Production Cross Research Articles

Angular and Orbital Angular Momenta in the Tight Focus of a Circularly Polarized Optical Vortex

Based on the Richards-Wolf (RW) formalism, we obtain two different exact expressions for the angular momentum (AM) density of light in the focus of an optical vortex with a topological charge n and right circular polarization. One expression for the AM density is derived as the cross product of the position vector and the Poynting vector and has a nonzero value in the focus for an arbitrary integer n. Another expression for the AM density is equal to a sum of the orbital angular momentum (OAM) and the spin angular momentum (SAM) and, in the focus of a considered light field, is equal to zero at n = −1. These expressions are not equal at each point in space, but their 3D integrals are equal. Thus, we derive exact expressions for the AM, SAM and OAM densities in the focus of an optical vortex with right circular polarization and demonstrate that the identity for the densities AM = SAM + OAM is not valid. In addition, we show that the expressions for the strength vectors of the electric and magnetic field near the tight focus, obtained on the basis of the RW formalism, are exact solutions of Maxwell’s equations. Thus, the RW theory exactly describes the behavior of light near the tight focus in free space.

Random Integration Analysis of Recombinant Adeno-Associated Virus 6 Packaged in Sf9 Insect Cells

Recently, there have been growing concerns over the integration of recombinant adeno-associated virus (rAAV) used in gene therapy. Wild-type adeno-associated virus (AAV) site specifically integrates into AAVS1 site of human genome, while rAAV randomly integrates into host chromosomes at low frequencies. This research aims to study the random integration events of rAAV6-EGFP packaged in Sf9 insect cells. Baculo-Sf9 manufacturing platform has the advantages of high-density suspension culture of Sf9 insect cells and large-scale production of rAAV vectors. In this study, we used different doses of Baculo-Sf9 produced rAAV6-EGFP to transduce HEK293T cells and A549-implanted tumors in vitro and in vivo. Using flow cytometry and fluorescence microscopy, we studied their EGFP gene expression efficiencies and EGFP fluorescence intensities. Using inverse nested PCR and DNA sequencing, random integration sites of rAAV6-EGFP genome into human chromosomes were identified. In vitro results showed that gene expression efficiencies became stable after 20 days and random integration frequencies were 0.2-4.2%. Both in vitro and in vivo results indicated that random integration of Baculo-Sf9 rAAV6 was dose-dependent. Sequencing results showed two random integration sites, which were on human chromosomes 8 and 12. The findings suggest that we should use as low dose of rAAV vector as possible for safe gene therapy.

Fold2Vec: Towards a Statement-Based Representation of Code for Code Comprehension

We introduce a novel approach to source code representation to be used in combination with neural networks. Such a representation is designed to permit the production of a continuous vector for each code statement. In particular, we present how the representation is produced in the case of Java source code. We test our representation for three tasks:code summarization,statement separation, andcode search. We compare with the state-of-the-artnon-autoregressiveandend-to-endmodels for these tasks. We conclude that all tasks benefit from the proposed representation to boost their performance in terms of F1-score, accuracy, and mean reciprocal rank, respectively. Moreover, we show how models trained on code summarization and models trained on statement separation can be combined to address methods with tangled responsibilities, meaning that these models can be used to detect code misconduct.

Intrinsic aberration coefficients for plane-symmetric optical systems consisting ofspherical surfaces.

This paper presents the analytical form of the intrinsic aberration coefficients for spherical plane-symmetric optical systems expressed as a function of first-order system parameters and the paraxial chief and marginal ray angles and heights. The derived aberration coefficients are in the third and fourth groups with the multiplication of two or three vector products of pupil and field vectors.

Highly selective transgene expression through the flip-excision switch system by using a unilateral spacer sequence

The flip-excision switch (FLEX) system with an adeno-associated viral (AAV) vector allows expression of transgenes in specific cell populations having Cre recombinase. A significant issue with this system is non-specific expression of transgenes in tissues after vector injection. We show here that Cre-independent recombination events in the AAV genome carrying the FLEX sequence occur mainly during the production of viral vectors in packaging cells, which results in transgene expression in off-target populations. Introduction of a relatively longer nucleotide sequence between two recognition sites at the unilateral side of the transgene cassette, termed a unilateral spacer sequence (USS), is useful to suppress the recombination in the viral genome, leading to the protection of non-specific transgene expression with enhanced gene expression selectivity. Our FLEX/USS system offers a powerful strategy for highly specific Cre-dependent transgene expression, aiming at various applications for structural and functional analyses of target cell populations.

