Infinite dimensional Lie algebras in 4D conformal quantum field theory

The concept of global conformal invariance (GCI) opens the way of applying algebraic techniques, developed in the context of 2-dimensional chiral conformal field theory, to a higher (even) dimensional space-time. In particular, a system of GCI scalar fields of conformal dimension two gives rise to a Lie algebra of harmonic bilocal fields, V_m(x,y), where the m span a finite dimensional real matrix algebra M closed under transposition. The associative algebra M is irreducible iff its commutant M' coincides with one of the three real division rings. The Lie algebra of (the modes of) the bilocal fields is in each case an infinite dimensional Lie algebra: a central extension of sp(infty,R) corresponding to the field R of reals, of u(infty,infty) associated to the field C of complex numbers, and of so*(4 infty) related to the algebra H of quaternions. They give rise to quantum field theory models with superselection sectors governed by the (global) gauge groups O(N), U(N), and U(N,H)=Sp(2N), respectively.Comment: 16 pages, with minor improvements as to appear in J. Phys.

Jumping-Droplet Electrostatic Energy Harvesting

Micro- and nanoscale wetting phenomena has been an active area of research due to its potential for improving engineered system performance involving phase change. With the recent advancements in micro/nanofabrication techniques, structured surfaces can now be designed to allow condensing coalesced droplets to spontaneously jump off the surface due to the conversion of excess surface energy into kinetic energy. In addition to being removed at micrometric length scales (~10 μm), jumping water droplets also attain a positive electrostatic charge (~10-100 fC) from the hydrophobic coating/condensate interaction. In this work, we take advantage of this droplet charging to demonstrate jumping-droplet electrostatic energy harvesting. The charged droplets jump between superhydrophobic copper oxide and hydrophilic copper surfaces to create an electrostatic potential and generate power during formation of atmospheric dew. We demonstrated power densities of ~15 pW/cm[superscript 2], which, in the near term, can be improved to ~1 μW/cm[superscript 2]. This work demonstrates a surface engineered platform that promises to be low cost and scalable for atmospheric energy harvesting and electric power generation.United States. Dept. of Energy. Office of Basic Energy Sciences (Award DE-FG02-09ER46577)United States. Office of Naval ResearchNational Science Foundation (U.S.). Graduate Research Fellowship Program (Grant 1122374

Restrictions of generalized Verma modules to symmetric pairs

We initiate a new line of investigation on branching problems for generalized Verma modules with respect to complex reductive symmetric pairs (g,k). Here we note that Verma modules of g may not contain any simple module when restricted to a reductive subalgebra k in general. In this article, using the geometry of K_C orbits on the generalized flag variety G_C/P_C, we give a necessary and sufficient condition on the triple (g,k, p) such that the restriction X|_k always contains simple k-modules for any g-module $X$ lying in the parabolic BGG category O^p attached to a parabolic subalgebra p of g. Formulas are derived for the Gelfand-Kirillov dimension of any simple k-module occurring in a simple generalized Verma module of g. We then prove that the restriction X|_k is multiplicity-free for any generic g-module X \in O if and only if (g,k) is isomorphic to a direct sum of (A_n,A_{n-1}), (B_n,D_n), or (D_{n+1},B_n). We also see that the restriction X|_k is multiplicity-free for any symmetric pair (g, k) and any parabolic subalgebra p with abelian nilradical and for any generic g-module X \in O^p. Explicit branching laws are also presented.Comment: 31 pages, To appear in Transformation Group

Invariant Differential Operators for Non-Compact Lie Groups: the Sp(n,R) Case

In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebras sp(n,R), in detail for n=6. Our choice of these algebras is motivated by the fact that they belong to a narrow class of algebras, which we call 'conformal Lie algebras', which have very similar properties to the conformal algebras of Minkowski space-time. We give the main multiplets and the main reduced multiplets of indecomposable elementary representations for n=6, including the necessary data for all relevant invariant differential operators. In fact, this gives by reduction also the cases for n<6, since the main multiplet for fixed n coincides with one reduced case for n+1.Comment: Latex2e, 27 pages, 8 figures. arXiv admin note: substantial text overlap with arXiv:0812.2690, arXiv:0812.265

Defining forgiveness: Christian clergy and general population perspectives.

