1. A "good regulator theorem" for embodied agents
   2025/08/04 by Nathaniel Virgo, Martin Biehl, Virgo, Nathaniel +5 · 4 citations
   Computer Science · Neuroscience · Psychology · #Artificial Intelligence (cs.AI) #Computability, Logic, AI Algorithms #Counterexample #Embodied and Extended Cognition #Embodied cognition #FOS: Computer and information sciences #FOS: Electrical engineering #Intuition #Observer (physics) #Philosophy and Theoretical Science #Property (philosophy) #Regulator #Systems and Control (eess.SY) #electronic engineering #information engineering
2. A novel class of functionals for perturbative algebraic quantum field theory
   2023/12/23 by Eli Hawkins, Kasia Rejzner, Hawkins, Eli +4 · 2 citations
   Mathematics · #Advanced Topics in Algebra #Algebra over a field #Algebraic number #Algebraic structures and combinatorial models #Axiom #Class (philosophy) #Computer science #Counterexample #Discrete mathematics #Field (mathematics) #Gauge theory #Homogeneous space #Homotopy and Cohomology in Algebraic Topology #Mathematical analysis #Mathematical physics #Mathematics #Physics #Product (mathematics) #Pure mathematics #Quantum #Quantum field theory #Quantum mechanics #Star product #Theoretical physics #math-ph #math.MP
3. Do Black Holes have Singularities?
   2023/12/01 by R. P. Kerr, Kerr, R. P. · 11 voices · 5 citations
   Mathematics · Physics and Astronomy · #Affine transformation #Black Holes and Theoretical Physics #Black hole (networking) #Combinatorics #Computer science #Cosmology and Gravitation Theories #Counterexample #Economics #Event horizon #Geometry #Gravitational singularity #Hawking #Horizon #Mathematical analysis #Mathematical physics #Mathematics #Metric (unit) #Physics #Point (geometry) #Pure mathematics #Relativity and Gravitational Theory #Theoretical physics #gr-qc
4. Response: Emergent analogical reasoning in large language models
   2023/08/30 by Damian Hodel, Jevin D. West, Jevin West +2 · 1 voice · 3 citations
   Computer Science · Mathematics · Psychology · Social Sciences · #Analogical reasoning #Analogy #Artificial intelligence #Cognitive psychology #Cognitive science #Computer science #Counterexample #Epistemology #Field (mathematics) #Language and cultural evolution #Linguistics #Mathematics #Memorization #Natural Language Processing Techniques #Philosophy #Physics #Psychology #Range (aeronautics) #Shot (pellet) #Simple (philosophy) #String (physics) #Theoretical physics #Topic Modeling #Zero (linguistics) #cs.AI #cs.CL
5. A Note on the Base-p Expansions of Putative Counterexamples to the p-adic Littlewood Conjecture
   2023/06/16 by John Blackman, Simon Kristensen, Blackman, John +3 · 2 citations
   Mathematics · #11J04 11J61 #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Base (topology) #Base change #Combinatorics #Combinatorics (math.CO) #Conjecture #Counterexample #Discrete mathematics #FOS: Mathematics #Geometry #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Number Theory (math.NT) #Omega #Physics #Pure mathematics #Word (group theory)
6. A Barrier-Based Scenario Approach to Verify Safety-Critical Systems
   2022/02/22 by Prithvi Akella, Aaron D. Ames, Akella, Prithvi +1 · 1 citation
   Computer Science · Engineering · Mathematics · #Algorithm #Artificial intelligence #Computer science #Counterexample #Discrete mathematics #Engineering #FOS: Electrical engineering #Formal Methods in Verification #Formal verification #Function (biology) #Functional verification #Mathematics #Probabilistic logic #Problem statement #Safety Systems Engineering in Autonomy #Scheme (mathematics) #Software Reliability and Analysis Research #State (computer science) #Statement (logic) #Systems and Control (eess.SY) #Trajectory #electronic engineering #information engineering
7. On the Liouville property for fully nonlinear equations with superlinear first-order terms
   2021/07/28 by Marco Cirant, Alessandro Goffi, Cirant, Marco +1 · 3 citations
