Riemannian Gaussian distributions on the space of positive-definite quaternion matrices

Recently, Riemannian Gaussian distributions were defined on spaces of positive-definite real and complex matrices. The present paper extends this definition to the space of positive-definite quaternion matrices. In order to do so, it develops the Riemannian geometry of the space of positive-definite quaternion matrices, which is shown to be a Riemannian symmetric space of non-positive curvature. The paper gives original formulae for the Riemannian metric of this space, its geodesics, and distance function. Then, it develops the theory of Riemannian Gaussian distributions, including the exact expression of their probability density, their sampling algorithm and statistical inference.Comment: 8 pages, submitted to GSI 201

Decompounding on compact Lie groups

Noncommutative harmonic analysis is used to solve a nonparametric estimation problem stated in terms of compound Poisson processes on compact Lie groups. This problem of decompounding is a generalization of a similar classical problem. The proposed solution is based on a char- acteristic function method. The treated problem is important to recent models of the physical inverse problem of multiple scattering.Comment: 26 pages, 3 figures, 25 reference

Positron emission tomography imaging of endometrial cancer using engineered anti-EMP2 antibody fragments.

PurposeAs imaging of the cell surface tetraspan protein epithelial membrane protein-2 (EMP2) expression in malignant tumors may provide important prognostic and predictive diagnostic information, the goal of this study is to determine if antibody fragments to EMP2 may be useful for imaging EMP2 positive tumors.ProceduresThe normal tissue distribution of EMP2 protein expression was evaluated by immunohistochemistry and found to be discretely expressed in both mouse and human tissues. To detect EMP2 in tumors, a recombinant human anti-EMP2 minibody (scFv-hinge-C(H)3 dimer; 80 kDa) was designed to recognize a common epitope in mice and humans and characterized. In human tumor cell lines, the antibody binding induced EMP2 internalization and degradation, prompting the need for a residualizing imaging strategy. Following conjugation to DOTA (1,4,7,10-tetraazacyclododecane-N,N',N',N'″-tetraacetic acid), the minibody was radiolabeled with (64)Cu (t (1/2) = 12.7 h) and evaluated in mice as a positron emission tomography (PET) imaging agent for human EMP2-expressing endometrial tumor xenografts.ResultsThe residualizing agent, (64)Cu-DOTA anti-EMP2 minibody, achieved high uptake in endometrial cancer xenografts overexpressing EMP2 (10.2 ± 2.6, percent injected dose per gram (%ID/g) ± SD) with moderate uptake in wild-type HEC1A tumors (6.0 ± 0.1). In both cases, precise tumor delineation was observed from the PET images. In contrast, low uptake was observed with anti-EMP2 minibodies in EMP2-negative tumors (1.9 ± 0.5).ConclusionsThis new immune-PET agent may be useful for preclinical assessment of anti-EMP2 targeting in vivo. It may also have value for imaging of tumor localization and therapeutic response in patients with EMP2-positive malignancies

Biotin Supplementation Ameliorates Murine Colitis by Preventing NF-κB Activation.

Background & aimsBiotin is a water-soluble vitamin that is indispensable for human health. Biotin deficiency can cause failure-to-thrive, immunodeficiency, alopecia, dermatitis, and conjunctivitis. We previously reported that biotin deficiency also can lead to severe colitis in mice, which is completely reversed with supplementation. Our aim in this study was to determine if high-dose biotin supplementation can provide a therapeutic benefit in a preclinical model for inflammatory bowel disease (IBD) and to identify the molecular mechanism by which this occurs.MethodsMice were challenged with dextran sodium sulfate to induce colitis and were treated with 1 mmol/L biotin to induce or maintain remission. Clinical response was monitored by the Disease Activity Index and fecal calprotectin levels. The colon tissue was investigated for histology, length, as well as expression of inflammatory cytokines (interleukin 6, tumor necrosis factor-α, interleukin 1β), intestinal permeability, tight junctions (zonula occludens-1 and claudin-2), and the transcription factor nuclear factor-κB (NF-κB).ResultsBiotin therapy led to delayed onset and severity of colitis as well as accelerated healing. There was improvement in the Disease Activity Index, fecal calprotectin levels, colon length, and histology. In addition, biotin-treated mice had reduced expression of inflammatory cytokines, reduced intestinal permeability, and reduced activation of NF-κB.ConclusionsOral supplementation with biotin provides benefit for maintenance and induction of remission in the dextran sodium sulfate preclinical model for IBD. Biotin does this by reducing the activation of NF-κB, which prevents the production of inflammatory cytokines and helps maintain the integrity of the intestinal barrier. Clinically, the NF-κB pathway is important in the development of IBD and this finding suggests that biotin may have therapeutic potential for patients with IBD

Autonomous Calibration of Single Spin Qubit Operations

Fully autonomous precise control of qubits is crucial for quantum information processing, quantum communication, and quantum sensing applications. It requires minimal human intervention on the ability to model, to predict and to anticipate the quantum dynamics [1,2], as well as to precisely control and calibrate single qubit operations. Here, we demonstrate single qubit autonomous calibrations via closed-loop optimisations of electron spin quantum operations in diamond. The operations are examined by quantum state and process tomographic measurements at room temperature, and their performances against systematic errors are iteratively rectified by an optimal pulse engineering algorithm. We achieve an autonomous calibrated fidelity up to 1.00 on a time scale of minutes for a spin population inversion and up to 0.98 on a time scale of hours for a Hadamard gate within the experimental error of 2%. These results manifest a full potential for versatile quantum nanotechnologies.Comment: 9 pages, 5 figure

Hidden Markov chains and fields with observations in Riemannian manifolds

Hidden Markov chain, or Markov field, models, with observations in a Euclidean space, play a major role across signal and image processing. The present work provides a statistical framework which can be used to extend these models, along with related, popular algorithms (such as the Baum-Welch algorithm), to the case where the observations lie in a Riemannian manifold. It is motivated by the potential use of hidden Markov chains and fields, with observations in Riemannian manifolds, as models for complex signals and images.Comment: accepted for publication at MTNS 202