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.

Sleep during the third trimester of pregnancy: the role of depression and anxiety

Depression has been associated with sleep disturbances in pregnancy; however, no previous research has controlled the possible confounding effect of anxiety on this association. This study aims to analyze the effect of depression on sleep during the third trimester of pregnancy controlling for anxiety. The sample was composed by 143 depressed (n = 77) and non-depressed (n = 66) pregnant women who completed measures of depression, anxiety, and sleep. Differences between groups in sleep controlling for anxiety were found. Depressed pregnant women present higher number of nocturnal awakenings and spent more hours trying falling asleep during the night and the entire 24 h period. Present findings point out the effect of depression on sleep in late pregnancy, after controlling for anxiety.