Algebraic generality versus arithmetic generality in the 1874 controversy between C. Jordan and L. Kronecker
This article revisits the 1874 controversy between Camille Jordan and Leopold Kronecker over two theorems, namely Jordan’s canonical forms and Karl Weierstrass’s elementary divisors theorem. In particular, it compares the perspectives of Jordan and Kronecker on generality and how their debate turned into an opposition over the algebraic or arithmetic nature of the ‘theory of forms’. It also examines the ways in which the various actors used the the categories of algebraic generality and arithmetic generality. After providing a background on the Jordan-Kronecker controversy, the article explains Jordan’s canonical reduction and Kronecker’s invariant computations in greater detail. It argues that Jordan and Kronecker aimed to ground the ‘theory of forms’ on new forms of generality, but could not agree on the types of generality and on the treatments of the general they were advocating.
This article discusses the connection between the matrix models and algebraic geometry. In particular, it considers three specific applications of matrix models to algebraic geometry, namely: the Kontsevich matrix model that describes intersection indices on moduli spaces of curves with marked points; the Hermitian matrix model free energy at the leading expansion order as the prepotential of the Seiberg-Witten-Whitham-Krichever hierarchy; and the other orders of free energy and resolvent expansions as symplectic invariants and possibly amplitudes of open/closed strings. The article first describes the moduli space of algebraic curves and its parameterization via the Jenkins-Strebel differentials before analysing the relation between the so-called formal matrix models (solutions of the loop equation) and algebraic hierarchies of Dijkgraaf-Witten-Whitham-Krichever type. It also presents the WDVV (Witten-Dijkgraaf-Verlinde-Verlinde) equations, along with higher expansion terms and symplectic invariants.
Hedibert Lopes and Nicholas Polson
This article discusses the use of Bayesian multiscale spatio-temporal models for the analysis of economic data. It demonstrates the utility of a general modelling approach for multiscale analysis of spatio-temporal processes with areal data observations in an economic study of agricultural production in the Brazilian state of Espìrito Santo during the period 1990–2005. The article first describes multiscale factorizations for spatial processes before presenting an exploratory multiscale data analysis and explaining the motivation for multiscale spatio-temporal models. It then examines the temporal evolution of the underlying latent multiscale coefficients and goes on to introduce a Bayesian analysis based on the multiscale decomposition of the likelihood function along with Markov chain Monte Carlo (MCMC) methods. The results from agricultural production analysis show that the spatio-temporal framework can effectively analyse massive economics data sets.
D. Daghero, G.A. Ummarino, and R.S. Gonnelli
This article investigates the potential of the point contact Andreev reflection spectroscopy (PCARS) technique for measuring the symmetry of the energy gap and other key parameters of various 0-, 1-, and 2-dimensional superconducting systems. It begins with a brief description of PCARS, explaining what a point contact is and how it can be made and the conditions under which a PC is ballistic, as well as why and to what extent a PC between normal metals is spectroscopic. It then discusses the basics of Andreev reflection and the length scales in mesoscopic systems before considering the limits of applicability of PCARS for spectroscopy of ‘small’ superconductors. Finally, it reviews some examples of PCARS in quasi-0D, quasi-1D and quasi-2D superconductors.
Pontus Lurcock and Fabio Florindo
Antarctic climate changes have been reconstructed from ice and sediment cores and numerical models (which also predict future changes). Major ice sheets first appeared 34 million years ago (Ma) and fluctuated throughout the Oligocene, with an overall cooling trend. Ice volume more than doubled at the Oligocene-Miocene boundary. Fluctuating Miocene temperatures peaked at 17–14 Ma, followed by dramatic cooling. Cooling continued through the Pliocene and Pleistocene, with another major glacial expansion at 3–2 Ma. Several interacting drivers control Antarctic climate. On timescales of 10,000–100,000 years, insolation varies with orbital cycles, causing periodic climate variations. Opening of Southern Ocean gateways produced a circumpolar current that thermally isolated Antarctica. Declining atmospheric CO2 triggered Cenozoic glaciation. Antarctic glaciations affect global climate by lowering sea level, intensifying atmospheric circulation, and increasing planetary albedo. Ice sheets interact with ocean water, forming water masses that play a key role in global ocean circulation.
