Related papers: Interpolative fusions II: Preservation results
We prove that for every simple theory $T$ (or even simple thick compact abstract theory) there is a (unique) compact abstract theory $T^\fP$ whose saturated models are the lovely pairs of $T$. Independence-theoretic results that were proved…
We consider the following property of a first order theory T with a distinguished unary predicate P: every model of the theory of P occurs as the P-part of some model of T. We call this property the Gaifman property. Gaifman conjectured…
In this paper, we extend the idea of "geometric reconstruction" to couple a nonlocal diffusion model directly with the classical local diffusion in one dimensional space. This new coupling framework removes interfacial inconsistency,…
In ESOP 2008, Gulwani and Musuvathi introduced a notion of cover and exploited it to handle infinite-state model checking problems. Motivated by applications to the verification of data-aware processes, we proved in a previous paper that…
Classical statistical learning theory predicts a U-shaped relationship between test loss and model capacity, driven by the bias-variance trade-off. Recent advances in modern machine learning have revealed a more complex pattern,…
E.T. Jaynes, originator of the maximum entropy interpretation of statistical mechanics, emphasized that there is an inevitable trade-off between the conflicting requirements of robustness and accuracy for any inferencing algorithm. This is…
Algebraic persistence studies persistence modules (typically, linear representations of the poset $\mathbf{R}^n$ with $n \geq 1$) and the algebraic relationships between persistence modules that are interleaved. The notion of…
Finite mixture such as the Gaussian mixture is a flexible and powerful probabilistic modeling tool for representing the multimodal distribution widely involved in many estimation and learning problems. The core of it is representing the…
The paper is concerned with the problem of shape preserving interpolatory subdivision. For arbitrarily spaced, planar input data an efficient non-linear subdivision algorithm is presented that results in $G^1$ limit curves, reproduces conic…
We revisit the classical problem of absolute stability; assessing the robust stability of a given linear time-invariant (LTI) plant in feedback with a nonlinearity belonging to some given function class. Standard results typically take the…
Incorporation of a new knowledge into neural networks with simultaneous preservation of the previous one is known to be a nontrivial problem. This problem becomes even more complex when new knowledge is contained not in new training…
This paper investigates type isomorphism in a lambda-calculus with intersection and union types. It is known that in lambda-calculus, the isomorphism between two types is realised by a pair of terms inverse one each other. Notably,…
Consider the expansion $T_S$ of a theory $T$ by a predicate for a submodel of a reduct $T_0$ of $T$. We present a setup in which this expansion admits a model companion $TS$. We show that the nice features of the theory $T$ transfer to…
We investigate preservation results for the independent fusion of one-variable first-order modal logics. We show that, without equality, Kripke completeness and decidability of the global and local consequence relation are preserved, under…
Existing infrared and visible image fusion methods often face the dilemma of balancing modal information. Generative fusion methods reconstruct fused images by learning from data distributions, but their generative capabilities remain…
Motivated by structural properties of differential field extensions, we introduce the notion of a theory $T$ being derivation-like with respect to another model complete theory $T_0$. We prove that when $T$ admits a model companion $T_+$,…
Information fusion is used widely to improve document classification by the integration of multiple data sources (multimodal) or representations (multiview). However, the field lacks a unified framework, a quantitative synthesis of its…
This paper deals with iteration stable (STIT) tessellations, and, more generally, with a certain class of tessellations that are infinitely divisible with respect to iteration. They form a new, rich and flexible class of spatio-temporal…
We examine interpolatory model reduction methods that are well-suited for treating large scale port-Hamiltonian differential-algebraic systems in a way that is able to preserve and indeed, take advantage of the underlying structural…
Uniform interpolation is the property that, for any formula and set of atoms, there exists the strongest consequence omitting those atoms. It plays a central role in knowledge representation and reasoning tasks such as knowledge update and…