Rational solutions of the discrete time Toda lattice and the alternate discrete Painleve II equation

The Yablonskii-Vorob'ev polynomials $y_{n}(t)$, which are defined by a second order bilinear differential-difference equation, provide rational solutions of the Toda lattice. They are also polynomial tau-functions for the rational solutions of the second Painlev\'{e} equation ($P_{II}$). Here we define two-variable polynomials $Y_{n}(t,h)$ on a lattice with spacing $h$, by considering rational solutions of the discrete time Toda lattice as introduced by Suris. These polynomials are shown to have many properties that are analogous to those of the Yablonskii-Vorob'ev polynomials, to which they reduce when $h=0$. They also provide rational solutions for a particular discretisation of $P_{II}$, namely the so called {\it alternate discrete} $P_{II}$, and this connection leads to an expression in terms of the Umemura polynomials for the third Painlev\'{e} equation ($P_{III}$). It is shown that B\"{a}cklund transformation for the alternate discrete Painlev\'{e} equation is a symplectic map, and the shift in time is also symplectic. Finally we present a Lax pair for the alternate discrete $P_{II}$, which recovers Jimbo and Miwa's Lax pair for $P_{II}$ in the continuum limit $h\to 0$.Comment: 23 pages, IOP style. Title changed, and connection with Umemura polynomials adde

Integrable semi-discretization of the coupled nonlinear Schr\"{o}dinger equations

A system of semi-discrete coupled nonlinear Schr\"{o}dinger equations is studied. To show the complete integrability of the model with multiple components, we extend the discrete version of the inverse scattering method for the single-component discrete nonlinear Schr\"{o}dinger equation proposed by Ablowitz and Ladik. By means of the extension, the initial-value problem of the model is solved. Further, the integrals of motion and the soliton solutions are constructed within the framework of the extension of the inverse scattering method.Comment: 27 pages, LaTeX2e (IOP style

Introductory clifford analysis

In this chapter an introduction is given to Clifford analysis and the underlying Clifford algebras. The functions under consideration are defined on Euclidean space and take values in the universal real or complex Clifford algebra, the structure and properties of which are also recalled in detail. The function theory is centered around the notion of a monogenic function, which is a null solution of a generalized Cauchy–Riemann operator, which is rotation invariant and factorizes the Laplace operator. In this way, Clifford analysis may be considered as both a generalization to higher dimension of the theory of holomorphic functions in the complex plane and a refinement of classical harmonic analysis. A notion of monogenicity may also be associated with the vectorial part of the Cauchy–Riemann operator, which is called the Dirac operator; some attention is paid to the intimate relation between both notions. Since a product of monogenic functions is, in general, no longer monogenic, it is crucial to possess some tools for generating monogenic functions: such tools are provided by Fueter’s theorem on one hand and the Cauchy–Kovalevskaya extension theorem on the other hand. A corner stone in this function theory is the Cauchy integral formula for representation of a monogenic function in the interior of its domain of monogenicity. Starting from this representation formula and related integral formulae, it is possible to consider integral transforms such as Cauchy, Hilbert, and Radon transforms, which are important both within the theoretical framework and in view of possible applications

Allele-Specific Impairment of GJB2 Expression by GJB6 Deletion del(GJB6-D13S1854)

Mutations in the GJB2 gene, which encodes connexin 26, are a frequent cause of congenital non-syndromic sensorineural hearing loss. Two large deletions, del(GJB6-D13S1830) and del(GJB6-D13S1854), which truncate GJB6 (connexin 30), cause hearing loss in individuals homozygous, or compound heterozygous for these deletions or one such deletion and a mutation in GJB2. Recently, we have demonstrated that the del(GJB6-D13S1830) deletion contributes to hearing loss due to an allele-specific lack of GJB2 mRNA expression and not as a result of digenic inheritance, as was postulated earlier. In the current study we investigated the smaller del(GJB6-D13S1854) deletion, which disrupts the expression of GJB2 at the transcriptional level in a manner similar to the more common del(GJB6-D13S1830) deletion. Interestingly, in the presence of this deletion, GJB2 expression remains minimally but reproducibly present. The relative allele-specific expression of GJB2 was assessed by reverse-transcriptase PCR and restriction digestions in three probands who were compound heterozygous for a GJB2 mutation and del(GJB6-D13S1854). Each individual carried a different sequence variant in GJB2. All three individuals expressed the mutated GJB2 allele in trans with del(GJB6-D13S1854), but expression of the GJB2 allele in cis with the deletion was almost absent. Our study clearly corroborates the hypothesis that the del(GJB6-D13S1854), similar to the larger and more common del(GJB6-D13S1830), removes (a) putative cis-regulatory element(s) upstream of GJB6 and narrows down the region of location

