Quotients of Bounded Natural Functors

The functorial structure of type constructors is the foundation for many definition and proof principles in higher-order logic (HOL). For example, inductive and coinductive datatypes can be built modularly from bounded natural functors (BNFs), a class of well-behaved type constructors. Composition, fixpoints, and, under certain conditions, subtypes are known to preserve the BNF structure. In this article, we tackle the preservation question for quotients, the last important principle for introducing new types in HOL. We identify sufficient conditions under which a quotient inherits the BNF structure from its underlying type. Surprisingly, lifting the structure in the obvious manner fails for some quotients, a problem that also affects the quotients of polynomial functors used in the Lean proof assistant. We provide a strictly more general lifting scheme that supports such problematic quotients. We extend the Isabelle/HOL proof assistant with a command that automates the registration of a quotient type as a BNF, reducing the proof burden on the user from the full set of BNF axioms to our inheritance conditions. We demonstrate the command's usefulness through several case studies.Comment: Extended version of homonymous IJCAR 2020 pape

Quotients of Bounded Natural Functors

The functorial structure of type constructors is the foundation for many definition and proof principles in higher-order logic (HOL). For example, inductive and coinductive datatypes can be built modularly from bounded natural functors (BNFs), a class of well-behaved type constructors. Composition, fixpoints, and, under certain conditions, subtypes are known to preserve the BNF structure. In this article, we tackle the preservation question for quotients, the last important principle for introducing new types in HOL. We identify sufficient conditions under which a quotient inherits the BNF structure from its underlying type. Surprisingly, lifting the structure in the obvious manner fails for some quotients, a problem that also affects the quotients of polynomial functors used in the Lean proof assistant. We provide a strictly more general lifting scheme that supports such problematic quotients. We extend the Isabelle/HOL proof assistant with a command that automates the registration of a quotient type as a BNF, reducing the proof burden on the user from the full set of BNF axioms to our inheritance conditions. We demonstrate the command's usefulness through several case studies

Automated DNA mutation detection using universal conditions direct sequencing: application to ten muscular dystrophy genes

<p>Abstract</p> <p>Background</p> <p>One of the most common and efficient methods for detecting mutations in genes is PCR amplification followed by direct sequencing. Until recently, the process of designing PCR assays has been to focus on individual assay parameters rather than concentrating on matching conditions for a set of assays. Primers for each individual assay were selected based on location and sequence concerns. The two primer sequences were then iteratively adjusted to make the individual assays work properly. This generally resulted in groups of assays with different annealing temperatures that required the use of multiple thermal cyclers or multiple passes in a single thermal cycler making diagnostic testing time-consuming, laborious and expensive.</p> <p>These factors have severely hampered diagnostic testing services, leaving many families without an answer for the exact cause of a familial genetic disease. A search of GeneTests for sequencing analysis of the entire coding sequence for genes that are known to cause muscular dystrophies returns only a small list of laboratories that perform comprehensive gene panels.</p> <p>The hypothesis for the study was that a complete set of universal assays can be designed to amplify and sequence any gene or family of genes using computer aided design tools. If true, this would allow automation and optimization of the mutation detection process resulting in reduced cost and increased throughput.</p> <p>Results</p> <p>An automated process has been developed for the detection of deletions, duplications/insertions and point mutations in any gene or family of genes and has been applied to ten genes known to bear mutations that cause muscular dystrophy: DMD; CAV3; CAPN3; FKRP; TRIM32; LMNA; SGCA; SGCB; SGCG; SGCD. Using this process, mutations have been found in five DMD patients and four LGMD patients (one in the FKRP gene, one in the CAV3 gene, and two likely causative heterozygous pairs of variations in the CAPN3 gene of two other patients). Methods and assay sequences are reported in this paper.</p> <p>Conclusion</p> <p>This automated process allows laboratories to discover DNA variations in a short time and at low cost.</p

Measurement of the electroweak production of dijets in association with a Z-boson and distributions sensitive to vector boson fusion in proton-proton collisions at √s = 8 TeV using the ATLAS detector

Measurements of fiducial cross sections for the electroweak production of two jets in association with a Z-boson are presented. The measurements are performed using 20.3 fb−1 of proton-proton collision data collected at a centre-of-mass energy of p s = 8TeV by the ATLAS experiment at the Large Hadron Collider. The electroweak component is extracted by a fit to the dijet invariant mass distribution in a fiducial region chosen to enhance the electroweak contribution over the dominant background in which the jets are produced via the strong interaction. The electroweak cross sections measured in two fiducial regions are in good agreement with the Standard Model expectations and the background-only hypothesis is rejected with significance above the 5ơ level. The electroweak process includes the vector boson fusion production of a Z-boson and the data are used to place limits on anomalous triple gauge boson couplings. In addition, measurements of cross sections and differential distributions for inclusive Z-boson-plus-dijet production are performed in five fiducial regions, each with different sensitivity to the electroweak contribution. The results are corrected for detector effects and compared to predictions from the Sherpa and Powheg event generators

