Fine-grained Expressivity of Graph Neural Networks

Numerous recent works have analyzed the expressive power of message-passing graph neural networks (MPNNs), primarily utilizing combinatorial techniques such as the $1$-dimensional Weisfeiler-Leman test ($1$-WL) for the graph isomorphism problem. However, the graph isomorphism objective is inherently binary, not giving insights into the degree of similarity between two given graphs. This work resolves this issue by considering continuous extensions of both $1$-WL and MPNNs to graphons. Concretely, we show that the continuous variant of $1$-WL delivers an accurate topological characterization of the expressive power of MPNNs on graphons, revealing which graphs these networks can distinguish and the level of difficulty in separating them. We identify the finest topology where MPNNs separate points and prove a universal approximation theorem. Consequently, we provide a theoretical framework for graph and graphon similarity combining various topological variants of classical characterizations of the $1$-WL. In particular, we characterize the expressive power of MPNNs in terms of the tree distance, which is a graph distance based on the concepts of fractional isomorphisms, and substructure counts via tree homomorphisms, showing that these concepts have the same expressive power as the $1$-WL and MPNNs on graphons. Empirically, we validate our theoretical findings by showing that randomly initialized MPNNs, without training, exhibit competitive performance compared to their trained counterparts. Moreover, we evaluate different MPNN architectures based on their ability to preserve graph distances, highlighting the significance of our continuous $1$-WL test in understanding MPNNs' expressivity

Symmetries of Nonlinear PDEs on Metric Graphs and Branched Networks

This Special Issue focuses on recent progress in a new area of mathematical physics and applied analysis, namely, on nonlinear partial differential equations on metric graphs and branched networks. Graphs represent a system of edges connected at one or more branching points (vertices). The connection rule determines the graph topology. When the edges can be assigned a length and the wave functions on the edges are defined in metric spaces, the graph is called a metric graph. Evolution equations on metric graphs have attracted much attention as effective tools for the modeling of particle and wave dynamics in branched structures and networks. Since branched structures and networks appear in different areas of contemporary physics with many applications in electronics, biology, material science, and nanotechnology, the development of effective modeling tools is important for the many practical problems arising in these areas. The list of important problems includes searches for standing waves, exploring of their properties (e.g., stability and asymptotic behavior), and scattering dynamics. This Special Issue is a representative sample of the works devoted to the solutions of these and other problems

Proceedings of the Fifth European Workshop on Probabilistic Graphical Models

Peer reviewe

Multisensor Data Fusion in Pervasive Artificial Intelligence Systems

Intelligent systems designed to manage smart environments exploit numerous sensing and actuating devices, pervasively deployed so as to remain invisible to users and subtly learn their preferences and satisfy their needs. Nowadays, such systems are constantly evolving and becoming ever more complex, so it is increasingly difficult to develop them successfully. A possible solution to this problem might lie in delegating certain decisions to the machines themselves, making them more autonomous and able to self-configure and self-manage. This work presents a multi-tier architecture for a complete pervasive system capable of understanding the state of the surrounding environment, as well as using this knowledge to decide what actions should be performed to provide the best possible environmental conditions for end-users, in line with the Ambient Intelligence (AmI) paradigm. To achieve such high-level goals, the system has to effectively merge and analyze heterogeneous data collected by multiple sensors, pervasively deployed in a smart environment. To this end, the proposed system includes a context-aware, self-optimizing, adaptive module for sensor data fusion. Contextual information is leveraged in the fusion process, so as to increase the accuracy of inference and hence decision making in a dynamically changing environment. Additionally, two self-optimization modules are responsible for dynamically determining the subset of sensors to use, finding an optimal trade-off to minimize energy consumption and maximize sensing accuracy. The effectiveness of the proposed approach is demonstrated with the application scenario of user activity recognition in an AmI system managing a smart home environment. In order to increase the resilience of the system to highly uncertain and unreliable information, the architecture is enriched by a filtering module to pre-process raw data coming from lower levels, before feeding them to the data fusion and reasoning modules in the higher levels.Intelligent systems designed to manage smart environments exploit numerous sensing and actuating devices, pervasively deployed so as to remain invisible to users and subtly learn their preferences and satisfy their needs. Nowadays, such systems are constantly evolving and becoming ever more complex, so it is increasingly difficult to develop them successfully. A possible solution to this problem might lie in delegating certain decisions to the machines themselves, making them more autonomous and able to self-configure and self-manage. This work presents a multi-tier architecture for a complete pervasive system capable of understanding the state of the surrounding environment, as well as using this knowledge to decide what actions should be performed to provide the best possible environmental conditions for end-users, in line with the Ambient Intelligence (AmI) paradigm. To achieve such high-level goals, the system has to effectively merge and analyze heterogeneous data collected by multiple sensors, pervasively deployed in a smart environment. To this end, the proposed system includes a context-aware, self-optimizing, adaptive module for sensor data fusion. Contextual information is leveraged in the fusion process, so as to increase the accuracy of inference and hence decision making in a dynamically changing environment. Additionally, two self-optimization modules are responsible for dynamically determining the subset of sensors to use, finding an optimal trade-off to minimize energy consumption and maximize sensing accuracy. The effectiveness of the proposed approach is demonstrated with the application scenario of user activity recognition in an AmI system managing a smart home environment. In order to increase the resilience of the system to highly uncertain and unreliable information, the architecture is enriched by a filtering module to pre-process raw data coming from lower levels, before feeding them to the data fusion and reasoning modules in the higher levels