Optimizing vector production & purification to enhance scalable AAV manufacturing

Optimizing vector production & purification to enhance scalable AAV manufacturing

Machine learning and metabolic modelling assisted implementation of a novel process analytical technology in cell and gene therapy manufacturing

Process analytical technology (PAT) has demonstrated huge potential to enable the development of improved biopharmaceutical manufacturing processes by ensuring the reliable provision of quality products. However, the complexities associated with the manufacture of advanced therapy medicinal products have resulted in a slow adoption of PAT tools into industrial bioprocessing operations, particularly in the manufacture of cell and gene therapy products. Here we describe the applicability of a novel refractometry-based PAT system (Ranger system), which was used to monitor the metabolic activity of HEK293T cell cultures during lentiviral vector (LVV) production processes in real time. The PAT system was able to rapidly identify a relationship between bioreactor pH and culture metabolic activity and this was used to devise a pH operating strategy that resulted in a 1.8-fold increase in metabolic activity compared to an unoptimised bioprocess in a minimal number of bioreactor experiments; this was achieved using both pre-programmed and autonomous pH control strategies. The increased metabolic activity of the cultures, achieved via the implementation of the PAT technology, was not associated with increased LVV production. We employed a metabolic modelling strategy to elucidate the relationship between these bioprocess level events and HEK293T cell metabolism. The modelling showed that culturing of HEK293T cells in a low pH (pH 6.40) environment directly impacted the intracellular maintenance of pH and the intracellular availability of oxygen. We provide evidence that the elevated metabolic activity was a response to cope with the stress associated with low pH to maintain the favourable intracellular conditions, rather than being indicative of a superior active state of the HEK293T cell culture resulting in enhanced LVV production. Forecasting strategies were used to construct data models which identified that the novel PAT system not only had a direct relationship with process pH but also with oxygen availability; the interaction and interdependencies between these two parameters had a direct effect on the responses observed at the bioprocess level. We present data which indicate that process control and intervention using this novel refractometry-based PAT system has the potential to facilitate the fine tuning and rapid optimisation of the production environment and enable adaptive process control for enhanced process performance and robustness.

Including thermal network operation in the optimization of a Multi Energy System

The combined production of different energy vectors with Multi Energy Systems is a very attractive opportunity to increase the generation efficiency, compensate the oscillations of renewable sources, and improve the flexibility in power generation. Optimizing their operation is a complex task, since the problem can easily reach high dimensions, representing a challenge for commercial solvers. The inclusion in the optimization of a thermal network whose simulation is based on temperatures and flowrates allows to significantly improve the applicability of the obtained results. In addition, the effect of the operating temperatures on the performances of thermal components should be included as well. With these purposes, the present study proposes a strategy for the operation optimization of a MES and its internal thermal network. The model relies on a decomposition approach, where the original problem is divided in two subproblems. In the first one, the MES operating costs are minimized without considering the effects of the thermal network, while in the second one, the thermal network operation is optimized in order to find the operating conditions that are more favourable to the ones found for the MES. These subproblems are iteratively solved until the process converges to a stable solution. Some efforts are taken to keep the mathematical formulation as simple as possible (the MES is a Mixed Integer Linear Programming, while the heating network is a Quadratically Constrained Programming). The developed model allows to find near-optimal solutions which satisfy the numerous physical and technical constraints addressed. The results provide an optimized schedule for the thermal storage in terms of mass flowrates and temperature. One of the strengths of the model is the relatively low computational time required to reach the convergence and, despite not being the global optimum, the high quality of the solution obtained.

Doubly Fed Induction Machine-Based DC Voltage Generator with Reduced Oscillations of Torque and Output Voltage

