Superselectors: Efficient Constructions and Applications

We introduce a new combinatorial structure: the superselector. We show that superselectors subsume several important combinatorial structures used in the past few years to solve problems in group testing, compressed sensing, multi-channel conflict resolution and data security. We prove close upper and lower bounds on the size of superselectors and we provide efficient algorithms for their constructions. Albeit our bounds are very general, when they are instantiated on the combinatorial structures that are particular cases of superselectors (e.g., (p,k,n)-selectors, (d,\ell)-list-disjunct matrices, MUT_k(r)-families, FUT(k, a)-families, etc.) they match the best known bounds in terms of size of the structures (the relevant parameter in the applications). For appropriate values of parameters, our results also provide the first efficient deterministic algorithms for the construction of such structures

Radio morphological changes in the femoral and tibial condyles in patients with arthrosis deformans of the knee

Objective: to investigate the quantitative X-ray manifestations of gonarthrosis in patients in different age groups.Material and methods. The results of radiography, computed tomography, and 64-slice multidetector computed tomography (MDCT) were analyzed in 86 patients aged 18 to 70 years with arthrosis deformans of the knee.Results. Knee radiographic anatomic changes in arthrosis deformans are  accompanied by the characteristic rearrangement of the femoral and tibial condyles. Quantitative bone density changes appear as an overall decrease in the bone  mineral density of the femoral and tibial condyles in 18–35-year-old patients with arthrosis deformans (p<0.05) and a relative increase in that of medial tibial condyles in patients older than 55/60 years, in those with genu varum in particular.Conclusion. In the patients with arthrosis deformans, the bone radio morphological changes detected by MDCT have a much wider range of qualitative and quantitative characteristics. The data on condylar bone density are directly related to a treatment choice. Data postprocessing using the current visualization programs of working stations identifies minor bone structural changes that are also of importance in solving the tactical problems of medical and surgical treatments