How an antenna launches its input power into radiation: the pattern of the Poynting vector at and near an antenna

In this paper I first address the question of whether the seat of the power radiated by an antenna made of conducting members is distributed over the ``arms'' of the antenna according to -J . E, where J is the specified current density and E is the electric field produced by that source. Poynting's theorem permits only a global identification of the total input power, usually from a localized generator, with the total power radiated to infinity, not a local correspondence of -J . E dv with some specific radiated power, r^2 S . n dO. I then describe a model antenna consisting of two perfectly conducting hemispheres of radius a separated by a small equatorial gap across which occurs the driving oscillatory electric field. The fields and surface current are determined by solution of the boundary value problem. In contrast to the first approach (not a boundary value problem), the tangential electric field vanishes on the metallic surface. There is no radial Poynting vector normal to the surface. Numerical examples are shown to illustrate how the energy flows from the input region of the gap and is guided near the antenna by its ``arms'' until it is launched at larger r/a into the radiation pattern determined by the value of ka.Comment: 24pages, 8 figures, submitted for publicatio

Short wavelength spectrum and Hamiltonian stability of vortex rings

We compare dynamical and energetical stability criteria for vortex rings. It is argued that vortex rings will be intrinsically unstable against perturbations with short wavelengths below a critical wavelength, because the canonical vortex Hamiltonian is unbounded from below for these modes. To explicitly demonstrate this behaviour, we derive the oscillation spectrum of vortex rings in incompressible, inviscid fluids, within a geometrical cutoff procedure for the core. The spectrum develops an anomalous branch of negative group velocity, and approaches the zero of energy for wavelengths which are about six times the core diameter. We show the consequences of this dispersion relation for the thermodynamics of vortex rings in superfluid $^4$He at low temperatures.Comment: 7 pages, 4 figures, final version to appear in Phys. Rev.

Quantum Calogero-Moser Models: Integrability for all Root Systems

The issues related to the integrability of quantum Calogero-Moser models based on any root systems are addressed. For the models with degenerate potentials, i.e. the rational with/without the harmonic confining force, the hyperbolic and the trigonometric, we demonstrate the following for all the root systems: (i) Construction of a complete set of quantum conserved quantities in terms of a total sum of the Lax matrix (L), i.e. (\sum_{\mu,\nu\in{\cal R}}(L^n)_{\mu\nu}), in which ({\cal R}) is a representation space of the Coxeter group. (ii) Proof of Liouville integrability. (iii) Triangularity of the quantum Hamiltonian and the entire discrete spectrum. Generalised Jack polynomials are defined for all root systems as unique eigenfunctions of the Hamiltonian. (iv) Equivalence of the Lax operator and the Dunkl operator. (v) Algebraic construction of all excited states in terms of creation operators. These are mainly generalisations of the results known for the models based on the (A) series, i.e. (su(N)) type, root systems.Comment: 45 pages, LaTeX2e, no figure

Clustered Gene Expression Changes Flank Targeted Gene Loci in Knockout Mice

Gene expression profiling using microarrays is a powerful technology widely used to study regulatory networks. Profiling of mRNA levels in mutant organisms has the potential to identify genes regulated by the mutated protein.Using tissues from multiple lines of knockout mice we have examined genome-wide changes in gene expression. We report that a significant proportion of changed genes were found near the targeted gene.The apparent clustering of these genes was explained by the presence of flanking DNA from the parental ES cell. We provide recommendations for the analysis and reporting of microarray data from knockout mice

De novo CNV analysis implicates specific abnormalities of postsynaptic signalling complexes in the pathogenesis of schizophrenia

A small number of rare, recurrent genomic copy number variants (CNVs) are known to substantially increase susceptibility to schizophrenia. As a consequence of the low fecundity in people with schizophrenia and other neurodevelopmental phenotypes to which these CNVs contribute, CNVs with large effects on risk are likely to be rapidly removed from the population by natural selection. Accordingly, such CNVs must frequently occur as recurrent de novo mutations. In a sample of 662 schizophrenia proband–parent trios, we found that rare de novo CNV mutations were significantly more frequent in cases (5.1% all cases, 5.5% family history negative) compared with 2.2% among 2623 controls, confirming the involvement of de novo CNVs in the pathogenesis of schizophrenia. Eight de novo CNVs occurred at four known schizophrenia loci (3q29, 15q11.2, 15q13.3 and 16p11.2). De novo CNVs of known pathogenic significance in other genomic disorders were also observed, including deletion at the TAR (thrombocytopenia absent radius) region on 1q21.1 and duplication at the WBS (Williams–Beuren syndrome) region at 7q11.23. Multiple de novos spanned genes encoding members of the DLG (discs large) family of membrane-associated guanylate kinases (MAGUKs) that are components of the postsynaptic density (PSD). Two de novos also affected EHMT1, a histone methyl transferase known to directly regulate DLG family members. Using a systems biology approach and merging novel CNV and proteomics data sets, systematic analysis of synaptic protein complexes showed that, compared with control CNVs, case de novos were significantly enriched for the PSD proteome (P=1.72 × 10−6). This was largely explained by enrichment for members of the N-methyl-D-aspartate receptor (NMDAR) (P=4.24 × 10−6) and neuronal activity-regulated cytoskeleton-associated protein (ARC) (P=3.78 × 10−8) postsynaptic signalling complexes. In an analysis of 18 492 subjects (7907 cases and 10 585 controls), case CNVs were enriched for members of the NMDAR complex (P=0.0015) but not ARC (P=0.14). Our data indicate that defects in NMDAR postsynaptic signalling and, possibly, ARC complexes, which are known to be important in synaptic plasticity and cognition, play a significant role in the pathogenesis of schizophrenia

