Computational approach for identification,characterization, three-dimensional structure modelling and machine learning-based thermostability prediction of xylanases from the genome of Aspergillus fumigatus

Identification of thermostable and alkaline xylanases from different fungal and bacterial species have gained an interest for the researchers because of its biotechnological relevance in many industries, such as pulp, paper, and bioethanol. In this study, we have identified and characterized xylanases from the genome of the thermophilic fungus of Aspergillus fumigatus by in silico analysis. Genome data mining revealed that the A fumigatus genome has six xylanase genes that belong to GH10, GH11, GH43 glycoside hydrolase families. In general, most of the bacterial and fungal GH11 xylanases are alkaline, and GH10 xylanases are acidic; however, we found that one identified xylanase from A fumigatus that belongs to the GH10 family is alkaline while the rest are acidic. Moreover, physicochemical properties also stated that most of the xylanases identified have lower molecular weight except one that belongs to the GH43 family. Structure prediction by homology modelling gave optimized structures of the xylanases. It suggests that GH10 family structure models adapt (β∕α) 8 barrel type, GH11 homology models adapt β-jelly type, and the GH43 family has a fivefold β-propeller type structure. Molecular docking of identified xylanases with xylan revealed that GH11 xylanases have strong interaction (-9.6 kcal/mol) with xylan than the GH10 (-8.5 and -9.3 kcal/mol) and GH43 (-8.8 kcal/mol). We used the machine learning approach based TAXyl server to predict the thermostability of the xylanases. It revealed that two GH10 xylanases and one GH11 xylanase are thermo-active up to 75ᵒC. We have explored the physiochemical properties responsible for maintaining thermostability for bacterial and fungal GH10 and GH11 xylanases by comparing crystal structures. All the analyzed parameters specified that GH10 xylanases from both the fungi and bacteria are more thermostable due to higher hydrogen bonds, salt bridges, and helical content.     

Difference Equations for the Masses of Leptons and Quarks in TeV Quantum Gravity

It is shown here that a 3 2 4 lattice in the wall for TeV quantum gravity with n =2 extra small-scale spatial dimensions can account for the fermion masses in a strikingly accurate manner. The family index, the electromagnetic charge number coupling, and the Yukawa coupling for lepton and quark mass generation in the minimal Standard Model (with a single Higgs) are related here to t' Hooft discreteness in the wall. Discrete values for the two transverse spatial distances in the wall are viewed as geometrical correspondents of the family index and the electromagnetic charge number coupling. The mass spectrum of Dirac leptons and quarks can then be understood as a manifestation of a Yukawa coupling that depends on the transverse wall coordinates. Linear homogeneous difference equations are considered to govern the Yukawa coupling or, more appropriately, the Yukawa field on the wall lattice. The solution to the latter difference equations yields experimentally consistent pole mass values for all twelve leptons and quarks. With the Yukawa field extending through the bulk, mass elevation for the second and third families features the torus radii ratio R 2 / R 1 =41/10.     

Spectral Analysis for an Indefinite Singular Sturm-Liouville Problem

Direct and inverse problems of spectral analysis are studied for an indefinite singular boundary value problem coming from astrophysics. We establish properties of the spectrum, prove completeness and expansion theorems and investigate the inverse problem of recovering the differential equation from the given spectral characteristics.     

Effects of Hydrostatic and Chemical Pressures on Impurities Determined through Optical Parameters

A survey on the influence of hydrostatic and chemical pressures upon optical properties due to Transition-Metal impurities in insulators is offered in this article. Aside from recalling the theoretical framework where the properties of impurities in insulating materials are reasonably explained particular attention is paid to the dependence of crystal field and charge transfer transitions upon the impurity-ligand distance, R . By means of 10 Dq dependent d-.d transitions or the energy of charge transfer transitions it is pointed out that j R variations around 0.1 pm can be detected. The R dependence of 10 Dq is shown to determine also the corresponding dependence of Huang-Rhys factors and Stokes shift. The Huang-Rhys factor, S A , of the A 1 local mode is found to increase when R does a conclusion supported by recent experimental data on Cs 2 NaScCl 6 : Cr 3+ under hydrostatic pressure. The increase of the Stokes shift when R increases observed in the series of cubic fluoroperovskites doped with Mn 2+ is also discussed. It is pointed out that for the same j R variation, j y A changes produced by chemical pressures can be bigger than those produced through a hydrostatic pressure.     

