible infections without changing the total number of infections. As there is no biological evidence that plasmid-based beta-lactam resistance increases virulence, these findings suggest that the burden of disease is determined by attributable effects of resistance rather than by an increase in the number of infections.

Climate response metrics are used to quantify the Earth's climate response to anthropogenic changes of atmospheric CO2. Equilibrium Climate Sensitivity (ECS) is one such metric that measures the equilibrium response to CO2 doubling. However, both in their estimation and their usage, such metrics make assumptions on the linearity of climate response, although it is known that, especially for larger forcing levels, response can be nonlinear. Such nonlinear responses may become visible immediately in response to a larger perturbation, or may only become apparent after a long transient. In this paper, we illustrate some potential problems and caveats when estimating ECS from transient simulations. We highlight ways that very slow timescales may lead to poor estimation of ECS even if there is seemingly good fit to linear response over moderate timescales. Moreover, such slow timescale might lead to late abrupt responses ("late tipping points") associated with a system's nonlinearities. We illustrate these ideas using simulations on a global energy balance model with dynamic albedo. We also discuss the implications for estimating ECS for global climate models, highlighting that it is likely to remain difficult to make definitive statements about the simulation times needed to reach an equilibrium., Comment: 27 pages, 14 figures

Background: Long-acting injectable cabotegravir pre-exposure prophylaxis (PrEP) is recommended by WHO as an additional option for HIV prevention in sub-Saharan Africa, but there is concern that its introduction could lead to an increase in integrase-inhibitor resistance undermining treatment programmes that rely on dolutegravir. We aimed to project the health benefits and risks of cabotegravir-PrEP introduction in settings in sub-Saharan Africa. Methods: With HIV Synthesis, an individual-based HIV model, we simulated 1000 setting-scenarios reflecting both variability and uncertainty about HIV epidemics in sub-Saharan Africa and compared outcomes for each with and without cabotegravir-PrEP introduction. PrEP use is assumed to be risk-informed and to be used only in 3-month periods (the time step for the model) when having condomless sex. We consider three groups at risk of integrase-inhibitor resistance emergence: people who start cabotegravir-PrEP after (unknowingly) being infected with HIV, those who seroconvert while on PrEP, and those with HIV who have residual cabotegravir drugs concentrations during the early tail period after recently stopping PrEP. We projected the outcomes of policies of cabotegravir-PrEP introduction and of no introduction in 2022 across 50 years. In 50% of setting-scenarios we considered that more sensitive nucleic-acid-based HIV diagnostic testing (NAT), rather than regular antibody-based HIV rapid testing, might be used to reduce resistance risk. For cost-effectiveness analysis we assumed in our base case a cost of cabotegravir-PrEP drug to be similar to oral PrEP, resulting in a total annual cost of USD$144 per year ($114 per year and $264 per year considered in sensitivity analyses), a cost-effectiveness threshold of $500 per disability-adjusted life years averted, and a discount rate of 3% per year. Findings: Reflecting our assumptions on the appeal of cabotegravir-PrEP, its introduction is predicted to lead to a substantial increase in PrEP use with approximately 2·6% of the adult population (and 46% of those with a current indication for PrEP) receiving PrEP compared with 1·5% (28%) without cabotegravir-PrEP introduction across 20 years. As a result, HIV incidence is expected to be lower by 29% (90% range across setting-scenarios 6–52%) across the same period compared with no introduction of cabotegravir-PrEP. In people initiating antiretroviral therapy, the proportion with integrase-inhibitor resistance after 20 years is projected to be 1·7% (0–6·4%) without cabotegravir-PrEP introduction but 13·1% (4·1–30·9%) with. Cabotegravir-PrEP introduction is predicted to lower the proportion of all people on antiretroviral therapy with viral loads less than 1000 copies per mL by 0·9% (–2·5% to 0·3%) at 20 years. For an adult population of 10 million an overall decrease in number of AIDS deaths of about 4540 per year (–13 000 to –300) across 50 years is predicted, with little discernible benefit with NAT when compared with standard antibody-based rapid testing. AIDS deaths are predicted to be averted with cabotegravir-PrEP introduction in 99% of setting-scenarios. Across the 50-year time horizon, overall HIV programme costs are predicted to be similar regardless of whether cabotegravir-PrEP is introduced (total mean discounted annual HIV programme costs per year across 50 years is $151·3 million vs $150·7 million), assuming the use of standard antibody testing. With antibody-based rapid HIV testing, the introduction of cabotegravir-PrEP is predicted to be cost-effective under an assumed threshold of $500 per disability-adjusted life year averted in 82% of setting-scenarios at the cost of $144 per year, in 52% at $264, and in 87% at $114. Interpretation: Despite leading to increases in integrase-inhibitor drug resistance, cabotegravir-PrEP introduction is likely to reduce AIDS deaths in addition to HIV incidence. Long-acting cabotegravir-PrEP is predicted to be cost-effective if delivered at similar cost to oral PrEP with antibody-based rapid HIV testing. Funding: Bill & Melinda Gates Foundation, National Institute of Allergy and Infectious Diseases of the National Institutes of Health.

