79 research outputs found

    Undergraduate Catalog of Studies, 2023-2024

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    Undergraduate Catalog of Studies, 2023-2024

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    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    Second-order sufficient conditions for sparse optimal control of singular Allen--Cahn systems with dynamic boundary conditions

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    In this paper we study the optimal control of a parabolic initial-boundary value problem of Allen--Cahn type with dynamic boundary conditions. Phase field systems of this type govern the evolution of coupled diffuse phase transition processes with nonconserved order parameters that occur in a container and on its surface, respectively. It is assumed that the nonlinear function driving the physical processes within the bulk and on the surface are double well potentials of logarithmic type whose derivatives become singular at the boundary of their respective domains of definition. For such systems, optimal control problems have been studied in the past. We focus here on the situation when the cost functional of the optimal control problem contains a nondifferentiable term like the L1L^1-norm leading to sparsity of optimal controls. For such cases, we derive second-order sufficient conditions for locally optimal controls

    Collected Papers (on Physics, Artificial Intelligence, Health Issues, Decision Making, Economics, Statistics), Volume XI

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    This eleventh volume of Collected Papers includes 90 papers comprising 988 pages on Physics, Artificial Intelligence, Health Issues, Decision Making, Economics, Statistics, written between 2001-2022 by the author alone or in collaboration with the following 84 co-authors (alphabetically ordered) from 19 countries: Abhijit Saha, Abu Sufian, Jack Allen, Shahbaz Ali, Ali Safaa Sadiq, Aliya Fahmi, Atiqa Fakhar, Atiqa Firdous, Sukanto Bhattacharya, Robert N. Boyd, Victor Chang, Victor Christianto, V. Christy, Dao The Son, Debjit Dutta, Azeddine Elhassouny, Fazal Ghani, Fazli Amin, Anirudha Ghosha, Nasruddin Hassan, Hoang Viet Long, Jhulaneswar Baidya, Jin Kim, Jun Ye, Darjan Karabašević, Vasilios N. Katsikis, Ieva Meidutė-Kavaliauskienė, F. Kaymarm, Nour Eldeen M. Khalifa, Madad Khan, Qaisar Khan, M. Khoshnevisan, Kifayat Ullah,, Volodymyr Krasnoholovets, Mukesh Kumar, Le Hoang Son, Luong Thi Hong Lan, Tahir Mahmood, Mahmoud Ismail, Mohamed Abdel-Basset, Siti Nurul Fitriah Mohamad, Mohamed Loey, Mai Mohamed, K. Mohana, Kalyan Mondal, Muhammad Gulfam, Muhammad Khalid Mahmood, Muhammad Jamil, Muhammad Yaqub Khan, Muhammad Riaz, Nguyen Dinh Hoa, Cu Nguyen Giap, Nguyen Tho Thong, Peide Liu, Pham Huy Thong, Gabrijela Popović‬‬‬‬‬‬‬‬‬‬, Surapati Pramanik, Dmitri Rabounski, Roslan Hasni, Rumi Roy, Tapan Kumar Roy, Said Broumi, Saleem Abdullah, Muzafer Saračević, Ganeshsree Selvachandran, Shariful Alam, Shyamal Dalapati, Housila P. Singh, R. Singh, Rajesh Singh, Predrag S. Stanimirović, Kasan Susilo, Dragiša Stanujkić, Alexandra Şandru, Ovidiu Ilie Şandru, Zenonas Turskis, Yunita Umniyati, Alptekin Ulutaș, Maikel Yelandi Leyva Vázquez, Binyamin Yusoff, Edmundas Kazimieras Zavadskas, Zhao Loon Wang.‬‬‬

    The evolution of language: Proceedings of the Joint Conference on Language Evolution (JCoLE)

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    Stable numerical methodology for variational inequalities with application in quantitative finance and computational mechanics