The hour of traces: an analysis of the presuppositions, axiomatic formalization, and ontological implications of Reichenbach's frequency interpretation of probability

Thesis (M.A.)--Boston Universit

Collected Papers (on Neutrosophic Theory and Applications), Volume VI

This sixth volume of Collected Papers includes 74 papers comprising 974 pages on (theoretic and applied) neutrosophics, written between 2015-2021 by the author alone or in collaboration with the following 121 co-authors from 19 countries: Mohamed Abdel-Basset, Abdel Nasser H. Zaied, Abduallah Gamal, Amir Abdullah, Firoz Ahmad, Nadeem Ahmad, Ahmad Yusuf Adhami, Ahmed Aboelfetouh, Ahmed Mostafa Khalil, Shariful Alam, W. Alharbi, Ali Hassan, Mumtaz Ali, Amira S. Ashour, Asmaa Atef, Assia Bakali, Ayoub Bahnasse, A. A. Azzam, Willem K.M. Brauers, Bui Cong Cuong, Fausto Cavallaro, Ahmet Çevik, Robby I. Chandra, Kalaivani Chandran, Victor Chang, Chang Su Kim, Jyotir Moy Chatterjee, Victor Christianto, Chunxin Bo, Mihaela Colhon, Shyamal Dalapati, Arindam Dey, Dunqian Cao, Fahad Alsharari, Faruk Karaaslan, Aleksandra Fedajev, Daniela Gîfu, Hina Gulzar, Haitham A. El-Ghareeb, Masooma Raza Hashmi, Hewayda El-Ghawalby, Hoang Viet Long, Le Hoang Son, F. Nirmala Irudayam, Branislav Ivanov, S. Jafari, Jeong Gon Lee, Milena Jevtić, Sudan Jha, Junhui Kim, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Darjan Karabašević, Songül Karabatak, Abdullah Kargın, M. Karthika, Ieva Meidute-Kavaliauskiene, Madad Khan, Majid Khan, Manju Khari, Kifayat Ullah, K. Kishore, Kul Hur, Santanu Kumar Patro, Prem Kumar Singh, Raghvendra Kumar, Tapan Kumar Roy, Malayalan Lathamaheswari, Luu Quoc Dat, T. Madhumathi, Tahir Mahmood, Mladjan Maksimovic, Gunasekaran Manogaran, Nivetha Martin, M. Kasi Mayan, Mai Mohamed, Mohamed Talea, Muhammad Akram, Muhammad Gulistan, Raja Muhammad Hashim, Muhammad Riaz, Muhammad Saeed, Rana Muhammad Zulqarnain, Nada A. Nabeeh, Deivanayagampillai Nagarajan, Xenia Negrea, Nguyen Xuan Thao, Jagan M. Obbineni, Angelo de Oliveira, M. Parimala, Gabrijela Popovic, Ishaani Priyadarshini, Yaser Saber, Mehmet Șahin, Said Broumi, A. A. Salama, M. Saleh, Ganeshsree Selvachandran, Dönüș Șengür, Shio Gai Quek, Songtao Shao, Dragiša Stanujkić, Surapati Pramanik, Swathi Sundari Sundaramoorthy, Mirela Teodorescu, Selçuk Topal, Muhammed Turhan, Alptekin Ulutaș, Luige Vlădăreanu, Victor Vlădăreanu, Ştefan Vlăduţescu, Dan Valeriu Voinea, Volkan Duran, Navneet Yadav, Yanhui Guo, Naveed Yaqoob, Yongquan Zhou, Young Bae Jun, Xiaohong Zhang, Xiao Long Xin, Edmundas Kazimieras Zavadskas

LONG-TERM DYNAMIC SIMULATION OF POWER SYSTEMS USING PYTHON, AGENT BASED MODELING, AND TIME-SEQUENCED POWER FLOWS

Automated controls facilitate reliable and efficient operation of modern power systems. Engineers employ computer simulations to develop, analyze, and tune such controls. Short-term dynamic, or transient, power system simulation is a useful and standardized power industry tool. Researchers have developed effective long-term dynamic (LTD) simulators, but there is not yet an industry standard computational method or software package for LTD simulation. This work introduces a novel LTD simulation tool and provides examples of various engineering applications. The newly created software tool, Power System Long-Term Dynamic Simulator (PSLTDSim), uses a time-sequenced power flow (TSPF) technique to simulate LTD events. The TSPF technique incorporates a number of modeling assumptions that simplify certain engineering calculations. Despite such simplifications, PSLTDSim demonstrates an acceptable amount of accuracy for ramp and small step type perturbations when compared to industry standard transient simulation software. Demonstrated PSLTDSim engineering applications include: investigation of long-term governor deadband effects, automatic generation control tuning, and switched shunt coordination during multi-hour events. Further demonstrated examples consist of user modified turbine speed governor behavior and variable system damping and inertia. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, under Award Number DE-SC0012671