Finite Generation Problem and n-ary Quantifiers

We consider the problem of generating a time-optimal quadrotor trajectory for highly maneuverable vehicles, such as quadrotor aircraft. The problem is challenging because the optimal trajectory is located on the boundary of the set of dynamically feasible trajectories. This boundary is hard to model as it involves limitations of the entire system, including complex aerodynamic and electromechanical phenomena, in agile high-speed flight. In this work, we propose a multi-fidelity Bayesian optimization framework that models the feasibility constraints based on analytical approximation, numerical simulation, and real-world flight experiments. By combining evaluations at different fidelities, trajectory time is optimized while the number of costly flight experiments is kept to a minimum. The algorithm is thoroughly evaluated for the trajectory generation problem in two different scenarios: (1) connecting predetermined waypoints; (2) planning in obstacle-rich environments. For each scenario, we conduct both simulation and real-world flight experiments at speeds up to 11 m/s. Resulting trajectories were found to be significantly faster than those obtained through minimum-snap trajectory planning.

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GRASSMANN COORDINATES FOR PARTICLE CLASSIFICATION

Modern Physics Letters A ◽

10.1142/s021773238900157x ◽

1989 ◽

Vol 04 (14) ◽

pp. 1381-1387 ◽

Cited By ~ 3

Author(s):

R. DELBOURGO

Keyword(s):

Particle Spectrum ◽

Present Particle ◽

Generation Problem ◽

Particle Classification

We show that five complex anticommuting coordinates are sufficient to describe the present particle spectrum, including the possibility of understanding the generation problem.

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A Survey on Variational Autoencoders from a Green AI Perspective

SN Computer Science ◽

10.1007/s42979-021-00702-9 ◽

2021 ◽

Vol 2 (4) ◽

Author(s):

Andrea Asperti ◽

Davide Evangelista ◽

Elena Loli Piccolomini

Keyword(s):

Architectural Design ◽

Mathematical Formulation ◽

Representation Learning ◽

Generative Models ◽

Model Description ◽

Energetic Efficiency ◽

Detailed Model ◽

Latent Distribution ◽

Quantitative Results ◽

Generation Problem

AbstractVariational Autoencoders (VAEs) are powerful generative models that merge elements from statistics and information theory with the flexibility offered by deep neural networks to efficiently solve the generation problem for high-dimensional data. The key insight of VAEs is to learn the latent distribution of data in such a way that new meaningful samples can be generated from it. This approach led to tremendous research and variations in the architectural design of VAEs, nourishing the recent field of research known as unsupervised representation learning. In this article, we provide a comparative evaluation of some of the most successful, recent variations of VAEs. We particularly focus the analysis on the energetic efficiency of the different models, in the spirit of the so-called Green AI, aiming both to reduce the carbon footprint and the financial cost of generative techniques. For each architecture, we provide its mathematical formulation, the ideas underlying its design, a detailed model description, a running implementation and quantitative results.

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A reversible evolvable Boolean network architecture and methodology to overcome the heat generation problem. In molecular scale brain building

Proceedings 2002 NASA/DoD Conference on Evolvable Hardware ◽

10.1109/eh.2002.1029894 ◽

2003 ◽

Cited By ~ 3

Author(s):

H. de Garis ◽

J. Dinerstein ◽

R. Sriram

Keyword(s):

Heat Generation ◽

Network Architecture ◽

Boolean Network ◽

Molecular Scale ◽

Generation Problem

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Classical Groups, Probabilistic Methods, and the (2, 3)-Generation Problem

Annals of Mathematics ◽

10.2307/2118584 ◽

1996 ◽

Vol 144 (1) ◽

pp. 77 ◽

Cited By ~ 61

Author(s):

Martin W. Liebeck ◽

Aner Shalev

Keyword(s):

Probabilistic Methods ◽

Classical Groups ◽

Generation Problem

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Research Notes: Binary Test-Suites Using Covering Arrays

International Journal of Software Engineering and Knowledge Engineering ◽

10.1142/s0218194018500377 ◽

2018 ◽

Vol 28 (09) ◽

pp. 1321-1337 ◽

Cited By ~ 1

Author(s):

Jose Torres-Jimenez ◽

Himer Avila-George ◽

Ezra Federico Parra-González

Keyword(s):

Software Testing ◽

Test Generation ◽

Software Systems ◽

Combinatorial Testing ◽

Covering Array ◽

Covering Arrays ◽

Almost All ◽

Generation Problem ◽

Test Suites

Software testing is an essential activity to ensure the quality of software systems. Combinatorial testing is a method that facilitates the software testing process; it is based on an empirical evidence where almost all faults in a software component are due to the interaction of very few parameters. The test generation problem for combinatorial testing can be represented as the construction of a matrix that has certain properties; typically this matrix is a covering array. Covering arrays have a small number of tests, in comparison with an exhaustive approach, and provide a level of interaction coverage among the parameters involved. This paper presents a repository that contains binary covering arrays involving many levels of interaction. Also, it discusses the importance of covering array repositories in the construction of better covering arrays. In most of the cases, the size of the covering arrays included in the repository reported here are the best upper bounds known, moreover, the files containing the matrices of these covering arrays are available to be downloaded. The final purpose of our Binary Covering Arrays Repository (BCAR) is to provide software testing practitioners the best-known binary test-suites.

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Non-branching RCD(0,N) Geodesic Spaces with Small Linear Diameter Growth have Finitely Generated Fundamental Groups

Canadian Mathematical Bulletin ◽

10.4153/cmb-2015-052-4 ◽

2015 ◽

Vol 58 (4) ◽

pp. 787-798 ◽

Cited By ~ 1

Author(s):

Yu Kitabeppu ◽

Sajjad Lakzian

Keyword(s):

Diameter Growth ◽

Fundamental Groups ◽

Finitely Generated ◽

Finite Generation ◽

Alexandrov Spaces ◽

Geodesic Spaces ◽

Special Case ◽

Linear Diameter

AbstractIn this paper, we generalize the finite generation result of Sormani to non-branching RCD(0, N) geodesic spaces (and in particular, Alexandrov spaces) with full supportmeasures. This is a special case of the Milnor’s Conjecture for complete non-compact RCD(0, N) spaces. One of the key tools we use is the Abresch–Gromoll type excess estimates for non-smooth spaces obtained by Gigli–Mosconi.

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