Integral Expression Research Articles

Virtual source for the fractional-order Bessel–Gauss beams

First, the nonparaxial integral expression of fractional-order Bessel–Gauss (FBG) beams during propagation is rigorously derived by using the virtual source technique and the principle of independent transmission and superposition of light, together with Weber integral formula and Fourier–Bessel transform pair. Then, the analytic expression of the important axial optical field amplitude of FBG beams is obtained. Finally, the on-axis intensity and phase of FBG beams are calculated on the basis of the analytic expression. Calculated results quantitatively revealed some important intensity information regarding the near-field propagation characteristic of FBG beams.

Psilocybin-induced changes in brain network integrity and segregation correlate with plasma psilocin level and psychedelic experience

The emerging novel therapeutic psilocybin produces psychedelic effects via engagement of cerebral serotonergic targets by psilocin (active metabolite). The serotonin 2A receptor critically mediates these effects by altering distributed neural processes that manifest as increased entropy, reduced functional connectivity (FC) within discrete brain networks (i.e., reduced integrity) and increased FC between networks (i.e., reduced segregation). Reduced integrity of the default mode network (DMN) is proposed to play a particularly prominent role in psychedelic phenomenology, including perceived ego-dissolution. Here, we investigate the effects of a psychoactive peroral dose of psilocybin (0.2–0.3 mg/kg) on plasma psilocin level (PPL), subjective drug intensity (SDI) and their association in fifteen healthy individuals. We further evaluate associations between these measures and resting-state FC, measured with functional magnetic resonance imaging, acquired over the course of five hours after psilocybin administration. We show that PPL and SDI correlate negatively with measures of network integrity (including DMN) and segregation, both spatially constrained and unconstrained. We also find that the executive control network and dorsal attention network desegregate, increasing connectivity with other networks and throughout the brain as a function of PPL and SDI. These findings provide direct evidence that psilocin critically shapes the time course and magnitude of changes in the cerebral functional architecture and subjective experience following psilocybin administration. Our findings provide novel insight into the neurobiological mechanisms underlying profound perceptual experiences evoked by this emerging transnosological therapeutic and implicate the expression of network integrity and segregation in the psychedelic experience and consciousness.

Integrative DNA Methylation and Gene Expression Analysis in the Prefrontal Cortex of Mexicans Who Died by Suicide.

BackgroundSuicide represents a major health concern, especially in developing countries. While many demographic risk factors have been proposed, the underlying molecular pathology of suicide remains poorly understood. A body of evidence suggests that aberrant DNA methylation and expression is involved. In this study, we examined DNA methylation profiles and concordant gene expression changes in the prefrontal cortex of Mexicans who died by suicide.MethodsIn collaboration with the coroner’s office in Mexico City, brain samples of males who died by suicide (n = 35) and age-matched sudden death controls (n = 13) were collected. DNA and RNA were extracted from prefrontal cortex tissue and analyzed with the Infinium Methylation480k and the HumanHT-12 v4 Expression Beadchips, respectively.ResultsWe report evidence of altered DNA methylation profiles at 4430 genomic regions together with 622 genes characterized by differential expression in cases vs controls. Seventy genes were found to have concordant methylation and expression changes. Metacore-enriched analysis identified 10 genes with biological relevance to psychiatric phenotypes and suicide (ADCY9, CRH, NFATC4, ABCC8, HMGA1, KAT2A, EPHA2, TRRAP, CD22, and CBLN1) and highlighted the association that ADCY9 has with various pathways, including signal transduction regulated by the cAMP-responsive element modulator, neurophysiological process regulated by the corticotrophin-releasing hormone, and synaptic plasticity. We therefore went on to validate the observed hypomethylation of ADCY9 in cases vs control through targeted bisulfite sequencing.ConclusionOur study represents the first, to our knowledge, analysis of DNA methylation and gene expression associated with suicide in a Mexican population using postmortem brain, providing novel insights for convergent molecular alterations associated with suicide.

