Applications of Commutator-Type Operators to pp-Groups

For a p-group G admitting an automorphism $\phi$ of order $p^n$ with exactly $p^m$ fixed points such that $\phi^{p^{n-1}}$ has exactly $p^k$ fixed points, we prove that G has a fully-invariant subgroup of m-bounded nilpotency class with $(p,n,m,k)$-bounded index in G. We also establish its analogue for Lie p-rings. The proofs make use of the theory of commutator-type operators.Comment: 11 page

On Automorphisms and Focal Subgroups of Blocks

Given a p-block B of a finite group with defect group P and fusion system on P, we show that the rank of the group is invariant under stable equivalences of Morita type. The main ingredients are the construction, due to Broué and Puig, a theorem of Weiss on linear source modules, arguments of Hertweck and Kimmerle applying Weiss’ theorem to blocks, and connections with integrable derivations in the Hochschild cohomology of block algebras

Open Data as Open Educational Resources: Case studies of emerging practice

This collection presents the stories of our contributors’ experiences and insights, in order to demonstrate the enormous potential for openly-licensed and accessible datasets (Open Data) to be used as Open Educational Resources (OER). Open Data is an umbrella term describing openly-licensed, interoperable, and reusable datasets which have been created and made available to the public by national or local governments, academic researchers, or other organisations. These datasets can be accessed, used and shared without restrictions other than attribution of the intellectual property of their creators1.While there are various definitions of OER, these are generally understood as openly-licensed digital resources that can be used in teaching and learning. On the basis of these definitions, it is reasonable to assert that while Open Data is not always OER, it certainly becomes OER when used within pedagogical contexts. Yet while the question may appear already settled at the level of definition, the potential and actual pedagogical uses of Open Data appear to have been under-discussed. As open education researchers who take a wider interest in the various open ‘movements’, we have observed that linkages between them are not always strong, in spite of shared and interconnecting values. So, Open Data tends to be discussed primarily in relation to its production, storage, licensing and accessibility, but less often in relation to its practical subsequent uses. And, in spite of widespread understanding that use of the term ‘OER’ is actually context-dependent, and, therefore, could be almost all-encompassing, the focus of OER practice and research has tended to be on educator-produced learning materials. The search for relevant research literature in the early stages of this project turned up sources which discuss the benefits of opening data, and others advocating improving student engagement with data3, but on the topic of Open Data as an educational resource specifically, there appeared to be something of a gap

Backprojection for Training Feedforward Neural Networks in the Input and Feature Spaces

After the tremendous development of neural networks trained by backpropagation, it is a good time to develop other algorithms for training neural networks to gain more insights into networks. In this paper, we propose a new algorithm for training feedforward neural networks which is fairly faster than backpropagation. This method is based on projection and reconstruction where, at every layer, the projected data and reconstructed labels are forced to be similar and the weights are tuned accordingly layer by layer. The proposed algorithm can be used for both input and feature spaces, named as backprojection and kernel backprojection, respectively. This algorithm gives an insight to networks with a projection-based perspective. The experiments on synthetic datasets show the effectiveness of the proposed method.Comment: Accepted (to appear) in International Conference on Image Analysis and Recognition (ICIAR) 2020, Springe

ICP curve morphology and intracranial flow-volume changes: a simultaneous ICP and cine phase contrast MRI study in humans

Background: The intracranial pressure (ICP) curve with its different peaks has been extensively studied, but the exact physiological mechanisms behind its morphology are still not fully understood. Both intracranial volume change (ΔICV) and transmission of the arterial blood pressure have been proposed to shape the ICP curve. This study tested the hypothesis that the ICP curve correlates to intracranial volume changes. Methods: Cine phase contrast magnetic resonance imaging (MRI) examinations were performed in neuro-intensive care patients with simultaneous ICP monitoring. The MRI was set to examine cerebral arterial inflow and venous cerebral outflow as well as flow of cerebrospinal fluid over the foramen magnum. The difference in total flow into and out from the cranial cavity (Flowtot) over time provides the ΔICV. The ICP curve was compared to the Flowtot and the ΔICV. Correlations were calculated through linear and logarithmic regression. Student’s t test was used to test the null hypothesis between paired samples. Results: Excluding the initial ICP wave, P1, the mean R2 for the correlation between the ΔICV and the ICP was 0.75 for the exponential expression, which had a higher correlation than the linear (p = 0.005). The first ICP peaks correlated to the initial peaks of Flowtot with a mean R2 = 0.88. Conclusion: The first part, or the P1, of the ICP curve seems to be created by the first rapid net inflow seen in Flowtot while the rest of the ICP curve seem to correlate to the ΔICV

Large FHE Gates from tensored homomorphic accumulator

The main bottleneck of all known Fully Homomorphic Encryption schemes lies in the bootstrapping procedure invented by Gentry (STOC’09). The cost of this procedure can be mitigated either using Homomorphic SIMD techniques, or by performing larger computation per bootstrapping procedure.In this work, we propose new techniques allowing to perform more operations per bootstrapping in FHEW-type schemes (EUROCRYPT’13). While maintaining the quasi-quadratic Õ(n2) complexity of the whole cycle, our new scheme allows to evaluate gates with Ω(log n) input bits, which constitutes a quasi-linear speed-up. Our scheme is also very well adapted to large threshold gates, natively admitting up to Ω(n) inputs. This could be helpful for homomorphic evaluation of neural networks.Our theoretical contribution is backed by a preliminary prototype implementation, which can perform 6-to-6 bit gates in less than 10s on a single core, as well as threshold gates over 63 input bits even faster.<p

Implementation of the Projector Augmented Wave LDA+U Method: Application to the Electronic Structure of NiO

The so-called local density approximation plus the multi-orbital mean-field Hubbard model (LDA+U) has been implemented within the all-electron projector augmented-wave method (PAW), and then used to compute the insulating antiferromagnetic ground state of NiO and its optical properties. The electronic and optical properties have been investigated as a function of the Coulomb repulsion parameter U. We find that the value obtained from constrained LDA (U=8 eV) is not the best possible choice, whereas an intermediate value (U=5 eV) reproduces the experimental magnetic moment and optical properties satisfactorily. At intermediate U, the nature of the band gap is a mixture of charge transfer and Mott-Hubbard type, and becomes almost purely of the charge-transfer type at higher values of U. This is due to the enhancement of the oxygen 2p states near the top of the valence states with increasing U value.Comment: 23 pages, 6 figures, submitted to Phys. Rev.

Identifying Diffusion Patterns of Research Articles on Twitter: A Case Study of Online Engagement with Open Access Articles

The growing presence of research shared on social media, coupled with the increase in freely available research, invites us to ask whether scientific articles shared on platforms like Twitter diffuse beyond the academic community. We explore a new method for answering this question by identifying 11 articles from two open access biology journals that were shared on Twitter at least 50 times and by analyzing the follower network of users who tweeted each article. We find that diffusion patterns of scientific articles can take very different forms, even when the number of times they are tweeted is similar. Our small case study suggests that most articles are shared within single-connected communities with limited diffusion to the public. The proposed approach and indicators can serve those interested in the public understanding of science, science communication, or research evaluation to identify when research diffuses beyond insular communities. &nbsp