The doubly fed induction machine (DFIM)-based DC voltage generator is equipped with a stator-connected diode rectifier. The six-pulse diode rectifier as a nonlinear circuit introduces harmonics in the stator and rotor current and distorts the machine stator voltage, as well as the stator flux. This causes electromagnetic torque oscillations and instantaneous power components oscillations. The torque oscillations adversely impact the mechanical parts of the drive-train and oscillations of the p component of instantaneous power influence DC-bus voltage oscillations. The oscillations can be somewhat cancelled by control methods. However, cancellation of electromagnetic torque is not strictly coupled with cancellation of oscillations of the p component of instantaneous power. The paper presents an analysis of influence of the control methods aimed at a reduction of torque oscillations on the output voltage oscillations level in the stand-alone DFIM-based DC voltage generator. Field-oriented control FOC with current controllers and space vector modulation-based direct torque control DTC-SVM with flux module regulation have been compared with control in which electromagnetic torque is one of the commanded variables, whereas the second variable is the dot product of stator flux and rotor current space vectors. The contributions of this paper are the introduction of a new variable in the second control path in the DTC-SVM method instead of flux vector length and the proof that it can reduce torque and DC-bus voltage oscillations in the DFIG-DC system. Additionally, this paper reveals that for proper stator-to-rotor-turns ratio of a doubly fed machine necessary for reduction of the rotor converter power, lower DC-bus voltage can be obtained than is required for full realization rotor side voltage requested by rotor current controllers. This is the reason why, regardless of the control method, torque oscillations cannot be always fully cancelled, and a comparative study of the methods at these conditions has been conducted in simulation and in laboratory tests.

Deterministic and Random Generalized Complex Numbers Related to a Class of Positively Homogeneous Functionals

Based upon a new general vector-valued vector product, generalized complex numbers with respect to certain positively homogeneous functionals including norms and antinorms are introduced and a vector-valued Euler type formula for them is derived using a vector valued exponential function. Furthermore, generalized Cauchy–Riemann differential equations for generalized complex differentiable functions are derived. For random versions of the considered new type of generalized complex numbers, moments are introduced and uniform distributions on discs with respect to functionals of the considered type are analyzed. Moreover, generalized uniform distributions on corresponding circles are studied and a connection with generalized circle numbers, which are natural relatives of π, is established. Finally, random generalized complex numbers are considered which are star-shaped distributed.

Dynamic reliability analysis of stochastic structures under non-stationary random excitations based on an explicit time-domain method

For the analysis of the dynamic reliability of stochastic structures subjected to non-stationary random excitations, an effective hybrid approach is proposed. In this approach, the explicit time-domain method is employed to obtain the dynamic responses of each deterministic structure. Dynamic responses for the explicit time-domain method can be expressed as a series of products of deterministic coefficient matrices and random load vectors, which can significantly enhance computational efficiency. For the issue of stochastic structures, the double-hidden-layer backpropagation neural network is introduced as a surrogate model for reconstructing the coefficient matrices to avoid repeated construction of the coefficient matrices for each sample with different structural parameters using the extremely time-intensive regular method. For more effective training of the backpropagation neural network, the Latin hypercube sampling technique is introduced to generate representative samples of random structural parameters. In consideration of the intrinsic benefit of the explicit time-domain method, parallel computation is incorporated into the method. Finally, the explicit time-domain method is used to perform the Monte Carlo simulation in conjunction with the parallel computing technique to resolve the problem of small failure probabilities. To demonstrate the efficacy of the proposed method, numerical examples are presented.

A Unified Definition of Electrostatic and Magnetic Fields

This article originates from the observation that field lines are drawn using distinctive rules in magnetic field and electrostatic fields. It aims at reconciliating the definitions of these fields and thus reaching a consensus on the interpretation of field lines. Our unified field definition combines three orthogonal vectors and a unique scalar value. Field lines are then defined as isovalue lines of the scalar value, rendering it simpler to interpret in both field types. Specific to our field definition is the use of square root of vector’s cross product so that all vectors have the same physical unit. This enhanced field definition also enables a more efficient calculation of Biot-Savart law. This article is the first of a series allowing the drawing of isovalue contour lines.

FRACTAL ALGEBRA A MATHEMATICAL ALLEGORY

An abstract fractal algebra is developed with structures analogous to conventional linear algebra. Focus is on group properties and symmetries forming an abstract algebraic structure over the body of real numbers. The new algebra is worked out on a sample fractal geometry. Correspondences between fractal and linear algebra are explained with numerical examples, including fractal vectors and fractal versions of the vector sum, projections, scalar product, cross product, matrix, and matrix product. We allude to possible applications of fractal vectors in physics. This fractal algebra may open novel possibilities for analysis of fractal systems.

