Article
Multidisciplinary Sciences
Kaifeng Bu, Weichen Gu, Arthur Jaffe
Summary: We propose a framework for studying discrete-variable (DV) quantum systems based on qudits, introducing concepts such as mean state (MS), minimal stabilizer-projection state (MSPS), and a new convolution. Notable findings include the MS being the closest MSPS to a given state in terms of relative entropy and being extremal in von Neumann entropy, thereby demonstrating a maximum entropy principle in DV systems. We establish a series of inequalities for quantum entropies and Fisher information based on convolution, which leads to a second law of thermodynamics for quantum convolutions. Furthermore, we show that the convolution of two stabilizer states also gives a stabilizer state. We present a central limit theorem involving the iteration of convolution for a zero-mean quantum state, with convergence to the MS characterized by the magic gap defined in terms of the state's characteristic function support. Finally, we provide detailed analysis of two examples: the DV beam splitter and the DV amplifier.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
(2023)
Article
Physics, Mathematical
Simon Becker, Nilanjana Datta, Ludovico Lami, Cambyse Rouze
Summary: The article examines the convergence rate of the quantum central limit theorem and extends the analysis to non-i.i.d. scenarios. By studying a lossy optical fiber model, it is concluded that the effective channel converges to a thermal attenuator, establishing bounds on the capacity of the cascade channel. Several independent results are derived, such as the boundedness of quantum characteristic functions outside of any neighborhood of the origin.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2021)
Article
Mathematics, Applied
Li-Xin Zhang
Summary: The central limit theorem and functional central limit theorem for martingale like random variables under the sub-linear expectation are obtained in this paper. Applications include the Lindeberg central limit theorem for independent but not necessarily identically distributed random variables, and a new proof of the Leevy characterization of a G-Brownian motion without using stochastic calculus. Rosenthal's inequality and the exponential inequality for the martingale like random variables are used to prove the results.
SCIENCE CHINA-MATHEMATICS
(2021)
Article
Mathematics
Artur Nicolau, Odi Soler i Gibert
Summary: A Central Limit Theorem for linear combinations of iterates of an inner function is proven, utilizing the Aleksandrov Desintegration Theorem for Aleksandrov-Clark measures as the main technical tool.
ADVANCES IN MATHEMATICS
(2022)
Article
Robotics
Sangsin Park
Summary: The researcher presented and derived a closed-form solution for an optimal ZMP pattern, meeting ZMP boundary conditions and an additional constraint. The solution allows for generating a walking pattern for every step period and connecting seamlessly with previous patterns. Real-time adjustments to the walking pattern are demonstrated based on varying step lengths.
JOURNAL OF FIELD ROBOTICS
(2022)
Article
Statistics & Probability
Miles E. Lopes
Summary: This paper investigates non-asymptotic bounds for Gaussian and bootstrap approximations in high-dimensional statistics. Berry-Esseen bounds for such approximations with respect to the multivariate Kolmogorov distance are studied, considering a sum of n random vectors that are p-dimensional and i.i.d. The paper establishes bounds with nearly n(-1/2) dependence on n, for both Gaussian and bootstrap approximation, within the setting of random vectors with sub-Gaussian or subexponential entries. The proofs utilize an implicit smoothing operation in the Lindeberg interpolation and differ from other recent approaches.
ANNALS OF STATISTICS
(2022)
Review
Chemistry, Analytical
Pollyanna G. Faria Dias, Mateus C. Silva, Geraldo P. Rocha Filho, Patricia A. Vargas, Luciano P. Cota, Gustavo Pessin
Summary: Swarm Robotics is a developing study field investigating bio-inspired collaborative control approaches, offering a platform for researchers to explore new knowledge. The paper reviews the essential qualities and features of Swarm Robotics systems, compares them to generic multi-robotic systems, and discusses current hardware platforms and multi-robot simulators.
Article
Mathematics, Interdisciplinary Applications
Leonardo Ricci
Summary: This study presents a novel proof of the central limit theorem for Markov chains, relying on time-independent quantum-mechanical perturbation theory, aiming to enhance the usability of this cornerstone theorem, especially in nonlinear dynamics and physics of complex systems.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Chemistry, Analytical
Francisco Antonio Belo, Manoel Brasileiro Soares, Abel Cavalcante Lima Filho, Thyago Leite de Vasconcelos Lima, Marceu Oliveira Adissi
Summary: This paper presents a method to enhance the accuracy and precision of liquid temperature measurements based on the central limit theorem. By immersing a thermometer in the liquid, it provides a precise and accurate response. The measurement is integrated with an instrumentation and control system that enforces the conditions of the central limit theorem. The oversampling method improves measurement resolution, and periodic sampling of large groups leads to increased accuracy and precision.
