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We present a detailed computation of the cyclic and the Hochschild homology and cohomology of generic and 3-Calabi–Yau homogeneous down–up algebras. This family was defined by Benkart and Roby in [3] in their study of differential posets. Our calculations ...
We numerically construct asymptotically AdS(4) solutions to Einstein-Maxwell-dilaton theory. These have a dipolar electrostatic potential turned on at the conformal boundary S-2 x R-t. We find two classes of geometries: AdS soliton solutions that encode th ...
In this article we give a new proof of Ngô's Geometric Stabilisation Theorem, which implies the Fundamental Lemma. This is a statement which relates the cohomology of Hitchin fibres for a quasi-split reductive group scheme G to the cohomology of Hitchin fi ...
We generalize the ham sandwich theorem to d +1 measures on R-d as follows. Let mu(1), mu(2),..., mu(d+1) be absolutely continuous finite Borel measures on R-d. Let omega(i) = mu(i) (R-d) for i is an element of [d + 1], omega = min{omega(i) : i is an elemen ...
We propose a method to design a decentralized energy market which guarantees individual rationality (IR) in expectation, in the presence of system-level grid constraints. We formulate the market as a welfare maximization problem subject to IR constraints, ...
We prove the Topological Mirror Symmetry Conjecture by Hausel-Thaddeus for smooth moduli spaces of Higgs bundles of type SLn and PGLn. More precisely, we establish an equality of stringy Hodge numbers for certain pairs of algebraic orbifolds generica ...
Using duality arguments from optimization theory, this work develops an effective distributed gradient boosting strategy for inference and classification by networked clusters of learners. By sharing local dual variables with their immediate neighbors thro ...
Organizing is a managerial process which demands a sense of purpose. When stories about "who we are" and "what we do" are salient and coherent (Voss, Cable & Voss, 2006), organizations can better plan, explain and justify collective action (Whetten & Macke ...
We prove, in a purely combinatorial way, the spectral curve topological recursion for the problem of enumeration of bi-colored maps, which are dual objects to dessins d'enfant. Furthermore, we give a proof of the quantum spectral curve equation for this pr ...
A two-compartment model of diffusion in white matter, which accounts for intra- and extra-axonal spaces, is associated with two plausible mathematical scenarios: either the intra-axonal axial diffusivity Da,‖ is higher than the extra-axonal De,‖ (Branch 1) ...
