搜索结果：Acta crystallographica. Section A, Foundations and advances

We give a concise presentation of the Univalent Foundations of mathematics outlining the main ideas, followed by a discussion of the UniMath library of formalized mathematics implementing the ideas of the Univalent Foundations (section 1), and the challenges one faces in attempting to design a large-scale library of formalized mathematics (section 2). This leads us to a general discussion about the links between architecture and mathematics where a meeting of minds is revealed between architects and mathematicians (section 3). On the way our odyssey from the foundations to the "horizon" of mathematics will lead us to meet the mathematicians David Hilbert and Nicolas Bourbaki as well as the architect Christopher Alexander.

This Report summarises the results of the second year's activities of the LHC Higgs Cross Section Working Group. The main goal of the working group was to present the state of the art of Higgs Physics at the LHC, integrating all new results that have appeared in the last few years. The first working group report Handbook of LHC Higgs Cross Sections: 1. Inclusive Observables (CERN-2011-002) focuses on predictions (central values and errors) for total Higgs production cross sections and Higgs branching ratios in the Standard Model and its minimal supersymmetric extension, covering also related issues such as Monte Carlo generators, parton distribution functions, and pseudo-observables. This second Report represents the next natural step towards realistic predictions upon providing results on cross sections with benchmark cuts, differential distributions, details of specific decay channels, and further recent developments.

The detection and characterization of exoplanets and brown dwarfs (BDs) around massive AF-type stars is essential to investigate and constrain the impact of stellar mass on planet properties. However, such targets are still poorly explored in radial velocity (RV) surveys because they only feature a small number of stellar lines and those are usually broadened and blended by stellar rotation as well as stellar jitter. As a result, the available information about the formation and evolution of planets and BDs around hot stars is limited. We aim to increase the sample and precisely measure the masses and eccentricities of giant planets and BDs transiting AF-type stars detected by the Transiting Exoplanet Survey Satellite (TESS). We followed bright (V < 12 mag) stars with $T_{\mathrm{eff}}$ > 6200 K that host giant companions (R > 7 $\mathrm{R_{\rm \oplus}}$) using ground-based photometric observations as well as high precision RV measurements from the CORALIE, CHIRON, TRES, FEROS, and MINERVA-Australis spectrographs. In the context, we present the discovery of three BD companions, TOI-629b, TOI-1982b, and TOI-2543b, and one massive planet, TOI-1107b. From the joint analysis w

This chapter introduces a conceptual framework for qualitative risk assessment of AI, particularly in the context of the EU AI Act. The framework addresses the complexities of legal compliance and fundamental rights protection by itegrating definitional balancing and defeasible reasoning. Definitional balancing employs proportionality analysis to resolve conflicts between competing rights, while defeasible reasoning accommodates the dynamic nature of legal decision-making. Our approach stresses the need for an analysis of AI deployment scenarios and for identifying potential legal violations and multi-layered impacts on fundamental rights. On the basis of this analysis, we provide philosophical foundations for a logical account of AI risk analysis. In particular, we consider the basic building blocks for conceptually grasping the interaction between AI deployment scenarios and fundamental rights, incorporating in defeasible reasoning definitional balancing and arguments about the contextual promotion or demotion of rights. This layered approach allows for more operative models of assessment of both high-risk AI systems and General Purpose AI (GPAI) systems, emphasizing the broader

We study strong gravitational lensing by spiral galaxies, modeling them as infinitely thin uniform disks embedded in singular isothermal spheres. We derive general properties of the critical curves and caustics analytically. The multiple-image cross section is a sensitive function of the inclination angle of the disk relative to the observer. We compute the inclination averaged cross section for several sets of lensing parameters. For realistic disk mass and size parameters, we find that the cross section for multiple imaging is increased by only a modest factor and no dramatic increase in the optical depth for strong lensing of QSOs would be expected. However, the cross section for high magnifications is significantly increased due to the inclusion of a disk, especially for nearly edge-on configurations; due to the strong observational selection effects favoring high magnifications, there might be significant consequences for lensing statistics.