A generalization of complex, dual and hyperbolic quaternions: Hybrid quaternions

Hybrid numbers are a new non-commutative number system which is a generalization of the complex (i2 = ?1), dual (?2 = 0), and hyperbolic numbers (h2 = 1). In this article, firstly we define a new quaternion system called hybrid quaternions by taking the coefficients of real quaternions as hybrid numbers. This new quaternion system is a combination of complex quaternions (biquaternions), hyperbolic (perplex) quaternions, and dual quaternions, and it can be viewed as a generalization of these quaternion systems. Then, we present the basic properties of hybrid quaternions including fundamental operations, conjugates, inner product, vector product, and norm. Finally, we give a schematic representation of numbers and quaternions.

On the Expression of Composite Natural Numbers as Tensorial Products of Prime Natural Powers Vectors

On the Expression of Composite Natural Numbers as Tensorial Products of Prime Natural Powers Vectors

ЧИСЕЛЬНЕ ДИФЕРЕНЦІЮВАННЯ ТАБЛИЧНИХ ФУНКЦІЙ У ДОВІЛЬНО РОЗТАШОВАНИХ ВУЗЛАХ ІНТЕРПОЛЯЦІЇ

A methodology has been developed for numerically differentiating table-given functions using a Taylor polynomial of degree n, which enables the computation of k-th order derivatives (k £ n) at any point between arbitrarily located interpolation nodes in one, two, or multiple independent variables. Recent research and publications have been analysed, allowing for the assessment of the task complexity of computing derivatives of a function based on the values of independent variables within a certain interval of a table-given function. The formulation of the problem of numerical differentiation of periodic table-given functions using the Taylor polynomial of the nth order from one, two, and multiple independent variables is described. It is established that any tabulated function should be initially smoothed by some function whose analytical expression is a global (local) interpolating polynomial or a polynomial obtained by least squares approximation with some error. The derivative of such a table-given function is understood as the derivative of its interpolant. A method of numerical differentiation of table-given functions is developed, the essence of which is reduced to the product of the Taylor row vector of the n-th degree by the matrix of the k-th order of its differentiation (k £ n) and on the column vector of the coefficients of the corresponding interpolant. Some problem formulations of numerical differentiation of table-given functions using Taylor polynomials of degree n, corresponding solution algorithms, and specific implementation examples are provided. It has been established that to compute the k-th order derivative of a table-given function at a given value of the independent variable, the following steps need to be performed: based on the given table data, form a matrix equation, solve it to obtain the coefficients of the interpolant; substitute into the corresponding matrix expression the obtained interpolant coefficients and the independent variable value, and perform the matrix multiplication operations specified in the expression. The verification of the accuracy of the calculations using the appropriate central difference formulas was made. It was established that the calculated derivatives of the k-th order using the formulas of central finite differences practically coincide with the values ​​obtained using the Taylor polynomial interpolation of the n-th order, that is, the values ​​of the derivatives are calculated correctly.

Microfluidic production of nanogels as alternative triple transfection reagents for the manufacture of adeno-associated virus vectors.

Adeno-associated viral vectors (AAVs) have proved a mainstay in gene therapy, owing to their remarkable transduction efficiency and safety profile. Their production, however, remains challenging in terms of yield, the cost-effectiveness of manufacturing procedures and large-scale production. In this work, we present nanogels produced by microfluidics as a novel alternative to standard transfection reagents such as polyethylenimine-MAX (PEI-MAX) for the production of AAV vectors with comparable yields. Nanogels were formed at pDNA weight ratios of 1 : 1 : 2 and 1 : 1 : 3, of pAAV cis-plasmid, pDG9 capsid trans-plasmid and pHGTI helper plasmid respectively, where vector yields at a small scale showed no significant difference to those of PEI-MAX. Weight ratios of 1 : 1 : 2 showed overall higher titers than 1 : 1 : 3, where nanogels with nitrogen/phosphate ratios of 5 and 10 produced yields of ≈8.8 × 108 vg mL-1 and ≈8.1 × 108 vg mL-1 respectively compared to ≈1.1 × 109 vg mL-1 for PEI-MAX. In larger scale production, optimised nanogels produced AAV at a titer of ≈7.4 × 1011 vg mL-1, showing no statistical difference from that of PEI-MAX at ≈1.2 × 1012 vg mL-1, indicating that equivalent titers can be achieved with easy-to-implement microfluidic technology at comparably lower costs than traditional reagents.

