X-ray emission from clusters and groups of galaxies

Recent major advances in x-ray imaging and spectroscopy of clusters have allowed the determination of their mass and mass profile out to ≈1/2 the virial radius. In rich clusters, most of the baryonic mass is in the gas phase, and the ratio of mass in gas/stars varies by a factor of 2–4. The baryonic fractions vary by a factor of ≈3 from cluster to cluster and almost always exceed 0.09 h50−[3/2] and thus are in fundamental conflict with the assumption of Ω = 1 and the results of big bang nucleosynthesis. The derived Fe abundances are 0.2–0.45 solar, and the abundances of O and Si for low redshift systems are 0.6–1.0 solar. This distribution is consistent with an origin in pure type II supernova. The amount of light and energy produced by these supernovae is very large, indicating their importance in influencing the formation of clusters and galaxies. The lack of evolution of Fe to a redshift of z ≈ 0.4 argues for very early enrichment of the cluster gas. Groups show a wide range of abundances, 0.1–0.5 solar. The results of an x-ray survey indicate that the contribution of groups to the mass density of the universe is likely to be larger than 0.1 h50−2. Many of the very poor groups have large x-ray halos and are filled with small galaxies whose velocity dispersion is a good match to the x-ray temperatures.

Adjoint modular Galois representations and their Selmer groups

In the last 15 years, many class number formulas and main conjectures have been proven. Here, we discuss such formulas on the Selmer groups of the three-dimensional adjoint representation ad(φ) of a two-dimensional modular Galois representation φ. We start with the p-adic Galois representation φ0 of a modular elliptic curve E and present a formula expressing in terms of L(1, ad(φ0)) the intersection number of the elliptic curve E and the complementary abelian variety inside the Jacobian of the modular curve. Then we explain how one can deduce a formula for the order of the Selmer group Sel(ad(φ0)) from the proof of Wiles of the Shimura–Taniyama conjecture. After that, we generalize the formula in an Iwasawa theoretic setting of one and two variables. Here the first variable, T, is the weight variable of the universal p-ordinary Hecke algebra, and the second variable is the cyclotomic variable S. In the one-variable case, we let φ denote the p-ordinary Galois representation with values in GL2(Zp[[T]]) lifting φ0, and the characteristic power series of the Selmer group Sel(ad(φ)) is given by a p-adic L-function interpolating L(1, ad(φk)) for weight k + 2 specialization φk of φ. In the two-variable case, we state a main conjecture on the characteristic power series in Zp[[T, S]] of Sel(ad(φ) ⊗ ν−1), where ν is the universal cyclotomic character with values in Zp[[S]]. Finally, we describe our recent results toward the proof of the conjecture and a possible strategy of proving the main conjecture using p-adic Siegel modular forms.

The structure of Selmer groups

The purpose of this article is to describe certain results and conjectures concerning the structure of Galois cohomology groups and Selmer groups, especially for abelian varieties. These results are analogues of a classical theorem of Iwasawa. We formulate a very general version of the Weak Leopoldt Conjecture. One consequence of this conjecture is the nonexistence of proper Λ-submodules of finite index in a certain Galois cohomology group. Under certain hypotheses, one can prove the nonexistence of proper Λ-submodules of finite index in Selmer groups. An example shows that some hypotheses are needed.

Zeta functions and Eisenstein series on classical groups

We construct an Euler product from the Hecke eigenvalues of an automorphic form on a classical group and prove its analytic continuation to the whole complex plane when the group is a unitary group over a CM field and the eigenform is holomorphic. We also prove analytic continuation of an Eisenstein series on another unitary group, containing the group just mentioned defined with such an eigenform. As an application of our methods, we prove an explicit class number formula for a totally definite hermitian form over a CM field.

Patterns of kinship in groups of free-living sperm whales (Physeter macrocephalus) revealed by multiple molecular genetic analyses.

Mature female sperm whales (Physeter macrocephalus) live in socially cohesive groups of 10-30, which include immature animals of both sexes, and within which there is communal care of the young. We examined kinship in such groups using analyses of microsatellite DNA, mitochondrial DNA sequence, and sex-linked markers on samples of sloughed skin collected noninvasively from animals in three groups off the coast of Ecuador. Social groups were defined through photographic identification of individuals. Each group contained about 26 members, mostly female (79%). Relatedness was greater within groups, as compared to between groups. Particular mitochondrial haplotypes were characteristic of groups, but all groups contained more than one haplotype. The data are generally consistent with each group being comprised of several matrillines from which males disperse at about the age of 6 years. There are indications of paternal relatedness among grouped individuals with different mitochondrial haplotypes, suggesting long-term associations between different matrilines.

Physical and functional independency of p70 and p58 natural killer (NK) cell receptors for HLA class I: their role in the definition of different groups of alloreactive NK cell clones.

Natural killer (NK) cells express clonally distributed receptors for different groups of HLA class I alleles. The Z27 monoclonal antibody described in this study recognizes a p70 receptor specific for HLA-B alleles belonging to the Bw4 supertypic specificity. Single amino acid substitutions in the peptide-binding groove of HLA-B2705 molecules influenced the recognition by some, but not all, p7O/Z27+ clones. This suggests the existence of a limited polymorphism within the p7O family of receptors. The pattern of reactivity of monoclonal antibody Z27 revealed that Bw4-specific receptors may be expressed alone or in combination with different (GL183 and/or EB6) p58 molecules. Analysis of NK clones coexpressing p58 and p7O receptors allowed us to demonstrate that the two molecules represent physically and functionally independent receptors. The expression of p7O molecules either alone or in combination with EB6 molecules provided the molecular basis for understanding the cytolytic pattern of two previously defined groups of "alloreactive" NK cell clones ("group 3" and "group 5").

Major histocompatibility complex class II DR alleles DRB1*1501 and those encoding HLA-DR13 are preferentially associated with a diminution in maternally transmitted human immunodeficiency virus 1 infection in different ethnic groups: determination by an automated sequence-based typing method.

Transmission of human immunodeficiency virus 1 (HIV-1) from an infected women to her offspring during gestation and delivery was found to be influenced by the infant's major histocompatibility complex class II DRB1 alleles. Forty-six HIV-infected infants and 63 seroreverting infants, born with passively acquired anti-HIV antibodies but not becoming detectably infected, were typed by an automated nucleotide-sequence-based technique that uses low-resolution PCR to select either the simpler Taq or the more demanding T7 sequencing chemistry. One or more DR13 alleles, including DRB1*1301, 1302, and 1303, were found in 31.7% of seroreverting infants and 15.2% of those becoming HIV-infected [OR (odds ratio) = 2.6 (95% confidence interval 1.0-6.8); P = 0.048]. This association was influenced by ethnicity, being seen more strongly among the 80 Black and Hispanic children [OR = 4.3 (1.2-16.4); P = 0.023], with the most pronounced effect among Black infants where 7 of 24 seroreverters inherited these alleles with none among 12 HIV-infected infants (Haldane OR = 12.3; P = 0.037). The previously recognized association of DR13 alleles with some situations of long-term nonprogression of HIV suggests that similar mechanisms may regulate both the occurrence of infection and disease progression after infection. Upon examining for residual associations, only only the DR2 allele DRB1*1501 was associated with seroreversion in Caucasoid infants (OR = 24; P = 0.004). Among Caucasoids the DRB1*03011 allele was positively associated with the occurrence of HIV infection (P = 0.03).