Combinatorial duality for Poincaré series, polytopes and invariants of plumbed 3-manifolds

Assume that the link of a complex normal surface singularity is a rational homology sphere. Then its Seiberg-Witten invariant can be computed as the ‘periodic constant’ of the topological multivariable Poincaré series (zeta function). This involves a complicated regularization procedure (via quasipolynomials measuring the asymptotic behaviour of the coefficients). We show that the (a Gorenstein type) symmetry of the zeta function combined with Ehrhart–Macdonald–Stanley reciprocity (of Ehrhart theory of polytopes) provide a simple expression for the periodic cosntant. Using these dualities we also find a multivariable polynomial generalization of the Seiberg–Witten invariant, and we compute it in terms of lattice points of certain polytopes. All these invariants are also determined via lattice point counting, in this way we establish a completely general topological analogue of formulae of Khovanskii and Morales valid for singularities with non-degenerate Newton principal part

Surgery formulae for the Seiberg-Witten invariant of plumbed 3-manifolds

Assume that $M(\mathcal{T})$ is a rational homology sphere plumbed 3--manifold associated with a connected negative definite graph $\mathcal{T}$. We consider the combinatorial multivariable Poincar\'e series associated with $\mathcal{T}$ and its counting functions, which encode rich topological information. Using the `periodic constant' of the series (with reduced variables) we prove surgery formulae for the normalized Seiberg--Witten invariants: the periodic constant appears as the difference of the Seiberg--Witten invariants associated with $M(\mathcal{T})$ and $M(\mathcal{T}\setminus \mathcal{I})$, where $\mathcal{I}$ is an arbitrary subset of the set of vertices of $\mathcal{T}$

A foszfor- és a lipidtartalom, valamint a kondíciófaktor összefüggése és szezonális változása három halfaj példáján

A sztöchiometriai elmélet szerint az élőlények elemi összetétele és a testben raktározott tápanyagok egymáshoz viszonyított aránya fajra jellemző, állandó érték. Újabb vizsgálatok azonban bebizonyították, hogy egy fajon belül is lehetnek szignifikáns különbségek tápanyagtartalom tekintetében. Munkánk során három halfaj (amurgéb, naphal, vörösszárnyú keszeg) foszfortartalmát, lipidtartalmát és kondíciófaktorát mértük, továbbá vizsgáltuk ezek szezonális változását a populációkon belül. A test foszfortartalmának szezonális változását megvizsgálva elmondható, hogy egy populáción belül is előfordulnak szignifikáns különbségek. Hozzá kell tennünk azonban, hogy a fajok közötti különbségek sokkal számottevőbbek. Feltételezésünk szerint a lipidtartalom mennyiségének csak jelentős változása révén képes a test foszfortartalmát megváltoztatni a szén‐foszfor arány befolyásolásán keresztül. A lipidtartalom és a kondíciófaktor közötti szoros kapcsolat nem minden populáció esetében figyelhető meg. Előfordulhat, hogy a kondíciófaktor emelkedését nem a lipidtartalom növekedése, hanem más szövetek gyarapodása okozza

Enhancing Hungarian students’ English language skills on the basis of literary texts in the three-dimensional space

In our paper we introduce a bilingual language learning material developed in the framework of the so-called three dimensional virtual library model (3DVLM). This model inspired by the history and organization of the famous ancient Library of Alexandria forms the basis of the virtual library project which started about eight years ago as part of the Cognitive Infocommunications (CogInfoCom) research. The current version of the 3DVLM uses the excellent 3D features of the MaxWhere Seminar System which makes it suitable for both individual learning and classroom use. In the following, we would like to introduce first the basic framework of our development, then describe in detail the data structure and organization of the developed bilingual language learning material. The basic idea of the material is to present selected phrases and contexts from classical literary works in English and from their parallel translations in Hungarian in order to improve both the language skills and background knowledge of Hungarian language learners at an advanced level. We found that using web technology was especially useful for developing the language learning material and the developed hypertext structure formed a scale-free network of interconnected nodes