CONTEXT Climate change mitigation in the agricultural sector is a key policy goal. Marginal abatement cost curves allow comparing the cost-effectiveness of agricultural greenhouse gas mitigation measures. Existing studies often do not account for the heterogeneity of farms and interactions between mitigation measures. OBJECTIVE The objective of this study is to present a new approach that allows the calculation of a marginal abatement cost curve that considers farm level interaction effects of climate change mitigation measures. We assess the influence of farm structural heterogeneity on the greenhouse gas abatement potential and the corresponding abatement costs when measures are implemented jointly on the farm level. METHODS We use the bio-economic farm model FarmDyn to simulate farm-specific abatement potential and mitigation costs for a set of mixed dairy farms in a Swiss case study region (n = 66) and develop an approach to calculate a bottom-up, marginal abatement cost curve based on our sample of farms. Simulation results are used to identify and quantify the effect of heterogeneous farm structures (e.g., size, land use, etc.) on the interactions of climate change mitigation measures using regression analysis. RESULTS AND CONCLUSIONS In our study, interaction effects reduce marginal abatement costs by 7% and the overall greenhouse gas abatement potential by 3% compared to a stand-alone consideration of four climate change mitigation measures. Our analysis of how the underlying farm structures affect interaction effects between climate change mitigation measures shows that complex processes on the farm level can have ambiguous effects (i.e., increasing or decreasing greenhouse gas emissions). We conclude that our approach can provide important knowledge about how heterogeneity affects marginal abatement costs when mitigation measures interact with each other. SIGNIFICANCE Knowledge about the effectiveness and efficiency of climate change mitigation measures and their interaction effects improves our understanding and development of bottom-up marginal abatement cost curves, which represent an important and widely used tool to inform policymakers and stakeholders on cost-efficient and cost-effective climate change mitigation in agriculture., Agricultural Systems, 207, ISSN:0308-521X

Starting from three-dimensional nonlinear elasticity under the restriction of incompressibility, we derive reduced models to capture the behavior of strings in response to external forces. Our $\Gamma$-convergence analysis of the constrained energy functionals in the limit of shrinking cross sections gives rise to explicit one-dimensional limit energies. The latter depend on the scaling of the applied forces. The effect of local volume preservation is reflected either in their energy densities through a constrained minimization over the cross-section variables or in the class of admissible deformations. Interestingly, all scaling regimes allow for compression and/or stretching of the string. The main difficulty in the proof of the $\Gamma$-limit is to establish recovery sequences that accommodate the nonlinear differential constraint imposed by the incompressibility. To this end, we modify classical constructions in the unconstrained case with the help of an inner perturbation argument tailored for $3$d-$1$d dimension reduction problems., Comment: 20 pages, 3 figures

