Integral Formulation Research Articles

Randomized, Double-Blind, Active Comparator Pharmacodynamic Study of Platelet Inhibition with Crushed and Integral Formulations of Clopidogrel and Ticagrelor in Acute Coronary Syndrome.

Crushed formulations of specific antiplatelet agents produce earlier and stronger platelet inhibition. We studied the platelet inhibitory effect of crushed clopidogrel in patients with acute coronary syndrome (ACS) and its relative efficacy compared with integral clopidogrel, crushed and integral ticagrelor. We aimed to compare the platelet inhibitory effect of crushed and integral formulations of clopidogrel and ticagrelor in patients with acute coronary syndrome (ACS). Overall, 142 patients with suspected ACS were randomly assigned to receive crushed or integral formulations of clopidogrel or ticagrelor. Platelet inhibition at baseline and 1 and 8h was assessed using the VerifyNow assay. High on-treatment platelet reactivity (HTPR) ≥ 235 P2Y12reaction units (PRUs) 1h after the medication loading dose was also determined. The PRU and percentage inhibition median (interquartile range) at 1h for the different formulations were as follows: crushed clopidogrel: 196.50 (155.50, 246.50), 9.36 (- 1.79, 25.10); integral clopidogrel: 189.50 (159.00, 214.00), 2.32 (- 2.67, 19.89); crushed ticagrelor: 59.00 (10.00, 96.00), 75.53 (49.12, 95.18); and integral ticagrelor: 126.50 (50.00, 168.00), 40.56 (25.59, 78.69). There was no significant difference in PRU or percentage platelet inhibition between the crushed and integral formulations of clopidogrel (p=0.990, p=0.479); both formulations of ticagrelor were superior to the clopidogrel formulations (p<0.05). On paired comparison, crushed ticagrelor showed robust early inhibition of platelets compared with the integral formulation (p=0.03). Crushed clopidogrel exhibited the maximal HTPR of 34.3%, but was < 3% for both formulations of ticagrelor. The platelet inhibitory effect of crushed clopidogrel is not superior to integral preparation in patients with ACS. Crushed ticagrelor produced maximal platelet inhibition acutely. HTPR rates in ACS are similar and very low with both formulations of ticagrelor, and maximal with crushed clopidogrel. Clinical Trials Registry of India identifier number CTRI/2020/06/025647.

Epistemologis Tafsir Tematik: Menuju Tafsir Al-Qur’an Yang Holistik

The aim of this research is to discuss the Epistemological Efforts of Thematic Interpretation in Holistic Interpretation of the Qur'an. This research falls under the category of qualitative research, therefore the researcher only conducts a literature review. The first step involves gathering literature sources, both primary and secondary sources. The next step in this research is to provide a description of the literature sources that discuss the history, meaning, principles, and steps of thematic interpretation. The conclusion of this research is obtained through an analysis or epistemological approach to the method of thematic interpretation. The results and discussions of this research reveal that the discourse on the thematic method among scholars and scientists has led to the development of this method through the collaboration of modern scientific knowledge in the field of interpretation. This collaborative interpretation is referred to as integrative thematic interpretation, which enhances the existing classification of thematic interpretation. Ideally, all classifications of thematic interpretation can be interwoven into an integrative formulation of thematic interpretation, thus resulting in a holistic thematic interpretation of the Qur'an. Holistic thematic interpretation of the Qur'an is an epistemological effort to establish the validity of interpretation as a divine truth and as a rational and sensory truth that can be justified apriori, aposteriori, and pragmatically.&#x0D; Keywords: qur’an; thematic interpretation; epistemological; holistic.

