IA Scholar Query: Games, Probability and the Quantitative µ-Calculus qMµ.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgSat, 09 Jul 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Quantum Mechanics and General Relativity are fully compatible, and have a common origin: the expanding (hyper) balloon universe
https://scholar.archive.org/work/7ozxv77owjd5nos4tgjj76n3mq
Modern physics rests on two pillars: Quantum Mechanics and General Relativity. Nature simply can't afford to make them incompatible! Although physicists have made intense efforts towards unification, nobody cared to dig deeply to see why exactly our two best theories become incompatible. As a result, over eight decades have passed since physicists realized that the theories of quantum mechanics and gravity don't fit together, and the puzzle of how to combine the two remains unsolved. We have made a series of mistakes, in our mathematics, and in our understanding of physics as well as cosmology. Consequently, we failed to decipher the deepest secret of nature: Nature does not use two separate rule books, but two different viewpoints. Everything, from the tiniest quark to the Galaxy clusters is telling one single story. Relativity and quantum mechanics both have a common origin. Entire Physics & Cosmology is united.Subhajit Waughwork_7ozxv77owjd5nos4tgjj76n3mqSat, 09 Jul 2022 00:00:00 GMTQuantum Mechanics and General Relativity are fully compatible, and have a common origin: the expanding (hyper) balloon universe
https://scholar.archive.org/work/5krvt5emzbaojn2bdm5u3xcv7q
Please see the abstract directly from the paper (since formulas are not appearing in this window). This is just an overall view: Physics and cosmology are intimately linked. Consequently, our level of understanding of one of them strongly affects our depth of knowledge of the other. On the one hand, the greatest challenges facing cosmology today are dark matter, dark energy, information loss (paradox) due to singularity inside black hole etc. which are just relics of our misunderstanding of General Relativity (GR) of physics. All those problems magically vanish when we realize that GR is just an inside view (since there is no concept of 'outside' in GR). That is exactly why GR can't predict the global structure of the universe, nor can it account for 'external field effect' (which has now been confirmed to 11 Sigma accuracy in galaxies and galaxy clusters). On the other hand, Quantum Mechanics and General Relativity (which are our two greatest physics theories, and the two pillars on which our modern physics rests) seem to be utterly incompatible. But in fact, relativity and quantum principles are like two sides of the same coin, and have a common origin, which can be understood only through the proper model of our universe. Quantum Mechanics and General Relativity have been spectacularly successful, but limited to their own domain (i.e. for the tiniest and largest scales respectively). The reason for their divergent predictions lies hidden within the words 'tiniest and largest scales'. The mechanism is very simple, but to make sense of it, we have to ditch our ridiculous, currently accepted model of the universe, and build the correct model. This is what is happening: 3+1 (Classical regime) <=> 2+2 (Compton regime) <=> 1+3 (Planck regime) Relativistic Quantum Mechanics uses the Compton scale lying intermediate between (3+1) and (1+3), and has a spacetime dimension of 2+2 (as proved by G.N. Ord; Fractal space-time: a geometric analogue of relativistic quantum mechanics. 1983 J. Phys. [...]Subhajit Waughwork_5krvt5emzbaojn2bdm5u3xcv7qFri, 08 Jul 2022 00:00:00 GMTQuantum Mechanics and General Relativity are fully compatible, and have a common origin: the expanding (hyper) balloon universe
https://scholar.archive.org/work/havpqbcjjrd7hmuoc6z4mn7jqu
Please see the abstract directly from the paper (since formulas are not appearing in this window). This is a overall view: Modern physics rests on two pillars: Quantum Mechanics and General Relativity. Nature simply can't afford to make them incompatible! Although physicists have made intense efforts towards unification, nobody cared to dig deeply to see why exactly our two best theories become incompatible. As a result, over eight decades have passed since physicists realized that the theories of quantum mechanics and gravity don't fit together, and the puzzle of how to combine the two remains unsolved. We have made a series of mistakes, in our mathematics, and in our understanding of physics as well as cosmology. Consequently, we failed to decipher the deepest secret of nature: Nature does not use two separate rule books, but two different viewpoints. Everything, from the tiniest quark to the Galaxy clusters is telling one single story. Relativity and quantum mechanics both have a common origin. Entire Physics & Cosmology is united.Subhajit Waughwork_havpqbcjjrd7hmuoc6z4mn7jquFri, 08 Jul 2022 00:00:00 GMTThe Vertical Logic of Hamiltonian Methods (Part 1)
https://scholar.archive.org/work/jmufliqaazakvfxwtf5lso62dy
We discuss the key role that Hamiltonian notions play in physics. Five examples are given that illustrate the versatility and generality of Hamiltonian notions. The given examples concern the interconnection between quantum mechanics, special relativity and electromagnetism. We demonstrate that a derivation of these core concepts of modern physics requires little more than a proper formulation in terms of classical Hamiltonian theory.C. Baumgartenwork_jmufliqaazakvfxwtf5lso62dyMon, 09 May 2022 00:00:00 GMTLinear Superposition as a Core Theorem of Quantum Empiricism
https://scholar.archive.org/work/uwilqzxw65g4dis6cuegd5eozq
