One-dimensional Cross-section Research Articles

A system of Schrödinger equations in a wave guide

We consider a system of Schrödinger equations in a wave guide, with coupling and damping at the boundary. It is related to the same problem on the one-dimensional cross-section. We prove in particular that we have a spectral gap and exponential decay of the energies for these problems. For the transverse problem we also study the localization of the eigenvalues and prove that the corresponding generalized eigenfunctions form a Riesz basis.

Effective two-body scatterings around a massive object

ABSTRACT Two-body scatterings under the potential of a massive object are very common in astrophysics. If the massive body is far enough away that the two small bodies are in their own gravitational sphere of influence, the gravity of the massive body can be temporarily ignored. However, this requires the scattering process to be fast enough that the small objects do not spend too much time at distances near the surface of the sphere of influence. In this paper, we derive the validation criteria for effective two-body scattering and establish a simple analytical solution for this process, which we verify through numerical scattering experiments. We use this solution to study star–black hole scatterings in the discs of active galactic nuclei and planet–planet scatterings in planetary systems, and calculate their one-dimensional cross-section analytically. Our solution will be valuable in reducing computational time when treating two-body scatterings under the potential of a much more massive third body, provided that the problem settings are in the valid parameter space region identified by our study.

An automated neural network-based stage-specific malaria detection software using dimension reduction: The malaria microscopy classifier

Due to climate change and the COVID-19 pandemic, the number of malaria cases and deaths, caused by the Plasmodium genus, of which P. falciparum is the most common and lethal to humans, increased between 2019 and 2020. Reversing this trend and eliminating malaria worldwide requires improvements in malaria diagnosis, in which artificial intelligence (AI) has recently been demonstrated to have a great potential. One of the main reasons for the use of neural networks (NNs) is the time saving through automatising the process and the elimination of human error. When classifying with two-dimensional images of red blood cells (RBCs), the number of parameters fitted by the NN for the classification of RBCs is extremely high, which strongly influences the performance of the network, especially for training sets of moderate size. The complicated handling of malaria culturing and sample preparation does not only limit the efficiency of NNs due to small training sets, but also because of the uneven distribution of red blood cell (RBC) categories. To boost the performance of microscopy techniques in malaria diagnosis, our approach aims at resolving these drawbacks by reducing the dimension of the input data and by data augmentation, respectively. We assess the performance of our approach on images recorded by light (LM), atomic force (AFM), and fluorescence microscopy (FM). Our tool, the Malaria Stage Classifier, provides a fast, high-accuracy recognition by (1) identifying individual RBCs in multi-cell microscopy images, (2) extracting characteristic one-dimensional cross-sections from individual RBC images. These cross-sections are selected by a simple algorithm to contain key information about the status of the RBCs and are used to (3) classify the malaria blood stages. We demonstrate that our method is applicable to images recorded by various microscopy techniques and available as a software package.•Identifying individual RBCs in multi-cell microscopy images.•Extracting characteristic one-dimensional cross-sections from individual RBC images. These cross-sections are selected by a simple algorithm to contain key information about the status of the RBCs and are used to.•Classify the malaria blood stages. We demonstrate that our method is applicable to images recorded by various microscopy techniques and available as a software package.

Reducing data dimension boosts neural network-based stage-specific malaria detection

Although malaria has been known for more than 4 thousand years1, it still imposes a global burden with approx. 240 million annual cases2. Improvement in diagnostic techniques is a prerequisite for its global elimination. Despite its main limitations, being time-consuming and subjective, light microscopy on Giemsa-stained blood smears is still the gold-standard diagnostic method used worldwide. Autonomous computer assisted recognition of malaria infected red blood cells (RBCs) using neural networks (NNs) has the potential to overcome these deficiencies, if a fast, high-accuracy detection can be achieved using low computational power and limited sets of microscopy images for training the NN. Here, we report on a novel NN-based scheme that is capable of the high-speed classification of RBCs into four categories—healthy ones and three classes of infected ones according to the parasite age—with an accuracy as high as 98%. Importantly, we observe that a smart reduction of data dimension, using characteristic one-dimensional cross-sections of the RBC images, not only speeds up the classification but also significantly improves its performance with respect to the usual two-dimensional NN schemes. Via comparative studies on RBC images recorded by two additional techniques, fluorescence and atomic force microscopy, we demonstrate that our method is universally applicable for different types of microscopy images. This robustness against imaging platform-specific features is crucial for diagnostic applications. Our approach for the reduction of data dimension could be straightforwardly generalised for the classification of different parasites, cells and other types of objects.

Regional Deposition: Deposition Models.

