WDVV equations and invariant bi-Hamiltonian formalism

The purpose of the paper is to show that, in low dimensions, the WDVV equations are bi-Hamiltonian. The invariance of the bi-Hamiltonian formalism is proved for N = 3. More examples in higher dimensions show that the result might hold in general. The invariance group of the bi-Hamiltonian pairs that we find for WDVV equations is the group of projective transformations. The significance of projective invariance of WDVV equations is discussed in detail. The computer algebra programs that were used for calculations throughout the paper are provided in a GitHub repository

WDVV equations: symbolic computations of Hamiltonian operators

We describe software for symbolic computations that we developed in or- der to find Hamiltonian operators for Witten–Dijkgraaf–Verlinde–Verlinde (WDVV) equations, and verify their compatibility. The computation involves nonlocal (integro- differential) operators, for which specific canonical forms and algorithms have been used

Basic Blood Analysis of Rabbits Immunized with Vaccine Against Myxomatosis

The aim of this preliminary study was to assess the immune response of rabbits triggered by vaccination against myxomatosis. In experiments, 14 New Zealand White rabbits (7 does – D and 7 bucks – B at the age of 1 to 3 years) were used. Samples of rabbit peripheral blood (PB) were collected from a. auricularis centralis to heparinised tubes 2 weeks before and 4 days after the subcutaneous injection (0.5 mL) of vaccine against myxomatosis (Pharmavac MXT). Mononuclear cells from peripheral blood (PBMCs) were isolated using Ficoll centrifugation. Isolated PBMCs were then frozen and stored at -192 °C. For phenotyping, the frozen cells were thawed and stained with the following anti-rabbit monoclonal antibodies (mAbs): anti-IgM (NRBM, IgG1), anti-CD4 (RTH1A, IgG1), anti-CD8 (ISC27A, IgG2a), anti-pan T2 (RTH21A, IgG1) and anti-CD45 (L12/201, IgG1). As the secondary immunoreagent, fluorescein isothiocyanate (FITC) or R-phycoerythrin (R-PE) labelled anti-mouse conjugates of appropriate subisotypes were used. We found significantly (P<0.05) increased percentage of either T-cells (does D5 and D7, and bucks B5, B6 and B7), or B-cells (bucks B2 and B7) in the rabbit peripheral blood. In conclusion, fast and adequate immune response to antigen (vaccine against myxomatosis) was indicated by the increase in T lymphocyte subsets 4 days after immunization. Thus, rabbit does (D5 and D7) and bucks (B5, B6 and B7) might be selected to create F1 generation for the future experiments

Decrease in C-reactive protein levels in rabbits after vaccination with a live attenuated myxoma virus vaccine

The aim of this study was to evaluate the acute phase reaction and immune response of rabbits triggered by vaccination with a live attenuated myxoma virus (MXT) vaccine. Thirteen adult and 11 juvenile New Zealand white rabbit-based crossbreed rabbits, were used. Samples of rabbit peripheral blood were collected from vena auricularis centralis into heparinised tubes before vaccination and 48 h after vaccination. All animals were vaccinated by subcutaneous injection (0.5 ml) with a MXT vaccine. The blood plasma C-reactive protein level was measured by an ELISA kit using a double-antibody sandwich. For phenotyping of lymphocytes the fresh cells were stained with the following anti-rabbit monoclonal antibodies: anti-IgM, anti-CD4, anti-CD8 and anti-pan T2. Our results show that the use of attenuated myxoma virus vaccine significantly decreases the level of C-reactive protein in blood plasma of adult rabbits by 38.14% (P &lt; 0.05) and of juvenile rabbits by 37.63% (P &lt; 0.001), within 48 h. The rabbit C-reactive protein after MXT vaccination is a negative acute phase protein. In the group of adult rabbits the immune response to MXT vaccination was accompanied by a non-significant decrease in CD4+, pT2+, IgM+ subsets. On the other hand the values of CD8+, CD4+CD8+ and CD4+/CD8+ were non-significantly higher after MXT vaccination

Can a Loan Valuation Adjustment (LVA) Approach Immunize Collateralized Debt from Defaults?

