Minimal positive realizations for a class of transfer functions

It is a standard result in linear-system theory that an nth-order rational transfer function of a single-input single-output system always admits a realization of order n. In some applications, however, one is restricted to realizations with nonnegative entries (i.e. a positive system), and it is known that this restriction may force the order N of realizations to be strictly larger than n. In this brief we present a class of transfer functions where positive realizations of order n do exist. With the help of our result we give improvements on some earlier results in positive-system theory

An efficient algorithm for positive realizations

We observe that successive applications of known results from the theory of positive systems lead to an {\it efficient general algorithm} for positive realizations of transfer functions. We give two examples to illustrate the algorithm, one of which complements an earlier result of \cite{large}. Finally, we improve a lower-bound of \cite{mn2} to indicate that the algorithm is indeed efficient in general

Közönséges differenciálegyenletek a BME Matematika Intézetéből = Ordinary differential equations from the Mathematical Institute of the BUTE

A kutatási feladat két fő célja az volt, hogy eredményeket érjünk el (1) a végtelen dimenziós dinamika, valamint a (2) numerika, pontosabban differenciálegyenletek numerikus analízise területén. (1) Az első céllal kapcsolatos reprezentatív eredmény HORVÁTH MIKLÓS ''Inverse spectral problems and closed exponential systems, Annals of Mathematics 162(2005), 885-918'' dolgozata, amely -- csakúgy mint a kísérő Transactions és Proceedings of the AMS cikkek -- akkor és csak akkor feltételeket ad bizonyos típusú Schrödinger operatorok potenciáljának unicitására. (2) A második céllal kapcsolatos fő eredmény -- közreműködők BÁNHELYI BALÁZS és CSENDES TIBOR (Informatika Intézet, Szeged) -- az az észrevétel, hogy az intervallum aritmetikával támogatott globális optimalizációk elmélete kényelmes keretet biztosít dinamikai rendszerek kaotikus voltának számítógép által segített bizonyítására. Az elméleti újdonság az, hogy az algebrai topógia eszköztára, jelesen a korábbi megközelítésekre annyira jellemző Conley index és a további indexek, legalábbis az esetek egy részében, kiválthatóak a Brouwer-féle fixponttétel alkalmazásával. | The two main goals of the research project have been (1) results in infinite-dimensional dynamics, and (2) results in numerics--more precisely, in the numerics of differential equations. (1) As for the first goal, the representative publication is ''Inverse spectral problems and closed exponential systems, Annals of Mathematics 162(2005), 885-918'' by MIKLÓS HORVÁTH. Together with the accompanying papers in the Transaction and the Proceedings of the AMS, the ''Inverse spectral problems and closed exponential systems'' establishes if and only if conditions on the uniqueness of the potential of certain Schrödinger operators. (2) As for the second goal, the main result - achieved in cooperation with BALÁZS BÁNHELYI and TIBOR CSENDES, Szeged Institute of Informatics--is that interval arithmetics based global optimization constitutes a comfortable framework for computer-assisted proofs of chaotic behaviour of dynamical systems. The theoretical novelty is that tools from algebraic topology including Conley and other indices in earlier approaches can be, at least in several cases, replaced by applications of the Brouwer fixed point theorem

Investigating physiological effects due to artificial infections of grapevine with <i>Verticillium nonalfalfae</i>

Ailanthus altissima is among the most invasive woody species worldwide, outcompeting native trees. The fungus Verticillium nonalfalfae (VN) is promising for A. altissima biocontrol, and its effects on the host have been studied via visual assessment in a range of host species. However, little research was performed to address fungal effects on the physiological processes of non-target woody plants. We investigated the occurrence of visual and non-visually recognisable perturbations of VN infection on potted vines to evaluate the potential risks of the biocontrol pathogen on viticulture. Eighteen four-years-old Vitis vinifera (cultivar Grüner Veltliner grafted on Kober 5BB) potted plants were inoculated with VN conidial suspension of the fungus (F), while nine plants were treated with sterile water (C, control). Disease symptoms and physiological parameters were monitored throughout the experiment (seven evaluation dates), while leaf water potential, leaf mass per area (LMA) and biomass were measured at the end of the study when plant tissue was sampled for re-isolation of the fungus. In our trial, inoculations with VN induced characteristic wilting symptoms only in Ailanthus (used as side control of the inoculum), while vines remained asymptomatic, thus indicating a high degree of host specificity of VN. Limited or no impact was detected on the physiology of the non-target V. vinifera. Furthermore, the LMA and biomass measured in the two experimental groups were not different. Although fungal colonisation induced vascular discolouration in both species, the fungus could only be re-isolated from dying Ailanthus but not from vine tissue. Results suggest that V. vinifera cv Grüner Veltliner is resistant to the applied VN isolate. However, the susceptibility and physiology of additional grapevine cultivars, as well as other native woody species to VN, should be studied before promoting large-scale use of the biocontrol agent