Search for nonpointing and delayed photons in the diphoton and missing transverse momentum final state in 8 TeV pp collisions at the LHC using the ATLAS detector

A search has been performed, using the full 20.3  fb −1 data sample of 8 TeV proton-proton collisions collected in 2012 with the ATLAS detector at the LHC, for photons originating from a displaced vertex due to the decay of a neutral long-lived particle into a photon and an invisible particle. The analysis investigates the diphoton plus missing transverse momentum final state, and is therefore most sensitive to pair production of long-lived particles. The analysis technique exploits the capabilities of the ATLAS electromagnetic calorimeter to make precise measurements of the flight direction, as well as the time of flight, of photons. No excess is observed over the Standard Model predictions for background. Exclusion limits are set within the context of gauge mediated supersymmetry breaking models, with the lightest neutralino being the next-to-lightest supersymmetric particle and decaying into a photon and gravitino with a lifetime in the range from 250 ps to about 100 ns

Search for pair and single production of new heavy quarks that decay to a ℤ boson and a third-generation quark in pp collisions at √ s=8 TeV with the ATLAS detector

A search is presented for the production of new heavy quarks that decay to a Z boson and a third-generation Standard Model quark. In the case of a new charge +2/3 quark (T), the decay targeted is T → Zt, while the decay targeted for a new charge −1/3 quark (B) is B → Zb. The search is performed with a dataset corresponding to 20.3 fb−1 of pp collisions at √ s = 8TeV recorded in 2012 with the ATLAS detector at the CERN Large Hadron Collider. Selected events contain a high transverse momentum Z boson candidate reconstructed from a pair of oppositely charged same-flavor leptons (electrons or muons), and are analyzed in two channels defined by the absence or presence of a third lepton. Hadronic jets, in particular those with properties consistent with the decay of a b-hadron, are also required to be present in selected events. Different requirements are made on the jet activity in the event in order to enhance the sensitivity to either heavy quark pair production mediated by the strong interaction, or single production mediated by the electroweak interaction. No significant excess of events above the Standard Model expectation is observed, and lower limits are derived on the mass of vector-like T and B quarks under various branching ratio hypotheses, as well as upper limits on the agnitude of electroweak coupling parameters

Waveguide-Based Biosensors for Pathogen Detection

Optical phenomena such as fluorescence, phosphorescence, polarization, interference and non-linearity have been extensively used for biosensing applications. Optical waveguides (both planar and fiber-optic) are comprised of a material with high permittivity/high refractive index surrounded on all sides by materials with lower refractive indices, such as a substrate and the media to be sensed. This arrangement allows coupled light to propagate through the high refractive index waveguide by total internal reflection and generates an electromagnetic wave—the evanescent field—whose amplitude decreases exponentially as the distance from the surface increases. Excitation of fluorophores within the evanescent wave allows for sensitive detection while minimizing background fluorescence from complex, “dirty” biological samples. In this review, we will describe the basic principles, advantages and disadvantages of planar optical waveguide-based biodetection technologies. This discussion will include already commercialized technologies (e.g., Corning’s EPIC® Ô, SRU Biosystems’ BIND™, Zeptosense®, etc.) and new technologies that are under research and development. We will also review differing assay approaches for the detection of various biomolecules, as well as the thin-film coatings that are often required for waveguide functionalization and effective detection. Finally, we will discuss reverse-symmetry waveguides, resonant waveguide grating sensors and metal-clad leaky waveguides as alternative signal transducers in optical biosensing

Search for the lepton flavor violating decay Z→eμ in pp collisions at √s =8 TeV with the ATLAS detector

The ATLAS detector at the Large Hadron Collider is used to search for the lepton flavor violating process Z→eμ in pp collisions using 20.3  fb −1 of data collected at s √ =8  TeV . An enhancement in the eμ invariant mass spectrum is searched for at the Z -boson mass. The number of Z bosons produced in the data sample is estimated using events of similar topology, Z→ee and μμ , significantly reducing the systematic uncertainty in the measurement. There is no evidence of an enhancement at the Z -boson mass, resulting in an upper limit on the branching fraction, B(Z→eμ)<7.5×10 −7 at the 95% confidence level