Uniformisation techniques for stochastic simulation of chemical reaction networks

This work considers the method of uniformisation for continuous-time Markov chains in the context of chemical reaction networks. Previous work in the literature has shown that uniformisation can be beneficial in the context of time-inhomogeneous models, such as chemical reaction networks incorporating extrinsic noise. This paper lays focus on the understanding of uniformisation from the viewpoint of sample paths of chemical reaction networks. In particular, an efficient pathwise stochastic simulation algorithm for time-homogeneous models is presented which is complexity-wise equal to Gillespie's direct method. This new approach therefore enlarges the class of problems for which the uniformisation approach forms a computationally attractive choice. Furthermore, as a new application of the uniformisation method, we provide a novel variance reduction method for (raw) moment estimators of chemical reaction networks based upon the combination of stratification and uniformisation

Virtual counts on Quot schemes and the higher rank local DT/PT correspondence

We show that the Quot scheme $\text{Quot}_{\mathbf{A}^3}(\mathcal{O}^r,n)$ admits a symmetric obstruction theory, and we compute its virtual Euler characteristic. We extend the calculation to locally free sheaves on smooth $3$-folds, thus refining a special case of a recent Euler characteristic calculation of Gholampour-Kool. We then extend Toda's higher rank DT/PT correspondence on Calabi-Yau $3$-folds to a local version centered at a fixed slope stable sheaf. This generalises (and refines) the local DT/PT correspondence around the cycle of a Cohen-Macaulay curve. Our approach clarifies the relation between Gholampour-Kool's functional equation for Quot schemes, and Toda's higher rank DT/PT correspondence.Comment: v2. Minor changes and corrections following referee's comments, 40 pages. Accepted for publication in Math. Res. Let

Virtual counts on Quot schemes and the higher rank local DT/PT correspondence

We show that the Quot scheme $\text{Quot}_{\mathbf{A}^3}(\mathcal{O}^r,n)$ admits a symmetric obstruction theory, and we compute its virtual Euler characteristic. We extend the calculation to locally free sheaves on smooth $3$-folds, thus refining a special case of a recent Euler characteristic calculation of Gholampour-Kool. We then extend Toda's higher rank DT/PT correspondence on Calabi-Yau $3$-folds to a local version centered at a fixed slope stable sheaf. This generalises (and refines) the local DT/PT correspondence around the cycle of a Cohen-Macaulay curve. Our approach clarifies the relation between Gholampour-Kool's functional equation for Quot schemes, and Toda's higher rank DT/PT correspondence

Higher-order interactions in statistical physics and machine learning: A model-independent solution to the inverse problem at equilibrium

The problem of inferring pair-wise and higher-order interactions in complex systems involving large numbers of interacting variables, from observational data, is fundamental to many fields. Known to the statistical physics community as the inverse problem, it has become accessible in recent years due to real and simulated 'big' data being generated. Current approaches to the inverse problem rely on parametric assumptions, physical approximations, e.g. mean-field theory, and ignoring higher-order interactions which may lead to biased or incorrect estimates. We bypass these shortcomings using a cross-disciplinary approach and demonstrate that none of these assumptions and approximations are necessary: We introduce a universal, model-independent, and fundamentally unbiased estimator of all-order symmetric interactions, via the non-parametric framework of Targeted Learning, a subfield of mathematical statistics. Due to its universality, our definition is readily applicable to any system at equilibrium with binary and categorical variables, be it magnetic spins, nodes in a neural network, or protein networks in biology. Our approach is targeted, not requiring fitting unnecessary parameters. Instead, it expends all data on estimating interactions, hence substantially increasing accuracy. We demonstrate the generality of our technique both analytically and numerically on (i) the 2-dimensional Ising model, (ii) an Ising-like model with 4-point interactions, (iii) the Restricted Boltzmann Machine, and (iv) simulated individual-level human DNA variants and representative traits. The latter demonstrates the applicability of this approach to discover epistatic interactions causal of disease in population biomedicine.Comment: 25 pages, 25 figures. Comments welcom

