On optimal and near-optimal shapes of external shading of windows in apartment buildings.

We studied previously optimal shape of external shading of windows in a cellular office with an outer edge modeled by a non-uniform rational basis spline (NURBS) curve whose control points were placed uniformly around western fin, overhang and eastern fin of the window, and whose depths were allowed to vary independently. We observed there that for each climate considered in the study there exists a shading shape close to the optimal one, but with a substantially simpler structure of control points for the NURBS curve. This simpler structure was reflected in partitioning control points into six groups such that all control points in the same group have equal depths, with groups corresponding to lower part of the western fin, upper part of the western fin, joint of the western fin and the overhang, internal part of the overhang, joint of the overhang and the eastern fin and the remaining part of the eastern fin. Here we confirm that shadings with control point structure restricted in such way can perform as well as shadings with unrestricted control points by optimising shape of external shading of windows in an apartment room for both restricted and unrestricted control point structure for the same range of climates, and showing that differences in heating and cooling demands between Pareto optimal shadings in both cases are negligibly small. This grouping of control points thus gives a simple and natural division of shading into a small number of basic constituents that have most impact on its heating and cooling demands. We further consider the convex hull of the Pareto front for shadings with restricted control points, as it contains shadings that minimise equivalent source energy in terms of the ratio of efficiencies and source energy conversion factors for district heating and cooling. We show that, in cases when depths of control point groups in convex hull shadings do not experience sudden changes between their extremal values, these depths can be fitted reasonably well by a sigmoid function that results in functional shadings that satisfactorily approximate heating and cooling demands of shadings in the Pareto front.

Optimisation of curvilinear external shading of windows in cellular offices.

Shading of windows influences building cooling and heating loads through control of solar heat gains, and lighting load through access to available daylight. Shading shape thus presents an important factor both in building energy analysis and building aesthetics. Curvilinearity of solar paths suggests that the optimal shading shape may be curvilinear as well, and our aim here is to test this expectation. To accommodate curvilinearity of shading shape, outer edges of shading, which consists of overhang, western and eastern fins, are modeled as non-uniform rational basis spline (NURBS) curves, a widely accepted representation standard for curves in design industry. As a case study, a cellular office is considered in the Pacific Northwest National Laboratory (PNNL) office building model, with its overhang lined up by seven control points, and the fins lined up by five control points each, with two ending control points joint for the overhang and the fins. With control points allowed to take on nine different alternative depths, genetic optimisation is employed for 16 representative USA climates with respect to total equivalent source energy for heating, cooling and lighting loads. The main finding is that in a very close proximity to optimal shadings found by genetic optimisation there exist shadings with much simpler control point structure, obtained by identifying depths of successive control points, that have nearly rectangular overhangs. Since the difference between these simpler shadings and the optimal ones is less than 0.24%, this partially rejects the expectation that the optimal shading shape should be curvilinear. Structure of these near-optimal shadings also suggests a new way to partition shadings into independent regions: the lower and the upper parts of the western fin, joints of the overhang with the western and the eastern fin, the interior part of the overhang and the rest of the eastern fin.

Comment on "Subgraph centrality in complex networks".

We disprove a conjecture of Estrada and Rodríguez-Velázquez [Phys. Rev. E 71, 056103 (2005)] that if a graph has identical subgraph centrality for all nodes, then the closeness and betweenness centralities are also identical for all nodes.

Decreasing the spectral radius of a graph by link removals.

The decrease of the spectral radius, an important characterizer of network dynamics, by removing links is investigated. The minimization of the spectral radius by removing m links is shown to be an NP-complete problem, which suggests considering heuristic strategies. Several greedy strategies are compared, and several bounds on the decrease of the spectral radius are derived. The strategy that removes that link l=i~j with largest product (x(1))(i)(x(1))(j) of the components of the eigenvector x(1) belonging to the largest adjacency eigenvalue is shown to be superior to other strategies in most cases. Furthermore, a scaling law where the decrease in spectral radius is inversely proportional to the number of nodes N in the graph is deduced. Another sublinear scaling law of the decrease in spectral radius versus the number m of removed links is conjectured.

[LEAP (Lantus Early Access Programme) in Sarajevo]. / LEAP (Lantus Early Access Programme)--program za ranu dostupnost Lantusa u Sarajevu.

LEAP is multicentric study in phase IV. The first aim was to affirm Lantus efficacy and safety in every day practice, in local conditions. The second aims were to verify therapy successful by measuring fast blood glucose (FBG) and HbA1c and to estimate patients' pleasure. Duration of study was 2 months. Lantus was administrated subcutaneously daily. Doses were individual. HbA1c was measured at the begining of therapy and at the last control. Blood glucose was measured every day. The study included patients who did not reach the control of glycemy, or patients with frequent hypoglycemic crysis, older then 6 year. LEAP study in Sarajevo included 114 patients. Fifty four patients (47%) were men, and 60 (53%) were women. 46% diabetics have type 1 of diabetes mellitus and 54% have type 2 diabetes mellitus. The results of study demonstrated statistically significant decreasing of FBG and HbA1c in both groups (I group--patients younger than 18 years and II group--patients older than 18 years), p<0.05. FBG in I group on the start of Lantus therapy was 9.9+/-3.9 mmol/l but on ending control was 8.7+/-4.4 mmol/l (p<0.05). HbA1c on start of therapy was 9.4+/-1.9%, but on end control was 8.0+/-1.8% (p<0.05). FBG in II group on start was 13.6+/-4.7 mmol/l but on finish was 7.3+/-2.9 mmol/l (p<0.01). HbA1c on start was 9.3+/-1.8% and on end was 7.2+/-1.2% (p<0.01). These results showed that the Lantus is very efficacious for good glycoregulation. Just for two months, HbA1c decreased for 2%. Undesirable effects were not registered. We concluded that Lantus is very safe. Most patients (89%) were satisfied with therapy.