The sharp interface limit of an Ising game

The Ising model of statistical physics has served as a keystone example of phase transitions, thermodynamic limits, scaling laws, and many other phenomena and mathematical methods. We introduce and explore an Ising game, a variant of the Ising model that features competing agents influencing the behavior of the spins. With long-range interactions, we consider a mean-field limit resulting in a nonlocal potential game at the mesoscopic scale. This game exhibits a phase transition and multiple constant Nash-equilibria in the supercritical regime. Our analysis focuses on a sharp interface limit for which potential minimizing solutions to the Ising game concentrate on two of the constant Nash-equilibria. We show that the mesoscopic problem can be recast as a mixed local/nonlocal space-time Allen-Cahn type minimization problem. We prove, using a $\Gamma$-convergence argument, that the limiting interface minimizes a space-time anisotropic perimeter type energy functional. This macroscopic scale problem could also be viewed as a problem of optimal control of interface motion. Sharp interface limits of Allen-Cahn type functionals have been well studied. We build on that literature with new techniques to handle a mixture of local derivative terms and nonlocal interactions. The boundary conditions imposed by the game theoretic considerations also appear as novel terms and require special treatment

Support for graphicacy: a review of textbooks available to accounting students

This Teaching Note reports on the support available in textbooks for graphicacy that will help students understand the complexities of graphical displays. Graphical displays play a significant role in financial reporting, and studies have found evidence of measurement distortion and selection bias. To understand the complexities of graphical displays, students need a sound understanding of graphicacy and support from the textbooks available to them to develop that understanding. The Teaching Note reports on a survey that examined the textbooks available to students attending two Scottish universities. The support of critical graphicacy skills was examined in conjunction with textbook characteristics. The survey, which was not restricted to textbooks designated as required reading, examined the textbooks for content on data measurement and graphical displays. The findings highlight a lack of support for graphicacy in the textbooks selected. The study concludes that accounting educators need to scrutinize more closely the selection of textbooks and calls for more extensive research into textbooks as a pedagogic tool

Galaxy Pairs in the 2dF Survey I. Effects of Interactions in the Field

We study galaxy pairs in the field selected from the 100 K public release of the 2dF galaxy redshift survey. Our analysis provides a well defined sample of 1258 galaxy pairs, a large database suitable for statistical studies of galaxy interactions in the local universe, $z \le 0.1$. Galaxy pairs where selected by radial velocity ($\Delta V$) and projected separation ($r_{\rm p}$) criteria determined by analyzing the star formation activity within neighbours (abridged). The ratio between the fractions of star forming galaxies in pairs and in isolation is a useful tools to unveil the effects of having a close companion. We found that about fifty percent of galaxy pairs do not show signs of important star formation activity (independently of their luminosities) supporting the hypothesis that the internal properties of the galaxies play a crucial role in the triggering of star formation by interactions.Comment: 9 pages, 11 Postscript figures. Submitted to MNRAS. Revised versio

Brain Specificity of Diffuse Optical Imaging: Improvements from Superficial Signal Regression and Tomography

Functional near infrared spectroscopy (fNIRS) is a portable monitor of cerebral hemodynamics with wide clinical potential. However, in fNIRS, the vascular signal from the brain is often obscured by vascular signals present in the scalp and skull. In this paper, we evaluate two methods for improving in vivo data from adult human subjects through the use of high-density diffuse optical tomography (DOT). First, we test whether we can extend superficial regression methods (which utilize the multiple source–detector pair separations) from sparse optode arrays to application with DOT imaging arrays. In order to accomplish this goal, we modify the method to remove physiological artifacts from deeper sampling channels using an average of shallow measurements. Second, DOT provides three-dimensional image reconstructions and should explicitly separate different tissue layers. We test whether DOT's depth-sectioning can completely remove superficial physiological artifacts. Herein, we assess improvements in signal quality and reproducibility due to these methods using a well-characterized visual paradigm and our high-density DOT system. Both approaches remove noise from the data, resulting in cleaner imaging and more consistent hemodynamic responses. Additionally, the two methods act synergistically, with greater improvements when the approaches are used together

Air entrainment through free-surface cusps

In many industrial processes, such as pouring a liquid or coating a rotating cylinder, air bubbles are entrapped inside the liquid. We propose a novel mechanism for this phenomenon, based on the instability of cusp singularities that generically form on free surfaces. The air being drawn into the narrow space inside the cusp destroys its stationary shape when the walls of the cusp come too close. Instead, a sheet emanates from the cusp's tip, through which air is entrained. Our analytical theory of this instability is confirmed by experimental observation and quantitative comparison with numerical simulations of the flow equations

Bias Correction of Hydrologic Projections Strongly Impacts Inferred Climate Vulnerabilities in Institutionally Complex Water Systems

Water-resources planners use regional water management models (WMMs) to identify vulnerabilities to climate change. Frequently, dynamically downscaled climate inputs are used in conjunction with land-surface models (LSMs) to provide hydrologic streamflow projections, which serve as critical inputs for WMMs. Here, we show how even modest projection errors can strongly affect assessments of water availability and financial stability for irrigation districts in California. Specifically, our results highlight that LSM errors in projections of flood and drought extremes are highly interactive across timescales, path-dependent, and can be amplified when modeling infrastructure systems (e.g., misrepresenting banked groundwater). Common strategies for reducing errors in deterministic LSM hydrologic projections (e.g., bias correction) can themselves strongly distort projected climate vulnerabilities and misrepresent their inferred financial consequences. Overall, our results indicate a need to move beyond standard deterministic climate projection and error management frameworks that are dependent on single simulated climate change scenario outcomes

Theoretical studies of the historical development of the accounting discipline: a review and evidence

Many existing studies of the development of accounting thought have either been atheoretical or have adopted Kuhn's model of scientific growth. The limitations of this 35-year-old model are discussed. Four different general neo-Kuhnian models of scholarly knowledge development are reviewed and compared with reference to an analytical matrix. The models are found to be mutually consistent, with each focusing on a different aspect of development. A composite model is proposed. Based on a hand-crafted database, author co-citation analysis is used to map empirically the entire literature structure of the accounting discipline during two consecutive time periods, 1972–81 and 1982–90. The changing structure of the accounting literature is interpreted using the proposed composite model of scholarly knowledge development

A weak lensing analysis of a STIS dark-lens candidate

We perform a weak lensing analysis on a previously reported dark-lens candidate on STIS Parallel data (Miralles et al. 2002). New VLT-data indicate that the reported signal originates from a small number of galaxies tangentially aligned towards the center of the STIS field but no signature for an extended mass distribution is found. We argue that we should be able to detect a massive cluster ($M\geq 3.2\times 10^{14}M_{\odot}$) through its lensing signal up to a redshift of $z\approx 0.6$ with our data. Also the double image hypothesis of two galaxies with very similar morphologies in the STIS data is ruled out with colour information.Comment: 9 pages, 8 figures, submitted to A&A main journa