Clarifying the nature of the quantum state |Ψ⟩ is at the root of the problems with insight into counter-intuitive quantum postulates. We provide a direct—and math-axiom free—empirical derivation of this object as an element of a vector space. Establishing the linearity of this structure—quantum superposition—is based on a set-theoretic creation of ensemble formations and invokes the following three principia: (I) quantum statics, (II) doctrine of the number in the physical theory, and (III) mathematization of matching the two observations with each other (quantum covariance). All of the constructs rest upon a formalization of the minimal experimental entity—the registered micro-event, detector click. This is sufficient for producing the C-numbers, axioms of linear vector space (superposition principle), statistical mixtures of states, eigenstates and their spectra, and non-commutativity of observables. No use is required of the spatio-temporal concepts. As a result, the foundations of theory are liberated to a significant extent from the issues associated with physical interpretations, philosophical exegeses, and mathematical reconstruction of the entire quantum edifice.Yurii Brezhnevwork_uwilqzxw65g4dis6cuegd5eozqMon, 28 Mar 2022 00:00:00 GMTPlaying (Almost-)Optimally in Concurrent Büchi and co-Büchi Games
https://scholar.archive.org/work/j7dssmpdwra55aqthcqw4fdio4
We study two-player concurrent stochastic games on finite graphs, with Büchi and co-Büchi objectives. The goal of the first player is to maximize the probability of satisfying the given objective. Following Martin's determinacy theorem for Blackwell games, we know that such games have a value. Natural questions are then: does there exist an optimal strategy, that is, a strategy achieving the value of the game? what is the memory required for playing (almost-)optimally? The situation is rather simple to describe for turn-based games, where positional pure strategies suffice to play optimally in games with parity objectives. Concurrency makes the situation intricate and heterogeneous. For most ω-regular objectives, there do indeed not exist optimal strategies in general. For some objectives (that we will mention), infinite memory might also be required for playing optimally or almost-optimally. We also provide characterizations of local interactions of the players to ensure positionality of (almost-)optimal strategies for Büchi and co-Büchi objectives. This characterization relies on properties of game forms underpinning the formalism for defining local interactions of the two players. These well-behaved game forms are like elementary bricks which, when they behave well in isolation, can be assembled in graph games and ensure the good property for the whole game.Benjamin Bordais, Patricia Bouyer, Stéphane Le Rouxwork_j7dssmpdwra55aqthcqw4fdio4Mon, 14 Mar 2022 00:00:00 GMTLoss as the Inconsistency of a Probabilistic Dependency Graph: Choose Your Model, Not Your Loss Function
https://scholar.archive.org/work/vrqpcqfqaraezm6vop4g5zngfi
In a world blessed with a great diversity of loss functions, we argue that that choice between them is not a matter of taste or pragmatics, but of model. Probabilistic depencency graphs (PDGs) are probabilistic models that come equipped with a measure of "inconsistency". We prove that many standard loss functions arise as the inconsistency of a natural PDG describing the appropriate scenario, and use the same approach to justify a well-known connection between regularizers and priors. We also show that the PDG inconsistency captures a large class of statistical divergences, and detail benefits of thinking of them in this way, including an intuitive visual language for deriving inequalities between them. In variational inference, we find that the ELBO, a somewhat opaque objective for latent variable models, and variants of it arise for free out of uncontroversial modeling assumptions -- as do simple graphical proofs of their corresponding bounds. Finally, we observe that inconsistency becomes the log partition function (free energy) in the setting where PDGs are factor graphs.Oliver E Richardsonwork_vrqpcqfqaraezm6vop4g5zngfiThu, 24 Feb 2022 00:00:00 GMTIntegration of Education, Science and Business in Modern Environment: Winter Debates: Proceedings of the 3rd International Scientific and Practical Internet Conference, February 3-4, 2022. FOP Marenichenko V.V., Dnipro, Ukraine, 463 p. ISBN 978-617-95218-3-6
https://scholar.archive.org/work/muypuufexbg57lxt2pcbxog3m4
3rd International Scientific and Practical Internet Conference "Integration of Education, Science and Business in Modern Environment: Winter Debates" devoted to the search for the latest ideas for the development of state at the international, national and regional levels.V.V. FOP Marenichenkowork_muypuufexbg57lxt2pcbxog3m4Mon, 14 Feb 2022 00:00:00 GMTKnitting quantum knots: Topological phase transitions in Two-Dimensional systems
https://scholar.archive.org/work/q5pzyq2bsfff5imghmcyh7dkhy
