A new procedure to analyze RNA non-branching structures

RNA structure prediction and structural motifs analysis are challenging tasks in the investigation of RNA function. We propose a novel procedure to detect structural motifs shared between two RNAs (a reference and a target). In particular, we developed two core modules: (i) nbRSSP_extractor, to assign a unique structure to the reference RNA encoded by a set of non-branching structures; (ii) SSD_finder, to detect structural motifs that the target RNA shares with the reference, by means of a new score function that rewards the relative distance of the target non-branching structures compared to the reference ones. We integrated these algorithms with already existing software to reach a coherent pipeline able to perform the following two main tasks: prediction of RNA structures (integration of RNALfold and nbRSSP_extractor) and search for chains of matches (integration of Structator and SSD_finder)

Non-Lipschitz points and the SBV regularity of the minimum time function

This paper is devoted to the study of the Hausdorff dimension of the singular set of the minimum time function $T$ under controllability conditions which do not imply the Lipschitz continuity of $T$. We consider first the case of normal linear control systems with constant coefficients in $\mathbb{R}^N$. We characterize points around which $T$ is not Lipschitz as those which can be reached from the origin by an optimal trajectory (of the reversed dynamics) with vanishing minimized Hamiltonian. Linearity permits an explicit representation of such set, that we call $\mathcal{S}$. Furthermore, we show that $\mathcal{S}$ is $\mathcal{H}^{N-1}$-rectifiable with positive $\mathcal{H}^{N-1}$-measure. Second, we consider a class of control-affine \textit{planar} nonlinear systems satisfying a second order controllability condition: we characterize the set $\mathcal{S}$ in a neighborhood of the origin in a similar way and prove the $\mathcal{H}^1$-rectifiability of $\mathcal{S}$ and that $\mathcal{H}^1(\mathcal{S})>0$. In both cases, $T$ is known to have epigraph with positive reach, hence to be a locally $BV$ function (see \cite{CMW,GK}). Since the Cantor part of $DT$ must be concentrated in $\mathcal{S}$, our analysis yields that $T$ is $SBV$, i.e., the Cantor part of $DT$ vanishes. Our results imply also that $T$ is locally of class $\mathcal{C}^{1,1}$ outside a $\mathcal{H}^{N-1}$-rectifiable set. With small changes, our results are valid also in the case of multiple control input.Comment: 23 page

Schur functions and their realizations in the slice hyperholomorphic setting

we start the study of Schur analysis in the quaternionic setting using the theory of slice hyperholomorphic functions. The novelty of our approach is that slice hyperholomorphic functions allows to write realizations in terms of a suitable resolvent, the so called S-resolvent operator and to extend several results that hold in the complex case to the quaternionic case. We discuss reproducing kernels, positive definite functions in this setting and we show how they can be obtained in our setting using the extension operator and the slice regular product. We define Schur multipliers, and find their co-isometric realization in terms of the associated de Branges-Rovnyak space

