Coefficient Space Research Articles

Stability Region for Discrete Time Systems and Its Boundary

MSC: 11C08, 52B11, 93D05 DOI: 10.21538/0134-4889-2021-27-3-246-255 In this paper we investigate the Schur stability region of the $n$th order polynomials in the coefficient space. Parametric description of the boundary set is obtained. We show that all the boundary can be obtained as a multilinear image of three $(n-1)$-dimensional boxes. For even and odd $n$ these boundary

Type 0 ℤ2 × ℤ2 heterotic string orbifolds and misaligned supersymmetry

The [Formula: see text] heterotic string orbifold yielded a large space of phenomenological three generation models and serves as a testing ground to explore how the Standard Model of particle physics may be incorporated in a theory of quantum gravity. In this paper, we explore the existence of type 0 models in this class of string compactifications. We demonstrate the existence of type 0 [Formula: see text] heterotic string orbifolds, and show that there exist a large degree of redundancy in the space of GGSO projection coefficients when the type 0 restrictions are implemented. We explore the existence of such configurations in several constructions. The first correspond to essentially a unique configuration out of a priori [Formula: see text] discrete GGSO choices. We demonstrate this uniqueness analytically, as well as by the corresponding analysis of the partition function. A wider classification is performed in [Formula: see text]-models and [Formula: see text]-models, where the first class correspond to compactifications of a tachyonic ten-dimensional heterotic string vacuum, whereas the second correspond to compactifications of the ten-dimensional nontachyonic [Formula: see text]. We show that the type 0 models in both cases contain physical tachyons at the free fermionic point in the moduli space. These vacua are therefore necessarily unstable, but may be instrumental in exploring the string dynamics in cosmological scenarios. We analyze the properties of the string one-loop amplitude. Naturally, these are divergent due to the existence of tachyonic states. We show that once the tachyonic states are removed by hand the amplitudes are finite and exhibit a form of misaligned supersymmetry.

Efficacy of the Method of Four Coefficients to Determine Charge-Carrier Scattering

The investigation of the electronic properties of semiconductors is inherently challenging due to the ensemble averaging of fundamentals to transport measurements (i.e., resistivity, Hall, and Seebeck coefficient measurements). Here, we investigate the incorporation of a fourth measurement of electronic transport, the Nernst coefficient, into the analysis, termed the method of four-coefficients. This approach yields the Fermi level, effective mass, scattering exponent, and relaxation time. We begin with a review of the underlying mathematics and investigate the mapping between the four-dimensional material property and transport coefficient spaces. We then investigate how the traditional single parabolic band method yields a single, potentially incorrect point on the solution sub-space. This uncertainty can be resolved through Nernst coefficient measurements and we map the span of the ensuing sub-space. We conclude with an investigation of how sensitive the analysis of transport coefficients is to experimental error for different sample types.

A fast regression via SVD and marginalization

We describe a numerical scheme for evaluating the posterior moments of Bayesian linear regression models with partial pooling of the coefficients. The principal analytical tool of the evaluation is a change of basis from coefficient space to the space of singular vectors of the matrix of predictors. After this change of basis and an analytical integration, we reduce the problem of finding moments of a density over \(k + 2\) dimensions, to finding moments of a 2-dimensional density, where k is the number of coefficients. Moments can then be computed using, for example, MCMC, the trapezoid rule, or adaptive Gaussian quadrature. An evaluation of the SVD of the matrix of predictors is the dominant computational cost and is performed once during the precomputation stage. We demonstrate numerical results of the algorithm.

Preservation of external positivity in discretization of linear systems

We study the preservation of impulse response non-negativity, also known as external positivity, for general discretization methods. The results yield new subsets in the space of transfer function coefficients which ensure external positivity. Consequently, linear programming approaches for designing controllers ensuring monotonic step responses are derived for both continuous and discrete-time systems.

