Zagreb indices belong to better known and better researched topological indices. We investigate here their ability to discriminate among benzenoid graphs and arrive at some quite unexpected conclusions. Along the way we establish tight (and sometimes sharp) lower and upper bounds on various classes of benzenoids.

Aim To analyze the pharmacy network (structure and resources) in Bulgaria, Croatia, Serbia, and Slovenia and its relation to public expenditures for medicines. Methods We performed a cross-sectional study using the officially published data for the period 2003-2008 in four selected countries. Data sources were relevant national institutions. Results In 2008, Serbia had 27.5, Bulgaria 66.8, Croatia 59.5, and Slovenia 71.2 pharmacists per 100 000 inhabitants. There was a significant difference in the number of pharmacists per 100 000 inhabitants between all countries except between Bulgaria and Slovenia. The number of inhabitants per one pharmacy was significantly different between all observed countries. The expenditures for medicines per capita in 2008 were between €30.34 in Bulgaria to €137.03 in Slovenia, with a significant difference between all countries except between Bulgaria and Serbia. The number of pharmacists per 100 000 inhabitants and expenditures for medicines per capita were positively correlated in all observed countries, except in Bulgaria. Conclusion There were significant difference in the structure and availability of the pharmacy service in all selected countries. Expenditures for medicines were positively correlated with the number of pharmacists in all countries, except in Bulgaria. Our findings could be valuable to national regulatory bodies for the creation of national drug policies.

Dendritic cells (DCs) as professional antigen-presenting cells play an important role in the initiation and modulation of the adaptive immune response. However, their role in the innate immune response against bacterial infections is not completely defined. Here we have analyzed the role of DCs and their impact on the innate anti-bacterial host defense in an experimental infection model of Yersinia enterocolitica (Ye). We used CD11c-diphtheria toxin (DT) mice to deplete DCs prior to severe infection with Ye. DC depletion significantly increased animal survival after Ye infection. The bacterial load in the spleen of DC-depleted mice was significantly lower than that of control mice throughout the infection. DC depletion was accompanied by an increase in the serum levels of CXCL1, G-CSF, IL-1α, and CCL2 and an increase in the numbers of splenic phagocytes. Functionally, splenocytes from DC-depleted mice exhibited an increased bacterial killing capacity compared to splenocytes from control mice. Cellular studies further showed that this was due to an increased production of reactive oxygen species (ROS) by neutrophils. Adoptive transfer of neutrophils from DC-depleted mice into control mice prior to Ye infection reduced the bacterial load to the level of Ye-infected DC-depleted mice, suggesting that the increased number of phagocytes with additional ROS production account for the decreased bacterial load. Furthermore, after incubation with serum from DC-depleted mice splenocytes from control mice increased their bacterial killing capacity, most likely due to enhanced ROS production by neutrophils, indicating that serum factors from DC-depleted mice account for this effect. In summary, we could show that DC depletion triggers phagocyte accumulation in the spleen and enhances their anti-bacterial killing capacity upon bacterial infection.

This review provides a comprehensive description of the self-guided Langevin dynamics (SGLD) and the self-guided molecular dynamics (SGMD) methods and their applications. Example systems are included to provide guidance on optimal application of these methods in simulation studies. SGMD/SGLD has enhanced ability to overcome energy barriers and accelerate rare events to affordable time scales. It has been demonstrated that with moderate parameters, SGLD can routinely cross energy barriers of 20 kT at a rate that molecular dynamics (MD) or Langevin dynamics (LD) crosses 10 kT barriers. The core of these methods is the use of local averages of forces and momenta in a direct manner that can preserve the canonical ensemble. The use of such local averages results in methods where low frequency motion "borrows" energy from high frequency degrees of freedom when a barrier is approached and then returns that excess energy after a barrier is crossed. This self-guiding effect also results in an accelerated diffusion to enhance conformational sampling efficiency. The resulting ensemble with SGLD deviates in a small way from the canonical ensemble, and that deviation can be corrected with either an on-the-fly or a post processing reweighting procedure that provides an excellent canonical ensemble for systems with a limited number of accelerated degrees of freedom. Since reweighting procedures are generally not size extensive, a newer method, SGLDfp, uses local averages of both momenta and forces to preserve the ensemble without reweighting. The SGLDfp approach is size extensive and can be used to accelerate low frequency motion in large systems, or in systems with explicit solvent where solvent diffusion is also to be enhanced. Since these methods are direct and straightforward, they can be used in conjunction with many other sampling methods or free energy methods by simply replacing the integration of degrees of freedom that are normally sampled by MD or LD.

Abstract This paper offers a geometric framework for modeling port-Hamiltonian systems on discrete manifolds. The simplicial Dirac structure, capturing the topological laws of the system, is defined in terms of primal and dual cochains related by the coboundary operators. This finite-dimensional Dirac structure, as discrete analogue of the canonical Stokes-Dirac structure, allows for the formulation of finite-dimensional port-Hamiltonian systems that emulate the behaviour of the open distributed-parameter systems with Hamiltonian dynamics.