Elements of the random walk : an introduction for advanced students and researchers / / Joseph Rudnick, George Gaspari [[electronic resource]]

• Record Nr.: UNINA9910457872203321
• Autore: Rudnick Joseph Alan <1944->
• Pubbl/distr/stampa: Cambridge : , : Cambridge University Press, , 2004
• ISBN: 1-107-14767-0; 1-282-39477-0; 9786612394775; 0-511-64435-3; 0-511-64813-8; 0-511-18750-5; 0-511-56649-2; 0-511-61091-2; 0-511-18657-6
• Descrizione fisica: 1 online resource (xv, 329 pages) : digital, PDF file(s)
• Disciplina: 519.2/82
• Soggetti: Random walks (Mathematics)
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Title from publisher's bibliographic system (viewed on 05 Oct 2015).
• Nota di bibliografia: Includes bibliographical references (p. 323-325) and index.
• Nota di contenuto: Cover; Half-title; Title; Copyright; Dedication; Contents; Preface; 1 Introduction to techniques; 2 Generating functions I; 3 Generating functions II: recurrence, sites visited, and the role of dimensionality; 4 Boundary conditions, steady state, and the electrostatic analogy; 5 Variations on the random walk; 6 The shape of a random walk; 7 Path integrals and self-avoidance; 8 Properties of the random walk: introduction to scaling; 9 Scaling of walks and critical phenomena; 10 Walks and the O(n) model: mean field theory and spin waves; 11 Scaling, fractals, and renormalization; 12 More on the renormalization groupReferences; Index
• Sommario/riassunto: Random walks have proven to be a useful model in understanding processes across a wide spectrum of scientific disciplines. Elements of the Random Walk is an introduction to some of the most powerful and ; general techniques used in the application of these ideas. The mathematical construct that runs through the analysis of the topics covered in this book, unifying the mathematical treatment, is the generating function. Although the reader is introduced to analytical tools, such as path-integrals and field-theoretical formalism, the book is self-contained in that basic concepts are developed and relevant fundamental findings fully discussed. Mathematical background is provided in supplements at the end of each chapter, when appropriate. This text will appeal to graduate students across science, engineering and mathematics who need to understand the applications of random walk techniques, as well as to established researchers.

Formal Methods for Industrial Critical Systems : 29th International Conference, FMICS 2024, Milan, Italy, September 9–11, 2024, Proceedings / / edited by Anne E. Haxthausen, Wendelin Serwe