Modeling particle deposition in the human lung requires information about the morphology of the lung in terms of simple geometric units, e.g., characterizing bronchial airways by straight cylindrical tubes. Five different regional deposition models are discussed in this section with respect to morphometric lung models and related mathematical modeling techniques: 1) one-dimensional cross-section or "trumpet" model, 2) deterministic symmetric generation or "single-path" model, 3) deterministic asymmetric generation or "multiple-path" model, 4) stochastic asymmetric generation or "multiple-path" model, and 5) single-path computational fluid and particle dynamics (CFPD) model. Current deposition models can predict the following regional deposition quantities relevant for the administration of medical aerosols: 1) regional bronchial and alveolar deposition, 2) generational lung deposition, 3) lobar deposition, 4) generational lobar deposition, and 5) generational surface deposition. Although deposition fractions predicted by the different models depend on the selection of a specific morphometric lung model and a specific set of analytical deposition equations, all models predict the same trends as functions of particle diameter and breathing parameters. In general, the overall agreement between the modeling predictions obtained by the various deposition models and the available experimental evidence indicates that current deposition models correctly predict regional and generational deposition.

Modelling solute transport in the brain microcirculation: is it really well mixed inside the blood vessels?

Most network models describing solute transport in the brain microcirculation use the well-mixed hypothesis and assume that radial gradients inside the blood vessels are negligible. Recent experimental data suggest that these gradients, which may result from heterogeneities in the velocity field or consumption in the tissue, may in fact be important. Here, we study the validity of the well-mixed hypothesis in network models of solute transport using theoretical and computational approaches. We focus on regimes of weak coupling where the transport problem inside the vasculature is independent of the concentration field in the tissue. In these regimes, the boundary condition between vessels and tissue can be modelled by a Robin boundary condition. For this boundary condition and for a single cylindrical capillary, we derive a one-dimensional cross-section average transport problem with dispersion and exchange coefficients capturing the effects of radial gradients. We then extend this model to a network of connected tubes and solve the problem in a complex anatomical network. By comparing with results based on the well-mixed hypothesis, we find that dispersive effects are a fundamental component of transport in transient situations with relatively rapid injections, i.e. frequencies above one Hertz. For slowly varying signals and steady states, radial gradients also significantly impact the spatial distribution of vessel/tissue exchange for molecules that easily cross the blood brain barrier. This suggests that radial gradients cannot be systematically neglected and that there is a crucial need to determine the impact of spatio-temporal heterogeneities on transport in the brain microcirculation.

Space-time signal processing in MIMO antennas system with the Earth surface reflections

The generalized correlation integral for space-time signal processing at the output of a MIMO antenna system radio altimeter in the Earth’s surface reflections presence is obtained. The results of calculation of one-dimensional cross-section of the generalized correlation integral at an elevation angle with a known target range and two-dimensional crosssection of the generalized correlation integral «horizontal range-height» for specific surface reflection coefficient are presented.

Conformal boundary conditions, loop gravity and the continuum

In this paper, we will make an attempt to clarify the relation between three-dimensional euclidean loop quantum gravity with vanishing cosmological constant and quantum field theory in the continuum. We will argue, in particular, that in three spacetime dimensions the discrete spectra for the geometric boundary observables that we find in loop quantum gravity can be understood from the quantisation of a conformal boundary field theory in the continuum without ever introducing spin networks or triangulations of space. At a technical level, the starting point is the Hamiltonian formalism for general relativity in regions with boundaries at finite distance. At these finite boundaries, we choose specific conformal boundary conditions (the boundary is a minimal surface) that are derived from a boundary field theory for an SU(2) boundary spinor, which is minimally coupled to the spin connection in the bulk. The resulting boundary equations of motion define a conformal field theory with vanishing central charge. We will quantise this boundary field theory and show that the length of a one-dimensional cross section of the boundary has a discrete spectrum. In addition, we will introduce a new class of coherent states, study the quasi-local observables that generate the quasi-local Virasoro algebra and discuss some strategies to evaluate the partition function of the theory.

Quantum gravity in three dimensions, Witten spinors and the quantisation of length

In this paper, I investigate the quantisation of length in euclidean quantum gravity in three dimensions. The starting point is the classical hamiltonian formalism in a cylinder of finite radius. At this finite boundary, a counter term is introduced that couples the gravitational field in the interior to a two-dimensional conformal field theory for an SU(2) boundary spinor, whose norm determines the conformal factor between the fiducial boundary metric and the physical metric in the bulk. The equations of motion for this boundary spinor are derived from the boundary action and turn out to be the two-dimensional analogue of the Witten equations appearing in Witten's proof of the positive mass theorem. The paper concludes with some comments on the resulting quantum theory. It is shown, in particular, that the length of a one-dimensional cross section of the boundary turns into a number operator on the Fock space of the theory. The spectrum of this operator is discrete and matches the results from loop quantum gravity in the spin network representation.