   Mathematics · #Analysis of PDEs (math.AP) #Combinatorics #Counterexample #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical analysis #Mathematical physics #Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations #Nonlinear system #Order (exchange) #Philosophy #Physics #Property (philosophy) #Pure mathematics #Quantum mechanics #Variable (mathematics)
8. The formal derivative operator and multifactorial numbers
   2019/07/01 by Juan Triana, Rodrigo Aquino Castro · 1 citation
   Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Chemistry · #DNA and Biological Computing #semigroups and automata theory #Algorithms and Data Compression #Counterexample #Operator (biology) #Rule-based machine translation #Context (archaeology) #Connection (principal bundle) #Grammar #Mathematics #Derivative (finance) #Computer science #Context-free grammar #Discrete mathematics #Algebra over a field #Linguistics #Pure mathematics #Artificial intelligence #Philosophy #Chemistry
9. On the Baker-Campbell-Hausdorff Theorem: non-convergence and prolongation issues
   2018/11/01 by Stefano Biagi, Andrea Bonfiglioli, Marco Matone · 1 citation
   Mathematics · Computer Science · #Advanced Topics in Algebra #Matrix Theory and Algorithms #Fractional Differential Equations Solutions #BCH code #Mathematics #Hausdorff space #Series (stratigraphy) #Counterexample #Convergence (economics) #Logarithm #Absolute convergence #Prolongation #Discrete mathematics #Pure mathematics #Mathematical analysis #Algorithm
10. Action always involves attention
    2018/10/12 by Wayne Wu · 2 citations
    Arts and Humanities · Mathematics · Medicine · Neuroscience · Psychology · #Action (physics) #Agency (philosophy) #Argument (complex analysis) #Cognitive science #Computer science #Counterexample #Epistemology #Epistemology, Ethics, and Metaphysics #Feature (linguistics) #Free Will and Agency #Linguistics #Mathematics #Medicine #Neuroethics, Human Enhancement, Biomedical Innovations #Philosophy #Psychology
11. Private Information Retrieval from MDS Coded Data with Colluding Servers: Settling a Conjecture by Freij-Hollanti et al.
    2017/01/26 by Hua Sun, Syed A. Jafar, Sun, Hua +1 · 2 citations
    Computer Science · Mathematics · #Automorphism #Combinatorics #Complexity and Algorithms in Graphs #Computer network #Computer science #Conjecture #Counterexample #Cryptography and Data Security #Cryptography and Security (cs.CR) #Discrete mathematics #FOS: Computer and information sciences #Information Retrieval (cs.IR) #Information Theory (cs.IT) #Mathematics #Privacy-Preserving Technologies in Data #Private information retrieval #Programming language #Server #Set (abstract data type) #Statistics #Theoretical computer science #cs.CR #cs.IR #cs.IT #math.IT
12. On problems about judicious bipartitions of graphs
    2017/01/25 by Yuliang Ji, Jie Ma, Ji, Yuliang +5 · 1 citation
    Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #Bipartite graph #Combinatorics #Combinatorics (math.CO) #Conjecture #Counterexample #Discrete mathematics #FOS: Mathematics #Graph #Lambda #Limits and Structures in Graph Theory #Mathematical analysis #Mathematics #Physics #Upper and lower bounds #graph theory and CDMA systems #math.CO
13. Generation and properties of snarks
    2012/06/30 by Gunnar Brinkmann, Jan Goedgebeur, Jonas Hägglund +1 · 1 citation
    Computer Science · Mathematics · #Advanced Graph Theory Research #Class (philosophy) #Commutative Algebra and Its Applications #Conjecture #Counterexample #Cover (algebra) #Cubic graph #Limits and Structures in Graph Theory #cs.DM #math.CO
14. The distribution of weighted sums of the Liouville function and Pólyaʼs conjecture
    2011/08/31 by Peter Humphries · 1 citation
    Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics #Conjecture #Counterexample #Distribution (mathematics) #Function (biology) #Limits and Structures in Graph Theory #Logarithm #Mathematical analysis #Mathematics #Zero (linguistics) #math.NT #msc:11M26 #msc:11N56 #msc:11N64
