75 research outputs found
The -torsion polytope of amenable groups
We introduce the notion of groups of polytope class and show that
torsion-free amenable groups satisfying the Atiyah Conjecture possess this
property. A direct consequence is the homotopy invariance of the -torsion
polytope among -CW-complexes for these groups. As another application we
prove that the -torsion polytope of an amenable group vanishes provided
that it contains a non-abelian elementary amenable normal subgroup.Comment: 21 page
An Upper Bound on the Number of Extreme Shortest Paths in Arbitrary Dimensions
Graphs with multiple edge costs arise naturally in the route planning domain when apart from travel time other criteria like fuel consumption or positive height difference are also objectives to be minimized. In such a scenario, this paper investigates the number of extreme shortest paths between a given source-target pair s, t. We show that for a fixed but arbitrary number of cost types d ? 1 the number of extreme shortest paths is in n^O(log^{d-1}n) in graphs G with n nodes. This is a generalization of known upper bounds for d = 2 and d = 3
Preference-Based Trajectory Clustering - An Application of Geometric Hitting Sets
In a road network with multicriteria edge costs we consider the problem of computing a minimum number of driving preferences such that a given set of paths/trajectories is optimal under at least one of these preferences. While the exact formulation and solution of this problem appears theoretically hard, we show that in practice one can solve the problem exactly even for non-homeopathic instance sizes of several thousand trajectories in a road network of several million nodes. We also present a parameterized guaranteed-polynomial-time scheme with very good practical performance
DISCO-10M: A Large-Scale Music Dataset
Music datasets play a crucial role in advancing research in machine learning
for music. However, existing music datasets suffer from limited size,
accessibility, and lack of audio resources. To address these shortcomings, we
present DISCO-10M, a novel and extensive music dataset that surpasses the
largest previously available music dataset by an order of magnitude. To ensure
high-quality data, we implement a multi-stage filtering process. This process
incorporates similarities based on textual descriptions and audio embeddings.
Moreover, we provide precomputed CLAP embeddings alongside DISCO-10M,
facilitating direct application on various downstream tasks. These embeddings
enable efficient exploration of machine learning applications on the provided
data. With DISCO-10M, we aim to democratize and facilitate new research to help
advance the development of novel machine learning models for music
Responsibility and verification: Importance value in temporal logics
We aim at measuring the influence of the nondeterministic choices of a part
of a system on its ability to satisfy a specification. For this purpose, we
apply the concept of Shapley values to verification as a means to evaluate how
important a part of a system is. The importance of a component is measured by
giving its control to an adversary, alone or along with other components, and
testing whether the system can still fulfill the specification. We study this
idea in the framework of model-checking with various classical types of
linear-time specification, and propose several ways to transpose it to
branching ones. We also provide tight complexity bounds in almost every case.Comment: 22 pages, 12 figure
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