differential geometry

Multiplexed, real-time fluorescence detection at the single-molecule level can reveal the stoichiometry, dynamics and interactions of multiple molecular species in mixtures and other complex samples. However, fluorescence-based sensing is typically limited to the detection of just 3-4 colours at a time due to low signal-to-noise ratio, high spectral overlap and the need to maintain the chemical compatibility of dyes. Here we engineered a palette of several dozen composite fluorescent labels, called FRETfluors, for multiplexed spectroscopic measurements at the single-molecule level...

Learning disabilities affect a significant proportion of children worldwide, with far-reaching consequences for their academic, professional, and personal lives. Here we develop digital twins - biologically plausible personalized Deep Neural Networks (pDNNs) - to investigate the neurophysiological mechanisms underlying learning disabilities in children. Our pDNN reproduces behavioral and neural activity patterns observed in affected children, including lower performance accuracy, slower learning rates, neural hyper-excitability, and reduced neural differentiation of numerical problems...

By studying a nonlinear model by inspecting a p-dimensional parameter space through <mml:math xmlns:mml="https://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>(</mml:mo> <mml:mi>p</mml:mi> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo></mml:mrow> </mml:math> -dimensional cuts, one can detect changes that are only determined by the geometry of the manifolds that make up the bifurcation set. We refer to these changes as geometric bifurcations...

Strokes are one of the leading causes of death in the United States. Stroke treatment involves removal or dissolution of the obstruction (usually a clot) in the blocked artery by catheter insertion. A computer simulation to systematically plan such patient-specific treatments needs a network of about 105 blood vessels including collaterals. The existing computational fluid dynamic (CFD) solvers are not employed for stroke treatment planning as they are incapable of providing solutions for such big arterial trees in a reasonable amount of time...

Tuning cell adhesion geometry can affect cytoskeleton organization and the distribution of cytoskeleton forces, which play critical roles in controlling cell functions. To elucidate the geometrical relationship with cytoskeleton force distribution, it is necessary to control cell morphology. In this study, a series of dextral vortex micropatterns were prepared to precisely control cell morphology for investigating the influence of the curvature degree of adhesion curves on intracellular force distribution and stem cell differentiation at a sub-cellular level...

The present study aims to investigate the potential of the 3D printing technique to design gastroretentive floating tablets (GFTs) for modifying the drug release profile of an immediate-release tablet. A 3D-printed floating shell enclosing a captopril tablet was designed having varying number of drug-release windows. The impact of geometrical changes in the design of delivery system and thermal cross-linking of polymers were evaluated to observe the influence on floating ability and drug release. Water uptake, water insolubilization, Differential Scanning Calorimetry (DSC), and Attenuated Total Reflection-Fourier Transform Infrared Spectroscopy (ATR-FTIR) were performed to assess the degree of thermal cross-linking of polyvinyl alcohol (PVA) filament...

Simplicial Kuramoto models have emerged as a diverse and intriguing class of models describing oscillators on simplices rather than nodes. In this paper, we present a unified framework to describe different variants of these models, categorized into three main groups: "simple" models, "Hodge-coupled" models, and "order-coupled" (Dirac) models. Our framework is based on topology and discrete differential geometry, as well as gradient systems and frustrations, and permits a systematic analysis of their properties...

Bone proliferation is an important pathological feature of inflammatory rheumatic diseases. Although recent advance in high-resolution peripheral quantitative computed tomography (HR-pQCT) enables physicians to study microarchitectures, physicians' annotation of proliferation suffers from slice inconsistency and subjective variations. Also, there are only few effective automatic or semi-automatic tools for proliferation detection. In this study, by integrating pathological knowledge of proliferation formation with the advancement of statistical shape analysis theory, we present an unsupervised method, named Deformation-Controllable Elastic Shape model, for 3D bone Proliferation Analysis (DCES-PA)...

Tip-enhanced Raman spectroscopy (TERS) under ultrahigh vacuum and cryogenic conditions enables exploration of the relations between the adsorption geometry, electronic state, and vibrational fingerprints of individual molecules. TERS capability of reflecting spin states in open-shell molecular configurations is yet unexplored. Here, we use the tip of a scanning probe microscope to lift a perylene-3,4,9,10-tetracarboxylic dianhydride (PTCDA) molecule from a metal surface to bring it into an open-shell spin one-half anionic state...

Dynamic changes in mechanical microenvironments, such as cell crowding, regulate lineage fates as well as cell proliferation. Although regulatory mechanisms for contact inhibition of proliferation have been extensively studied, it remains unclear how cell crowding induces lineage specification. Here we found that a well-known oncogene, ETS variant transcription factor 4 (ETV4), serves as a molecular transducer that links mechanical microenvironments and gene expression. In a growing epithelium of human embryonic stem cells, cell crowding dynamics is translated into ETV4 expression, serving as a pre-pattern for future lineage fates...

