A Proof of Goldbach Conjecture by Mirror Prime Decomposition

Prof.Yingxu Wang
President, International Institute of Cognitive Informatics and Cognitive Computing (ICIC)
Director, Laboratory for Computational Intelligence, Cognitive Systems, and Software Science
Dept. of Electrical and Computer Engineering
Schulich School of Engineering and Hotchkiss Brain Institute
University of Calgary
Canada
Email: yingxu@ucalgary.ca

Abstract:

This work presents a formal proof of Goldbach conjecture based on a novel theory of Mirror-Prime Decomposition (MPD) for arbitrary even integers. A new concept of mirror primes $$ \Bbb{P}_{μ}\subset \Bbb{P} \times \Bbb{P} $$ is introduced as a set of pairs of primes that are symmetrically adjacent to any pivotal even number $$ n_{e} \in \Bbb{N}_{e} \subset \Bbb{N} $$ on both sides in finite distance k bounded by 1 ≤ k ≤ (ne/2) − 2. As a counterpart of the Euclidean Fundamental Theorem of Arithmetic for natural number factorization, the MPD theory enables arbitrary even number decomposition by mirror primes. MPD paves a way to prove the Goldbach conjecture, i.e., where denoted by the big-R calculus for representing recursive structures and manipulating recursive functions. An algorithm of Goldbach conjecture testing is designed for demonstrating the formal proof of the Goldbach theorem. i.e., $$\forall 4 \leq \frac{n_{e}}{2}<\infty$$,
$$n_{e}= f(p^\frac{n_{e}}{2}_{\mathrm{μ}^{-}}, p^\frac{n_{e}}{2}_{\mathrm{μ}^{+}} ) = R_{k=1}^{(\frac{n_{e}}{2}-2)}(p^\frac{n_{e}}{2}_{\mathrm{μ}^{-}}+ p^\frac{n_{e}}{2}_{\mathrm{μ}^{+}} )$$, where
$$(p^\frac{n_{e}}{2}_{\mathrm{μ}^{-}}= \frac{n_{e}}{2}-k, p^\frac{n_{e}}{2}_{\mathrm{μ}^{+}}+k) \in \Bbb{P}_{μ}$$ denoted by the big-R calculus for representing recursive structures and manipulating recursive functions. An algorithm of Goldbach conjecture testing is designed for demonstrating the formal proof of the Goldbach theorem.

Biography:

Yingxu Wang is professor of cognitive informatics, brain science, software science, and denotational mathematics, President of International Institute of Cognitive Informatics and Cognitive Computing (ICIC, http://www.ucalgary.ca/icic/). He is a Fellow of ICIC, a Fellow of WIF (UK), a P.Eng of Canada, and a Senior Member of IEEE and ACM. He is/was visiting professor (on sabbatical leave) at Oxford University (1995), Stanford University (2008|2016), UC Berkeley (2008), and MIT (2012), respectively. He received a PhD in Computer Science from the Nottingham Trent University in 1998 and has been a full professor science 1994. He is the founder and steering committee chair of the annual IEEE International Conference on Cognitive Informatics and Cognitive Computing (ICCI*CC) since 2002. He is founding Editor-in-Chief of Int’l Journal of Cognitive Informatics & Natural Intelligence, founding Editor-in-Chief of Int’l Journal of Software Science & Computational Intelligence, Associate Editor of IEEE Trans. on SMC - Systems, and Editor-in-Chief of Journal of Advanced Mathematics & Applications. Dr. Wang is the initiator of a few cutting-edge research fields such as cognitive informatics, denotational mathematics (concept algebra, process algebra, system algebra, semantic algebra, inference algebra, big data algebra, fuzzy truth algebra, and fuzzy probability algebra, visual semantic algebra, granular algebra), abstract intelligence (?I), the neural circuit theory, mathematical models of the brain, cognitive computing, cognitive learning engines, cognitive knowledge base theory, and basic studies across contemporary disciplines of intelligence science, robotics, knowledge science, computer science, information science, brain science, system science, software science, data science, neuroinformatics, cognitive linguistics, and computational intelligence. He has published 400+ peer reviewed papers and 29 books in aforementioned transdisciplinary fields. He has presented 30 invited keynote speeches in international conferences. He has served as general chairs or program chairs for more than 20 international conferences. He is the recipient of dozens international awards on academic leadership, outstanding contributions, best papers, and teaching in the last three decades. He is one of the popular scholars according to the big data system of ResearchGate worldwide stats.

