An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds

For a given self-map f of M, a closed smooth connected and simply-connected manifold of dimension m ≥ 4, we provide an algorithm for estimating the values of the topological invariant Dm r [f], which equals the minimal number of r-periodic points in the smooth homotopy class of f. Our results are based on the combinatorial scheme for computing Dm r [f] introduced by G. Graff and J. Jezierski [J. Fixed Point Theory Appl. 13 (2013), 63–84]. An open-source implementation of the algorithm programmed in C++ is publicly available at http://www.pawelpilarczyk.com/combtop/.

Low f-number microlenses for integration on optical microsystems

This paper presents microlenses (MLs) with low f-number made of AZ4562 photoresist for integration on optical microsystems. The fabrication process was based on the thermal reflow and rehydration. Large series of MLs were fabricated with a width of 35 μm, a thickness of 5 μm, and spaced apart by 3 μm. The MLs were fabricated directly on the surface of a die with type n+/p-substrate junction photodiode fabricated in a standard CMOS process. The measured focal length was 49 μm with a tolerance of ±2 μm (maximum error of ±4%), resulting in a numerical aperture of 33.6 × 10-2 (±1.3 × 10-2). The measurements also revealed an f-number of 1.4.

Ancestry of the Brazilian TP53 c.1010G>A (p.Arg337His, R337H) founder mutation : clues from haplotyping of short tandem repeats on Chromosome 17p

Rare germline mutations in TP53 (17p13.1) cause a highly penetrant predisposition to a specific spectrum of early cancers, defining the Li-Fraumeni Syndrome (LFS). A germline mutation at codon 337 (p.Arg337His, c1010G>A) is found in about 0.3% of the population of Southern Brazil. This mutation is associated with partially penetrant LFS traits and is found in the germline of patients with early cancers of the LFS spectrum unselected for familial his- tory. To characterize the extended haplotypes carrying the mutation, we have genotyped 9 short tandem repeats on chromosome 17p in 12 trios of Brazilian p.Arg337His carriers. Results confirm that all share a common ancestor haplotype of Caucasian/Portuguese-Ibe- ric origin, distant in about 72–84 generations (2000 years assuming a 25 years intergenera- tional distance) and thus pre-dating European migration to Brazil. So far, the founder p. Arg337His haplotype has not been detected outside Brazil, with the exception of two resi- dents of Portugal, one of them of Brazilian origin. On the other hand, increased meiotic recombination in p.Arg337His carriers may account for higher than expected haplotype diversity. Further studies comparing haplotypes in populations of Brazil and of other areas of Portuguese migration are needed to understand the historical context of this mutation in Brazil.