MultivariateResidues - a Mathematica package for computing multivariate residues

We present the Mathematica package MultivariateResidues, which allows for the efficient evaluation of multivariate residues based on methods from computational algebraic geometry. Multivariate residues appear in several contexts of scattering amplitude computations. Examples include applications to the extraction of master integral coefficients from maximal unitarity cuts, the construction of canonical bases of loop integrals and the construction of tree amplitudes from scattering equations.Comment: 7 pages, 2 figures, contribution to the proceedings of the 13th International Symposium on Radiative Corrections (RADCOR 2017

Imaginary parts and discontinuities of Wilson line correlators

We introduce a notion of position-space cuts of eikonal diagrams, the set of diagrams appearing in the perturbative expansion of the correlator of a set of straight semi-infinite Wilson lines. The cuts are applied directly to the position-space representation of any such diagram and compute its imaginary part to the leading order in the dimensional regulator. Our cutting prescription thus defines a position-space analog of the standard momentum-space Cutkosky rules. Unlike momentum-space cuts which put internal lines on shell, position-space cuts constrain a number of the gauge bosons exchanged between the energetic partons to be lightlike, leading to a vanishing and a non-vanishing imaginary part for space- and timelike kinematics, respectively.Comment: 5 pages, 2 figures; minor changes; version published in PR

Position-space cuts for Wilson line correlators

We further develop the formalism for taking position-space cuts of eikonal diagrams introduced in [Phys.Rev.Lett. 114 (2015), no. 18 181602, arXiv:1410.5681]. These cuts are applied directly to the position-space representation of any such diagram and compute its discontinuity to the leading order in the dimensional regulator. We provide algorithms for computing the position-space cuts and apply them to several two- and three-loop eikonal diagrams, finding agreement with results previously obtained in the literature. We discuss a non-trivial interplay between the cutting prescription and non-Abelian exponentiation. We furthermore discuss the relation of the imaginary part of the cusp anomalous dimension to the static interquark potential.Comment: 39+18 pages, 16 figures; elaborated the discussion of the comparison of numerical and analytic results for the three-gluon vertex diagram in the caption of fig. 16; version to be published in JHE

Double-real contribution to the quark beam function at N3^{3}LO QCD

We compute the master integrals required for the calculation of the double-real emission contributions to the matching coefficients of 0-jettiness beam functions at next-to-next-to-next-to-leading order in perturbative QCD. As an application, we combine these integrals and derive the double-real gluon emission contribution to the matching coefficient $I_{qq}(t,z)$ of the quark beam function.Comment: 28 pages, 1 figure; updated ancillary file (accessible through url in the section "Results"

Automatic spin-entangled decays of heavy resonances in Monte Carlo simulations

We present a general method that allows one to decay narrow resonances in Les Houches Monte Carlo events in an efficient and accurate way. The procedure preserves both spin correlation and finite width effects to a very good accuracy, and is therefore particularly suited for the decay of resonances in production events generated at next-to-leading-order accuracy. The method is implemented as a generic tool in the MadGraph framework, giving access to a very large set of possible applications. We illustrate the validity of the method and the code by applying it to the case of single top and top quark pair production, and show its capabilities on the case of top quark pair production in association with a Higgs boson.Comment: 17 pages, 6 figures, published versio

Triple-real contribution to the quark beam function in QCD at next-to-next-to-next-to-leading order

We compute the three-loop master integrals required for the calculation of the triple-real contribution to the N$^3$LO quark beam function due to the splitting of a quark into a virtual quark and three collinear gluons, $q \to q^*+ggg$. This provides an important ingredient for the calculation of the leading-color contribution to the quark beam function at N$^3$LO.Comment: 31 pages, 2 figures; published version, updated ancillary file (accessible through url in the section "Results"

Bistability and regular spatial patterns in arid ecosystems.

A variety of patterns observed in ecosystems can be explained by resource–concentration mechanisms. A resource–concentration mechanism occurs when organisms increase the lateral flow of a resource toward them, leading to a local concentration of this resource and to its depletion from areas farther away. In resource–concentration systems, it has been proposed that certain spatial patterns could indicate proximity to discontinuous transitions where an ecosystem abruptly shifts from one stable state to another. Here, we test this hypothesis using a model of vegetation dynamics in arid ecosystems. In this model, a resource– concentration mechanism drives a positive feedback between vegetation and soil water availability. We derived the conditions leading to bistability and pattern formation. Our analysis revealed that bistability and regular pattern formation are linked in our model. This means that, when regular vegetation patterns occur, they indicate that the system is along a discontinuous transition to desertification. Yet, in real systems, only observing regular vegetation patterns without identifying the pattern-driving mechanism might not be enough to conclude that an ecosystem is along a discontinuous transition because similar patterns can emerge from different ecological mechanisms

Nutrients and Hydrology Indicate the Driving Mechanisms of Peatland Surface Patterning

Peatland surface patterning motivates studies that identify underlying structuring mechanisms. Theoretical studies so far suggest that different mechanisms may drive similar types of patterning. The long time span associated with peatland surface pattern formation, however, limits possibilities for empirically testing model predictions by field manipulations. Here, we present a model that describes spatial interactions between vegetation, nutrients, hydrology, and peat. We used this model to study pattern formation as driven by three different mechanisms: peat accumulation, water ponding, and nutrient accumulation. By on-and-off switching of each mechanism, we created a full-factorial design to see how these mechanisms affected surface patterning (pattern of vegetation and peat height) and underlying patterns in nutrients and hydrology. Results revealed that different combinations of structuring mechanisms lead to similar types of peatland surface patterning but contrasting underlying patterns in nutrients and hydrology. These contrasting underlying patterns suggest that the presence or absence of the structuring mechanisms can be identified by relatively simple short-term field measurements of nutrients and hydrology, meaning that longer-term field manipulations can be circumvented. Therefore, this study provides promising avenues for future empirical studies on peatland patternin

Tailoring care for older adults:understanding older adults' goals and preferences

The increasing amount of older adults with multi-morbidity and increasing care complexity demands a fundamental change in care delivery. It entails a shift from a disease-oriented approach to a tailored approach for frail older adults. Nowadays, proactive integrated person-centred care is strived for in order to face these aging population challenges and achieve tailored care. Despite all efforts, the effects of these care reforms are unclear and the reasons for their hampered implementation are not fully understood. Therefore, the realist evaluation approach can be of help, which focusses not only on the outcomes of new care initiatives, but also on the mechanisms and context in which these reforms take place. We used this approach to study the role of goal setting within proactive care services for frail older adults. We evaluated three different perspectives in this regard: the extent to which goal setting programs have improved outcomes for older adults, the mechanisms of goal setting within proactive care, and the context of older adult’s preferences inferencing these outcomes and mechanisms. Multiple resources were combined (medical records, audio-taped assessments, older adults’ self-reported preferences and wellbeing status, and semi-structured interviews with older adults and care professionals), which led to the following conclusion: Tailored care for older adults experiencing frailty and multi-morbidity by means of goal setting and involvement adapted to their engagement preferences, supports their need for holistic care, but can only have an impact on individual goals when embedded within a durable contact with professionals who actively align care with each other. Of course, this demands for future research, as well as commitment of policy makers and care professionals