Extremal effective field theories

Effective field theories (EFT) parameterize the long-distance effects of short-distance dynamics whose details may or may not be known. Previous work showed that EFT coefficients must obey certain positivity constraints if causality and unitarity are satisfied at all scales. We explore those constraints from the perspective of 2 → 2 scattering amplitudes of a light real scalar field, using semi-definite programming to carve out the space of allowed EFT coefficients for a given mass threshold M. We point out that all EFT parameters are bounded both below and above, effectively showing that dimensional analysis scaling is a consequence of causality. This includes the coefficients of s2 + t2 + u2 and stu type interactions. We present simple 2 → 2 extremal amplitudes which realize, or “rule in”, kinks in coefficient space and whose convex hull span a large fraction of the allowed space.

Difference Schemes for a Drain Transfer Equation Based on Analysis in the Space of Undefined Coefficients

Difference Schemes for a Drain Transfer Equation Based on Analysis in the Space of Undefined Coefficients

Effect of La2Li0.5Co0.5O4 in semiconductive nanocomposites on suppression of space charge injection to the insulating medium for high-voltage direct current cables

Space charge accumulation in the insulating layers of high-voltage direct current cables is a key factor in the degradation of such cables and limits their operational safety. It is necessary to weaken charge injection to the insulation. The semiconductive shielding layer sandwiched between the conductive core and the insulating layer plays a vital role in preventing carrier injecting into the insulation. In this study, a new method is proposed to suppress charge injection. A certain amount of La2Li0.5Co0.5O4 nanopowder was doped in the semiconductive screen to enhance the internal conductive network and block charge injection in the insulation. The influence of La2Li0.5Co0.5O4 in the nanocomposite on the positive temperature coefficient effect and space charge injection process were explored. The results revealed that the peak resistivity of the specimen containing 5 wt% La2Li0.5Co0.5O4 decreased by 50.5% compared to the composites without La2Li0.5Co0.5O4, and charge quantity in the insulating layer was reduced by 41.2%.

Efficient sliding locomotion of three-link bodies.

We study the efficiency of sliding locomotion for three-link bodies with prescribed joint angle motions. The bodies move with no inertia, under dry (Coulomb) friction that is anisotropic (different in the directions normal and tangent to the links) and directional (different in the forward and backward tangent directions). Friction coefficient space can be partitioned into several regions, each with distinct types of efficient kinematics. These include kinematics resembling lateral undulation with very anisotropic friction, small-amplitude reciprocal kinematics, very large-amplitude kinematics near isotropic friction, and kinematics that are very asymmetric about the flat state. In the two-parameter shape space, zero net rotation for elliptical trajectories occurs mainly with bilateral or antipodal symmetry. These symmetric subspaces have about the same peak efficiency as the full space but with much smaller dimension. Adding the second or third harmonics greatly increases the numbers of local optimal for efficiency, but only modestly increases the peak efficiency. Random ensembles with higher harmonics have efficiency distributions that peak near a certain nonzero value and decay rapidly up to the maximum efficiency. A stochastic optimization algorithm is developed to compute optima with higher harmonics. These are simple closed curves, sharpened versions of the elliptical optima in most cases, and achieve much higher efficiencies mainly for small normal friction. With a linear (viscous) resistance law, the optimal trajectories are similar in much of the friction coefficient space, and relative efficiencies are much lower except with very large normal friction.

Genetic origin and climate determine fruit quality and antioxidant traits on apple (Malus x domestica Borkh)

Apples are highly appreciated in terms of flavor, nutritional and health-promoting compounds and are associated with a reduced risk to develop age-related and chronic diseases. In this study, 155 accessions of Malus x domestica Borkh from the apple germplasm collection, located at the Experimental Station of Aula Dei in NE Spain, were analyzed during five consecutive years (2014–2018). Basic fruit quality traits including soluble solids content (SSC), titratable acidity (TA) and the ratio SSC/TA (ripening index - RI) were obtained. In addition, biochemical compounds such as total phenolics content (TPC), flavonoids (TFC), vitamin C (Ascorbic acid - AsA) and relative antioxidant capacity (RAC) were determined. Statistical analysis was used to determine differences in trait values among accessions and years. The well adapted local accessions showed, in general, higher average content of antioxidants and RAC compared with the foreign and commercial ones. A multivariate model was fitted with the accessions and climate features of each year as independent variables. A cluster analysis was then performed on the model coefficients space to classify the 155 accessions within five groups. The cluster analysis showed that foreign cultivars (those not originating from Spain) were concentrated in two groups while local accessions could not be segregated and had very different profiles. Furthermore, they increased the concentration of bioactive compounds tended to decrease with higher temperatures, while increased with higher solar radiation. Statistical analyses emphasized differences between groups and highlighted accessions and climate as main factors affecting metabolite profiles and fruit characteristics.

