The inducibility of complete bipartite graphs

For any s ≥ 1 and t ≥ (^S₂), we prove that among all graphs with n vertices the graph that contains the maximal number of induced copies of K_{t, t+s} for any fixed s ≥ 1 and t ≥ (^s₂) is K_{(n/2)+α(n/2)-α} for some function α = o(n). We show that this is not valid for t < (^s₂). Analogous results for complete multipartite graphs are also obtained.     

The neuroblast and angioblast chemotaxic factor SDF-1 (CXCL12) expression is briefly up regulated by reactive astrocytes in brain following neonatal hypoxic-ischemic injury

Background  

Stromal cell-derived factor 1 (SDF-1 or CXCL12) is chemotaxic for CXCR4 expressing bone marrow-derived cells. It functions in brain embryonic development and in response to ischemic injury in helping guide neuroblast migration and vasculogenesis. In experimental adult stroke models SDF-1 is expressed perivascularly in the injured region up to 30 days after the injury, suggesting it could be a therapeutic target for tissue repair strategies. We hypothesized that SDF-1 would be expressed in similar temporal and spatial patterns following hypoxic-ischemic (HI) injury in neonatal brain.     

Efficient parallel resolution of an active ester of 2-phenylpropionic acid using quasi-enantiomeric Evans’ oxazolidinones

The parallel kinetic resolution of pentafluorophenyl 2-phenylpropionate using an equimolar combination of quasi-enantiomeric oxazolidinones is discussed. The levels of diastereocontrol were excellent leading to separable quasi-enantiomeric syn-oxazolidinone adducts in good yield.     

Molecular origins of nonlinear viscoelasticity

Polymer melts are discussed in terms of relationships between their nonlinear viscoelasticity and molecular structure. The challenges of making nonlinear measurements and the rheometers available for studying nonlinear viscoelasticity are presented. Theories and constitutive models are reviewed and compared with one another and experimental data. Future studies of the molecular origins of nonlinear viscoelasticity are discussed especially in terms of rheometer development and future prospects for nonlinear viscoelastic models.     

Families of rationally connected varieties

We prove that every one-parameter family of complex rationally connected varieties has a section.

     

Finite Affine Groups: Cycle Indices, Hall–Littlewood Polynomials, and Probabilistic Algorithms

The study of asymptotic properties of the conjugacy class of a random element of the finite affine group leads one to define a probability measure on the set of all partitions of all positive integers. Four different probabilistic understandings of this measure are given—three using symmetric function theory and one using Markov chains. This leads to non-trivial enumerative results. Cycle index generating functions are derived and are used to compute the large dimension limiting probabilities that an element of the affine group is separable, cyclic, or semisimple and to study the convergence to these limits. The semisimple limit involves both Rogers–Ramanujan identities. This yields the first examples of such computations for a maximal parabolic subgroup of a finite classical group.     

Reducing hypothalamic AGRP by RNA interference increases metabolic rate and decreases body weight without influencing food intake

Background  

Several lines of evidence strongly suggest that agouti-related peptide (AGRP) plays a key role in the regulation of metabolic function but ablation of the AGRP gene has no apparent effect on metabolic function. Since specific pharmacological antagonists of AGRP do not presently exist, we assessed if reduction of hypothalamic AGRP mRNA by RNA interference (RNAI) would influence metabolic function, an outcome suggesting that pharmacological antagonists might constitute useful reagents to treat obesity.     

On the minimum ropelength of knots and links

The ropelength of a knot is the quotient of its length by its thickness, the radius of the largest embedded normal tube around the knot. We prove existence and regularity for ropelength minimizers in any knot or link type; these are C ^1,1 curves, but need not be smoother. We improve the lower bound for the ropelength of a nontrivial knot, and establish new ropelength bounds for small knots and links, including some which are sharp. Oblatum 11-IV-2001 & 20-III-2002?Published online: 17 June 2002