Algebraic approach to q-deformed supersymmetric variants of the Hubbard model with pair hoppings

We construct two quantum spin chains Hamiltonians with quantum sl(2|1) invariance. These spin chains define variants of the Hubbard model and describe electron models with pair hoppings. A cubic algebra that admits the Birman-Wenzl-Murakami algebra as a quotient allows exact solvability of the periodic chain. The two Hamiltonians, respectively built using the distinguished and the fermionic bases of U_q(sl(2|1)) differ only in the boundary terms. They are actually equivalent, but the equivalence is non local. Reflection equations are solved to get exact solvability on open chains with non trivial boundary conditions. Two families of diagonal solutions are found. The centre and the Scasimirs of the quantum enveloping algebra of sl(2|1) appear as tools for the construction of exactly solvable Hamiltonians.Comment: 22 pages, LaTeX2e, uses amsfonts; some references added and typos correcte

The Multivariate Resultant is NP-hard in any Characteristic

The multivariate resultant is a fundamental tool of computational algebraic geometry. It can in particular be used to decide whether a system of n homogeneous equations in n variables is satisfiable (the resultant is a polynomial in the system's coefficients which vanishes if and only if the system is satisfiable). In this paper we present several NP-hardness results for testing whether a multivariate resultant vanishes, or equivalently for deciding whether a square system of homogeneous equations is satisfiable. Our main result is that testing the resultant for zero is NP-hard under deterministic reductions in any characteristic, for systems of low-degree polynomials with coefficients in the ground field (rather than in an extension). We also observe that in characteristic zero, this problem is in the Arthur-Merlin class AM if the generalized Riemann hypothesis holds true. In positive characteristic, the best upper bound remains PSPACE.Comment: 13 page

A novel method of non-clinical dispatch is associated with a higher rate of critical Helicopter Emergency Medical Service intervention

Background - Helicopter Emergency Medical Services (HEMS) are a scarce resource that can provide advanced emergency medical care to unwell or injured patients. Accurate tasking of HEMS is required to incidents where advanced pre-hospital clinical care is needed. We sought to evaluate any association between non-clinically trained dispatchers, following a bespoke algorithm, compared with HEMS paramedic dispatchers with respect to incidents requiring a critical HEMS intervention. Methods - Retrospective analysis of prospectively collected data from two 12-month periods was performed (Period one: 1st April 2014 – 1st April 2015; Period two: 1st April 2016 – 1st April 2017). Period 1 was a Paramedic-led dispatch process. Period 2 was a non-clinical HEMS dispatcher assisted by a bespoke algorithm. Kent, Surrey & Sussex HEMS (KSS HEMS) is tasked to approximately 2500 cases annually and operates 24/7 across south-east England. The primary outcome measure was incidence of a HEMS intervention.Results - A total of 4703 incidents were included; 2510 in period one and 2184 in period two. Variation in tasking was reduced by introducing non-clinical dispatchers. There was no difference in median time from 999 call to HEMS activation between period one and two (period one; median 7 min (IQR 4–17) vs period two; median 7 min (IQR 4–18). Non-clinical dispatch improved accuracy of HEMS tasking to a mission where a critical care intervention was required (OR 1.25, 95% CI 1.04–1.51, p = 0.02).Conclusion - The introduction of non-clinical, HEMS-specific dispatch, aided by a bespoke algorithm improved accuracy of HEMS tasking. Further research is warranted to explore where this model could be effective in other HEMS services.Peer reviewedFinal Published versio

Evaluation of a conditional knockout of Ikaros in peripheral T-cell differentiation into helper T-cell subsets

CD4 T helper (Th) cells differentiate into distinct effector or regulatory subsets as needed during the course of an infection. Ikaros is a transcription factor that is necessary for proper thymic T cell development. In order to study the role of Ikaros in peripheral CD4 T-cell differentiation and function, a novel Ikaros conditional knockout mouse in which Ikaros is deleted in mature T-cells (CKO mice) was developed. In this thesis, this model is characterized and used to evaluated how absence of Ikaros affects lymphocyte and myeloid populations in vivo, and CD4 T-cell differentiation into T helper 17 (Th17) and inducible regulatory T cell (iTreg) subsets in vitro. CKO mice had normal thymocyte development and normal percentages of T-cells and B-cells in the spleen. However, they had increased percentages of myeloid cells, and an abnormal population of "naive-like" CD4 T-cells that expressed low levels of CD62L and CD44, markers that identify naive and memory T cell populations. CKO CD4 T-cells cultured under Th17 polarizing conditions showed normal expression of the Th17 factors, RORγt and IL-17A, but overexpressed the pro-inflammatory factors T-bet, IFNγ and GM-CSF. CKO CD4 T-cells had a decreased ability to become iTregs as shown by significantly less Foxp3+ CD4+ T-cells in polarizing cultures, and overexpress T-bet, IFNγ and GM-CSF. Therefore, T-cells that lack Ikaros do not properly differentiate into either Th17 or iTreg lineages, but instead become cells with altered pro-inflammatory characteristics. In conclusion, the data highlights new roles of Ikaros in maintaining proper CD4 T-cell populations in the periphery and in suppressing abnormal pro-inflammatory responses

Florence speech falls short on the details of a bespoke arrangement with the EU

Theresa May stepped in to lead the discussion on what the UK hopes to achieve from its Brexit negotiations with the EU. Swati Dhingra and Josh De Lyon (CEP, LSE) argue that her Florence speech has set the tone for details that are yet to come. On trade, the PM reiterated that the UK would be outside the Single Market and the Customs Union after Brexit. ..

To recover from COVID and Brexit, the UK must upskill its workforce

The twin forces of COVID and Brexit are altering the skills that people require to succeed in work. Skill levels remain low in the UK, compared to other advanced nations. About 30% of adults have low skill levels in literacy and/or numeracy, putting the UK as 12th highest out of 29 OECD countries. Job-related education and training is the key pathway to upskilling and wage progression for adult workers, and one of the biggest components of intangible investments by firms. Josh De Lyon and Swati Dhingra explore ways to incentivise employers to invest in training