Singular Density Research Articles

In-silico insights into personalised therapy selection of anti-arrhythmic drugs and ablation using patient-specific biatrial models for atrial fibrillation

Abstract Introduction Current treatment approaches for Atrial Fibrillation (AF) often lack personalisation, adopting a one-size-fits-all paradigm that disregards inter-patient diversity and its unique interplay with therapeutic responses. In-silico drug trials have demonstrated some value in the personalisation of care; however, their integration with patient-specific anatomical data and the synergistic effects of combined therapies remain unknown. Purpose To evaluate the patient-specific response to anti-arrhythmic drugs (AADs) and their efficacy both individually and in combination with pulmonary vein isolation (PVI) using personalised biatrial models created from imaging data. Methods Patient-specific biatrial models (n=70) were constructed from late gadolinium-enhanced MRI images by manual segmentation from the Atrial Segmentation Challenge (2018) dataset (Fig.1A). Models were pre-processed with landmark selection, regional assignment, and fibre allocation before simulations (Fig.1B). PVI was modelled as electrically inert rings around the pulmonary veins (Fig.1C) and AADs were administered via ionic modulation within CARPentry software (Fig.1D). Four commonly used AADs were evaluated: vernakalant, acute and chronic amiodarone, flecainide, and digoxin. Finite element simulations were performed with the addition of AADs, both individually and in combination with PVI, to evaluate their efficacy in terminating AF (Fig.2A). These simulations were post-processed to produce phase singularity (PS) density maps to evaluate changes in wavefront patterns and locations of re-entry and wavefront break-up (Fig.2B). Results The combination of digoxin with PVI and digoxin alone demonstrated the highest effectiveness in terminating AF, both achieving success in 68.4% of cases (95% CI: 67.5% to 89.3%, p≤0.0001). This efficacy significantly exceeded that of other AADs used either alone or in combination with PVI (15.8%-57.9%), whereas PVI alone demonstrated 0% efficacy (p≤0.05). The combined therapy exhibited a multi-faceted localisation pattern (Fig.2A), with AADs initially redistributing PSs to the pulmonary veins and left atrial appendage. This redistribution resulted in synergistic effects in terminating AF episodes in 52.6% more cases when combined with PVI (Fig.2B). Comparative analyses showed an inverse correlation between baseline PS density count and anatomical surface area with AF termination across all treatments, with significant correlations observed with vernakalant alone (rho=-0.55, p≤0.05) and combined with PVI (rho=-0.77, p≤0.05). Conclusions This study demonstrates the significance of personalised treatment selection in optimising patient outcomes. Combined therapeutic interventions have shown synergistic benefits in AF termination, surpassing individual therapies in this patient-specific model cohort. This shows the translational potential of using patient-specific stratification to inform treatment selection.Biatrial model generationAF therapeutic simulation and processing

Selective signal enhancement in Fourier space as a tool for discovering ultrastructural organization of macromolecules from in situ TEM

We present a Fourier transform (FT) based analytical method that allows to obtain of ultrastructural details from TEM images at sub-nanometer scale applying a selective filtering for singular macromolecule electron microscopy density information. It can be applied to high-pressure frozen, frozen hydrated and epoxy freeze substituted and embedded biological species. Both 2D projections and orthoslices from reconstructed tomograms can be used as a source of structural information. The key to the method is to select the macromolecule or organelle of interest with an accuracy of ≥ 7 – 3 nm (depending on pixel size of initial tilt series or singular image acquisition) and explore both the central low frequency FT intensity and diffraction regions to obtain the spatial structural organization and its dimensional characteristics, respectively. We also introduce a structure-specific selective mask FT filtering approach that can significantly improve image information even in poorly contrasted TEM of resin sections without heavy metal been used. The described method elucidates chromatin architecture without the need of averaging. A zigzag symmetry of 30 nm diameter chromatin fibers which in general is a controversial topic of research has been identified for C. elegans cells in vivo with sub-nanometer details being preserved in the images.

