Discrete Lines Research Articles

Minimum-projection in the Integer Lattice

According to the l1 norm, the minimum-projection Pi(x, v) is the smallest element of the intersection of the discrete straight line t(x, v) = {x + t * v, t ∈ Z} and the half-plane Zi2= {x &isin ZxZ sign(i) * x|i| ⋜ 0}. The minimum- projection is, among other things, also used to execute effective routing algo- rithms in circulant graphs. This arti- cle presents an algorithm for calculat- ing the minimum-projections and an al- gorithm for calculating the smallest ele- ment of the discrete straight line t(x, v) in the whole plane ZxZ. Both algorithms have the time complexity O(1). The arti- cle also discusses the k-dimensional gen- eralization of the above-mentioned algo- rithms.

Estimation of systematic errors of discrete line approximation by triangular tessellation and marching squares algorithm

This paper presents methods to calculate the length overestimation errors which are being made when approximating a discrete line by edges of triangular tessellation and marching squares algorithm. The maximum error and its average value are 15.47 % and 10.27 % for the triangular tessellation, while for the marching squares approach they are 8.24 % and 5.49 %, respectively. Mathematical calculations were compared with experimental results obtained by the Electron Backscatter Diffraction technique showing their usefulness as correction coefficients to obtain more accurate boundary length estimates.

Achieving Accuracy through Ambiguity: the Interactivity of Risk Communication in Severe Weather Events

Risks associated with natural hazards such as hurricanes are increasingly communicated on social media. For hurricane risk communication, visual information products—graphics—generated by meteorologists and scientists at weather agencies portray forecasts and atmospheric conditions and are offered to parsimoniously convey predictions of severe storms. This research considers risk interactivity by examining a particular hurricane graphic which has shown in previous research to have a distinctive diffusion signature: the ‘spaghetti plot’, which contains multiple discrete lines depicting a storm’s possible path. We first analyzed a large dataset of microblog interactions around spaghetti plots between members of the public and authoritative weather sources within the US during the 2017 Atlantic hurricane season. We then conducted interviews with a sample of the weather authorities after preliminary findings sketched the role that experts have in such communications. Findings describe how people make sense of risk dialogically over graphics, and show the presence of a fundamental tension in risk communication between accuracy and ambiguity. The interactive effort combats the unintended declarative quality of the graphical risk representation through communicative acts that maintain a hazard’s inherent ambiguity until risk can be foreclosed. We consider theoretical and practice-based implications of the limits and potentials of graphical risk representations and of widely diffused scientific communication, and offer reasons we need CSCW attention paid to the larger enterprise of risk communication.

Discrete line integral on uniform grids: Probabilistic interpretation and applications

Following the methodology developed by (Comput. Math. Appl. 33 (1997) 81–104), we define a discrete version of gradient vector and associated line integral along arbitrary path connecting two nodes of uniform grid. An exponential representation of joint survival function of bivariate discrete non-negative integer-valued random variables in terms of discrete line integral is established. We apply it to generate a discrete analogue of the Sibuya-type aging property, incorporating many classical and new bivariate discrete models. Several characterizations and closure properties of this class of bivariate discrete distributions are presented.

On the relevance of implementing the discrete line of digitization of professional education

On the relevance of implementing the discrete line of digitization of professional education

Assessing the reliability of the Raman peak counting method for the characterization of SWCNT diameter distributions: a cross characterization with TEM

Resonant Raman spectroscopy is a widely used technique for single-walled carbon nanotube (SWCNT) characterization, in particular in the radial breathing mode (RBM) range which provides direct information on the structure of the nanotube in resonance. The RBM peak counting method, i.e. acquiring Raman spectrum grids on a substrate with a select set of discrete laser lines and counting RBM peaks as single nanotubes, is frequently used to characterize SWCNT growth samples, despite the many factors that can induce errors in the results. In this work, we cross-characterize the diameter distributions obtained through this methodology with diameter distributions obtained by counting SWCNT diameters in transmission electron microscopy (TEM) and discuss the different results and biases between the techniques. This study is performed on a broad diameter distribution sample, and on two chirality-enriched samples whose chirality distributions are determined by photoluminescence excitation spectroscopy (PLE) and statistical analysis of high resolution TEM (HRTEM) images. We show that the largest differences between the Raman peak counting and TEM diameter distributions stem from the chirality-dependence of SWCNT Raman cross-sections and the patchy vision offered by the use of only a few discrete excitation wavelengths. The effect of the substrate and TEM-related biases are also discussed.

