429 research outputs found

    Solving the 100 Swiss Francs Problem

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    Sturmfels offered 100 Swiss Francs in 2005 to a conjecture, which deals with a special case of the maximum likelihood estimation for a latent class model. This paper confirms the conjecture positively

    Hipster: Integrating Theory Exploration in a Proof Assistant

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    This paper describes Hipster, a system integrating theory exploration with the proof assistant Isabelle/HOL. Theory exploration is a technique for automatically discovering new interesting lemmas in a given theory development. Hipster can be used in two main modes. The first is exploratory mode, used for automatically generating basic lemmas about a given set of datatypes and functions in a new theory development. The second is proof mode, used in a particular proof attempt, trying to discover the missing lemmas which would allow the current goal to be proved. Hipster's proof mode complements and boosts existing proof automation techniques that rely on automatically selecting existing lemmas, by inventing new lemmas that need induction to be proved. We show example uses of both modes

    Exotic solutions in string theory

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    Solutions of classical string theory, correspondent to the world sheets, mapped in Minkowsky space with a fold, are considered. Typical processes for them are creation of strings from vacuum, their recombination and annihilation. These solutions violate positiveness of square of mass and Regge condition. In quantum string theory these solutions correspond to physical states |DDF>+|sp> with non-zero spurious component.Comment: accepted in Il Nuovo Cimento A for publication in 199

    Multiplicity of solutions to GW-type approximations

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    We show that the equations underlying the GWGW approximation have a large number of solutions. This raises the question: which is the physical solution? We provide two theorems which explain why the methods currently in use do, in fact, find the correct solution. These theorems are general enough to cover a large class of similar algorithms. An efficient algorithm for including self-consistent vertex corrections well beyond GWGW is also described and further used in numerical validation of the two theorems

    Triangle-generation in topological D-brane categories

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    Tachyon condensation in topological Landau-Ginzburg models can generally be studied using methods of commutative algebra and properties of triangulated categories. The efficiency of this approach is demonstrated by explicitly proving that every D-brane system in all minimal models of type ADE can be generated from only one or two fundamental branes.Comment: 34 page

    Two-dimensional ferromagnetic extension of a topological insulator

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    Inducing a magnetic gap at the Dirac point of the topological surface state (TSS) in a three-dimensional (3D) topological insulator (TI) is a route to dissipationless charge and spin currents. Ideally, magnetic order is present only at the surface, as through proximity of a ferromagnetic (FM) layer. However, experimental evidence of such a proximity-induced Dirac mass gap is missing, likely due to an insufficient overlap of TSS and the FM subsystem. Here, we take a different approach, namely ferromagnetic extension (FME), using a thin film of the 3D TI Bi2Te3, interfaced with a monolayer of the lattice-matched van der Waals ferromagnet MnBi2Te4. Robust 2D ferromagnetism with out-of-plane anisotropy and a critical temperature of Tc ≈ 15 K is demonstrated by x-ray magnetic dichroism and electrical transport measurements. Using angle-resolved photoelectron spectroscopy, we observe the opening of a sizable magnetic gap in the 2D FM phase, while the surface remains gapless in the paramagnetic phase above Tc. Ferromagnetic extension paves the way to explore the interplay of strictly 2D magnetism and topological surface states, providing perspectives for realizing robust quantum anomalous Hall and chiral Majorana states.</p
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