Synthesizing Distributed Algorithms for Combinatorial Network Optimization

Prof. Minghua Chen
City University of Hong Kong, Kowloon Tong, Kowloon, Hong Kong
E-mail: minghua.chen@cityu.edu.hk

Abstract:

Many important network design problems are fundamentally combinatorial optimization problems. A large number of such problems, however, cannot readily be tackled by distributed algorithms. We develop a Markov approximation technique for synthesizing distributed algorithms for network combinatorial problems with near-optimal performance. We show that when using the log- sum-exp function to approximate the optimal value of any combinatorial problem, we end up with a solution that can be interpreted as the stationary probability distribution of a class of time-reversible Markov chains. Selected Markov chains among this class, or their carefully-perturbed versions, yield distributed algorithms that solve the log-sum-exp approximated problem. The Markov Approximation technique allows one to leverage the rich theories of Markov chains to design distributed schemes with performance guarantees. By case studies, we illustrate that it not only can provide fresh perspective to existing distributed solutions, but also can help us generate new distributed algorithms in other problem domains with provable performance, including cloud computing, edge computing, and IoT scheduling.

Biography:

Minghua Chen received his B.Eng. and M.S. degrees from the Department of Electronic Engineering at Tsinghua University. He received his Ph.D. degree from the Department of Electrical Engineering and Computer Sciences at University of California Berkeley. He is currently a Professor of School of Data Science, City University of Hong Kong. He received the Eli Jury award from UC Berkeley (presented to a graduate student or recent alumnus for outstanding achievement in the area of Systems, Communications, Control, or Signal Processing) and several best paper awards, including IEEE ICME Best Paper Award in 2009, IEEE Transactions on Multimedia Prize Paper Award in 2009, ACM Multimedia Best Paper Award in 2012, and IEEE INFOCOM Best Poster Award in 2021. He is currently a Senior Editor for IEEE Systems Journal and an Executive Member of ACM SIGEnergy (as the Award Chair). His recent research interests include online optimization and algorithms, machine learning in power systems, intelligent transportation systems, distributed optimization, and delay-critical networked systems. He is an ACM Distinguished Scientist and an IEEE Fellow.

Second Order Constraint Qualifications in Optimal Control

Prof. Javier F Rosenblueth
National Autonomous University of Mexico, Mexico
E-mail: jfrl@unam.mx

Abstract:

For constrained problems in mathematical programming, second order conditions for optimality are well established under different constraint qualifications such as linearly independence, normality, properness or regularity. For optimal control problems involving equality and inequality constraints, some implications between the corresponding constraint qualifications may fail to hold and, in this talk, we explain how new assumptions are required to provide second order necessary conditions for optimality.

Biography:

Professor Rosenblueth holds a BSc in Mathematics from the National Autonomous University of Mexico and a PhD in Control Theory from the Imperial College of Science, Technology and Medicine, London, UK. He worked as a researcher in the Centre for Research in Mathematics, Guanajuato, Mexico and, since 1989, joined the Applied Mathematics and Systems Research Institute of the National Autonomous University of Mexico. He is Full Professor and currently a member of the Mathematical Physics Department. He has published more than 90 refereed papers, has spent sabbatical visits at the Weizmann Institute of Science, Rehovot, and Technion Israel Institute of Technology, Haifa, Israel; Imperial College and University of Bath, UK; University of Porto, Portugal, amongst others. He is associate editor of several refereed journals and has participated in numerous international conferences. His main research interests are in optimal control theory, calculus of variations, variational analysis, and optimization.

Model Analogies Between Mechanics and Electrodynamics

Prof. Elias C. Aifantis
Mercator Fellow, Friedrich-Alexander University, Erlangen-Nuremberg,
90762 Fürth, Germany
E-mail:

Abstract:

Beyond the formal analogies between Newton's law of gravitation and Coulomb's law of electrostatics, there is a number of follow-up developments in electrodynamics and the theory of circuits which resemble preceding developments in classical mechanics and the theory of structures. After a brief illustration of such examples, it is shown that this recipe can also be applied to include the case of generalized mechanics and its electrodynamics counterpart. In particular, a nonlocal gradient extension of Newton's and Coulomb's laws is discussed, along with a similar discussion of Hooke's and Ohm's laws as applied to the theory of mechanical trusses/frames and electrical circuits, respectively.

