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John Murray

Publications and source records attributed to John Murray.

At least 19 recordsLinked to original sources
arXiv2026

Parallelobox: Improved Decomposition for Optimized Parallel Printing using Axis-Aligned Bounding Boxes

Much contemporary research in additive manufacturing focuses on breaking down models into constituent parts in the pursuit of various factors, such as printability of large models in smaller printing volumes, or reduction of support structures. Newer research has begun to focus on using these decomposition processes for printing models across multiple printers in parallel. We present a novel approach to this that incorporates axisaligned bounding boxes as height fields to improve the characteristics of decomposition, including printing time, feasibility, and aesthetics. By expanding these bounding boxes according to a parallel printing objective, with additional improved efficiency from a metaheuristic process, these boxes can then be used for rapid decomposition using simple out-of-the-box mesh clipping operations. This algorithm is experimentally evaluated across a range of models against two other contemporary approaches to parallel printing that use more rudimentary techniques, such as recursive symmetry and cube skeletonization. Parallelobox outperformed each of these across a range of sample models on the basis of a parallel printing time metric using simulated 3D printing to compute the results

cs.GR↗
arXiv2022

A solution to Brauer's Problem 14

It is well known that the number of real irreducible characters of a finite group G coincides with the number of real conjugacy classes of G. Richard Brauer has asked if the number of irreducible characters with Frobenius-Schur indicator 1 can also be expressed in group theoretical terms. We show that this can done by counting solutions of $g_1^2\ldots g_n^2=1$ with $g_1,\ldots,g_n\in G$.

math.RT↗
arXiv2020

Self-dual modules in characteristic two and normal subgroups

We prove Clifford theoretic results on the representations of finite groups which only hold in characteristic $2$. Let $G$ be a finite group, let $N$ be a normal subgroup of $G$ and let $\varphi$ be an irreducible $2$-Brauer character of $N$ which is self-dual. We prove that there is a unique self-dual irreducible Brauer character $\theta$ of $G$ such that $\varphi$ occurs with odd multiplicity in the restriction of $\theta$ to $N$. Moreover this multiplicity is $1$. Conversely if $\theta$ is an irreducible $2$-Brauer character of $G$ which is self-dual but not of quadratic type, the restriction of $\theta$ to $N$ is a sum of distinct self-dual irreducible Brauer character of $N$, none of which have quadratic type. Let $b$ be a real $2$-block of $N$. We show that there is a unique real $2$-block of $G$ covering $b$ which is weakly regular.

math.RT↗
arXiv2020

Causal Mediation Analysis with Multiple Treatments and Latent Confounders

Causal mediation analysis is used to evaluate direct and indirect causal effects of a treatment on an outcome of interest through an intermediate variable or a mediator.It is difficult to identify the direct and indirect causal effects because the mediator cannot be randomly assigned in many real applications. In this article, we consider a causal model including latent confounders between the mediator and the outcome. We present sufficient conditions for identifying the direct and indirect effects and propose an approach for estimating them. The performance of the proposed approach is evaluated by simulation studies. Finally, we apply the approach to a data set of the customer loyalty survey by a telecom company.

stat.AP↗
arXiv2019

Quantum Computing at the Frontiers of Biological Sciences

The search for meaningful structure in biological data has relied on cutting-edge advances in computational technology and data science methods. However, challenges arise as we push the limits of scale and complexity in biological problems. Innovation in massively parallel, classical computing hardware and algorithms continues to address many of these challenges, but there is a need to simultaneously consider new paradigms to circumvent current barriers to processing speed. Accordingly, we articulate a view towards quantum computation and quantum information science, where algorithms have demonstrated potential polynomial and exponential computational speedups in certain applications, such as machine learning. The maturation of the field of quantum computing, in hardware and algorithm development, also coincides with the growth of several collaborative efforts to address questions across length and time scales, and scientific disciplines. We use this coincidence to explore the potential for quantum computing to aid in one such endeavor: the merging of insights from genetics, genomics, neuroimaging and behavioral phenotyping. By examining joint opportunities for computational innovation across fields, we highlight the need for a common language between biological data analysis and quantum computing. Ultimately, we consider current and future prospects for the employment of quantum computing algorithms in the biological sciences.

quant-ph↗
arXiv2019

Frobenius-Schur indicators of characters in blocks with cyclic defect

Let $p$ be an odd prime and let $B$ be a $p$-block of a finite group which has cyclic defect groups. We show that all exceptional characters in $B$ have the same Frobenius-Schur indicators. Moreover the common indicator can be computed, using the canonical character of $B$. We also investigate the Frobenius-Schur indicators of the non-exceptional characters in $B$. For a finite group which has cyclic Sylow $p$-subgroups, we show that the number of irreducible characters with Frobenius-Schur indicator $-1$ is greater than or equal to the number of conjugacy classes of weakly real $p$-elements in $G$.