Extreme Localization of Eigenfunctions to One-Dimensional High-Contrast Periodic Problems with a Defect

Following a number of recent studies of resolvent and spectral convergence of nonuniformly elliptic families of differential operators describing the behavior of periodic composite media with high contrast, we study the corresponding one-dimensional version that includes a “defect”: an inclusion of fixed size with a given set of material parameters. It is known that the spectrum of the purely periodic case without the defect and its limit, as the period $\varepsilon$ goes to zero, has a band-gap structure. We consider a sequence of eigenvalues $\lambda_\varepsilon$ that are induced by the defect and converge to a point $\lambda_0$ located in a gap of the limit spectrum for the periodic case. We show that the corresponding eigenfunctions are “extremely” localized to the defect, in the sense that the localization exponent behaves as $\exp(-\nu/\varepsilon),$ $\nu>0,$ which has not been observed in the existing literature. In two- and three-dimensional configurations, whose one-dimensional cross sections are described by the setting considered, this implies the existence of propagating waves that are localized to a vicinity of the defect. We also show that the unperturbed operators are norm-resolvent close to a degenerate operator on the real axis, which is described explicitly.

Identification of large-scale cellular structures on the Sun based on the SDO and PSPT data

Three independent sets of data: i). series of filtergrams obtained in line CaII K (393.416 nm) with the ground-based telescope Precision Solar Photometric Telescope (PSPT) of Mauna Loa Solar Observatory; ii). series of filtergrams of Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO) in {\lambda}160 nm and iii). series of magnetograms of Helioseismic and Magnetic Imager (HMI) of SDO have been processed to reveal reliably the existence of spatial cellular structures on the solar photosphere at scale about of 300 arcsec. This scale is intermediate between supergranules and giant cells (~30,000 and ~300,000 kilometers across, respectively). To identify the different spatial structures the tens of two-dimensional power spectra (2DFFT) have been averaged. For one-dimensional photometric cross sections of frames, the Fourier power spectra (FFT) and wavelet transforms (Morlet 5-th order) have been calculated.

Large amplitude oscillations of protons in water clusters

Synchronous oscillations of bridge protons in molecular rings of (H2O) n water clusters with n = 4–6, 8, and 12 are analyzed as large amplitude motions that result in the inversion of the hydrogen bond sequence in a single ring. The corresponding one-dimensional cross sections of the potential energy surfaces (symmetric double-well potentials) are constructed at the MP2/6–31++G(d, p) level. The eigenstates of the systems in the constructed potentials in the energy range up to the top of the barrier are determined. The synchronous oscillations of protons are shown to be coupled to vibrations of the oxygen skeleton of the molecular ring, and the typical frequencies of the complex vibrations lie in the range of 230–330 cm−1.

Power spectrum distortions in CMB map one-dimensional cross-sections depending on the cosmological model. II

Power spectrum distortions in CMB map one-dimensional cross-sections depending on the cosmological model. II

Power spectrum distortions in CMB map one-dimensional cross-sections depending on the cosmological model

We examine the effect produced by the variation of parameters of the cosmological model on the power spectrum of one-dimensional cross-sections of the cosmic microwave background maps. We also investigate the possibility of determining these parameters in the analysis of one-dimensional data. The features of the component separation procedure, leading to additional restrictions on the accuracy of reconstruction of the original spectrum are discussed. When the low harmonics remain in the map, the power spectrum of a one-dimensional cross-section is poorly sensitive to the variations of a number of cosmological parameters. Still, the analysis of one-dimensional data could be useful in the search and study of anomalous effects.

Coherence vortices in vortex-free partially coherent x-ray fields

We show that coherence vortices, namely screw-type topological defects in the phase of the cross-spectral density associated with a partially coherent scalar electromagnetic field, can be obtained for paraxial fields even in the absence of both scatterers and spatial vortices. The results are especially interesting at x-ray wavelengths, for which the paraxial (small-angle) approximation is usually met. A formal analogy is drawn between the cross-spectral density of a translation-invariant partially coherent system and a focused coherent wave field. This correspondence leads to a natural explanation of the coherence vortices as analogous to physical vortices that may appear around the focus of aberrated lenses. In addition, the Gouy phase shift, typical of any focused complex scalar wave field, is also derived for the one-dimensional cross section of cross-spectral density.

Modeling and optimization of the DMFC system: Relating materials properties to system size and performance

In designing a direct methanol fuel cell and evaluating the appropriateness of new materials for inclusion, it is helpful to consider the impact of material properties on the performance of a complete system: to some degree, poor fuel utilization and performance losses from methanol crossover can be mitigated by proper system design. Simple engineering models can be useful tools in facilitating this type of system design. In this paper, an analytical model is developed to determine the oxygen concentration profile in the cathode backing layer and flow channel along a one-dimensional cross-section of the fuel cell. An existing analytical model is then used to determine the methanol concentration profile in the anode backing layer and membrane and the methanol crossover current along the same cross-section. Applying a fixed cell potential and using Tafel kinetics to describe the charge-transfer reactions at the anode and the cathode, the local current density and the rates of methanol and oxygen consumption are determined. The process repeats for a fixed number of cross-sections down the entire length of the flow channels, and the average current density and stoichiometric ratios are calculated at the end. The model is applied to examine the effects of new low-crossover membranes and to suggest new design parameters for those membranes. Also, an analysis is presented in which the tradeoff between stack power and the size of system components is examined for a range of methanol and oxygen flow rates.

