Concept

Interior algebra

Related publications (16)

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Orthologic with Axioms

Viktor Kuncak, Simon Guilloud

We study the proof theory and algorithms for orthologic, a logical system based on ortholattices, which have shown practical relevance in simplification and normalization of verification conditions. Ortholattices weaken Boolean algebras while having po ...

2024

4M: Massively Multimodal Masked Modeling

Shuqing Teresa Yeo, Amir Roshan Zamir, Oguzhan Fatih Kar, Roman Christian Bachmann, David Mizrahi

Current machine learning models for vision are often highly specialized and limited to a single modality and task. In contrast, recent large language models exhibit a wide range of capabilities, hinting at a possibility for similarly versatile models in co ...

Neural Information Processing Systems (Nips)2023

On Polynomial Algorithms for Normalizing Formulas

Viktor Kuncak, Simon Guilloud, Mario Bucev

We propose a new approach for normalization and simplification of logical formulas. Our approach is based on algorithms for lattice-like structures. Specifically, we present two efficient algorithms for computing a normal form and deciding the word problem ...

2022

Forbidden induced subposets of given height

Istvan Tomon

Let P be a partially ordered set. The function La* (n, P) denotes the size of the largest family F subset of 2([n]) that does not contain an induced copy of P. It was proved by Methuku and Palvolgyi that there exists a constant C-P (depending only on P) su ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2019

Local Barycentric Coordinates

Sofien Bouaziz, Bailin Deng

Barycentric coordinates yield a powerful and yet simple paradigm to interpolate data values on polyhedral domains. They represent interior points of the domain as an affine combination of a set of control points, defining an interpolation scheme for any fu ...

Association for Computing Machinery2014

Surface second-harmonic generation from coupled spherical plasmonic nanoparticles: Eigenmode analysis and symmetry properties

Olivier Martin, Jérémy Butet, Shourya Dutta Gupta

The surface second-harmonic generation from interacting spherical plasmonic nanoparticles building different clusters (symmetric and asymmetric dimers, trimers) is theoretically investigated. The plasmonic eigenmodes of the nanoparticle clusters are first ...

Amer Physical Soc2014

Fano resonant plasmonic systems: Functioning principles and applications

Olivier Martin, Andrea Lovera, Benjamin Gallinet, Thomas Gerd Siegfried

Using a generalization of Fano formula that includes the intrinsic losses associated with metals, we retrieve the underlying modal structure that produces Fano resonances from the interference between a bright and a dark mode. This knowledge is used to det ...

Amer Inst Physics2012

Equivalence of synthesis and atomic formulations of sparse recovery

Volkan Cevher, Mitra Fatemi, Shayan Dashmiz

Recovery of sparse signals from linear, dimensionality reducing measurements broadly fall under two well-known formulations, named the synthesis and the analysis a ́ la Elad et al. Recently, Chandrasekaran et al. introduced a new algorithmic sparse recover ...

Ieee2012

Ordered Sets in the Calculus of Data Structures

Viktor Kuncak, Philippe Paul Henri Suter, Ruzica Piskac

Our goal is to identify families of relations that are useful for reasoning about software. We describe such families using decidable quantifier-free classes of logical constraints with a rich set of operations. A key challenge is to define such classes of ...

Springer2010

Building a Calculus of Data Structures

Viktor Kuncak, Philippe Paul Henri Suter, Ruzica Piskac

Techniques such as verification condition generation, predicate abstraction, and expressive type systems reduce software verification to proving formulas in expressive logics. Programs and their specifications often make use of data structures such as sets ...

Springer2010