The Mathematical History Behind the Granger–Johansen Representation Theorem
ABSTRACT When can a vector time series that is integrated once (i.e., becomes stationary after taking first differences) be described in error correction form? The answer to this is provided by the Granger–Johansen representation theorem. From a mathematical point of view, the theorem can be viewed as essentially a statement concerning the geometry of ...
Johannes M. Schumacher
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Source Attribution of PM<sub>2.5</sub> Health Benefits Over Northern Hemisphere Using Adjoint of Hemispheric CMAQ. [PDF]
Oztaner YB +4 more
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A trace–path integral formula over function fields
Abstract We show that an arithmetic path integral over the ℓ$\ell$‐torsion of a Jacobian J[ℓ]$J[\ell]$ is equal to the trace of the Frobenius action on a representation of the Heisenberg group H(J[ℓ])$H(J[\ell])$, up to an explicitly determined sign.
Yan Yau Cheng
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MF6-ADJ: A Non-Intrusive Adjoint Sensitivity Capability for MODFLOW 6. [PDF]
Hayek M +4 more
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KdV limit for the Vlasov–Poisson–Landau system
Abstract We are concerned with the fluid limit to KdV equations for the one‐dimensional Vlasov–Poisson–Landau system that describes the dynamics of ions in plasma with the electron density determined by the self‐consistent electric potential through the so‐called Boltzmann relation. Formally, it is well known that as the Knudsen number ε→0$\varepsilon \
Renjun Duan, Dongcheng Yang, Hongjun Yu
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Adjoint-Driven Inverse Design of a Quad-Spectral Metasurface Router for RGB-NIR Sensing. [PDF]
Arfin R +4 more
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Heights on ‘hybrid orbits’ in Shimura varieties
Abstract We prove the ‘hybrid conjecture’ which is a common generalisation of the André–Oort conjecture and the André–Pink–Zannier conjecture, in the case of Shimura varieties of abelian type.
Rodolphe Richard, Andrei Yafaev
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Intrinsic Quantization of Linear Hamiltonian Systems. [PDF]
Accardi L, Pandiscia C.
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Syntomic cohomology and real topological cyclic homology
Abstract We define motivic filtrations on real topological Hochschild homology and its companions. In particular, we prove that real topological cyclic homology admits a natural complete filtration whose graded pieces are equivariant suspensions of syntomic cohomology.
Doosung Park
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Visualising backward information propagation in deep reinforcement learning from a variational data assimilation perspective. [PDF]
Wang KY.
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