Algebraic KK-theory and Grothendieck-Witt theory of monoid schemes

We study the algebraic $K$-theory and Grothendieck-Witt theory of proto-exact categories of vector bundles over monoid schemes. Our main results are the complete description of the algebraic $K$-theory space of an integral monoid scheme $X$ in terms of its Picard group $\operatorname{Pic}(X)$ and pointed monoid of regular functions $\Gamma(X, \mathcal{O}_X)$ and a description of the Grothendieck-Witt space of $X$ in terms of an additional involution on $\operatorname{Pic}(X)$. We also prove space-level projective bundle formulae in both settings

Group completion in the K-theory and Grothendieck-Witt theory of proto-exact categories

We study the algebraic $K$-theory and Grothendieck-Witt theory of proto-exact categories, with a particular focus on classes of examples of $\mathbb{F}_1$-linear nature. Our main results are analogues of theorems of Quillen and Schlichting, relating the $K$-theory or Grothendieck-Witt theories of proto-exact categories defined using the (hermitian) $Q$-construction and group completion

Tides in the Last Interglacial: insights from notch geometry and palaeo tidal models in Bonaire, Netherland Antilles

The study of past sea levels relies largely on the interpretation of sea-level indicators. Palaeo tidal notches are considered as one of the most precise sea-level indicators as their formation is closely tied to the local tidal range. We present geometric measurements of modern and palaeo (Marine Isotope Stage (MIS) 5e) tidal notches on Bonaire (southern Caribbean Sea) and results from two tidal simulations, using the present-day bathymetry and a palaeo-bathymetry. We use these two tools to investigate changes in the tidal range since MIS 5e. Our models show that the tidal range changes most significantly in shallow areas, whereas both, notch geometry and models results, suggest that steeper continental shelves, such as the ones bordering the island of Bonaire, are less affected to changes in tidal range in conditions of MIS 5e sea levels. We use our data and results to discuss the importance of considering changes in tidal range while reconstructing MIS 5e sea level histories, and we remark that it is possible to use hydrodynamic modelling and notch geometry as first-order proxies to assess whether, in a particular area, tidal range might have been different in MIS 5e with respect to today

Modeling good research practices - overview: a report of the ISPOR-SMDM modeling good research practices task force - 1.

Models—mathematical frameworks that facilitate estimation of the consequences of health care decisions—have become essential tools for health technology assessment. Evolution of the methods since the first ISPOR modeling task force reported in 2003 has led to a new task force, jointly convened with the Society for Medical Decision Making, and this series of seven papers presents the updated recommendations for best practices in conceptualizing models; implementing state–transition approaches, discrete event simulations, or dynamic transmission models; dealing with uncertainty; and validating and reporting models transparently. This overview introduces the work of the task force, provides all the recommendations, and discusses some quandaries that require further elucidation. The audience for these papers includes those who build models, stakeholders who utilize their results, and, indeed, anyone concerned with the use of models to support decision making

Stripe-hexagon competition in forced pattern forming systems with broken up-down symmetry

We investigate the response of two-dimensional pattern forming systems with a broken up-down symmetry, such as chemical reactions, to spatially resonant forcing and propose related experiments. The nonlinear behavior immediately above threshold is analyzed in terms of amplitude equations suggested for a $1:2$ and $1:1$ ratio between the wavelength of the spatial periodic forcing and the wavelength of the pattern of the respective system. Both sets of coupled amplitude equations are derived by a perturbative method from the Lengyel-Epstein model describing a chemical reaction showing Turing patterns, which gives us the opportunity to relate the generic response scenarios to a specific pattern forming system. The nonlinear competition between stripe patterns and distorted hexagons is explored and their range of existence, stability and coexistence is determined. Whereas without modulations hexagonal patterns are always preferred near onset of pattern formation, single mode solutions (stripes) are favored close to threshold for modulation amplitudes beyond some critical value. Hence distorted hexagons only occur in a finite range of the control parameter and their interval of existence shrinks to zero with increasing values of the modulation amplitude. Furthermore depending on the modulation amplitude the transition between stripes and distorted hexagons is either sub- or supercritical.Comment: 10 pages, 12 figures, submitted to Physical Review

Adapted continuous unitary transformation to treat systems with quasiparticles of finite lifetime

An improved generator for continuous unitary transformations is introduced to describe systems with unstable quasiparticles. Its general properties are derived and discussed. To illustrate this approach we investigate the asymmetric antiferromagnetic spin-1/2 Heisenberg ladder which allows for spontaneous triplon decay. We present results for the low energy spectrum and the momentum resolved spectral density of this system. In particular, we show the resonance behavior of the decaying triplon explicitly.Comment: 40 pages, 12 figure

Validation of Agent-Based Models in Economics and Finance

Since the survey by Windrum et al. (Journal of Artificial Societies and Social Simulation 10:8, 2007), research on empirical validation of agent-based models in economics has made substantial advances, thanks to a constant flow of high-quality contributions. This Chapter attempts to take stock of such recent literature to offer an updated critical review of the existing validation techniques. We sketch a simple theoretical framework that conceptualizes existing validation approaches, which we examine along three different dimensions: (i) comparison between artificial and real-world data; (ii) calibration and estimation of model parameters; and (iii) parameter space exploration. Finally, we discuss open issues in the field of ABM validation and estimation. In particular, we argue that more research efforts should be devoted toward advancing hypothesis testing in ABM, with specific emphasis on model stationarity and ergodicity