differential geometry

Many single-reference coupled cluster (CC) methods offer adiabatically incorrect potentials when calculating the diatomic carbon molecule, so this problem has been studied extensively. Analysis of the full configuration interaction (FCI) wave function indicates that the main cause of the adiabatic collapse of potentials calculated by the CC method with singles, doubles, and triples (CCSDT) is the strongly increasing bonding character of the T 4 FCI cluster contribution. In turn, comparative analysis of the CCSDTQ adiabats X 1 Σ g + and B '1 Σ g + demonstrates that the gap between them near the avoided crossing geometry is significantly reduced by quantitatively differentiating the character of the T 4 and <mml:math xmlns:mml="https://www...

A novel X-ray field produced by an ultrathin conical target is described in the literature. However, the optimal design for an associated collimator remains ambiguous. Current optimization methods using Monte Carlo calculations restrict the efficiency and robustness of the design process. A more generic optimization method that reduces parameter constraints while minimizing computational load is necessary. A numerical method for optimizing the longitudinal collimator hole geometry for a cylindrically-symmetrical X-ray tube is demonstrated and compared to Monte Carlo calculations...

The topological properties of DNA have long been a focal point in biophysics. In the 1970s, White proposed that the topology of closed DNA double helix follows White's formula: Lk =Wr +Tw . However, there has been controversy in the calculation of DNA twisting number, partly due to discrepancies in the definition of torsion in differential geometry. In this paper, we delved into a detailed study of torsion, revealing that the calculation of DNA twisting number should use the curve's geodesic torsion. Furthermore, we found that the discrepancy in DNA twisting numbers calculated using different torsion is N...

Time-domain solutions of Maxwell's equations in homogeneous and isotropic media are paramount to studying transient or broadband phenomena. However, analytical solutions are generally unavailable for practical applications, while numerical solutions are computationally intensive and require significant memory. Semi-analytical solutions (e.g., series expansion), such as those provided by the current theoretical framework of the multipole expansion, can be discouraging for practical case studies. This paper shows how sophisticated mathematical tools standard in modern physics can be leveraged to find semi-analytical solutions for arbitrary localized time-varying current distributions thanks to the novel time-domain Cartesian multipole expansion...

The surface topological features of bioimplants are among the key indicators for bone tissue replacement because they directly affect cell morphology, adhesion, proliferation, and differentiation. In this study, we investigated the physical, electrochemical, and biological responses of sandblasted titanium (SB-Ti) surfaces with pore geometries fabricated using a plasma electrolytic oxidation (PEO) process. The PEO treatment was conducted at an applied voltage of 280 V in a solution bath consisting of 0...

We propose a method for optimizing the geometry of a freeform lens to redirect the light emitted from an extended source into a desired irradiance distribution. We utilize a gradient-based optimization approach with MITSUBA 3, an algorithmic differentiable non-sequential ray tracer that allows us to obtain the gradients of the freeform surface parameters with respect to the produced irradiance distribution. To prevent the optimizer from getting trapped in local minima, we gradually increase the number of degrees of freedom of the surface by using Truncated Hierarchical B-splines (THB-splines) during optimization...

OBJECTIVES: Reduced cardiac outflow due to left ventricular hypertrophy has been suggested as a potential risk factor for development of cerebral white matter disease. Our study aimed to examine the correlation between left ventricular geometry and white matter disease volume to establish a clearer understanding of their relationship, as it is currently not well-established. METHODS: Consecutive patients from 2016 to 2021 who were ≥18 years and underwent echocardiography, cardiac MRI, and brain MRI within one year were included...

Bacterial communities exhibit complex self-organization that contributes to their survival. To better understand the molecules that contribute to transforming a small number of cells into a heterogeneous surface biofilm community, we studied acellular aggregates, structures seen by light microscopy in Pseudomonas aeruginosa colony biofilms using light microscopy and chemical imaging. These structures differ from cellular aggregates, cohesive clusters of cells important for biofilm formation, in that they are visually distinct from cells using light microscopy and are reliant on metabolites for assembly...

BACKGROUND: Studies of VT mechanisms are largely based on a 2D portrait of reentrant circuits on one surface of the heart. This oversimplifies the 3D circuit that involves the depth of the myocardium. Simultaneous epicardial and endocardial (epi-endo) mapping was shown to facilitate a 3D delineation of VT circuits, which is however difficult via invasive mapping. OBJECTIVE: This study investigates the capability of noninvasive epicardial-endocardial electrocardiographic imaging (ECGI) to elucidate the 3D construct of VT circuits, emphasizing the differentiation of epicardial, endocardial, and intramural circuits and to determine the proximity of mid-wall exits to the epicardial or endocardial surfaces...

