Brooksʼ Theorem for generalized dart graphs

The well-known Brooks? Theorem says that each graph G of maximum degree $k?3$ is k-colorable unless $G=K_{k+1}$. We generalize this theorem by allowing higher degree vertices with prescribed types of neighborhood.     

SN-38 loading capacity of hydrophobic polymer blend nanoparticles: formulation,optimization and efficacy evaluation

One of the most important problems in nanoencapsulation of extremely hydrophobic drugs is poor drug loading due to rapid drug crystallization outside the polymer core. The effort to use nanoprecipitation, as a simple one-step procedure with good reproducibility and FDA approved polymers like Poly(lactic-co-glycolic acid) (PLGA) and Polycaprolactone (PCL), will only potentiate this issue. Considering that drug loading is one of the key defining characteristics, in this study we attempted to examine whether the nanoparticle (NP) core composed of two hydrophobic polymers will provide increased drug loading for 7-Ethyl-10-hydroxy-camptothecin (SN-38), relative to NPs prepared using individual polymers. D-optimal design was applied to optimize PLGA/PCL ratio in the polymer blend and the mode of addition of the amphiphilic copolymer Lutrol^®F127 in order to maximize SN-38 loading and obtain NPs with acceptable size for passive tumor targeting. Drug/polymer and polymer/polymer interaction analysis pointed to high degree of compatibility and miscibility among both hydrophobic polymers, providing core configuration with higher drug loading capacity. Toxicity studies outlined the biocompatibility of the blank NPs. Increased in vitro efficacy of drug-loaded NPs compared to the free drug was confirmed by growth inhibition studies using SW-480 cell line. Additionally, the optimized NP formulation showed very promising blood circulation profile with elimination half-time of 7.4?h.     

Prevalence of anxiety and depressive illness and help seeking behaviour in African Caribbeans and white Europeans: two phase general population survey

OBJECTIVE: To determine the prevalence of common mental disorders (anxiety and depression) and help seeking behaviour in African Caribbeans and white Europeans. DESIGN: Two phase survey in a general population sample. The first phase comprised screening with the 12 item general health questionnaire; the second phase was standardised psychiatric assessment and interview about help seeking. SETTING: People registered with four general practices in central Manchester. PARTICIPANTS: Of 1467 people randomly selected from family health services authority lists, 864 were still resident. 337 African Caribbeans and 275 white Europeans completed the screening phase (response rate 71%); 127 African Caribbeans and 103 white Europeans were interviewed in the second phase. MAIN OUTCOME MEASURES: One month period prevalence of anxiety and depressive disorders in each ethnic group. RESULTS: 13% of African Caribbeans (95% confidence interval 10% to 16%) and 14% (10% to 18%) of white Europeans had one or more disorder. Anxiety disorders were significantly less common among African Caribbeans (3% (1% to 5%) v 9% (6% to 12%) in white Europeans). Depressive disorders were significantly more common among African Caribbean women than white women (difference 8% (1% to 15%)). Medical help seeking was similar in the two groups, but African Caribbeans with mental disorders were more likely to seek additional help from non-medical sources (12/29 v 5/29, P=0.082). CONCLUSIONS: In an inner city setting the prevalence of common mental disorders is similar in these two ethnic groups.     

Line graph operation and small worlds

Complex networks, such as small world networks, are the focus of recent interest because of their potential as models for the interaction networks of complex systems. Most of the well-known models of small world networks are stochastic. The randomness makes it more difficult to gain a visual understanding of how networks are shaped, and how different vertices relate to each other. In this paper, we present and study a method for constructing deterministic small worlds using the line graph operator. This operator introduces cliques at every vertex of the original graph, which may imply larger clustering coefficients. On the other hand, this operator can increase the diameter at most by one and assure the small world property.     

On generalized middle-level problem

Let be the subgraph of the hypercube Q_n induced by levels between k and n-k, where n?2k+1 is odd. The well-known middle-level conjecture asserts that is Hamiltonian for all k?1. We study this problem in for fixed k. It is known that and are Hamiltonian for all odd n?3. In this paper we prove that also is Hamiltonian for all odd n?5, and we conjecture that is Hamiltonian for every k?0 and every odd n?2k+1.