Supersymmetry and Combinatorics

We show how a recently proposed supersymmetric quantum mechanics model leads to non-trivial results/conjectures on the combinatorics of binary necklaces and linear-feedback shift-registers. Pauli's exclusion principle plays a crucial role: by projecting out certain states/necklaces, it allows to represent the supersymmetry algebra in the resulting subspace. Some of our results can be rephrased in terms of generalizations of the well-known Witten index.Comment: 14 pages, 3 figures, text expanded, references adde

On the Backbending Mechanism of 48^{48}Cr

The mechanism of backbending in $^{48}$Cr is investigated in terms of the Projected Shell Model and the Generator Coordinate Method. It is shown that both methods are reasonable shell model truncation schemes. These two quite different quantum mechanical approaches lead to a similar conclusion that the backbending is due to a band crossing involving an excited band which is built on simultaneously broken neutron and proton pairs in the ``intruder'' subshell $f_{7/2}$. It is pointed out that this type of band crossing is usually known to cause the second backbending in rare-earth nuclei.Comment: 4 pages, 4 figures, accepted for publication in Phys. Rev. Let

A test of the coevolution theory of autumn colours: colour preference of Rhopalosiphum padi on Prunus padus

According to the coevolution theory of autumn colours, the bright colours of trees evolved as a warning signal towards parasites colonizing the plant in autumn. We monitored colonization of the aphid Rhopalosiphum padi on individual tress of Prunus padus in autumn and observed a strong preference of aphids for trees with green leaves. This is the first direct observation of a key assumption of the theory, that parasites avoid bright colours. Moreover our observations, compared with previous data gathered on the same species, suggest that aphids colonizing trees with green leaves develop better in spring than aphids colonizing trees with bright autumn colours, which is consistent with the second main assumption of the coevolution theory

Discovery of continental-scale travelling waves and lagged synchrony in geometrid moth outbreaks prompt a re-evaluation of mountain birch/geometrid studies

The spatio-temporal dynamics of populations of two 9-10 year cyclic-outbreaking geometrids, Operophtera brumata and Epirrita autumnata in mountain birch forests in northern Fennoscandia, have been studied since the 1970´s by a Swedish-Norwegian research team and, during the last decade, by Norwegian and Finnish research teams. Some of the early results have been challenged by the Norwegian team. To examine the base for disagreements, five of the papers published by the Norwegian team (2004-2011) are reviewed. It is found that conclusions in these papers are questionable or data could not be interpreted fully because two decisive traits in the spatio-temporal behaviour of outbreaks of the two species were not considered

The Square Frobenius Number

Let $S=\left\langle s_1,\ldots,s_n\right\rangle$ be a numerical semigroup generated by the relatively prime positive integers $s_1,\ldots,s_n$. Let $k\geqslant 2$ be an integer. In this paper, we consider the following $k$-power variant of the Frobenius number of $S$ defined as $${}^{k\!}r\!\left(S\right):= \text{ the largest } k \text{-power integer not belonging to } S.$$In this paper, we investigate the case $k=2$. We give an upper bound for ${}^{2\!}r\!\left(S_A\right)$ for an infinity family of semigroups $S_A$ generated by {\em arithmetic progressions}. The latter turns out to be the exact value of ${}^{2\!}r\!\left(\left\langle s_1,s_2\right\rangle\right)$ under certain conditions. We present an exact formula for ${}^{2\!}r\!\left(\left\langle s_1,s_1+d\right\rangle\right)$ when $d=3,4$ and $5$, study ${}^{2\!}r\!\left(\left\langle s_1,s_1+1\right\rangle\right)$ and ${}^{2\!}r\!\left(\left\langle s_1,s_1+2\right\rangle\right)$ and put forward two relevant conjectures. We finally discuss some related questions

Temporal and spatial correlation in chick production of willow grouse Lagopus lagopus in Sweden and Norway

