Congruent families and invariant tensors

Classical results of Chentsov and Campbell state that -- up to constant multiples -- the only $2$-tensor field of a statistical model which is invariant under congruent Markov morphisms is the Fisher metric and the only invariant $3$-tensor field is the Amari-Chentsov tensor. We generalize this result for arbitrary degree $n$, showing that any family of $n$-tensors which is invariant under congruent Markov morphisms is algebraically generated by the canonical tensor fields defined in an earlier paper

On the behavior of the algebraic transfer

Let Tr_k : ��_2 (⊗ over GL_k) PH_i(B��_k) → Ext^(k,k+i)_A(��_2,��_2) be the algebraic transfer, which is defined by W. Singer as an algebraic version of the geometrical transfer tr_k : π_∗^S((B��_k)_+) → π_∗^S(S^0). It has been shown that the algebraic transfer is highly nontrivial and, more precisely, that Tr_k is an isomorphism for k = 1,2,3. However, Singer showed that Tr_5 is not an epimorphism. In this paper, we prove that Tr_4 does not detect the non zero element g_s ∈ Ext^(4,12·2^s)_A(��_2,��_2) for every s ≥ 1. As a consequence, the localized (Sq^0)^(−1)Tr_4 given by inverting the squaring operation Sq^0 is not an epimorphism. This gives a negative answer to a prediction by Minami

The Force Balance of Electrons During Kinetic Anti-parallel Magnetic Reconnection

Fully kinetic simulations are applied to the study of 2D anti-parallel reconnection, elucidating the dynamics by which the electron fluid maintains force balance within both the electron diffusion region (EDR) and the ion diffusion region (IDR). Inside the IDR, magnetic field-aligned electron pressure anisotropy ($p_{e\parallel}\gg p_{e\perp})$ develops upstream of the EDR. Compared to previous investigations, the use of modern computer facilities allows for simulations at the natural proton to electron mass ratio $m_i/m_e=1836$. In this high-$m_i/m_e$-limit the electron dynamics changes qualitatively, as the electron inflow to the EDR is enhanced and mainly driven by the anisotropic pressure. Using a coordinate system with the $x$-direction aligned with the reconnecting magnetic field and the $y$-direction aligned with the central current layer, it is well-known that for the much studied 2D laminar anti-parallel and symmetric scenario the reconnection electric field at the $X$-line must be balanced by the $\partial p_{exy}/ \partial x$ and $\partial p_{eyz}/ \partial z$ off-diagonal electron pressure stress components. We find that the electron anisotropy upstream of the EDR imposes large values of $\partial p_{exy}/ \partial x$ within the EDR, and along the direction of the reconnection $X$-line this stress cancels with the stress of a previously determined theoretical form for $\partial p_{eyz}/ \partial z$. The electron frozen-in law is instead broken by pressure tensor gradients related to the direct heating of the electrons by the reconnection electric field. The reconnection rate is free to adjust to the value imposed externally by the plasma dynamics at larger scales.Comment: Submitted to Physics of Plasmas, 11 October 202

Misconceptions of the Deaf: Giving voice to the voiceless

 The Deaf usually do not see themselves as having a disability; however, discourses and social stereotyping continue to portray the Deaf rather negatively. These discourses may lead to misconceptions, prejudice and possibly discrimination. A study was conducted to identify the challenges members of the Deaf community experience accessing quality health care in a small Island state of Australia. Using a qualitative approach, semi-structured interviews and focus groups were conducted with service providers and the Deaf community. Audist discourses of deafness as deficiency, disability and disease remain dominant in contemporary society and are inconsistency with the Deaf community’s own perception of their reality. Despite the dominant constructions of deafness and their affect on the Deaf’s experience of health service provision, many Deaf have developed skills, confidence and resilience to live in the hearing world. The Deaf were pushing back on discourses that construct deafness as a disempowering impairment

Automatic generation of dense non-rigid optical flow

There hardly exists any large-scale datasets with dense optical flow of non-rigid motion from real-world imagery as of today. The reason lies mainly in the difficulty of human annotation to generate optical flow ground-truth. To circumvent the need for human annotation, we propose a framework to automatically generate optical flow from real-world videos. The method extracts and matches objects from video frames to compute initial constraints, and applies a deformation over the objects of interest to obtain dense optical flow fields. We propose several ways to augment the optical flow variations. Extensive experimental results show that training on our automatically generated optical flow outperforms methods that are trained on rigid synthetic data using FlowNet-S, PWC-Net, and LiteFlowNet. Datasets and algorithms of our optical flow generation framework is available at https://github.com/lhoangan/arap_flow.Comment: The paper is under consideration at Computer Vision and Image Understandin

Singularities and Topology of Meromorphic Functions

We present several aspects of the "topology of meromorphic functions", which we conceive as a general theory which includes the topology of holomorphic functions, the topology of pencils on quasi-projective spaces and the topology of polynomial functions.Comment: 21 pages, 1 figur