Pricing weather derivatives under a tri-variate stochastic model

Weather derivatives are used to protect farmers in sub-Saharan Africa (SSA) from yield loss caused by climate change. However, mispricing these contracts poses a significant risk due to the interconnected nature and combined impact of the principal climate determinants of maize yield, including rainfall amount, daily temperature, and reference evapotranspiration. To address this issue, this research extends the pricing of derivatives to a joint stochastic process of the three variables, which captures the non-linearity and non-stationarity in the data. Tri-variate models constructed through copulas capture the interdependence properties of the dataset. Pricing models are derived from these processes in a manner that satisfies path integral and market-consistent properties, hence providing more realistic prices for weather derivatives for maize in Malawi. The analysis findings identify possible ranges within the stochastic process that align with varying levels of maize yield loss in the area. Under path integral formulation, call option prices increase with the severity of the tri-variate process, while put option or market environment consistent formulation prices decrease with severity. Thus, this research provides a framework for pricing weather derivatives that incorporates the joint stochastic nature of multiple climate variables, allowing for more accurate risk management for farmers in the area.

Mitigation of hydroelastic response in pneumatically supported floating structures

Pneumatically supported floating structures, which utilize an aircushion below the structural bottom, have been suggested to remedy the excessive hydroelastic response of the conventional pontoon-type floating structures. This paper presents an analytical study to examine the hydroelastic responses of the pneumatically supported floating structures. For the hydroelastic analysis, the fluid was modeled as a 2D-strip of finite depth seawater, whilst the floating structure was modeled as a beam with zero-draft. A direct coupled model was then constructed by using the boundary integral formulation for the fluid and FEM for the structure and by incorporating a pneumatic factor at the fluid-structure interface to consider the compressibility of the aircushion. Additionally, hydroelastic responses of the pneumatically supported type were compared for the pontoon-type for a wide range of pneumatic factors and regular waves. As a result, the pneumatic supports could significantly reduce the hydroelastic responses in most cases and that the response reduction may be markedly enhanced when the pneumatic factor was taken as small for a relatively short incident wave. Substantially, the analytical technique used in the present study can examine the design conditions, as being essential for practical applications of the pneumatically supported floating structures.

Integral formulation of the macroscopic quantum electrodynamics in dispersive dielectric objects

We propose an integral formulation of macroscopic quantum electrodynamics in the Heisenberg picture for linear dispersive dielectric objects of finite size, utilizing the Hopfield-type approach. By expressing the electromagnetic field operators as a function of the polarization density field operator via the retarded Green function for the vacuum, we obtain an integral equation that governs the evolution of the polarization density field operator. This formulation offers significant advantages, as it allows for the direct application of well-established computational techniques from classical electrodynamics to perform quantum electrodynamics computations in open, dispersive, and absorbing environments.

Pedagogically treating topics as having several ways to be addressed: Harmonically varying states of free-edge circular plates.

The paper is mainly concerned with the training of students by treating exercises as having several ways to be addressed. The topic considered herein focuses on the vibrations of a free edge axisymmetric homogeneous circular thin plate excited by a time-periodic source. This topic is prepared using the three analytic methods available (but these are not fully used analytically in the literature) to show the different aspects of the problem: modal expansion, integral formulation, and exact general solution, against which the other models are tested. Several results are provided when the source is localized at the center of the plate to validate the methods with each other, and these are discussed before concluding.

On Preconditioners of the FFT-JVIE for Inhomogeneous Dielectric Objects

An improved block-diagonal preconditioner (IBDP) is developed for the FFT accelerated the volume integral equation formulation based on equivalent volumetric currents (FFT-JVIE). A comparative study on the realistic models is carried out among the IBDP, BDP, the previously developed analytical preconditioner (AnP) and the circulant-based preconditioners (CBP).

