Dipole Representation Research Articles

Explainable AI for myocardial infarction using the vectorcardiogram

Abstract Background and purpose Myocardial infarction (MI), a widespread cardiovascular ailment, often lacks immediate patient awareness being early and accurate MI diagnosis crucial for lifesaving interventions. In artificial intelligence studies, ECG signals are extensively explored, while fewer examine the potential of vectorcardiogram (VCG) which offers a three-dimensional cardiac dipole representation. Traditional Machine Learning methods manually extract features; some studies advocate VCG features. Deep Learning, especially Convolutional Neural Networks (CNN), automates feature extraction. Although ECG contains redundant information from the VCG's 12 projections, no studies directly apply CNNs to VCG, nor assess the impact of redundancy on predictive ability. This study aims to bridge this gap by investigating CNNs' diagnostic capabilities with VCG inputs, specifically focusing on improving MI classification. Methods The PTB-XL database was used for this study, containing 10-seconds ECG data from various pathologies, including MI. The database encompasses 9,481 records from healthy patients and 4,129 records from patients with MI. Data was divided into 80% for training and 20% for testing. Consequently, the dataset was expanded to have 52% representing MI and 48% representing healthy cases. We designed a 1D-CNN classifier (Figure 1.A) with three convolutional layers. The network was trained using both ECG and VCG reconstruction through the Inverse Dower Transform. Results The trained model achieved accuracy values of 0.895 and 0.914 for the test set when utilizing ECG and VCG, respectively. These results underscore how the information condensation in the VCG contributes to an enhanced predictive capacity of the model. In a qualitative analysis, activation maps extracted from the CNN illustrate heightened activation in the QRS complex when the disease is present, contrasting with diminished activation in its absence. These maps depict the weight assigned to each signal segment, enabling the classification of signals into healthy and diseased categories. The presented figure exemplifies a notable activation in the QRS loop in the case of myocardial infarction (MI), aligning with the observed alteration in the cardiac signal associated with this pathology (Figure 1.B). Conclusion In this study, an interpretable CNN has been designed for MI detection, with the VCG yielding better results than the ECG for this task due to information compression. This provides a new insight for enhancing classification capability in Deep Learning models, allowing for advancements in the MI detection.

Analysis of the Cutoff Wavenumber for Arbitrarily Shaped Waveguides Using Method of Dipole Representations With an Excitation Source

Analysis of the Cutoff Wavenumber for Arbitrarily Shaped Waveguides Using Method of Dipole Representations With an Excitation Source

Quantum Hall bilayer in dipole representation

Quantum Hall bilayer in dipole representation

Angular Momentum Multiplexing via a Shared Aperture Patch Antenna

Angular momentum (AM) multiplexing technique provides multiple information channels for electromagnetic waves (EMWs) modulation at the same frequency, improving spectrum efficiency effectively. Among AM multiplexing techniques, the patch antenna has the advantage of minimization, simple feeding circuits, and easy integration. Nevertheless, limited reports provide theoretical guidance for designing AM multiplexing patch antennas. Herein, we propose a scheme to achieve AM multiplexing via a shared-aperture patch antenna. The radiating structure consists of multiple radiating patches sharing a common physical aperture, each of which is responsible for producing different AM-carrying waves. By analyzing the theoretical model built on a dipole representation of the patch antenna, the shapes and the desired current patterns of these patches can be determined according to the AM mode of the expected EMWs. Besides, the sizes and feeding structures of these patches can be studied by investigating their radiating characteristics using characteristic mode (CM) theory. For proof-of-concept, a prototype was designed, fabricated, and measured for the generation of four orthogonal AM-carrying waves coaxially at 5.8GHz. The experimental results agree reasonably well with the simulated ones, demonstrating that the proposed scheme provides an efficient guidance for the design of AM multiplexing patch antennas.

