Article
Engineering, Manufacturing
Sameer Mehta, Milind Dawande, Ganesh Janakiraman, Vijay Mookerjee
Summary: This paper proposes an approximation scheme for the multidimensional mechanism-design problem in data markets, aiming to maximize the revenue of data sellers. The scheme generates a menu of item-price pairs, with the menu length increasing as the desired guarantee gets closer to zero. Additionally, the paper demonstrates how buyers' preferences can be exploited to derive practical rules of thumb for implementing the scheme effectively.
PRODUCTION AND OPERATIONS MANAGEMENT
(2022)
Article
Automation & Control Systems
Umit Kose, Andrzej Ruszczynski
Summary: In this study, a novel reinforcement learning methodology was proposed to evaluate system performance using linear value function approximations and Markov coherent dynamic risk measures. Risk-averse dynamic programming equations were constructed and their properties were studied. New risk-averse counterparts of basic and multi-step temporal difference methods were introduced and their convergence with probability one was proven, along with an empirical study on a complex transportation problem.
JOURNAL OF MACHINE LEARNING RESEARCH
(2021)
Article
Computer Science, Hardware & Architecture
Pedro Reviriego, Jorge Martinez, Ori Rottenstreich, Shanshan Liu, Fabrizio Lombardi
Summary: Estimating the number of distinct elements is important in computing applications, and this article focuses on the HyperLogLog algorithm for cardinality estimate and proposes a protection technique to mitigate the impact of soft errors.
IEEE TRANSACTIONS ON DEPENDABLE AND SECURE COMPUTING
(2022)
Article
Engineering, Multidisciplinary
M. S. Hashmi, Urfa Aslam, Jagdev Singh, Kottakkaran Sooppy Nisar
Summary: This study proposes a novel approach for the numerical solution of the fractional telegraph equation using a combination of differential quadrature method and modified cubic B-spline. The stability of the proposed scheme is ensured using a matrix-based technique, and the feasibility and applicability of the algorithm are demonstrated through test problems.
ALEXANDRIA ENGINEERING JOURNAL
(2022)
Article
Mathematics
Bartosz Malman
Summary: This paper studies the structure of the closure of analytic polynomials, P2(μ), in the Lebesgue space L2(μ) of a compactly supported Borel measure μ living in the complex plane. By extending the ideas of Khrushchev and considering measures supported on the closed unit disk D and the unit circle T, the exact form of the Thomson decomposition of P2(μ) is calculated. The results show that the space splits according to a natural decomposition of measurable subsets of T.
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
(2023)
Article
Astronomy & Astrophysics
Slava G. Turyshev, Viktor T. Toth
Summary: This passage discusses the study of the optical properties of the solar gravitational lens by characterizing the gravitational field of the Sun using multipole moments. By solving Maxwell's equations for electromagnetic waves in the gravitational field, accounting for multipole contributions, and using wave-theoretical methods, the text explores how multipoles affect the optical properties of the lens and cause the appearance of caustics in the diffraction patterns. This new wave-theoretical solution allows for a better understanding of gravitational lensing by realistic lenses with multiple gravitational multipoles.
Article
Mathematics, Applied
Byeongseon Jeong, Hyoseon Yang, Jungho Yoon
Summary: This paper presents a new non-uniform corner-cutting (NUCC) subdivision scheme that improves the accuracy compared to classical methods. By selecting a shape parameter, the scheme can achieve an improved approximation order of three, in contrast to the second-order accuracy of classical methods. Analysis of convergence and smoothness shows that the proposed scheme has the same smoothness as the classical Chaikin's corner-cutting algorithm, C1.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Computer Science, Software Engineering
Simon Bruggmann, Rico Zenklusen
Summary: This paper introduces the relaxation and rounding approaches as a versatile tool for constrained submodular function maximization. It proposes a polyhedral viewpoint for designing contention resolution schemes, which avoids explicit dealing with randomization. The framework allows for employing polyhedral techniques and simplifies the construction and analysis of contention resolution schemes.
MATHEMATICAL PROGRAMMING
(2022)
Article
Mathematics
Ababi Hailu Ejere, Gemechis File Duressa, Mesfin Mekuria Woldaregay, Tekle Gemechu Dinka
Summary: This study focuses on formulating and analyzing an exponentially fitted numerical scheme by decomposing the domain into subdomains to solve singularly perturbed differential equations with large negative shift. By constructing an exponentially fitted numerical scheme on each boundary and interior layer subdomains and combining with the solutions on the regular subdomains, a second order epsilon-uniformly convergent numerical scheme is obtained.
