Derived Equivalences of K3 Surfaces and Twined Elliptic Genera

We use the unique canonically-twisted module over a certain distinguished super vertex operator algebra---the moonshine module for Conway's group---to attach a weak Jacobi form of weight zero and index one to any symplectic derived equivalence of a projective complex K3 surface that fixes a stability condition in the distinguished space identified by Bridgeland. According to work of Huybrechts, following Gaberdiel--Hohenegger--Volpato, any such derived equivalence determines a conjugacy class in Conway's group, the automorphism group of the Leech lattice. Conway's group acts naturally on the module we consider. In physics the data of a projective complex K3 surface together with a suitable stability condition determines a supersymmetric non-linear sigma model, and supersymmetry preserving automorphisms of such an object may be used to define twinings of the K3 elliptic genus. Our construction recovers the K3 sigma model twining genera precisely in all available examples. In particular, the identity symmetry recovers the usual K3 elliptic genus, and this signals a connection to Mathieu moonshine. A generalization of our construction recovers a number of the Jacobi forms arising in umbral moonshine. We demonstrate a concrete connection to supersymmetric non-linear K3 sigma models by establishing an isomorphism between the twisted module we consider and the vector space underlying a particular sigma model attached to a certain distinguished K3 surface.Comment: 62 pages including 7 pages of tables; updated references and minor editing in v.2; to appear in Research in the Mathematical Science

The Moonshine Module for Conway's Group

We exhibit an action of Conway's group---the automorphism group of the Leech lattice---on a distinguished super vertex operator algebra, and we prove that the associated graded trace functions are normalized principal moduli, all having vanishing constant terms in their Fourier expansion. Thus we construct the natural analogue of the Frenkel--Lepowsky--Meurman moonshine module for Conway's group. The super vertex operator algebra we consider admits a natural characterization, in direct analogy with that conjectured to hold for the moonshine module vertex operator algebra. It also admits a unique canonically-twisted module, and the action of the Conway group naturally extends. We prove a special case of generalized moonshine for the Conway group, by showing that the graded trace functions arising from its action on the canonically-twisted module are constant in the case of Leech lattice automorphisms with fixed points, and are principal moduli for genus zero groups otherwise.Comment: 54 pages including 11 pages of tables; minor revisions in v2, submitte

Adaptive processing for LANDSAT data

Analytical and test results on the use of adaptive processing on LANDSAT data are presented. The Kalman filter was used as a framework to contain different adapting techniques. When LANDSAT MSS data were used all of the modifications made to the Kalman filter performed the functions for which they were designed. It was found that adaptive processing could provide compensation for incorrect signature means, within limits. However, if the data were such that poor classification accuracy would be obtained when the correct means were used, then adaptive processing would not improve the accuracy and might well lower it even further

Miracles of the Virgin

The collection of Miracles of the Virgin here edited for the first i time is contained in a manuscript (MSS. B. 14) belonging to the President White Library of Cornell University. Yhe volume is a small quarto (size of leaf cm. 10.2 X 13.7; of text cm. 13.2 X 10) of 184 folios, vellum, written in two columns (except f. 96, written in one), and contains works in various hands and of different dates, from the late thirteenth and the fourteenth centuries. Our collection, of the late thirteenth century, written in two columns of twenty-five lines, occupies fols. 104-110. The contents of the whole manuscript is as follows: (l) Meditationes piissimae beati Bernardi de cognitione humanae conditionis, incomplete, lacking chaps. XIV-XV, cf. Mabillon's ed. of St. Bernarrd's Opera, Paris, 1690, Vol. II, coll. 319-335, f. 1; (2) A mystical treatise, the beginning of which is missing, a leaf of the quire being lost, f. 16; (3) Vitas Patrum, f. 33vo; (4) The present article, f. 104; (5) Sermons, f. i2ovo; (6) Moral reflections, f. I40vo; (7) Two chapters of Gregory's Dialogues, Bk. IV, 37, 38, f. i4ivo; Treatise on canonical law, f. 143; (9) Theological treatise, f. 168; (10) Letter of Presbyter John to the Emperor Manuel, fols. 17IVO - 172VO. Articles (1)-(5) appear to be in the same hand and of the thirteenth century. The remaining articles are in different hands of the fourteenth century. I have written out the abbreviations, punctuated, and corrected a few evident slips of the scribe's pen. I have left the text as it is in the manuscript, with the usual mediaeval orthography (e for ae, etc), and I have not attempted to correct the scribe's construction

