Dirac Spectrum in Piecewise Constant One-Dimensional Potentials

We study the electronic states of graphene in piecewise constant potentials using the continuum Dirac equation appropriate at low energies, and a transfer matrix method. For superlattice potentials, we identify patterns of induced Dirac points which are present throughout the band structure, and verify for the special case of a particle-hole symmetric potential their presence at zero energy. We also consider the cases of a single trench and a p-n junction embedded in neutral graphene, which are shown to support confined states. An analysis of conductance across these structures demonstrates that these confined states create quantum interference effects which evidence their presence.Comment: 10 pages, 12 figures, additional references adde

Peripheral Nerve Activation Evokes Machine-Learnable Signals in the Dorsal Column Nuclei

The brainstem dorsal column nuclei (DCN) are essential to inform the brain of tactile and proprioceptive events experienced by the body. However, little is known about how ascending somatosensory information is represented in the DCN. Our objective was to investigate the usefulness of high-frequency (HF) and low-frequency (LF) DCN signal features (SFs) in predicting the nerve from which signals were evoked. We also aimed to explore the robustness of DCN SFs and map their relative information content across the brainstem surface. DCN surface potentials were recorded from urethane-anesthetized Wistar rats during sural and peroneal nerve electrical stimulation. Five salient SFs were extracted from each recording electrode of a seven-electrode array. We used a machine learning approach to quantify and rank information content contained within DCN surface-potential signals following peripheral nerve activation. Machine-learning of SF and electrode position combinations was quantified to determine a hierarchy of information importance for resolving the peripheral origin of nerve activation. A supervised back-propagation artificial neural network (ANN) could predict the nerve from which a response was evoked with up to 96.8 ± 0.8% accuracy. Guided by feature-learnability, we maintained high prediction accuracy after reducing ANN algorithm inputs from 35 (5 SFs from 7 electrodes) to 6 (4 SFs from one electrode and 2 SFs from a second electrode). When the number of input features were reduced, the best performing input combinations included HF and LF features. Feature-learnability also revealed that signals recorded from the same midline electrode can be accurately classified when evoked from bilateral nerve pairs, suggesting DCN surface activity asymmetry. Here we demonstrate a novel method for mapping the information content of signal patterns across the DCN surface and show that DCN SFs are robust across a population. Finally, we also show that the DCN is functionally asymmetrically organized, which challenges our current understanding of somatotopic symmetry across the midline at sub-cortical levels

Peripheral nerve activation evokes machine-learnable signals in the dorsal column nuclei

The brainstem dorsal column nuclei (DCN) are essential to inform the brain of tactile and proprioceptive events experienced by the body. However, little is known about how ascending somatosensory information is represented in the DCN. Our objective was to investigate the usefulness of high-frequency (HF) and low-frequency (LF) DCN signal features (SFs) in predicting the nerve from which signals were evoked. We also aimed to explore the robustness of DCN SFs and map their relative information content across the brainstem surface. DCN surface potentials were recorded from urethane-anesthetized Wistar rats during sural and peroneal nerve electrical stimulation. Five salient SFs were extracted from each recording electrode of a seven-electrode array. We used a machine learning approach to quantify and rank information content contained within DCN surface-potential signals following peripheral nerve activation. Machine-learning of SF and electrode position combinations was quantified to determine a hierarchy of information importance for resolving the peripheral origin of nerve activation. A supervised back-propagation artificial neural network (ANN) could predict the nerve from which a response was evoked with up to 96.8 ± 0.8% accuracy. Guided by feature-learnability, we maintained high prediction accuracy after reducing ANN algorithm inputs from 35 (5 SFs from 7 electrodes) to 6 (4 SFs from one electrode and 2 SFs from a second electrode). When the number of input features were reduced, the best performing input combinations included HF and LF features. Feature-learnability also revealed that signals recorded from the same midline electrode can be accurately classified when evoked from bilateral nerve pairs, suggesting DCN surface activity asymmetry. Here we demonstrate a novel method for mapping the information content of signal patterns across the DCN surface and show that DCN SFs are robust across a population. Finally, we also show that the DCN is functionally asymmetrically organized, which challenges our current understanding of somatotopic symmetry across the midline at sub-cortical levels.The authors are extremely grateful to the Bootes Medical Research Foundation which funded this project. AL was supported by the Australian Government Research Training Program

Tax Evasion, Tax Avoidance and Tax Planning in Australia: The participation in mass-marketed tax avoidance schemes in the Pilbara region of Western Australia in the 1990s

This paper will examine the development of mass-marketed tax avoidance schemes in Australia. It will consider changes in approach to tax avoidance from the ‘bottom of the harbour’ schemes of the 1960s and 1970s to the mass-marketed tax avoidance schemes of the 1990s. It will examine the changing structure of tax avoidance from individually crafted tax avoidance structures designed by accountants and lawyers used by high wealth individuals to mass produced structures targeted at highly paid, and therefore highly taxed, blue collar workers in Australia’s mining industry in the 1990s. In the latter half of the twentieth century ‘unacceptable’ tax planning went from highly expensive, individually ‘tailor made’ structures afforded and used only by the very wealthy, to inexpensive replicated structures marketed to skilled and unskilled tradespeople and labourers. By 1998 over 42 000 Australian taxpayers were engaged in tax avoidance schemes with the highest proportion focussed in the mining regions of Western Australia. In the remote and inhospitable mining community of Pannawonica, which has one of the highest paid workforces in Australia, the Australian Taxation Office identified that as many as one in five taxpayers were engaged in a mass-marketed tax avoidance scheme. The paper will identify the causes of these changes, including the advent of the computerised information technology which permitted ‘mass production’ of business structures designed to exploit business incentives in the Australian taxation system in the 1990s. It will also set these developments within the broader context of the tax compliance culture prevailing in Australia and overseas during this period

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The mandatory life sentence for murder : an argument for judicial discretion in England

In 1965, alongside the abolition of capital punishment, a mandatory life sentence for murder was implemented in England and Wales. The mandatory life sentence served as a signal to the public that the criminal justice system would still implement the most severe sanction of life imprisonment in cases of murder. Nearly 50 years later, this article examines whether the imposition of a mandatory life sentence for murder is still in the best interests of justice or whether English homicide law would be better served by a discretionary sentencing system. In doing so, the article considers debates surrounding the political and public need for a mandatory life sentence for murder by drawing upon interviews conducted with 29 members of the English criminal justice system. This research concludes that a discretionary sentencing framework is required to adequately respond to the many contexts within which the crime of murder is committed