15. Weak approximation on del Pezzo surfaces of degree 1
    2008/09/10 by Anthony Várilly-Alvarado, Anthony Várilly‐Alvarado · 4 citations
    Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Combinatorics #Counterexample #Degree (music) #Field (mathematics) #Mathematics #Perfect field #Pure mathematics #Space (punctuation)
16. Lower bounds on the coefficients of Ehrhart polynomials
    2008/04/21 by Martin Henk, Makoto Tagami · 1 citation
    Agricultural and Biological Sciences · Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Botanical Research and Chemistry #Combinatorics #Convex optimization #Convex polytope #Convex set #Counterexample #Discrete mathematics #Geometry #Lattice (music) #Mathematical analysis #Mathematics #Physics #Polytope #Regular polygon #Series (stratigraphy) #Upper and lower bounds
17. Algebraic characterization of uniquely vertex colorable graphs
    2007/09/28 by Christopher J. Hillar, Troels Windfeldt · 1 citation
    Computer Science · Mathematics · #Advanced Graph Theory Research #Algebraic number #Characterization (materials science) #Combinatorics #Conjecture #Counterexample #Discrete mathematics #Graph #Graph Labeling and Dimension Problems #Mathematics #Vertex (graph theory)
18. Internalizing emission externality on road networks
    2006/07/01 by Yafeng Yin, Siriphong Lawphongpanich · 1 citation
    Economics, Econometrics and Finance · Engineering · Mathematics · Social Sciences · #Computer network #Computer science #Congestion pricing #Counterexample #Economic and Environmental Valuation #Economics #Engineering #Environmental economics #Externality #Mathematics #Microeconomics #Road pricing #Singapore Area Licensing Scheme #Subsidy #Traffic congestion #Traffic flow (computer networking) #Transport engineering #Transportation Planning and Optimization #Urban Transport and Accessibility
19. Configuration spaces are not homotopy invariant
    2005/01/07 by Riccardo Longoni, Paolo Salvatore · 2 citations
    Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Cofibration #Conjecture #Counterexample #Discrete mathematics #Homotopy #Homotopy and Cohomology in Algebraic Topology #Homotopy group #Homotopy lifting property #Homotopy sphere #Invariant (physics) #Mathematical physics #Mathematics #Pure mathematics #Regular homotopy #Whitehead theorem #n-connected
20. Computer Search for Counterexamples to Wilkie’s Identity
    2005/01/01 by Jian Zhang · 1 citation
    Computer Science · Decision Sciences · Mathematics · #Advanced Algebra and Logic #Aesthetics #Algorithm #Archaeology #Artificial intelligence #Basis (linear algebra) #Computer science #Counterexample #Discrete mathematics #Fuzzy and Soft Set Theory #Geometry #History #Identity (music) #Logic, Reasoning, and Knowledge #Mathematics #Natural (archaeology) #Natural number #Philosophy #Programming language #Set (abstract data type)
21. Tachyonic perturbations inAdS5orbifolds
    2004/09/30 by Cyril Cartier, Ruth Durrer · 1 citation
    Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Brane #Combinatorics #Context (archaeology) #Cosmology and Gravitation Theories #Counterexample #Galaxies: Formation, Evolution, Phenomena #Geology #Mathematical physics #Mathematics #Orbifold #Physics #astro-ph #hep-th
22. Consistency of a counterexample to Naimark's problem
    2003/12/06 by Charles Akemann, Charles A. Akemann, Nik Weaver · 2 citations
    Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Advanced Topology and Set Theory #Algebra over a field #Axiom #Computer science #Counterexample #Decidability #Discrete mathematics #Equivalence (formal languages) #Hilbert space #Mathematics #Pure mathematics #Set (abstract data type) #Statement (logic) #Undecidable problem #math.FA #math.LO #math.OA
23. Counterexample-guided abstraction refinement for symbolic model checking
    2003/09/01 by Edmund Clarke, Edmund M. Clarke, Orna Grumberg +4 · 57 citations
