Rank Two Sheaves on K3 Surfaces: A Special Construction

Let X be a K3 surface of degree 8 in P^5 with hyperplane section H. We associate to it another K3 surface M which is a double cover of P^2 ramified on a sextic curve C. In the generic case when X is smooth and a complete intersection of three quadrics, there is a natural correspondence between M and the moduli space M' of rank two vector bundles on X with Chern classes c_1=H and c_2=4. We build on previous work of Mukai and others, giving conditions and examples where M' is fine, compact, non-empty; and birational or isomorphic to M. We also present an explicit calculation of the Fourier-Mukai transform when X contains a line and has Picard number two.Comment: Fixed various minor errors and reworked some argument

Confusion is the first step towards understanding: Fixing the problems of E-learning in COVID-19 pandemic

Background: The COVID-19 pandemic forced institutions worldwide to adopt online learning, which opened a new era of challenges. Our research was designed to explore the effect of the pandemic on teaching and learning and identify the solutions to the problems based on participants’ perspectives. Methods: A qualitative study of the phenomenological design was conducted at a medical institute in Pakistan. The participants were selected using the purposive sampling technique. Semi-structured interviews were done which were later audio-recorded, transcribed, and subjected to manual thematic analysis. Credibility was ensured by using multiple data collection sources. Results: The 20 participants selected as interviewees were faculty with more than 5 years teaching experience in the medical institute and had gone through online teaching and learning during COVID-19 pandemic.  The thematic analyses of the data generated six themes which were: 1. “I see what you mean”; Re-exploration of educational psychology, 2. Reorganization of curriculum, 3. Mentoring and coaching, 4. Technology: as ubiquities as oxygen, 5. Constructive feedback: a stimulus in pearl formation and 6. Turn the tables: fixing the problem. Conclusion: Online education has emerged as an important mechanism in delivering medical education to undergraduate medical students. Instead of shying away, efforts are needed to restructure the curricula, incorporating various online innovative teaching, and learning tools that are at par with the changing global demands of medical education. Keywords: E-learning, COVID-19, Challenges                                                                                                          

Comparison of Constrained Induced Movement Therapy and Bimanual Training on Functional Outcome of Hemiplegic Cerebral Palsy

OBJECTIVES The aim of this study was to compare the effects of constrained induced movement therapy (CIMT) and BimanualIntensive Training (BIT) on functional outcomes of hemiplegic cerebral palsy children. METHODOLOGY Cerebral palsy children with age groups of 5 to 12 years were included with a total sample size of 38. Simplerandom sampling was done, and data was collected from Islamabad. Two groups were formed and named groupA: constrained induced movement therapy with 19% and group B: bimanual training with 19% respectively. Thefunctional outcome for the CIMPT and for the BIT group was assessed on the pretest and post-test scoreevaluation of QUEST and JTHF tests. RESULTS Statistically significant (p <0.05) improvement was found in The Quality of Upper Extremity Skills Test (QUEST)and Jebsen-Taylor Test of Hand Function (JTHF) in the between -group analysis. For within the group analysisthe p-value <0.05 suggests that there was a significant diffe rence in within-group analysis too. The values forgrasp and dissociated movements suggest that QUEST post-test values are impactful in the CMIT group whereasin the BIT group simultaneous and spontaneous movement was increased but JTHF post -test values were moresignificant in CMIT. CONCLUSION BIT is more beneficial for both hand’s simultaneous and spontaneous movement, whereas CMIT is morebeneficial for grip and overcoming the “learned-nonuse” phenomena in cerebral palsy children

Validation of plasma protein glycation and oxidation biomarkers for the diagnosis of autism