Current Based Automated Design of Realizable Metasurface Antennas With Arbitrary Pattern Constraints

We present a 3-D method to numerically design a realizable metasurface, which transforms a given incident field into a radiated field that satisfies mask-type (inequality) constraints. The method is based on an integral equation formulation, with local impedance boundary condition (IBC) approximation. The procedure yields the spatial distribution of the impedance, yet the process involves the synthesis of the equivalent current only. This current is constrained to correspond to a realizable surface impedance, i.e., passive, lossless, and with reactance values bounded by practical realizability limits. The current-based design avoids any solution to the forward problem, and the impedance is obtained from the synthesized current only at the end of the process. The procedure is gradient-based, with the gradient expressed in closed form. This allows handling large metasurfaces, with full spatial variability of the impedance in two dimensions. The method requires no a priori information, and all relevant operations in the iterative process can be evaluated with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol { O}(N~\log~{N})$ </tex-math></inline-formula> complexity. Application examples concentrate on the case of on-surface excitation and far-field (FF) pattern specifications; they show designs of circular and rectangular metasurface antennas of 20 wavelengths in size, with pencil- and shaped-beam patterns, and for both circular and linear polarizations.

The Phase Response of a Rough Rectangular Facet for Radar Sounder Simulations of Both Coherent and Incoherent Scattering

AbstractWith radar sounders, coherent backscattering simulations from global planetary digital elevation models (DEMs) typically display a deficit in diffuse clutter, which is mainly due to the implicit assumption that roughness at scales below the resolution of the DEM is absent. Indeed, while polynomial approximations of the phase evolution across the facet allow for fast and mathematically rigorous simulators, the coarse resolution of these planetary DEMs leads to a potentially significant portion of the backscattering response being neglected. In this paper, we derive the analytical phase response of a rough rectangular facet characterized by Gaussian roughness and a Gaussian isotropic correlation function under the linear phase approximation. Formulae for the coherent and incoherent power scattered by such an object are obtained for arbitrary bistatic scattering angles. Validation is done both in isolation and after inclusion in different Stratton‐Chu simulators. In order to illustrate the different uses of such a formulation, we reproduce two lunar radargrams acquired by the Lunar Radar Sounder instrument with a Stratton‐Chu simulator incorporating the proposed rough facet phase integral, and we show that the original radargrams are significantly better‐reproduced than with state‐of‐the‐art methods, at a similar computational cost. We also show how the rough facet integral formulation can be used in isolation to better characterize subglacial water bodies on Earth.

What quantum matter tells about quantisation of gravity in a statistical mechanics context

We propose a “guide” towards quantisation of gravity based on quantum matter in a statistical mechanics context. On one hand, a statistical mechanics model naturally arises from the thermodynamic interpretation of horizons in Rindler space. On the other hand, the path integral formulation of quantum field theory can be interpreted from the point of view of statistical mechanics. From these perspectives, gravity and matter are related to each other in the same way as a gas and its chemical potential are. This statistical mechanics interpretation of gravity and matter suggests that gravity should be quantised in a precise way which is determined by the quantisation of matter. Although, in a first step, quantisation of gravity applies for small perturbations of the metric with respect to the vacuum, the most central and general features of quantisation (quantisation prescription, quantum space dimensions) are supported from statistical mechanics and remain valid non-perturbatively.

75 years of the path integral formulation

75 years of the path integral formulation

Demonstration of the quantum principle of least action with single photons

The principle of least action is arguably the most fundamental principle in physics as it can be used to derive the equations of motion in various branches of physics. However, this principle has not been experimentally demonstrated at the quantum level because the propagators for Feynman’s path integrals have never been observed. The propagator is a fundamental concept and contains various significant properties of a quantum system in the path integral formulation, so its experimental observation is itself essential in quantum mechanics. Here we theoretically propose and experimentally observe the propagators of single photons based on the method of directly measuring quantum wave functions. Furthermore, we obtain the classical trajectories of single photons in free space and in a harmonic trap based on the extremum of the observed propagators, thereby experimentally demonstrating the quantum principle of least action. Our work paves the way for experimentally exploring the fundamental problems of quantum theory in the formulation of path integrals. Propagators of single photons based on directly measuring quantum wave functions are experimentally observed. Classical trajectories that satisfy the principle of least action are successfully extracted in the case of free space and harmonic potential.