A Peptide Potential Based on a Bond Dipole Representation of Electrostatics

A potential based on a bond dipole representation of electrostatics is reported for peptides. Different from those popular force fields using atom-centered point-charge or point-multipole to express the electrostatics, our peptide potential uses the chemical bond dipole–dipole interactions to express the electrostatic interactions. The parameters for permanent and induced bond dipoles are derived from fitting to the MP2 three-body interaction energy curves. The parameters for van der Waals are taken from AMBER99sb and further refined from fitting to the MP2 stacking interaction energy curve. The parameters for bonded terms are taken from AMBER99sb without any modification. The scale factors for intramolecular dipole–dipole interactions are determined from reproducing the highly qualified ab initio conformational energies of dipeptides and tetrapeptides. The resulting potential is validated by use to evaluate the conformational energies of polypeptides containing up to 15 amino acid residues. The calculation results show that our peptide potential produces the conformational energies much closer to the famous density functional theory M06-2X/cc-pVTZ results than the famous AMBER99sb and AMOEBAbio18 force fields. Our potential also produces accurate intermolecular interaction energies for hydrogen-bonded and stacked dimers. We anticipate the peptide potential proposed here could be helpful in computer simulations of polypeptides and proteins.

Dipole representation of half-filled Landau level

We introduce a variant of a dipole representation for composite fermions in a half-filled Landau level, taking into account the symmetry under an exchange of particles and holes. This is implemented by a special constraint on a composite fermion and a composite hole degree of freedom (of an enlarged space), which makes the resulting composite particle (dipole) a symmetric object. We study an effective Hamiltonian that commutes with the constraint on the physical space and fulfills the requirement for boost invariance on the Fermi level. The calculated Fermi liquid parameter ${F}_{2}$ is in good agreement with numerical investigations in Phys. Rev. Lett. 121, 147601 (2018).

A unique cardiac electrocardiographic 3D model. Toward interpretable AI diagnosis.

Mathematical models of cardiac electrical activity are one of the most important tools for elucidating information about heart diagnostics. In this paper, we present an efficient mathematical formulation for this modeling simple enough to be easily parameterized and rich enough to provide realistic signals. It relies on a five dipole representation of the cardiac electric source, each one associated with the well-known waves of the electrocardiogram signal. Beyond the physical basis of the model, the parameters are physiologically interpretable as they characterize the wave shape, similar to what a physician would look for in signals, thus making them very useful in diagnosis. The model accurately reproduces the electrocardiogram signals of any diseased or healthy heart. This new discovery represents a significant advance in electrocardiography research. It is especially useful for diagnosis, patient follow-up or decision-making on new therapies; is also a promising tool for well-performing, transparent and interpretable AI approaches.

Insights into the intracardiac electrogram from analytical and numerical modelling

Abstract Funding Acknowledgements Type of funding sources: Foundation. Main funding source(s): FWO-Flanders, KU Leuven internal starting grant Introduction and Purpose Cardiac electrograms (EGMs) are one of the most important recordings obtained during electroanatomical voltage mapping and lie at the basis for planning most clinical electrophysiological interventions. Despite its widespread use, the relation of EGM shape and amplitude to the underlying excitation patterns and properties of cardiac tissue is not completely understood. Recent clinical studies [1] have provided important new guidelines on the relation between EGM amplitudes and the thickness of myocardial walls. The aim of this study is to quantify the effect of the wall thickness on EGM amplitudes and duration using analytical and in-silico approaches. Methods We study bipolar EGMs both in-silico and analytically in a homogeneous slab of cardiac tissue (70 x 70 x L mm), where L = 2, 5, or 10 mm, with parallel fiber direction. Simulations were performed using the cardiac electrophysiology simulator openCARP [2]. Cardiac cells were described by the ten Tusscher-Panfilov 2006 model (TP06) [4] with epicardial tissue parameters. A plane wave propagating along the fiber direction was initiated. The extracellular voltage at 147 points arranged in a hemisphere around a point was measured to study the effect of bipolar electrode orientation (see Fig. 1A [3]). In addition, we developed an analytical approach to obtain an EGM, using an equivalent dipole representation of the depolarization wavefront and analytical evaluation of the corresponding integrals. Results Fig. 1B and 1C show the dependency of the EGM properties on the electrode orientation, as represented by the angles α (incidence angle) and β (angle between electrode and propagation direction) [3]. Solid lines represent data from a state-of-the-art numerical methodology, the dashed lines show our analytical estimations. Both the peak-to-peak amplitude and EGM width are well approximated by our theory for all orientations of the electrodes. Fig. 2 shows how the EGM is influenced by the myocardial wall thickness L. Both the amplitude and the duration are in good agreement with our theory. We observe that the amplitude as well as the width increase with the slab thickness, confirming the result in [1] but also delivering an accurate analytical expression for this change. It may thus allow to discriminate effects of thickness and other factors affecting the EGMs, such as substrate abnormalities, for example. Conclusion We developed an analytical approach which can correctly describe the amplitude, duration, and shape of the depolarization part of the EGM. Our theory agrees with the previous in-silico and clinical studies on the influence of catheter orientation [3,5], and wall thickness [1,3]. Subsequent work in this direction is expected to provide better guidelines for clinical interpretation of EGMs, accounting for the effects of the thickness of myocardial wall in the characterization of the substrate of cardiac arrhythmias.