We start by describing a symmetry enforced nodal line semi-metal (NLSM) in the 2D flat form of honeycomb Group - V and its non trivial thermo-electric response. We will then proceed to show that, upon buckling, the system undergoes its dirac-merging phase transitions. Further buckling leads to these unpinned Dirac cones annihilating in pairs at two distinct critical angle leading to a second topological phase transition to an insulating state. We then show that this seemingly innocuous insulating state is indeed a weak topological crystalline insulator. Furthermore, upon closer look, this insulating state turns out to be a Higher Order Topological Insulator (HOTI) that is protected by 𝒮_6 symmetry. In a broader context, we will see that the the topological properties of buckled Group - V stem from the fact that they topologically belong to the class of Obstructed Atomic Limit (OAL) insulators. Combining all these, we will prove that annihilating pairs of Dirac fermions necessitate a topological phase transition from the critical semi-metallic phase to an OAL insulator phase. We also uncover the rich set of phases in the phase diagram in case of annihilating Dirac fermions and study their entanglement properties using entanglement entropy. Finally, based on the non-trivial topology of these systems, we propose the conceptual design of a quantized switch that is protected by topology. Last part of the thesis involves the remarkable discovery of a spin polarized 2D electron/hole gas at the surfaces of a well known system - LiCoO2.Santosh Kumar Radhawork_q5pzyq2bsfff5imghmcyh7dkhySat, 12 Feb 2022 00:00:00 GMTDirac's Refined Unification Of Quantum Mechanics And Special Relativity: An Intertheoretic Context
https://scholar.archive.org/work/ygz6ycz22rf6nactcop5jv62lu
One of the key episodes of history of modern physics – Paul Dirac's startling contrivance of the relativistic theory of the electron – is elicited in the context of lucid epistemological model of mature theory change. The peculiar character of Dirac's synthesis of special relativity and quantum mechanics is revealed by comparison with Einstein's sophisticated methodology of the General Relativity contrivance. The subtle structure of Dirac's scientific research program and first and foremost the odd principles that put up its powerful heuristics is scrutinized with special emphasis on the highly controversial tenet of "mathematical beauty." It is contended that despite the relentless Dirac's remarks denigrating the controversial role of philosophy one can trace its indirect influence through Arthur Eddington's and Hermann Weyl's whimsical mathematical models. Accordingly, the milestones of Dirac's research programme realization in the distinctive context of the applied epistemological doctrine are indicated.Rinat Magdievich Nugayevwork_ygz6ycz22rf6nactcop5jv62luTue, 18 Jan 2022 00:00:00 GMTError estimates for DeepOnets: A deep learning framework in infinite dimensions
https://scholar.archive.org/work/o3xucm5m4fhfdau2ohasccub7y
DeepONets have recently been proposed as a framework for learning nonlinear operators mapping between infinite dimensional Banach spaces. We analyze DeepONets and prove estimates on the resulting approximation and generalization errors. In particular, we extend the universal approximation property of DeepONets to include measurable mappings in non-compact spaces. By a decomposition of the error into encoding, approximation and reconstruction errors, we prove both lower and upper bounds on the total error, relating it to the spectral decay properties of the covariance operators, associated with the underlying measures. We derive almost optimal error bounds with very general affine reconstructors and with random sensor locations as well as bounds on the generalization error, using covering number arguments. We illustrate our general framework with four prototypical examples of nonlinear operators, namely those arising in a nonlinear forced ODE, an elliptic PDE with variable coefficients and nonlinear parabolic and hyperbolic PDEs. While the approximation of arbitrary Lipschitz operators by DeepONets to accuracy ϵ is argued to suffer from a "curse of dimensionality" (requiring a neural networks of exponential size in 1/ϵ), in contrast, for all the above concrete examples of interest, we rigorously prove that DeepONets can break this curse of dimensionality (achieving accuracy ϵ with neural networks of size that can grow algebraically in 1/ϵ). Thus, we demonstrate the efficient approximation of a potentially large class of operators with this machine learning framework.Samuel Lanthaler and Siddhartha Mishra and George Em Karniadakiswork_o3xucm5m4fhfdau2ohasccub7yThu, 13 Jan 2022 00:00:00 GMTOptimal strategies in concurrent reachability games
https://scholar.archive.org/work/czjd3t7lc5eznf25ptyg2dwk3i
We study two-player reachability games on finite graphs. At each state the interaction between the players is concurrent and there is a stochastic Nature. Players also play stochastically. The literature tells us that 1) Player B, who wants to avoid the target state, has a positional strategy that maximizes the probability to win (uniformly from every state) and 2) from every state, for every ϵ > 0, Player A has a strategy that maximizes up to ϵ the probability to win. Our work is two-fold. First, we present a double-fixed-point procedure that says from which state Player A has a strategy that maximizes (exactly) the probability to win. This is computable if Nature's probability distributions are rational. We call these states maximizable. Moreover, we show that for every ϵ > 0, Player A has a positional strategy that maximizes the probability to win, exactly from maximizable states and up to ϵ from sub-maximizable states. Second, we consider three-state games with one main state, one target, and one bin. We characterize the local interactions at the main state that guarantee the existence of an optimal Player A strategy. In this case there is a positional one. It turns out that in many-state games, these local interactions also guarantee the existence of a uniform optimal Player A strategy. In a way, these games are well-behaved by design of their elementary bricks, the local interactions. It is decidable whether a local interaction has this desirable property.Benjamin Bordais, Patricia Bouyer, Stéphane Le Rouxwork_czjd3t7lc5eznf25ptyg2dwk3iWed, 27 Oct 2021 00:00:00 GMT