Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics

In quantum theory, symmetry has to be defined necessarily in terms of the family of unit rays, the state space. The theorem of Wigner asserts that a symmetry so defined at the level of rays can always be lifted into a linear unitary or an antilinear antiunitary operator acting on the underlying Hilbert space. We present two proofs of this theorem which are both elementary and economical. Central to our proofs is the recognition that a given Wigner symmetry can, by post-multiplication by a unitary symmetry, be taken into either the identity or complex conjugation. Our analysis often focuses on the behaviour of certain two-dimensional subspaces of the Hilbert space under the action of a given Wigner symmetry, but the relevance of this behaviour to the larger picture of the whole Hilbert space is made transparent at every stage.

Quasi-2D XY Magnetic Properties and Slow Relaxation in a Body Centered Metal Organic Network of [Co-4] Clusters

Octahedral Co2+ centers have been connected by mu(3)-OH and mu(2)-OH2 units forming [Co-4] clusters which are linked by pyrazine forming a two-dimensional network. The two-dimensional layers are bridged by oxybisbenzoate (OBA) ligands giving rise to a three-dimensional structure. The [Co-4] clusters bond with the pyrazine and the OBA results in a body-centered arrangement of the clusters, which has been observed for the first time. Magnetic studies reveal a noncollinear frustrated spin structure of the bitriangular cluster, resulting in a net magnetic moment of 1.4 mu B per cluster. For T > 32 K, the correlation length of the cluster moments shows a stretched-exponential temperature dependence typical of a Berezinskii-Kosterlitz-Thouless model, which points to a quasi-2D XY behavior. At lower temperature and down to 14 K, the compound behaves as a soft ferromagnet and a slow relaxation is observed, with an energy barrier of ca. 500 K. Then, on further cooling, a hysteretic behavior takes place with a coercive field that reaches 5 Tat 4 K. The slow relaxation is assigned to the creation/annihilation of vortex-antivortex pairs, which are the elementary excitations of a 2D XY spin system.

Bond-order wave phase, spin solitons, and thermodynamics of a frustrated linear spin-1/2 Heisenberg antiferromagnet

The linear spin-1/2 Heisenberg antiferromagnet with exchanges J(1) and J(2) between first and second neighbors has a bond-order wave (BOW) phase that starts at the fluid-dimer transition at J(2)/J(1)=0.2411 and is particularly simple at J(2)/J(1)=1/2. The BOW phase has a doubly degenerate singlet ground state, broken inversion symmetry, and a finite-energy gap E-m to the lowest-triplet state. The interval 0.4 < J(2)/J(1) < 1.0 has large E-m and small finite-size corrections. Exact solutions are presented up to N = 28 spins with either periodic or open boundary conditions and for thermodynamics up to N = 18. The elementary excitations of the BOW phase with large E-m are topological spin-1/2 solitons that separate BOWs with opposite phase in a regular array of spins. The molar spin susceptibility chi(M)(T) is exponentially small for T << E-m and increases nearly linearly with T to a broad maximum. J(1) and J(2) spin chains approximate the magnetic properties of the BOW phase of Hubbard-type models and provide a starting point for modeling alkali-tetracyanoquinodimethane salts.

Protection of adult but not newborn mice against lethal intracerebral challenge with Japanese encephalitis virus by adoptively transferred virus-specific cytotoxic T lymphocytes: Requirement for L3T4(+) T cells

The protective ability of cytotoxic T cells (CTL) raised in vitro against Japanese encephalitis virus (JEV) was examined by adoptive transfer experiments. Adoptive transfer of anti-JEV effecters by intracerebral (i.c.) but not by intraperitoneal (i.p.) or intravenous (i.v.) routes protected adult BALB/c mice against lethal i.c. JEV challenge. In contrast to adult mice, adoptive transfer of anti-JEV effecters into newborn (4-day-old) and suckling (8-14-day-old) mice did not confer protection. However, virus-induced death was delayed in suckling mice compared to newborn mice upon adoptive transfer. The specific reasons for lack of protection in newborn mice are not clear but virus load was found to be higher in newborn mice brains compared to those of adults and virus clearance was observed only in adult mice brains but not in newborn mice brains upon adoptive transfer. Specific depletion of Lyt 2.2(+), L3T4(+) or Thy-1(+) T cell populations before adoptive transfer abrogated the protective ability of transferred effecters. However, when Lyt 2.2(+) cell-depleted and L3T4(+) cell-depleted effecters were mixed and transferred into adult mice the protective activity was retained, demonstrating that both Lyt 2.2(+) and L3T4(+) T cells are necessary to confer protection. Although the presence of L3T4(+) T cells in adoptively transferred effector populations enhanced virus-specific serum neutralizing antibodies, the presence of neutralizing antibodies alone without Lyt 2.2(+) cells was not sufficient to confer protection.

Some aspects of information processing in biological vision

An attempt is made to present some challenging problems (mainly to the technically minded researchers) in the development of computational models for certain (visual) processes which are executed with, apparently, deceptive ease by the human visual system. However, in the interest of simplicity (and with a nonmathematical audience in mind), the presentation is almost completely devoid of mathematical formalism. Some of the findings in biological vision are presented in order to provoke some approaches to their computational models, The development of ideas is not complete, and the vast literature on biological and computational vision cannot be reviewed here. A related but rather specific aspect of computational vision (namely, detection of edges) has been discussed by Zucker, who brings out some of the difficulties experienced in the classical approaches.Space limitations here preclude any detailed analysis of even the elementary aspects of information processing in biological vision, However, the main purpose of the present paper is to highlight some of the fascinating problems in the frontier area of modelling mathematically the human vision system.