In this paper, we explore the 'equivalence principle' (EP): roughly, statements about mathematical objects should be invariant under an appropriate notion of equivalence for the kinds of objects under consideration. In set theoretic foundations, EP may not always hold: for instance, the statement '1 \in N' is not invariant under isomorphism of sets. In univalent foundations, on the other hand, EP has been proven for many mathematical structures. We first give an overview of earlier attempts at designing foundations that satisfy EP. We then describe how univalent foundations validates EP.

This Report summarizes the results of the first 10 months' activities of the LHC Higgs Cross Sections Working Group. The main goal of the working group was to present the status-of-art on Higgs Physics at the LHC integrating all new results that have appeared in the last few years. The Report is more than a mere collection of the proceedings of the general meetings. The subgroups have been working in different directions. An attempt has been made to present the first Report from these subgroups in a complete and homogeneous form. The subgroups' contributions correspondingly comprise the main parts of the Report. A significant amount of work has been performed in providing higher-order corrections to the Higgs-boson cross sections and pinning down the theoretical uncertainty of the Standard Model predictions. This Report comprises explicit numerical results on total cross sections, leaving the issues of event selection cuts and differential distributions to future publications. The subjects for further study are identified.

This preprint contains a detailed Preface to Proceedinngs of the International Conference ``Foundations of Probability and Physics-3'' held in Växjö, Sweden, 7-12 June 2004; table of contents and round table. The main theme of the round table was {\it ``Fundamental problems in quantum mechanics, probabilistic description of reality, and quantum information.''} The topics that were specifically discussed were that of Quantum Cryptography, Quantum computing, and Quantum Macroscopic Structures. For each of these topics, the participants were asked to discuss which are the crucial Quantum features required among the following : violation of Bell's inequality, Entanglement, Complementarity, and Interference of Probabilities. Finally, the connection between Mental states and Quantum states was discussed.

Our aim in this paper is to take quite seriously Heinz Post's claim that the non-individuality and the indiscernibility of quantum objects should be introduced right at the start, and not made a posteriori by introducing symmetry conditions. Using a different mathematical framework, namely, quasi-set theory, we avoid working within a label-tensor-product-vector-space-formalism, to use Redhead and Teller's words, and get a more intuitive way of dealing with the formalism of quantum mechanics, although the underlying logic should be modified. Thus, this paper can be regarded as a tentative to follow and enlarge Heinsenberg's suggestion that new phenomena require the formation of a new "closed" (that is, axiomatic) theory, coping also with the physical theory's underlying logic and mathematics.

As the worldwide population gets increasingly aged, in-home telemedicine and mobile-health solutions represent promising services to promote active and independent aging and to contribute to a paradigm shift towards patient-centric healthcare. In this work, we present ACTA (Advanced Cognitive Training for Aging), a prototype mobile-health solution to provide advanced cognitive training for senior citizens with mild cognitive impairments. We disclose here the conceptualization of ACTA as the integration of two promising rehabilitation strategies: the "Nudge theory", from the cognitive domain, and the neurofeedback, from the neuroscience domain. Moreover, in ACTA we exploit the most advanced machine learning techniques to deliver customized and fully adaptive support to the elderly, while training in an ecological environment. ACTA represents the next-step beyond SENIOR, an earlier mobile-health project for cognitive training based on Nudge theory, currently ongoing in Lombardy Region. Beyond SENIOR, ACTA represents a highly-usable, accessible, low-cost, new-generation mobile-health solution to promote independent aging and effective motor-cognitive training support, while empowering

Due to its longevity and enormous information density, DNA is an attractive medium for archival data storage. Thanks to rapid technological advances, DNA storage is becoming practically feasible, as demonstrated by a number of experimental storage systems, making it a promising solution for our society's increasing need of data storage. While in living things, DNA molecules can consist of millions of nucleotides, due to technological constraints, in practice, data is stored on many short DNA molecules, which are preserved in a DNA pool and cannot be spatially ordered. Moreover, imperfections in sequencing, synthesis, and handling, as well as DNA decay during storage, introduce random noise into the system, making the task of reliably storing and retrieving information in DNA challenging. This unique setup raises a natural information-theoretic question: how much information can be reliably stored on and reconstructed from millions of short noisy sequences? The goal of this monograph is to address this question by discussing the fundamental limits of storing information on DNA. Motivated by current technological constraints on DNA synthesis and sequencing, we propose a probabilistic