An Approach for Modelling Harnesses in the Extreme near Field for Low Frequencies

A key part of every space science mission, in the system-level approach, is the detailed study and modeling of the emissions from transmission lines. Harnesses usually emit electromagnetic fields due to the currents (of common and/or differential modes) that flow on their shields. These fields can be identified via conducted emissions measurements. Relying on the operating frequency, any cable can be considered as a dipole or a traveling-wave antenna. Limited work can be found in the literature regarding modeling methodologies for cable topologies, especially in the low frequency (ELF, SLF, VLF, LF) domain. This work intends to provide perceptions for the precise estimation of harness radiated emissions, consider a mission-specific measurement point (where the sensors are placed), and follow ESA’s recent science mission studies for electromagnetic cleanliness applications. For the low frequencies considered herein, any linear cable path is considered as a point source (infinitesimal dipole) and we evaluate its effect on the calculated electric field extremely close to the source. For such distances, it is shown that the dipole representation is not accurate. To remedy this phenomenon, this article proposes a methodology, which can be easily expanded to complex cable geometry cases.

Electroproduction of heavy quarkonia: Significance of dipole orientation

The differential cross section $d\sigma/dq^2$ of diffractive electroproduction of heavy quarkonia on protons is a sensitive study tool for the interaction dynamics within the dipole representation. Knowledge of the transverse momentum transfer $\vec q$ provides a unique opportunity to identify the reaction plane, due to a strong correlation between the directions of $\vec q$ and impact parameter $\vec b$. On top of that, the elastic dipole-proton amplitude is subject to a strong correlation between $\vec b$ and dipole orientation $\vec r$. Most of models for $b$-dependent dipole cross section either completely miss this information, or make unjustified assumptions. We perform calculations basing on a realistic model for $\vec r$-$\vec b$ correlation, which significantly affect the $q$-dependence of the cross section, in particular the ratio of $\psi^{\,\prime}(2S)$ to $J/\psi$ yields. We rely on realistic potential models for the heavy quarkonium wave function, and the Lorentz-boosted Schr\"odinger equation. Good agreement with data on $q$-dependent diffractive electroproduction of heavy quarkonia is achieved.

Representation of the Third Adiabatic Invariant in Flux Form and Some Consequences of Its Conservation by Examples of Specific Axial Magnetic Systems

The dynamics of invariant magnetic surfaces is considered with examples of axially symmetric magnetic systems. The inner trap (magnetic mirror) and the outer trap (dipole) are distinguished in a system formed by two coils with current. The dynamics of noninteracting particles moving in the plane of the magnetic equator is considered in the drift approximation for the perturbation vector satisfying the third invariant conservation condition. The results are extended to the equator of the geomagnetic trap, in which the external perturbing field is given by the ring current. It is shown that the real effect of the ring current on plasma dynamics in the bounded magnetosphere of the Earth in the approximation of constancy of the third invariant differs from conventional model calculations based on dipole representations of the geomagnetic field. In this case, it is not the magnetic flux that makes practical sense but only its change, which is equal to the difference between the final and initial fluxes calculated by the parameters of the real field. The minimum values of the energies of charged particles in the radiation belts required to satisfy the third condition of adiabatic invariant conservation are estimated for the main phase of a particular magnetic storm.