In this paper, we perform the parameter-dependent center manifold reduction near the generalized Hopf (Bautin), fold-Hopf, Hopf-Hopf, and transcritical-Hopf bifurcations in delay differential equations (DDEs). This allows us to initialize the continuation of codimension one equilibria and cycle bifurcations emanating from these codimension two bifurcation points. The normal form coefficients are derived in the functional analytic perturbation framework for dual semigroups (sun-star calculus) using a normalization technique based on the Fredholm alternative. The obtained expressions give explicit formulas which have been implemented in the freely available numerical software package DDE-BifTool. While our theoretical results are proven to apply more generally, the software implementation and examples focus on DDEs with finitely many discrete delays. Together with the continuation capabilities of DDE-BifTool, this provides a powerful tool to study the dynamics near equilibria of such DDEs. The effectiveness is demonstrated on various models.

We study the inverse scattering problem for a Schrödinger operator related to a static wave operator with variable velocity, using the GLM (Gelfand–Levitan–Marchenko) integral equation. We assume to have noisy scattering data, and we derive a stability estimate for the error of the solution of the GLM integral equation by showing the invertibility of the GLM operator between suitable function spaces. To regularise the problem, we formulate a variational total least squares problem, and we show that, under certain regularity assumptions, the optimisation problem admits minimisers. Finally, we compute numerically the regularised solution of the GLM equation using the total least squares method in a discrete sense.

Percolation is a process that impairs network connectedness by deactivating links or nodes. This process features a phase transition that resembles paradigmatic critical transitions in epidemic spreading, biological networks, traffic and transportation systems. Some biological systems, such as networks of neural cells, actively respond to percolation-like damage, which enables these structures to maintain their function after degradation and aging. Here we study percolation in networks that actively respond to link damage by adopting a mechanism resembling synaptic scaling in neurons. We explain critical transitions in such active networks and show that these structures are more resilient to damage as they are able to maintain a stronger connectedness and ability to spread information. Moreover, we uncover the role of local rescaling strategies in biological networks and indicate a possibility of designing smart infrastructures with improved robustness to perturbations., Link damages and failures can break the functionality of the whole complex network. Inspired by biological systems that respond to damages, the authors propose a mathematical model revealing the effect of homeostatic response to damage of links to keep the network’s global function.

To minimize the communication in parallel sparse matrix-vector multiplication while maintaining load balance, we need to partition the sparse matrix optimally into k disjoint parts, which is an NP-complete problem. We present an exact algorithm based on the branch and bound (BB) method which partitions a matrix for any k, and we explore exact sparse matrix partitioning beyond bipartitioning. The algorithm has been implemented in a software package General Matrix Partitioner (GMP). We also present an integer linear programming (ILP) model for the same problem, based on a hypergraph formulation. We used both methods to determine optimal 2,3,4-way partitionings for a subset of small matrices from the SuiteSparse Matrix Collection. For k=2, BB outperforms ILP, whereas for larger k, ILP is superior. We used the results found by these exact methods for k=4 to analyse the performance of recursive bipartitioning (RB) with exact bipartitioning. For 46 matrices of the 89 matrices in our test set of matrices with less than 250 nonzeros, the communication volume determined by RB was optimal. For the other matrices, RB is able to find 4-way partitionings with communication volume close to the optimal volume.

Funder: Grantová Agentura Ceské Republiky, Funder: H2020 European Research Council; Id: http://dx.doi.org/10.13039/100010663, An independent transversal of a graph G $G$ with a vertex partition P ${\mathscr{P}}$ is an independent set of G $G$ intersecting each block of P ${\mathscr{P}}$ in a single vertex. Wanless and Wood proved that if each block of P ${\mathscr{P}}$ has size at least t $t$ and the average degree of vertices in each block is at most t ∕ 4 $t\unicode{x02215}4$ , then an independent transversal of P ${\mathscr{P}}$ exists. We present a construction showing that this result is optimal: for any ε > 0 $\varepsilon \gt 0$ and sufficiently large t $t$ , there is a forest with a vertex partition into parts of size at least t $t$ such that the average degree of vertices in each block is at most ( 1 4 + ε ) t $(\frac{1}{4}+\varepsilon )t$ , and there is no independent transversal. This unexpectedly shows that methods related to entropy compression such as the Rosenfeld–Wanless–Wood scheme or the Local Cut Lemma are tight for this problem. Further constructions are given for variants of the problem, including the hypergraph version.

