Discrete moving frames on lattice varieties and lattice based multispace

In this paper, we develop the theory of the discrete moving frame in two different ways. In the first half of the paper, we consider a discrete moving frame defined on a lattice variety and the equivalence classes of global syzygies that result from the first fundamental group of the variety. In the second half, we consider the continuum limit of discrete moving frames as a local lattice coalesces to a point. To achieve a well-defined limit of discrete frames, we construct multispace, a generalization of the jet bundle that also generalizes Olver’s one dimensional construction. Using interpolation to provide coordinates, we prove that it is a manifold containing the usual jet bundle as a submanifold. We show that continuity of a multispace moving frame ensures that the discrete moving frame converges to a continuous one as lattices coalesce. The smooth frame is, at the same time, the restriction of the multispace frame to the embedded jet bundle. We prove further that the discrete invariants and syzygies approximate their smooth counterparts. In effect, a frame on multispace allows smooth frames and their discretisations to be studied simultaneously. In our last chapter we discuss two important applications, one to the discrete variational calculus, and the second to discrete integrable systems. Finally, in an appendix, we discuss a more general result concerning equicontinuous families of discretisations of moving frames, which are consistent with a smooth frame

Counterexample-Guided Polynomial Loop Invariant Generation by Lagrange Interpolation

We apply multivariate Lagrange interpolation to synthesize polynomial quantitative loop invariants for probabilistic programs. We reduce the computation of an quantitative loop invariant to solving constraints over program variables and unknown coefficients. Lagrange interpolation allows us to find constraints with less unknown coefficients. Counterexample-guided refinement furthermore generates linear constraints that pinpoint the desired quantitative invariants. We evaluate our technique by several case studies with polynomial quantitative loop invariants in the experiments

Systematic mutation analysis of KIAA0767 and KIAA1646 in chromosome 22q-linked periodic catatonia

BACKGROUND: Periodic catatonia is a familial subtype of schizophrenia characterized by hyperkinetic and akinetic episodes, followed by a catatonic residual syndrome. The phenotype has been evaluated in two independent genome-wide linkage scans with evidence for a major locus on chromosome 15q15, and a second independent locus on chromosome 22q(tel). METHODS: In the positional and brain-expressed candidate genes KIAA0767 and KIAA1646, we searched for variants in the complete exons and adjacent splice-junctions as well as in parts of the 5'- and 3'-untranslated regions by means of a systematic mutation screening in individuals from chromosome 22q-linked pedigrees. RESULTS: The mutation scan revealed 24 single nucleotide polymorphisms, among them two rare codon variants (KIAA0767: S159I; KIAA1646: V338G). However, both were neither found segregating with the disease in the respective pedigree nor found at a significant frequency in a case-control association sample. CONCLUSION: Starting from linkage signals at chromosome22q(tel )in periodic catatonia, we screened two positional brain-expressed candidate genes for genetic variation. Our study excludes genetic variations in the coding and putative promoter regions of KIAA0767 and KIAA1646 as causative factors for periodic catatonia

Glial Cell Line-Derived Neurotrophic Factor (GDNF) as a Novel Candidate Gene of Anxiety.