Synthesis of Automatic Control for Plane-Type UAV Landing and Stability Analysis of Desired Motion Regimes

This paper is concerned with small UAV (unmanned aerial vehicle) control algorithm development during landing. The UAV landing problem for small UAVs (less than 20 kg) remains actual despite the great amount of books, papers, and monographs devoted to this topic. In this paper, a model with V-shaped keel is under consideration. Mechanization of such a vehicle consists of flaperons and ailerons. To describe a flight, a system of nonlinear differential equations is developed. The automatic control both for longitudinal and lateral motion as well as for thrust is designed. The stability analysis of the controlled system is conducted by plotting stability regions in the space of the feedback coefficients. The results of a numerical modeling of a flight with external disturbances are given.

Shift-type SMEFT effects in dileptons at the LHC

We explore the constraints which can be derived on Wilson coefficients in the Standard Model Effective Field Theory from dilepton production, notably including the constraints on operators which do not lead to cross sections growing with energy relative to the Standard Model rate, i.e. shifts. We incorporate essential theory error estimates from higher EFT orders in the analysis in order to provide robust bounds. We find that constraints on four-fermion operator contributions which do grow with energy are not materially weakened by the inclusion of these shifts, and that a constraint on the shifts can also be derived, with a characteristic strength comparable to, and a directionality in parameter space complementary to, those from LEP data. This completes the study of hadronically-quiet dilepton production in the SMEFT, and provides two new constraints which are linearly independent from others arising at the LHC and also rotated in Wilson coefficient space relative to, though not completely independent from, the LEP bounds.

The Hilbert Space of Double Fourier Coefficients for an Abstract Wiener Space

Fourier series is a well-established subject and widely applied in various fields. However, there is much less work on double Fourier coefficients in relation to spaces of general double sequences. We understand the space of double Fourier coefficients as an abstract space of sequences and examine relationships to spaces of general double sequences: p-power summable sequences for p = 1, 2, and the Hilbert space of double sequences. Using uniform convergence in the sense of a Cesàro mean, we verify the inclusion relationships between the four spaces of double sequences; they are nested as proper subsets. The completions of two spaces of them are found to be identical and equal to the largest one. We prove that the two-parameter Wiener space is isomorphic to the space of Cesàro means associated with double Fourier coefficients. Furthermore, we establish that the Hilbert space of double sequence is an abstract Wiener space. We think that the relationships of sequence spaces verified at an intermediate stage in this paper will provide a basis for the structures of those spaces and expect to be developed further as in the spaces of single-indexed sequences.

Completeness and complementarity for \u03bc \u2192 e\u03b3, \u03bc \u2192 eoverline{e}e and \u03bcA \u2192 eA

Lepton Flavour Violation (LFV) is New Physics that must occur, but is stringently constrained by experiments searching for μ ↔ e flavour change, such as μ → eγ, μ → eoverline{e}e or μ → e conversion. However, in an Effective Field Theory(EFT) parametrisation, there are many more μ ↔ e operators than restrictive constraints, so determining operator coefficients from data is a remote dream. It is nonetheless interesting to learn about New Physics from data, so this manuscript introduces “observable-vectors” in the space of operator coefficients, which identify at any scale the combination of coefficients probed by the observable. These vectors have an overlap ≳ 10−3 with most of the coefficients, and are used to study whether μ → eγ, μ → eoverline{e}e and μ → e conversion give complementary information about New Physics. The appendix gives updated sensitivities of these processes, (and a subset of τ → ℓ decays), to operator coefficients at the weak scale in the SMEFT and in the EFT below mW.

