Topological transversals to a family of convex sets

Let $\mathcal F$ be a family of compact convex sets in $\mathbb R^d$. We say that $\mathcal F$ has a \emph{topological $\rho$-transversal of index $(m,k)$} ($\rho<m$, $0<k\leq d-m$) if there are, homologically, as many transversal $m$-planes to $\mathcal F$ as $m$-planes containing a fixed $\rho$-plane in $\mathbb R^{m+k}$. Clearly, if $\mathcal F$ has a $\rho$-transversal plane, then $\mathcal F$ has a topological $\rho$-transversal of index $(m,k),$ for $\rho<m$ and $k\leq d-m$. The converse is not true in general. We prove that for a family $\mathcal F$ of $\rho+k+1$ compact convex sets in $\mathbb R^d$ a topological $\rho$-transversal of index $(m,k)$ implies an ordinary $\rho$-transversal. We use this result, together with the multiplication formulas for Schubert cocycles, the Lusternik-Schnirelmann category of the Grassmannian, and different versions of the colorful Helly theorem by B\'ar\'any and Lov\'asz, to obtain some geometric consequences

Fishing in the mesolithic-neolithic danube gorges in the early holocene (10th-6th millennium BC)

Disertacija obuhvata proučavanje ribolovačkih aktivnosti u Đerdapu tokom ranog holocena, tj. perioda mezolita i ranog/srednjeg neolita (9500-5500. pre n. e.), prvenstveno iz perspektive arheozoologije ribljih ostataka. Važna uloga ribolova u naseljavanju Đerdapa u praistoriji prepoznata je još tokom prvobitnih arheoloških istraživanja 1960ih i 1970ih godina. U okviru ovih kampanja, registrovan je i istražen veliki broj lokaliteta na levoj (rumunskoj) i desnoj (srpskoj) obali Dunava, od kojih su na desnoj obali najdetaljnije istraženi Padina, Lepenski Vir i Vlasac u klisuri Gospođin Vir. Smešteni na rečnim terasama u blizini virova, ova nalazišta su samim svojim položajem ukazivala na upućenost na reku. Pored položaja naselja, hipoteze o njihovom ribolovačkom karakteru zasnivale su se na velikim količinama otkrivenih ribljih kostiju, prisustvu ‘ribolikih’ skulptura i drugih artefakata sa predstavama akvatičkih motiva, a u novije vreme i na vrednostima stabilnih izotopa ugljenika i azota u kolagenu iz ljudskih kostiju koje su ukazivale na značajan udeo ribe u ishrani...Dissertation focuses on fishing activities in the Danube Gorges in early Holocene, i.e. in the Mesolithic and Early/Middle Neolithic (c. 9500-5500 cal BC), primarily from an archaeozoological perspective. The role of aquatic resource exploitation in site locations and settlement practices has long been recognized, ever since the initial archaeological excavations in the 1960s and the 1970s. These campaigns uncovered a great number of sites on the left (Romanian) and right (Serbian) bank of the Danube, with the excavations on the latter focused mainly on the sites of Padina, Lepenski Vir and Vlasac in the Gospođin Vir gorge. The reliance on the river was manifested by the location of sites, which were situated on riverine terraces in vicinity of whirlpools. In addition, their interpretations as fishing settlements were based on large amounts of recovered fish bones, presence of sculpted boulders and other artefacts depicting ‘fishlike’ beings, as well as more recent stable isotope analyses indicating a significant intake of aquatic resources in human diet..

A Tverberg type theorem for matroids

Let b(M) denote the maximal number of disjoint bases in a matroid M. It is shown that if M is a matroid of rank d+1, then for any continuous map f from the matroidal complex M into the d-dimensional Euclidean space there exist t \geq \sqrt{b(M)}/4 disjoint independent sets \sigma_1,\ldots,\sigma_t \in M such that \bigcap_{i=1}^t f(\sigma_i) \neq \emptyset.Comment: This article is due to be published in the collection of papers "A Journey through Discrete Mathematics. A Tribute to Jiri Matousek" edited by Martin Loebl, Jaroslav Nesetril and Robin Thomas, due to be published by Springe

Analogues of the central point theorem for families with dd-intersection property in Rd\mathbb R^d

In this paper we consider families of compact convex sets in $\mathbb R^d$ such that any subfamily of size at most $d$ has a nonempty intersection. We prove some analogues of the central point theorem and Tverberg's theorem for such families

Faktori rizika za pojavu intraoperativnih varijacija vrednosti krvnog pritiska i srčanih disritmija tokom tireoidne hirurgije