Schizophrenia copy number variants and associative learning

Large-scale genomic studies have made major progress in identifying genetic risk variants for schizophrenia. A key finding from these studies is that there is an increased burden of genomic copy number variants (CNVs) in schizophrenia cases compared with controls. The mechanism through which these CNVs confer risk for the symptoms of schizophrenia, however, remains unclear. One possibility is that schizophrenia risk CNVs impact basic associative learning processes, abnormalities of which have long been associated with the disorder. To investigate whether genes in schizophrenia CNVs impact on specific phases of associative learning we combined human genetics with experimental gene expression studies in animals. In a sample of 11 917 schizophrenia cases and 16 416 controls, we investigated whether CNVs from patients with schizophrenia are enriched for genes expressed during the consolidation, retrieval or extinction of associative memories. We show that CNVs from cases are enriched for genes expressed during fear extinction in the hippocampus, but not genes expressed following consolidation or retrieval. These results suggest that CNVs act to impair inhibitory learning in schizophrenia, potentially contributing to the development of core symptoms of the disorder

Common schizophrenia alleles are enriched in mutation-intolerant genes and maintained by background selection

Schizophrenia is a debilitating psychiatric condition often associated with poor quality of life and decreased life expectancy. Lack of progress in improving treatment outcomes has been attributed to limited knowledge of the underlying biology, although large-scale genomic studies have begun to provide such insight. We report the largest single cohort genome-wide association study of schizophrenia (11,260 cases and 24,542 controls) and through meta-analysis with existing data we identify 50 novel GWAS loci. Using gene-wide association statistics we implicate an additional set of 22 novel associations that map onto a single gene. We show for the first time that the common variant association signal is highly enriched among genes that are intolerant to loss of function mutations and that variants in these genes persist in the population despite the low fecundity associated with the disorder through the process of background selection. Associations point to novel areas of biology (e.g. metabotropic GABA-B signalling and acetyl cholinesterase), reinforce those implicated in earlier GWAS studies (e.g. calcium channel function), converge with earlier rare variants studies (e.g. NRXN1, GABAergic signalling), identify novel overlaps with autism (e.g. RBFOX1, FOXP1, FOXG1), and support early controversial candidate gene hypotheses (e.g. ERBB4 implicating neuregulin signalling). We also demonstrate the involvement of six independent central nervous system functional gene sets in schizophrenia pathophysiology. These findings provide novel insights into the biology and genetic architecture of schizophrenia, highlight the importance of mutation intolerant genes and suggest a mechanism by which common risk variants are maintained in the population

Differential Functional Constraints on the Evolution of Postsynaptic Density Proteins in Neocortical Laminae

The postsynaptic density (PSD) is a protein dense complex on the postsynaptic membrane of excitatory synapses that is implicated in normal nervous system functions such as synaptic plasticity, and also contains an enrichment of proteins involved in neuropsychiatric disorders. It has recently been reported that the genes encoding PSD proteins evolved more slowly than other genes in the human brain, but the underlying evolutionary advantage for this is not clear. Here, we show that cortical gene expression levels could explain most of this effect, indicating that expression level is a primary contributor to the evolution of these genes in the brain. Furthermore, we identify a positive correlation between the expression of PSD genes and cortical layers, with PSD genes being more highly expressed in deep layers, likely as a result of layer-enriched transcription factors. As the cortical layers of the mammalian brain have distinct functions and anatomical projections, our results indicate that the emergence of the unique six-layered mammalian cortex may have provided differential functional constraints on the evolution of PSD genes. More superficial cortical layers contain PSD genes with less constraint and these layers are primarily involved in intracortical projections, connections that may be particularly important for evolved cognitive functions. Therefore, the differential expression and evolutionary constraint of PSD genes in neocortical laminae may be critical not only for neocortical architecture but the cognitive functions that are dependent on this structure

Exome arrays capture polygenic rare variant contributions to schizophrenia

Schizophrenia is a highly heritable disorder. Genome-wide association studies based largely on common alleles have identified over 100 schizophrenia risk loci, but it is also evident from studies of copy number variants (CNVs) and from exome-sequencing studies that rare alleles are also involved. Full characterization of the contribution of rare alleles to the disorder awaits the deployment of sequencing technology in very large sample sizes, meanwhile, as an interim measure, exome arrays allow rare non-synonymous variants to be sampled at a fraction of the cost. In an analysis of exome array data from 13 688 individuals (5585 cases and 8103 controls) from the UK, we found that rare (minor allele frequency < 0.1%) variant association signal was enriched among genes that map to autosomal loci that are genome-wide significant (GWS) in common variant studies of schizophrenia genome-wide association study (PGWAS = 0.01) as well as gene sets known to be enriched for rare variants in sequencing studies (PRARE = 0.026). We also identified the gene-wise equivalent of GWS support for WDR88 (WD repeat-containing protein 88), a gene of unknown function (P = 6.5 × 10−7). Rare alleles represented on exome chip arrays contribute to the genetic architecture of schizophrenia, but as is the case for GWAS, very large studies are required to reveal additional susceptibility alleles for the disorder