The analytic structure and the transcendental weight of the BFKL ladder at NLL accuracy

We study some analytic properties of the BFKL ladder at next-to-leading logarithmic accuracy (NLLA). We use a procedure by Chirilli and Kovchegov to construct the NLO eigenfunctions, and we show that the BFKL ladder can be evaluated order by order in the coupling in terms of certain generalised single-valued multiple polylogarithms recently introduced by Schnetz. We develop techniques to evaluate the BFKL ladder at any loop order, and we present explicit results up to five loops. Using the freedom in defining the matter content of the NLO BFKL eigenvalue, we obtain conditions for the BFKL ladder in momentum space at NLLA to have maximal transcendental weight. We observe that, unlike in moment space, the result in momentum space in N = 4 SYM is not identical to the maximal weight part of QCD, and moreover that there is no gauge theory with this property. We classify the theories for which the BFKL ladder at NLLA has maximal weight in terms of their field content, and we find that these theories are highly constrained: there are precisely four classes of theories with this property involving only fundamental and adjoint matter, all of which have a vanishing one-loop beta function and a matter content that fits into supersymmetric multiplets. Our findings indicate that theories which have maximal weight are highly constrained and point to the possibility that there is a connection between maximal transcendental weight and superconformal symmetry.Comment: 45 pages, 1 figure, 1 table. v2: published versio

The Full-Color Two-Loop Four-Gluon Amplitude in N=2\mathcal{N} = 2 Super-QCD

We present the fully integrated form of the two-loop four-gluon amplitude in $\mathcal{N} = 2$ supersymmetric quantum chromodynamics with gauge group SU$(N_c)$ and with $N_f$ massless supersymmetric quarks (hypermultiplets) in the fundamental representation. Our result maintains full dependence on $N_c$ and $N_f$, and relies on the existence of a compact integrand representation that exhibits the duality between color and kinematics. Specializing to the $\mathcal{N} = 2$ superconformal theory, where $N_f = 2N_c$ , we obtain remarkably simple amplitudes that have an analytic structure close to that of $\mathcal{N} = 4$ super-Yang-Mills theory, except that now certain lower-weight terms appear. We comment on the corresponding results for other gauge groups.Comment: 5 pages + refs, 1 figure, 2 ancillary file

Coordinated Schematization for Visualizing Mobility Patterns on Networks

GPS trajectories of vehicles moving on a road network are a valuable source of traffic information. However, the sheer volume of available data makes it challenging to identify and visualize salient patterns. Meaningful visual summaries of trajectory collections require that both the trajectories and the underlying network are aggregated and simplified in a coherent manner. In this paper we propose a coordinated fully-automated pipeline for computing a schematic overview of mobility patterns from a collection of trajectories on a street network. Our pipeline utilizes well-known building blocks from GIS, automated cartography, and trajectory analysis: map matching, road selection, schematization, movement patterns, and metro-map style rendering. We showcase the results of our pipeline on two real-world trajectory collections around The Hague and Beijing

Two-loop N=1\mathcal{N}=1 SYM Amplitudes via SUSY Decomposition and Massive Spinor-Helicity

We obtain a color-kinematics-dual representation of the two-loop four-vector amplitude a general renormalizable massless $\mathcal{N}=1$ SYM theory, including internal matter as chiral supermultiplets. The integrand is constructed to be compatible with dimensional regularization and supersymmetry by employing two strategies (implicitly defining our regularization scheme): supersymmetric decomposition and matching to massive spinor-helicity amplitudes. All internal vector components inherit their $D$-dimensional properties by relating them to the previously constructed $D\leq6$, $\mathcal{N}=2$ SQCD amplitude using supersymmetric decomposition identities of individual diagrams. This leaves only diagrams with internal matter lines as unknown masters, which are in turn constrained on $D$-dimensional unitarity cuts by reinterpreting the extra-dimensional momentum components as masses for the chiral supermultiplets. We rely on the massive spinor-helicity formalism and massive on-shell $\mathcal{N}=1$ superspace, generalized here to complex masses. Finally, we extend the kinematic numerator algebra to include three-term identities that are dual to color identities linear in the matter Clebsch-Gordan coefficients, as well as two new optional identities satisfied by mass-deformed $\mathcal{N}=4$ and $\mathcal{N}=2$ SYM theories that preserve $\mathcal{N}=1$ supersymmetry. Altogether, these identities makes it possible to completely reduce the two-loop integrand to only two master numerators.Comment: 61 pages, 4 figures, 2 ancillary file