Traveling and localized solitary wave solutions of the nonlinear electrical transmission line model equation

Analytical solutions describing the kink–antikink type, hyperbolic, trigonometric, doubly periodic, localized bright and dark soliton like, breather and rational periodic train solutions to the discrete nonlinear electrical transmission line in $$(2+1)$$ -dimensions have been investigated with the Kudryashov method, the fractional linear transform method, and the simplest equation method with its modified and extended versions. Consequently, many new and more general explicit forms of traveling waves are retrieved under parametric conditions. The 3D, 2D, and density profile of some of the obtained results are numerically simulated by selecting suitable values of the various parameters of the NLTL model equation. Furthermore, all the obtained results were checked and verified by putting back into the considered nonlinear transmission line model equation with Maple and Mathematica software. The acquired results show the validity and reliability of the proposed schemes to the studied nonlinear electrical transmission line model.

Development of a new type of metamaterial and its application in antenna technology

In this paper, we consider a method for creating left-sided metamaterials. We select a method for creating metamaterials from a system with distributed parameters that are non-resonant structures. The equation of a discrete transmission line is solved taking into account the conditions for creating a metamaterial. The resulting solution in the form of effective permittivity shows that such a medium really has a double negative value of both the dielectric and magnetic permittivity. A generalized scheme of a universal method for searching for creating metamaterials is considered.

A note on “Envelope periodic solutions for a discrete network with the Jacobi elliptic functions and the alternative (G′/G)-expansion method including the generalized Riccati equation”

Employing Jacobi elliptic functions and the so-called alternative ( $$ G^{\prime}/G $$ )-expansion method including the generalized Riccati equation, Tala-Tebue et al. (Eur Phys J Plus 129:136, 2014) derived exact solutions for a discrete nonlinear electrical transmission line in (2 + 1)-dimensions. We show that the obtained solutions of the model given in Tala-Tebue et al. (2014) are all incorrect due to the incorrect reduced ODE Eq. (14) in that paper.

Bifurcation analysis with chaotic motion of oblique plane wave for describing a discrete nonlinear electrical transmission line with conformable derivative

The present work discusses the basic features of bifurcation properties with chaotic motion of oblique plane wave in the discrete nonlinear electrical transmission lines having conformable derivative evolution. The planar dynamical systems are obtained to understand such physical issues for this model. In addition, the analytical plane wave solutions of nonlinear mathematical leading equation are determined by using two different mathematical methods. Both methods are supported only by the shock plane wave solutions. The conditions for other types of oscillatory plane wave solutions are also determined. The effect of obliqueness on the bifurcation properties, chaotic motion and shock plane waves structures are focused graphically with discussions by considering both of locality and non-locality in the system. It is found that the parameter of non-local operator is only affected on the nonlinear shock wave phenomena, whereas all basic features of discrete nonlinear electrical transmission line are changed with the changes of obliqueness.

Genetic Variability and Structure of the Caucasian Shrew Sorex satunini in the North Caucasus according to the Variability of Microsatellite Loci

The variability of the microsatellite loci of the Caucasian shrew Sorex satunini in the North Caucasus was evaluated. It was shown that this species on this territory is represented by two discrete genetic lines associated with the basins of the Kuban and Terek rivers. The genetic diversity of the Caucasian shrew from the line of the Kuban River basin is characterized by a significantly higher polymorphism compared to the line from the Terek River basin. These differences are associated with both modern habitat conditions of S. satunini and the history of this species in the Western and Central Caucasus.