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    Coercivity is a characteristic property of the bilinear term in a weak form of a partial differential equation in both infinite space and the corresponding finite space utilized by a numerical scheme. This concept implies \textit{stability} and \textit{well-posedness} of the weak form in both the exact solution and the numerical solution. In fact, the loss of this property especially in finite dimension cases leads to instability of the numerical scheme. This phenomenon occurs in three major families of problems consisting of advection-diffusion equation with dominant advection term, elastic analysis of very thin beams, and associated plasticity and non-associated plasticity problems. There are two main paths to overcome the loss of coercivity, first manipulating and stabilizing a weak form to ensure that the discrete weak form is coercive, second using an automatically stable method to estimate the solution space such as the Discontinuous Petrov Galerkin (DPG) method in which the optimal test space is attained during the design of the method in such a way that the scheme keeps the coercivity inherently. In this dissertation, A stable numerical method for the aforementioned problems is proposed. A stabilized finite element method for the problem of migration risk problem which belongs to the family of the advection-diffusion problems is designed and thoroughly analyzed. Moreover, DPG method is exploited for a wide range of valuing option problems under the black-Scholes model including vanilla options, American options, Asian options, double knock barrier options where they all belong to family of advection-diffusion problem, and elastic analysis of Timoshenko beam theory. Besides, The problem of American option pricing, migration risk, and plasticity problems can be categorized as a free boundary value problem which has their extra complexity, and optimization theory and variational inequality are the main tools to study these families of the problems. Thus, an overview of the classic definition of variational inequalities and different tools and methods to study analytically and numerically this family of problems is provided and a novel adjoint sensitivity analysis of variational inequalities is proposed

    Optimization Methods for Mobility Resource Allocation, Pricing and Demand Management in Mobility-as-a-Service Systems

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    In the Mobility-as-a-Service (MaaS) systems under government contracting, this thesis proposes innovative auction-based MaaS mechanisms where users arrive dynamically and compete for mobility resources by bidding for mode-agnostic mobility resources based on their willingness to pay and preferences on service experience. This thesis takes the perspective of a MaaS regulator, which aims to maximize social welfare by allocating mobility resources to users. This thesis proposes two MaaS mechanisms that allow users to either pay for the immediate use of mobility service, Pay-as-You-Go (PAYG), or subscribe to mobility service packages, Pay-as-a-Package (PAAP). This thesis casts the proposed mechanisms as online mobility resource allocation problems to accommodate user bids based on available mobility resources. It is shown that the proposed PAYG mechanism is incentive-compatible, individually rational, and budget-balanced. This thesis proposes two polynomial-time online algorithms for both mechanisms and derives its corresponding competitive ratio relative to an offline optimization problem. The thesis also explores rolling horizon configurations with varying look-ahead policies to implement the proposed mechanisms. In the MaaS systems under economic deregulation, a MaaS platform can be viewed as a two-sided market where travelers and transportation service providers (TSPs) are two groups of interacting agents. This thesis proposes an optimization framework for the regulation of two-sided MaaS markets, uses an auction mechanism to model the behavior of travelers and TSPs, and casts this problem as a single-leader multi-follower game (SLMFG) where the leader is the MaaS regulator and two groups of follower problems represent the travelers and the TSPs. The MaaS regulator aims to maximize its profits by optimizing service prices and resource allocation. In response, travelers (resp. TSPs) adjust their participation level in the MaaS platform to minimize their travel costs (resp. maximize their profits). This thesis analyzes network effects in the two-sided MaaS market and formulates SLMFGs without/with network effects. This thesis provides constraint qualifications for the proposed SLMFGs and develops customized branch-and-bound algorithms based on strong-duality reformulations to solve SLMFGs. Considering the MaaS ecosystems with multi-disciplinary collaborators, this thesis models a MaaS ecosystem providing mobility services and instant delivery services by sharing the same transport system. This thesis derives integrated mobility and delivery user equilibrium (IMDUE) in the MaaS ecosystem and proposes a bilateral surcharge and reward scheme (BSRS) to manage the integrated mobility and delivery demand in different scenarios. This thesis proposes a bilevel model to optimize the proposed BSRS, where the upper-level problem aims to minimize the total system equilibrium costs of mobility and delivery users and the lower-level problem is the derived IMDUE under BSRS. After exploring the properties of the BSRS, a trial-and-error solution algorithm is proposed to solve the proposed bilevel optimization problem based on the properties of the optimal solutions under BSRS. Overall, this thesis proposes a unified framework and tractable optimization methodologies for the innovative MaaS paradigm, exploits the potentialities of MaaS systems to evaluate futuristic transport scenarios, and provides meaningful managerial insights for the regulation of MaaS systems

    Progress in Group Field Theory and Related Quantum Gravity Formalisms

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    Following the fundamental insights from quantum mechanics and general relativity, geometry itself should have a quantum description; the search for a complete understanding of this description is what drives the field of quantum gravity. Group field theory is an ambitious framework in which theories of quantum geometry are formulated, incorporating successful ideas from the fields of matrix models, ten-sor models, spin foam models and loop quantum gravity, as well as from the broader areas of quantum field theory and mathematical physics. This special issue collects recent work in group field theory and these related approaches, as well as other neighbouring fields (e.g., cosmology, quantum information and quantum foundations, statistical physics) to the extent that these are directly relevant to quantum gravity research
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