Incorporating Student Response Systems in mathematics classes

In the past decade, Student Response Systems (SRS) have been used more widely in higher education as advancement in technology makes them more affordable, easier to use and of compact design. This technology shows potential in enhancing the student experience, especially in traditionally hard subjects like mathematics. Major reasons for introducing the technology into classrooms include positive student perception, anonymity, active teaching and learning and providing a natural break from straight content delivery. There remain issues related to the integration of the technology within mathematics courses - in particular related to the time required during lectures to successfully embed SRS without impinging too greatly on the delivery of the syllabus. In this study the appropriate number of questions that should be posed during a lecture is investigated, as is the time interval that should be permitted per question and when each question is posed. It has been suggested that SRS are not utilized effectively unless questions used provoke deep learning but this can be problematic and impact on endemic math anxiety regardless of anonymity. It is proposed that questions involving higher order thinking may be better explored within a tutorial environment using a Team Base Learning approach

Purely radiative perfect fluids

We study `purely radiative' (div E = div H = 0) and geodesic perfect fluids with non-constant pressure and show that the Bianchi class A perfect fluids can be uniquely characterized --modulo the class of purely electric and (pseudo-)spherically symmetric universes-- as those models for which the magnetic and electric part of the Weyl tensor and the shear are simultaneously diagonalizable. For the case of constant pressure the same conclusion holds provided one also assumes that the fluid is irrotational.Comment: 12 pages, minor grammatical change

Purely gravito-magnetic vacuum space-times

It is shown that there are no vacuum space-times (with or without cosmological constant) for which the Weyl-tensor is purely gravito-magnetic with respect to a normal and timelike congruence of observers.Comment: 4 page

Minimal tensors and purely electric or magnetic spacetimes of arbitrary dimension

We consider time reversal transformations to obtain twofold orthogonal splittings of any tensor on a Lorentzian space of arbitrary dimension n. Applied to the Weyl tensor of a spacetime, this leads to a definition of its electric and magnetic parts relative to an observer (i.e., a unit timelike vector field u), in any n. We study the cases where one of these parts vanishes in particular, i.e., purely electric (PE) or magnetic (PM) spacetimes. We generalize several results from four to higher dimensions and discuss new features of higher dimensions. We prove that the only permitted Weyl types are G, I_i and D, and discuss the possible relation of u with the WANDs; we provide invariant conditions that characterize PE/PM spacetimes, such as Bel-Debever criteria, or constraints on scalar invariants, and connect the PE/PM parts to the kinematic quantities of u; we present conditions under which direct product spacetimes (and certain warps) are PE/PM, which enables us to construct explicit examples. In particular, it is also shown that all static spacetimes are necessarily PE, while stationary spacetimes (e.g., spinning black holes) are in general neither PE nor PM. Ample classes of PE spacetimes exist, but PM solutions are elusive, and we prove that PM Einstein spacetimes of type D do not exist, for any n. Finally, we derive corresponding results for the electric/magnetic parts of the Riemann tensor. This also leads to first examples of PM spacetimes in higher dimensions. We also note in passing that PE/PM Weyl tensors provide examples of minimal tensors, and we make the connection hereof with the recently proved alignment theorem. This in turn sheds new light on classification of the Weyl tensors based on null alignment, providing a further invariant characterization that distinguishes the types G/I/D from the types II/III/N.Comment: 43 pages. v2: new proposition 4.10; some text reshuffled (former sec. 2 is now an appendix); references added; some footnotes cancelled, others incorporated into the main text; some typos fixed and a few more minor changes mad

On the classification of type D spacetimes

We give a classification of the type D spacetimes based on the invariant differential properties of the Weyl principal structure. Our classification is established using tensorial invariants of the Weyl tensor and, consequently, besides its intrinsic nature, it is valid for the whole set of the type D metrics and it applies on both, vacuum and non-vacuum solutions. We consider the Cotton-zero type D metrics and we study the classes that are compatible with this condition. The subfamily of spacetimes with constant argument of the Weyl eigenvalue is analyzed in more detail by offering a canonical expression for the metric tensor and by giving a generalization of some results about the non-existence of purely magnetic solutions. The usefulness of these results is illustrated in characterizing and classifying a family of Einstein-Maxwell solutions. Our approach permits us to give intrinsic and explicit conditions that label every metric, obtaining in this way an operational algorithm to detect them. In particular a characterization of the Reissner-Nordstr\"{o}m metric is accomplished.Comment: 29 pages, 0 figure

Gravito-electromagnetic analogies

We reexamine and further develop different gravito-electromagnetic (GEM) analogies found in the literature, and clarify the connection between them. Special emphasis is placed in two exact physical analogies: the analogy based on inertial fields from the so-called "1+3 formalism", and the analogy based on tidal tensors. Both are reformulated, extended and generalized. We write in both formalisms the Maxwell and the full exact Einstein field equations with sources, plus the algebraic Bianchi identities, which are cast as the source-free equations for the gravitational field. New results within each approach are unveiled. The well known analogy between linearized gravity and electromagnetism in Lorentz frames is obtained as a limiting case of the exact ones. The formal analogies between the Maxwell and Weyl tensors are also discussed, and, together with insight from the other approaches, used to physically interpret gravitational radiation. The precise conditions under which a similarity between gravity and electromagnetism occurs are discussed, and we conclude by summarizing the main outcome of each approach.Comment: 60 pages, 2 figures. Improved version (compared to v2) with some re-write, notation improvements and a new figure that match the published version; expanded compared to the published version to include Secs. 2.3 and

Mutations in DSTYK and dominant urinary tract malformations.

