Terence Tao : The Liouville pseudorandomness principle (a close cousin of the Mobius pseudorandomness principle) asserts that the Liouville function λ(n), which is the completely multiplicative function that equals −1 at every prime, should be "pseudorandom" in the sense that it behaves statistically like a random function taking values in −1,+1. Various formalizations of this principle include the Chowla conjecture, the Sarnak conjecture, the local uniformity conjecture, and the Riemann hypothesis. In this talk we survey some recent progress on some of these conjectures. Hausdorff Center for Mathematics AIFI - Artificial Intelligence Finance Institute https://lnkd.in/dgxCuN3b
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My fellow colleague from Math and Quantum Field Theory, and a good friend, Timothy Nguyen, explains the importance of mathematical rigor, particularly in formulating perturbative methods like Feynman diagrams. We used to spend countless hours on Gauge Theory, QFT, 'Theory of Everything,' Quantum Physics, etc., during COVID. I believe that most of us are guilty of taking shortcuts 'as long as the final answer is correct.' This is a dangerous approach, especially when it comes to high-dimensional concepts. Tim's paper deserves recognition for showing us the correct treatment of perturbative path integrals. Here is a video of him explaining the paper. Video: https://lnkd.in/gjACcMYM #QuantumPhysics #Math
The Perturbative Approach to Path Integrals
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Georgy Voronoi was a Ukrainian mathematician, mostly famous for introducing the Voronoi diagram: A mathematical method for segmenting planes into cells, where each cell is defined by the distance from a single point called a "seed." The borders of each cell represent an equal distance between one seed and another. In #SuperResolution #microscopy, #VoronoiDiagrams can be used to determine the localization of labeled targets. He died on the 20th of November 1908 at the age of 40. #CuriousMinds #Nanoimager #VoronoiDiagram #DataSegmentation #CellLocalization #HistoryOfScience #HistoryOfMicroscopy
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Mathematics is indeed the language of the Gods.
Euler's constant (𝛾), defined as the limiting difference between the harmonic series and the natural logarithm, is not known to be algebraic or transcendental. In fact, it is not even known whether it is irrational.
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Consultant & Trainer - Cultural Intelligence - Intercultural Mng - Research Based Training for Managers - The Trust Factor / Guest Assoc. Prof. ISG Business & Economics School - Lisbon - Portugal / Friends of Hofstede
The fighting hypothesis Human Handedness: A Meta-Analysis • Around 10.6% of people are left-handed • Left-handedness is more common in men • The same evolutionary mechanisms maintain the 1:10 ratio worldwide • Mixed-handedness is about as common as left-handedness (~9.33%) Why are most humans right-handed? The modified "fighting hypothesis" proposes that right-handed weapon use would better protect the heart and aorta, reducing the number of fatal wounds https://lnkd.in/dNw5Sbfu
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HEMANTH LINGAMGUNTA Challenging the Law of Conservation of Mass using fractal patterns involves reinterpreting mass distribution and transformation at various scales. Fractals, with their self-similar structures, suggest that mass can be perceived as not merely conserved but dynamically redistributed in complex systems. For instance, in quantum materials like neodymium nickel oxide, fractal patterns emerge at atomic scales, indicating that mass and energy may interact in non-linear ways during transitions between states[3][4]. This perspective could lead to new insights into mass-energy relationships and challenge traditional interpretations of conservation laws. Citations: [1] Fractals, nature's best-kept secret, could help solve energy crisis https://lnkd.in/edCRzPq6 [2] [PDF] energy innovation and fractals https://lnkd.in/eq9xBGft [3] Fractal patterns spotted in the quantum realm – Physics World https://lnkd.in/eTBJP4uj [4] Scientists discover fractal patterns in a quantum material https://lnkd.in/eKCyZy4k [5] Leap into Fractal Wormholes with the McGinty Equation (MEQ) https://lnkd.in/efJ_Fvfh [6] For The First Time Ever, Scientists Discover Fractal Patterns in a Quantum Material https://lnkd.in/eCCe7U_Y [7] Exploring Fractals & Quantum Materials: A Fusion of Science https://lnkd.in/e-uyCnN6 [8] Fractals and The Theory of Everything | A Guy With AI https://lnkd.in/etr_8XPY