Radiation reaction in higher-order electrodynamics

This paper considers the relativistic motion of charged particles coupled with electromagnetic fields in the higher-order theory proposed by Bopp, Landé–Thomas, and Podolsky. We rigorously derive a world line integral expression for the self-force of the charged particle from a distributional equation for the conservation of four-momentum only. This naturally leads to an equation of motion for charged particles that incorporates a history-dependent self-interaction. We show additionally that the same equation of motion follows from a variational principle for retarded fields. Our work thus gives a rigorous vindication of an expression for the self-force first proposed by Landé and Thomas, studied by Zayats for straight line motion, and, more generally, obtained by Gratus, Perlick, and Tucker on the basis of an averaging axiom.

INNOVATIVE DEVELOPMENT OF UKRAINE’S ECONOMY

Abstract. The development of the world economy, despite the barriers, is quite dynamic. The drivers of growth and stabilization of national economies at present are not raw materials industries, nor even industrial enterprises, but companies that generate innovative products. The enterprises that are most dynamically developing and producing innovations include enterprises in the field of medicine and IT. The updated list of S&P 500 companies showed that 50% of all the most innovative companies in the world are registered in the United States. Despite the pandemic challenges, some economies have not suffered significant losses due to quarantine restrictions. Since the level of innovative development of the national economy is a total (integrated) expression of the whole complex of innovative products created by companies of such a country, the initial elements are the creation of favorable regulatory and state support for developers of innovative products, tax benefits and incentives, export support for innovative products and so on. In order to assess these achievements, international organizations have developed appropriate methods for measuring the index of innovation development, namely: Global Innovation Index (GII) (WIPO and Cornell University), Bloomberg Innovation Index (BII) (Bloomberg), Global Competitiveness Index (World Economic Forum), World Competitiveness Index (IMD World Competitiveness Center). Studies have shown that against the background of the flagship countries (Switzerland, Sweden, Singapore, USA, Germany, China, etc.), Ukraine is constantly losing its position in the rankings, which is an objective reason for deindustrialization of the economy and denationalization and privatization of strategic enterprises of national importance. Today, Ukraine ranks 45th (GII) and 56th (BII), respectively, and belongs to the group of countries with below-average incomes per capita. At the same time, Ukraine ranks 71st in terms of innovation spending and 37th in terms of innovation development (profit). The development of Ukraine’s innovation component, according to experts and specialists, is ahead of forecast values.
 Keywords: national economy, innovations, innovative development, innovative products, innovative companies, indices of innovative development, gross national income per capita.
 JEL Classification O30
 Formulas: 0; fig.: 1; tabl.: 4; bibl.: 19.

Fourier Integral Transformation Method for Solving Two Dimensional Elasticity Problems in Plane Strain Using Love Stress Functions

The Fourier integral method was used in this work to determine the stress fields in a two dimensional (2D) elastic soil mass of semi-infinite extent subject to line and strip loads of uniform intensity acting on the boundary. The two dimensional plane strain problem was formulated using stress-based method. The Fourier integral was used to transform the biharmonic stress compatibility equation to a fourth order linear ordinary differential equation (ODE) in terms of the stress function. The ODE was solved subject to the boundedness condition to obtain the bounded stress function. Cartesian stress components were obtained using the Love stress functions. Application of the stress boundary conditions for the case of line load of uniform intensity and the cases of uniformly distributed load on a strip of finite width gave the respective unknown constants of the Love stress functions; and hence the complete determination of the Cartesian stress components for the two cases considered. Inversion of the Fourier integral expressions obtained for the normal and shear stresses in the Fourier parameter gave respective expressions for the normal and shear stress fields for line and finite strip loads of finite width in the physical domain variables. The results obtained agreed with the results from previous studies which used displacement based methods.

Construction of an Integrated mCherry Red Fluorescent Protein Expression System for Labeling and Tracing in Lactiplantibacillus plantarum WCFS1.