Automatic CHIEF Point Selection for Finite Element–Boundary Element Acoustic Backscattering

Computing the backscattering of harmonic acoustic waves from underwater elastic targets of arbitrary shapes is a challenging problem of considerable practical significance. The finite element method is well suited for the discretization of the target, while the boundary element method addresses the radiation boundary condition at infinity. A disadvantage of the boundary integral method is that it yields non-unique solutions at certain wavenumbers. This failure is associated with the existence of eigensolutions of the Helmholtz equation in the interior of the complement of the fluid domain (acoustic modes). The combined Helmholtz integral equation formulation (CHIEF) credited to Schenk is employed to combine the surface Helmholtz boundary integral with equations of the interior Helmholtz relation written down at selected points within the cavity of the scatterer (i.e., in the complement of the fluid domain).The difficulty associated with this approach has always been the lack of guidance on the necessary number of interior points and on their locations. The solution to this problem proposed here is to compute the acoustic modes using the finite element method to complement of the fluid domain and to identify locations of the peaks.This novel approach aids the decision as to how many points should be employed and where they should be located. Our numerical experiments demonstrate the robustness of the proposed automatic selection of the CHIEF points’ numbers and locations.

Probabilistic construction of Toda Conformal Field Theories

Following the 1984 seminal work of Belavin, Polyakov and Zamolodchikov on two-dimensional conformal field theories, Toda conformal field theories were introduced in the physics literature as a family of two-dimensional conformal field theories that enjoy, in addition to conformal symmetry, an extended level of symmetry usually referred to as W-symmetry or higher-spin symmetry. More precisely Toda conformal field theories provide a natural way to associate to a finite-dimensional simple and complex Lie algebra a conformal field theory for which the algebra of symmetry contains the Virasoro algebra. In this document we use the path integral formulation of these models to provide a rigorous mathematical construction of Toda conformal field theories based on probability theory. By doing so we recover expected properties of the theory such as the Weyl anomaly formula with respect to the change of background metric by a conformal factor and the existence of Seiberg bounds for the correlation functions.

The Hawking Radiation in Massive Gravity: Path Integral and the Bogoliubov Method

We prove the consistency of the different approaches for deriving the black hole radiation for the spherically symmetric case inside the theory of Massive Gravity. By comparing the results obtained by using the Bogoliubov transformations with those obtained by using the Path Integral formulation, we find that in both cases, the presence of the extra-degrees of freedom creates the effect of extra-particles creation due to the distortions on the definitions of time defined by the different observers at large scales. This, however, does not mean extra-particle creation at the horizon level. Instead, the apparent additional particles perceived at large scales emerge from how distant observers define their time coordinate, which is distorted due to the existence of extra-degrees of freedom.

An Excitation-Aware and Self-Adaptive Frequency Normalization for Low-Frequency Stabilized Electric Field Integral Equation Formulations

The accurate solution of quasi-Helmholtz decomposed electric field integral equations (EFIEs) in the presence of arbitrary excitations is addressed: Depending on the specific excitation, the quasi-Helmholtz components of the induced current density do not have the same asymptotic scaling in frequency, and thus, the current components are solved for with, in general, different relative accuracies. In order to ensure the same asymptotic scaling, we propose a frequency normalization scheme of quasi-Helmholtz decomposed EFIEs which adapts itself to the excitation and which is valid irrespective of the specific excitation and irrespective of the underlying topology of the structure. Specifically, neither an ad-hoc adaption nor <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a-priori</i> information about the excitation is needed as the scaling factors are derived based on the norms of the right-hand side (RHS) components and the frequency. Numerical results corroborate the presented theory and show the effectiveness of our approach.

