Parameterized Complexity of Directed Spanner Problems

We initiate the parameterized complexity study of minimum t-spanner problems on directed graphs. For a positive integer t, a multiplicative t-spanner of a (directed) graph G is a spanning subgraph H such that the distance between any two vertices in H is at most t times the distance between these vertices in G, that is, H keeps the distances in G up to the distortion (or stretch) factor t. An additive t-spanner is defined as a spanning subgraph that keeps the distances up to the additive distortion parameter t, that is, the distances in H and G differ by at most t. The task of Directed Multiplicative Spanner is, given a directed graph G with m arcs and positive integers t and k, decide whether G has a multiplicative t-spanner with at most $$m-k$$ m - k arcs. Similarly, Directed Additive Spanner asks whether G has an additive t-spanner with at most $$m-k$$ m - k arcs. We show that (i) Directed Multiplicative Spanner admits a polynomial kernel of size $$\mathcal {O}(k^4t^5)$$ O ( k 4 t 5 ) and can be solved in randomized $$(4t)^k\cdot n^{\mathcal {O}(1)}$$ ( 4 t ) k · n O ( 1 ) time, (ii) the weighted variant of Directed Multiplicative Spanner can be solved in $$k^{2k}\cdot n^{\mathcal {O}(1)}$$ k 2 k · n O ( 1 ) time on directed acyclic graphs, (iii) Directed Additive Spanner is $${{\,\mathrm{\mathsf{W}}\,}}[1]$$ W [ 1 ] -hard when parameterized by k for every fixed $$t\ge 1$$ t ≥ 1 even when the input graphs are restricted to be directed acyclic graphs. The latter claim contrasts with the recent result of Kobayashi from STACS 2020 that the problem for undirected graphs is $${{\,\mathrm{\mathsf{FPT}}\,}}$$ FPT when parameterized by t and k.

Analysis of Errors in Active Power and Energy Measurements Under Random Harmonic Distortion Conditions

As harmonic distortion of voltage and current is reality in the power system, the need for accurate measurement of electrical power and energy goes beyond the instruments’ specifications and calibration procedures regarding pure sine wave signals. Several international standards and recommendations provide test signals for examination of electricity meters under non-sinusoidal conditions, however, not all of the test signal parameters’ possible states are faithfully represented in those documents. Because the high order harmonics may possess random amplitudes and phase shifts in relation to components at fundamental frequency, it is important that the meter’s performance is verified with random waveforms as well. The non-linear dependence between the measured power/energy and the phase shifts, both between fundamental and harmonic components, provides additional complexity of such an analysis. Simple test signals, which are in accordance with the standards’ demands and propositions, are used for determination of the measurement error in case of different harmonic distortion parameter change. In order for a general error function for any measurement device to be determined, mathematical modelling, regarding the results from multiple tests, is performed. The mathematical model presents a strong dependence between a single component’s phase shifts and a meter’s error and it provides a systematization of all signal parameters’ influence on the measurement accuracy.

Spectroscopic Elucidation of Some Complexes of Vanillin Semicarbazone

3-Phenyl-4-methoxybenzaldehyde undergoes condensation with semicarbazide hydrochloride to form a Schiff-base i.e. 3-phenyl-4-methoxybenzaldehyde semicarbazone (abbreviated as MBS). It undergoes complexation with Vanadium(II), Manganese(II), and Copper(II). The comparison of FTIR-spectra of complexes with that of free ligand helps ascertain the coordination points of ligand through the nitrogen of –CH=N– group and oxygen of group. The axial ligands have been varied by chloride, acetate and nitrate ions. The UV/Visible and ESR spectra of complexes predicts their tetragonally distorted octahedral (D4h) symmetry. The tetragonal distortion parameter (Dt) is observed maximum for chloride while it is minimum for nitrate along z-axis. Both vanillin and semicarbazide are established biologically active compounds and hence their biological activities may be enhanced by their complexation and than a versatile field may be developed for further exploration.