BACKGROUND: X-ray multi-contrast imaging with gratings provides a practical method to detect differential phase and dark-field contrast images in addition to the x-ray absorption image traditionally obtained in laboratory or hospital environments. Systems have been developed for preclinical applications in areas including breast imaging, lung imaging, rheumatoid arthritis hand imaging and kidney stone imaging. PURPOSE: Prevailing x-ray interferometers for multi-contrast imaging include Talbot-Lau interferometers and universal moiré effect-based phase-grating interferometers...

BACKGROUND: The Hill classification characterizes the geometry of gastroesophageal junction (GEJ) and Hill grades (HGs) III and IV have a high association with pathologic reflux. This study aimed to understand the utilization of the Hill classification and correlate the prevalence of pathologic reflux across different HGs. STUDY DESIGN: A retrospective review of 477 patients who underwent upper endoscopy and BRAVO™ pH monitoring between 8/2018 and 10/2021 was performed...

INTRODUCTION: Despite evidence suggesting deleterious effects of cannabis and nicotine tobacco product (NTP) use on white matter integrity, there have been limited studies examining white matter integrity among users of both cannabis and nicotine. Further, updated white matter methodology provides opportunities to investigate use patterns on neurite orientation dispersion and density (NODDI) indices and subtle tissue changes related to the intra- and extra-neurite compartment. We aimed to investigate how cannabis and NTP use among adolescents and young adults interacts to impact the white matter integrity microstructure...

In this work, we explore information geometry theoretic measures for characterizing neural information processing from EEG signals simulated by stochastic nonlinear coupled oscillator models for both healthy subjects and Alzheimer's disease (AD) patients with both eyes-closed and eyes-open conditions. In particular, we employ information rates to quantify the time evolution of probability density functions of simulated EEG signals, and employ causal information rates to quantify one signal's instantaneous influence on another signal's information rate...

This paper is concerned with the growth-driven shape-programming problem, which involves determining a growth tensor that can produce a deformation on a hyperelastic body reaching a given target shape. We consider the two cases of globally compatible growth, where the growth tensor is a deformation gradient over the undeformed domain, and the incompatible one, which discards such hypothesis. We formulate the problem within the framework of optimal control theory in hyperelasticity. The Hausdorff distance is used to quantify dissimilarities between shapes; the complexity of the actuation is incorporated in the cost functional as well...

The ability to amplify, translate, and process small ionic potential fluctuations of neural processes directly at the recording site is essential to improve the performance of neural implants. Organic front-end analog electronics are ideal for this application, allowing for minimally invasive amplifiers owing to their tissue-like mechanical properties. Here, we demonstrate fully organic complementary circuits by pairing depletion- and enhancement-mode p- and n-type organic electrochemical transistors (OECTs)...

The mouse ocular lens is an excellent vertebrate model system for studying hexagonal cell packing and shape changes during tissue morphogenesis and differentiation. The lens is composed of two types of cells, epithelial and fiber cells. During the initiation of fiber cell differentiation, lens epithelial cells transform from randomly packed cells to hexagonally shaped and packed cells to form meridional row cells. The meridional row cells further differentiate and elongate into newly formed fiber cells that maintain hexagonal cell shape and ordered packing...

Although 3D human pose estimation has recently made strides, it is still difficult to precisely recreate a 3D human posture from a single image without the aid of 3D annotation for the following reasons. Firstly, the process of reconstruction inherently suffers from ambiguity, as multiple 3D poses can be projected onto the same 2D pose. Secondly, accurately measuring camera rotation without laborious camera calibration is a difficult task. While some approaches attempt to address these issues using traditional computer vision algorithms, they are not differentiable and cannot be optimized through training...

Human pluripotent stem cells (hPSCs) dynamically respond to their chemical and physical microenvironment, dictating their behavior. However, conventional in vitro studies predominantly employ plastic culture wares, which offer a simplified representation of the in vivo microenvironment. Emerging evidence underscores the pivotal role of mechanical and topological cues in hPSC differentiation and maintenance. In this study, we cultured hPSCs on hydrogel substrates with spatially controlled stiffness. The use of culture substrates that enable precise manipulation of spatial mechanical properties holds promise for better mimicking in vivo conditions and advancing tissue engineering techniques...

Cortical folding is a critical process during brain development, resulting in morphologies that are both consistent and distinct between individuals and species. While earlier studies have highlighted important aspects of cortical folding, most existing computational models, based on the differential growth theory, fall short of explaining why folds tend to appear in particular locations. The axon tension hypothesis may provide insight into this conundrum; however, there has been significant controversy about a potential role of axonal tension during the gyrification...

Nanoparticles present in various environments can interact with living organisms, potentially leading to deleterious effects. Understanding how these nanoparticles interact with cell membranes is crucial for rational assessment of their impact on diverse biological processes. While previous research has explored particle-membrane interactions, the dynamic processes of particle wrapping by fluid vesicles remain incompletely understood. In this study, we introduce a force-based, continuum-scale model utilizing triangulated mesh representation and discrete differential geometry to investigate particle-vesicle interaction dynamics...