We analysed the spatial and temporal dynamics of chick production of willow grouse "Lagopus lagopus" in the Swedish and Norwegian mountain region using harvest data covering 24-38 years and line-transect counts covering 6-10 years from the period 1960-2003. Juvenile and adult grouse were counted in the bag of harvested willow grouse in late August and throughout September at six sites in Sweden and Norway. In addition, numbers of juvenile and adult willow grouse were obtained from ine-transect counts at 21 sites in Sweden just before the hunting season started on 25 August. The juvenile:adult ratio from the harvest data, estimated as number of juveniles per two adults, showed similar long-term averages and distributions between all six sites. The results from the line-transect counts revealed an overall higher average and a greater range of production between sites. We suggest that the difference between estimates based on line-transect counts and harvest data are caused by hunter behaviour. Hunters did not sample the juvenile and adult grouse in proportion to what was present in the population, e.g., productivity estimates derived from harvest samples will underestimate the proportion of juveniles in autumn in most years. We suggest that it is the harvest process that acts to adjust the juvenile to old bird ratio in the harvest data to a similar distribution in different sites. We found little evidence of regular fluctuations/cycles in annual production of juveniles from either harvest data or line-transect data. We conclude that chick production in willow grouse appears to fluctuate more irregularly than was previously believed based on harvest data and can not be used as a potential forecasting tool in willow grouse management as suggested earlier. Spatial correlation was weak and investigating only a limited number of sites to predict the proportion of juveniles in autumn should not be considered as a management tool for large areas such as the state-owned land in Sweden. Line-transect counts are costly, but do provide a more accurate estimate of the proportion of juveniles in the fall population than is revealed by harvest data. A more detailed understanding of hunter behaviour is obviously needed for better interpretation of harvest data

Prancūzų kalbos konstrukcijų su veiksmažodžiais devoir ‘privalėti’, falloir ‘reikėti’ multifunkcionalumas: prancūzų–lietuvių kalbų tekstynu paremtas tyrimas