Homotopy type theory is a new branch of mathematics, based on a recently discovered connection between homotopy theory and type theory, which brings new ideas into the very foundation of mathematics. On the one hand, Voevodsky's subtle and beautiful "univalence axiom" implies that isomorphic structures can be identified. On the other hand, "higher inductive types" provide direct, logical descriptions of some of the basic spaces and constructions of homotopy theory. Both are impossible to capture directly in classical set-theoretic foundations, but when combined in homotopy type theory, they permit an entirely new kind of "logic of homotopy types". This suggests a new conception of foundations of mathematics, with intrinsic homotopical content, an "invariant" conception of the objects of mathematics -- and convenient machine implementations, which can serve as a practical aid to the working mathematician. This book is intended as a first systematic exposition of the basics of the resulting "Univalent Foundations" program, and a collection of examples of this new style of reasoning -- but without requiring the reader to know or learn any formal logic, or to use any computer proof ass

The purpose of this paper is to survey some topics on mathematical foundations of quantum information developed mainly by the present author and co-workers for the last three decades. The topics include an axiomatic construction of quantum measurement theory based on completely positive map-valued measures, a universally valid new formulation of the uncertainty principle for error and disturbance in quantum measurements, the Wigner-Araki-Yanase limit of quantum measurements, the accuracy limit of quantum computing based on conservation laws, and a quantum interpretation based on quantum set theory.

We present here our introduction to the contributed volume "Quantum Theory: Informational Foundations and Foils", Springer Netherlands (2016). It highlights recent trends in quantum foundations and offers an overview of the contributions appearing in the book.

Understanding the quantum aspects of gravity is not only a matter of equations and experiments. Gravity is intimately connected with the structure of space and time, and understanding quantum gravity requires us to find a conceptual structure appropriate to make sense of the quantum aspects of space and time. In the course of the last decades, an extensive discussion on this problem has led to a clear conceptual picture, that provides a coherent conceptual foundation of today's Loop Quantum Gravity. We review this foundation, addressing issues such as the sense in which space and time are emergent, the notion of locality, the role of truncation that enables physical computations on finite graphs, the problem of time, and the characterization of the observable quantities in quantum gravity.

This is the first paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In this paper, we lay the foundations for this study by introducing the notion of formal manifolds in the context of differential geometry, inspired by the notion of formal schemes in algebraic geometry. We develop the basic theory for formal manifolds, and establish a fully faithful contravariant functor from the category of formal manifolds to the category of topological $\mathbb{C}$-algebras. We also prove the existence of finite products in the category of formal manifolds by studying vector-valued formal functions.

We discuss new approach to mathematical foundations of quantum theory, which is completely independent of Hilbert spaces and measure spaces. New kinematics is defined by non-linear geometry of spaces of integrals on abstract non-commutative algebras. New dynamics is defined by constrained maximisation of quantum relative entropy. We recover Hilbert space based approach (including unitary evolution and the von Neumann--Lüders rule) and measure theoretic approach to probability theory (including Bayes' rule) as special cases of our approach.

The Feynman quantum-classical isomorphism between classical statistical mechanics in 3+1 dimensions and quantum statistical mechanics in 3 dimensions is used to connect classical polymer self-consistent field theory with quantum time-dependent density functional theory. This allows the theorems of density functional theory to relate non-relativistic quantum mechanics back to a classical statistical mechanical derivation of polymer self-consistent field theory for ring polymers in a 4 dimensional thermal-space. One dynamic postulate is added to two static postulates which allows for a complete description of quantum physics from a 5 dimensional thermal-space-time ensemble perspective which also removes the measurement problem. In the classical limit, a cylinder condition naturally arises as the thermal dimension becomes irrelevant, providing a justification for using 5 dimensions and a cylinder condition in general relativity, which is known to produce 4 dimensional space-time gravity and Maxwell's equations. Thus, in this approach, the postulates of electromagnetism become derived results of a special case of a ring polymer interpretation of quantum foundations.

We prove a topological version of the section conjecture for the profinite completion of the fundamental group of finite CW-complexes equipped with the action of a group of prime order $p$ whose $p$-torsion cohomology can be killed by finite covers. As an application we derive the section conjecture for the real points of a large class of varieties defined over the field of real numbers and the natural analogue of the section conjecture for fixed points of finite group actions on projective curves of positive genus defined over the field of complex numbers.