JOURNAL OF MATHEMATICS
(2022)
Article
Computer Science, Information Systems
Xingyu Cui, Yong Li, Lili Xu
Summary: This paper presents a new algorithm called adaptive extension fitting scheme (AEFS) to determine a piecewise Bezier curve that best fits a given sequence of data points as well as locate the coordinates of the connecting points between the pieces adaptively. The experimental results indicate that AEFS outperforms other models involved in terms of execution time, fitting accuracy, number of segments, and the authenticity of shape contours.
Article
Chemistry, Physical
J. Leitner, A. L. Dempwolff, A. Dreuw
Summary: Until now, perturbation-theoretical consistent algebraic diagrammatic construction (ADC) schemes up to third order have been developed for the quantum chemical investigation of electronic transitions and excited-state properties. In this study, we derive for the first time a consistent fourth-order ADC(4) scheme using novel techniques of automated equation and code generation. The resulting ADC(4) excitation energies have been benchmarked against high-level reference data, demonstrating their accuracy. These advancements also open new possibilities for highly accurate ADC methods in studying electron-detached and attached states.
JOURNAL OF CHEMICAL PHYSICS
(2022)
Article
Chemistry, Physical
Ryan S. Kingsbury, Andrew S. Rosen, Ayush S. Gupta, Jason M. Munro, Shyue Ping Ong, Anubhav Jain, Shyam Dwaraknath, Matthew K. Horton, Kristin A. Persson
Summary: Computational materials discovery relies on large databases of properties, and while it is now possible to use more accurate methods for high-throughput calculations, recalculating the entire database is not practical. Therefore, a general procedure is proposed to combine high-fidelity calculations with low-fidelity calculations. Experimental results from the Materials Project database show that this method improves solid and aqueous phase stability predictions.
NPJ COMPUTATIONAL MATERIALS
(2022)
Article
Computer Science, Information Systems
Changzhong Wang, Yang Huang, Weiping Ding, Zehong Cao
Summary: Fuzzy rough sets combined with the concept of self-information are used to construct four uncertainty measures to evaluate the classification ability of attribute subsets. The fourth measure, relative decision self-information, is proven to be better for attribute reduction. A greedy algorithm is designed for attribute reduction, and the effectiveness of the method is validated through experimental results.
INFORMATION SCIENCES
(2021)
Article
Computer Science, Information Systems
Yang Gao, Xiangzhan Yu, Hongli Zhang
Summary: Graph clustering, an important topic in network analysis, often focuses on lower-order network structures but fails to capture higher-order information. Recent methods introduce higher-order units (motifs) to construct motif-based hypergraphs, increasing accuracy. However, hypergraph fragmentation in sparse networks remains a challenge that requires novel solutions.
INFORMATION SCIENCES
(2022)
Article
Chemistry, Physical
Deep M. Patel, Connor W. Schroeder, Luke T. Roling
Summary: This study presents a model to predict interaction energies in adsorbate systems using an interaction-counting approach, and extends it to interactions between different adsorbate types. The findings are significant for predicting energetics of catalytic reactions and practical reaction studies.
JOURNAL OF PHYSICAL CHEMISTRY C
(2023)
Article
Mathematics, Applied
Diogo A. Gomes, Joao Saude
Summary: The study develops numerical methods for finite-state mean-field games (MFGs) that meet a monotonicity condition to address the difficulty of non-standard boundary conditions. By constructing a contraction flow based on this condition, the study illustrates how fixed points of the flow can solve for both stationary and time-dependent MFGs, using a MFG modeling paradigm-shift problem as an example.
APPLIED MATHEMATICS AND OPTIMIZATION
(2021)
Article
Mathematics, Applied
Rita Ferreira, Diogo Gomes, Teruo Tada
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2019)
Article
Mathematics, Interdisciplinary Applications
Diogo A. Gomes, Joao Saude
Summary: The study introduces a price formation model based on constrained mean-field game theory, exploring how a large number of small players can store and trade commodities. By employing a fixed-point argument, the existence of a unique solution is established, and linear-quadratic models are analyzed.