A Generalized Scalar Potential Integral Equation Formulation for the DC Analysis of Conductors

The electrostatic modeling of conductors is a fundamental challenge in various applications, including the prediction of parasitic effects in electrical interconnects, the design of biasing networks, and the modeling of biological, microelectromechanical, and sensing systems. The boundary element method (BEM) can be an effective simulation tool for these problems because it allows modeling three-dimensional objects with only a surface mesh. However, existing BEM formulations can be restrictive because they make assumptions specific to particular applications. For example, capacitance extraction formulations usually assume a constant electric scalar potential on the surface of each conductor and cannot be used to model a flowing current, nor to extract the resistance. When modeling steady currents, many existing techniques do not address mathematical challenges such as the null space associated with the operators representing the internal region of a conductor. We propose a more general BEM framework based on the electric scalar potential for modeling conductive objects in various scenarios in a unified manner. Restrictive application-specific assumptions are not made, and the aforementioned operator null space is handled in an intuitive and rigorous manner. Numerical examples drawn from diverse applications confirm the accuracy and generality of the proposed method.

A High-Order-Accurate 3D Surface Integral Equation Solver for Uniaxial Anisotropic Media

This paper introduces a high-order accurate surface integral equation method for solving 3D electromagnetic scattering for dielectric objects with uniaxially anisotropic permittivity tensors. The N-Müller formulation is leveraged resulting in a second-kind integral formulation, and a finite-difference-based approach is used to deal with the strongly singular terms resulting from the dyadic Green’s functions for uniaxially anisotropic media while maintaining the high-order accuracy of the discretization strategy. The integral operators are discretized via a Nyström-collocation approach, which represents the unknown surface densities in terms of Chebyshev polynomials on curvilinear quadrilateral surface patches. The convergence is investigated for various geometries, including a sphere, cube, a complicated NURBS geometry imported from a 3D CAD modeler software, and a nanophotonic silicon waveguide, and results are compared against a commercial finite element solver. To the best of our knowledge, this is the first demonstration of high-order accuracy for objects with uniaxially anisotropic materials using surface integral equations.

Accurate Boundary Integral Formulations for the Calculation of Electrostatic Forces with an Implicit-Solvent Model

An accurate force calculation with the Poisson-Boltzmann equation is challenging, as it requires the electric field on the molecular surface. Here we present a calculation of the electric field on the solute-solvent interface that is exact for piecewise linear variations of the potential and analyze four different alternatives to compute the force using a boundary element method. We performed a verification exercise for two cases: the isolated and two interacting molecules. Our results suggest that the boundary element method outperforms the finite difference method, as the latter needs a much finer mesh than in solvation energy calculations to get acceptable accuracy in the force, whereas the same surface mesh as in a standard energy calculation is appropriate for the boundary element method. Among the four evaluated alternatives of force calculation, we saw that the most accurate one is based on the Maxwell stress tensor. However, for a realistic application, like the barnase-barstar complex, the approach based on variations of the energy functional, which is less accurate, gives equivalent results. This analysis is useful toward using the Poisson-Boltzmann equation for force calculations in applications where high accuracy is key, for example, to feed molecular dynamics models or to enable the study of the interaction between large molecular structures, like viruses adsorbed onto substrates.

Unlocking the general relationship between energy and entanglement spectra via the wormhole effect

Based on the path integral formulation of the reduced density matrix, we develop a scheme to overcome the exponential growth of computational complexity in reliably extracting low-lying entanglement spectrum from quantum Monte Carlo simulations. We test the method on the Heisenberg spin ladder with long entangled boundary between two chains and the results support the Li and Haldane’s conjecture on entanglement spectrum of topological phase. We then explain the conjecture via the wormhole effect in the path integral and show that it can be further generalized for systems beyond gapped topological phases. Our further simulation results on the bilayer antiferromagnetic Heisenberg model with 2D entangled boundary across the (2 + 1)D O(3) quantum phase transition clearly demonstrate the correctness of the wormhole picture. Finally, we state that since the wormhole effect amplifies the bulk energy gap by a factor of β, the relative strength of that with respect to the edge energy gap will determine the behavior of low-lying entanglement spectrum of the system.