Glial cell line-derived neurotrophic factor (GDNF) is a neurotrophic factor for dopaminergic neurons with promising therapeutic potential in Parkinson's disease. A few association analyses between GDNF gene polymorphisms and psychiatric disorders such as schizophrenia, attention deficit hyperactivity disorder and drug abuse have also been published but little is known about any effects of these polymorphisms on mood characteristics such as anxiety and depression. Here we present an association study between eight (rs1981844, rs3812047, rs3096140, rs2973041, rs2910702, rs1549250, rs2973050 and rs11111) GDNF single nucleotide polymorphisms (SNPs) and anxiety and depression scores measured by the Hospital Anxiety and Depression Scale (HADS) on 708 Caucasian young adults with no psychiatric history. Results of the allele-wise single marker association analyses provided significant effects of two single nucleotide polymorphisms on anxiety scores following the Bonferroni correction for multiple testing (p = 0.00070 and p = 0.00138 for rs3812047 and rs3096140, respectively), while no such result was obtained on depression scores. Haplotype analysis confirmed the role of these SNPs; mean anxiety scores raised according to the number of risk alleles present in the haplotypes (p = 0.00029). A significant sex-gene interaction was also observed since the effect of the rs3812047 A allele as a risk factor of anxiety was more pronounced in males. In conclusion, this is the first demonstration of a significant association between the GDNF gene and mood characteristics demonstrated by the association of two SNPs of the GDNF gene (rs3812047 and rs3096140) and individual variability of anxiety using self-report data from a non-clinical sample

Assessing the Quality of Clinical Teachers: A Systematic Review of Content and Quality of Questionnaires for Assessing Clinical Teachers

BACKGROUND: Learning in a clinical environment differs from formal educational settings and provides specific challenges for clinicians who are teachers. Instruments that reflect these challenges are needed to identify the strengths and weaknesses of clinical teachers. OBJECTIVE: To systematically review the content, validity, and aims of questionnaires used to assess clinical teachers. DATA SOURCES: MEDLINE, EMBASE, PsycINFO and ERIC from 1976 up to March 2010. REVIEW METHODS: The searches revealed 54 papers on 32 instruments. Data from these papers were documented by independent researchers, using a structured format that included content of the instrument, validation methods, aims of the instrument, and its setting. Results : Aspects covered by the instruments predominantly concerned the use of teaching strategies (included in 30 instruments), supporter role (29), role modeling (27), and feedback (26). Providing opportunities for clinical learning activities was included in 13 instruments. Most studies referred to literature on good clinical teaching, although they failed to provide a clear description of what constitutes a good clinical teacher. Instrument length varied from 1 to 58 items. Except for two instruments, all had to be completed by clerks/residents. Instruments served to provide formative feedback ( instruments) but were also used for resource allocation, promotion, and annual performance review (14 instruments). All but two studies reported on internal consistency and/or reliability; other aspects of validity were examined less frequently. CONCLUSIONS: No instrument covered all relevant aspects of clinical teaching comprehensively. Validation of the instruments was often limited to assessment of internal consistency and reliability. Available instruments for assessing clinical teachers should be used carefully, especially for consequential decisions. There is a need for more valid comprehensive instruments

Astrocytes: biology and pathology

Astrocytes are specialized glial cells that outnumber neurons by over fivefold. They contiguously tile the entire central nervous system (CNS) and exert many essential complex functions in the healthy CNS. Astrocytes respond to all forms of CNS insults through a process referred to as reactive astrogliosis, which has become a pathological hallmark of CNS structural lesions. Substantial progress has been made recently in determining functions and mechanisms of reactive astrogliosis and in identifying roles of astrocytes in CNS disorders and pathologies. A vast molecular arsenal at the disposal of reactive astrocytes is being defined. Transgenic mouse models are dissecting specific aspects of reactive astrocytosis and glial scar formation in vivo. Astrocyte involvement in specific clinicopathological entities is being defined. It is now clear that reactive astrogliosis is not a simple all-or-none phenomenon but is a finely gradated continuum of changes that occur in context-dependent manners regulated by specific signaling events. These changes range from reversible alterations in gene expression and cell hypertrophy with preservation of cellular domains and tissue structure, to long-lasting scar formation with rearrangement of tissue structure. Increasing evidence points towards the potential of reactive astrogliosis to play either primary or contributing roles in CNS disorders via loss of normal astrocyte functions or gain of abnormal effects. This article reviews (1) astrocyte functions in healthy CNS, (2) mechanisms and functions of reactive astrogliosis and glial scar formation, and (3) ways in which reactive astrocytes may cause or contribute to specific CNS disorders and lesions