A generalization of MacMahon's formula

We generalize the generating formula for plane partitions known as MacMahon's formula as well as its analog for strict plane partitions. We give a 2-parameter generalization of these formulas related to Macdonald's symmetric functions. The formula is especially simple in the Hall-Littlewood case. We also give a bijective proof of the analog of MacMahon's formula for strict plane partitions.Comment: 19 pages, 5 figure

Plane overpartitions and cylindric partitions

Generating functions for plane overpartitions are obtained using various methods such as nonintersecting paths, RSK type algorithms and symmetric functions. We extend some of the generating functions to cylindric partitions. Also, we show that plane overpartitions correspond to certain domino tilings and we give some basic properties of this correspondence.Comment: 42 pages, 11 figures, corrected typos, revised parts, figures redrawn, results unchange

Asymptotics of pure dimer coverings on rail-yard graphs

We study asymptotic limit of random pure dimer coverings on rail yardgraphs when the mesh sizes of the graphs go to 0. Each pure dimer covering correspondsto a sequence of interlacing partitions starting with an empty partition and ending inan empty partition. Under the assumption that the probability of each dimer covering isproportional to the product of weights of present edges, we obtain the limit shape (Law ofLarge Numbers) of the rescaled height function and the convergence of unrescaled heightfluctuation to a diffeomorphic image of Gaussian Free Field (Central Limit Theorem); an-swering a question in [6]. Applications include the limit shape and height fluctuations forpure steep tilings ([8]) and pyramid partitions ([20, 35, 36, 37]). The technique to obtainthese results is to analyze a class of Mcdonald processes which involve dual partitions as well

Perfect sampling algorithm for Schur processes

We describe random generation algorithms for a large class of random combinatorial objects called Schur processes, which are sequences of random (integer) partitions subject to certain interlacing conditions. This class contains several fundamental combinatorial objects as special cases, such as plane partitions, tilings of Aztec diamonds, pyramid partitions and more generally steep domino tilings of the plane. Our algorithm, which is of polynomial complexity, is both exact (i.e. the output follows exactly the target probability law, which is either Boltzmann or uniform in our case), and entropy optimal (i.e. it reads a minimal number of random bits as an input). The algorithm encompasses previous growth procedures for special Schur processes related to the primal and dual RSK algorithm, as well as the famous domino shuffling algorithm for domino tilings of the Aztec diamond. It can be easily adapted to deal with symmetric Schur processes and general Schur processes involving infinitely many parameters. It is more concrete and easier to implement than Borodin's algorithm, and it is entropy optimal. At a technical level, it relies on unified bijective proofs of the different types of Cauchy and Littlewood identities for Schur functions, and on an adaptation of Fomin's growth diagram description of the RSK algorithm to that setting. Simulations performed with this algorithm suggest interesting limit shape phenomena for the corresponding tiling models, some of which are new.Comment: 26 pages, 19 figures (v3: final version, corrected a few misprints present in v2