Thorough intestinal adhesion and colonization greatly promote the probiotic properties of lactic acid bacteria (LAB). Labeling and tracing with fluorescent proteins are effective and reliable for studying the in vivo physiological activities of LAB including localization, adhesion, and colonization. Lactiplantibacillus plantarum WCFS1 was successfully traced with a red fluorescent protein (RFP), which was expressed by the bacteria-carrying recombinant plasmids. In this study, we aimed to construct a stable RFP mCherry expression system, whose encoding gene was integrated into the bacterial chromosome via double-crossed homologous recombination, and use it for labeling WCFS1 with the goal of avoiding the potential loss of non-chromosomal plasmids along with intestinal growth. First, the constitutive expression of the mCherry protein was improved after adjusting the length of the spacer between the promoter and the gene start codon. Then, the optimized mCherry gene expression cassette was integrated into the chromosome of WCFS1. The resulting strain had normal unimpaired growth and strong fluorescent signals, even after 100 generations, indicating its stability. Furthermore, quantitative polymerase chain reaction (PCR) results revealed a strong positive correlation between the fluorescence intensity of the strain and the number of viable cells, demonstrating its potential usage for the quantification of in vivo WCFS1 cells. Finally, the increased adhesion ability of WCFS1 due to the recombinant expression of the bsh gene was visualized and evaluated using fluorescence intensity, the results of which were consistent with those obtained using the previously established quantification methods. These results suggest that the chromosomal-integrated mCherry labeling system can be extensively used to examine the distribution, colonization, and survival of LAB in vivo in order to determine the mechanism of its probiotic function.

Модификация методики оценки жизнеспособности интродуцентов в соответствии с условиями сухостепной зоны оренбургского Предуралья

The work was carried out to modify the method of assessing the viability of plants, taking into account the limiting factors of the climatic conditions of the Orenburg Preduralie. Are studied several species of plants, during the introduction at the steppe zone (on example of Оrenburg). Introduction study of all taxons was carried out for 8 years (20122020). The results of visual and laboratory observations of the seasonal development of species. During the entire observation period such indicators, as lignification of shoots, heat resistance, drought resistance, winter hardiness, shoot-forming capacity, height increase, generative development, and possible ways of reproduction in culture were evaluated annually. For each indicator numerical values in points corresponding to a certain state of the plant were selected. Based on the integrated assessment, the total viability score was calculated separately for each year of observations and the average score for the observation period. The sum of the average scores is an integral numerical expression of the viability of the introduced plants. Was established that the studied species belong to the I and II group relatively the criterion of life skills. The most species and sorts are among the most promising plants for introduction.

О некоторых числах оператора Харди в пространствах Лоренца

In the paper conditions are found under which the compact operator $Tf(x)=\varphi(x)\int_0^ xf(\tau)v(\tau)\,d\tau,$ $x>0,$ acting in weighted Lorentz spaces $T:L^{r,s}_{v} (\mathbb{R^+})\to L^{p,q}_{\omega}(\mathbb{R^+})$ in the domain $1<\max (r,s)\le \min(p,q)<\infty,$ belongs to operator ideals $\mathfrak{S}^{(a)}_\alpha$ and $\mathfrak{E}_\alpha$, $0<\alpha<\infty$. And estimates are also obtained for the quasinorms of operator ideals in terms of integral expressions which depend on operator weight functions.

The Role of Capsid in the Early Steps of HIV-1 Infection: New Insights into the Core of the Matter.

In recent years, major advances in research and experimental approaches have significantly increased our knowledge on the role of the HIV-1 capsid in the virus life cycle, from reverse transcription to integration and gene expression. This makes the capsid protein a good pharmacological target to inhibit HIV-1 replication. This review covers our current understanding of the role of the viral capsid in the HIV-1 life cycle and its interaction with different host factors that enable reverse transcription, trafficking towards the nucleus, nuclear import and integration into host chromosomes. It also describes different promising small molecules, some of them in clinical trials, as potential targets for HIV-1 therapy.