The shape of Africa on Iberian nautical charts of the late-fifteenth and earlysixteenth century is surprisingly mature. The portrayal of the outline of Africa on the Cantino planisphere of 1502 is so good that it was not surpassed in the next two, possibly three centuries. The African coastline on the Cantino planisphere is a mosaic of accurate regional charts on the plate-carrée projection, each with its own scale and orientation. The same holds for its berian predecessors. The shape of the parts of Africa depicted on these regional charts was essentially correct on the oldest chart (c. 1471) and was copied to later charts. The projective properties of the regional charts are incompatible with the navigation and charting techniques used in that period. Therefore, serious doubt is cast on the established view that Portuguese pilots and cartographers were the original creators of the source charts.

In Cipriani et al. (2017), the authors proved that, with the appropriate rescaling, the odometer of the (nearest neighbours) divisible sandpile on the unit torus converges to a bi-Laplacian field. Here, we study α -long-range divisible sandpiles, similar to those introduced in Frometa and Jara (2018). We show that, for α ∈ ( 0 , 2 ) , the limiting field is a fractional Gaussian field on the torus with parameter α / 2 . However, for α ∈ [ 2 , ∞ ) , we recover the bi-Laplacian field. This provides an alternative construction of fractional Gaussian fields such as the Gaussian Free Field or membrane model using a diffusion based on the generator of Levy walks. The central tool for obtaining our results is a careful study of the spectrum of the fractional Laplacian on the discrete torus. More specifically, we need the rate of divergence of the eigenvalues as we let the side length of the discrete torus go to infinity. As a side result, we obtain precise asymptotics for the eigenvalues of discrete fractional Laplacians. Furthermore, we determine the order of the expected maximum of the discrete fractional Gaussian field with parameter γ = min { α , 2 } and α ∈ R + ∖ { 2 } on a finite grid.

Tomography is a powerful tool for reconstructing the interior of an object from a series of projection images. Typically, the source and detector traverse a standard path (e.g., circular, helical). Recently, various techniques have emerged that use more complex acquisition geometries. Current software packages require significant handwork, or lack the flexibility to handle such geometries. Therefore, software is needed that can concisely represent, visualize, and compute reconstructions of complex acquisition geometries. We present tomosipo, a Python package that provides these capabilities in a concise and intuitive way. Case studies demonstrate the power and flexibility of tomosipo. (C) 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Summary In this abstract, we review the gradient-based Markov Chain Monte Carlo (MCMC) and demonstrate its applicability in inferring the uncertainty in seismic inversion. There are many flavours of gradient-based MCMC; here, we will only focus on the Unadjusted Langevin algorithm (ULA) and Metropolis-Adjusted Langevin algorithm (MALA). We propose an adaptive step-length based on the Lipschitz condition within ULA to automate the tuning of step-length and suppress the Metropolis-Hastings acceptance step in MALA. We consider the linear seismic travel-time tomography problem as a numerical example to demonstrate the applicability of both methods.

Despite their relevance in mathematical biology, there are, as yet, few general results about the asymptotic behaviour of measure valued solutions of renewal equations on the basis of assumptions concerning the kernel. We characterise, via their kernels, a class of renewal equations whose measure-valued solution can be expressed in terms of the solution of a scalar renewal equation. The asymptotic behaviour of the solution of the scalar renewal equation, is studied via Feller’s classical renewal theorem and, from it, the large time behaviour of the solution of the original renewal equation is derived.