Introduction/Objective Intraoperative variations in blood pressure and/or cardiac dysrhythmias (IOVBP/CD) represent one of the most common causes of morbidity and mortality in surgical patients. The aim of the study was to determine the incidence and risk factors for IOVBP/CD in thyroid surgery patients with comorbidities. Methods The study included 1,252 euthyroid patients with ASA 2 and ASA 3 status (American Society of Anesthesiologists - physical status classification) who underwent thyroid surgery. The following risk factors were examined: sex, age, body mass index (BMI), ASA status, admission diagnoses, type of operation, duration of surgery, time under general anesthesia, difficult intubation of trachea, and coexisting diseases - hypertension, cardiomyopathy, cardiac arrhythmias, angina pectoris, diabetes mellitus, kidney disease. The following intraoperative events were recorded: hypertension, severe hypertension, hypotension, and cardiac arrhythmias. We used Pearson χ2 square test, univariate, and multivariate logistic regression for statistical analysis. Results The majority of patients were female (86.3%). In 903 (72.1%) patients IOVBP/CD were detected. The most common problem was intraoperative hypertension (61.4%). Eight risk factors for IOVBP/CD were registered by univariate analysis: advanced age, ASA 3 status, BMI > 25 kg/m2, duration of surgery, time under general anesthesia, hypertension, and cardiomyopathy as a coexisting disease. The multivariate regression model identified three independent predictors for IOVBP/CD: age, hypertension, and cardiomyopathy. Conclusion IOVBP/CD are common in thyroid surgery. The most common is intraoperative hypertension. Older age, hypertension, and cardiomyopathy as a coexisting disease are independent risk factors for IOVBP/CD.Uvod/Cilj Intraoperativne varijacije krvnog pritiska i/ ili srčane disritmije (IVKP/SD) jedan su od najčešćih uzročnika morbiditeta i mortaliteta hirurških bolesnika. Cilj studije je bio da ispita učestalost i faktore rizika za pojavu IVKP/SD u tireoidnoj hirurgiji kod bolesnika sa komorbiditetima. Metode Ispitivanje je obuhvatilo 1252 eutireoidna bolesnika ASA 2 i ASA 3 statusa podvrgnutih tireoidnoj hirurgiji. Ispitivan je uticaj sledećih faktora rizika: pol, starost, indeks telesne mase (ITM), ASA status, prijemna dijagnoza, tip operacije, trajanje operacije, trajanje anestezije, otežana intubacija traheje, kao i komorbiditeti: hipertenzija, kardiomiopatija, srčane aritmije, angina pektoris, dijabetes melitus, bolesti bubrega. Registrovani su intraoperativno: hipertenzija, hipertenzivna kriza, hipotenzija i srčane aritmije. Korišćen je Pirsonov χ2-test, univarijantna i multivarijantna regresiona analiza za statističku obradu podataka. Rezultati Većinu bolesnika su činile žene (86,3%). IVKP/ SD su registrovani kod 903 (72,1%) bolesnika. Najčešći poremećaj je bila intraoperativna hipertenzija - 61,4%. Univarijantnom analizom je registrovano sedam faktora rizika za pojavu IVKP/SD: godine života, ASA 3 status, ITM > 25 kg/m2, trajanje hirurgije, trajanje anestezije, hipertenzija i kardiomiopatija kao komorbiditet. Multivarijantnom regresionom analizom izdvojila su se tri nezavisna prediktora pojave IVKP/SD: godine starosti, hipertenzija i kardiomiopatija. Zaključak IVKP/SD su česte u tireoidnoj hirurgiji. Najčešća je intraoperativna hipertenzija. Starije životno doba, hipertenzija i kardiomiopatija kao koegzistirajuće bolesti su nezavisni faktori rizika za pojavu IVKP/SD

Knaster's problem for (Z2)k(Z_2)^k-symmetric subsets of the sphere S2k−1S^{2^k-1}

We prove a Knaster-type result for orbits of the group $(Z_2)^k$ in $S^{2^k-1}$, calculating the Euler class obstruction. Among the consequences are: a result about inscribing skew crosspolytopes in hypersurfaces in $\mathbb R^{2^k}$, and a result about equipartition of a measures in $\mathbb R^{2^k}$ by $(Z_2)^{k+1}$-symmetric convex fans

Projective center point and Tverberg theorems

We present projective versions of the center point theorem and Tverberg's theorem, interpolating between the original and the so-called "dual" center point and Tverberg theorems. Furthermore we give a common generalization of these and many other known (transversal, constraint, dual, and colorful) Tverberg type results in a single theorem, as well as some essentially new results about partitioning measures in projective space.Comment: 10 page

Risk Factors for Intraoperative Hypertension during Surgery for Primary Hyperparathyroidism

