Are biseparable extensions Frobenius?

In Secion~1 we describe what is known of the extent to which a separable extension of unital associative rings is a Frobenius extension. A problem of this kind is suggested by asking if three algebraic axioms for finite Jones index subfactors are dependent. In Section~2 the problem in the title is formulated in terms of separable bimodules. In Section~3 we specialize the problem to ring extensions, noting that a biseparable extension is a two-sided finitely generated projective, split, separable extension. Some reductions of the problem are discussed and solutions in special cases are provided. In Section~4 various examples are provided of projective separable extensions that are neither finitely generated nor Frobenius and which give obstructions to weakening the hypotheses of the question in the title. We show in Section~5 that existing characterizations of the separable extensions among the Frobenius extensions in are special cases of a result for adjoint functors.Comment: 22 page

What is the nature of RX J0720.4-3125?

RX J0720.4-3125 has recently been identified as a pulsating soft X-ray source in the ROSAT all-sky survey with a period of 8.391 s. Its spectrum is well characterized by a black-body with a temperature of $8 \times 10^5$ K. We propose that the radiation from this object is thermal emission from a cooling neutron star. For this black-body temperature we can obtain a robust estimate of the object's age of $\sim 3 \times 10^5$ yr, yielding a polar field $\sim 10^{14}$ G for magnetic-dipole spin down and a value of ${\dot P}$ compatible with current observations.Comment: 4 pages, 1 figures, to appear in Monthly Notice

A QED Model for Non-thermal Emission from SGRs and AXPs

Previously, we showed that, owing to effects arising from quantum electrodynamics (QED), magnetohydrodynamic fast modes of sufficient strength will break down to form electron-positron pairs while traversing the magnetospheres of strongly magnetised neutron stars. The bulk of the energy of the fast mode fuels the development of an electron-positron fireball. However, a small, but potentially observable, fraction of the energy ($\sim 10^{33}$ ergs) can generate a non-thermal distribution of electrons and positrons far from the star. In this paper, we examine the cooling and radiative output of these particles. We also investigate the properties of non-thermal emission in the absence of a fireball to understand the breakdown of fast modes that do not yield an optically thick pair plasma. This quiescent, non-thermal radiation associated with fast mode breakdown may account for the recently observed non-thermal emission from several anomalous X-ray pulsars and soft-gamma repeaters.Comment: 14 pages, 2 figures, submitted to MNRA

The significance of memory in sensory cortex

Early sensory cortex is typically investigated in response to sensory stimulation, masking the contribution of internal signals. Recently, van Kerkoerle and colleagues reported that attention and memory signals segregate from sensory signals within specific layers of primary visual cortex, providing insight into the role of internal signals in sensory processing

The laminar integration of sensory inputs with feedback signals in human cortex

The cortex constitutes the largest area of the human brain. Yet we have only a basic understanding of how the cortex performs one vital function: the integration of sensory signals (carried by feedforward pathways) with internal representations (carried by feedback pathways). A multi-scale, multi-species approach is essential for understanding the site of integration, computational mechanism and functional role of this processing. To improve our knowledge we must rely on brain imaging with improved spatial and temporal resolution and paradigms which can measure internal processes in the human brain, and on the bridging of disciplines in order to characterize this processing at cellular and circuit levels. We highlight apical amplification as one potential mechanism for integrating feedforward and feedback inputs within pyramidal neurons in the rodent brain. We reflect on the challenges and progress in applying this model neuronal process to the study of human cognition. We conclude that cortical-layer specific measures in humans will be an essential contribution for better understanding the landscape of information in cortical feedback, helping to bridge the explanatory gap

Forecasting faces in the cortex: Comment on ‘High-level prediction signals in a low-level area of the macaque face-processing hierarchy’, by Schwiedrzik and Freiwald, Neuron (2017)

Although theories of predictive coding in the brain abound, we lack key pieces of neuronal data to support these theories. Recently, Schwiedrzik and Freiwald found neurophysiological evidence for predictive codes throughout the face-processing hierarchy in macaque cortex. We highlight how these data enhance our knowledge of cortical information processing, and the impact of this more broadly