This work proposes a model-reduction methodology that preserves Lagrangian structure (equivalently Hamiltonian structure) and achieves computational efficiency in the presence of high-order nonlinearities and arbitrary parameter dependence. As such, the resulting reduced-order model retains key properties such as energy conservation and symplectic timeevolution maps. We focus on parameterized s...

We present a general approach for the treatment of parameterized geometries in projection-based model order reduction. During offline stage, given (i) family domains $\{ \Omega_{\mu}: \mu \in \mathcal{P} \} \subset \mathbb{R}^D$ where $\mu \mathbb{R}^P$ denotes vector parameters, (ii) mapping ${\Phi}_{\mu}$ between reference domain $\Omega$ and parameter-dependent $\Omega_{\mu}$, (iii) finite e...

We construct a fixed parameter algorithm parameterized by d and k that takes as an input a graph G′ obtained from a d-degenerate graph G by complementing on at most k arbitrary subsets of the vertex set of G and outputs a graph H such that G and H agree on all but f(d, k) vertices. Our work is motivated by the first order model checking in graph classes that are first order interpretable in cla...

We study a variant of the ferromagnetic Potts model, recently introduced by Tamura, Tanaka and Kawashima, consisting of a ferromagnetic interaction among q “visible” colours along with the presence of r non-interacting “invisible” colours. We introduce a random-cluster representation for the model, for which we prove the existence of a first-order transition for any q > 0, as long as r is large...

The stable model semantics was recently generalized by Ferraris, Lee and Lifschitz to the full first-order language with a syntax translation approach that is very similar to McCarthy’s circumscription. In this paper, we investigate the decidability and undecidability of various fragments of first-order language under both semantics of stable models and circumscription. Some maximally decidable...

We construct an optimal execution strategy for the purchase of a large number of shares of a financial asset over a fixed interval of time. Purchases of the asset have a nonlinear impact on price, and this is moderated over time by resilience in the limit-order book that determines the price. The limit-order book is permitted to have arbitrary shape. The form of the optimal execution strategy i...

An answer set program with variables is first-order definable on finite structures if the set of its finite answer sets can be captured by a first-order sentence. Characterizing classes of programs that are first-order definable on finite structures is theoretically challenging and of practical relevance to Answer Set Programming. In this paper, we identify a non-trivial class of answer set pro...