Artificial drainage of peatlands: hydrological and hydrochemical process and wetland restoration

Peatlands have been subject to artificial drainage for centuries. This drainage has been in response to agricultural demand, forestry, horticultural and energy properties of peat and alleviation of flood risk. However, the are several environmental problems associated with drainage of peatlands. This paper describes the nature of these problems and examines the evidence for changes in hydrological and hydrochemical processes associated with these changes. Traditional black-box water balance approaches demonstrate little about wetland dynamics and therefore the science of catchment response to peat drainage is poorly understood. It is crucial that a more process-based approach be adopted within peatland ecosystems. The environmental problems associated with peat drainage have led, in part, to a recent reversal in attitudes to peatlands and we have seen a move towards wetland restoration. However, a detailed understanding of hydrological, hydrochemical and ecological process-interactions will be fundamental if we are to adequately restore degraded peatlands, preserve those that are still intact and understand the impacts of such management actions at the catchment scale

Biomarker Driven Antifungal Stewardship (BioDriveAFS) in acute leukaemia—a multi-centre randomised controlled trial to assess clinical and cost effectiveness: a study protocol for a randomised controlled trial

BACKGROUND: Acute leukaemias (AL) are life-threatening blood cancers that can be potentially cured with treatment involving myelosuppressive, multiagent, intensive chemotherapy (IC). However, such treatment is associated with a risk of serious infection, in particular invasive fungal infection (IFI) associated with prolonged neutropenia. Current practice guidelines recommend primary antifungal (AF) prophylaxis to be administered to high-risk patients to reduce IFI incidence. AFs are also used empirically to manage prolonged neutropenic fever. Current strategies lead to substantial overuse of AFs. Galactomannan (GM) and β-D-glucan (BG) biomarkers are also used to diagnose IFI. Combining both biomarkers may enhance the predictability of IFI compared to administering each test alone. Currently, no large-scale randomised controlled trial (RCT) has directly compared a biomarker-based diagnostic screening strategy without AF prophylaxis to AF prophylaxis (without systematic biomarker testing). METHODS: BioDriveAFS is a multicentre, parallel, two-arm RCT of 404 participants from UK NHS Haematology departments. Participants will be allocated on a 1:1 basis to receive either a biomarker-based antifungal stewardship (AFS) strategy, or a prophylactic AF strategy, which includes existing standard of care (SoC). The co-primary outcomes will be AF exposure in the 12-month post randomisation and the patient-reported EQ-5D-5L measured at 12-month post randomisation. Secondary outcomes will include total AF exposure, probable/proven IFI, survival (all-cause mortality and IFI mortality), IFI treatment outcome, AF-associated adverse effects/events/complications, resource use, episodes of neutropenic fever requiring hospital admission or outpatient management, AF resistance in fungi (non-invasive and invasive) and a Desirability of Outcome Ranking. The trial will have an internal pilot phase during the first 9 months. A mixed methods process evaluation will be integrated in parallel to the internal pilot phase and full trial, aiming to robustly assess how the intervention is delivered. Cost-effectiveness analysis will also be performed. DISCUSSION: The BioDriveAFS trial aims to further the knowledge of strategies that will safely optimise AF use through comparison of the clinical and cost-effectiveness of a biomarker-led diagnostic strategy versus prophylactic AF to prevent and manage IFI within acute leukaemia. The evidence generated from the study will help inform global clinical practice and approaches within antifungal stewardship. TRIAL REGISTRATION: ISRCTN11633399. Registered 24/06/2022

Field Longevity of a Fluorescent Protein Marker in an Engineered Strain of the Pink Bollworm, Pectinophora gossypiella (Saunders)