Odgovor korenovog sistema klijanaca kukuruza na osmotski stres

Field testing for drought tolerance was performed on 6,000 accessions from the Maize Research Institute gene bank, under severe drought conditions in Egypt, as well as, under moderate climate conditions in Zemun Polje and Skopje. Five inbred lines, considered as drought tolerant, were chosen for further investigations under controlled experimental conditions. Osmotic stress caused by drought is one of the most important abiotic stresses. In this study osmotic stress was applied with polyethylene glycol (PEG) 10 000. The response to the PEG treatment of these genotypes was analysed in respect to their root morphology, root length, root fresh and dry weight, proline content and peroxidase activity. Results showed that the root development was less in all genotypes under the PEG treatment. The proline content increased, while the peroxidase activity declined in PEG-treated plants.Suša je jedan od najznačajnijih abiotičkih faktora, koji značajno utiče na smanjenje konačnog prinosa zrna kod kukuruza. Predviđanja globalnih klimatskih promena za XXI vek idu u pravcu povećanja temperature vazduha, veće evapotranspiracije i učestalije pojave suše. Za selekciju kukuruza danas, kao i u doglednoj budućnosti, izvori poželjnih svojstava koji se nalaze u bankama gena biće od velikog značaja. Materijal koji se čuva u banci gena Instituta za kukuruz, po obimu i sadržaju, pruža velike mogućnosti. Na osnovu ispitivanja tolerantnosti na sušu kod 6.000 uzoraka iz banke gena Instituta za kukuruz u poljskim uslovima umerenog (Zemun Polje i Skoplje) i aridnog klimata (Egipat), odabrano je pet inbred linija, okarakterisanih kao tolerantne, za dalja ispitivanja u kontrolisanim laboratorijskim uslovima. Linije pripadaju različitim FAO grupama zrenja (A5 - FAO 400 i A1, A2, A3 i A4 - FAO 500). Osmotski stres izazvan sušom je jedan od najznačajnijih abiotičkih faktora. U ovom radu je ispitivan efekat polietilen glikola (PEG) 10.000, kao osmotikuma, na rast korena klijanaca. Merena je dužina, sveža i suva masa korena, određivan je sadržaj prolina u korenu i merena je aktivnost antioksidativnih enzima. Rezultati ispitivanja pokazuju smanjenje porasta korenovog sistema, povećanje sadržaja prolina, kao i smanjenje specifične aktivnosti peroksidaza kod svih tretmana u odnosu na kontrolnu varijantu, kao odgovor na primenjeni osmotski stres. Naredna istraživanja vezana za odgovor biljke na osmotski stres bi uključila i nadzemni deo klijanaca, kao i molekularnu karakterizaciju genotipova tolerantnih prema suši. Odabrani genotipovi poslužiće za formiranje core kolekcije koja će u sebi sadržati ovo svojstvo i biti osnova u programima oplemenjivanja kukuruza

The Bioethical Complexity of the Issues of Surrogate Motherhood

Zamjensko majčinstvo, kao najsloženija metoda medicinski pomognute oplodnje i posljednje sredstvo u borbi protiv neplodnosti, u svijetu pobuđuje velike rasprave, kucajući i na vrata našega zakonodavstva, medicine i pravosuđa, što je osnovni razlog za cjelovito promatranje takve pojave s bioetičkoga motrišta kako bi se ukazalo na kompleksne moralne posljedice koje zamjensko majčinstvo sa sobom nosi u složenim odnosima (zamjenske majke, supružnika, naručiteljskoga para, djeteta).Surrogate motherhood as the most complex method of medically assisted reproduction and the last tool in the fight against infertility, stirs great debates around the world, knocking also on the doors of our own legislation, medicine and judiciary, which is the main reason for a comprehensive analysis of this phenomenon from a bioethical point of view in order to show the complex moral consequences that follow surrogate motherhood in the complex relationships (of the surrogate mother, spouses, the client couple, the child)

The Bioethical Complexity of the Issues of Surrogate Motherhood

Zamjensko majčinstvo, kao najsloženija metoda medicinski pomognute oplodnje i posljednje sredstvo u borbi protiv neplodnosti, u svijetu pobuđuje velike rasprave, kucajući i na vrata našega zakonodavstva, medicine i pravosuđa, što je osnovni razlog za cjelovito promatranje takve pojave s bioetičkoga motrišta kako bi se ukazalo na kompleksne moralne posljedice koje zamjensko majčinstvo sa sobom nosi u složenim odnosima (zamjenske majke, supružnika, naručiteljskoga para, djeteta).Surrogate motherhood as the most complex method of medically assisted reproduction and the last tool in the fight against infertility, stirs great debates around the world, knocking also on the doors of our own legislation, medicine and judiciary, which is the main reason for a comprehensive analysis of this phenomenon from a bioethical point of view in order to show the complex moral consequences that follow surrogate motherhood in the complex relationships (of the surrogate mother, spouses, the client couple, the child)

