Constructing flag-transitive, point-imprimitive designs

We give a construction of a family of designs with a specified point-partition and determine the subgroup of automorphisms leaving invariant the point-partition. We give necessary and sufficient conditions for a design in the family to possess a flag-transitive group of automorphisms preserving the specified point-partition. We give examples of flag-transitive designs in the family, including a new symmetric 2-(1408,336,80) design with automorphism group 2^12:((3⋅M22):2) and a construction of one of the families of the symplectic designs (the designs S^−(n) ) exhibiting a flag-transitive, point-imprimitive automorphism group.PostprintPeer reviewe

A single-photon sampling architecture for solid-state imaging

Advances in solid-state technology have enabled the development of silicon photomultiplier sensor arrays capable of sensing individual photons. Combined with high-frequency time-to-digital converters (TDCs), this technology opens up the prospect of sensors capable of recording with high accuracy both the time and location of each detected photon. Such a capability could lead to significant improvements in imaging accuracy, especially for applications operating with low photon fluxes such as LiDAR and positron emission tomography. The demands placed on on-chip readout circuitry imposes stringent trade-offs between fill factor and spatio-temporal resolution, causing many contemporary designs to severely underutilize the technology's full potential. Concentrating on the low photon flux setting, this paper leverages results from group testing and proposes an architecture for a highly efficient readout of pixels using only a small number of TDCs, thereby also reducing both cost and power consumption. The design relies on a multiplexing technique based on binary interconnection matrices. We provide optimized instances of these matrices for various sensor parameters and give explicit upper and lower bounds on the number of TDCs required to uniquely decode a given maximum number of simultaneous photon arrivals. To illustrate the strength of the proposed architecture, we note a typical digitization result of a 120x120 photodiode sensor on a 30um x 30um pitch with a 40ps time resolution and an estimated fill factor of approximately 70%, using only 161 TDCs. The design guarantees registration and unique recovery of up to 4 simultaneous photon arrivals using a fast decoding algorithm. In a series of realistic simulations of scintillation events in clinical positron emission tomography the design was able to recover the spatio-temporal location of 98.6% of all photons that caused pixel firings.Comment: 24 pages, 3 figures, 5 table

On partitions of finite vector spaces of low dimension over GF(2)

AbstractLet Vn(q) denote a vector space of dimension n over the field with q elements. A set P of subspaces of Vn(q) is a partition of Vn(q) if every nonzero vector in Vn(q) is contained in exactly one subspace of P. If there exists a partition of Vn(q) containing ai subspaces of dimension ni for 1≤i≤k, then (ak,ak−1,…,a1) must satisfy the Diophantine equation ∑i=1kai(qni−1)=qn−1. In general, however, not every solution of this Diophantine equation corresponds to a partition of Vn(q). In this article, we determine all solutions of the Diophantine equation for which there is a corresponding partition of Vn(2) for n≤7 and provide a construction of each of the partitions that exist

Projection pursuit for discrete data

This paper develops projection pursuit for discrete data using the discrete Radon transform. Discrete projection pursuit is presented as an exploratory method for finding informative low dimensional views of data such as binary vectors, rankings, phylogenetic trees or graphs. We show that for most data sets, most projections are close to uniform. Thus, informative summaries are ones deviating from uniformity. Syllabic data from several of Plato's great works is used to illustrate the methods. Along with some basic distribution theory, an automated procedure for computing informative projections is introduced.Comment: Published in at http://dx.doi.org/10.1214/193940307000000482 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Selected Papers in Combinatorics - a Volume Dedicated to R.G. Stanton

Professor Stanton has had a very illustrious career. His contributions to mathematics are varied and numerous. He has not only contributed to the mathematical literature as a prominent researcher but has fostered mathematics through his teaching and guidance of young people, his organizational skills and his publishing expertise. The following briefly addresses some of the areas where Ralph Stanton has made major contributions