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).

Is water structure around hydrophobic groups clathrate-like?

The term "clathrate structure" is quantified for solvation of nonpolar groups by enumerating hydrogen-bonded ring sizes both in the solvation shell and through the shell-bulk interface and comparing it to a bulk control using the ST4 water model. For clathrate-like structure to be evident, the distributions along the hydrophobic surface are expected to be dominated by pentagons, with significant depletion of hexagons and larger polygons. While the distribution in this region is indeed distinguished by a large number of pentagons, there are significant contributions from hexagons and larger rings as well. Calculated polygon distributions through the shell-bulk interface indicate that when water structure is highly cooperative along the hydrophobic surface, hydrogen-bonded pathways leading back into bulk are then reduced. These results are qualitatively consistent with the observation that hydrophobicity is proportional to the nonpolar solute surface area.

Assessment of groups in a network organization based on the Shapley group value.

The focus of this paper is the assessment of groups of agents or units in a network organization. Given a social network, the relations between agents are modeled by means of a graph, and its functionality will be codified by means of a cooperative game. Building on previous work of Gomez et al. (2003) for the individual case, we propose a Myerson group value to evaluate the ability of each group of agents inside the social network to achieve the organization's goals. We analyze this centrality measure, and in particular we offer several decompositions that facilitate obtaining a precise interpretation of it.

Groups, information theory, and Einstein's likelihood principle

We propose a unifying picture where the notion of generalized entropy is related to information theory by means of a group-theoretical approach. The group structure comes from the requirement that an entropy be well defined with respect to the composition of independent systems, in the context of a recently proposed generalization of the Shannon-Khinchin axioms. We associate to each member of a large class of entropies a generalized information measure, satisfying the additivity property on a set of independent systems as a consequence of the underlying group law. At the same time, we also show that Einstein's likelihood function naturally emerges as a byproduct of our informational interpretation of (generally nonadditive) entropies. These results confirm the adequacy of composable entropies both in physical and social science contexts.

Characterizations of logarithmic Besov spaces in terms of differences, Fourier-analytical decompositions, wavelets and semi-groups.

We work with Besov spaces Bp,q0,b defined by means of differences, with zero classical smoothness and logarithmic smoothness with exponent b. We characterize Bp,q0,b by means of Fourier-analytical decompositions, wavelets and semi-groups. We also compare those results with the well-known characterizations for classical Besov spaces Bp,qs.