M.J. Rob Nout, Bei-Zhong Han, and Cherl-Ho Lee
This article discusses the fermentation process for Asian foods, with particular emphasis on fermented food products made from major primary produce such as soybeans, cereals, and meat. A selection of representative fermentations in Asian countries or subregions is provided and fermentations dominated by different types of microorganisms (bacteria, yeasts, and filamentous fungi) are described. Furthermore, fermentations are distinguished according to the inclusion of salt. The article first considers the scientific knowledge referring to food production, microbiological, and chemical composition and (bio)chemical changes taking place during the fermentation before giving an overview of fermented soybean products such as soybean sauce and soybean paste. It then examines fermented meat products and cereal products and concludes with an assessment of prospects for research and development relating to the fermentation of Asian products.
James S. Clark, Dave Bell, Michael Dietze, Michelle Hersh, Ines Ibanez, Shannon LaDeau, Sean McMahon, Jessica Metcalf, Emily Moran, Luke Pangle, and Mike Wolosin
This article focuses on the use of Bayesian methods in assessing the probability of rare climate events, and more specifically the potential collapse of the meridional overturning circulation (MOC) in the Atlantic Ocean. It first provides an overview of climate models and their use to perform climate simulations, drawing attention to uncertainty in climate simulators and the role of data in climate prediction, before describing an experiment that simulates the evolution of the MOC through the twenty-first century. MOC collapse is predicted by the GENIE-1 (Grid Enabled Integrated Earth system model) for some values of the model inputs, and Bayesian emulation is used for collapse probability analysis. Data comprising a sparse time series of five measurements of the MOC from 1957 to 2004 are analysed. The results demonstrate the utility of Bayesian analysis in dealing with uncertainty in complex models, and in particular in quantifying the risk of extreme outcomes.
Joan Martí Molist
Volcanoes represent complex geological systems capable of generating many dangerous phenomena. To evaluate and manage volcanic risk, we need first to assess volcanic hazard (i.e., identify past volcanic system behavior to infer future behavior. This requires acquisition of all relevant geological and geophysical information, such as stratigraphic studies, geological mapping, sedimentological studies, petrologic studies, and structural studies. All this information is then used to elaborate eruption scenarios and hazard maps. Stratigraphic studies represent the main tool for the reconstruction of past activity of volcanoes over time periods exceeding their historical record. This review presents a systematic approach to volcanic hazard assessment, paying special attention to reconstruction of past eruptive history. It reviews concepts and methods most commonly used in long- and short-term hazard assessment and analyzes how they help address the various serious consequences derived from the occurrence (and nonoccurrence in some crisis alerts) of volcanic eruptions and related phenomena.
Antonia Tulino and Sergio Verdu
This article examines asymptotic singular value distributions in information theory, with particular emphasis on some of the main applications of random matrices to the capacity of communication channels. Results on the spectrum of random matrices have been adopted in information theory. Furthermore, information theorists, motivated by certain channel models, have obtained a number of new results in random matrix theory (RMT). Most of those results are related to the asymptotic distribution of the (square of) the singular values of certain random matrices that model data communication channels. The article first provides an overview of three transforms that are useful in expressing the asymptotic spectrum results — Stieltjes transform, η-transform, and Shannon transform — before discussing the main results on the limit of the empirical distributions of the eigenvalues of various random matrices of interest in information theory.
M. Stamenova and S. Sanvito
This article reviews recent advances towards the development of a truly atomistic time-dependent theory for spin-dynamics. The focus is on the s-d tight-binding model [where conduction electrons (s) are exchange-coupled to a number of classical spins (d)], including electrostatic corrections at the Hartree level, as the underlying electronic structure theory. In particular, the article considers one-dimensional (1D) magnetic atomic wires and their electronic structure, described by means of the s-d model. The discussion begins with an overview of the model spin Hamiltonian, followed by molecular-dynamics simulations of spin-wave dispersion in a s-d monoatomic chain and spin impurities in a non-magnetic chain. The current-induced motion in a magnetic domain wall (DW) is also explored, along with how an electric current can affect the magnetization landscape of a magnetic nano-object. The article concludes with an assessment of spin-motive force, and especially whether a driven magnetization dynamics can generate an electrical signal.