Homotopy-based surface reconstruction with application to acoustic signals

This work introduces a new algorithm for surface reconstruction in ℝ3 from spatially arranged one-dimensional cross sections embedded in ℝ3. This is generally the case with acoustic signals that pierce an object non-destructively. Continuous deformations (homotopies) that smoothly reconstruct information between any pair of successive cross sections are derived. The zero level set of the resulting homotopy field generates the desired surface. Four types of homotopies are suggested that are well suited to generate a smooth surface. We also provide derivation of necessary higher order homotopies that can generate a C 2 surface. An algorithm to generate surface from acoustic sonar signals is presented with results. Reconstruction accuracies of the homotopies are compared by means of simulations performed on basic geometric primitives.

Spatially-chirped modulation imaging of absorbtion and fluorescent objects on single-element optical detector

Line imaging of fluorescent and absorptive objects with a single-pixel imaging technique that acquires one-dimensional cross-sections through a sample by imposing a spatially-varying amplitude modulation on the probing beam is demonstrated. The fluorophore concentration or absorber distribution of the sample is directly mapped to modulation frequency components of the spatially-integrated temporal signal. Time-domain signals are obtained from a single photodiode, with object spatial frequency correlation encoded in time-domain bursts in the electronic signal from the photodiode.

Riffle-pool maintenance and flow convergence routing observed on a large gravel-bed river

Geomorphologists have studied and debated over the processes responsible for natural riffle-pool maintenance for decades. Most studies have focused on small wadable rivers, but they lack much description of overbank flood conditions or a spatially explicit characterization of morphodynamics. In this study, 1-m horizontal resolution digital elevation models were collected from a riffle-pool-run sequence before and after an overbank flood with a 7.7-year recurrence interval on the relatively large gravel-bed lower Yuba River, California. Digital elevation model differencing was used to quantify the magnitude and pattern of flood-induced morphodynamic change. Cross section based analysis and two-dimensional hydrodynamic modeling of flows ranging from 0.147 to 7.63 times bankful discharge were completed to evaluate the hydraulic mechanisms responsible for the observed topographic changes. One key finding was that riffle-pool relief increased by 0.42 m, confirming the occurrence of natural hydrogeomorphic maintenance. Spatially complex patterns of scour and deposition exceeding 0.15 m at the scale of subwidth morphological units were reasonably predicted by the two-dimensional mechanistic model that accounts for convective acceleration. The one-dimensional cross section based method underperformed the two-dimensional model significantly. Consequently, multiple scales of channel non-uniformity and a dynamic flow regime caused the observed maintenance of the pool-riffle morphology through the mechanism of “flow convergence routing” proposed by MacWilliams et al. [MacWilliams, M.L., Wheaton, J.M., Pasternack, G.B., Kitanidis, P.K., Street, R.L., 2006. The flow convergence-routing hypothesis for riffle-pool maintenance in alluvial rivers. Water Resources Research 42, W10427, doi:10.1029/2005WR004391].

High Accuracy Correction of Critical Dimension Errors Appearing in Large Scale Integrated Circuits Fabrication Processes: Pattern-Based Model

The pattern density model has been used for correcting critical dimension (CD) errors appearing in LSI fabrication processes. However, this method has an inherent uncertainty in the figure position and a correction error caused by this uncertainty. In this paper, we introduce a pattern-based model for discussing CD errors in order to avoid this uncertainty. Based on the pattern-based model, a new nonlinear equation for correction is derived, and a formula for obtaining a high-accuracy numerical solution for the correction equation is also derived. The correction accuracy of the solution is evaluated with several approximate solutions by both analytical and numerical methods under the condition that (1) the point spread function g(x) of the position shift of a point on a figure edge is the Gaussian function, and (2) a one-dimensional cross section of lines and spaces is used for evaluation. The proposed method can provide a high-accuracy correction both in the case in which the interaction distance σ≫figure size and also when σ≪figure size. Furthermore, even in the case in which σ is comparable with figure size, the method provides higher-accuracy corrections than other methods. For example, when σ is 10 nm, the figure size is 20 nm, and the maximum deviation γd(=2γd*) from the designed size is 20 nm, our correction method supresses the dimensional error of lines and speces pattern less than 0.9 nm. These results suggest that the method proposed in this paper has a wide range of applications for future LSI fabrication.