Potential antagonism of some Trichoderma strains isolated from Moroccan soil against three phytopathogenic fungi of great economic importance

Dans cette étude, 17 souches de Trichoderma on été isolées à partir d’échantillons du sol de différentes origines (champs et forêt d’arganier). Les espèces ont été identifiées par la caractérisation moléculaire des cultures monospores des isolats de Trichoderma et leur potentiel d’antagonisme a été évalué contre trois champignons phyto-pathogènes telluriques (Fusarium oxyxporum, verticillium dahlia et rhizoctonia solani). Après l’extraction de l’ADN, le facteur d’élongation et de traduction tef1 a été utilisé comme marqueur moléculaire pour amplifier, séquencer et par la suite caractériser les 17 souches qui ont été comparées avec leur ex-types déjà référencés. Par conséquent, l’identification moléculaire par tef1 a permis la caractérisation de trois espèces de Trichoderma à savoir T. afroharzianum, et T. guizhouense appartenant à la branche Harzianum, et T. longibrachiatum appartenant à la branche Longibrachiatum. Les 17 isolats candidats ont été sélectionnés par une méthode de criblage basée sur la PCR (polymerase chain reaction). L’évaluation du potentiel antagoniste des souches de Trichoderma contre les champignons phytopathogènes telluriques (F. oxysporum, R. solani et V. dahliae) a été réalisée par la méthode de confrontation sur boîtes de pétrie. L’étude in vitro de l’activité antagoniste par le «Pourcentage of Radial Inhibition Growth» (PRIG %) a permis de suivre l’évolution de la croissance radiale du mycélium des différents champignons phytopathogènes. Le pourcentage le plus élevé (PRIG% = 98%) a été observé pour la confrontation entre l’isolat 8A2.3 et R. solani et le pourcentage le plus faible (PRIG% = 67%) a été observé pour la confrontation entre l’isolat T9i10 et F. oxysporum. D’un autre coté, T9i12 qui est un isolat de l’espèce T. reeseia a engendré une inhibition élevée de la croissance radiale du mycélium des différents pathogènes. Mots clés: Trichoderma spp, Fusarium oxysporum, Verticillium dahlia, Rhizoctonia solani, champignons antagonistes.In this study, 17 Trichoderma strains were isolated from different soils (crop fields and Argan forests) in Morocco. Purified monospore cultures were identified using molecular methods and tested for their potential antagonism against three phytopathogenic fungi (Fusarium oxyxporum, verticillium dahlia and rhizoctonia solani). After DNA extraction, translation elongation factor (tef1) was amplified in extracts of 17 strains, sequenced and compared with their ex-types. As a result, three species were identified among the strains, which clustered in two different subclades of Trichoderma: the species T. afroharzianum, and T. guizhouense belong to the Harzianum clade, while T. longibrachiatum belongs to the Longibrachiatum clade. Investigation of potential antagonistic effects of these strains against the soil-borne phytopathogens F. oxysporum, R. solani and V. dahliae was conducted in a dual culture plate assay, using 17 promising Trichoderma strains that have been selected based on a polymerase chain reaction (PCR) screening approach. In vitro, Trichoderma isolates showed effective antagonistic performance by decreasing soil borne pathogens mycelium radial growth. Trichoderma afroharzianum showed the highest Percentage of Radial Inhibition Growth (PRIG %). The highest PRIG% = 98% was for 8A2.3 isolate against R. solani and the lowest PRIG%= 67% for T9i10 against F. oxysporum. On the other hand, T9i12, which is T. reesei species, led to a high radial inhibition of pathogens’ mycelium. Keywords: Trichoderma spp, Fusarium oxysporum, Verticillium dahlia, Rhizoctonia solani, antagonistic fungi

Data Descriptor: Ash leaf metabolomes reveal differences between trees tolerant and susceptible to ash dieback disease

CMS was funded by the ‘Nornex’ project jointly by UK BBSRC (BBS/E/J/000CA5323) and DEFRA and a BBSRC Tools and Resources grant (BB/N021452/1) awarded to M.G. and D.J.S