Fields and rings with few types

Let R be an associative ring with possible extra structure. R is said to be weakly small if there are countably many 1-types over any finite subset of R. It is locally P if the algebraic closure of any finite subset of R has property P. It is shown here that a field extension of finite degree of a weakly small field either is a finite field or has no Artin-Schreier extension. A weakly small field of characteristic 2 is finite or algebraically closed. Every weakly small division ring of positive characteristic is locally finite dimensional over its centre. The Jacobson radical of a weakly small ring is locally nilpotent. Every weakly small division ring is locally, modulo its Jacobson radical, isomorphic to a product of finitely many matrix rings over division rings

Physics of non-Gaussian fields and the cosmological genus statistic

We report a technique to calculate the impact of distinct physical processes inducing non-Gaussianity on the cosmological density field. A natural decomposition of the cosmic genus statistic into an orthogonal polynomial sequence allows complete expression of the scale-dependent evolution of the morphology of large-scale structure, in which effects including galaxy bias, nonlinear gravitational evolution and primordial non-Gaussianity may be delineated. The relationship of this decomposition to previous methods for analysing the genus statistic is briefly considered and the following applications are made: i) the expression of certain systematics affecting topological measurements; ii) the quantification of broad deformations from Gaussianity that appear in the genus statistic as measured in the Horizon Run simulation; iii) the study of the evolution of the genus curve for simulations with primordial non-Gaussianity. These advances improve the treatment of flux-limited galaxy catalogues for use with this measurement and further the use of the genus statistic as a tool for exploring non-Gaussianity.Comment: AASTeX preprint, 24 pages, 8 figures, includes several improvements suggested by anonymous reviewe

In support for the Supreme Court, partisanship trumps concern around gender equality

Recent decisions by the US Supreme Court such as the overturning of Roe. vs Wade have raised questions about the institution’s legitimacy in the eyes of the American public. In a new study, Jin Woo Kim and María Celeste Wagner look at whether the Roe decision has affected trust in the Supreme Court. They find that since 2018, trust in the Supreme Court has become increasingly partisan with Democratic voters’ trust falling from 60 to 16 percent while Republicans’ confidence has remained almost the same. They also find that there is little difference in trust in the Supreme Court between men and women

A Method For Iris Liveness Detection Using Passive Light Trigger

The present disclosure relates to a passive liveness detection method for a camera-based iris biometric system. The method comprising: detecting an initiation of transaction on one of a user device and a payment terminal in supervised/unsupervised payment environments, introducing a passive light trigger to record real-time involuntary biological response of user’s eye when the initiation of transaction is detected, comparing the recorded real-time involuntary biological response of the user’s eye to similar biological response of the user’s eye recorded at the time of enrollment and/or a previous successful transaction by the user stored in a database, and determining if the artifact being presented to the iris biometric system at the time of transaction is real or spoof based on the comparison. The present disclosure uses shutter speed and aperture of camera lens, and image sensor sensitivity settings coupled with a passive light trigger for liveness detection. This approach overcomes the need for specialized expensive hardware and the limitation of detecting a fixed set of fake artifacts (spoofs) for passive liveness detection

System And Method For Validating A Multi-Digit Number

The present disclosure provides a modified type of MOD 10 algorithm for validating a multi-digit number. Such MOD 10 algorithm may also be referred to as modified Luhn check or modifies Wagner check. The proposed modified Luhn check extends range of the Luhn check from 1 to 10 while preserving integrity of the multi-digit number when the multi-digit number is manually captured or typed. Also, by the proposed method, 9 times more PANs may be introduced without increasing the length of the PAN

California Micro Devices Corp.: A Class Discussion Of Auditors Ethical, Legal, And Professional Responsibilities

This short case is best for an open discussion in an upper-division auditing class. The class discussion questions intensify students learning experience on (1) auditors ethical responsibility to resolve tough ethical issues, (2) auditors legal responsibility to detect fraudulent financial reporting, and (3) auditors professional responsibility to conform to auditing standards. Additional class discussion questions, optional hands-on internet experience, and class discussion guide are provided. The case illustrates how a high-technology company succumbed to the pressure of unrealistic financial goals in an industry that is characterized by rapid technology change, intense competitive pressure, and volatile demand patterns for computer chips. High-level management at the company orchestrated fraudulent financial reporting schemes by creating fictitious sales and shipping bogus inventories. The fraud was uncovered only after the companys Board of Directors appointed a third auditor to investigate the sophisticated fraudulent schemes. However, the action came a little too late as the shareholders began to file class-action securities lawsuits against the company and its former auditor

Application of Zhangs Square Root Law and Herding to Financial Markets

We apply an asymmetric version of Kirman's herding model to volatile financial markets. In the relation between returns and agent concentration we use the square root law proposed by Zhang. This can be derived by extending the idea of a critical mean field theory suggested by Plerou et al. We show that this model is equivalent to the so called 3/2-model of stochastic volatility. The description of the unconditional distribution for the absolute returns is in good agreement with the DAX independent whether one uses the square root or a conventional linear relation. Only the statistic of extreme events prefers the former. The description of the autocorrelations are in much better agreement for the square root law. The volatility clusters are described by a scaling law for the distribution of returns conditional to the value at the previous day in good agreement with the data.Comment: 25 pages, 3 figures, Late