Line immunoassay for detection of IgG antibodies to hepatitis E virus (Hepeviridae, Orthohepevirus, Orthohepevirus A)

The diagnostic efficacy of methods for hepatitis E serodiagnostic varies over a wide range; therefore, the combined use of tests of various formats is recommended. The aim of the research was to develop a test system for the detection of IgG antibodies to hepatitis E virus (HEV) in human serum by linear immunoassay (LIA). Serum samples from patients with hepatitis and healthy individuals were tested using commercial enzyme-linked immunosorbent assay systems for the presence of IgG antibodies to viral agents causing hepatitis and other infections associated with liver pathology. Recombinant antigens ORF2 and ORF3 of HEV genotypes 1 and 3 were used. The "RecomLine HEV IgG/IgM" reagent kit (Mikrogen GmbH, Germany) was used as a comparison test system. The first Russian diagnostic kit "Blot-HEV", designed to detect IgG antibodies to individual HEV proteins in human serum using LIA, was developed. The antigenic base is represented by strips of a nitrocellulose membrane with immobilized recombinant antigens ORF2 (aa 406-660) and ORF3 (aa 1-113) of HEV genotypes 1 and 3, and control antigens in the form of discrete lines. The conjugate was mouse monoclonal antibodies to human class G immunoglobulins labeled with horseradish peroxidase. The chromogen solution contained the 3,3',5,5'-tetramethylbenzidine. A visual and digital recording of results was provided. The analytical sensitivity of the test kit was 0.625 IU/ml for ORF2 antigens and 2.5 IU/ml for ORF3 antigens. The absence of the influence of endogenous interfering substances on the results of the analysis and the absence of cross-reactions with antibodies to hepatitis pathogens of the other etiologies had been shown. The sensitivity of the test system compared to the "RecomLine HEV IgG/IgM" kit was 92%, specificity 97%. Shelf life in condition of storage was determined to be 12 months. The developed test can be used to confirm the results of ELISA in laboratory diagnosis of hepatitis E.

Multidimensional synthetic chiral-tube lattices via nonlinear frequency conversion

Geometrical dimensionality plays a fundamentally important role in the topological effects arising in discrete lattices. Although direct experiments are limited by three spatial dimensions, the research topic of synthetic dimensions implemented by the frequency degree of freedom in photonics is rapidly advancing. The manipulation of light in these artificial lattices is typically realized through electro-optic modulation; yet, their operating bandwidth imposes practical constraints on the range of interactions between different frequency components. Here we propose and experimentally realize all-optical synthetic dimensions involving specially tailored simultaneous short- and long-range interactions between discrete spectral lines mediated by frequency conversion in a nonlinear waveguide. We realize triangular chiral-tube lattices in three-dimensional space and explore their four-dimensional generalization. We implement a synthetic gauge field with nonzero magnetic flux and observe the associated multidimensional dynamics of frequency combs, all within one physical spatial port. We anticipate that our method will provide a new means for the fundamental study of high-dimensional physics and act as an important step towards using topological effects in optical devices operating in the time and frequency domains.

Social learning with coordination motives

We study observational learning among agents with coordination motives. On a discrete time line, communities of agents receive private information about an uncertain state, observe some predecessors' actions, and then take their own action. An agent's payoff is both state-dependent and increasing in the number of her peers taking the same action as hers. We find that connectivity between observations is the key determinant of the equilibrium pattern of information aggregation. When observations are connected, coordination motives inevitably lead to herding even when private beliefs are unbounded; when observations are separated, asymptotic learning becomes achievable. Herding can also be eliminated by making private information public within each community, and reduced by making observation endogenous and costly.