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A Penrose triangle illusion adorned with a Sierpiński triangle fractal, seamlessly fusing optical mystique and mathematical intricacy. Explore more: https://lnkd.in/djXNUadk
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Volume 20, Issue 3 (May and June 2023) of the #Iranian Journal of Fuzzy Systems (IJFS) has been published, which includes the following papers: [1] A. Khastan and R. Rodríguez-López, Some aspects on computation of scalar valued and fuzzy valued integrals over fuzzy domains, Iranian Journal of Fuzzy Systems, Volume 20, Number 3, (2023), pp. 1-17. [2] M. Aggarwal and A. F. Tehrani, Heuristics-based modelling of human decision process, Iranian Journal of Fuzzy Systems, Volume 20, Number 3, (2023), pp. 19-30. [3] M. R. Karimzadeh, B. Daraby and A. Rahimi, Diaz-Metcalf type inequality for Sugeno and pseudo-integrals, Iranian Journal of Fuzzy Systems, Volume 20, Number 3, (2023), pp. 31-41. [4] V. M. Tam, On existence and stability results to fuzzy Caputo fractional differential inclusions driven by fuzzy mixed quasivariational inequalities, Iranian Journal of Fuzzy Systems, Volume 20, Number 3, (2023), pp. 43-59. [5] S. Anvari, M. Abdollahi Azgomi, M. R. Ebrahimi Dishabi and M. Maheri, Weighted K-nearest neighbors classification based on Whale optimization algorithm, Iranian Journal of Fuzzy Systems, Volume 20, Number 3, (2023), pp. 61-74. [6] L. W. Ma, Q. Gao, X. Y. Shi and X. C. Zhao, Fuzzy accompanied approximation space under fuzzy relation, Iranian Journal of Fuzzy Systems, Volume 20, Number 3, (2023), pp. 75-94. [7] B. Wu and H. Zhou, A new extension of a triangular norm on a subinterval [0, α] via an interior operator to the underlying entire bounded lattice, Iranian Journal of Fuzzy Systems, Volume 20, Number 3, (2023), pp. 95-113. [8] V. Miler Jerković, B. Mihailović and B. Malešević, The general algebraic solution of fuzzy linear systems based on a block representation of {1}-inverses, Iranian Journal of Fuzzy Systems, Volume 20, Number 3, (2023), pp. 115-126. [9] S. Das, D. Chakraborty and L. T. Kóczy, Forward and backward fuzzy rule base interpolation using fuzzy geometry, Iranian Journal of Fuzzy Systems, Volume 20, Number 3, (2023), pp. 127-146. [10] Y. Zhu, G. X. Wang and C. J. Li, Weighted approximation of fuzzy numbers by using m-n−step type fuzzy number, Iranian Journal of Fuzzy Systems, Volume 20, Number 3, (2023), pp. 147-158. [11] M. Esfahani, M. Amini, G. R. Mohtashami-Borzadaran and A. Dolati, A new copula-based bivariate Gompertz–Makeham model and its application to COVID-19 mortality data, Iranian Journal of Fuzzy Systems, Volume 20, Number 3, (2023), pp. 159-175. [12] J. C. Wu, H. F. Li and X. Y. Liu, Probabilistic fuzzy argumentation frameworks with finite fuzzy statuses, Iranian Journal of Fuzzy Systems, Volume 20, Number 3, (2023), pp. 177-189. [13] W. Yao, G. X. Zhang and Y. Shi, Type-2 lattice-valued preorders: A common framework of lattice-valued preorders and various kinds of metrics, Iranian Journal of Fuzzy Systems, Volume 20, Number 3, (2023), pp. 191-203. https://lnkd.in/dR5BPNBW #Integrals over fuzzy domains #Attitudinal#Diaz-Metcalf type#K-nearest#Triangular norm#ordinal sum
Iranian Journal of Fuzzy Systems - Articles List
ijfs.usb.ac.ir
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The Riemann Hypothesis: A Geometric Solution - Geometric Maths Read more :https://lnkd.in/eQCQsJYf The Riemann Hypothesis is the number one mathematical challenge of today. We offer a geometric solution to the problem, that confirms all non-trivial zero will appear on the critical strip. #GeometricMath #Mathmatics #Aleph0.5 #infinity #numberi #numbertheory #riemannhypothesis #in2infinity #davincischool #geometricuniverse #sacredgeometry #geometry #science #metaphysics #matrix #fractal #holographic
The Riemann Hypothesis: A Geometric Solution - In2Infinity
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Technical Writer/Editor | Mathematics & Philosophy | Finance & Risk | Systems Thinking
9moSurely if we find the Riemann hypothesis to be true, would that not then imply that, given the Liouville function is defined on the basis of powers of irreducibles, that it *isn't* pseudorandom at all?