Oceanic circulation and mass‐field variability play important roles in exciting Earth's wobbles and length‐of‐day changes (ΔΛ), on time scales from days to several years. Modern descriptions of these effects employ oceanic angular momentum (OAM) series from numerical forward models or ocean state estimates, but nothing is known about how ocean reanalyses with sequential data assimilation (DA) would fare in that context. Here, we compute daily OAM series from three 1/4° global ocean reanalyses that are based on the same hydrodynamic core and input data (e.g., altimetry, Argo) but different DA schemes. Comparisons are carried out (a) among the reanalyses, (b) with an established ocean state estimate, and (c) with Earth rotation data, all focusing on the period 2006–2015. The reanalyses generally provide credible OAM estimates across a range of frequencies, although differences in amplitude spectra indicate a sensitivity to the adopted DA scheme. For periods less than 120 days, the reanalysis‐based OAM series explain ∼40%–50% and ∼30%–40% of the atmosphere‐corrected equatorial and axial geodetic excitation, similar to what is achieved with the state estimate. We find mixed performance of the reanalyses in seasonal excitation budgets, with some questionable mean ocean mass changes affecting the annual cycle in ΔΛ. Modeled excitations at interannual frequencies are more uncertain compared to OAM series from the state estimate and show hints of DA artifacts in one case. If users are to choose any of the tested reanalyses for rotation research, our study points to the Ocean Reanalysis System 5 as the most sensible choice., Key Points: We evaluate three ocean reanalyses for their skill in explaining Earth rotation variations on different time scales from 2006 to 2015. For periods, Deutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/501100001659, https://resources.marine.copernicus.eu/product-detail/GLOBAL_REANALYSIS_PHY_001_031/INFORMATION, https://isdc.gfz-potsdam.de/ggfc-oceans/oam/, https://www.ncei.noaa.gov/access/metadata/landing-page/bin/iso?id=gov.noaa.ngdc.mgg.dem:316, https://podaac-tools.jpl.nasa.gov/drive/files/GeodeticsGravity/tellus/L3/mascon/RL06/JPL/v02/CRI/netcdf, https://keof.jpl.nasa.gov/combinations/

An ensemble data assimilation method is proposed that is based on optimal control minimizing the cost of mismatch in the Wasserstein metric on the observation space. The new method achieved the optimal state without calculating the posterior distribution of the particle state and the particle states are evolved deterministically, which is easy to be implemented. The method is appropriate for systems in which multiple, noisy, partial observations are available (e.g. citizen weather stations or smart phones). The method is demonstrated for: (i) deterministic dynamics with uncertain initial conditions, (ii) multiple noisy observations of a randomly forced ordinary differential equation (ODE), (iii) observations from multiple sample paths from a stochastic differential equation (SDE). A bi-modal measure and a measure supported on a strange attractor are tested. The numerical results show that our method performs a relatively small Wasserstein distance which measures the approximation performance. But numerical implementation is a bit expensive due to the complexity of Wasserstein distance computation, especially with large set of particles.

We prove supercongruences modulo p2 for values of truncated hypergeometric series at some special points. The parameters of the hypergeometric series are d copies of 1/2 and d copies of 1 for any integer d≥2. In addition we describe their relation to hypergeometric motives.

We study the parameterized complexity of computing the tree-partition-width, a graph parameter equivalent to treewidth on graphs of bounded maximum degree. On one hand, we can obtain approximations of the tree-partition-width efficiently: we show that there is an algorithm that, given an n-vertex graph G and an integer k, constructs a tree-partition of width O(k⁷) for G or reports that G has tree-partition width more than k, in time k^O(1) n². We can improve slightly on the approximation factor by sacrificing the dependence on k, or on n. On the other hand, we show the problem of computing tree-partition-width exactly is XALP-complete, which implies that it is W[t]-hard for all t. We deduce XALP-completeness of the problem of computing the domino treewidth. Finally, we adapt some known results on the parameter tree-partition-width and the topological minor relation, and use them to compare tree-partition-width to tree-cut width., LIPIcs, Vol. 249, 17th International Symposium on Parameterized and Exact Computation (IPEC 2022), pages 7:1-7:20

