A novel method for solving high-dimensional backward stochastic differential equations using Malliavin calculus and deep learning

Backward stochastic differential equations (BSDE) are known to be a powerful tool in mathematical modeling due to their inherent connection with second-order parabolic partial differential equations (PDE) established by the non-linear Feynman-Kac relations. The fundamental power of BSDEs lies in the fact that with them one does not merely obtain the solution of the corresponding PDE but also its spatial gradient through the control process Z. Classical numerical methods tackling the system face the so-called curse of dimensionality and cannot be used to solve high-dimensional problems. In recent years, multiple approaches have been developed to overcome this computational burden, building on deep learning and showing remarkable empirical success even beyond 10 dimensions. However, such Deep BSDE methods struggle with giving accurate approximations for the Z-process throughout the whole time horizon. In this thesis we propose a novel approach aimed to give better estimations for the control problem, exploiting the natural dynamics of the Z-process given by Malliavin calculus. The proposed methods use deep learning parametrizations taking advantage of the universal approximation capability of neural networks. The Malliavin derivatives are estimated through the Malliavin chain rule. Two discrete numerical methods are developed which are called One-Step Malliavin (OSM) and Multi-Step Malliavin (MSM) schemes respectively. An error analysis is carried out proving the consistency of the algorithms and showing first-order convergence under certain assumptions. Numerical experiments are presented to demonstrate the efficiency of the Malliavin formulation compared to other Deep BSDE solvers

Élőhely-rekonstrukció lápi halfajok számára.

A Lápi póc Fajvédelmi Mintaprogram célja a nemzetközi jelentőségű lápi póc kárpát-medencei állományának megőrzése és gyarapítása. 2008-2010 között a Szadai Mintaterület (Pesti-síkság) degradált részein 6 db. kubikgödör méretű, egymástól elszigetelt vízteret hoztunk létre („Illés-tavak”). Az új vizekben és a lápi póc (Umbra krameri) természetes élőhelyein botanikai, vízkémiai, hidrobiológiai és halfaunisztikai vizsgálatokat végeztünk. A lápi póc egykori jelentős élőhelyein az amurgéb terjeszkedését figyeltük meg. 2009-ben saját szaporítású réti csíkot (Misgurnus fossilis) és széles kárászt (Carassius carassius) telepítettünk az 1. sz. Illés-tóba túlélési vizsgálat céljából. 2010-2011-ben 26 db. mentett póc anyahalat szaporítottunk, illetve 660 db. lárvát neveltünk fel. Az 1. sz. Illés-tó fizikai-kémiai vízminősége és a táplálékul szolgáló zooplankton és makrozoobenton faj- és egyedszáma két év alatt elérte a természetes „pócos” vizekre jellemző értékeket. A betelepített réti csíkok és széles kárászok jól fejlődtek, ezért 2010-2011 folyamán lápi póc anyahalakat és előnevelt pócokat telepítettünk az Illés-tavakba (génmegőrzés) és eredeti élőhelyükre. 2010-2011 tavaszán a széles kárász és a lápi póc sikeresen leívott az Illés-tavakban, a természetes póc szaporulat megközelítőleg 1000 db. lárva volt

Economic calculations of an investment of a slicing and packaging production line of a meat processing factory in Csongrád county

We test a Csongrád county meat-packing factory’s new slicing-packing production line’s investment. We value the different tenders from five main viewpoints, these are the following: the NPV (Net Present Value), IRR (Internal Rate of Return), DPB (Dynamic Payback), PI (Profitability Index), PB (Payback Time). During the calculation, we have experienced that both tenders would be viable financially. We recommended the offer of the GEA Group AG

Faunistical records and annotations for a better knowledge of the Tajikistani moth and butterfly fauna (Lepidoptera: Noctuoidea, Papilionoidea)