The present study examines the morphosyntactic features and functions of the constructionsje dois dire (que) ‘I must say (that)’ and (il) faut dire (que) ‘it is necessary to say (that)’ in French and their correspondences in Lithuanian. The study is corpus-based and the data have been retrieved from the bidirectional parallel corpus CTLFR-LT-FR. The thorough semantic functional analysis of the construction je dois dire (que) ‘I must say (that)’ in theCTLFR-LT shows that the verbs devoir ‘must’ and dire ‘say’ clearly express the meanings of necessity and saying. However, in initial position the construction with the complementizer que ‘that’ represents a lexical variant and may not be functionally transparent. Its functional indeterminacy may be clarified by its prosodic realizations. The conceptual meanings of the verbs devoir ‘must’ and dire ‘say’ in the construction je dois dire (que) ‘I must say (that)’ are bleached and the construction may function as a marker that initiates conversation with the addressee, expresses the author’s argumentation and links clauses or parts of discourse. In initial and medial position, it may hedge an utterance or modify a word or a phrase. Thus the construction je dois dire (que) ‘I must say (that)’ is not primary in the communicative structure of the sentence and functions as a marker of author stance. The construction (il) faut dire (que) ‘it is necessary to say (that)’ is less frequent in the CTLFR-LT and displays minor structural variation. It shows traces of parentheticalization, namely deverbalization (omission of the formal subject il), omission of the complementizer que ‘that’, syntactic mobility in the sentence, semantic bleaching of the verbs falloir ‘need’ and dire ‘say’, alternation with mental verbs (Pusch 2007), interpersonal and intertextual functions. The structure (il) faut dire + NP‘it is necessary + NP’ clearly expresses the meaning of necessity to say. The Lithuanian constructions turiu pasakyti/pripažinti ‘I must say/admit’ and reikia pasakyti/pripažinti ‘it is necessary to say/admit’ in the CTLLT-FR are not statistically significant and functionally they do not differ from the equivalent constructions in French. The data in the CTLFR-LT-FR and the CCLL (Contemporary Corpus of the Lithuanian Language) reveal that the constructions under study are not dominant either in French or Lithuanian but possible in authentic language use. Although the generalizations made above should be corroborated by more empirical data, the present study contributes to the research on parenthetical constructions in French and Lithuanian and can be supplemented by the analysis of the constructions in academic discourse.Le Corpus parallèle de Textes Littéraires CTLFR-LT-FR comportant deux composantesCTLFR-LT et CTL LT-FR a montré que les tournures je dois dire (que) et (il) faut dire (que)ne sont pas extrêmement fréquentes dans le français écrit mais suffisamment présentes pour permettre la description de leur variation structurale et l’analyse des sens qu’elles peuvent exprimer.Comme les deux verbes devoir et falloir peuvent véhiculer une obligation et une nécessité il fallait donc s’attendre à trouver un certain nombre d’occurrences qui expriment une modalité déontique. Les occurrences qui étaient classifiées comme appartenant à l’usage déontique correspondent à la structure (il) faut dire/je dois dire +NP, tandis que les autres suivent le schéma (il) faut/je dois dire+Ø et ont une valeur parenthétique. Pour l’identification de la valeur des structures (il) faut dire/je dois dire que+CP l’analyse prosodique aurait pu être bien pertinente.Au niveau morphosyntaxique les unités analysées s’apparentent beaucoup à des constructions parenthétiques par leur érosion sémantique, liberté de position, variabilité morphologique (présence ou absence du pronom il, du complémentateur que). Sur le plan pragmatique elles peuvent fonctionner comme connecteurs textuels portant la relation d’adversativité et par leur pouvoir énonciatif multifonctionnel elles ressemblent aux adverbes modalisateurs. Les indices énumérés ci-dessus peuvent être interprétés comme marqueurs de la pragmaticalisation des unités je dois dire (que) et (il) faut dire (que) en français.Ce travail se veut une modeste contribution à l’étude de telles structures dont le vaste inventaire d’occurrences dans le français reste à être décrit de manière systématique.Straipsnyje aptariamas prancūzų kalbos vienetų je dois dire (que) ‘turiu pasakyti, (kad)’ ir (il) faut dire (que) ‘reikia pasakyti, (kad)’ morfosintaksinis statusas ir funkcijų įvairovė autentiškos prancūzų kalbos vartosenoje. Remiantis lingvistinėje literatūroje publikuotais tyrimais apie mentalinių ir sakymo veiksmažodžių (verba cogitandi ir verba dicendi) multifunkcionalumą ir reikšmių įvairovę, šiame darbe analizuojamos lygiagrečiajame CTLFR-LT-FR tekstyne rastų minėtų veiksmažodinių konstrukcijų reikšmės ir funkcijos. Aiškinamasi, ar prancūzų kalbos veiksmažodžiai devoir ‘privalėti’, falloir ‘reikėti’, dire ‘sakyti’, įeinantys į struktūrinių vienetų je dois dire (que) ‘turiu pasakyti, (kad)’ ir (il) faut dire (que) ‘reikia pasakyti, (kad)’ sudėtį, išlaiko savo konceptualiąsias reikšmes ir kokiomis aplinkybėmis šie vienetai virsta pragmatiniais žymikliais, įgaudami jiems tipiškų bruožų. Mokslinėje literatūroje vyraujanti nuomonė pasitvirtina – sintaksinis mobilumas, struktūrinis sustabarėjimas, leksinių reikšmių blukimas, pragmatinių funkcijų įvairovė – tai požymiai, rodantys kalbos vienetų statuso pasikeitimą sakinyje ar didesniame teksto fragmente. Tokie vienetai praranda pagrindinę – informacijos perteikimo sakinio komunikacinėje struktūroje – poziciją ir tampa parentezinėmis konstrukcijomis, papildomai aiškinančiomis išreikštos propozicijos turinį arba teksto atkarpoje jungiančiomis kelis pasakymus