math.GR↗
arXiv2018

A bijection for Euler's partition theorem in the spirit of Bressoud

For each positive integer $n$, we construct a bijection between the odd partitions and the distinct partitions of $n$ which extends Bressoud's bijection between the odd-and-distinct partitions of $n$ and the splitting partitions of $n$. We compare our bijection with the classical bijections of Glaisher and Sylvester, and also with a recent bijection due to Chen, Gao, Ji and Li.

math.CO↗
arXiv2018

Quadratic principal indecomposable modules and strongly real elements of finite Groups

Let $P$ be a principal indecomposable module of a finite group $G$ in characteristic $2$ and let $\varphi$ be the Brauer character of the corresponding simple $G$-module. We show that $P$ affords a non-degenerate $G$-invariant quadratic form if and only if there are involutions $s,t\in G$ such that $st$ has odd order and $\varphi(st)/2$ is not an algebraic integer. We then show that the number of isomorphism classes of quadratic principal indecomposable $G$-modules is equal to the number of strongly real conjugacy classes of odd order elements of $G$.

math.RT↗
arXiv2017

Indecomposable symplectic $k(C_2\times C_2)$--modules and their quadratic forms

For the Klein-Four Group $G$ and a perfect field $k$ of characteristic two we determine all indecomposable symplectic $kG$-modules, that is, $kG$-modules with a symplectic, $G$-invariant form which do not decompose into smaller such modules, and classify them up to isometry. Also we determine all quadratic forms that have one of the above symplectic forms as their associated bilinear form and describe their isometry classes.

math.RT↗
arXiv2015

The Visible and Infrared Survey Telescope for Astronomy (VISTA): Design, Technical Overview and Performance

The Visible and Infrared Survey Telescope for Astronomy (VISTA) is the 4-metre wide-field survey telescope at ESO's Paranal Observatory, equipped with the world's largest near-infrared imaging camera (VISTA IR Camera, VIRCAM), with 1.65 degree diameter field of view, and 67 Mpixels giving 0.6 square degrees active pixel area, operating at wavelengths 0.8 - 2.3 microns. We provide a short history of the project, and an overview of the technical details of the full system including the optical design, mirrors, telescope structure, IR camera, active optics, enclosure and software. The system includes several innovative design features such as the f/1 primary mirror, the dichroic cold-baffle camera design and the sophisticated wavefront sensing system delivering closed-loop 5-axis alignment of the secondary mirror. We conclude with a summary of the delivered performance, and a short overview of the six ESO public surveys in progress on VISTA.

astro-ph.IM↗
arXiv2014

Linked determinantal loci and limit linear series

We study (a generalization of) the notion of linked determinantal loci recently introduced by the second author, showing that as with classical determinantal loci, they are Cohen-Macaulay whenever they have the expected codimension. We apply this to prove Cohen-Macaulayness and flatness for moduli spaces of limit linear series, and to prove a comparison result between the scheme structures of Eisenbud-Harris limit linear series and the spaces of limit linear series recently constructed by the second author. This comparison result is crucial in order to study the geometry of Brill-Noether loci via degenerations.

math.AG↗
arXiv2012

On a result of Kiyota, Okuyama and Wada

M. Kiyota, T. Okuyama and T. Wada recently proved that each 2-block of a finite symmetric group contains a unique irreducible Brauer character that has height 0. We present a more conceptual proof of this result.

math.GR↗
arXiv2008

Real Subpairs and Frobenius-Schur Indicators of Characters in 2-Blocks

Let B be a real 2-block of a finite group G. Then B has a real defect class. Let g be an element of such a class. A defect couple of B is (D,E), where E is a Sylow 2-subgroup of the extended centralizer C^*(g) of g, and D is the intersection of E with the centralizer C(g). It is known that (D,E) is uniquely determined up to G-conjugacy. We show that (D,E) determines which B-subpairs are real. We also outline how (D,E) influences the vertices of components of the G-permutation module corresponding to the conjugation action of G on its involutions. We apply these methods to enumerate the Frobenius-Schur indicators of the irreducible characters in a real block that has a dihedral defect group. We also determine the vertices of the components of the involution module in such a block.

math.RT↗
arXiv2007

Enhancing single-molecule photostability by optical feedback from quantum-jump detection

We report an optical technique that yields an enhancement of single-molecule photostability, by greatly suppressing photobleaching pathways which involve photoexcitation from the triplet state. This is accomplished by dynamically switching off the excitation laser when a quantum-jump of the molecule to the triplet state is optically detected. This procedure leads to a lengthened single-molecule observation time and an increased total number of detected photons. The resulting improvement in photostability unambiguously confirms the importance of photoexcitation from the triplet state in photobleaching dynamics, and may allow the investigation of new phenomena at the single-molecule level.

quant-ph↗