Biography:

Elias C. Aifantis is currently an Emeritus Professor of Mechanics at Aristotle University of Thessaloniki/Greece and Michigan Technological University/USA, as well as Mercator fellow at Friedrich-Alexander University/Germany and a Distinguished Professor at Beijing University of Civil Engineering and Architecture/China. Formerly, he has also been a Distinguished Faculty Advisor at King Abdulaziz University/Saudi Arabia, Distinguished Visiting Expert at ITMO University/Russia and Southwest Jiaotong University/China, as well as MegaGrant Director at Togliatti State University /Russia. He has promoted highly interdisciplinary work in mechanics of materials by bringing into the field of solid mechanics ideas from diffusion theory, chemical reactions, and nonlinear physics. He has coined the terms dislocation patterning, material instabilities, gradient plasticity/elasticity, chemo/nanomechanics, and pioneered internal length gradient (ILG) theories in these fields. Currently, he is extending the ILG framework to revisit electromagnetism and Maxwell’s equations, as well as gravitation and Newton’s Law. He has published over 650 articles and received about 14,700 citations with 58 h-index (Scopus); 13,580 citations with 57 h-index (Web of Science); 21,880 citations with 70 h-index (Google Scholar). He is included in the ISI Web of knowledge list of the world’s most highly cited authors in engineering

Advances in Quantum Computing Algorithms and their applications in Robotics

Prof. Dimitrios A. Karras, PhD
National and Kapodistrian University of Athens (NKUA),
Dept. General, Greece
E-mail: dakarras@uoa.gr

Abstract:

Abstract The subject of plenary speech is the presentation of the state of the art in quantum computing systems and algorithms aiming at illustrating these algorithms and systems as well as the main associated open problems in the field along with the so far proposed relevant solutions, with emphasis on the application of these systems and algorithms especially to complex real-time computational problems in the field of Robotics. More specifically, the following issues will be mainly considered regarding the state of the art and the related open problems in quantum computing and especially quantum algorithms design in solving real world problems:
● Designing Quantum Algorithms focused on Robots path planning: Which are their advantages in solving benchmark and real world robot path planning problems
● Quantum error tolerance and error correction --- necessary to achieve large-scale computations in robotics
● Simulation of quantum computing algorithms in general purpose computers and quantum computers in particular, in robotic problems applications

Biography:

Short CV: Dimitrios A. Karras received his Diploma and M.Sc. Degree in Electrical and Electronic Engineering from the National Technical University of Athens (NTUA), Greece in 1985 and the Ph.D in Electrical Engineering, NTUA, Greece in 1995, with honors. During 1990-2004 he collaborated as visiting professor and researcher with several universities and research institutes in Greece and Heidelberg, Germany (DKFZ). During 2004-2018 he has been with the Sterea Hellas Institute of Technology, Automation Dept., Greece as assoc. prof. in Digital Systems and Signal Processing, as well as visiting prof. of Hellenic Open University, Dept. Informatics in Communication Systems (2002-2010). Since 1/2019 is Associate Prof. in Digital and Intelligent Systems & Signal Processing, in National & Kapodistrian University of Athens, Greece, School of Science, Dept. General as well as adjunct Assoc. Prof. Dr. with the School of Basic Sciences, BIHER University, Chennai, India, as well as with the GLA university, Mathura, India (https://www.gla.ac.in/academics/faculty-detail/871/prof-dimitrios-karras) and EPOKA & CIT universities, Computer Engineering Dept., Tirana (https://cit.edu.al/faculty-of-engineering-staff/). He has published more than 70 research refereed journal papers in intelligent and distributed/multiagent systems, pattern recognition, image/signal processing and neural networks as well as in bioinformatics and more than 185 research papers in International refereed scientific Conferences. His research interests span the fields of intelligent & distributed systems, multiagent systems, pattern recognition and computational intelligence, image & signal processing/systems, biomedical systems, communications and networking as well as security and sustainability applications. He has served as program committee member as well as program/general chair at several international workshops and conferences in signal, image, communication and automation systems. He is, also, former editor in chief (2008-2016) of the International Journal in Signal and Imaging Systems Engineering (IJSISE), academic editor in the Applied Computational Intelligence and Soft Computing, TWSJ, ISRN Communications and the Applied Mathematics Hindawi journals as well as associate editor in various scientific journals, including CAAI, IET and Sustainable Solutions and Society journal (Editorial Team | Sustainable Solutions and Society (spast.org)). He has been cited in more than 2500 research papers ( https://scholar.google.com/citations?user=IxQurTMAAAAJ&hl=en), his H/G-indices are 21/51 (Google Scholar) and his Erdos number is 5. His RG score is 31.72 ( https://www.researchgate.net/profile/Dimitrios_Karras2/), in the highest 10% of scientific researchers. Apart from his scientific research, Assoc.Prof. Dr. D.A. Karras is involved in humanitarian projects as Sustainability, Human Rights and Peace passionate being Director of Research and Documentation at AdiAfrica NGO (https://www.adiafricadev.org/team/). His Linkedin profile and full CV can be found at https://www.linkedin.com/in/dimitrios-a-karras-39a89826/