Objective: To investigate the incidence and identify risk factors for the occurrence of intraoperative hypertension (IOH) during surgery for primary hyperparathyroidism (pHPT). Subjects and Methods: The study included 269 patients surgically treated between January 2008 and January 2012 for pHPT. IOH was defined as an increase in systolic blood pressure >= 20% compared to baseline values which lasted for 15min. The investigated influence were demographic characteristics, surgical risk score related to physical status (based on the American Society of Anesthesiologists [ASA] classification), comorbidities, type and duration of surgery, and duration of anesthesia on IOH occurrence. The investigated factors were obtained from the patients' medical history, anesthesia charts, and the daily practice database. Logistic regression analysis was done to determine the predictors of IOH. Results: Of the 269 patients, 153 (56.9%) had IOH. Based on the univariate analysis, age, body mass index, ASA status, duration of anesthesia, and preoperative hypertension were risk factors for the occurrence of IOH. Multivariate analysis showed that independent predictors of IOH were a history of hypertension (OR = 2.080, 95% CI: 1.102-3.925, p = 0.024) and age (OR = 0.569, 95% CI: 0.360-0.901, p = 0.016). Conclusion: In this study, a high percentage (56%) of the patients developed IOH during surgery for pHPT, which indicates that special attention should be paid to these patients, especially to the high-risk groups: older patients and those with a history of hypertension. Further, this study showed that advanced age and hypertension as a coexisting disease prior to parathyroid surgery were independent risk factors for the occurrence of IOH

Fishing in the mesolithic-neolithic danube gorges in the early holocene (10th-6th millennium BC)

Disertacija obuhvata proučavanje ribolovačkih aktivnosti u Đerdapu tokom ranog holocena, tj. perioda mezolita i ranog/srednjeg neolita (9500-5500. pre n. e.), prvenstveno iz perspektive arheozoologije ribljih ostataka. Važna uloga ribolova u naseljavanju Đerdapa u praistoriji prepoznata je još tokom prvobitnih arheoloških istraživanja 1960ih i 1970ih godina. U okviru ovih kampanja, registrovan je i istražen veliki broj lokaliteta na levoj (rumunskoj) i desnoj (srpskoj) obali Dunava, od kojih su na desnoj obali najdetaljnije istraženi Padina, Lepenski Vir i Vlasac u klisuri Gospođin Vir. Smešteni na rečnim terasama u blizini virova, ova nalazišta su samim svojim položajem ukazivala na upućenost na reku. Pored položaja naselja, hipoteze o njihovom ribolovačkom karakteru zasnivale su se na velikim količinama otkrivenih ribljih kostiju, prisustvu ‘ribolikih’ skulptura i drugih artefakata sa predstavama akvatičkih motiva, a u novije vreme i na vrednostima stabilnih izotopa ugljenika i azota u kolagenu iz ljudskih kostiju koje su ukazivale na značajan udeo ribe u ishrani...Dissertation focuses on fishing activities in the Danube Gorges in early Holocene, i.e. in the Mesolithic and Early/Middle Neolithic (c. 9500-5500 cal BC), primarily from an archaeozoological perspective. The role of aquatic resource exploitation in site locations and settlement practices has long been recognized, ever since the initial archaeological excavations in the 1960s and the 1970s. These campaigns uncovered a great number of sites on the left (Romanian) and right (Serbian) bank of the Danube, with the excavations on the latter focused mainly on the sites of Padina, Lepenski Vir and Vlasac in the Gospođin Vir gorge. The reliance on the river was manifested by the location of sites, which were situated on riverine terraces in vicinity of whirlpools. In addition, their interpretations as fishing settlements were based on large amounts of recovered fish bones, presence of sculpted boulders and other artefacts depicting ‘fishlike’ beings, as well as more recent stable isotope analyses indicating a significant intake of aquatic resources in human diet..

Polytopal Bier Spheres and Kantorovich–Rubinstein Polytopes of Weighted Cycles

© 2019, Springer Science+Business Media, LLC, part of Springer Nature. The problem of deciding if a given triangulation of a sphere can be realized as the boundary sphere of a simplicial, convex polytope is known as the ‘Simplicial Steinitz problem’. It is known by an indirect and non-constructive argument that a vast majority of Bier spheres are non-polytopal. Contrary to that, we demonstrate that the Bier spheres associated to threshold simplicial complexes are all polytopal. Moreover, we show that all Bier spheres are starshaped. We also establish a connection between Bier spheres and Kantorovich–Rubinstein polytopes by showing that the boundary sphere of the KR-polytope associated to a polygonal linkage (weighted cycle) is isomorphic to the Bier sphere of the associated simplicial complex of “short sets”