VALUATION OF URBAN FOREST BENEFITS: A LITERATURE REVIEW

Urbane šume vrijedni su prirodni resursi koji modernom društvu pružaju višestruke koristi, pri čemu proizvodnja drva nije prioritet (Konijnendijk 2000). Stoga koristi od urbanih šuma vrlo često imaju obilježja netržišnih dobara i usluga. Prilikom donošenja odluka vezanih za urbane šume javlja se potreba za konkretnim informacijama, u idealnom slučaju rezultatima analize troškova i koristi, gdje su koristi od urbanih šuma važan ulazni podatak. Rezultati dobiveni znanstvenim metodama vrednovanja urbanih šuma mogu poslužiti za savjetovanje sudionika u procesu odlučivanja i donošenja politika u skladu s konceptom uporabljive znanosti (engl. usable science) (Stevanov i dr. 2011). Cilj je ovog rada kvalitativno analizirati literaturu koja se odnosi na vrednovanje koristi od urbanih šuma metodama vrednovanja netržišnih dobara i usluga. Na osnovi pretrage baze Science Direct izdvojeno ukupno 38 članaka koji su obuhvatili razdoblje od 1997. do 2012. godine. Analiza pokazuje da se najčešće primjenjuju metoda hedonističkih cijena (HPM) i metoda vrednovanja kontingenta (CVM), dok su metaanalize za sada rijetke. Odabrane studije obuhvaćaju različite tipove urbanih šuma (drveće, parkove, šume, rekreacijska područja) ili se odnose općenito na koncept otvorenog prostora (engl. open space) unutar kojih se nalaze i urbane šume. Većinu studija objavili su autori iz SAD-a (13) i Kine (8), a gledano po kontinentima najviše ih se odnosi na Europu (14), Sj. Ameriku (13) i Aziju (9). Istraživanja koja primjenjuju HPM pokazuju da blizina urbanih šuma (do 500 m) znatno utječe na porast vrijednosti nekretnine, a osim blizine, ključne varijable su tip i veličina urbane šume, slobodan pristup (ne naplaćuju se ulaznice) te razina kriminala. Najčešće vrednovana korist je mogućnost rekreacije. Rezultate vrednovanja različitim metodama treba tumačiti s oprezom, jer svaka pojedina metoda ima svojih prednosti i nedostataka. Analiza literature otkriva manjak ovakvih istraživanja u Hrvatskoj i upućuje na potrebu za jačom zastupljenosti ovakvih tema u budućnosti. Svrha je članka dati pregled studija vrednovanja koristi od urbanih šuma, pokazati koje varijable utječu na rezultat vrednovanja te općenito upozoriti na potrebu provođenja ovakvih studija. Prikazana analiza literature može poslužiti istraživačima, urbanistima, krajobraznim arhitektima te uživateljima koristi od urbanih šuma.Urban forests provide multiple benefits whereas wood production is less important in comparison to benefits such as mitigating air pollution and heath island effect, providing fresh water or recreational opportunities to growing urban population (Konijnendijk 2000). However these benefits are usually non-marketable. There are several typologies of forest benefits (services), while Tyrväinen et al. (2005) brings typology of benefits and uses of urban forests and trees (Table 1). Putting value on urban forest benefits helps decision makers to make informed decisions about urban forests, ideally based on cost- benefit analysis. This is in line with concept of usable science, whereas scientific results can serve as valuable information to political actors in the process of deliberation (Stevanov et al. 2011). The purpose of this paper was to give a literature analysis related to valuation of non-marketable urban forest benefits. Search engine Science Direct gave 38 results covering the period 1997-2012, with 24 papers published in the last five years (Table 2). Qualitative analysis showed that the most common valuation methods were hedonic pricing method (HPC) and contingent valuation method (CVM), while meta-analysis, as one of benefit transfer methods, was rare (Table 2). These methods use urban residents’ stated or revealed wiliness to pay (WTP) for urban forest benefits. Selected papers addressed different types of urban forests (street trees, trees in the park, forests or recreation areas) or trees as element of open spaces. Majority of studies are published by authors from USA (13) and China (8). Urban forest located within range of up to 500 m significantly affected valuation, as well as type, size, free access or level of crime in the neighbourhood. Recreational benefits were most commonly valuated. Results of valuation studies have to be interpreted in context of limitations of each method applied. Valuation studies of urban forest benefits in Croatia are still rare. Growing urban population and other pressures negatively influence urban forests. Putting monetary values on them could help in their conservation. This paper may be helpful to researchers, urban planners, landscape architects, and other consumers of urban forest benefits. There is almost no such research in Croatia, which indicates need to put more emphasis on this type of research in future