Development of the full Lagrangian approach for modeling dilute dispersed media flows (a review)

Continuum models of media with zero pressure are widely used in various branches of physics and mechanics, including studies of a dilute dispersed phase in multiphase flows. In zero-pressure media, the particle trajectories may intersect, “folds” and “puckers” of the phase volume may arise, and “caustics” (the envelopes of particle trajectories) may appear, near which the density of the medium sharply increases. In recent decades, the phenomena of clustering and aerodynamic focusing of inertial admixture in gas and liquid flows have attracted increasing attention of researchers. This is due to the importance of taking into account the inhomogeneities in the impurity concentration when describing the transport of aerosol pollutants in the environment, the mechanisms of droplet growth in rain clouds, scattering of radiation by dispersed inclusions, initiation of detonation in two-phase mixtures, as well as when solving problems of two-phase aerodynamics, interpretation of measurements obtained by LDV or PIV methods, and in many other applications. These problems gave an impetus to a significant increase in the number of publications devoted to the processes of accumulation and clustering of inertial particles in gas and liquid flows. Within the framework of classical two-fluid models and standard Eulerian approaches assuming single-valuedness of continuum parameters of the media, it turns out impossible to describe zones of multi-valued velocity fields and density singularities in flows with crossing particle trajectories. One of the alternatives is the full Lagrangian approach proposed by the author earlier. In recent years, this approach has been further developed in combination with averaged Eulerian and Lagrangian (vortex-blob method) methods for describing the dynamics of the carrier phase. Such combined approaches made it possible to study the structure of local zones of accumulation of inertial particles in vortex, transient, and turbulent flows. This article describes the basic ideas of the full Lagrangian approach, provides examples of the most significant results which illustrate the unique capabilities of the method, and gives an overview of the main directions of further development of the method as applied to transient, vortex, and turbulent flows of “gas-particle” media. Some of the ideas discussed and the results presented below are of a more general interest, since they are also applicable to other models of zero-pressure media.

Large-scale homogeneity and isotropy versus fine-scale condensation. A model based on Muckenhoupt type densities

In this brief note we aim to provide, through a well known class of singular densities in harmonic analysis, a simple approach to the fact that the homogeneity of the universe on scales of the order of a hundred millions light years is completely compatible with the fine-scale condensation of matter and energy. We give precise and quantitative definitions of homogeneity and isotropy on large scales. Then we show that Muckenhoupt densities have the ingredients required to a model for the large-scale homogeneity and the fine-scale condensation of the universe. In particular, these densities can take locally infinitely large values (black holes) and at once, in the large scales they are independent of the location. We also show some locally singular densities satisfying the large scale isotropy property.

New one-parameter models of dynamical particles in spatially flat FLRW space-times

New one-parameter models of non-rotating dynamical particles are derived as isotropic solutions of Einstein’s equations with perfect fluid in space-times with FLRW asymptotic behaviour, thus generalizing the models recently proposed by Cotăescu (Eur. Phys. J. C 82:86, 2022). These particles are produced by central singularities of the fluid density but without changing the pressure of the asymptotic FLRW space-times. The principal features of these models are investigated using a brief graphical analysis to elucidate the role of the new free parameter. The conclusion is that this gives rise to families of models which behave as non-rotating black holes in the physical space domain bordered by the black hole and cosmological horizons.

Complex angular structure of three elliptical galaxies from high-resolution ALMA observations of strong gravitational lenses

The large-scale mass distributions of galaxy-scale strong lenses have long been assumed to be well described by a singular ellipsoidal power-law density profile with external shear. However, the inflexibility of this model could lead to systematic errors in astrophysical parameters inferred with gravitational lensing observables. Here, we present observations with the Atacama Large (sub-)Millimetre Array (ALMA) of three strongly lensed dusty star-forming galaxies at $ mas angular resolution and investigate the sensitivity of these data to angular structure in the lensing galaxies. We jointly infer the lensing mass distribution and the full surface brightness of the lensed sources with multipole expansions of the power-law density profile up to the fourth order using a technique developed for interferometric data. All three datasets strongly favour third and fourth-order multipole amplitudes of $ percent of the convergence. While the infrared stellar isophotes and isodensity shapes agree for one lens system, for the other two the isophotes disagree to varying extents, suggesting contributions to the angular structure from dark matter intrinsic or extrinsic to the lensing galaxy.