A REVIEW OF THE ONE-PARAMETER DIVISION UNDISTORTION MODEL

The one-parameter division undistortion model by (Lenz, 1987) and (Fitzgibbon, 2001) is a simple radial distortion model with beneficial algebraic properties that allows to reason about some problems analytically that can only be handled numerically in other distortion models. One property of this distortion model is that straight lines in the undistorted image correspond to circles in the distorted image. These circles are fully described by their center point, as the radius can be calculated from the position of the center and the distortion parameter only. This publication collects the properties of this distortion model from several sources and reviews them. Moreover, we show in this publication that the space of this center is projectively isomorphic to the dual space of the undistorted image plane, i.e. its line space. Therefore, projective invariant measurements on the undistorted lines are possible by the according measurements on the centers of the distorted circles. As an example of application, we use this to find the metric distance of two parallel straight rails with known track gauge in a single uncalibrated camera image with significant radial distortion.

Control of gaps in technical structures during ground vibration testing

Introduction. A fair number of technical structures have gaps (backlashes) which can be contingently divided into two types. One of them is the gaps in connections between substructures which are introduced so that the connections may operate correctly. Sizes of such gaps are usually normalized. Another type is the backlashes which occur during operation. Due to the normalized gaps usually expand while operating, both of the types may lead to increased loading and wear of mechanical parts, an alteration in dynamical characteristics and a deterioration in a technical state of mechanical structures. It explains the necessity to control the gaps. When the ground vibration testing of the structures is performed, it seems appropriate to use these tests to detect such gaps. Research Objective: developing the method to control the gaps in the technical structures during the ground vibration testing based on distortions of portraits of forced oscillations. Research Technique. The steady-state forced oscillations of the technical structures, which were measured by acceleration sensors, are excited by means of shakers. The sensor signals are represented as the portraits: the vertical scanning is proportional to the signal and the horizontal scanning – to its first harmonic with the phase shift of π/2. In case of a linear system, the portraits are circles. The presence of the gaps distorts the portraits of oscillations specifically. To estimate the distortions numerically, the first harmonic is subtracted from the Fourier series of the portrait of oscillations, the absolute maximum of the residue is calculated over the oscillation period and used subsequently as the distortion parameter Ψ. The value of the parameter Ψ is normalized and denoted as ξ. The ξ distributions are plotted on controlled objects. The locations of the gaps are determined through the positions of the local maxima of the distortions. While calculating the parameter ξ, the two types of normalization, which were conditionally named the global and local ones, are being used. In case of the global normalization, the value of Ψ is related to the amplitude of the first harmonic at the control point of the structure. The local normalization means that the magnitude of Ψ is related to the amplitude of the first harmonic of the sensor where that parameter was previously calculated. The global normalization is required to analyze the distortion distribution of the portraits of oscillations of the entire technical structure. The local normalization of the distortions of the portraits of oscillations is utilized to establish the locations of the gaps in the mechanical parts and structural connections. The ground vibration tests were carried out via Test.Lab software. The subprogram is integrated into the software interface in order to analyze the portraits of oscillations. It enabled one to calculate the distortions of the portraits of oscillations, plot the distortion distributions of the structure and save it for further use. It allowed one to control the gaps during vibration strength tests, as well as while the structures being used, by means of comparing the distortion distributions of the parameter ξ related to different states of the structure. Additionally, the plotting of the distortion distributions of the portraits of oscillations for each structural component is added to the subprogram so as to control the defects subsequently. Not only the locations of the gaps are determined in the force-displacement application systems but also the equation is given to calculate its magnitudes. The practical recommendations on using that equation are presented. Results and Discussion. The possibility of detecting the gaps by the distortions of the portraits of oscillations is illustrated with the example of the diagnostics of the layout of the control wiring and the airplanes during the ground vibration testing as well as the open-type spacecraft structures. It is shown that the developed method enables one to detect all the gaps in the testing object which distort the portraits of oscillations.

