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Linearized partial data Calderón problem for Biharmonic operators
(2023)SAM Research ReportWe consider a linearized partial data Calderón problem for biharmonic operators extending the analogous result for harmonic operators. We construct special solutions and utilize Segal-Bargmann transform to recover lower order perturbations.Report -
Conditioning on Stochastic Processes via Signatures
(2023)SAM Research ReportIn this working paper, the conditional expectation of a random vector given a stochastic process is characterised as the solution of some convex (semi-)infinite linear least squares problem. This result is based on a functional monotone class argument involving the robust signature of the conditioning process, and it enables the nonparametric and practically feasible computation of conditional distributions for very general classes of ...Report -
Sharp Hadamard local well-posedness, enhanced uniqueness and pointwise continuation criterion for the incompressible free boundary Euler equations
(2023)SAM Research ReportWe provide a complete local well-posedness theory in \(H^s\) based Sobolev spaces for the free boundary incompressible Euler equations with zero surface tension on a connected fluid domain. Our well-posedness theory includes: (i) Local well-posedness in the Hadamard sense, i.e., local existence, uniqueness, and the first proof of continuous dependence on the data, all in low regularity Sobolev spaces; (ii) Enhanced uniqueness: Our uniqueness ...Report -
Inverse Problems for Third-Order Nonlinear Perturbations of Biharmonic Operatiors
(2023)SAM Research ReportWe study inverse boundary problems for third-order nonlinear tensorial perturbations of biharmonic operators on a bounded domain in \(\mathbb{R}^n\), where \(n\ge 3\). By imposing appropriate assumptions on the nonlinearity, we demonstrate that the Dirichlet-to-Neumann map, known on the boundary of the domain, uniquely determines the genuinely nonlinear tensorial third-order perturbations of the biharmonic operator. The proof relies on ...Report -
Low regularity solutions for the general quasilinear ultrahyperbolic Schrödinger equation
(2023)SAM Research ReportWe present a novel method for establishing large data local well-posedness in low regularity Sobolev spaces for general quasilinear Schrödinger equations with non-degenerate and nontrapping metrics. Our result represents a definitive improvement over the landmark results of Kenig, Ponce, Rolvung and Vega, as it weakens the regularity and decay assumptions to the same scale of spaces considered by Marzuola, Metcalfe and Tataru, but removes ...Report -
Gender Analysis and the Treaty on the Prohibition of Nuclear Weapons: A Response to Daarstad, Park, and Balogh
(2023)I4R Discussion Paper SeriesWe are grateful to Haley Daarstad, RyuGyung Park, and Timea Balogh for their thoughtful engagement with our 2022 short article in The Journal of Politics. In that article, we tested the malleability of U.S. public support for nuclear disarmament, specifically in the context of the 2017 Treaty on the Prohibition of Nuclear Weapons (TPNW). Our survey experiment reveals that––despite majority public support for eliminating nuclear ...Report -
The Altered Nuclear Order in the Wake of the Russia-Ukraine War
(2023)In this American Academy of Arts and Sciences study, Rebecca Davis Gibbons, Stephen Herzog, Wilfred Wan, and Doreen Horschig unpack the challenges to the global nuclear order posed by the Russian war against Ukraine. On February 24, 2022, Russia invaded nonnuclear-armed Ukraine and leveraged threats with its nuclear arsenal as a “shield” to deter third-party intervention. The well-publicized horrors on the ground in Ukraine are, unfortunately, ...Report -
Civil Engineering Market
(2023)96th Euroconstruct Summary Report: Winter 2023. European Construction: Market Trends until 2026Report -
Switzerland
(2023)96th Euroconstruct Country Report: Winter 2023. European Construction: Market Trends until 2026Report -
A closed-loop strategy for design of robust model predictive controllers
(2023)A novel robust model predictive control (MPC) algorithm is presented, whereby closed-loop constraint satisfaction is ensured using recursive feasibility of the MPC optimization. The proposed strategy only considers the effects of model perturbations and disturbances occurring at {\em one time step}. This is in contrast to existing formulations which compute control policies that are feasible under the worst-case realizations of all model ...Report