A PC-SAFT model for hydrocarbons III: Phantom dipole representation of dipole induced dipole interactions in unsaturated hydrocarbons

Inclusion of polar contributions into the statistical associating fluid theory class of equations of state has been demonstrated to allow for the accurate prediction of solution non-idealities of mixtures composed of paraffins and polar molecules. However, as we demonstrate in this paper, these theories necessarily overpredict the non-idealities in mixtures composed of polar molecules with unsaturated hydrocarbons. The reason for this is that the dipole moment of the polar molecule polarizes the unsaturated bond resulting in a significant dipole-induced dipole attraction. We develop a simple, general and predictive methodology to incorporate this missing physics into the dipolar contribution to the theory. The new approach is shown to accurately predict the phase behavior of unsaturated hydrocarbons with polar molecules.

Diffractive dijet production: Breakdown of factorization

We analyse the origin of dramatic breakdown of diffractive factorisation, observed in single-diffractive (SD) dijet production in hadronic collisions. One of the sources is the application of the results of measurements of the diagonal diffractive DIS to the off-diagonal hadronic diffractive process. The suppression caused by a possibility of inelastic interaction with the spectator partons is calculated at the amplitude level, differently from the usual probabilistic description. It turns out, however, that interaction with the spectator partons not only suppresses the SD cross section, but also gives rise to the main mechanism of SD dijet production, which is another important source of factorization failure. Our parameter-free calculations of SD-to-inclusive cross section ratio, performed in the dipole representation, agrees with the corresponding CDF Tevatron (Run II) data at $\sqrt{s}=1.96$ TeV in the relevant kinematic regions. The energy and hard scale dependences demonstrate a trend, opposite to the factorisation-based expectations, similarly to the effect observed earlier in diffractive Abelian radiation.

Disentangling Somatosensory Evoked Potentials of the Fingers: Limitations and Clinical Potential

In searching for clinical biomarkers of the somatosensory function, we studied reproducibility of somatosensory potentials (SEP) evoked by finger stimulation in healthy subjects. SEPs induced by electrical stimulation and especially after median nerve stimulation is a method widely used in the literature. It is unclear, however, if the EEG recordings after finger stimulation are reproducible within the same subject. We tested in five healthy subjects the consistency and reproducibility of responses through bootstrapping as well as test–retest recordings. We further evaluated the possibility to discriminate activity of different fingers both at electrode and at source level. The lack of consistency and reproducibility suggest responses to finger stimulation to be unreliable, even with reasonably high signal-to-noise ratio and adequate number of trials. At sources level, somatotopic arrangement of the fingers representation was only found in one of the subjects. Although finding distinct locations of the different fingers activation was possible, our protocol did not allow for non-overlapping dipole representations of the fingers. We conclude that despite its theoretical advantages, we cannot recommend the use of somatosensory potentials evoked by finger stimulation to extract clinical biomarkers.

Electrostatic Potential and a Simple Extended Electric Dipole Model of Hydrogen Fluoride as Probes of Non-Bonding Electron Pairs in the Cyclic Ethers 2,5-Dihydrofuran, Oxetane and Oxirane

The electrostatic potential near to the oxygen atom in each of the cyclic ethers 2,5-dihydrofuran, oxetane and oxirane has been calculated by using a distributed multipole analysis (DMA) of each molecule. The electrostatic potential energy V(φ) of a unit non-perturbing positive charge was calculated (via the DMA of the cyclic ether molecule) as a function of the angle φ between the C2 axis of the cyclic ether and a vector of length r from the O atom to the unit charge. The resulting potential energy functions each has two equivalent minima. The angles φmin at the minima are compared with the angles φ0 and φe made by the O⋯H bond with the C2 axes in the cyclic ether⋯HF complexes, as determined by rotational spectroscopy and ab initio calculations at the CCSD(T)-F12c/cc-pVTZ-F12 level of theory, respectively. An electrostatic model of cyclic ether⋯HF complexes in which the DMA of the cyclic ether interacts with a simple extended electric dipole representation of HF is also used to calculate the variation of the potential energy VHF(φ) of the HF molecule with φ. The angles φmin generated by this model are also compared with φ0 and φe. The extent to which the electrostatic potential and the extended electric dipole HF model can be used as probes for the directions of non-bonding electron pairs carried by O in these cyclic ethers is discussed.