The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy

We present an all-loop dispersion integral, well-defined to arbitrary logarithmic accuracy, describing the multi-Regge limit of the 2->5 amplitude in planar N=4 super Yang-Mills theory. It follows from factorization, dual conformal symmetry and consistency with soft limits, and specifically holds in the region where the energies of all produced particles have been analytically continued. After promoting the known symbol of the 2-loop N-particle MHV amplitude in this region to a function, we specialize to N=7, and extract from it the next-to-leading order (NLO) correction to the BFKL central emission vertex, namely the building block of the dispersion integral that had not yet appeared in the well-studied six-gluon case. As an application of our results, we explicitly compute the seven-gluon amplitude at next-to-leading logarithmic accuracy through 5 loops for the MHV case, and through 3 and 4 loops for the two independent NMHV helicity configurations, respectively.Comment: 56 pages, 4 figures, 1 table; v2: minor corrections and clarifications, matches published versio

How the interrelated physical, social and organizational environment impacts daily life of residents with dementia on a Green Care Farm

Green Care Farms (GCF) are innovative long-term care environments and an alternative to regular nursing homes in the Netherlands. Following a culture change movement, GCFs have radically altered the care environment. Research suggests positive effects on residents. However, knowledge is limited regarding their physical, social and organizational environment. This article explores the care environment of 24-h GCFs for people with dementia and its impact on residents and their daily life. An ethnographic study using mixed methods was carried out at a GCF in the Netherlands between June and October 2021. Researchers lived on the GCF and completed 28 days of participatory observations in three groups. During the day, informal conversations were held with residents (; n; = 48), staff and family members. Twenty four semi-structured interviews were conducted with residents, their family members, staff and the managers, complemented by a focus group with staff. The physical environment was additionally assessed with the OAZIS-dementia tool. Data collection methods informed each other. Qualitative data was thematically analyzed, quantitative data descriptively. Four themes were identified as crucial during daily life on the GCF: stimulating the senses, engaging in purposeful activities, sharing responsibilities and creating a community in a new home. Realizing these topics in practice, physical, social and organizational environmental components were highly interrelated. The physical environment encouraged and facilitated meaningful in-/outdoor activities and social encounters. The organizational environment supported the use of the physical environment by aligning processes and transporting the vision. The social environment focused on collaboration and creating a home-like atmosphere by including residents in household- and farm chores. This community-building led to more meaningful activities and social interaction. In conclusion, this study revealed the central influence of the management in paving the way for a new form of care delivery. As leaders shape the three environments, the organization influences the design of the physical environment and the actions taking place within it. By creating a community, the care home benefits residents, their families and staff equally. The conscious interrelation and harmonization of the physical, social and organizational components of a long-term care environment has the potential to improve the daily life of residents

Motivic coaction and single-valued map of polylogarithms from zeta generators

We introduce a new Lie-algebraic approach to explicitly construct the motivic coaction and single-valued map of multiple polylogarithms in any number of variables. In both cases, the appearance of multiple zeta values is controlled by conjugating generating series of polylogarithms with Lie-algebra generators associated with odd zeta values. Our reformulation of earlier constructions of coactions and single-valued polylogarithms preserves choices of fibration bases, exposes the correlation between multiple zeta values of different depths and paves the way for generalizations beyond genus zero.Comment: 12 page