Escape and absorption probabilities for obliquely reflected Brownian motion in a quadrant

We consider an obliquely reflected Brownian motion Z with positive drift in a quadrant stopped at time T, where T≔inf{t>0:Z(t)=(0,0)} is the first hitting time at the origin. Such a process can be defined even in the non-standard case in which the reflection matrix is not completely-S. We show in this case that the process has two possible behaviors: either it tends to infinity or it hits the corner (origin) in finite time. Given an arbitrary starting point (u,v) in the quadrant, we consider the escape (resp. absorption) probabilities P(u,v)[T=∞] (resp. P(u,v)[T<∞]). We establish the partial differential equations and the oblique Neumann boundary conditions which characterize the escape probability and provide a functional equation satisfied by the Laplace transform of the escape probability. Asymptotics for the absorption probability in the simpler case in which the starting point in the quadrant is (u,0) are then given. We proceed to show a geometric criterion on the parameters which characterizes the case in which the absorption probability has a product form and is exponential. We call this new criterion the dual skew symmetry condition due to its natural connection with the skew symmetry condition for the stationary distribution. We then obtain an explicit integral expression for the Laplace transform of the escape probability and conclude by presenting exact asymptotics for the escape probability at the origin.

Identification of lymphocyte cell-specific protein-tyrosine kinase (LCK) as a driver for invasion and migration of oral cancer by tumor heterogeneity exploitation

BackgroundCancer metastases are the main cause of lethality. The five-year survival rate for patients diagnosed with advanced stage oral cancer is 30%. Hence, the identification of novel therapeutic targets is an urgent need. However, tumors are comprised of a heterogeneous collection of cells with distinct genetic and molecular profiles that can differentially promote metastasis making therapy development a challenging task. Here, we leveraged intratumoral heterogeneity in order to identify drivers of cancer cell motility that might be druggable targets for anti-metastasis therapy.MethodsWe used 2D migration and 3D matrigel-based invasion assays to characterize the invasive heterogeneity among and within four human oral cancer cell lines in vitro. Subsequently, we applied mRNA-sequencing to map the transcriptomes of poorly and strongly invasive subclones as well as primary tumors and matched metastasis.ResultsWe identified SAS cells as a highly invasive oral cancer cell line. Clonal analysis of SAS yielded a panel of 20 subclones with different invasive capacities. Integrative gene expression analysis identified the Lymphocyte cell-specific protein-tyrosine kinase (LCK) as a druggable target gene associated with cancer cell invasion and metastasis. Inhibition of LCK using A-770041 or dasatinib blocked invasion of highly aggressive SAS cells. Interestingly, reduction of LCK activity increased the formation of adherens junctions and induced cell differentiation.ConclusionAnalysis of invasive heterogeneity led to the discovery of LCK as an important regulator of motility in oral cancer cells. Hence, small molecule mediated inhibition of LCK could be a promising anti-metastasis therapy option for oral cancer patients.

A semi-analytical pulsating source incorporated with the panel method for wave-body interactions

ABSTRACT To deal with hydrodynamics, numerical integration of pulsating source Green’s function over a panel is very important. However, little research is focused on it. In the present paper, a semi-analytical integral expression of pulsating source over the panel is proposed. A coordinate transformation is performed and the panel is mapped into a unit rectangle. The space integral is carried out beforehand. Thus, the integral of Green’s function can be expressed as a θ-type single integral expression. Numerical results show that the present expression provides a new robust approach to obtain the integral of Green’s function over a panel in an accurate and stable manner. Based on the above method, radiation-diffraction problems of Wigley III and LNG carrier in waves are calculated, then ship motion responses versus various wave frequencies are computed. The calculated motions of ship acquired agree well with experimental data.

General expression of aerodynamic force under different boundary conditions (slip, partial slip, no-slip)

Integral expression is derived for aerodynamic forces in unsteady separated flows of an incompressible Newtonian fluid via the characteristics of the flow on the body surface including the vortex flux generated by it. The expression obtained is valid for unsteady and steady flows under the no-slip or the partial slip boundary conditions in a viscous fluid as well as for complete slip in the case of an ideal fluid including the flows with tangential discontinuity of the velocity field. Unlike the number of existing formulas, the expression does not contain the volume integrals and is applicable for the case of multiple bodies. The expression greatly simplifies a calculation of the hydrodynamic force when using vortex meshless methods. The formula obtained satisfies the fundamental law of hydrodynamic momentum conservation. It is derived mathematically rigorously without any assumptions.

