Constructing genus 3 hyperelliptic Jacobians with CM

Given a sextic CM field $K$, we give an explicit method for finding all genus 3 hyperelliptic curves defined over $\mathbb{C}$ whose Jacobians are simple and have complex multiplication by the maximal order of this field, via an approximation of their Rosenhain invariants. Building on the work of Weng, we give an algorithm which works in complete generality, for any CM sextic field $K$, and computes minimal polynomials of the Rosenhain invariants for any period matrix of the Jacobian. This algorithm can be used to generate genus 3 hyperelliptic curves over a finite field $\mathbb{F}_p$ with a given zeta function by finding roots of the Rosenhain minimal polynomials modulo $p$.Comment: 20 pages; to appear in ANTS XI

Fe3+-hydroxide ligation in the superoxide reductase from Desulfoarculus baarsii is associated with pH dependent spectral changes.

International audienceSuperoxide reductase (SOR) catalyzes the reduction of O2*- to H2O2. Its active site consists of a non-heme Fe2+ center in an unusual square-pyramidal [His4 Cys] coordination. Like many SORs, the electronic absorption band corresponding to the oxidized active site of the SOR from Desulfoarculus baarsii exhibits a pH-dependent alkaline transition changing from ca. 644 to 560 nm as the pH increases and with an apparent pKa of 9.0. Variants in which the conserved amino acids glutamate 47 and lysine 48 were replaced by the neutral residues alanine (E47A) and isoleucine (K48I), respectively, exhibited the same alkaline transition but at lower apparent pKa values of 6.7 and 7.6, respectively. Previous work [Nivière, V.; Asso, M.; Weill, C. O.; Lombard, M.; Guigliarelli, B.; Favaudon, V.; Houée-Levin, C. Biochemistry 2004, 43, 808-818] has shown that this alkaline transition is associated with the protonation/deprotonation of an unidentified base, B-, which is neither E47 nor K48. In this work, we show by resonance Raman spectroscopy that at basic pH a high-spin Fe3+-OH species is formed at the active site. The presence of the HO- ligand was directly associated with an absorption band maximum at 560 nm, whereas upon protonation, the band shifts to 644 nm. With respect to our previous work, B- can be identified with this high-spin Fe3+-OH species, which upon protonation results in a water molecule at the active site. Implications for the SOR catalytic cycle are proposed

Personalized modeling for real-time pressure ulcer prevention in sitting posture

, Ischial pressure ulcer is an important risk for every paraplegic person and a major public health issue. Pressure ulcers appear following excessive compression of buttock's soft tissues by bony structures, and particularly in ischial and sacral bones. Current prevention techniques are mainly based on daily skin inspection to spot red patches or injuries. Nevertheless, most pressure ulcers occur internally and are difficult to detect early. Estimating internal strains within soft tissues could help to evaluate the risk of pressure ulcer. A subject-specific biomechanical model could be used to assess internal strains from measured skin surface pressures. However, a realistic 3D non-linear Finite Element buttock model, with different layers of tissue materials for skin, fat and muscles, requires somewhere between minutes and hours to compute, therefore forbidding its use in a real-time daily prevention context. In this article, we propose to optimize these computations by using a reduced order modeling technique (ROM) based on proper orthogonal decompositions of the pressure and strain fields coupled with a machine learning method. ROM allows strains to be evaluated inside the model interactively (i.e. in less than a second) for any pressure field measured below the buttocks. In our case, with only 19 modes of variation of pressure patterns, an error divergence of one percent is observed compared to the full scale simulation for evaluating the strain field. This reduced model could therefore be the first step towards interactive pressure ulcer prevention in a daily setup. Highlights-Buttocks biomechanical modelling,-Reduced order model,-Daily pressure ulcer prevention

Counterexamples to a Conjecture of Ahmadi and Shparlinski

Ahmadi-Shparlinski conjectured that every ordinary, geometrically simple Jacobian over a finite field has maximal angle rank. Using the L-Functions and Modular Forms Database, we provide two counterexamples to this conjecture in dimension 4.Comment: 6 page