A slice-torus invariant is an R-valued homomorphism on the knot concordance group whose value gives a lower bound for the 4-genus such that the equality holds for any positive torus knot. Such invariants have been dis...
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In this paper, we introduce the first algorithmic framework for Blackwell approachability on the sequence-form polytope, the class of convex polytopes capturing the strategies of players in extensive-form games (EFGs)...
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Nonadiabatic holonomic quantum computation has been proposed as a method to implement quantum logic gates with robustness comparable to that of adiabatic holonomic gates but with shorter execution times. In this paper...
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Take a drinking straw and bend it from its ends. After sufficient bending, the tube buckles forming a kink, where the curvature is localized in a very small area. This instability, known generally as the Brazier effec...
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作者：
Schuler, YannikUniversity of Sheffield
School of Mathematics and Statistics Hounsfield Road SheffieldS3 7RH United Kingdom University of Cambridge
Department of Pure Mathematics and Mathematical Statistics Wilberforce Road CambridgeCB3 0WB United Kingdom
A two-component Looijenga pair is a rational smooth projective surface with an anticanonical divisor consisting of two transversally intersecting curves. We establish an all-genus correspondence between the logarithmi...
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Brain-like self-assembled networks can infer and analyze information out of unorganized noisy signals with minimal power consumption. These networks are characterized by spatiotemporal avalanches and their crackling b...
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We give a practical computer algebra implementation of the Covering Lemma for finite transformation semigroups. The lemma states that given a surjective relational morphism (X, S) → (Y, T), we can establish emulation...
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Kernels are a fundamental technical primitive in machine learning. In recent years, kernel-based methods such as Gaussian processes are becoming increasingly important in applications where quantifying uncertainty is ...
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ChatGPT is notorious for its intransparent behavior. This paper tries to shed light on this, providing an in-depth analysis of the dark personality traits and conspiracy beliefs of GPT-3.5 and GPT-4. Different psychol...
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We resolve the long-standing problem of the nature of the quantum phase transition between a Néel antiferromagnet and a spontaneously dimerized valence-bond solid in two-dimensional spin-1/2 magnets. We study a c...
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We resolve the long-standing problem of the nature of the quantum phase transition between a Néel antiferromagnet and a spontaneously dimerized valence-bond solid in two-dimensional spin-1/2 magnets. We study a class of J-Q models, in which the standard Heisenberg exchange J competes with multi-spin interactions Qn formed by products of n singlet projectors on adjacent parallel links of the lattice. Using large-scale quantum Monte Carlo (QMC) calculations, we provide unambiguous evidence for first-order transitions in these models, with the strength of the discontinuities increasing with n. In the case of the widely studied n = 2 and n = 3 models, the first-order signatures are very weak, but observable in correlation functions on large lattices. On intermediate length scales (up to hundreds of lattice constants, depending on the observable) we can extract well-defined scaling dimensions (critical exponents) that are common to the models with small n, indicating close proximity to a universal quantum critical point. By combining two different Q terms, specifically we consider the J-Q2-Q6 model, the transition can be continuously tuned from weak to more strongly first-order. In the plane (Q2, Q6), with J = 1 − Q2, the two coexisting order parameters on the first-order line scale with an unusually large exponent β ≈ 0.85. This exponent and others coincide closely with known rigorous bounds for an SO(5) symmetric conformal field theory (CFT), but, in contrast to prevailing scenarios, the leading SO(5) singlet operator is relevant and responsible for the first-order transition ending at a fine-tuned multicritical point. We quantitatively characterize the emergent SO(5) symmetry by computing the scaling dimensions of its leading irrelevant perturbations. The large β value and a large correlation length exponent, ν ≈ 1.4, partially explain why the transition remains near-critical on the first-order line even quite far away from the critical point and in many different mod
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