The lack of any consensual definition of forgiveness is a serious weakness in the research literature (McCullough, Pargament &amp; Thoresen, 2000). As forgiveness is at the core of Christianity, this study returns to the Christian source of the concept to explore the meaning of forgiveness for practicing Christian clergy. Comparisons are made with a general population sample and social science definitions of forgiveness to ensure that a shared meaning of forgiveness is articulated. Anglican and Roman Catholic clergy (N = 209) and a general population sample (N = 159) completed a postal questionnaire about forgiveness. There is agreement on the existence of individual differences in forgiveness. Clergy and the general population perceive reconciliation as necessary for forgiveness while there is no consensus within psychology. The clergy suggests that forgiveness is limitless and that repentance is unnecessary while the general population suggests that there are limits and that repentance is necessary. Psychological definitions do not conceptualize repentance as necessary for forgiveness and the question of limits has not been addressed although within therapy the implicit assumption is that forgiveness is limitless.</p

Molecular evidence of synaptic pathology in the CA1 region in schizophrenia.

Alterations of postsynaptic density (PSD)95-complex proteins in schizophrenia ostensibly induce deficits in synaptic plasticity, the molecular process underlying cognitive functions. Although some PSD95-complex proteins have been previously examined in the hippocampus in schizophrenia, the status of other equally important molecules is unclear. This is especially true in the cornu ammonis (CA)1 hippocampal subfield, a region that is critically involved in the pathophysiology of the illness. We thus performed a quantitative immunoblot experiment to examine PSD95 and several of its associated proteins in the CA1 region, using post mortem brain samples derived from schizophrenia subjects with age-, sex-, and post mortem interval-matched controls (n=20/group). Our results indicate a substantial reduction in PSD95 protein expression (-61.8%). Further analysis showed additional alterations to the scaffold protein Homer1 (Homer1a: +42.9%, Homer1b/c: -24.6%), with a twofold reduction in the ratio of Homer1b/c:Homer1a isoforms (P=0.011). Metabotropic glutamate receptor 1 (mGluR1) protein levels were significantly reduced (-32.7%), and Preso, a protein that supports interactions between Homer1 or PSD95 with mGluR1, was elevated (+83.3%). Significant reduction in synaptophysin (-27.8%) was also detected, which is a validated marker of synaptic density. These findings support the presence of extensive molecular abnormalities to PSD95 and several of its associated proteins in the CA1 region in schizophrenia, offering a small but significant step toward understanding how proteins in the PSD are altered in the schizophrenia brain, and their relevance to overall hippocampal and cognitive dysfunction in the illness

Serum levels of mature microRNAs in DICER1-mutated pleuropulmonary blastoma.

DICER1 is a critical gene in the biogenesis of mature microRNAs, short non-coding RNAs that derive from either -3p or -5p precursor microRNA strands. Germline mutations of DICER1 are associated with a range of human malignancies, including pleuropulmonary blastoma (PPB). Additional somatic 'hotspot' mutations in the microRNA processing ribonuclease IIIb (RNase IIIb) domain of DICER1 are reported in cancer, and which affect microRNA biogenesis, resulting in a -3p mature microRNA strand bias. Here, in a germline (exon11 c.1806_1810insATTGA) DICER1-mutated PPB, we first confirmed the presence of an additional somatic RNase IIIb hotspot mutation (exon25 c.5425G>A [p.G1809R]) by conventional sequencing. Second, we investigated serum levels of mature microRNAs at the time of PPB diagnosis, and compared the findings with serum results from a comprehensive range of pediatric cancer patients and controls (n=52). We identified a panel of 45 microRNAs that were present at elevated levels in the serum at the time of PPB diagnosis, with a significant majority noted be derived from the -3p strand (P=0.013). In addition, we identified a subset of 10 serum microRNAs (namely miR-125a-3p, miR-125b-2-3p, miR-380-5p, miR-125b-1-3p, let-7f-2-3p, let-7a-3p, let-7b-3p, miR-708-3p, miR-138-1-3p and miR-532-3p) that were most abundant in the PPB case. Serum levels of two representative microRNAs, miR-125a-3p and miR-125b-2-3p, were not elevated in DICER1 germline-mutated relatives. In the PPB case, serum levels of miR-125a-3p and miR-125b-2-3p increased before chemotherapy, and then showed an early reduction following treatment. These microRNAs may offer future utility as serum biomarkers for screening patients with known germline DICER1 mutations for early detection of PPB, and for potential disease-monitoring in cases with confirmed PPB.We would like to thank the following for providing financial support: SPARKS (NC, MJM), Medical Research Council Fellowship (MJM), TD Bank/LDI scholarship (LdK), Alex’s Lemonade Stand Foundation (WDF), Cancer Research UK (NC) and European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement No. 310018 (MT).This is the final published version. It first appeared at http://www.nature.com/oncsis/journal/v3/n2/full/oncsis20141a.html