Patterned sequence in the transcriptome of vascular plants

<p>Abstract</p> <p>Background</p> <p>Microsatellites (repeated subsequences based on motifs of one to six nucleotides) are widely used as codominant genetic markers because of their frequent polymorphism and relative selective neutrality. Minisatellites are repeats of motifs having seven or more nucleotides. The large number of EST sequences now available in public databases offers an opportunity to compare microsatellite and minisatellite properties and evaluate their evolution over a broad range of plant taxa.</p> <p>Results</p> <p>Repeated motifs from one to 250 nucleotides long were identified in 6793306 expressed sequence tags (ESTs) from 88 genera of vascular plants, using a custom data-processing pipeline that allowed limited variation among repeats. The pipeline processed trimmed but otherwise unfiltered sequence and output nonredundant loci of at least 15 nucleotides, with degree of polymorphism and PCR primers wherever possible. Motifs that were an integral multiple of three in length were more abundant and richer in G/C than other motifs. From 80 to 85% of minisatellite motifs represented repeats within proteins, up to the 228-nucleotide repeat of ubiquitin, but not all of these repeats preserved reading frame. The remaining 15 to 20% of minisatellite motifs were associated with transcribed repetitive elements, e.g., retrotransposons. Relative microsatellite motif frequencies did not correlate tightly to phylogenetic relationship. Evolution of increased microsatellite and EST GC content was evident within the grasses. Microsatellites were less frequent in the transcriptome of genera with large genomes, but there was no evidence for greater dilution of the transcriptome with transposable element transcripts in these genera.</p> <p>Conclusion</p> <p>The relatively low correlation of microsatellite spectrum to phylogeny suggests that repeat loci evolve more rapidly than the surrounding sequence, although tissue specificity of the different EST libraries is a complicating factor. In-frame motifs are more abundant and higher in GC than frame-shifting motifs, but most EST minisatellite loci appear to represent repeats in translated sequence, regardless of whether reading frame is preserved. Motifs of four to six nucleotides are as polymorphic in EST collections as the commonly used motifs of two and three nucleotides, and they can be exploited as genetic markers with little additional effort.</p

Motion streaks improve motion detection

AbstractA number of studies were conducted to determine whether motion-streaks assist motion extraction, and whether a purely motion-based model could account for any observed facilitation. A 3-frame global-motion stimulus was used. Signal dots were manipulated in order to control the strength of the motion-streak. In the long-streak condition, the same dots carried the global-motion signal over successive motion frames, while in the short-streak condition, different dots carried the signal over successive frames. Noise dots always moved in different directions over successive frames. While lower thresholds in the long-streak condition could be explain by motion-streak facilitation, it could also be explained in terms of interactions purely within the motion system. Specifically, by excitatory feed-forward connections between neighbouring local-motion units tuned to the same or similar directions of motion. In order to test these two models, speed and contrast were varied. If lower thresholds are due to motion streaks (form input to motion) then maximum facilitation should occur at high speeds (no streak at low speeds) and high contrast (due to reduced streak magnitude and the low contrast sensitivity of the form cells that extract the motion-streak). Lower thresholds were obtained for the long-streak condition but only at high speeds and this facilitation was lost, or at least greatly reduced, at low (5%) contrast. These results support the notion that detection thresholds were facilitated by a motion-streak system

Spectral characteristics of normal and nutrient-deficient maize leaves

Reflectance, transmittance and absorbance spectra of normal and six types of mineral-deficient (N,P,K,S,Mg and Ca) maize (Zea mays L.) leaves were analyzed at 30 selected wavelengths along the electromagnetic spectrum from 500 to 2600 nm. Chlorophyll content and percent leaf moisture were also determined. Leaf thermograms were obtained for normal, N- and S- deficient leaves. The results of the analysis of variance showed significant differences in reflectance, transmittance and absorbance in the visible wavelengths among leaf numbers 3, 4, and 5, among the seven nutrient treatments, and among the interactions of leaves and treatments. In the reflective infrared wavelengths only treatments produced significant differences. The chlorophyll content of leaves was reduced in all deficiencies in comparison to controls. Percent moisture was increased in S-, Mg- and N- deficiencies. Positive correlation (r = 0.707) between moisture content and percent absorption at both 1450 and 1930 nm were obtained. Polynomial regression analysis of leaf thickness and leaf moisture content showed that these two variables were significantly and directly related (r = 0.894)

Autistic girls and school exclusion: perspectives of students and their parents

BACKGROUND AND AIMS: If a child’s behaviour does not conform to school policy or causes harm to either peers or staff, they may be temporarily or permanently excluded from school. Whilst it is unlawful to exclude children due to their needs, school exclusion is common amongst children with special educational needs, including autism. Currently, little is known about experiences of school exclusion from the perspectives of autistic students and/or their parents. This is particularly the case for girls on the autism spectrum. METHODS: Semi-structured interviews were conducted with eight autistic girls and their parents (seven mothers, one father). Interviews explored experiences of mainstream schooling; alternative educational provisions that were offered (if any); the school exclusion process; and the girls’ current educational provision. As well as asking the girls and their parents about positive and negative aspects of their past and current experiences, participants were asked to reflect on areas for potential improvements. RESULTS: Interviews were analysed using thematic analysis and three key themes emerged from the data: inappropriate school environments (including problems with the sensory environment, difficulties when placed with inappropriate peers and general pressures of mainstream classrooms), tensions in school relationships (including problems with staff and peers, alongside a general lack of communication), and problems with staff responses (including a perceived lack of understanding of the girls’ needs and a lack of appropriate support being provided, resulting in ‘battles’ between parents and schools). CONCLUSIONS: The themes and subthemes that emerged from the interviews were not unique to autistic girls. Indeed, issues such as inappropriate school environments, a lack of staff understanding and breakdowns in relationships have been repeatedly raised by parents and young autistic people (mostly boys) in other studies, albeit in different environments. Nevertheless, the results highlight that more needs to be done to positively influence the direction of the girls’ educational journeys. IMPLICATIONS: To improve the inclusion of autistic girls, it is recommended that educational establishments be proactive in developing inclusive environments, build positive relationships (both in and outside of the classroom) and, if exclusion is unavoidable, better support students both before and after the process