UAV Photogrammetry under Poor Lighting Conditions—Accuracy Considerations

The use of low-level photogrammetry is very broad, and studies in this field are conducted in many aspects. Most research and applications are based on image data acquired during the day, which seems natural and obvious. However, the authors of this paper draw attention to the potential and possible use of UAV photogrammetry during the darker time of the day. The potential of night-time images has not been yet widely recognized, since correct scenery lighting or lack of scenery light sources is an obvious issue. The authors have developed typical day- and night-time photogrammetric models. They have also presented an extensive analysis of the geometry, indicated which process element had the greatest impact on degrading night-time photogrammetric product, as well as which measurable factor directly correlated with image accuracy. The reduction in geometry during night-time tests was greatly impacted by the non-uniform distribution of GCPs within the study area. The calibration of non-metric cameras is sensitive to poor lighting conditions, which leads to the generation of a higher determination error for each intrinsic orientation and distortion parameter. As evidenced, uniformly illuminated photos can be used to construct a model with lower reprojection error, and each tie point exhibits greater precision. Furthermore, they have evaluated whether commercial photogrammetric software enabled reaching acceptable image quality and whether the digital camera type impacted interpretative quality. The research paper is concluded with an extended discussion, conclusions, and recommendation on night-time studies.

Measuring the Hubble function with standard candle clustering

Supernova Ia magnitude surveys measure the dimensionless luminosity distance H0DL. However, from the distances alone one cannot obtain quantities like H(z) or the dark energy equation of state, unless further cosmological assumptions are imposed. Here we show that by measuring the power spectrum of density contrast and of peculiar velocities of supernovae one can estimate also H(z)/H0 regardless of background or linearly perturbed cosmology and of galaxy-matter bias. This method, dubbed Clustering of Standard Candles (CSC) also yields the redshift distortion parameter β(k, z) and the biased matter power spectrum in a model-independent way. We forecast that an optimistic (pessimistic) LSST may be able to constrain H(z)/H0 to 5–13% (9–40%) in redshift bins of Δz = 0.1 up to at least z = 0.6.

Magnetic Normal Mode Calculations in Big Systems: A Highly Scalable Dynamical Matrix Approach Applied to a Fibonacci-Distorted Artificial Spin Ice

We present a new formulation of the dynamical matrix method for computing the magnetic normal modes of a large system, resulting in a highly scalable approach. The motion equation, which takes into account external field, dipolar and ferromagnetic exchange interactions, is rewritten in the form of a generalized eigenvalue problem without any additional approximation. For its numerical implementation several solvers have been explored, along with preconditioning methods. This reformulation was conceived to extend the study of magnetization dynamics to a broader class of finer-mesh systems, such as three-dimensional, irregular or defective structures, which in recent times raised the interest among researchers. To test its effectiveness, we applied the method to investigate the magnetization dynamics of a hexagonal artificial spin-ice as a function of a geometric distortion parameter following the Fibonacci sequence. We found several important features characterizing the low frequency spin modes as the geometric distortion is gradually increased.

Effect of the ionic radius on structural properties of orthochromites RCrO3 (R = La, Gd, Y)

The main objective of this work was to detail out how to obtain important parameters in the structural analysis of materials with perovskite structure in order to help beginning researchers in this area. In particular, a thorough comparative and investigative study of the effect of ionic radius on the structural properties of orthochromites RCrO3 (R = La, Gd, Y) were presented. It is observed that the b and c lattice parameters increased, whereas a lattice parameter decreased as the ionic radius increased. Consequently, an increase in the unit-cell volume and tolerance factor was observed. The angles and bond lengths increased with an increase in the ionic radius, albeit the inclination angle, as well as the rotation angle, tends to decrease. The distortion parameter suffered a fluctuation in its value according to the increasing ionic radius. Lastly, Williamson-Hall (W-H) analysis caused a decrement in the strain according to decreasing ionic radius.

OctaDist: a tool for calculating distortion parameters in spin crossover and coordination complexes

OctaDist, a program for calculating three common octahedral distortion parameters, is presented and the calculation of the trigonal distortion parameter, Θ is standardized for the first time.