Compact Matrix Quantum Group Equivariant Neural Networks

We derive the existence of a new type of neural network, called a compact matrix quantum group equivariant neural network, that learns from data that has an underlying quantum symmetry. We apply the Woronowicz formulation of Tannaka-Krein duality to characterise the weight matrices that appear in these neural networks for any easy compact matrix quantum group. We show that compact matrix quantum group equivariant neural networks contain, as a subclass, all compact matrix group equivariant neural networks. Moreover, we obtain characterisations of the weight matrices for many compact matrix group equivariant neural networks that have not previously appeared in the machine learning literature.Comment: 15 page

Brauer's Group Equivariant Neural Networks

We provide a full characterisation of all of the possible group equivariant neural networks whose layers are some tensor power of $\mathbb{R}^{n}$ for three symmetry groups that are missing from the machine learning literature: $O(n)$, the orthogonal group; $SO(n)$, the special orthogonal group; and $Sp(n)$, the symplectic group. In particular, we find a spanning set of matrices for the learnable, linear, equivariant layer functions between such tensor power spaces in the standard basis of $\mathbb{R}^{n}$ when the group is $O(n)$ or $SO(n)$, and in the symplectic basis of $\mathbb{R}^{n}$ when the group is $Sp(n)$.Comment: ICML 2023 OralPoster; 22 page

How Jellyfish Characterise Alternating Group Equivariant Neural Networks

We provide a full characterisation of all of the possible alternating group ($A_n$) equivariant neural networks whose layers are some tensor power of $\mathbb{R}^{n}$. In particular, we find a basis of matrices for the learnable, linear, $A_n$-equivariant layer functions between such tensor power spaces in the standard basis of $\mathbb{R}^{n}$. We also describe how our approach generalises to the construction of neural networks that are equivariant to local symmetries.Comment: ICML 2023 Poster; 13 pages. arXiv admin note: text overlap with arXiv:2212.08648, arXiv:2212.0863

Metabolic control of dendritic cell activation and function: Recent advances and clinical implications

Dendritic cells (DCs) are key regulators of both immunity and tolerance by controlling activation and polarization of effector T helper cell and regulatory T cell responses. Therefore, there is a major focus on developing approaches to manipulate DC function for immunotherapy. It is well known that changes in cellular activation are coupled to profound changes in cellular metabolism. Over the past decade there is a growing appreciation that these metabolic changes also underlie the capacity of immune cells to perform particular functions. This has led to the concept that the manipulation of cellular metabolism can be used to shape innate and adaptive immune responses. While most of our understanding in this area has been gained from studies with T cells and macrophages, evidence is emerging that the activation and function of DCs are also dictated by the type of metabolism these cells commit to. We here discuss these new insights and explore whether targeting of metabolic pathways in DCs could hold promise as a novel approach to manipulate the functional properties of DCs for clinical purposes

The Mx/G/1 queue with queue length dependent service times

We deal with the MX/G/1 queue where service times depend on the queue length at the service initiation. By using Markov renewal theory, we derive the queue length distribution at departure epochs. We also obtain the transient queue length distribution at time t and its limiting distribution and the virtual waiting time distribution. The numerical results for transient mean queue length and queue length distributions are given.Bong Dae Choi, Yeong Cheol Kim, Yang Woo Shin, and Charles E. M. Pearc

Phylogenetic relationships of the Wolbachia of nematodes and arthropods

Wolbachia are well known as bacterial symbionts of arthropods, where they are reproductive parasites, but have also been described from nematode hosts, where the symbiotic interaction has features of mutualism. The majority of arthropod Wolbachia belong to clades A and B, while nematode Wolbachia mostly belong to clades C and D, but these relationships have been based on analysis of a small number of genes. To investigate the evolution and relationships of Wolbachia symbionts we have sequenced over 70 kb of the genome of wOvo, a Wolbachia from the human-parasitic nematode Onchocerca volvulus, and compared the genes identified to orthologues in other sequenced Wolbachia genomes. In comparisons of conserved local synteny, we find that wBm, from the nematode Brugia malayi, and wMel, from Drosophila melanogaster, are more similar to each other than either is to wOvo. Phylogenetic analysis of the protein-coding and ribosomal RNA genes on the sequenced fragments supports reciprocal monophyly of nematode and arthropod Wolbachia. The nematode Wolbachia did not arise from within the A clade of arthropod Wolbachia, and the root of the Wolbachia clade lies between the nematode and arthropod symbionts. Using the wOvo sequence, we identified a lateral transfer event whereby segments of the Wolbachia genome were inserted into the Onchocerca nuclear genome. This event predated the separation of the human parasite O. volvulus from its cattle-parasitic sister species, O. ochengi. The long association between filarial nematodes and Wolbachia symbionts may permit more frequent genetic exchange between their genomes

Western Distribution of Platanus occidentalis L. in Oklahoma

Determine the Western Distribution of Platanus occidentalis L. in Oklahoma. This was accomplished by making trips into Love, Carter, Murray, Garvin, McClain, Cleveland, Pontotoc, Seminole, Pottawatomine, Lincolin, Logan, Payne, Pawnee, Kay, and Grant Counties. Collections were made to verify the location. A distribution map of plant collected and they are on deposit in the Bebb Herbarium of the University of Oklahoma. A study was made of the unpublished Paper of the Ecology of the Bottomland of Oklahoma by Rice (1962). P. occidentalis L. are found along most of the creeks and rivers in the eastern half of the counties above. More abundant growth is along larger and wider creeks and rivers in the counties mentioned. P. ocddentalis L. are found growing with other species of trees. Few young trees were found in the narrow creeks. More trees were growing on limestone soils. P. occidentalis L. are found to be more abundant to the east of the distribution found in this paper.Natural Scienc

Classical and Quantum Imaging and Metrology Using Far Field Radiation

In this thesis I examine how the statistical properties of radiation limit our ability to perform imaging and metrological procedures. In particular I focus on radiation in the far field zone of the source. The classical and quantum theories of parameter estimation are introduced and subsequently utilised throughout, along with the theory of optical coherence. Classical and quantum imaging protocols are examined with the aid of a resolution criterion and the criterion is shown to reproduce the results of previous works. This method is also extended to previously un-investigated situations and the effect of imperfect measurements is explored. Intensity correlation measurements are investigated in great detail and for the first time a rigorous comparison is made between higher-order intensity correlation measurements of the type introduced by Hanbury Brown and Twiss. The importance of considering covariances in intensity correlation data is demonstrated and I give a full, detailed account of how to include this in the formulation. I also show how the optimal arrangement for an intensity correlation measurement can be found, therefore allowing the best precision in parameter estimation to be achieved. A quantum mechanical description of blackbody radiation is used to examine the state arriving at a detector in the far field. By using the quantum Fisher information an interesting connection is found between the statistical independence of photons in the source plane and the acquisition of information in the far field