The RNA m6A Reader YTHDF2 Is Essential for the Post-transcriptional Regulation of the Maternal Transcriptome and Oocyte Competence.

YTHDF2 binds and destabilizes N6-methyladenosine (m6A)-modified mRNA. The extent to which this branch of m6A RNA-regulatory pathway functions in vivo and contributes to mammalian development remains unknown. Here we find that YTHDF2 deficiency is partially permissive in mice and results in female-specific infertility. Using conditional mutagenesis, we demonstrate that YTHDF2 is autonomously required within the germline to produce MII oocytes that are competent to sustain early zygotic development. Oocyte maturation is associated with a wave of maternal RNA degradation, and the resulting relative changes to the MII transcriptome are integral to oocyte quality. The loss of YTHDF2 results in the failure to regulate transcript dosage of a cohort of genes during oocyte maturation, with enrichment observed for the YTHDF2-binding consensus and evidence of m6A in these upregulated genes. In summary, the m6A-reader YTHDF2 is an intrinsic determinant of mammalian oocyte competence and early zygotic development

Dirac cohomology, elliptic representations and endoscopy

The first part (Sections 1-6) of this paper is a survey of some of the recent developments in the theory of Dirac cohomology, especially the relationship of Dirac cohomology with (g,K)-cohomology and nilpotent Lie algebra cohomology; the second part (Sections 7-12) is devoted to understanding the unitary elliptic representations and endoscopic transfer by using the techniques in Dirac cohomology. A few problems and conjectures are proposed for further investigations.Comment: This paper will appear in `Representations of Reductive Groups, in Honor of 60th Birthday of David Vogan', edited by M. Nervins and P. Trapa, published by Springe

Effect of hydrocarbon adsorption on the wettability of rare earth oxide ceramics

Vapor condensation is routinely used as an effective means of transferring heat, with dropwise condensation exhibiting a 5 − 7x heat transfer improvement compared to filmwise condensation. However, state-of-the-art techniques to promote dropwise condensation rely on functional hydrophobic coatings, which are often not robust and therefore undesirable for industrial implementation. Natural surface contamination due to hydrocarbon adsorption, particularly on noble metals, has been explored as an alternative approach to realize stable dropwise condensing surfaces. While noble metals are prohibitively expensive, the recent discovery of robust rare earth oxide (REO) hydrophobicity has generated interest for dropwise condensation applications due to material costs approaching 1% of gold; however, the underlying mechanism of REO hydrophobicity remains under debate. In this work, we show through careful experiments and modeling that REO hydrophobicity occurs due to the same hydrocarbon adsorption mechanism seen previously on noble metals. To investigate adsorption dynamics, we studied holmia and ceria REOs, along with control samples of gold and silica, via X-Ray photoelectron spectroscopy (XPS) and dynamic time-resolved contact angle measurements. The contact angle and surface carbon percent started at ≈0 on in-situ argon-plasma-cleaned samples and increased asymptotically over time after exposure to laboratory air, with the rare earth oxides displaying hydrophobic (>90°) advancing contact angle behavior at long times (>4 days). The results indicate that REOs are in fact hydrophilic when clean and become hydrophobic due to hydrocarbon adsorption. Furthermore, this study provides insight into how REOs can be used to promote stable dropwise condensation, which is important for the development of enhanced phase change surfaces.United States. Office of Naval ResearchUnited States. Dept. of Energy (MIT S3TEC Energy Research Frontier Center, Award No. DE- FG02-09ER46577)National Science Foundation (U.S.) (Graduate research fellowship)National Science Foundation (U.S.) (Graduate Research Fellowship Program, Grant No. 1122374)Irish Research Council for Science, Engineering, and Technology (Marie Curie Actions under FP7