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Povzetek: In this paper, we study the bivariate truncated moment problem (TMP) on curves of the form $y = q(x), q(x) \in \mathbb{R} [x], \deg q ≥ 3$ and $yx^\ell = 1, \ell \in \mathbb{N}$ \ $\{1\}$. For even degree sequences, the solution based on the size of moment matrix extensions was first given by Fialkow [Fialkow L. Solution of the truncated moment problem with variety $y = x^3$. Trans Amer Math Soc. 2011;363:3133–3165.] using the truncated Riesz–Haviland theorem [Curto R, Fialkow L. An analogue of the Riesz–Haviland theorem for the truncated moment problem. J Funct Anal. 2008;255:2709–2731.] and a sum-of-squares representations for polynomials, strictly positive on such curves [Fialkow L. Solution of the truncated moment problem with variety $y = x^3$. Trans Amer Math Soc. 2011;363:3133–3165.; Stochel J. Solving the truncated moment problem solves the moment problem. Glasgow J Math. 2001;43:335–341.]. Namely, the upper bound on this size is quadratic in the degrees of the sequence and the polynomial determining a curve. We use a reduction to the univariate setting technique, introduced in [Zalar A. The truncated Hamburger moment problem with gaps in the index set. Integral Equ Oper Theory. 2021;93:36.doi: 10.1007/s00020-021-02628-6.; Zalar A. The truncated moment problem on the union of parallel lines. Linear Algebra Appl. 2022;649:186–239. doi.org/10.1016/j.laa.2022.05.008.; Zalar A. The strong truncated Hamburger moment problem with and without gaps. J Math Anal Appl. 2022;516:126563. doi: 10.1016/j.jmaa.2022. 126563.], and improve Fialkow’s bound to $\deg q − 1$ (resp. $\ell + 1$) for curves $y = q(x)$ (resp. $yx^\ell = 1$). This in turn gives analogous improvements of the degrees in the sum-of-squares representations referred to above. Moreover, we get the upper bounds on the number of atoms in the minimal representing measure, which are $k \deg q$ (resp. $k(\ell+ 1)$) for curves $y = q(x)$ (resp. $yx^\ell = 1$) for even degree sequences, while for odd ones they are $k \deg q − \bigl \lceil \frac{\deg q}{2} \bigr \rceil$ (resp. $k(\ell + 1) − \bigl \lfloor \frac{\ell}{2} \bigr \rfloor + 1$) for curves $y = q(x)$ (resp. $yx^\ell = 1$). In the even case, these are counterparts to the result by Riener and Schweighofer [Riener C, Schweighofer M. Optimization approaches to quadrature:a new characterization of Gaussian quadrature on the line and quadrature with few nodes on plane algebraic curves, on the plane and in higher dimensions. J Complex. 2018;45:22–54., Corollary 7.8], which gives the same bound for odd degree sequences on all plane curves. In the odd case, their bound is slightly improved on the curves we study. Further on, we give another solution to the TMP on the curves studied based on the feasibility of a linear matrix inequality, corresponding to the univariate sequence obtained, and finally we solve concretely odd degree cases to the TMP on curves $y = x^\ell, \ell = 2, 3,$ and add a new solvability condition to the even degree case on the curve $y = x^2$.
Ključne besede: truncated moment problems, K-moment problems, K-representing measure, minimal measure, moment matrix extensions, positivstellensatz, linear matrix inequality
Objavljeno v DiRROS: 25.07.2024; Ogledov: 274; Prenosov: 190
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Povzetek: The saproxylic beetle, Cucujus cinnaberinus, has received increasing research attention in Europe since the adoption of the Habitats Directive and establishment of the Natura 2000 network. The history of the species has been investigated as well as the influence of abiotic and biotic variables on the distribution of C. cinnaberinus in Slovenia which is at the limit of its range and also terra typica for the species. The species was first described in 1763 by Joannes A. Scopoli in Carniola, a duchy of the Habsburg Monarchy. Today, most of the territory of Carniola is situated within Slovenia. C. cinnaberinus is particularly common in the eastern part of the country, but very scarce in the mountainous western part. According to historical and recent distribution patterns of C. cinnaberinus in the former Carniolan territory, the region of Ribnica-Kočevje in southern Slovenia is proposed as the most probable type locality of the species. Although the bulk of the C. cinnaberinus population in Slovenia is confined to the lowlands, the species has been found up to 1095 m a.s.l., albeit at a much lower abundance due to the influence of climate and forest structure. Although C. cinnaberinus is a quite an opportunistic species regarding host tree selection, it has been shown to exhibit a preference for Tilia, Populus and Robinia. It is suspected that the high abundance of C. cinnaberinus in lowland floodplain forests is due to the recent human-induced increase in preferred fast-growing and short-lived host trees, i.e. the planting of poplar trees and spread of invasive Black Locust (Robinia pseudoacacia) after the 1960s. In contrast, in montane forests, preferred host trees (e.g. Tilia) represent < 1 % of all growing stock. Although montane C. cinnaberinus populations are rare, they could still be important for the conservation of the species, since montane habitats cover the largest area within the species’ distribution range.