This study focuses on structuring tangible asset backed loans to inhibit their endemic option to default. We adapt the pragmatic approach of a margin loan in the configuring of collateralized debt to yield a quasi‐default‐free facility. We link our practical method to the current Basel III (2017) regulatory framework. Our new concept of the Loan Valuation Adjustment (LVA) and novel method to minimize the LVA converts the risky loan into a quasi risk‐free loan and achieves value maximization for the lending financial institution. As a result, entrepreneurial activities are promoted and economic growth invigorated. Information asymmetry, costly bailouts and resulting financial fragility are reduced while depositors are endowed with a safety net equivalent to deposit insurance but without the associated moral hazard between risk‐averse lenders and borrowers

Multilevel D-loop PCR identification of hunting game

AbstractThe control region of mtDNA (D-loop) was used for hair samples of the five hunting game species identification: red deer (Cervus elaphus), roe deer (Capreolus capreolus), fallow deer (Dama dama), mouflon (Ovis aries musimon), and wild boar (Sus scrofa). For D-loop multilevel PCR detection scheme was applied in six primers (CE CVZV 1=5′-GATCACGAGCTTGATCACCA-3′; CE CVZV 2=5′-AGGAGTGGGCGATTTTAGGT-3′; DD CVZV 3=5′-CGCGTGAAACCAACAACCCGC-3′; DD CVZV 4=5′-CCGGGTCGGGGCCTTAGACG-3′; SSW CVZV 5=5′-ACACGTGCGTACACGCGCATA-3′; SSW CVZV 6=5′-GGTGCCTGCT T TCGTAGCACG-3′) designed to identify unknown biological samples of the hunting game animals. The PCR reaction volume was 25μl at conditions 95°C for 2min, 94°C for 30s, 60°C for 30s, 72°C for 30s, 35cycles, with last extension at 72°C for 10min. D-loop mtDNA amplicons of the game animals are characterized with specific PCR product sizes depending on species: red deer=163bp and 140bp, fallow deer=280bp and 138bp, roe deer=303bp, 280bp, 160bp and 138bp, mouflon=299bp and 178bp, wild boar=137bp and 229bp

Modeling electricity loads in California: a continuous-time approach

In this paper we address the issue of modeling electricity loads and prices with diffusion processes. More specifically, we study models which belong to the class of generalized Ornstein-Uhlenbeck processes. After comparing properties of simulated paths with those of deseasonalized data from the California power market and performing out-of-sample forecasts we conclude that, despite certain advantages, the analyzed continuous-time processes are not adequate models of electricity load and price dynamics.Comment: To be published in Physica A (2001): Proceedings of the NATO ARW on Application of Physics in Economic Modelling, Prague, Feb. 8-10, 200

Semantically-Oriented Mutation Operator in Cartesian Genetic Programming for Evolutionary Circuit Design

Despite many successful applications, Cartesian Genetic Programming (CGP) suffers from limited scalability, especially when used for evolutionary circuit design. Considering the multiplier design problem, for example, the 5x5-bit multiplier represents the most complex circuit evolved from a randomly generated initial population. The efficiency of CGP highly depends on the performance of the point mutation operator, however, this operator is purely stochastic. This contrasts with the recent developments in Genetic Programming (GP), where advanced informed approaches such as semantic-aware operators are incorporated to improve the search space exploration capability of GP. In this paper, we propose a semantically-oriented mutation operator (SOMO) suitable for the evolutionary design of combinational circuits. SOMO uses semantics to determine the best value for each mutated gene. Compared to the common CGP and its variants as well as the recent versions of Semantic GP, the proposed method converges on common Boolean benchmarks substantially faster while keeping the phenotype size relatively small. The successfully evolved instances presented in this paper include 10-bit parity, 10+10-bit adder and 5x5-bit multiplier. The most complex circuits were evolved in less than one hour with a single-thread implementation running on a common CPU.Comment: Accepted for Genetic and Evolutionary Computation Conference (GECCO '20), July 8--12, 2020, Canc\'un, Mexic

The Bivariate Normal Copula

We collect well known and less known facts about the bivariate normal distribution and translate them into copula language. In addition, we prove a very general formula for the bivariate normal copula, we compute Gini's gamma, and we provide improved bounds and approximations on the diagonal.Comment: 24 page

Moody's Correlated Binomial Default Distributions for Inhomogeneous Portfolios

This paper generalizes Moody's correlated binomial default distribution for homogeneous (exchangeable) credit portfolio, which is introduced by Witt, to the case of inhomogeneous portfolios. As inhomogeneous portfolios, we consider two cases. In the first case, we treat a portfolio whose assets have uniform default correlation and non-uniform default probabilities. We obtain the default probability distribution and study the effect of the inhomogeneity on it. The second case corresponds to a portfolio with inhomogeneous default correlation. Assets are categorized in several different sectors and the inter-sector and intra-sector correlations are not the same. We construct the joint default probabilities and obtain the default probability distribution. We show that as the number of assets in each sector decreases, inter-sector correlation becomes more important than intra-sector correlation. We study the maximum values of the inter-sector default correlation. Our generalization method can be applied to any correlated binomial default distribution model which has explicit relations to the conditional default probabilities or conditional default correlations, e.g. Credit Risk${}^{+}$, implied default distributions. We also compare some popular CDO pricing models from the viewpoint of the range of the implied tranche correlation.Comment: 29 pages, 17 figures and 1 tabl