Publications related to Hilbert's tenth problem

Complex Representation Learning with Graph Convolutional Networks for Knowledge Graph Alignment

Thanh Trung Huynh, Quoc Viet Hung Nguyen, Thành Tâm Nguyên

The task of discovering equivalent entities in knowledge graphs (KGs), so-called KG entity alignment, has drawn much attention to overcome the incompleteness problem of KGs. The majority of existing techniques learns the pointwise representations of entiti ...

London2023

On the Complexity of Modulo-q Arguments and the Chevalley - Warning Theorem

Mika Tapani Göös

We study the search problem class PPA_q defined as a modulo-q analog of the well-known polynomial parity argument class PPA introduced by Papadimitriou (JCSS 1994). Our first result shows that this class can be characterized in terms of PPA_p for prime p. ...

Schloss Dagstuhl - Leibniz-Zentrum für Informatik2020

A Local Law for Singular Values from Diophantine Equations

Marius Christopher Lemm

We introduce the

N\times N

random matrices

X_{j,k}=\exp\left(2\pi i \sum_{q=1}^d\ \omega_{j,q} k^q\right) \quad \text{with } \{\omega_{j,q}\}_{\substack{1\leq j\leq N\\ 1\leq q\leq d}} \text{ i.i.d. random variables},

and

d

a fixed integer. We pr ...

2020

Design, analysis, testing and applications of two-body and three-body kinematic mounts

Johannes Richard Cornelis Geerit Kruis

Kinematic couplings are used when two rigid bodies need to be repeatedly and accurately positioned with respect to each other. They allow for sub-micron positioning repeatability by suppressing play and reducing strains in the bodies. Typical applications ...

EPFL2016

Diophantine properties of nilpotent Lie groups

A finitely generated subgroup F of a real Lie group G is said to be Diophantine if there is beta > 0 such that non-trivial elements in the word ball B-Gamma(n) centered at 1 is an element of F never approach the identity of G closer than broken vertical ba ...

London Mathematical Society, Cambridge2015

Design Methods and Tools for 3D Integration

Giovanni De Micheli, David Atienza Alonso, Yusuf Leblebici, Vasileios Pavlidis

The design of 3-dimensional integrated circuits requires new specialized tools, methods and flows. Whereas some tools are on the market and some design flows for standard ICs are extended to handle die stacking and through-silicon vias, much R&D has still ...

2011

Decision Procedures for Multisets with Cardinality Constraints

Viktor Kuncak, Ruzica Piskac

Applications in software verification and interactive theorem proving often involve reasoning about sets of objects. Cardinality constraints on such collections also arise in these scenarios. Multisets arise for analogous reasons as sets: abstracting the c ...

Springer2008

Minimum-Energy Broadcast in All-Wireless Networks: NP-Completeness and Distribution Issues

Jean-Pierre Hubaux, Christian Enz, Mario Cagalj

In all-wireless networks a crucial problem is to minimize energy consumption, as in most cases the nodes are battery-operated. We focus on the problem of power-optimal broadcast, for which it is well known that the broadcast nature of the radio transmissio ...

2002

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A Local Law for Singular Values from Diophantine Equations

Marius Christopher Lemm

We introduce the

N\times N

random matrices

X_{j,k}=\exp\left(2\pi i \sum_{q=1}^d\ \omega_{j,q} k^q\right) \quad \text{with } \{\omega_{j,q}\}_{\substack{1\leq j\leq N\\ 1\leq q\leq d}} \text{ i.i.d. random variables},

and

d

a fixed integer. We pr ...

2020

Hilbert's tenth problem

Complex Representation Learning with Graph Convolutional Networks for Knowledge Graph Alignment

On the Complexity of Modulo-q Arguments and the Chevalley - Warning Theorem

A Local Law for Singular Values from Diophantine Equations

Design, analysis, testing and applications of two-body and three-body kinematic mounts

Diophantine properties of nilpotent Lie groups

Design Methods and Tools for 3D Integration

Decision Procedures for Multisets with Cardinality Constraints

Decision Procedures for Multisets with Cardinality Constraints

Large scale stereo reconstruction by a minimum s-t cut formulation

Minimum-Energy Broadcast in All-Wireless Networks: NP-Completeness and Distribution Issues

Graph Chatbot

Chat with Graph Search

On the Complexity of Modulo-q Arguments and the Chevalley - Warning Theorem

A Local Law for Singular Values from Diophantine Equations

Diophantine properties of nilpotent Lie groups

Design, analysis, testing and applications of two-body and three-body kinematic mounts

Decision Procedures for Multisets with Cardinality Constraints

Complex Representation Learning with Graph Convolutional Networks for Knowledge Graph Alignment

Design Methods and Tools for 3D Integration

Minimum-Energy Broadcast in All-Wireless Networks: NP-Completeness and Distribution Issues

Large scale stereo reconstruction by a minimum s-t cut formulation

Decision Procedures for Multisets with Cardinality Constraints