Quadratic three-dimensional autonomous systems may display complex behavior. Studying the systems Sprott A and NE9, we find families of tori and periodic solutions both involving canards. Using time-reversal and symmetry, we are able to explain in these two systems both the analysis and origin of tori, periodic solutions, and the numerics of these objects. For system NE9, unbounded solutions exist that admit analytic description by singular perturbation theory of the flow near infinity, also we observe torus destruction and a new chaotic attractor (Kaplan-Yorke dimension 2.1544) produced by a period-doubling scenario. The subtle numerics of periodic solutions involving canards is explained in the final section.

SUMMARY Receiver functions have been used for decades to study the Earth’s major discontinuities by focusing on converted waves. Deconvolution, which is the mathematical backbone of the method, is assumed to remove the source time function and the far-field dependence on structure, making it a useful method to map the nearby Earth structure and its discontinuities. Ray theory, a plane incoming wavefield, and a sufficiently well-known near-receiver background velocity model are conventionally assumed to map the observations to locations in the subsurface. Many researchers are aware of the shortcoming of these assumptions and several remedies have been proposed for mitigating their consequences. Adjoint tomography with a quasi-exact forward operator is now within reach for most researchers, and we believe is the way forward in receiver function studies. A first step is to calculate adjoint sensitivity kernels for a given misfit function. Here, we derive the adjoint source for a receiver function waveform misfit. Using a spectral element forward code, we have calculated sensitivity kernels for P-to-S converted waves using several 2-D models representing an average crust with an underlying mantle. The kernels show profound differences between P- and S-wave speed sensitivity. The sensitivity to P-wave speed is wide-ranging and related to the scattered P-wavefield which interferes with that of the P-to-S converted wave. The S-wave speed sensitivity is more local and mostly associated to potential locations of P-to-S conversion, although more distant sensitivity is also observed. Notably, there is virtually no sensitivity to impedance. We further observe the well-known trade-off between depth of the discontinuity and wave speed, but find that considering a longer waveform that includes more surface reverberations reduces this trade-off significantly.

SUMMARY In this study, we aim to solve the seismic inversion in the Bayesian framework by generating samples from the posterior distribution. This distribution incorporates the uncertainties in the seismic data, forward model, and prior information about the subsurface model parameters; thus, we obtain more information through sampling than through a point estimate (e.g. maximum a posteriori method). Based on the numerical cost of solving the forward problem and the dimensions of the subsurface model parameters and observed data, sampling with Markov chain Monte Carlo (MCMC) algorithms can be prohibitively expensive. Herein, we consider the promising Langevin dynamics MCMC algorithm. However, this algorithm has two central challenges: (1) the step size requires prior tuning to achieve optimal performance and (2) the Metropolis–Hastings acceptance step is computationally demanding. We approach these challenges by proposing an adaptive step-size rule and considering the suppression of the Metropolis–Hastings acceptance step. We highlight the proposed method’s potential through several numerical examples and rigorously validate it via qualitative and quantitative evaluation of the sample quality based on the kernelized Stein discrepancy (KSD) and other MCMC diagnostics such as trace and autocorrelation function plots. We conclude that, by suppressing the Metropolis–Hastings step, the proposed method provides fast sampling at efficient computational costs for large-scale seismic Bayesian inference; however, this inflates the second statistical moment (variance) due to asymptotic bias. Nevertheless, the proposed method reliably recovers important aspects of the posterior, including means, variances, skewness and 1-D and 2-D marginals. With larger computational budget, exact MCMC methods (i.e. with a Metropolis–Hastings step) should be favoured. The results thus obtained can be considered a feasibility study for promoting the approximate Langevin dynamics MCMC method for Bayesian seismic inversion on limited computational resources.