Prof. Imre J. Rudas, IEEE Fellow
Obuda University,
Budapest, Hungary
E-mail:

Abstract:

Biography:

Healthy Route Generation and Recommendation

Prof. Ivan Ganchev
University of Limerick, Limerick
Ireland
E-mail: ivan.ganchev@ul.ie

Abstract: This paper presents the utilization of a developed pilot wireless-based Air Quality Index (AQI) monitoring system, reporting live geo-grid resolved air quality data, for the purposes of healthy route generation and recommendation to users. The generated routes are visualized on a map and recommended to users through a specially developed client application, as part of the client tier of the supporting IoT platform EMULSION. A distributed computing architecture is utilized for the generation of healthy (more precisely, ‘least air pollution exposure’) routes, performed in near real-time by means of the dynamic Dijkstra algorithm, based on the interpolated AQI values. In addition, the fastest and shortest routes are generated as well.

Biography: Prof. Ivan Ganchev is a Senior Member of the IEEE1; the IEEE Communications Society (Essential); the IEEE Computer Society Special Technical Communities on: (i) Smart and Circular Cities, (ii) Wearable and Ubiquitous Computing, and (iii) Reliable, Safe, Secure and Time Deterministic Intelligent Systems; the IEEE Computer Society Technical Communities on: (i) Intelligent Informatics, (ii) Big Data, and (iii) Internet of Everything; the IEEE Computer Society Technical Committees on: (i) Internet, (ii) Computer Communications, and (iii) Cloud Computing; the IEEE Communities on: (i) Cloud Computing, (ii) Big Data, (iii) Future Networks, (iv) Internet of Things, and (v) IEEE Smart Cities; and the IEEE Consultants Network. He received his doctoral and engineering (summa cum laude) degrees from the Saint-Petersburg University of Telecommunications in 1995 and 1989, respectively. He is a URSI2 Senior Member, an ITU-T3 Invited Expert, and an IET4 Invited Lecturer. Prof. Ganchev was involved in 40+ international and national research projects. Previously he served as a member of the EU FP5 Academic Network for Wireless Internet Research in Europe (ANWIRE) and 8 European ‘COoperation in Science and Technology’ (COST) Actions: COST 285 “Modelling and Simulation Tools for Research in Emerging Multi-service Telecommunications”, COST 290 “Traffic and QoS Management in Wireless Multimedia Networks”, IC0906 “Wireless Networking for Moving Objects (WiNeMO)”, IC0905 “Techno-Economic Regulatory Framework for Radio Spectrum Access for Cognitive Radio/Software Defined Radio (TERRA)”, IC1304 “Autonomous Control for a Reliable Internet of Services (ACROSS)”, IC1303 “Algorithms, Architectures and Platforms for Enhanced Living Environments (AAPELE)”, CA15127 “Resilient Communication Services Protecting End-User Applications from Disaster-based Failures (RECODIS)”, CA16226 “Indoor Living Space Improvement: Smart Habitat for the Elderly (SHELD-ON)”. Prof. Ganchev’s research interests include novel telecommunication and information paradigms; modelling, simulation, and emulation of complex telecommunication and information systems, networks, and services; smart networks and services; smart ubiquitous networking; Internet of Things (IoT); Internet of Services; Internet tomography. Prof. Ganchev has served on the Technical Program Committee of 380+ prestigious international conferences, symposia, and workshops. He has authored/co-authored 1 monographic book, 3 textbooks, 4 edited books, and 300+ research papers in refereed international journals, books, and conference proceedings. He was a recipient of IEEE IAEAC 2017 Best Paper Award and IEEE IS 2012 Best Paper Award, and was nominated for the ITU-T Kaleidoscope 2008 Best Paper Award. He has given 20+ keynote/plenary/invited talks at international scientific forums. Prof. Ganchev is an Area Editor of the Elsevier “Computer Networks” journal, an Academic Editor of the Wiley “Wireless Communications and Mobile Computing” journal, an Editorial Board Member of the MDPI “Electronics”, MDPI “Mathematics”, and Wiley “Internet Technology Letters” journals, a Regional Editor (Europe) of the International Journal on Trust Management in Computing and Communications, and an Advisory Board Member of the MDPI “Engineering Proceedings” journal. He has also served as a Guest Editor for multiple prestigious international journals.