Unified framework for the separation property in binary phase-segregation processes with singular entropy densities

Abstract This paper investigates the separation property in binary phase-segregation processes modelled by Cahn-Hilliard type equations with constant mobility, singular entropy densities and different particle interactions. Under general assumptions on the entropy potential, we prove the strict separation property in both two and three-space dimensions. Namely, in 2D, we notably extend the minimal assumptions on the potential adopted so far in the literature, by only requiring a mild growth condition of its first derivative near the singular points $\pm 1$ , without any pointwise additional assumption on its second derivative. For all cases, we provide a compact proof using De Giorgi’s iterations. In 3D, we also extend the validity of the asymptotic strict separation property to the case of fractional Cahn-Hilliard equation, as well as show the validity of the separation when the initial datum is close to an ‘energy minimizer’. Our framework offers insights into statistical factors like particle interactions, entropy choices and correlations governing separation, with broad applicability.

A New CCERT System With Shielding for Gas-Liquid Two-Phase Flow

This work presents a new capacitively coupled electrical resistance tomography (CCERT) system with shielding for gas-liquid two-phase flow. The new system is developed from the aspects of hardware, image reconstruction algorithm and experiments. The hardware includes a 12-electrode CCERT sensor with shielding, a measurement circuit and an image reconstruction computer. The sensor with shielding is designed and the measurement circuit is developed to obtain the resistance information (real part of the impedance). Based on truncated singular value decomposition (TSVD) and density peaks clustering (DPC), a new image reconstruction algorithm is proposed. TSVD is introduced to obtain the initial image. DPC is improved and used to obtain the final image. Image reconstruction experiments were carried out with the new 12-electrode CCERT system with shielding. Experimental results show that the new CCERT system has good imaging performance. The design of the hardware is successful, and the new proposed image reconstruction algorithm is effective. Compared with the conventional image reconstruction algorithms, the proposed algorithm has higher imaging quality. The maximum relative image errors of the new system are 0.2887 under bubble flow and 0.4177 under stratified flow. Research results also indicate that the shielding design contributes to better imaging stability in interference environment.

Building stellar bulges and halo cores from massive clumps observed in the DYNAMO-HST sample

ABSTRACT We present N-body simulations of the process of bulge formation in disc galaxies due to inward migration of massive stellar clumps. The process is accompanied by dark halo heating, with a quasi-isothermal core replacing the initial central density cusp, transforming an initially dark matter dominated central region into a baryon dominated one. The characteristics of the clumps are chosen to be compatible with low redshift observations of stellar clumps in DYNAMO-HST galaxies, which may be relatively long lived in terms of being robust against internal starburst-instigated disruption. We thus test for disruption due to tidal stripping using different clump internal radial profiles; Plummer, Hernquist, and Jaffe, in ascending order of see per central density profile. Our calculations predict that in order for clump migration to be effective in building galactic bulges and dark halo cores, steeply increasing central clump profiles, or a less massive or less concentrated haloes, are preferred. The dependence on such factors may contribute to the diversity in observed total mass distributions and resulting rotation curves in galaxies. When the process is most efficient, a ‘bulge-halo conspiracy’, with a singular isothermal total density akin to that observed bright galaxies, results.

Inflation Driven by Nonlinear Electrodynamics in Anisotropic Spacetime

The well-known Big Bang theory has explained how the universe came into being. This extraordinary event caused the later universe to be accelerated by a scale factor a(t). However, standard Big Bang theory has had some problems that can’t be explained, such as monopoles, horizons, and flatness. To solve this problem, a model of inflation in the early universe is required. Recent studies show that nonlinear electrodynamics coupled with general relativity can describe the inflation of the universe. In this work, we consider a model of nonlinear electrodynamics in anisotropic spacetime. We derive the dynamical equation from Einstein’s field equation and the law of conservation of energy-momentum tensor. Then, we use the perturbation method to solve the dynamical equation of the universe and obtain the evolution of the non-singular scale factor with anisotropy parameter ϵ. Using a phase-space analysis of the inflationary model, we obtain a phase portrait in the presence of fixed points. Our result shows that in the model of nonlinear electrodynamics coupled to gravity in anisotropic spacetime, the universe can undergo an inflationary mechanism if ϵ < 1. We also show the absence of singularity in density and pressure using this model.