Nomenclature of the hydrotalcite supergroup: Natural layered double hydroxides

Layered double hydroxide (LDH) compounds are characterized by structures in which layers with a brucite-like structure carry a net positive charge, usually due to the partial substitution of trivalent octahedrally coordinated cations for divalent cations, giving a general layer formula [( M 2+ 1-x M 3+ x )(OH)2] x +. This positive charge is balanced by anions which are intercalated between the layers. Intercalated molecular water typically provides hydrogen bonding between the brucite layers. In addition to synthetic compounds, some of which have significant industrial applications, more than 40 mineral species conform to this description. Hydrotalcite, Mg6Al2(OH) 16[CO3]•4H2O, as the longest-known example, is the archetype of this supergroup of minerals. We review the history, chemistry, crystal structure, polytypic variation and status of all hydrotalcite-supergroup species reported to date. The dominant divalent cations, M 2+, that have been reported in hydrotalcite supergroup minerals are Mg, Ca, Mn, Fe, Ni, Cu and Zn; the dominant trivalent cations, M 3+, are Al, Mn, Fe, Co and Ni. The most common intercalated anions are (CO3)2-, (SO4)2- and Cl -; and OH-, S2- and [Sb(OH)6] - have also been reported. Some species contain intercalated cationic or neutral complexes such as [Na(H2O)6]+ or [MgSO4]0. We define eight groups within the supergroup on the basis of a combination of criteria. These are (1) the hydrotalcite group, with M 2+:M 3+ = 3:1 (layer spacing ∼7.8 Å); (2) the quintinite group, with M 2+:M 3+ = 2:1 (layer spacing ∼7.8 Å); (3) the fougèrite group, with M 2+ = Fe2+, M 3+ = Fe3+ in a range of ratios, and with O2- replacing OH- in the brucite module to maintain charge balance (layer spacing ∼7.8 Å); (4) the woodwardite group, with variable M 2+:M 3+ and interlayer [SO4] 2-, leading to an expanded layer spacing of ∼8.9 Å; (5) the cualstibite group, with interlayer [Sb(OH)6]- and a layer spacing of ∼9.7 Å; (6) the glaucocerinite group, with interlayer [SO4]2- as in the woodwardite group, and with additional interlayer H2O molecules that further expand the layer spacing to ∼11 Å; (7) the wermlandite group, with a layer spacing of ∼11 Å, in which cationic complexes occur with anions between the brucite-like layers; and (8) the hydrocalumite group, with M 2+ = Ca2+ and M 3+ = Al, which contains brucite-like layers in which the Ca:Al ratio is 2:1 and the large cation, Ca2+, is coordinated to a seventh ligand of 'interlayer' water. The principal mineral status changes are as follows. (1) The names manasseite, sjögrenite and barbertonite are discredited; these minerals are the 2H polytypes of hydrotalcite, pyroaurite and stichtite, respectively. Cyanophyllite is discredited as it is the 1M polytype of cualstibite. (2) The mineral formerly described as fougèrite has been found to be an intimate intergrowth of two phases with distinct Fe 2+:Fe3+ ratios. The phase with Fe2+:Fe 3+ = 2:1 retains the name fougèrite; that with Fe 2+:Fe3+ = 1:2 is defined as the new species trébeurdenite. (3) The new minerals omsite (IMA2012-025), Ni 2Fe3+(OH)6[Sb(OH)6], and mössbauerite (IMA2012-049), Fe3+ 6O 4(OH)8[CO3]•3H2O, which are both in the hydrotalcite supergroup are included in the discussion. (4) Jamborite, carrboydite, zincaluminite, motukoreaite, natroglaucocerinite, brugnatellite and muskoxite are identified as questionable species which need further investigation in order to verify their structure and composition. (5) The ranges of compositions currently ascribed to motukoreaite and muskoxite may each represent more than one species. The same applies to the approved species hydrowoodwardite and hydrocalumite. (6) Several unnamed minerals have been reported which are likely to represent additional species within the supergroup. This report has been approved by the Commission on New Minerals, Nomenclature and Classification (CNMNC) of the International Mineralogical Association, voting proposal 12-B. We also propose a compact notation for identifying synthetic LDH phases, for use by chemists as a preferred alternative to the current widespread misuse of mineral names. © 2012 Mineralogical Society.Fil: Mills, S.J.. Museum Victoria; AustraliaFil: Christy, A.G.. Australian National University. Centre for Advanced Microscopy; AustraliaFil: Génin, J. M. R.. CNRS-Université de Lorraine; FranciaFil: Kameda, T.. Tohoku University. Graduate School of Environmental Studies; JapónFil: Colombo, Fernando. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigaciones en Ciencias de la Tierra. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Centro de Investigaciones en Ciencias de la Tierra; Argentin

Shimura varieties in the Torelli locus via Galois coverings of elliptic curves

We study Shimura subvarieties of $\mathsf{A}_g$ obtained from families of Galois coverings $f: C \rightarrow C'$ where $C'$ is a smooth complex projective curve of genus $g' \geq 1$ and $g= g(C)$. We give the complete list of all such families that satisfy a simple sufficient condition that ensures that the closure of the image of the family via the Torelli map yields a Shimura subvariety of $\mathsf{A}_g$ for $g' =1,2$ and for all $g \geq 2,4$ and for $g' > 2$ and $g \leq 9$. In a previous work of the first and second author together with A. Ghigi [FGP] similar computations were done in the case $g'=0$. Here we find 6 families of Galois coverings, all with $g' = 1$ and $g=2,3,4$ and we show that these are the only families with $g'=1$ satisfying this sufficient condition. We show that among these examples two families yield new Shimura subvarieties of $\mathsf{A}_g$, while the other examples arise from certain Shimura subvarieties of $\mathsf{A}_g$ already obtained as families of Galois coverings of $\mathbb{P}^1$ in [FGP]. Finally we prove that if a family satisfies this sufficient condition with $g'\geq 1$, then $g \leq 6g'+1$.Comment: 18 pages, to appear in Geometriae Dedicat

Orbital dynamics of "smart dust" devices with solar radiation pressure and drag

This paper investigates how perturbations due to asymmetric solar radiation pressure, in the presence of Earth shadow, and atmospheric drag can be balanced to obtain long-lived Earth centred orbits for swarms of micro-scale 'smart dust' devices, without the use of active control. The secular variation of Keplerian elements is expressed analytically through an averaging technique. Families of solutions are then identified where Sun-synchronous apse-line precession is achieved passively to maintain asymmetric solar radiation pressure. The long-term orbit evolution is characterized by librational motion, progressively decaying due to the non-conservative effect of atmospheric drag. Long-lived orbits can then be designed through the interaction of energy gain from asymmetric solar radiation pressure and energy dissipation due to drag. In this way, the usual short drag lifetime of such high area-to-mass spacecraft can be greatly extended (and indeed selected). In addition, the effect of atmospheric drag can be exploited to ensure the rapid end-of-life decay of such devices, thus preventing long-lived orbit debris