We derive a necessary and sufficient condition for Poincaré Lie superalgebras in any dimension and signature to be isomorphic. This reduces the classification problem, up to certain discrete operations, to classifying the orbits of the Schur group on the vector space of superbrackets. We then classify four-dimensional [Formula: see text] supersymmetry algebras, which are found to be unique in Euclidean and in neutral signature, while in Lorentz signature there exist two algebras with R-symmetry groups [Formula: see text] and [Formula: see text], respectively.
We start developing a formalism which allows to construct supersymmetric theories systematically across space-time signatures. Our construction uses a complex form of the supersymmetry algebra, which is obtained by doubling the spinor representation. This allows one to partially disentangle the Lorentz and R-symmetry group and generalizes symplectic Majorana spinors. For the case where the spinor representation is complex-irreducible, the R-symmetry only acts on an internal multiplicity space, and we show that the connected groups which occur are SO(2), SO 0 (1, 1), SU (2) and SU (1, 1).As an application we construct the off-shell supersymmetry transformations and supersymmetric Lagrangians for five-dimensional vector multiplets in arbitrary signature (t, s). In this case the R-symmetry groups are SU (2) or SU (1, 1), depending on whether the spinor representation carries a quaternionic or para-quaternionic structure. In Euclidean signature the scalar and vector kinetic terms differ by a relative sign, which is consistent with previous results in the literature and shows that this sign flip is an inevitable consequence of the Euclidean supersymmetry algebra.
String theory, specifically type-II superstring theory, can be formulated in any ten-dimensional signature. To facilitate the study of supergravity and superstring theories in this setting, we present a uniform construction of supersymmetry algebras in arbitrary dimension and signature, which generalizes the ideas underlying symplectic Majorana spinors. In our formalism R-symmetry acts on an auxiliary multiplicity space which makes its action manifest. This allows us to provide extensive tables which list the R-symmetry groups of extended supersymmetry algebras for all signatures together with other useful information. Twisted (‘type-*’) supersymmetry algebras in Lorentz signature with non-compact R-symmetry groups are shown to be part of a general pattern resulting from the interplay between complex superbrackets and reality conditions. As an application we show how the relations between type-II string theories in ten and nine dimensions can be extracted from their supersymmetry algebras. We also use our results to determine the special geometry of vector and hypermultiplet scalar manifolds of four-dimensional $$ \mathcal{N} $$ N = 2 and three-dimensional $$ \mathcal{N} $$ N = 4 supergravity theories for all signatures.
Quantitative systems pharmacology (QSP) modeling has become an increasingly popular approach impacting our understanding of disease mechanisms and helping predict patients’ treatment responses to facilitate study design or development go/no-go decisions. In this paper, we highlight the notable contributions and opportunities that QSP approaches are to offer during the drug development process by sharing three examples that have facilitated internal decisions. The barriers to successful applications and the factors that facilitate the success of the modeling approach is discussed.
We have built a multi-scale agent-based model (ABM) that reproduces the self-organizing behaviour reported for the intestinal crypt. We demonstrate that a stable spatial organization emerges from the dynamic interaction of multiple signalling pathways, such as Wnt, Notch, BMP, RNF43/ZNRF3 and YAP-Hippo pathways, which regulate proliferation and differentiation, respond to environmental mechanical cues, form feedback mechanisms and modulate the dynamics of the cell cycle protein network. The model recapitulates the crypt phenotype reported after persistent stem cell ablation and after the inhibition of the CDK1 cycle protein. Moreover, we simulated 5-fluorouracil (5-FU)-induced toxicity at multiple scales starting from DNA and RNA damage, which disturbs the cell cycle, cell signalling, proliferation, differentiation and migration and leads to loss of barrier integrity. During recovery, our in-silico crypt regenerates its structure in a self-organizing, dynamic fashion driven by dedifferentiation and enhanced by negative feedback loops. Overall, we present a systems model able to simulate the disruption of molecular events and its impact across multiple levels of epithelial organization and demonstrate its application to epithelial research and drug discovery.
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