Universe inflation and nonlinear electrodynamics

We analyse the inflation of the universe when the source of gravity is electromagnetic fields obeying nonlinear electrodynamics, with two parameters and without singularities. The cosmology of the universe with stochastic magnetic fields is considered, and the condition for universe inflation is obtained. It is demonstrated that singularities of energy density and pressure are absent as the scale factor approaches zero. When the scale factor goes to infinity, we have the equation of state for the ultra-relativistic case. The curvature invariants do not possess singularities. The evolution of the universe shows that at large time scales, the scale factor corresponds to the radiation era. The duration of universe inflation is also analysed. We study the classical stability and causality by computing the speed of sound. Cosmological parameters including the spectral index ns\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_s$$\\end{document}, the tensor-to-scalar ratio r, and the running of the spectral index αs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha _s$$\\end{document} are evaluated.

Rectifiability of Flat Singular Points for Area-Minimizing mod 2Q Hypercurrents

Abstract Consider an $ m $-dimensional area minimizing mod$ (2Q) $ current $ T $, with $ Q\in {\mathbb {N}} $, inside a sufficiently regular Riemannian manifold of dimension $ m + 1 $. We show that the set of singular density-$ Q $ points with a flat tangent cone is $ (m-2) $-rectifiable. This complements the thorough structural analysis of the singularities of area-minimizing hypersurfaces modulo $ p $ that has been completed in the series of works of De Lellis–Hirsch–Marchese–Stuvard and De Lellis–Hirsch–Marchese–Stuvard–Spolaor, and the work of Minter–Wickramasekera.

Exploring the critical points in QCD with multi-point Padé and machine learning techniques in (2+1)-flavor QCD

Using simulations at multiple imaginary chemical potentials for (2 + 1)-flavor QCD, we construct multi-point Padé approximants. We determine the singularties of the Padé approximants and demonstrate that they are consistent with the expected universal scaling behaviour of the Lee-Yang edge singularities. We also use a machine learning model, Masked Autoregressive Density Estimator (MADE), to estimate the density of the Lee-Yang edge singularities at each temperature. This ML model allows us to interpolate between the temperatures. Finally, we extrapolate to the QCD critical point using an appropriate scaling ansatz.

In situ construction of PtSe2/Ge Schottky junction array with interface passivation for broadband infrared photodetection and imaging

AbstractInfrared (IR) detection is vital for various military and civilian applications. Recent research has highlighted the potential of two‐dimensional (2D) topological semimetals in IR detection due to their distinctive advantages, including van der Waals (vdW) stacking, gapless electronic structure, and Van Hove singularities in the electronic density of states. However, challenges such as large‐scale patterning, poor photoresponsivity, and high dark current of photodetectors based on 2D topological semimetals significantly impede their wider applications in low‐energy photon sensing. Here, we demonstrate the in situ fabrication of PtSe2/Ge Schottky junction by directly depositing 2D PtSe2 films with a vertical layer structure on a Ge substrate with an ultrathin AlOx layer. Due to high quality junction, the photodetector features a broadband response of up to 4.6 μm, along with a high specific detectivity of ~1012 Jones, and operates with remarkable stability in ambient conditions as well. Moreover, the highly integrated device arrays based on PtSe2/AlOx/Ge Schottky junction showcases excellent Mid‐IR (MIR) imaging capability at room temperature. These findings highlight the promising prospects of 2D topological semimetals for uncooled IR photodetection and imaging applications.image

Visualizing near-coexistence of massless Dirac electrons and ultra-massive saddle point electrons