The cotton pest, pink bollworm (Pectinophora gossypiella (Saunders)), is a significant pest in most cotton-growing areas around the world. In southwestern USA and northern Mexico, pink bollworm is the target of the sterile insect technique (SIT), which relies on the mass-release of sterile pink bollworm adults to over-flood the wild population and thereby reduce it over time. Sterile moths reared for release are currently marked with a dye provided in their larval diet. There are concerns, however, that this marker fails from time to time, leading to sterile moths being misidentified in monitoring traps as wild moths. This can lead to expensive reactionary releases of sterile moths. We have developed a genetically marked strain that is engineered to express a fluorescent protein, DsRed2, which is easily screened under a specialised microscope. In order to test this marker under field conditions, we placed wild-type and genetically marked moths on traps and placed them in field cages. The moths were then screened, in a double-blind fashion, for DsRed2 fluorescence at regular intervals to determine marker reliability over time. The marker was shown to be robust in very high temperatures and generally proved reliable for a week or longer. More importantly, genotyping of moths on traps by PCR screening of the moths was 100% correct. Our findings indicate that this strain - and fluorescent protein markers in general - could make a valuable contribution to SIT

Teachers’ appraisals of adjectives relating to mathematics tasks

Curricular implementations are unlikely to deliver the anticipated benefits for mathematics learners if written guidance to teachers is interpreted and enacted differently from the ways that policymakers and curriculum designers intend. One way in which this could happen is in relation to the mathematics tasks that teachers deploy in the classroom. Teachers and curriculum designers have developed an extensive vocabulary for describing tasks, using adjectives such as ‘rich’, ‘open’, ‘real-life’, ‘engaging’ and so on. But do teachers have a shared understanding of what these adjectives mean when they are applied to mathematics tasks? In Study 1 we investigated teachers’ appraisals of adjectives used to describe mathematics tasks, finding that task appraisals vary on seven dimensions, which we termed engagement, demand, routineness, strangeness, inquiry, context and interactivity. In Study 2, focusing on the five most prominent dimensions, we investigated whether teachers have a shared understanding of the meaning of adjectives when applied to mathematics tasks. We found that there was some agreement about inquiry and context, some disagreement about routineness, and clear disagreement about engagement and demand. We conclude that at least some adjectives commonly used to describe tasks are interpreted very differently by different teachers. Implications for how tasks might be discussed meaningfully by teachers, teacher educators and curriculum designers are highlighted

Bacterial endosymbiont Cardinium cSfur genome sequence provides insights for understanding the symbiotic relationship in Sogatella furcifera host

Background: Sogatella furcifera is a migratory pest that damages rice plants and causes severe economic losses. Due to its ability to annually migrate long distances, S.furcifera has emerged as a major pest of rice in several Asian countries. Symbiotic relationships of inherited bacteria with terrestrial arthropods have significant implications. The genus Cardinium is present in many types of arthropods, where it influences some host characteristics. We present a report of a newly # identified strain of the bacterial endosymbiont Cardinium cSfur in S. furcifera. Result: From the whole genome of S. furcifera previously sequenced by our laboratory, we assembled the whole genome sequence of Cardinium cSfur. The sequence comprised 1,103,593 bp with a GC content of 39.2%. The phylogenetic tree of the Bacteroides phylum to which Cardinium cSfur belongs suggests that Cardinium cSfur is closely related to the other strains (Cardinium cBtQ1 and cEper1) that are members of the Amoebophilaceae family. Genome comparison between the host-dependent endosymbiont including Cardinium cSfur and freeliving bacteria revealed that the endosymbiont has a smaller genome size and lower GC content, and has lost some genes related to metabolism because of its special environment, which is similar to the genome pattern observed in other insect symbionts. Cardinium cSfur has limited metabolic capability, which makes it less contributive to metabolic and biosynthetic processes in its host. From our findings, we inferred that, to compensate for its limited metabolic capability, Cardinium cSfur harbors a relatively high proportion of transport proteins, which might act as the hub between it and its host. With its acquisition of the whole operon related to biotin synthesis and glycolysis related genes through HGT event, Cardinium cSfur seems to be undergoing changes while establishing a symbiotic relationship with its host. Conclusion: A novel bacterial endosymbiont strain (Cardinium cSfur) has been discovered. A genomic analysis of the endosymbiont in S. furcifera suggests that its genome has undergone certain changes to facilitate its settlement in the host. The envisaged potential reproduction manipulative ability of the new endosymbiont strain in its S. furcifera host has vital implications in designing eco-friendly approaches to combat the insect pest