A natural example of evolution can be described by a time-dependent two degrees-of-freedom Hamiltonian. We choose the case where initially the Hamiltonian derives from a general cubic potential, the linearised system has frequencies 1 and ω&gt, 0. The time-dependence produces slow evolution to discrete (mirror) symmetry in one of the degrees-of-freedom. This changes the dynamics drastically depending on the frequency ratio ω and the timescale of evolution. We analyse the cases ω=1,2,3 where the ratio’s 1,2 turn out to be the most interesting. In an initial phase we find 2 adiabatic invariants with changes near the end of evolution. A remarkable feature is the vanishing and emergence of normal modes, stability changes and strong changes of the velocity distribution in phase-space. The problem is inspired by the dynamics of axisymmetric, rotating galaxies that evolve slowly to mirror symmetry with respect to the galactic plane, the model formulation is quite general.

We present an elementary elaboration of Dwork's idea of explicit $p$-adic limit formulas for zeta functions of toric hypersurfaces., Comment: This version is identical with the earlier one, we only change the numeration of theorems so that it agrees with the version published by IMRN

In the standard theory of delay equations, the fundamental solution does not ‘live’ in the state space. To eliminate this age-old anomaly, we enlarge the state space. As a consequence, we lose the strong continuity of the solution operators and this, in turn, has as a consequence that the Riemann integral no longer suffices for giving meaning to the variation-of-constants formula. To compensate, we develop the Stieltjes-Pettis integral in the setting of a norming dual pair of spaces. Part I provides general theory, Part II deals with “retarded” equations, and in Part III we show how the Stieltjes integral enables incorporation of unbounded perturbations corresponding to neutral delay equations.

X-ray imaging is a widely used technique for non-destructive inspection of agricultural food products. One application of X-ray imaging is the autonomous, in-line detection of foreign objects in food samples. Examples of such inclusions are bone fragments in meat products, plastic and metal debris in fish, fruit infestations. This article presents a processing methodology for unsupervised foreign object detection based on dual-energy X-ray absorptiometry (DEXA). A foreign object is defined as a fragment of material with different X-ray attenuation properties than those belonging to the food product. A novel thickness correction model is introduced as a pre-processing technique for DEXA data. The aim of the model is to homogenize regions in the image that belong to the food product and enhance contrast where the foreign object is present. In this way, the segmentation of the foreign object is more robust to noise and lack of contrast. The proposed methodology was applied to a dataset of 488 samples of meat products. The samples were acquired from a conveyor belt in a food processing factory. Approximately 60\% of the samples contain foreign objects of different types and sizes, while the rest of the samples are void of foreign objects. The results show that samples without foreign objects are correctly identified in 97% of cases, the overall accuracy of foreign object detection reaches 95%., Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible

Current statistical post-processing methods for probabilistic weather forecasting are not capable of using full spatial patterns from the numerical weather prediction (NWP) model. In this paper we incorporate spatial wind speed information by using convolutional neural networks (CNNs) and obtain probabilistic wind speed forecasts in the Netherlands for 48 hours ahead, based on KNMI's deterministic Harmonie-Arome NWP model. The probabilistic forecasts from the CNNs are shown to have higher Brier skill scores for medium to higher wind speeds, as well as a better continuous ranked probability score (CRPS) and logarithmic score, than the forecasts from fully connected neural networks and quantile regression forests. As a secondary result, we have compared the CNNs using 3 different density estimation methods (quantized softmax (QS), kernel mixture networks, and fitting a truncated normal distribution), and found the probabilistic forecasts based on the QS method to be best., 44 pages, 5 figures

The results of heat transfer mathematical model calculations in the “UO2-BeO” pellet are presented. The fuel pellet consists of uranium dioxide (UO2) and beryllium oxide (BeO) ceramics. Modeling of heat transfer was carried out by a system of generalized heat conduction equations with variable thermophysical properties. The calculated data of the temperature field in the fuel pellet were obtained using the COMSOL Multiphysics software code. The results of temperature calculations were compared with the data of other authors. The agreement of the calculated data shows the mathematical model and the COMSOL Multiphysics code algorithms correctness. Various arrangements of beryllium oxide ceramics BeO in a fuel pellet are considered. The arrangement of the BeO ceramics in the centre of the fuel pellet showed a noticeable decrease in temperature in the energy release zone. Calculations have shown that the composite fuel “UO2-BeO” is the most effective for regulating the thermal regime of fuel elements.