ABSTRACT Introduction Congenital abnormalities of the kidney of the urinary tract are the most common cause of pediatric kidney failure. These disorders are highly heterogeneous, and their etiology is poorly understood. Methods We performed genome-wide linkage analysis and whole-exome sequencing in a family with autosomal dominant congenital abnormalities of the kidney of the urinary tract (7 affected family members). We also performed sequence analysis in 311 unrelated patients, as well as histologic and functional studies. Results Linkage analysis identified five regions of the genome that were shared among all affected family members. Exome sequencing identified a single rare deleterious variant within these linkage intervals, a heterozygous splice-site mutation in dual serine/threonine and tyrosine protein kinase (DSTYK). This variant, which resulted in aberrant gene product splicing, was present in all affected family members. Additional independent DSTYK mutations, including nonsense and splice-site mutations, were detected among 7/311 unrelated patients. DSTYK is highly expressed in the maturing epithelia of all major organs, localizing to cell membranes. Knockdown in zebrafish resulted in multi-organ developmental defects, resembling loss of fibroblast growth factor (FGF) signaling. Consistent with this finding, DSTYK colocalizes with FGF receptors in the ureteric bud and metanephric mesenchyme. Finally, DSTYK knockdown in human embryonic kidney cells inhibited FGF-stimulated ERK-phosphorylation, the principal signal downstream of receptor tyrosine kinases. Conclusions We detected DSTYK mutations in 2.2% of patients with congenital abnormalities of the kidney and urinary tract whom we studied, suggesting that DSTYK is a major determinant of human urinary tract development, downstream of FGF signaling

Clinical and Functional Characterization of URAT1 Variants

Idiopathic renal hypouricaemia is an inherited form of hypouricaemia, associated with abnormal renal handling of uric acid. There is excessive urinary wasting of uric acid resulting in hypouricaemia. Patients may be asymptomatic, but the persistent urinary abnormalities may manifest as renal stone disease, and hypouricaemia may manifest as exercise induced acute kidney injury. Here we have identified Macedonian and British patients with hypouricaemia, who presented with a variety of renal symptoms and signs including renal stone disease, hematuria, pyelonephritis and nephrocalcinosis. We have identified heterozygous missense mutations in SLC22A12 encoding the urate transporter protein URAT1 and correlate these genetic findings with functional characterization. Urate handling was determined using uptake experiments in HEK293 cells. This data highlights the importance of the URAT1 renal urate transporter in determining serum urate concentrations and the clinical phenotypes, including nephrolithiasis, that should prompt the clinician to suspect an inherited form of renal hypouricaemia

Genetic drivers of kidney defects in the digeorge syndrome

BACKGROUND The DiGeorge syndrome, the most common of the microdeletion syndromes, affects multiple organs, including the heart, the nervous system, and the kidney. It is caused by deletions on chromosome 22q11.2; the genetic driver of the kidney defects is unknown. METHODS We conducted a genomewide search for structural variants in two cohorts: 2080 patients with congenital kidney and urinary tract anomalies and 22,094 controls. We performed exome and targeted resequencing in samples obtained from 586 additional patients with congenital kidney anomalies. We also carried out functional studies using zebrafish and mice. RESULTS We identified heterozygous deletions of 22q11.2 in 1.1% of the patients with congenital kidney anomalies and in 0.01% of population controls (odds ratio, 81.5; P = 4.5×1014). We localized the main drivers of renal disease in the DiGeorge syndrome to a 370-kb region containing nine genes. In zebrafish embryos, an induced loss of function in snap29, aifm3, and crkl resulted in renal defects; the loss of crkl alone was sufficient to induce defects. Five of 586 patients with congenital urinary anomalies had newly identified, heterozygous protein-Altering variants, including a premature termination codon, in CRKL. The inactivation of Crkl in the mouse model induced developmental defects similar to those observed in patients with congenital urinary anomalies. CONCLUSIONS We identified a recurrent 370-kb deletion at the 22q11.2 locus as a driver of kidney defects in the DiGeorge syndrome and in sporadic congenital kidney and urinary tract anomalies. Of the nine genes at this locus, SNAP29, AIFM3, and CRKL appear to be critical to the phenotype, with haploinsufficiency of CRKL emerging as the main genetic driver