The XMM Cluster Survey: new evidence for the 3.5-keV feature in clusters is inconsistent with a dark matter origin

ABSTRACT There have been several reports of a detection of an unexplained excess of X-ray emission at $\simeq$3.5 keV in astrophysical systems. One interpretation of this excess is the decay of sterile neutrino dark matter. The most influential study to date analysed 73 clusters observed by the XMM–Newton satellite. We explore evidence for a ≃3.5-keV excess in the XMM-PN spectra of 117 redMaPPer galaxy clusters (0.1 < z < 0.6). In our analysis of individual spectra, we identify three systems with an excess of flux at $\simeq$3.5 keV. In one case (XCS J0003.3+0204), this excess may result from a discrete emission line. None of these systems are the most dark matter dominated in our sample. We group the remaining 114 clusters into four temperature (TX) bins to search for an increase in ≃3.5-keV flux excess with TX – a reliable tracer of halo mass. However, we do not find evidence of a significant excess in flux at ≃3.5 keV in any TX bins. To maximize sensitivity to a potentially weak dark matter decay feature at ≃3.5 keV, we jointly fit 114 clusters. Again, no significant excess is found at ≃3.5 keV. We estimate the upper limit of an undetected emission line at ≃3.5 keV to be 2.41 × 10−6 photons cm−2 s−1, corresponding to a mixing angle of sin 2(2θ) = 4.4 × 10−11, lower than previous estimates from cluster studies. We conclude that a flux excess at ≃3.5 keV is not a ubiquitous feature in clusters and therefore unlikely to originate from sterile neutrino dark matter decay.

Development of a stabilized Fabry–Perot etalonbased calibrator for Hanle echelle spectrograph

Accurate wavelength calibration is an important factor for any measurement with high-resolution spectrographs. The stellar spectrum comprises discrete absorption or emission lines whose position is precisely determined by calibrating the spectrograph using known reference lines generated from laboratory sources. For the spectrograph to measure small variations in Doppler shift, the wavelength calibration must be sufficiently stable during observation time. Instrument instability, mainly due to environmental factors like temperature and pressure variations and limitations of traditional calibration methods, for example, Th–Ar lamps, is the main challenge with high-precision spectroscopy. Through proper environmental control, by maintaining pressure at few mbar and temperature fluctuations within ± 0.05 ∘ C , Fabry–Perot etalon (FP) can yield a velocity precision of 1–10 m/s when used for wavelength calibration. We have developed a passively stabilized FP-based wavelength calibrator for a Hanle echelle spectrograph (HESP) installed on the Himalayan Chandra Telescope (HCT) at Indian Astronomical Observatory (IAO), Hanle, India. The etalon has been characterized using a Fourier transform spectrograph (FTS), and initial test runs have been performed with HESP. In this paper, we present the design and construction of the instrument along with preliminary test results obtained from HESP.

Adaptive Intrawell Matched Stochastic Resonance with a Potential Constraint Aided Line Enhancer for Passive Sonars.

Remote passive sonar detection and classification are challenging problems that require the user to extract signatures under low signal-to-noise (SNR) ratio conditions. Adaptive line enhancers (ALEs) have been widely utilized in passive sonars for enhancing narrowband discrete components, but the performance is limited. In this paper, we propose an adaptive intrawell matched stochastic resonance (AIMSR) method, aiming to break through the limitation of the conventional ALE by nonlinear filtering effects. To make it practically applicable, we addressed two problems: (1) the parameterized implementation of stochastic resonance (SR) under the low sampling rate condition and (2) the feasibility of realization in an embedded system with low computational complexity. For the first problem, the framework of intrawell matched stochastic resonance with potential constraint is implemented with three distinct merits: (a) it can ease the insufficient time-scale matching constraint so as to weaken the uncertain affect on potential parameter tuning; (b) the inaccurate noise intensity estimation can be eased; (c) it can release the limitation on system response which allows a higher input frequency in breaking through the large sampling rate limitation. For the second problem, we assumed a particular case to ease the potential parameter . As a result, the computation complexity is greatly reduced, and the extremely large parameter limitation is relaxed simultaneously. Simulation analyses are conducted with a discrete line signature and harmonic related line signature that reflect the superior filtering performance with limited sampling rate conditions; without loss of generality of detection, we considered two circumstances corresponding to (periodic signal with noise) and (pure noise) hypotheses, respectively, which indicates the detection performance fairly well. Application verification was experimentally conducted in a reservoir with an autonomous underwater vehicle (AUV) to validate the feasibility and efficiency of the proposed method. The results indicate that the proposed method surpasses the conventional ALE method in lower frequency contexts, where there is about 10 dB improvement for the fundamental frequency in the sense of power spectrum density (PSD).