AIMS: Adequate differentiation of calcifications in contrast-enhanced CT scans remains difficult to assess TAVI parameters. The size of the aortic leaflets has not been taken into account so far in present studies. The aim of our study was to establish a new method for optimized quantification of the aortic valve calcification degree in contrast-enhanced CT scans for better preoperative prediction of postoperative paravalvular leak after TAVI. METHODS AND RESULTS: We retrospectively analyzed preoperative contrast-enhanced CT scans of patients who underwent TAVI in our institution between 2014 and 2017...

Alday and Maldacena conjectured an equivalence between string amplitudes in AdS_{5}×S^{5} and null polygonal Wilson loops in planar N=4 super-Yang-Mills (SYM) theory. At strong coupling this identifies SYM amplitudes with areas of minimal surfaces in anti-de Sitter space. For minimal surfaces in AdS_{3}, we find that the nontrivial part of these amplitudes, the remainder function, satisfies an integrable system of nonlinear differential equations, and we give its Lax form. The result follows from a new perspective on "Y systems," which defines a new psuedo-hyper-Kähler structure directly on the space of kinematic data, via a natural twistor space defined by the Y-system equations...

Protein generation has numerous applications in designing therapeutic antibodies and creating new drugs. Still, it is a demanding task due to the inherent complexities of protein structures and the limitations of current generative models. Proteins possess intricate geometry, and sampling their conformational space is challenging due to its high dimensionality. This paper introduces novel Markovian and non-Markovian generative diffusion models based on fractional stochastic differential equations and the Lévy distribution, allowing for a more effective exploration of the conformational space...

BACKGROUND: Clinical intensity modulated radiation therapy plans have been described using various complexity metrics to help identify problematic radiotherapy plans. Most previous studies related to the quantification of plan complexity and their utility have relied on institution-specific plans which can be highly variable depending on the machines, planning techniques, delivery modalities, and measurement devices used. In this work, 1723 plans treating one of only four standardized geometries were simultaneously analyzed to investigate how radiation plan complexity metrics vary across four different sets of common objectives...

Plant cells withstand mechanical stress originating from turgor pressure by robustly maintaining the mechanical properties of the cell wall. This applies at the organ scale as well; many plant stems act as pressurized cylinders, where the epidermis is under tension and inner tissues are under compression. The clavata3 de-etiolated3 (clv3-8 det3-1) double mutant of Arabidopsis thaliana displays cracks in its stems because of a conflict between the mechanical properties of the weak epidermis and over-proliferation of inner stem tissues...

We present a novel framework named NeuralRecon for real-time 3D scene reconstruction from a monocular video. Unlike previous methods that estimate single-view depth maps separately on each key-frame and fuse them later, we propose to directly reconstruct local surfaces represented as sparse TSDF volumes for each video fragment sequentially by a neural network. A learning-based TSDF fusion module based on gated recurrent units is used to guide the network to fuse features from previous fragments. This design allows the network to capture local smoothness prior and global shape prior of 3D surfaces when sequentially reconstructing the surfaces, resulting in accurate, coherent, and real-time surface reconstruction...

Fundamental knowledge of wet clutches' drag loss behavior is essential for designing low-loss clutch systems. In contrast to the widely investigated injection lubrication, more comprehensive knowledge is needed on the drag loss behavior of dip-lubricated wet clutches. In the development phase, data-driven models allow drag loss predictions with low computational effort and, at the same time, sufficient accuracy. Therefore, this study aimed to deepen and expand knowledge of the drag loss behavior of dip-lubricated wet clutches based on experimental investigations...

Geometric Deep Learning has recently made striking progress with the advent of continuous deep implicit fields. They allow for detailed modeling of watertight surfaces of arbitrary topology while not relying on a 3D Euclidean grid, resulting in a learnable parameterization that is unlimited in resolution. Unfortunately, these methods are often unsuitable for applications that require an explicit mesh-based surface representation because converting an implicit field to such a representation relies on the Marching Cubes algorithm, which cannot be differentiated with respect to the underlying implicit field...

Diffusion is a mass transport phenomenon caused by chaotic thermal movements of molecules. Studying the transport in specific domain is simplified by using evolutionary differential equations for local concentration of the molecules instead of complete information on molecular paths [1]. Compounds in a fluid mixture tend to smooth out its spatial concentration inhomogeneities by diffusion. Rate of the transport is proportional to the concentration gradient and coefficient of diffusion of the compound in ordinary diffusion...

Three-dimensional (3D) structures are actually the state-of-the-art technique to create porous scaffolds for tissue engineering. Since regeneration in cartilage tissue is limited due to intrinsic cellular properties this study aims to develop and characterize three-dimensional porous scaffolds of poly (L-co-D, L lactide-co-trimethylene carbonate), PLDLA-TMC, obtained by 3D fiber deposition technique. The PLDLA-TMC terpolymer scaffolds (70:30), were obtained and characterized by scanning electron microscopy, gel permeation chromatography, differential scanning calorimetry, thermal gravimetric analysis, compression mechanical testing and study on in vitro degradation, which showed its amorphous characteristics, cylindrical geometry, and interconnected pores...