    Computer Science · Engineering · Mathematics · #Abstraction #Abstraction model checking #Algorithm #Computer science #Counterexample #Formal Methods in Verification #Formal verification #Mathematics #Model checking #Programming language #Radiation Effects in Electronics #Software Testing and Debugging Techniques #Spurious relationship #State space #Symbolic data analysis #Symbolic trajectory evaluation #Theoretical computer science
24. Non-amenable finitely presented torsion-by-cyclic groups
    2003/05/07 by Alexander Olshanskii, Mark Sapir · 1 citation
    Mathematics · Computer Science · #Geometric and Algebraic Topology #semigroups and automata theory #Mathematical Dynamics and Fractals #Counterexample #Finitely-generated abelian group #Mathematics #Torsion (gastropod) #Stallings theorem about ends of groups #Cyclic group #Exponent #Pure mathematics #Amenable group #Finitely generated group #Von Neumann architecture #Group (periodic table) #Locally finite group #Combinatorics #Discrete mathematics #Physics
25. Scalar hairy black holes and solitons in asymptotically flat spacetimes
    2003/01/31 by Ulises Nucamendi, Marcelo Salgado · 1 citation
    Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Black Holes and Theoretical Physics #Black hole (networking) #Classical mechanics #Combinatorics #Conjecture #Cosmology and Gravitation Theories #Counterexample #Geometry #Mathematical physics #Mathematics #Physics #Pure mathematics #Scalar (mathematics) #Scalar field #gr-qc #hep-th
26. Pontryagin Duality in the Theory of Topological Vector Spaces and in Topological Algebra
    2003/01/01 by S. S. Akbarov · 5 citations
    Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #Artificial intelligence #Computer science #Counterexample #Disappointment #Discrete mathematics #Epistemology #Extension (predicate logic) #Face (sociological concept) #Field (mathematics) #Linguistics #Mathematics #Perplexity #Philosophy #Pure mathematics #Simple (philosophy) #Skepticism
27. Minds, Machines and Turing
    2000/10/01 by S. Harnad, Stevan Harnad · 1 citation
    Computer Science · Mathematics · Neuroscience · Psychology · #Algorithm #Argument (complex analysis) #Computability, Logic, AI Algorithms #Computation #Computer science #Counterexample #Discrete mathematics #Embodied and Extended Cognition #Function (biology) #Hierarchy #Mathematical economics #Mathematics #Philosophy and Theoretical Science #Programming language #Turing #Turing machine
28. Counterexample-Guided Abstraction Refinement
    2000/01/01 by Edmund Clarke, Edmund M. Clarke, Orna Grümberg +4 · 1 citation
    Computer Science · Mathematics · #Abstract interpretation #Abstraction #Abstraction model checking #Algorithm #Computer science #Counterexample #Discrete mathematics #Formal Methods in Verification #Logic, programming, and type systems #Mathematics #Model checking #Predicate abstraction #Programming language #Software Testing and Debugging Techniques #Spurious relationship #State space #Theoretical computer science
29. Beyond the Manin obstruction
    1999/01/15 by Alexei N. Skorobogatov · 1 citation
    Computer Science · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic number field #Counterexample #Descent (aeronautics) #Discrete mathematics #Elliptic curve #Geometry #Hasse principle #Mathematical analysis #Mathematics #Point (geometry) #Pure mathematics #Rational point #Topological and Geometric Data Analysis #Type (biology)
30. On the number of invariant straight lines for polynomial differential systems
    1998/06/01 by Joan C. Artés, Branko Grünbaum, Jaume Llibre · 1 citation
    Mathematics · Computer Science · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Polynomial and algebraic computation #Mathematics #Conjecture #Counterexample #Invariant (physics) #Degree (music) #Combinatorics #Polynomial #Invariant polynomial #Differential (mechanical device) #Discrete mathematics #Matrix polynomial #Mathematical analysis #Physics #Mathematical physics

more