E-tananyagfejlesztés virtuális 3D környezetben

Az oktatás és a tanulás hatékony elektronikus tananyagai iránti igény az utóbbi időben szinte minden tudományterületen jelentősen megnőtt köszönhetően az elmúlt időszakban teret nyerő digitális oktatásnak. Tanulmányunkban egy új és reményeink szerint ígéretes technológiát szeretnénk bemutatni az e-tananyagok fejlesztésére és prezentálására, amely hatékonyan alkalmazható különféle tanulási környezetekben. Ez a technológia a MaxWhere rendszer oktatási célú felhasználásán alapul. A MaxWhere egy néhány évvel ezelőtt kifejlesztett 3D-s prezentációs eszköz, amely látványos és könnyen használható három dimenziós virtuális környezetet kínál a megjeleníteni kívánt tartalmaknak. A rendszert kiválóan lehet használni az e-tananyagok fejlesztéséhez és bemutatásához mind a tanítás, mind a tanulás területén. Esetünkben a tananyag fejlesztésének és prezentálásának lehetőségeit egy kiválasztott informatikai téma kidolgozásával szeretnénk bemutatni és elemezni a MaxWhere 3D virtuális környezetében

Enhancing Hungarian students’ English language skills on the basis of literary texts in the three-dimensional space

In our paper we introduce a bilingual language learning material developed in the framework of the so-called three dimensional virtual library model (3DVLM). This model inspired by the history and organization of the famous ancient Library of Alexandria forms the basis of the virtual library project which started about eight years ago as part of the Cognitive Infocommunications (CogInfoCom) research. The current version of the 3DVLM uses the excellent 3D features of the MaxWhere Seminar System which makes it suitable for both individual learning and classroom use. In the following, we would like to introduce first the basic framework of our development, then describe in detail the data structure and organization of the developed bilingual language learning material. The basic idea of the material is to present selected phrases and contexts from classical literary works in English and from their parallel translations in Hungarian in order to improve both the language skills and background knowledge of Hungarian language learners at an advanced level. We found that using web technology was especially useful for developing the language learning material and the developed hypertext structure formed a scale-free network of interconnected nodes

Is early limited surgery associated with a more benign disease course in Crohn’s disease?

AIM: To analyze the difference in disease course and need for surgery in patients with Crohn's disease (CD). METHODS: Data of 506 patients with incident CD were analyzed (age at diagnosis: 31.5 ± 13.8 years). Both hospital and outpatient records were collected prospectively with a complete clinical follow-up and comprehensively reviewed in the population-based Veszprem province database, which includes incident CD patients diagnosed between January 1, 1977 and December 31, 2008. Follow-up data were collected until December 31, 2009. All patients included had at least 1 year of follow-up available. Patients with indeterminate colitis at diagnosis were excluded from the analysis. RESULTS: Overall, 73 patients (14.4%) required resective surgery within 1 year of diagnosis. Steroid exposure and need for biological therapy were lower in patients with early limited surgery (P < 0.001 and P = 0.09). In addition, surgery rates during follow-up in patients with and without early surgery differed significantly after matching on propensity scores (P < 0.001, HR = 0.23). The need for reoperation was also lower in patients with early limited resective surgery (P = 0.038, HR = 0.42) in a Kaplan-Meier and multivariate Cox regression (P = 0.04) analysis. However, this advantage was not observed after matching on propensity scores (P(Logrank) = 0.656, P(Breslow) = 0.498). CONCLUSION: Long-term surgery rates and overall exposure to steroids and biological agents were lower in patients with early limited resective surgery, but reoperation rates did not differ

Variance in Landscape Connectivity Shifts Microbial Population Scaling

Understanding mechanisms shaping distributions and interactions of soil microbes is essential for determining their impact on large scale ecosystem services, such as carbon sequestration, climate regulation, waste decomposition, and nutrient cycling. As the functional unit of soil ecosystems, we focus our attention on the spatial structure of soil macroaggregates. Emulating this complex physico-chemical environment as a patchy habitat landscape we investigate on-chip the effect of changing the connectivity features of this landscape as Escherichia coli forms a metapopulation. We analyze the distributions of E. coli occupancy using Taylor's law, an empirical law in ecology which asserts that the fluctuations in populations is a power law function of the mean. We provide experimental evidence that bacterial metapopulations in patchy habitat landscapes on microchips follow this law. Furthermore, we find that increased variance of patch-corridor connectivity leads to a qualitative transition in the fluctuation scaling. We discuss these results in the context of the spatial ecology of microbes in soil