Computing normalisers of highly intransitive groups

We investigate the normaliser problem, that is, given , ≤ ₙ, compute [sub](). The fastest known theoretical algorithm for this problem is simply exponential, but more efficient algorithms are known for some restriction of classes for and . In this thesis, we will focus on highly intransitive groups, which are groups with many orbits. We give new algorithms to compute [sub](ₙ)() for highly intransitive groups ≤ ₙ and for some subclasses that perform substantially faster than previous implementations in the computer algebra system GAP."This work was supported by the University of St Andrews (School of Computer Science and St Leonard’s College Scholarship)." -- Fundin

Computing normalisers of intransitive groups

Funding: The first and third authors would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme “Groups, Representations and Applications: New perspectives”, where work on this paper was undertaken. This work was supported by EPSRC grant no EP/R014604/1. This work was also partially supported by a grant from the Simons Foundation. The first and second authors are supported by the Royal Society (RGF\EA\181005 and URF\R\180015).The normaliser problem takes as input subgroups G and H of the symmetric group Sn, and asks one to compute NG(H). The fastest known algorithm for this problem is simply exponential, whilst more efficient algorithms are known for restricted classes of groups. In this paper, we will focus on groups with many orbits. We give a new algorithm for the normaliser problem for these groups that performs many orders of magnitude faster than previous implementations in GAP. We also prove that the normaliser problem for the special case G=Sn  is at least as hard as computing the group of monomial automorphisms of a linear code over any field of fixed prime order.Publisher PDFPeer reviewe

Structural Modeling and Biochemical Characterization of Recombinant KPN_02809, a Zinc-Dependent Metalloprotease from Klebsiella pneumoniae MGH 78578

Klebsiella pneumoniae is a Gram-negative, cylindrical rod shaped opportunistic pathogen that is found in the environment as well as existing as a normal flora in mammalian mucosal surfaces such as the mouth, skin, and intestines. Clinically it is the most important member of the family of Enterobacteriaceae that causes neonatal sepsis and nosocomial infections. In this work, a combination of protein sequence analysis, structural modeling and molecular docking simulation approaches were employed to provide an understanding of the possible functions and characteristics of a hypothetical protein (KPN_02809) from K. pneumoniae MGH 78578. The computational analyses showed that this protein was a metalloprotease with zinc binding motif, HEXXH. To verify this result, a ypfJ gene which encodes for this hypothetical protein was cloned from K. pneumoniae MGH 78578 and the protein was overexpressed in Escherichia coli BL21 (DE3). The purified protein was about 32 kDa and showed maximum protease activity at 30 °C and pH 8.0. The enzyme activity was inhibited by metalloprotease inhibitors such as EDTA, 1,10-phenanthroline and reducing agent, 1,4-dithiothreitol (DTT). Each molecule of KPN_02809 protein was also shown to bind one zinc ion. Hence, for the first time, we experimentally confirmed that KPN_02809 is an active enzyme with zinc metalloprotease activity

Impact of COVID-19 on cardiovascular testing in the United States versus the rest of the world

Objectives: This study sought to quantify and compare the decline in volumes of cardiovascular procedures between the United States and non-US institutions during the early phase of the coronavirus disease-2019 (COVID-19) pandemic. Background: The COVID-19 pandemic has disrupted the care of many non-COVID-19 illnesses. Reductions in diagnostic cardiovascular testing around the world have led to concerns over the implications of reduced testing for cardiovascular disease (CVD) morbidity and mortality. Methods: Data were submitted to the INCAPS-COVID (International Atomic Energy Agency Non-Invasive Cardiology Protocols Study of COVID-19), a multinational registry comprising 909 institutions in 108 countries (including 155 facilities in 40 U.S. states), assessing the impact of the COVID-19 pandemic on volumes of diagnostic cardiovascular procedures. Data were obtained for April 2020 and compared with volumes of baseline procedures from March 2019. We compared laboratory characteristics, practices, and procedure volumes between U.S. and non-U.S. facilities and between U.S. geographic regions and identified factors associated with volume reduction in the United States. Results: Reductions in the volumes of procedures in the United States were similar to those in non-U.S. facilities (68% vs. 63%, respectively; p = 0.237), although U.S. facilities reported greater reductions in invasive coronary angiography (69% vs. 53%, respectively; p < 0.001). Significantly more U.S. facilities reported increased use of telehealth and patient screening measures than non-U.S. facilities, such as temperature checks, symptom screenings, and COVID-19 testing. Reductions in volumes of procedures differed between U.S. regions, with larger declines observed in the Northeast (76%) and Midwest (74%) than in the South (62%) and West (44%). Prevalence of COVID-19, staff redeployments, outpatient centers, and urban centers were associated with greater reductions in volume in U.S. facilities in a multivariable analysis. Conclusions: We observed marked reductions in U.S. cardiovascular testing in the early phase of the pandemic and significant variability between U.S. regions. The association between reductions of volumes and COVID-19 prevalence in the United States highlighted the need for proactive efforts to maintain access to cardiovascular testing in areas most affected by outbreaks of COVID-19 infection

Disjoint direct product decompositions of permutation groups

Let H ≤ Sn be an intransitive group with orbits Ω1, Ω2, ... , Ωk. Then certainly H is a subdirect product of the direct product of its projections on each orbit, H|Ω1 x H|Ω2 x ... x H|Ωk. Here we provide a polynomial time algorithm for computing the finest partition P of the H-orbits such that H = Πc∈P H|c and we demonstrate its usefulness in some applications

Disjoint direct product decompositions of permutation groups

Funding: The first author is supported by an Engineering and Physical Sciences Research Council grant (EP/P015638/1). The second author is supported by a Royal Society University Research Fellowship (URF\R\180015).Let H ≤ Sn be an intransitive group with orbits Ω1, Ω2, ... , Ωk. Then certainly H is a subdirect product of the direct product of its projections on each orbit, H|Ω1 x H|Ω2 x ... x H|Ωk. Here we provide a polynomial time algorithm for computing the finest partition P of the H-orbits such that H = Πc∈P H|c and we demonstrate its usefulness in some applications.PostprintPeer reviewe

Primitive normalisers in quasipolynomial time

Funding: The first author is supported by a Royal Society grant (RGF\EA\181005).The normaliser problem has as input two subgroups H and K of the symmetric group Sn, and asks for a generating set for NK(H): it is not known to have a subexponential time solution. It is proved in [Roney-Dougal & Siccha, 2020] that if H is primitive then the normaliser problem can be solved in quasipolynomial time. We show that for all subgroups H and K of Sn, in quasipolynomial time we can decide whether NSn(H) is primitive, and if so compute NK(H). Hence we reduce the question of whether one can solve the normaliser problem in quasipolynomial time to the case where the normaliser in Sn is known not to be primitive.Publisher PDFPeer reviewe