WP 88 - Geïntegreerde dienstverlening in de keten van Werk en Inkomen

Dit rapport onderzoekt de voor- en nadelen van geïntegreerde dienstverlening in de keten van werk en inkomen, gebruik makend van een historische analyse. Het rapport geeft een beschrijving van alle ontwikkelingen op dit vlak in de Nederlandse geschiedenis, sinds de basis voor het sociale stelsel werd gelegd halverwege de negentiende eeuw. De visie van het huidige kabinet blijkt allerminst nieuw. Al voor 1900 zag men voordelen van geïntegreerde uitvoering van uitkeringsverstrekking en arbeidsbemiddeling. Toch is er sinds die tijd niet alleen een tendens geweest richting integratie van de dienstverlening. Perioden van (pogingen tot) integratie wisselden zich af met perioden waarin zowel in Nederland als internationaal de gedachte overheerste dat de uitvoering separaat moet gebeuren. Met het argument dat samenwerking kan helpen uitkeringsgerechtigden te activeren, keerde de integratievisie echter steeds terug. Dit rapport onderzoekt de voor- en nadelen die kunnen worden afgeleid uit de historische ervaringen van Nederland. Geïntegreerde dienstverlening heeft potentieel als voordeel dat het activering zou kunnen bevorderen, vriendelijker is voor werkzoekenden, de ruimte vermindert voor organisaties om kosten op elkaar af te wentelen en meer ruimte biedt voor gezamenlijk gebruik van middelen en inzichten. Daar staat tegenover dat koppeling van arbeidsvoorziening aan uitkeringsverstrekking in het verleden juist vaak heeft geleid tot verdringing van de bemiddelingstaak van de arbeidsvoorzieningorganisatie, vooral op momenten van hoge werkloosheid. Daarnaast bestaat het risico dat binnen de geïntegreerde dienstverlening onvoldoende ruimte is voor specialisatie, wat activering zou kunnen belemmeren. Bovendien is het de vraag of het optimale niveau van aansturing van arbeidsvoorzieningsorganisaties gelijk is aan dat van de verschillende uitkeringsverstrekkers. En dan zijn er nog de praktische problemen met de implementatie van samenwerking of integratie. Het blijkt dat de huidige opzet van geïntegreerde dienstverlening er niet in slaagt de valkuilen voor succesvolle samenwerking te ontlopen. De achterliggende partijen hebben nog steeds hun eigen doelen, worden op verschillende niveaus aangestuurd, worden op een andere manier gefinancierd, hebben hun eigen organisatiecultuur. h3. Abstract in English This paper examines the pros and cons of integrated benefit and employment services. The report describes the developments and trends in this field from the second part of the nineteenth century onwards, when the first social security and social welfare measures were implemented in the Netherlands. It appears that the current perspective on integrated services is not novel. Already in the nineteenth century integration of benefit and employment services was promoted. The trend towards increased integration has, however, not been stable during the observation period. There were periods, both in the Netherlands and internationally, when separate services were preferred over integrated services. Increased political pressure to activate benefit recipients, in combination with the argument that coordination and cooperation between benefit and employment services enhances the activating potential has been responsible for the even returning trend again towards integration of services. As benefits of integrated services this papers identifies the potential of enhanced activation, more friendly for and oriented to the benefit recipients, less room for organisations to free ride on one another and more potential to use each others knowledge and insights. On the other hand, history shows a tendency for the activating obligations to be oppressed by the tasks to register the unemployed, especially during economic recessions. Also, we identified the risk that there is not enough room for specialisation in an integrated organisation. Furthermore, the question has been asked in the past, and remains unanswered, whether the optimal level of organisation of employments services equals that of benefit services. On top of that there are various practical pitfalls, such as the own goals of the cooperating organisation, different levels of governing, different financial incentives and each organisation having its specific organisational culture. The present integration design appears to be unsuccessful in addressing the major integration pitfalls.