Gribov inelastic shadowing in the dipole representation

The dipole phenomenology, which has been quite successfully applied to various hard reactions, especially on nuclear targets, is applied for calculation of Gribov inelastic shadowing. This approach does not include ad hoc procedures, which are unavoidable in calculations done in hadronic representation. Several examples of Gribov corrections evaluated within the dipole description are presented.

Effects of substorm electrojet on declination along concurrent geomagnetic latitudes in the northern auroral zone

The geomagnetic field often experiences large fluctuations, especially at high latitudes in the auroral zones. We have found, using simulations, that there are significant differences in the substorm signature, in certain coordinate systems, as a function of longitude. This is confirmed by the analysis of real, measured data from comparable locations. Large geomagnetic fluctuations pose challenges for companies involved in resource exploitation since the Earth’s magnetic field is used as the reference when navigating drilling equipment. It is widely known that geomagnetic activity increases with increasing latitude and that the largest fluctuations are caused by substorms. In the auroral zones, substorms are common phenomena, occurring almost every night. In principle, the magnitude of geomagnetic disturbances from two identical substorms along concurrent geomagnetic latitudes around the globe, at different local times, will be the same. However, the signature of a substorm will change as a function of geomagnetic longitude due to varying declination, dipole declination, and horizontal magnetic field along constant geomagnetic latitudes. To investigate and quantify this, we applied a simple substorm current wedge model in combination with a dipole representation of the Earth’s magnetic field to simulate magnetic substorms of different morphologies and local times. The results of these simulations were compared to statistical data from observatories and are discussed in the context of resource exploitation in the Arctic. We also attempt to determine and quantify areas in the auroral zone where there is a potential for increased space weather challenges compared to other areas.

Magnetic field structure and evolution features of selected stars. II.

We present the results of modeling for about a hundred magnetic stars. It is shown that the dipole representation of magnetic field structures describes the distribution of the magnetic field over stellar surfaces fairly well. We analyze some patterns which support the relic hypothesis of magnetic field formation.Arguments are given in favor of the assumption that themain properties ofmagnetic stars—slow rotation, predominant orientation of magnetic field lines along the plane of the rotation equator, complex internal structures of magnetic fields—are acquired in the process of gravitational collapse. There are no conditions for that in the non-stationary Hayashi phase and in the stage of a radiative young star.

Pneumatic infrasound source: Model experiment and theory

In a previous presentation [J. Acoust. Soc. Am. 133, 3327 (2013)], an experimental model study of a pneumatic infrasound source that utilizes the pulsation of compressed air was discussed. The present paper discusses new measurements and theoretical modeling efforts that are currently underway. Measurements of the source level, directivity patterns, propagation loss, and frequency response are presented and analyzed. Acoustic and aerodynamic models are presented and discussed with a focus on modeling and predicting nearfield system performance using multipole (monopole, dipole, and quadrupole) representations of the sound source. Measurement techniques and engineering considerations are addressed, as are physical interpretations of the process. [Work supported by ARL:UT Austin.]

Quantitative study of geometrical scaling in charm production at HERA

We apply the method of ratios to search for geometrical scaling in the charm production in deep inelastic scattering. To this end we use recent combined data from H1 and ZEUS experiments. Two forms of geometrical scaling are tested: originally proposed scaling which results from Golec-Biernat-Wusthoff model and scaling motivated by a dipole representation which takes into account charm mass. It turns out that in both cases some residual scaling is present and charm mass inclusion improves scaling quality.