Strong singularities in the electronic density of states amplify correlation effects and play a key role in determining the ordering instabilities in various materials. Recently high order van Hove singularities (VHSs) with diverging power-law scaling have been classified in single-band electron models. We show that the 110 surface of Bismuth exhibits high order VHS with an usually high density of states divergence \sim (E)^{-0.7}∼(E)−0.7. Detailed mapping of the surface band structure using scanning tunneling microscopy and spectroscopy combined with first-principles calculations show that this singularity occurs in close proximity to Dirac bands located at the center of the surface Brillouin zone. The enhanced power-law divergence is shown to originate from the anisotropic flattening of the Dirac band just above the Dirac node. Such near-coexistence of massless Dirac electrons and ultra-massive saddle points enables to study the interplay of high order VHS and Dirac fermions.

Effect of van-Hove singularities in single-walled carbon nanotube leads on transport through T-shaped double quantum dot system

The T-shaped double quantum dot system with single-walled metallic armchair carbon nanotube leads has been studied using Green functions obtained by the equation of motion method. The effect of relative spacing between the energy levels of the dots, interdot tunneling matrix-element, interdot Coulomb interaction, and van-Hove singularities in density of states characteristics of quasi-one-dimensional carbon nanotube leads on the conductance of the double quantum dot system has been studied. The conductance and dot occupancies are calculated at finite temperatures. The density of states of the carbon nanotube leads is observed to play a significant role in determining the conductance profile. In particular, whenever the chemical potential of the isolated double quantum dot system is aligned with the position of a van-Hove singularity in the density of states of armchair carbon nanotube leads, the height of the corresponding conductance peak falls considerably. It is further observed that the suppression in the heights of the alternate peaks depends on the relative positions of the energy levels of the dots and their magnitude of separation.

A structure theory for stable codimension 1 integral varifolds with applications to area minimising hypersurfaces mod 𝑝

For any Q ∈ { 3 2 , 2 , 5 2 , 3 , … } Q\in \{\frac {3}{2},2,\frac {5}{2},3,\dotsc \} , we establish a structure theory for the class S Q \mathcal {S}_Q of stable codimension 1 stationary integral varifolds admitting no classical singularities of density &gt; Q &gt;Q . This theory comprises three main theorems which describe the nature of a varifold V ∈ S Q V\in \mathcal {S}_Q when: (i) V V is close to a flat disk of multiplicity Q Q (for integer Q Q ); (ii) V V is close to a flat disk of integer multiplicity &gt; Q &gt;Q ; and (iii) V V is close to a stationary cone with vertex density Q Q and supports the union of 3 or more half-hyperplanes meeting along a common axis. The main new result concerns (i) and gives in particular a description of V ∈ S Q V\in \mathcal {S}_Q near branch points of density Q Q . Results concerning (ii) and (iii) directly follow from parts of previous work of the second author [Ann. of Math. (2) 179 (2014), pp. 843–1007]. These three theorems, taken with Q = p / 2 Q=p/2 , are readily applicable to codimension 1 rectifiable area minimising currents mod p p for any integer p ≥ 2 p\geq 2 , establishing local structure properties of such a current T T as consequences of little, readily checked, information. Specifically, applying case (i) it follows that, for even p p , if T T has one tangent cone at an interior point y y equal to an (oriented) hyperplane P P of multiplicity p / 2 p/2 , then P P is the unique tangent cone at y y , and T T near y y is given by the graph of a p 2 \frac {p}{2} -valued function with C 1 , α C^{1,\alpha } regularity in a certain generalised sense. This settles a basic remaining open question in the study of the local structure of such currents near points with planar tangent cones, extending the cases p = 2 p=2 and p = 4 p=4 of the result which have been known since the 1970’s from the De Giorgi–Allard regularity theory [Ann. of Math. (2) 95 (1972), pp. 417–491] [Frontiere orientate di misura minima, Editrice Tecnico Scientifica, Pisa, 1961] and the structure theory of White [Invent. Math. 53 (1979), pp. 45–58] respectively. If P P has multiplicity &gt; p / 2 &gt; p/2 (for p p even or odd), it follows from case (ii) that T T is smoothly embedded near y y , recovering a second well-known theorem of White [Proc. Sympos. Pure Math., Amer. Math. Soc., Providence, RI, 1986, pp. 413–427]. Finally, the main structure results obtained recently by De Lellis–Hirsch–Marchese–Spolaor–Stuvard [arXiv:2105.08135, 2021] for such currents T T all follow from case (iii).

