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Software verification has emerged as a key concern for ensuring the continued progress of information technology. Full verification generally requires, as a crucial step, equipping each loop with a "loop invariant". Beyond their role in…

Software Engineering · Computer Science 2014-01-14 Carlo A. Furia , Bertrand Meyer , Sergey Velder

We classify all additive invariants of open Petri nets: these are $\mathbb{N}$-valued invariants which are additive with respect to sequential and parallel composition of open Petri nets. In particular, we prove two classification theorems:…

Category Theory · Mathematics 2025-07-30 Benjamin Merlin Bumpus , Sophie Libkind , Jordy Lopez Garcia , Layla Sorkatti , Samuel Tenka

In this revised version, we add some expository material and references and make some minor corrections.

alg-geom · Mathematics 2008-02-03 Robert Friedman , John W. Morgan

This paper is an appendix to the paper "Reasoning with Justifiable Exceptions in Contextual Hierarchies" by Bozzato, Serafini and Eiter, 2018. It provides further details on the language, the complexity results and the datalog translation…

Artificial Intelligence · Computer Science 2018-08-07 Loris Bozzato , Luciano Serafini , Thomas Eiter

In this paper, we introduce the concept of complementary edge ideals of graphs and study their algebraic properties and invariants.

Commutative Algebra · Mathematics 2025-08-22 Takayuki Hibi , Ayesha Asloob Qureshi , Sara Saeedi Madani

This is the draft of lecture notes for Phd students in Sichuan University. In this notes we expand Li-Ruan's paper with much more detailed explanations and calculations.

Symplectic Geometry · Mathematics 2018-07-24 An-Min Li , Li Sheng

We review computations of joint invariants on a linear symplectic space, discuss variations for an extension of group and space and relate this to other equivalence problems and approaches, most importantly to differential invariants.

Differential Geometry · Mathematics 2020-11-24 Fredrik Andreassen , Boris Kruglikov

Using an alternate description of support varieties of pairs of modules over a complete intersection, we give several new applications of such varieties, including results for support varieties of intermediate complete intersections.…

Commutative Algebra · Mathematics 2015-09-28 Petter Andreas Bergh , David A. Jorgensen

This is a companion piece to my paper on "Example-Based Procedural Modeling Using Graph Grammars." This paper examines some of the theoretical issues in more detail. This paper discusses some more complex parts of the implementation, why…

Graphics · Computer Science 2023-09-04 Paul Merrell

This is an appendix to our paper "An update of the Hirsch Conjecture" (arXiv:0907.1186), containing proofs of some of the results and comments that were omitted in it.

Combinatorics · Mathematics 2010-02-02 Edward D. Kim , Francisco Santos

This text is an appendix to our work "On the growth of Kronecker coefficients", arXiv:1607.02887. Here, we provide some complementary theorems, remarks, and calculations that for the sake of space are not going to appear into the final…

Representation Theory · Mathematics 2016-11-23 Emmanuel Briand , Amarpreet Rattan , Mercedes Rosas

We develop a framework for incorporating structured graphical models in the \emph{encoders} of variational autoencoders (VAEs) that allows us to induce interpretable representations through approximate variational inference. This allows us…

We study some new invariant measures arising from local inverse iterates. Examples are also given.

Dynamical Systems · Mathematics 2009-09-08 Eugen Mihailescu

We define here an analogue, for the N\'eron model of a semi-stable abelian variety defined over a number field, of M. J. Taylor's class-invariant homomorphism (defined for abelian schemes). Then we extend an annulation result (in the case…

Number Theory · Mathematics 2009-11-11 Jean Gillibert

This is the final version of the lecture notes of the 23rd Internet Seminar on Evolutionary Equations, see also https://www.mat.tuhh.de/isem23/.

Analysis of PDEs · Mathematics 2020-03-30 Christian Seifert , Sascha Trostorff , Marcus Waurick

New invariants for 2-dimensional cell complexes are defined, which can be interpreted as curvature bounds. These invariants are proved to be rational and computable in a companion article. This document is a survey that collects theorems…

Group Theory · Mathematics 2024-05-16 Henry Wilton

We demonstrate the complementary natures of neural knowledge graph embedding, fine-grain entity type prediction, and neural language modeling. We show that a language model-inspired knowledge graph embedding approach yields both improved…

Computation and Language · Computer Science 2020-10-13 Rajat Patel , Francis Ferraro

This paper describes adaptations for EaFi, a parser for easy-first parsing of discontinuous constituents, to adapt it to multiple languages as well as make use of the unlabeled data that was provided as part of the SPMRL shared task 2014.

Computation and Language · Computer Science 2014-09-15 Yannick Versley

Additional material for the original paper "Automated Verification of Interactive Rule-Based Configuration Systems".

Logic in Computer Science · Computer Science 2014-01-23 Deepak Dhungana , Ching Hoo Tang , Christoph Weidenbach , Patrick Wischnewski

This paper is devoted to a discussion of specific properties of invariants in the theory of forms.

Analysis of PDEs · Mathematics 2010-07-02 Mehdi Nadjafikhah , Parastoo Kabi-Nejad