Related papers: Modular Localization and the Bootstrap-Formfactor …
We study the two-point function of local operators in the critical O(N) model in the presence of a magnetic field localized on a line. We use a recently developed conformal dispersion relation to compute the correlator at first order in the…
Univalent homotopy type theory (HoTT) may be seen as a language for the category of $\infty$-groupoids. It is being developed as a new foundation for mathematics and as an internal language for (elementary) higher toposes. We develop the…
By double ideal quotient, we mean $(I:(I:J))$ where ideals $I$ and $J$. In our previous work [11], double ideal quotient and its variants are shown to be very useful for checking prime divisor and generating primary component. Combining…
We extend the free cornering of a symmetric monoidal category, a double categorical model of concurrent interaction, to support branching communication protocols and iterated communication protocols. We validate our constructions by showing…
We define a functor $\rr^\ast$ from the category of positively determined modules to the category of squarefree modules which plays the role of passing from a monomial ideal to its radical. By using this functor, we generalize several…
The fundamental matrix factorisations of the D-model superpotential are found and identified with the boundary states of the corresponding conformal field theory. The analysis is performed for both GSO-projections. We also comment on the…
We advocate a strategy of bootstrapping Feynman integrals from just knowledge of their singular behavior. This approach is complementary to other bootstrap programs, which exploit non-perturbative constraints such as unitarity, or…
We study self-adjoint operators defined by factorizing second order differential operators in first order ones. We discuss examples where such factorizations introduce singular interactions into simple quantum mechanical models like the…
We introduce layers to modal type theories, which subsequently enables type theories for pattern matching on code in meta-programming and clean and straightforward semantics.
Modular localization is the concise conceptual formulation of causal localization in the setting of local quantum physics. Unlike QM it does not refer to individual operators but rather to ensembles of observables which share the same…
Exploration remains a significant challenge in reinforcement learning, especially in environments where extrinsic rewards are sparse or non-existent. The recent rise of foundation models, such as CLIP, offers an opportunity to leverage…
Recent ideas on modular localization in local quantum physics are used to clarify the relation between on- and off-shell quantities in particle physics; in particular the relation between on-shell crossing symmetry and off-shell Einstein…
Node embedding learns a low-dimensional representation for each node in the graph. Recent progress on node embedding shows that proximity matrix factorization methods gain superb performance and scale to large graphs with millions of nodes.…
Following the works by Lin et al. (Circuits Syst. Signal Process. 20(6): 601-618, 2001) and Liu et al. (Circuits Syst. Signal Process. 30(3): 553-566, 2011), we investigate how to factorize a class of multivariate polynomial matrices. The…
We introduce an exact functor defined on multigraded modules which we call the expansion functor and study its homological properties. The expansion functor applied to a monomial ideal amounts to substitute the variables by monomial prime…
We compare the model-free reinforcement learning with the model-based approaches through the lens of the expressive power of neural networks for policies, $Q$-functions, and dynamics. We show, theoretically and empirically, that even for…
We define Wannier functions for interacting systems, and show that the results on the localization of the Wannier functions for non-interacting systems carry over to the Wannier functions for interacting systems. In addition we demonstrate…
This is a report on a joint project in experimental mathematics with Jonas Bergstr\"om and Carel Faber where we obtain information about modular forms by counting curves over finite fields.
In the recent paper [J. Funct. Anal. {\bf 259} (2010)], Naor and Tao introduce a new class of measures with a so-called micro-doubling property and present, via martingale theory and probability methods, a localization theorem for the…
A growing body of research on probabilistic programs and causal models has highlighted the need to reason compositionally about model classes that extend directed graphical models. Both probabilistic programs and causal models define a…