О постоянстве типа некоторых 6-мерных уплощающихся подмногообразий алгебры Кэли

The notion of type constancy was introduced by Alfred Gray for nearly Kählerian manifolds and later generalized by Vadim F. Kirichenko and Irina V. Tret’yakova for all Gray — Hervella classes of almost Her­mitian manifolds. In the present note, we consider the notion of type con­stancy for some six-dimensional almost Hermitian planar submanifolds of Cayley algebra. The almost Hermitian structure on such six-dimensional submanifolds is induced by means of so-called Brown — Gray three-fold vector cross products in Cayley algebra. We select the case when six-dimensional submanifolds of Cayley algebra are locally symmetric. It is proved that six-dimensional locally symmetric submanifolds of Ricci type of Cayley algebra are almost Hermitian manifolds of zero con­stant type. This result means that six-dimensional locally symmetric sub­manifolds of Ricci type of Cayley algebra possess a property of six-dimensional Kählerian submanifolds of Cayley algebra. However, there exist non-Kählerian six-dimensional locally symmetric submanifolds of Ricci type in Cayley algebra.

Formation and fragmentation of 2-hydroxyethylhydrazinium nitrate (HEHN) cluster ions: a combined electrospray ionization mass spectrometry, molecular dynamics and reaction potential surface study.

The 2-hydroxyethylhydrazinium nitrate ([HOCH2CH2NH2NH2]+NO3-, HEHN) ionic liquid has the potential to power both electric and chemical thrusters and provide a wider range of specific impulse needs. To characterize its capabilities as an electrospray propellant, we report the formation of HEHN cluster ions in positive electrospray ionization (ESI) and their collision-induced dissociation. The experiment was carried out using ESI guided-ion beam mass spectrometry which mimics an electrospray thruster in terms of ion emission, injection into a vacuum and fragmentation in space. Measurements include compositions of primary ions in the electrospray plume and their individual dissociation product ion cross sections and threshold energies. The results were interpreted in light of theoretical modeling. To determine cluster structures that are comprised of [HE + H]+ and NO3- constituents, classical mechanics simulations were used to create initial guesses; and for clusters that are formed by reactions between ionic constituents, quasi-classical direct dynamics trajectory simulations were used to mimic covalent bond formation and structures. All candidate structures were subject to density functional theory optimization, from which global minimum structures were identified and used for construction of reaction potential energy surface. The comparison between experimental values and calculated dissociation thermodynamics was used to verify the structures for the emitted species [(HEHN)nHE + H]+, [(HEHN)n(HE)2 + H]+, [(HE)n+1 + H]+ and [(HE)nC2H4OH]+ (n = 0-2), of which [(HE)1-2 + H]+ dominates. Due to the protic nature of HEHN, cluster fragmentation can be rationalized by proton transfer-mediated elimination of HNO3, HE and HE·HNO3, and the latter two become dominant in larger clusters. [(HE)2 + H]+ and [(HE)nC2H4OH]+ contain H-bonded water and consequently are featured by water elimination in fragmentation. These findings help to evaluate ion formation and fragmentation efficiencies and their impacts on electrospray propulsion.

On enhanced general linear groups: nilpotent orbits and support variety for Weyl module

<abstract><p>Associated with a reductive algebraic group $ G $ and its rational representation $ (\rho, M) $ over an algebraically closed filed $ {\bf{k}} $, the authors define the enhanced reductive algebraic group $ {\underline{G}}: = G\ltimes_\rho M $, which is a product variety $ G\times M $ and endowed with an enhanced cross product in <sup>[<xref ref-type="bibr" rid="b5">5</xref>]</sup>. If $ {\underline{G}} = GL(V)\ltimes_{\eta} V $ with the natural representation $ (\eta, V) $ of $ {\text{GL}}(V) $, it is called an enhanced general linear algebraic group. And the authors give a precise classification of finite nilpotent orbits via a finite set of so-called enhanced partitions of $ n = \dim V $ for the enhanced group $ {\underline{G}} = {\text{GL}}(V)\ltimes_{\eta}V $ in [<xref ref-type="bibr" rid="b6">6</xref>, Theorem 3.5]. We will give another way to prove this classification theorem in this paper. Then we focus on the support variety of the Weyl module for $ {\underline{G}} = {\text{GL}}(V)\ltimes_{\eta}V $ in characteristic $ p $, and obtain that it coinsides with the closure of an enhanced nilpotent orbit under some mild condition.</p></abstract>