The algebra and geometry of SU(3) matrices

We give an elementary treatment of the defining representation and Lie algebra of the three-dimensional unitary unimodular group SU(3). The geometrical properties of the Lie algebra, which is an eight dimensional real Linear vector space, are developed in an SU(3) covariant manner. The f and d symbols of SU(3) lead to two ways of 'multiplying' two vectors to produce a third, and several useful geometric and algebraic identities are derived. The axis-angle parametrization of SU(3) is developed as a generalization of that for SU(2), and the specifically new features are brought out. Application to the dynamics of three-level systems is outlined.

STAT-1 expression is regulated by IGFBP-3 in malignant glioma cells and is a strong predictor of poor survival in patients with glioblastoma Laboratory investigation

Object. Insulin-like growth factor binding proteins (IGEBPs) have been implicated in the pathogenesis of glioma. In a previous study the authors demonstrated that IGFBP-3 is a novel glioblastoma biomarker associated with poor survival. Since signal transducer and activator of transcription 1 (STAT-1) has been shown to be regulated by IGFBP-3 during chondrogenesis and is a prosurvival and radioresistant molecule in different tumors, the aim in the present study was to explore the functional significance of IGFBP-3 in malignant glioma cells, to determine if STAT-1 is indeed regulated by IGFBP-3, and to study the potential of STAT-1 as a biomarker in glioblastoma. Methods. The functional significance of IGFBP-3 was investigated using the short hairpin (sh)RNA gene knockdown approach on U251MG cells. STAT-1 regulation by IGFBP-3 was tested on U251MG and U87MG cells by shRNA gene knockdown and exogenous treatment with recombinant IGFBP-3 protein. Subsequently, the expression of STAT-1 was analyzed with real-time reverse transcription polymerase chain reaction (RT-PCR) and immunohistochemistry (IHC) in glioblastoma and control brain tissues. Survival analyses were done on a uniformly treated prospective cohort of adults with newly diagnosed glioblastoma (136 patients) using Kaplan-Meier and Cox regression models. Results. IGFBP-3 knockdown significantly impaired proliferation, motility, migration, and invasive capacity of U251MG cells in vitro (p < 0.005). Exogenous overexpression of IGFBP-3 in U251MG and U87MG cells demonstrated STAT-1 regulation. The mean transcript levels (by real-time RT-PCR) and the mean labeling index of STAT-1 (by IHC) were significantly higher in glioblastoma than in control brain tissues (p = 0.0239 and p < 0.001, respectively). Multivariate survival analysis revealed that STAT-1 protein expression (HR 1.015, p = 0.033, 95% CI 1.001-1.029) along with patient age (HR 1.025, p = 0.005, 95% CI 1.008-1.042) were significant predictors of shorter survival in patients with glioblastoma. Conclusions. IGFBP-3 influences tumor cell proliferation, migration, and invasion and regulates STAT-1 expression in malignant glioma cells. STAT-1 is overexpressed in human glioblastoma tissues and emerges as a novel prognostic biomarker.

Genome-wide methylation profiling identifies an essential role of reactive oxygen species in pediatric glioblastoma multiforme and validates a methylome specific for H3 histone family 3A with absence of G-CIMP/isocitrate dehydrogenase 1 mutation

Background. Pediatric glioblastoma multiforme (GBM) is rare, and there is a single study, a seminal discovery showing association of histone H3.3 and isocitrate dehydrogenase (IDH) 1 mutation with a DNA methylation signature. The present study aims to validate these findings in an independent cohort of pediatric GBM, compare it with adult GBM, and evaluate the involvement of important functionally altered pathways. Methods. Genome-wide methylation profiling of 21 pediatric GBM cases was done and compared with adult GBM data (GSE22867). We performed gene mutation analysis of IDH1 and H3 histone family 3A (H3F3A), status evaluation of glioma cytosine-phosphate-guanine island methylator phenotype (G-CIMP), and Gene Ontology analysis. Experimental evaluation of reactive oxygen species (ROS) association was also done. Results. Distinct differences were noted between methylomes of pediatric and adult GBM. Pediatric GBM was characterized by 94 hypermethylated and 1206 hypomethylated cytosine-phosphate-guanine (CpG) islands, with 3 distinct clusters, having a trend to prognostic correlation. Interestingly, none of the pediatric GBM cases showed G-CIMP/IDH1 mutation. Gene Ontology analysis identified ROS association in pediatric GBM, which was experimentally validated. H3F3A mutants (36.4%; all K27M) harbored distinct methylomes and showed enrichment of processes related to neuronal development, differentiation, and cell-fate commitment. Conclusions. Our study confirms that pediatric GBM has a distinct methylome compared with that of adults. Presence of distinct clusters and an H3F3A mutation-specific methylome indicate existence of epigenetic subgroups within pediatric GBM. Absence of IDH1/G-CIMP status further indicates that findings in adult GBM cannot be simply extrapolated to pediatric GBM and that there is a strong need for identification of separate prognostic markers. A possible role of ROS in pediatric GBM pathogenesis is demonstrated for the first time and needs further evaluation.