Review
Remote Sensing
Muhammad Muzamal Shahzad, Zubair Saeed, Asima Akhtar, Hammad Munawar, Muhammad Haroon Yousaf, Naveed Khan Baloach, Fawad Hussain
Summary: Swarm robots refer to the coordination of multiple robots to perform collective tasks and problem-solving more efficiently than a single robot. This research area has gained significant interest in the past decade due to its wide range of applications in military and civil fields. By replicating interaction rules from natural swarm systems, such as honey bees and bird flocks, robot swarms can be created.
Article
Mathematics
Li-Xin Zhang
Summary: In this paper, the functional central limit theorem is proved for martingale-like random vectors using the sub-linear expectations framework introduced by Shige Peng. As applications, the Lindeberg central limit theorem for independent random vectors is established, the sufficient and necessary conditions for the central limit theorem of independent and identically distributed random vectors are derived, and a Levy's characterization of a multi-dimensional G-Brownian motion is obtained.
COMMUNICATIONS IN MATHEMATICS AND STATISTICS
(2023)
Article
Mathematics
Michael Cranston, Thomas Mountford
Summary: In this paper, a new proof of the Erdos-Kac Central Limit Theorem is provided using the Riemann zeta distribution. By means of a Tauberian Theorem, the Central Limit Theorem for the uniform distribution is obtained from the result for the random variable X-s. The technique is also applied to different conditions of the Central Limit Theorem.
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
(2023)
Article
Robotics
Martin Jilek, Katerina Stranska, Michael Somr, Miroslav Kulich, Jan Zeman, Libor Preucil
Summary: The emerging field of passive macro-scale tile-based self-assembly (TBSA) shows promise in enabling effective manufacturing processes. A framework is proposed that utilizes magnetically-bonded tiles to increase stability as the assembly grows. The proposed approach has self-stabilizing characteristics and allows for the construction of assemblies containing hundreds of tiles.
IEEE ROBOTICS AND AUTOMATION LETTERS
(2022)
Article
Mathematics, Applied
Volker Betz, Steffen Polzer
Summary: The application of the Feynman-Kac formula to Polaron models of quantum theory leads to the path measure of Brownian motion perturbed by a translation-invariant pair potential. This study addresses the validity of a central limit theorem in infinite volume and shows the existence of relevant infinite volume limits. The results apply to the Frohlich Polaron for all coupling constants.
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
(2022)
Article
Computer Science, Theory & Methods
Mordechay B. Levin
Summary: This paper proves that the local discrepancy of a digital (t, s)-sequence in base 2 weakly converges to the standard Gaussian distribution as the sequence length increases. It also demonstrates the limit properties of certain mathematical formulas.
JOURNAL OF COMPLEXITY
(2023)
Article
Multidisciplinary Sciences
Johannes Nauta, Yara Khaluf, Pieter Simoens
JOURNAL OF THE ROYAL SOCIETY INTERFACE
(2020)
Article
Multidisciplinary Sciences
Ken Hasselmann, Antoine Ligot, Julian Ruddick, Mauro Birattari
Summary: Neuro-evolution methods perform well in simulation but often fail to transfer their performance to real-robot experiments, with the observed ranking disappearing. It is important to conduct real-robot experiments to reliably assess the performance of neuro-evolution methods and address robustness to the reality gap.
NATURE COMMUNICATIONS
(2021)
Article
Computer Science, Artificial Intelligence
Antoine Ligot, Andres Cotorruelo, Emanuele Garone, Mauro Birattari
Summary: This article proposes an experimental protocol for comparing fully automatic design methods for robot swarms, including defining benchmarks and sampling strategies, to address the lack of systematic analysis and comparison in the optimization-based design of robot swarms.
IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION
(2022)
Article
Physics, Multidisciplinary
Johannes Nauta, Pieter Simoens, Yara Khaluf
Summary: Foragers within a group can improve individual foraging efficiencies by using public information to assess local resource availability, especially in clustered or fractal resource landscapes. Joining nearby conspecifics in successful foraging efforts is beneficial on the group level, but individual advantages, such as increased survival rates, are greatest in parameter regions where group benefits are smallest. This study demonstrates the importance of environmental characteristics and group dynamics in determining optimal foraging strategies.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2022)
Article
Chemistry, Multidisciplinary
Yara Khaluf
Summary: This study examines the issue of measurement errors in robot swarms during the decision-making process and proposes three algorithms to address this problem.