• Record Nr.: UNINA9910881098303321
• Autore: Haxthausen Anne E
• Pubbl/distr/stampa: Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2024
• ISBN: 9783031681509; 9783031681493
• Edizione: [1st ed. 2024.]
• Descrizione fisica: 1 online resource (267 pages)
• Collana: Lecture Notes in Computer Science, , 1611-3349 ; ; 14952
• Altri autori (Persone): SerweWendelin
• Disciplina: 005.45
• Soggetti: Compilers (Computer programs); Software engineering; Application software; Artificial intelligence; Computer science; Computer engineering; Computer networks; Compilers and Interpreters; Software Engineering; Computer and Information Systems Applications; Artificial Intelligence; Theory of Computation; Computer Engineering and Networks
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di contenuto: Intro -- Preface -- Organization -- Contents -- Real-Time Systems/Robotics -- Safe Linear Encoding of Vehicle Dynamics for the Instantiation of Abstract Scenarios -- 1 Introduction -- 2 Related Work -- 3 Encoding of Abstract Scenarios -- 4 Encoding Vehicle Dynamics and Scenes -- 4.1 Encoding Trajectories as Splines -- 4.2 Encoding of Scenes -- 4.3 Encoding of Vehicle Dynamics -- 5 Correctness -- 6 Demonstration -- 7 Conclusion -- References -- Evaluating the Effectiveness of Digital Twins Through Statistical Model Checking with Feedback and Perturbations -- 1 Introduction -- 2 Case Studies -- 3 The Stark Tool -- 3.1 The Evolution Sequence Model -- 3.2 RobTL -- 4 DT-Stark -- 4.1 The Feedback Mechanism -- 5 Experiments -- 6 Related Work -- 7 Concluding Remarks -- References -- UPPAAL-Based Modeling and Verification of ROS 2 Multi-threaded Execution and Operating System Reservations -- 1 Introduction -- 2 Background -- 2.1 ROS 2 -- 2.2 Reservation Based Scheduling -- 2.3 Timed Automata and UPPAAL -- 2.4 Pattern-Based Verification of ROS 2 Systems -- 3 Modeling and Verification in UPPAAL -- 3.1 Feature Selection and Abstraction -- 3.2 Modeling of Callbacks -- 3.3 Modeling of the Multi-threaded Executor -- 3.4 System Declaration and Verification in UPPAAL -- 3.5 Modeling of Operating System Reservations -- 4 Evaluation -- 4.1 Experimental Setup -- 4.2 Multi-threaded Execution -- 4.3 Reservation-Based Scheduling -- 4.4 Answer to the Research Questions -- 5 Related Work -- 6 Conclusion and Future Work -- References -- Semantics and Verification -- Formalising the Industrial Language SMMT in mCRL2 -- 1 Introduction -- 2 The SMMT Language -- 3 A Formal Semantics of SMMT -- 4 Translational Semantics in mCRL2 -- 5 Validation and Experiments -- 6 Discussion -- 7 Conclusions -- References.; Fault Tree Inference Using Multi-objective Evolutionary Algorithms and Confusion Matrix-Based Metrics -- 1 Introduction -- 2 Preliminaries -- 2.1 Fault Trees -- 2.2 Failure Data Set -- 2.3 Inference of Fault Tree Models -- 3 FT-MOEA-CM's Methodology -- 4 Experimental Evaluation -- 5 Results -- 5.1 Feature Assessment -- 5.2 Comparing FT-MOEA and FT-MOEA-CM -- 5.3 FT-MOEA-CM's Features: Parallelization and Caching -- 6 Conclusions -- References -- Logika: The Sireum Verification Framework -- 1 Introduction -- 2 Design Goals and Background -- 3 Features -- 4 Assessment -- 5 Related Work -- 6 Conclusion -- References -- Case Studies -- Fuzzing an Industrial Proprietary Protocol -- 1 Introduction -- 2 Challenges -- 3 BinFuzz -- 3.1 Protocol Reconstruction Phase -- 3.2 Fuzzing Phase -- 4 Protocol Fuzzing -- 4.1 FTP Protocol -- 4.2 Proprietary Drone Control Protocol -- 4.3 Limitations and Potential Extensions -- 5 Related Work -- 6 Conclusion -- References -- Modelling and Analysis of DTLS: Power Consumption and Attacks -- 1 Introduction -- 2 Background -- 2.1 DTLS 1.3 -- 2.2 Uppaal -- 2.3 Uppaal SMC -- 3 Modelling DTLS -- 3.1 Default DTLS 1.3 Protocol -- 3.2 DTLS 1.3 with Heartbeat Extension on Server -- 3.3 DTLS 1.3 with Heartbeat Extension on Client -- 4 Modelling DTLS Under Attack -- 5 Experiments -- 5.1 Power Consumption Comparison -- 5.2 Power Consumption with Malicious Actor -- 6 Related Work -- 7 Conclusion -- References -- Verifying a Radio Telescope Pipeline Using HaliVer: Solving Nonlinear and Quantifier Challenges -- 1 Introduction -- 2 Background -- 3 Case Study Description -- 3.1 DDECAL -- 3.2 Halide Implementation -- 4 ; Verification Challenges and Solutions -- 4.1 Tuple Support -- 4.2 Verifying Flattened Multidimensional Arrays -- 4.3 Dealing with Quantifiers -- 5 Experiments -- 5.1 Micro-benchmarks -- 6 Lessons Learned -- 7 Related Work.; 8 Conclusion -- References -- Reconstructing the High-Level Structure of Legacy Code via Software Model Checking: An Experience Report -- 1 Introduction -- 2 Methodology -- 2.1 Operating Assumptions -- 2.2 Main FSM Extraction Algorithm -- 2.3 Code Abstractions -- 3 The fsm-explorer Tool -- 3.1 Configuration -- 3.2 Analysis -- 4 Analysis of a Legacy Heat Pump Controller -- 5 Conclusions -- References -- Formal Analysis and Monitoring of Legacy Safety-Critical Interlocking Systems with the Use of Certified Industrial Tools -- 1 Introduction -- 2 Relay-Based RIS -- 3 The CLEARSY Safety Platform (CSSP) -- 4 Logical Description of the RIS Behaviour -- 5 Creation and Use of the RIS CSSP Monitor -- 6 Case Studies -- 6.1 Temporary Reversed Direction Installation -- 6.2 Signalling Light Panel -- 7 Discussion -- 8 Conclusion -- References -- Neural Networks -- Unifying Syntactic and Semantic Abstractions for Deep Neural Networks -- 1 Introduction -- 2 Background -- 2.1 Notation -- 2.2 Formal Analysis of Neural Networks -- 2.3 Semantic Compressions and Abstractions with Empirical Guarantees -- 2.4 Strong Formal Connections Between N and N' -- 2.5 Syntactic Neural Network Splitting and Merging -- 2.6 Syntactic Refinement -- 3 Methodology -- 3.1 Semantic Closeness Factor -- 3.2 Tree of Merges -- 3.3 Tree-Cuts and Refinement -- 3.4 Optimality of Tree -- 3.5 CEGAR ch12cegarspsnn,ch12cegar Loop Framework -- 4 Experiments -- 5 Related Work -- 6 Conclusion and Future Work -- References -- Multimodal Model Predictive Runtime Verification for Safety of Autonomous Cyber-Physical Systems -- 1 Introduction -- 2 Preliminaries -- 2.1 Mission-Time Linear Temporal Logic (MLTL) ch13LVR19,ch13RRS14 -- 2.2 Abstract Syntax Tree Architecture -- 2.3 Model Predictive Runtime Verification (MPRV) ch13ZADJR23 -- 3 Multimodal Model Predictive Runtime Verification (MMPRV).; 3.1 Predictive Mission-Time Linear Temporal Logic (PMLTL) -- 3.2 MMPRV Algorithm -- 3.3 Memory Requirements for MMPRV -- 4 Autonomous Vehicle Case Study -- 4.1 F1Tenth Autonomous Racing -- 4.2 Argoverse Autonomous Driving -- 5 Conclusion and Future Work -- References -- Surrogate Neural Networks Local Stability for Aircraft Predictive Maintenance -- 1 Introduction -- 2 Related Work -- 3 Case Study: Aircraft Loads-to-Stress Prediction -- 3.1 Description -- 3.2 Tested Models -- 3.3 Property to be Ensured: Local Stability -- 4 Method Combination for Local Stability Assessment -- 5 Experiments -- 6 Results -- 6.1 A Significant Verification Time Gain -- 6.2 Insights into the Models -- 7 Conclusions and Future Work -- A Open-Source Verification Pipeline -- References -- Author Index.
• Sommario/riassunto: This book constitutes the proceedings of the 29th International Conference on Formal Methods for Industrial Critical Systems, FMICS 2024, held in Milan, Italy, during September 9–13, 2024. The 14 full papers included in this book were carefully reviewed and selected from 22 submissions. These papers have been organized in the following topical sections: Real-Time Systems/ Robotics; Semantics and Verification; Case Studies; Neural Networks.