Integrative DNA Methylation and Gene Expression Analysis of Cognitive Behavioral Therapy Response in Children and Adolescents with Obsessive-Compulsive Disorder; a Pilot Study.

PurposeHere, we propose an integrative analysis of genome-wide methylation and gene expression to provide new insight into the biological mechanisms of Cognitive behavioral therapy (CBT) in pediatric obsessive-compulsive disorder (OCD).Patients and MethodsTwelve children and adolescents with OCD receiving CBT for the first time were classified as responders or non-responders after eight weeks of CBT. Differentially methylated positions (DMPs) and gene co-expression modules were identified using specific R software packages. Correlations between the DMPs and gene co-expression modules were investigated.ResultsTwo genes were enriched with significant DMPs (Δβ > ± 0.2, FDR-adjusted p-value < 0.05): PIWIL1 and MIR886. The yellowgreen module of co-expressed genes was associated with CBT response (FDR-adjusted p-value = 0.0003). Significant correlations were observed between the yellowgreen module and the CpGs in PIWIL1 and MIR886 (p < 0.008). Patients showing hypermethylation in these CpGs presented an upregulation in the genes in the yellowgreen module.ConclusionTaken together, the preliminary results of this systems-level approach, despite the study limitations, provide evidence that the epigenetic regulation of ncRNAs could be a predictor of CBT response.LimitationsThe sample size limited the statistical power, and given that the study was hypothesis-driven, our results should be seen as preliminary.

An Analytical Solution of Wave Motion in a Transversely Isotropic Poroelastic Half-Space Underlying a Liquid Layer

In this paper, an analytical method is developed for the axisymmetric dynamic response of a finite thickness liquid layer overlying a transversely isotropic porous solid half-space due to body waves. Potential functions and integral transforms are used together to handle the equations of wave motion in two media. The time-harmonic excitation with axisymmetric shape is assumed to be distributed in the interface of liquid and porous media. Green’s functions of stress and displacement are derived as closed-form integral expressions. Demonstration of the effect of the liquid thickness, degree of material anisotropy, and frequency of excitation on the dynamic response is considered here. Numerical results for a uniform distributed disk load are comprised with the existing elastic and poroelastic solutions to illustrate the quality of the method. The results of the current paper can be used in analysis and modelling the rigid or flexible foundations in marine structures.

Overexpression of vacuolar H + ‐pyrophosphatase (H + ‐PPase) gene from Ammopiptanthus nanus enhances drought tolerance in maize

Maize is acutely vulnerable to water deficit. Due to the slow progress in conventional breeding, more beneficial genes should be transformed into maize for improvement of drought tolerance. In the present study, the vacuolar H+-pyrophosphatase (H+-PPase) gene (AnVP1) from Ammopiptanthus nanus was transformed into maize by Agrobacterium-mediated calli transformation. After identification of integration and ectopic expression of the AnVP1 gene by PCR amplification, DNA resequencing, reverse transcription PCR, real-time quantitative PCR, Western blotting and measurement of H+-PPase content, the transgenic lines were evaluated for their drought tolerance in greenhouse and field. The results of greenhouse phenotyping showed that the expression of AnVP1 decreased the negative effects of drought stress on transgenic maize with the improved performance, higher germination ratio, relative water content, biomass and more robust root system, slightly blasted leaves, lower electrolyte leakage and malondialdehyde content. The results of yield phenotyping showed that kernel yield of L1, L4 and L10 lines was significantly higher than WT under water deficit conditions. In conclusion, ectopic expression of the AnVP1 gene significantly enhanced drought tolerance of the transgenic maize, which is hopefully used for commercialized release after further safety assessment, because the expression of some endogenous genes was affected slightly.