DYNAMIC GAMES AND APPLICATIONS
(2021)
Article
Mathematics, Applied
R. Barkhudaryan, D. A. Gomes, H. Shahgholian, M. Salehi
Summary: This paper discusses multi-switching problems modeled as variational inequalities, which represent decision-making under uncertainty. The general existence theory is proven through monotone scheme, and iterative methods for numerical results are discussed. Furthermore, a connection is made between the recently developed models for asset bubbles (a non-local problem) and switching problems with two possible switching cases.
APPLICABLE ANALYSIS
(2022)
Article
Mathematics, Applied
Diogo A. Gomes, Xianjin Yang
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
(2020)
Article
Mathematics, Applied
Diogo Gomes, Julian Gutierrez, Mathieu Lauriere
Summary: In this study, machine learning architectures are used to solve a mean-field games system in price formation models. A training process is formulated based on a min-max characterization of the optimal control and price variables. The main theoretical contribution lies in the development of posteriori estimates as a tool to assess the convergence of the training process. Numerical experiments are conducted using linear dynamics, quadratic, and non-quadratic models to illustrate the results.
APPLIED MATHEMATICS AND OPTIMIZATION
(2023)
Article
Mathematics, Applied
Hector Sanchez Morgado
Summary: In this paper, we study Lagrangians defined only on the horizontal distribution of a sub-riemannian manifold. The associated Hamiltonian is neither strictly convex nor coercive. Following the approach in Contreras et al (2015), we prove a result on homogenization of the Hamilton-Jacobi equation. To establish this result, we extend weak KAM and Aubry-Mather theories to the sub-riemannian setting and obtain a Tonelli theorem. Along the way, we observe the long time convergence of the Lax-Oleinik semigroup and the vanishing discount convergence of the discounted value function.
Article
Business, Finance
Diogo Gomes, Julian Gutierrez, Ricardo Ribeiro
Summary: This paragraph describes a model in which a finite number of traders trade an asset in a market where supply is a stochastic process. The problem is to find a price process that ensures market clearing and supply meeting demand when traders act optimally to minimize their trading costs. This problem is relevant in market economies, such as electricity generation from renewable sources in smart grids. The model includes noise on the supply side, which is counterbalanced on the consumption side through energy storage or demand reduction based on a dynamic price process. By solving a constrained minimization problem, it is proven that the Lagrange multiplier corresponding to the market-clearing condition defines the solution of the price formation problem. The price process of a continuum population is characterized using optimal control techniques for the linear-quadratic structure. Numerical schemes for price computation in finite and infinite games are included, and the model is illustrated using real data.
SIAM JOURNAL ON FINANCIAL MATHEMATICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Marco Cirant, Diogo A. Gomes, Edgard A. Pimentel, Hector Sanchez-Morgado
Summary: This study proves the existence of smooth solutions for mean-field games with a singular mean-field coupling, where the coupling is not bounded from below. The research explores both stationary and time-dependent cases and introduces new bounds to establish the existence of solutions through an approximate problem. The unique coupling arises in models where agents have a preference for low-density regions, leading to paradoxical movement patterns.
JOURNAL OF DYNAMICS AND GAMES
(2021)
Article
Mathematics, Applied
Ermal Feleqi, Diogo Gomes, Teruo Tada
MINIMAX THEORY AND ITS APPLICATIONS
(2020)
Article
Mathematics, Interdisciplinary Applications
Diogo A. Gomes, Hiroyoshi Mitake, Kengo Terai
NETWORKS AND HETEROGENEOUS MEDIA
(2020)
Article
Automation & Control Systems
Rita Ferreira, Diogo Gomes, Xianjin Yang
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS
(2020)
Proceedings Paper
Automation & Control Systems
Diogo A. Gomes, Diego Marcon, Fatimah Al Saleh
2019 IEEE 58TH CONFERENCE ON DECISION AND CONTROL (CDC)
(2019)
Article
Mathematics, Applied
Diogo Gomes, Marc Sedjro
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S
(2018)
Article
Mathematics, Interdisciplinary Applications
Diogo Gomes, Julian Gutierrez, Ricardo Ribeiro
Summary: This paper introduces a mean-field game model for commodity price formation, taking into account random fluctuations in production. The model extends existing deterministic price formation models, with agents aiming to minimize average cost by choosing trading rates. For linear dynamics and quadratic costs, optimal trading rates are determined in feedback form, leading to the price being a solution to a stochastic differential equation.
MATHEMATICS IN ENGINEERING
(2021)