Autism Spectrum Disorder (ASD) is a common neurodevelopmental disorder in children. It is currently diagnosed by behaviour-based assessments made by observation and interview. In 2018 we reported a discovery study of a blood biomarker diagnostic test for ASD based on a combination of four plasma protein glycation and oxidation adducts. The test had 88% accuracy in children 5–12 years old. Herein, we present an international multicenter clinical validation study (N = 478) with application of similar biomarkers to a wider age range of 1.5–12 years old children. Three hundred and eleven children with ASD (247 male, 64 female; age 5.2 ± 3.0 years) and 167 children with typical development (94 male, 73 female; 4.9 ± 2.4 years) were recruited for this study at Sidra Medicine and Hamad Medical Corporation hospitals, Qatar, and Hospital Regional Universitario de Málaga, Spain. For subjects 5–12 years old, the diagnostic algorithm with features, advanced glycation endproducts (AGEs)—Nε-carboxymethyl-lysine (CML), Nω-carboxymethylarginine (CMA) and 3-deoxyglucosone-derived hydroimidazolone (3DG-H), and oxidative damage marker, o,o’-dityrosine (DT), age and gender had accuracy 83% (CI 79 – 89%), sensitivity 94% (CI 90–98%), specificity 67% (CI 57–76%) and area-under-the-curve of receiver operating characteristic plot (AUROC) 0.87 (CI 0.84–0.90). Inclusion of additional plasma protein glycation and oxidation adducts increased the specificity to 74%. An algorithm with 12 plasma protein glycation and oxidation adduct features was optimum for children of 1.5–12 years old: accuracy 74% (CI 70–79%), sensitivity 75% (CI 63–87%), specificity 74% (CI 58–90%) and AUROC 0.79 (CI 0.74–0.84). We conclude that ASD diagnosis may be supported using an algorithm with features of plasma protein CML, CMA, 3DG-H and DT in 5–12 years-old children, and an algorithm with additional features applicable for ASD screening in younger children. ASD severity, as assessed by ADOS-2 score, correlated positively with plasma protein glycation adducts derived from methylglyoxal, hydroimidazolone MG-H1 and Nε(1-carboxyethyl)lysine (CEL). The successful validation herein may indicate that the algorithm modifiable features are mechanistic risk markers linking ASD to increased lipid peroxidation, neuronal plasticity and proteotoxic stress.</p

K3 correspondences

We consider relationships between the derived categories of twisted coherent sheaves on various families of K3 surfaces, in the context of string theory. An important ingredient of string theory also of interest in algebraic geometry is T-duality; see for example the works of Morrison [Mo], Katz [K], Thomas and Yau [TY], Donagi and Pantev [DP]. Donagi and Pantev [DP] have extended the original duality on genus one fibred K3 surfaces with a section, to the case of any genus one fibration, via a Fourier-Mukai transform. We investigate possibilities of extending this result to the more general case of non-fibered K3s. In Chapter 5 we show the existence of a 19 dimensional family of pairs of isogenous K3 surfaces ((M, α), (Y, β)) where M is a double cover of P2, Y is a degree 8 surface in P5 and α, β are nontrivial elements of Br(X), Br(Y) respectively. Note that our family is not the same as Mukai\u27s example. Mukai\u27s family consists of pairs ((M, α), (Y, β)), where M is the moduli space of semistable sheaves on Y with prescribed Chern classes (see [Mu1], [Mu2]). The results in [Mu1] imply that TY embeds Hodge isometrically in TM as a sublattice of index 2. This forces β to be trivial. On the other hand for generic pairs ((M, α), (Y, β)) in our family, only a proper sublattice of TY embeds in TM and vice versa, which gives rise to a nonzero α and β. Hence we can consider nontrivial gerbes on both M and Y as opposed to just on M which is the case in Mukai\u27s papers. The locus we constructed is a natural candidate for extending the Donagi-Pantev duality and an equivalence [special characters omitted](M, α) ∼ [special characters omitted](Y, β) is expected. In addition for each integer n we construct an 18 dimensional family of genus one fibered K3 surfaces of index n (see Chapter 6). These families intersect the family of double covers of P 2 and deformation theory arguments should prove similar equivalences. These results also offer possibilities of further exploring Caldararu\u27s conjecture [Cal1], genus one curves over arbitrary number fields, and matrix models in string theory [BL]