On the basis of 3333 specimens, geographical, spatial and temporal records of 225 noctuid and 37 papilionoid Lepidoptera species are given for the better knowledge of the fauna of Tajikistan. The following 25 species are recorded as new for the Tajikistani fauna: Agrotis golickei Ershov, 1871, Amphipyra cancellata Warren, 1911, Anapoma riparia (Boisduval, 1829), Archanara insoluta (Warren, 1911), Autophila einsleri Amsel, 1935, A. laetifica (Staudinger, 1901), A. maculifera Staudinger, 1888, Callopistria latreillei (Duponchel, 1827), Chazaria incarnata (Freyer, 1838), Chersotis lehmanni Varga, Gyulai, Ronkay et Ronkay 2013, Cirrhia tunicata (Graeser, 1890), Conistra pseudopolitina Hacker, 1990, Cryphia maeonis (Lederer, 1865), Cucullia tecca Püngeler, 1906, Dichagyris naumanni Varga, 1996, Episema minuta Boursin et Ebert, 1976, Eugnorisma cuneiferum Varga et L. Ronkay, 1994, Hypena opulenta (Christoph, 1877), Lophoterges varians Ronkay, 2005, Mniotype dubiosa (Bang-Haas, 1912), Namangana cretacea Staudinger, 1888, Nonagria puengeleri pringlei (Wiltshire, 1958), Orthosia reshoefti Hrebaly et Plante, 1994, Oxytripia orbiculosa (Esper, 1799) and Shargacucullia zerkowitzi (Boursin, 1934). The hitherto unknown female of Perigrapha heidi Hreblay, 1996 and male of Orthosia reshoefti are described. The taxonomic and nomenclatorial problems of Polymixis roehrei Boursin, 1961 are discussed, resulting the new synonymy Dasysternum colluta Draudt, 1934 = Polymixis roehrei Boursin, 1961, syn. n. New distributional data for Ostheldera kondara Varga et Ronkay, 1991 (Darvaz Mts.) are given with some additional comments on the female genitalia characters in comparison with those of O. minna Ronkay et Varga, 1994

Control of the Root-Knot Nematode Meloidogyne incognita and Weeds in Protected Cucumber with Dimethyl Disulfide (DMDS) over Two Crop Cycles: The First Results in Hungary

The effectiveness of dimethyl disulfide (DMDS) to control root-knot nematodes (Meloidogyne spp.) and weeds was tested for the first time in Hungary in two consecutive protected cucumber crops with application made only before the first crop. The treatments were Accolade EC (DMDS 94.1%) at 400 l/ha applied by driplines, Nemathorin 10 G (fosthiazate) at 30 kg/ha, and an untreated control. During the first cucumber cycle vigour-index, yield, root-gall index, Meloidogyne juveniles in the soil and germination of weeds were evaluated. All considered parameters were significantly improved by using DMDS compared respectively to the chemical standard and untreated control: (i) vigour-index of 7.0, 4.3 and 3.6; (ii) cumulative yield/sample of 45.1 kg, 30.9 kg, and 16.6 kg; root-gall index (RGI) of 1.2, 4.9, and 5.9; (iii) M. incognita J2/25 g soil of 0.25, 48.5 and 78.0, and (iv) number of weed seedlings/sample in the 20–30 cm soil profile of 1.1, 2.6, and 4.2. During the second cucumber crop, only root-gall index was evaluated. Results showed that a single DMDS treatment applied before the first crop had a prolonged beneficial effect on the following crop. In the second crop cycle, root gall indices were 5.58, 9.18, and 8.44 for DMDS treated plots, chemical control and untreated control, respectively

Climatic fluctuations inferred for the Middle and Late Pleniglacial (MIS 2) based on high-resolution (∼ca. 20 y) preliminary environmental magnetic investigation of the loess section of the Madaras brickyard (Hungary)

Abstract The Madaras brickyard section found at the northernmost fringe of the Backa loess plateau is one of the thickest and best-developed last glacial loess sequences of Central Europe. In the present work high-resolution magnetic susceptibility measurements (at 2 cm) were implemented on samples from the 10 m-section corresponding to a period between 29 and 11 KY cal b2K. One aim was to compare the findings with the ice core records of northern Greenland in order to establish a high-resolution paleoclimatic record for the last climatic cycle and with findings documented in other biotic and abiotic proxies so far. Our results revealed a strong variability of loess/paleosol formation during MIS 2. Millennial time-scale climatic events that characterize the North Atlantic during the last climatic cycle have been identified. From 29 ka up to the start of the LGM, the recorded MS values show a weak, negative correlation with the temperature proxy, and a weak positive correlation with the dust concentration of Greenland. A strong correlation was observed with the local paleotemperatures. Local climatic factors must have had a more prominent effect here on loess/paleosol development than the climate shifts over Greenland. During the LGM the same pattern is seen with a stronger correlation with the dust concentrations and a weaker correlation with the local temperature. Local climatic factors, plus dust accumulation, must have had a prominent influence on loess/paleosol development here. From the terminal part of the LGM a strong positive correlation of the MS values with the temperature proxy for Greenland accompanied by a strong negative correlation with the dust concentration values is observed. Correlation with local paleotemperatures is positive and moderate, strong. Here climate shifts over Greenland, as well as local endowments equally had an important role on the development of the MS signal