Distinction of Push,pull effect and steric hindrance in disubstituted alkynes

The push,pull effect in two series of disubstituted alkynes was studied at the DFT level [B3LYP/6-311G(d)] by application of the ¹³C chemical shift differences (GIAO) between the alkyne carbon atoms (Δδ_CC), the charge difference between these carbons (Δq_CC), the occupation quotient (NBO) of anti-bonding π^∗, and bonding π orbitals (π^∗_CC/π_CC) and the bond length (d_CC) of the CC triple bond. The linear dependence of d_CC versus π^∗_CC/π_CC quantifies changes in the push,pull effect while deviations from the latter correlation indicate and ascertain quantitatively to what extent steric hindrance restricts the strain-less conjugation of the CC triple bond π-orbitals in the disubstituted alkynes.     

On the Explicit Solution of Certain First Order Systems of Partial Differential Equations

We consider two classes of systems of partial differential equations of first order. One consists of generalized Stokes-Beltrami equations $ Aw_z = w^*_z $ , $ \lambda Bw_{\bar z} -w^*_{\bar z} $ with square matrices A and B and a scalar factor u . The other may be written in matrix notation as $ v_{\bar z} = c{\bar v} $ where c denotes a square matrix. This system is known as a Pascali system. Both systems are in close connections to certain systems of second order for which the solutions can be represented using particular differential operators. On the basis of these relations we give the solutions of the first order systems explicitly.     

On Certain Fejér and Tchebychev Type Integrals

Let m and n denote a pair of positive integers. In this paper, we call upon the Hadamard product and computer algebra techniques to evaluate the Fejér integral π ^?1 ∫₀ ^π (sin mθ / sin θ) ²ⁿ dθ. Using symmetry arguments, it is proved that the value of this integral is an odd polynomial in m of degree 2n ? 1. This permits using polynomial curve fitting methods and mathematical software packages to obtain evaluation formulas for n relatively small. Some cases of the above integral with 2n replaced by 2n + 1 are also discussed. A familiar identity shows that these yield evaluations of integrals of powers of certain Tchebychev polynomials.     

Monte Carlo construction of hedging strategies against multi-asset European claims

For evaluating a hedging strategy we have to know at every moment the solution of the Cauchy problem for a corresponding parabolic equation (the value of the hedging portfolio) and its derivatives (the deltas). We suggest to find these quantities by Monte Carlo simulation of the corresponding system of stochastic differential equations using weak solution schemes. It turns out that with one and the same control function a variance reduction can be achieved simultaneously for the claim value as well as for the deltas. As illustrations we consider a Markovian multi-asset model with an instantaneously riskless saving bond and also some applications to the LIBOR rate model of Brace, Gatarck, Musiela and Jamshidian.     

Heuristic option pricing with neural networks and the neuro-computer synapse 3

Today’s option and warrant pricing is based on models developed by Black, Scholes and Merton in 1973 and Cox, Ross and Rubinstein in 1979. The price movement of the underlying asset is modeled by continuous-time or discrete-time stochastic processes. Unfortunately these models are based on severely unrealistic assumptions. Permanently an unsatisfactory and quite artificial adaption to the true market conditions is necessary (future volatility of the underlying price). Here, an alternative heuristic approach with a highly accurate neural network approximation is presented. Market prices of options and warrants and the values of the influence variables form the usually very large output/ input data set. Thousands of multi-layer perceptrons with various topologies and with different weight initializations are trained with a fast sequential quadratic programming (SQP) method. The best networks are combined to an expert council network to synthesize market prices accurately. All options and warrants can be compared to single out overpriced and underpriced ones for each trading day. For each option and warrant overpriced and underpriced trading days can be used to ascertain a better buy and sell timing. Furthermore the neural model gains deep insight into the market price sen-sitivities (option Greeks), e.g., ?, Г, Θ and Ω. As an illustrative example we inves-tigate BASF stock call warrants. Time series from the beginning of 1996 to mid 1997 of 74 BASF call warrant prices at the Frankfurter Wertpapierborse (Frankfurt Stock Exchange) form the data basis. Finally a possible speed up of the training with the neuro-computer SYNAPSE 3 is briefly discussed     

The Qualitative Behaviour of Newton Flows for Weierstrass’ ℘-Functions

We study the continuous, desingularized Newton method for Weierstrass' ?-functions. This leads to a family of autonomous differential equations in the plane, which depends on two complex parameters ω ₁ and ω ₂. For the associated flows there are, up to conjugacy, precisely three possibilities. These are determined by the form of the parallelogram spanned by ω ₁ and ω ₂: square, rectangular but not square, and non-rectangular.