Low temperature singularities of electron density in a two-gap superconductor ZrB12

Fine details of crystal structure of ZrB12 two-gap superconductor are studied at low temperatures by precise x-ray diffraction technique. Small static Jahn-Teller distortions of a face centered cubic lattice are observed in the range 30–70 K, leading to emergence of two types singularities of electron density (ED). These are: (i) dynamic charge stripes along selected directions <110> and <112> in the crystal and (ii) triangular lattice of the ED antinodes located in the interstices of the boron lattice in the {111} planes. The second anomaly was detected for the first time, and it is very pronounced for ZrB12, being intensified at low temperatures. The anisotropy of the two-gap superconductivity in ZrB12 is confirmed by measurements of the low temperature heat capacity in a magnetic field directed along three principal axes in the crystal, H || [100], H || [110] and H || [111]. We conclude in favor of the magnetic field-induced anisotropy arising from the interaction of vortex lattice in this superconductor with fluctuating ED (charge stripes) of a two-type filamentary structure.

Ultrafast enhancement of electron-phonon coupling via dynamic quantum well states

The density of states at the Fermi surface controls many material properties by influencing the low-energy interactions of conductive electrons. Typically, external tuning knobs generate only small perturbations to the density of states in crystals, since their band structure depends strongly on the lattice potential. In contrast, quantum well states are contingent on a localized potential extrinsic to the crystal lattice and can be easily modified leading to changes in the density of states at the Fermi level. Here, we are able to control the quantum well potential on the surface of Bi2Se3 with light, driving a density of states singularity below EF at ultrafast timescales, thereby triggering a reversible Lifshitz transition. We reveal a substantial ultrafast enhancement of the electron-phonon coupling with repercussions on the relaxation dynamics in the system. We argue that the relaxation dynamics are governed largely by the interplay of the dynamic density of states of the quantum wells with c-axis scattering from the {A}_{{{{{{{{rm{1g}}}}}}}}}^{2} optical phonon mode. These results demonstrate a powerful way to enhance electron-boson interaction on ultrafast timescales providing new avenues for controlling material properties and driving novel quantum phases of matter.

Phonons in the 1/f noise of topological insulators

In topological insulators, such as (Bi,Sb)2Te3 and BiSbTeSe1.6, the 1/f noise intensity features intriguing peaks, which develop at some specific temperatures. In search for their microscopic origin, we compared this noise structure with either phonon density of states or Raman spectrum of each topological insulator (TI), respectively. In (Bi,Sb)2Te3, the comparison revealed that the noise peaks track the van Hove singularities in the phonon density of states. The most intense noise peak observed in (Bi,Sb)2Te3 at 50 K is attributed to the thermal motion of the Bi atoms. Other less intense noise peaks are assigned to either a single phonon mode or multi-phonon combinations. We found that thermal vibrations of Bi and Te2 atoms in different symmetry directions are involved in most of the phonon combinations, which stand for the signature of the lattice anharmonicity in noise. The noise increase observed in (Bi,Sb)2Te3 and BiSbTeSe1.6 above a specific temperature threshold is attributed to the strengthening of the carrier–phonon coupling induced by anharmonicity. In the case of BiSbTeSe1.6, we show that all noise singularities are mirrored in the Raman spectrum of a structurally close TI (BiSbTeSe2) in the whole temperature range. This indicates that although transport can be at the surface or in the bulk or both of them, the carrier–phonon interaction is the only source of 1/f fluctuations in TIs. Inherently, these results imply that the microscopic origin of 1/f noise in solid is in the perpetual thermal motion of the atoms.