In this paper we consider memoryless one-bit compressed sensing with randomly subsampled Gaussian circulant matrices. We show that in a small sparsity regime and for small enough accuracy $\delta$, $m\sim \delta^{-4} s\log(N/s\delta)$ measurements suffice to reconstruct the direction of any $s$-sparse vector up to accuracy $\delta$ via an efficient program. We derive this result by proving that partial Gaussian circulant matrices satisfy an $\ell_1/\ell_2$ RIP-property. Under a slightly worse dependence on $\delta$, we establish stability with respect to approximate sparsity, as well as full vector recovery results., Comment: 20 pages

Bifurcation analysis is used to study an effective model of QCD$_4$ with four-fermi interactions. Our analysis supports the scenario of a fixed point merger at the lower edge of the conformal window. This indicates square root scaling of the anomalous scaling dimensions of the fermion fields just above the lower edge and exponential scaling just below. We also predict existence of new fixed points in this model whose (dis)appearance may indicate transitions of the flow within the conformal window. Furthermore, we make new predictions for the critical value $(N_{f}/N_{c})_{\textrm{crit}}$ at the lower edge. We also obtain exotic spiraling flows that are generated by complex scaling dimensions of the effective four-fermi interactions. Finally, we extend the model by adding a scalar field that couples with a Yukawa interaction term and study the modifications it causes to RG-flows., Comment: 31+26 pages; references added, typos corrected

We give a survey on local and semi-local bifurcations of divergence-free vector fields. These differ for low dimensions from generic' bifurcations of structure-less dissipative' vector fields, up to a dimension-threshold that grows with the co-dimension of the bifurcation.

We introduce a framework to systematically investigate the resonant double Hopf bifurcation. We use the basic invariants of the ensuing T 1 -action to analyse the approximating normal form truncations in a unified manner. In this way we obtain a global description of the parameter space and thus find the organising resonance droplet, which is the present analogue of the resonant gap. The dynamics of the normal form yields a skeleton for the dynamics of the original system. In the ensuing perturbation theory both normal hyperbolicity (centre manifold theory) and kam theory are being used.

This report summarizeswork done by, or in collaboration with, the Boreal Avian Modelling Projectbetween April 2021and March 2022.&nbsp

We consider regularized least-squares problems of the form $\min_{x} \frac{1}{2}\Vert Ax - b\Vert_2^2 + \mathcal{R}(Lx)$. Recently, Zheng et al., 2019, proposed an algorithm called Sparse Relaxed Regularized Regression (SR3) that employs a splitting strategy by introducing an auxiliary variable $y$ and solves $\min_{x,y} \frac{1}{2}\Vert Ax - b\Vert_2^2 + \frac{\kappa}{2}\Vert Lx - y\Vert_2^2 + \mathcal{R}(x)$. By minimizing out the variable $x$ we obtain an equivalent system $\min_{y} \frac{1}{2} \Vert F_{\kappa}y - g_{\kappa}\Vert_2^2+\mathcal{R}(y)$. In our work we view the SR3 method as a way to approximately solve the regularized problem. We analyze the conditioning of the relaxed problem in general and give an expression for the SVD of $F_{\kappa}$ as a function of $\kappa$. Furthermore, we relate the Pareto curve of the original problem to the relaxed problem and we quantify the error incurred by relaxation in terms of $\kappa$. Finally, we propose an efficient iterative method for solving the relaxed problem with inexact inner iterations. Numerical examples illustrate the approach., Comment: 25 pages, 14 figures, submitted to SIAM Journal for Scientific Computing special issue Sixteenth Copper Mountain Conference on Iterative Methods