A formula for the number of days between the winter solstice and the latest sunrise

A simple closed-form expression for the number of days between the winter solstice and the latest sunrise is derived. Formulas for the summer solstice and the sunset are derived as well. These approximate formulas make it easy to see the functional dependence on the latitude of the observer. An approximate expression for the difference in time of day between the latest sunrise and the sunrise on the solstice is also derived. The formulas are not valid in the Arctic, Antarctic or tropics.Comment: 9 pages, 1 figur

The expressions for the 2nd-order mixed partial derivatives of Slater-Koster matrix elements at spherical coordinate singularities

In a recent publication it has been shown how to generate derivatives with respect to atom coordinates of Slater-Koster matrix elements for the tight binding (TB) modelling of a system. For the special case of a mixed second partial derivative at coordinate singularities only the results were stated in that publication. In this work, the derivation of these results is given in detail. Though it may seem rather `technical' and only applicable to a very special case, atomic configurations where the connecting vector between the two atoms involved in a two-centre matrix element is aligned along the z-axis (in the usual approach) require results for precisely this case. The expressions derived in this work have been implemented in the DINAMO code.Comment: 9 pages, no figure

Angular Momentum Decomposition for an Electron

We calculate the orbital angular momentum of the `quark' in the scalar diquark model as well as that of the electron in QED (to order $\alpha$). We compare the orbital angular momentum obtained from the Jaffe-Manohar decomposition to that obtained from the Ji relation and estimate the importance of the vector potential in the definition of orbital angular momentum

Local spin operators for fermion simulations

Digital quantum simulation of fermionic systems is important in the context of chemistry and physics. Simulating fermionic models on general purpose quantum computers requires imposing a fermionic algebra on spins. The previously studied Jordan-Wigner and Bravyi-Kitaev transformations are two techniques for accomplishing this task. Here we re-examine an auxiliary fermion construction which maps fermionic operators to local operators on spins. The local simulation is performed by relaxing the requirement that the number of spins should match the number of fermionic modes. Instead, auxiliary modes are introduced to enable non-consecutive fermionic couplings to be simulated with constant low-rank tensor products on spins. We connect the auxiliary fermion construction to other topological models and give examples of the construction

Whole genome sequencing and microsatellite analysis of the Plasmodium falciparum E5 NF54 strain show that the var, rifin and stevor gene families follow Mendelian inheritance

Background: Plasmodium falciparum exhibits a high degree of inter-isolate genetic diversity in its variant surface antigen (VSA) families: P. falciparum erythrocyte membrane protein 1, repetitive interspersed family (RIFIN) and subtelomeric variable open reading frame (STEVOR). The role of recombination for the generation of this diversity is a subject of ongoing research. Here the genome of E5, a sibling of the 3D7 genome strain is presented. Short and long read whole genome sequencing (WGS) techniques (Ilumina, Pacific Bioscience) and a set of 84 microsatellites (MS) were employed to characterize the 3D7 and non-3D7 parts of the E5 genome. This is the first time that VSA genes in sibling parasites were analysed with long read sequencing technology. Results: Of the 5733 E5 genes only 278 genes, mostly var and rifin/stevor genes, had no orthologues in the 3D7 genome. WGS and MS analysis revealed that chromosomal crossovers occurred at a rate of 0–3 per chromosome. var, stevor and rifin genes were inherited within the respective non-3D7 or 3D7 chromosomal context. 54 of the 84 MS PCR fragments correctly identified the respective MS as 3D7- or non-3D7 and this correlated with var and rifin/stevor gene inheritance in the adjacent chromosomal regions. E5 had 61 var and 189 rifin/stevor genes. One large non-chromosomal recombination event resulted in a new var gene on chromosome 14. The remainder of the E5 3D7-type subtelomeric and central regions were identical to 3D7. Conclusions: The data show that the rifin/stevor and var gene families represent the most diverse compartments of the P. falciparum genome but that the majority of var genes are inherited without alterations within their respective parental chromosomal context. Furthermore, MS genotyping with 54 MS can successfully distinguish between two sibling progeny of a natural P. falciparum cross and thus can be used to investigate identity by descent in field isolates