Decoupling epithelial-mesenchymal transitions from stromal profiles by integrative expression analysis

Epithelial-to-mesenchymal transition (EMT) is the most commonly cited mechanism for cancer metastasis, but it is difficult to distinguish from profiles of normal stromal cells in the tumour microenvironment. In this study we use published single cell RNA-seq data to directly compare mesenchymal signatures from cancer and stromal cells. Informed by these comparisons, we developed a computational framework to decouple these two sources of mesenchymal expression profiles using bulk RNA-seq datasets. This deconvolution offers the opportunity to characterise EMT across hundreds of tumours and examine its association with metastasis and other clinical features. With this approach, we find three distinct patterns of EMT, associated with squamous, gynaecological and gastrointestinal cancer types. Surprisingly, in most cancer types, EMT patterns are not associated with increased chance of metastasis, suggesting that other steps in the metastatic cascade may represent the main bottleneck. This work provides a comprehensive evaluation of EMT profiles and their functional significance across hundreds of tumours while circumventing the confounding effect of stromal cells.

Local Number Fluctuations in Hyperuniform and Nonhyperuniform Systems: Higher-Order Moments and Distribution Functions

The local number variance associated with a spherical sampling window of radius $R$ enables a classification of many-particle systems in $d$-dimensional Euclidean space according to the degree to which large-scale density fluctuations are suppressed, resulting in a demarcation between hyperuniform and nonhyperuniform phyla. To better characterize density fluctuations, we carry out an extensive study of higher-order moments, including the skewness $\gamma_1(R)$, excess kurtosis $\gamma_2(R)$ and the corresponding probability distribution function $P[N(R)]$ of a large family of models across the first three space dimensions, including both hyperuniform and nonhyperuniform models. Specifically, we derive explicit integral expressions for $\gamma_1(R)$ and $\gamma_2(R)$ involving up to three- and four-body correlation functions, respectively. We also derive rigorous bounds on $\gamma_1(R)$, $\gamma_2(R)$ and $P[N(R)]$. High-quality simulation data for these quantities are generated for each model. We also ascertain the proximity of $P[N(R)]$ to the normal distribution via a novel Gaussian distance metric $l_2(R)$. Among all models, the convergence to a central limit theorem (CLT) is generally fastest for the disordered hyperuniform processes. The convergence to a CLT is slower for standard nonhyperuniform models, and slowest for the antihyperuniform model studied here. We prove that one-dimensional hyperuniform systems of class I or any $d$-dimensional lattice cannot obey a CLT. Remarkably, we discovered that the gamma distribution provides a good approximation to $P[N(R)]$ for all models that obey a CLT, enabling us to estimate the large-$R$ scalings of $\gamma_1(R)$, $\gamma_2(R)$ and $l_2(R)$. For any $d$-dimensional model that "decorrelates" or "correlates" with $d$, we elucidate why $P[N(R)]$ increasingly moves toward or away from Gaussian-like behavior, respectively.

Geometrically exact hybrid beam element based on nonlinear programming

AbstractThis work presents a hybrid shear‐flexible beam‐element, capable of capturing arbitrarily large inelastic displacements and rotations of planar frame structures with just one element per member. Following Reissner's geometrically exact theory, the finite element problem is herein formulated within nonlinear programming principles, where the total potential energy is treated as the objective function and the exact strain‐displacement relations are imposed as kinematic constraints. The approximation of integral expressions is conducted by an appropriate quadrature, and by introducing Lagrange multipliers, the Lagrangian of the minimization program is formed and solutions are sought based on the satisfaction of necessary optimality conditions. In addition to displacement degrees of freedom at the two element edge nodes, strain measures of the centroid act as unknown variables at the quadrature points, while only the curvature field is interpolated, to enforce compatibility throughout the element. Inelastic calculations are carried out by numerical integration of the material stress‐strain law at the cross‐section level. The locking‐free behavior of the element is presented and discussed, and its overall performance is demonstrated on a set of well‐known numerical examples. Results are compared with analytical solutions, where available, and outcomes based on flexibility‐based beam elements and quadrilateral elements, verifying the efficiency of the formulation.