APPLIED SCIENCES-BASEL
(2022)
Article
Computer Science, Artificial Intelligence
Fernando J. Mendiburu, David Garzon Ramos, Marcos R. A. Morais, Antonio M. N. Lima, Mauro Birattaria
Summary: This paper presents Mate, an automatic off-line design method for spatially-organizing behaviors in robot swarms. Experimental results show that Mate outperforms other automatic design methods in handling tasks with spatial distribution constraints.
SWARM AND EVOLUTIONARY COMPUTATION
(2022)
Article
Multidisciplinary Sciences
Antoine Ligot, Mauro Birattari
Summary: This paper investigates the reality gap problem in the prediction of robot swarm performance, comparing the accuracy of classical and pseudo-reality predictors. The results show that pseudo-reality predictors provide more accurate estimates of real-world performance compared to the classical approach.
Article
Multidisciplinary Sciences
Stef Van Havermaet, Pieter Simoens, Tim Landgraf, Yara Khaluf
Summary: Shepherding is an essential skill for guiding a herd in a desired direction and can be applied to various scenarios such as crowd control and rescue missions. Equipping robots with the ability to shepherd can improve efficiency and reduce labor costs. This study proposes a decentralized control algorithm for multi-robot shepherding, where the robots maintain a caging pattern around the herd to detect potential dangers. Simulations show that the proposed algorithm is successful in shepherding when the herd remains cohesive and enough robots are deployed.
ROYAL SOCIETY OPEN SCIENCE
(2023)
Proceedings Paper
Computer Science, Artificial Intelligence
Antoine Sion, Andreagiovanni Reina, Mauro Birattari, Elio Tuci
Summary: This paper investigates the impact of update time on the dynamics of self-organised aggregation and proposes the concept of dynamic update time.
FROM ANIMALS TO ANIMATS 16
(2022)
Article
Multidisciplinary Sciences
Johannes Nauta, Pieter Simoens, Yara Khaluf, Ricardo Martinez-Garcia
Summary: Increased fragmentation caused by habitat loss poses a major threat to animal populations, and the impact depends on the movement rate between spatially separated patches. This study uses a spatially explicit predator-prey model to investigate how fragmentation and optimal foraging behavior interact to affect predator-prey interactions and ecosystem stability. The results show that the Levy exponent and degree of fragmentation jointly determine coexistence probabilities, and in highly fragmented landscapes, only scale-free predators can coexist with prey.
JOURNAL OF THE ROYAL SOCIETY INTERFACE
(2022)
Article
Robotics
Federico Pagnozzi, Mauro Birattari
Summary: The paper proposes a technique based on off-policy evaluation to estimate how the performance of control software, particularly in robot swarms, would be impacted by modifying the structure and value of parameters. The technique can help reduce software complexity or evaluate parameter perturbations, aiding in prioritizing exploration of the current solution within an iterative improvement algorithm.
FRONTIERS IN ROBOTICS AND AI
(2021)
Review
Robotics
Miquel Kegeleirs, Giorgio Grisetti, Mauro Birattari
Summary: A robot swarm is a decentralized system with locality of sensing and communication, self-organization, and redundancy, allowing for scalability, flexibility, and fault tolerance. Swarm SLAM is a promising approach leveraging the decentralized nature of a robot swarm to achieve scalable, flexible, and fault-tolerant exploration and mapping. However, there are still challenges in gathering, sharing, and retrieving information in swarm SLAM, and the approach is compared to traditional multi-robot SLAM.
FRONTIERS IN ROBOTICS AND AI
(2021)
Article
Robotics
Muhammad Salman, David Garzon Ramos, Ken Hasselmann, Mauro Birattari
FRONTIERS IN ROBOTICS AND AI
(2020)
Article
Computer Science, Artificial Intelligence
Antoine Ligot, Jonas Kuckling, Darko Bozhinoski, Mauro Birattari
PEERJ COMPUTER SCIENCE
(2020)
Article
Computer Science, Artificial Intelligence
Mauro Birattari, Antoine Ligot, Ken Hasselmann
NATURE MACHINE INTELLIGENCE
(2020)