Chirped solitons in discrete electrical transmission line

I¸n this paper, we investigate the solitary waves to the discrete nonlinear electrical transmission lines with resonant tunneling diode (RTD). We derive the envelope Ginzburg Landau (GL) equation to the lattice by employing reductive perturbation method in a small amplitude. We analyze the steady state of the results by using the modulation instability (MI). We also use the traveling wave transformation to investigate chirped bright and dark soliton to the GL equation. We demonstrate our results by some graphical representation in 3-D and 2-D.

Recovery of discrete spectra radiated by substance in deep vacuum using integral approximation algorithm

Subject of Research. The topical spectroscopy inverse problem is considered: the recovery of a discrete (line) spectrum from the measured continuous spectrum and the spectrometer response (instrument, hardware, spread) function in the presence of noise. Method. The problem is reduced to solving a system of linear-nonlinear equations with respect to the intensities of lines entering linearly and the frequencies of lines entering nonlinearly in the spectrum. To solve the system of linear-nonlinear equations, an integral approximation algorithm is developed that combines the solution of a linear integral equation and a system of linear algebraic equations without solving non-linear equations. Main Results. The proposed solution makes it possible to determine the number of lines in the spectrum and their parameters and is confirmed by the solution of numerical examples. Practical Relevance. The proposed algorithm provides the increase of spectrometer resolution (resolve close lines and isolate weak lines from noise) by applying mathematical-computer processing of the discrete spectrum.

MON-351 Early Diagnosis and Management of Bilateral Transient Osteoporosis of the Hip in Pregnancy

Introduction: Transient osteoporosis of the hip (TOH) in pregnancy is a rare and under-reported condition. It is clinically characterized by a sudden onset of hip pain in young females without any history of systemic disorders or traumatic injuries (1). Bilateral involvement of the hips, such as in this case report, is less common than unilateral involvement. Clinical Case: A 33 year old G2P1 female presented to the hospital at 30 weeks gestation for described sharp, bilateral inguinal pain, greater on the left than right, worse with movement, and with progressive difficulty ambulating, of three weeks duration. She had no significant PMH, notably denying thyroid or calcium disorder, nephrolithiasis, osteoporosis, or steroid treatment. She denied tobacco, alcohol, or illicit substance usage. She only took prenatal vitamins. On physical examination, she had reduced active and passive range of motion of both hips, but normal muscle strength and no signs of infection or neurological deficits. Labs including CMP, LFTs, and TFTs were within normal range. 24 hour urine free cortisol was 54 mcg/24h (normal 3.5-45mcg/24h); repeat post-partum was 21 mcg/24h. 25OH-D was 18.3 ng/mL. MRI without contrast demonstrated “extensive abnormal marrow edema within the left femoral head and neck and small effusion, suspicious for transient osteoporosis of the hip. A subtle small focus of edema on the right was also noted. No discrete fracture line or subchondral collapse was noted.”The patient was managed conservatively with analgesics, thromboprophylaxis, and education regarding reduction of weight bearing activities, rest, and mobility aids with crutches. She was started on vitamin D. Her bilateral hip pain resolved by the 38th week. She had an uncomplicated cesarean delivery at 39 weeks to a healthy male neonate. At the one-month postpartum visit, she was ambulating independently without difficulty. She denied further pain, and passive and active ROM were intact without tenderness. Conclusion: TOH in pregnancy is usually a self-limiting disorder with no obvious etiology (2). It can present unexpectedly in the third trimester or early postpartum period in a healthy female with an otherwise uneventful pregnancy. In rare instances where fractures of the affected hip occur, surgical intervention may be necessary. MRI has become the diagnostic tool of choice for early diagnosis of TOH. Early diagnosis and optimal management are essential to prevent major complications such as traumatic fractures and deep vein thrombosis, as well as to prevent stress for the mother during the course of pregnancy.