Ključne besede: saproxylic beetle, Natura 2000, type locality, Carniola, altitudinal distribution, host tree selection, macrohabitat, large-scale survey
Objavljeno v DiRROS: 24.07.2024; Ogledov: 704; Prenosov: 228
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Povzetek: Background Quantitative molecular biology remains a challenge for researchers due to inconsistent approaches for control of errors in the final results. Due to several factors that can influence the final result, quantitative analysis and interpretation of qPCR data are still not trivial. Together with the development of high-throughput qPCR platforms, there is a need for a tool allowing for robust, reliable and fast nucleic acid quantification. Results We have developed “quantGenius” (http://quantgenius.nib.si), an open-access web application for a reliable qPCR-based quantification of nucleic acids. The quantGenius workflow interactively guides the user through data import, quality control (QC) and calculation steps. The input is machine- and chemistry–independent. Quantification is performed using the standard curve approach, with normalization to one or several reference genes. The special feature of the application is the implementation of user-guided QC-based decision support system, based on qPCR standards, that takes into account pipetting errors, assay amplification efficiencies, limits of detection and quantification of the assays as well as the control of PCR inhibition in individual samples. The intermediate calculations and final results are exportable in a data matrix suitable for further statistical analysis or visualization. We additionally compare the most important features of quantGenius with similar advanced software tools and illustrate the importance of proper QC system in the analysis of qPCR data in two use cases. Conclusions To our knowledge, quantGenius is the only qPCR data analysis tool that integrates QC-based decision support and will help scientists to obtain reliable results which are the basis for biologically meaningful data interpretation.
Ključne besede: quantitative molecular biology, quantitative PCR, nucleic acid quantification, web application, decision support system
Objavljeno v DiRROS: 24.07.2024; Ogledov: 301; Prenosov: 202
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Ključne besede: kulinarični recepti
Objavljeno v DiRROS: 24.07.2024; Ogledov: 325; Prenosov: 14
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Povzetek: Zoantharians are a group of cnidarians that are often found in association with marine invertebrates, including corals, in shallow and deep-sea environments. However, little is known about deep-sea zoantharian taxonomy, specificity and nature of their associations with their coral hosts. In this study, analyses of molecular data (mtDNA COI, 16S, and 12S rDNA) coupled with ecological and morphological characteristics were used to examine zoantharian specimens associated with cold-water corals (CWC) at depths between 110 and 800 m from seamounts and island slopes in the Azores region. The zoantharians examined were found living in association with stylasterids, antipatharians and octocorals. From the collected specimens, four new species were identified: (1) Epizoanthus martinsae sp. n. associated with the antipatharian Leiopathes sp.; (2) Parazoanthus aliceae sp. n. associated with the stylasterid Errina dabneyi (Pourtalès, 1871); (3) Zibrowius alberti sp. n. associated with octocorals of the family Primnoidae [Paracalyptrophora josephinae (Lindström, 1877)] and the family Plexauridae (Dentomuricea aff. meteor Grasshoff, 1977); (4) Hurlizoanthus hirondelleae sp. n. associated with the primnoid octocoral Candidella imbricata (Johnson, 1862). In addition, based on newly collected material, morphological and molecular data and phylogenic reconstruction, the zoantharian Isozoanthus primnoidus Carreiro-Silva, Braga-Henriques, Sampaio, de Matos, Porteiro & Ocaña, 2011, associated with the primnoid octocoral Callogorgia verticillata (Pallas, 1766), was reclassified as Zibrowius primnoidus comb. nov. The zoantharians, Z. primnoidus comb. nov., Z. alberti sp. n., and H. hirondelleae sp. n. associated with octocorals showed evidence of a parasitic relationship, where the zoantharian progressively eliminates gorgonian tissue and uses the gorgonian axis for structure and support, and coral sclerites for protection. In contrast, the zoantharian P. aliceae sp. n. associated with the stylasterid E. dabneyi and the zoantharian E. martinsae sp. n. associated with the antipatharian Leiopathes sp., appear to use the coral host only as support with no visible damage to the host. The monophyly of octocoral-associated zoantharians suggests that substrate specificity is tightly linked to the evolution of zoantharians.
Ključne besede: antipatharians, octocorals, Azores, gorgonians, molecular taxonomy, phylogeny, stylasterids
Objavljeno v DiRROS: 24.07.2024; Ogledov: 271; Prenosov: 190
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