New in situ aerosol hyperspectral optical measurements over 300–700 nm – Part 1: Spectral Aerosol Extinction (SpEx) instrument field validation during the KORUS-OC cruise

Abstract. In situ observations of spectrally resolved aerosol extinction coefficients (300–700 nm at ∼ 0.8 nm resolution) from the May–June 2016 Korea–United States Ocean Color (KORUS-OC) oceanographic field campaign are reported. Measurements were made with the custom-built Spectral Aerosol Extinction (SpEx) instrument that previously has been characterized only using laboratory-generated aerosols of known size and composition. Here, the performance of SpEx under realistic operating conditions in the field was assessed by comparison to extinction coefficients derived from commercial instruments that measured scattering and filter-based absorption coefficients at three discrete visible wavelengths. Good agreement was found between these two sets of extinction coefficients with slopes near unity for all three wavelengths within the SpEx measurement error (± 5 Mm−1). The meteorological conditions encountered during the cruise fostered diverse ambient aerosol populations with varying sizes and composition at concentrations spanning 2 orders of magnitude. The sampling inlet had a 50 % size cut of 1.3 µm diameter particles such that the in situ aerosol sampling suite deployed aboard ship measured fine-mode aerosols only. The extensive hyperspectral extinction data set acquired revealed that nearly all measured spectra exhibited curvature in logarithmic space, such that Ångström exponent (α) power law fits could lead to large errors compared to measured values. This problem was particularly acute for α values calculated over only visible wavelengths and then extrapolated to the UV, highlighting the need for measurements in this wavelength range. Second-order polynomial fits to the logarithmically transformed data provided a much better fit to the measured spectra than the linear fits of power laws. Building on previous studies that used total column aerosol optical depth observations to examine the information content of spectral curvature, the relationship between α and the second-order polynomial fit coefficients (a1 and a2) was found to depend on the wavelength range of the spectral measurement such that any given α maps into a line in (a1, a2) coefficient space with a slope of −2LN(λch), where λch is defined as the single wavelength that characterizes the wavelength range of the measured spectrum (i.e., the “characteristic wavelength”). Since the curvature coefficient values depend on λch, it must be taken into account when comparing values from spectra obtained from measurement techniques with different λch. Previously published work has shown that different bimodal size distributions of aerosols can exhibit the same α yet have differing spectral curvature with different (a1, a2). This implies that (a1, a2) contain more information about size distributions than α alone. Aerosol size distributions were not measured during KORUS-OC, and the data reported here were limited to the fine fraction, but the (a1, a2) maps obtained from the SpEx data set are consistent with the expectation that (a1, a2) may contain more information than α – a result that will be explored further with future SpEx and size distribution data sets.

Принципы построения программно-аппаратного комплекса для интеллектуальной поддержки экипажа и оценки уровня его подготовки

Presented is a new approach to aircraft crew intelligent support, which is based on comparing flight fragments (maneuvers) under study with the relevant patterns contained in the database and representing the system “empirical intelligence”. Principal components of this approach are four new metrics for comparing flight fragments, viz.: the Euclidean metric in the space of wavelet coefficients; the likelihood metric of eigenvalue trajectories for transformations of activity parameters; the Kohonen metric in the space of wavelet coefficients; the likelihood metric for comparing gaze trajectories. Features of the presented approach are: the presence of an “intelligent component” that is contained in empirical data and can be flexibly changed as they accumulate; the use of integral comparisons of the flight fragments under study and video oculography data with relevant patterns of various types and performance quality from a specialized database, with transferring characteristics of the nearest pattern from this specialized database to the fragment under study; applying a complex combination of the methods for stochastic processes analysis and multivariate statistical techniques.

МЕТОДИКА ИЗМЕРЕНИЯ КОМПЛЕКСНЫХ ОТРАЖЕНИЙ НАГРУЗОК ТРАНЗИСТОРА НА ИМИТАТОРЕ-АНАЛИЗАТОРЕ УСИЛИТЕЛЕЙ И АВТОГЕНЕРАТОРОВ СВЧ

The article considers a simulator/analyzer that provides simulation modeling of microwave ampli-fiers and oscillators in accordance with their technical specifications, followed by the measurement of complex load reflection coefficients of the active component of these devices for their design. It also considers a method of measurement of these parameters and a method of calibration of the simula-tor/analyzer providing transfer of measurement results from the coaxial measuring line of the simula-tor-analyzer to the microstrip line. In addition, the article considers a method for analyzing the stability of the active component in the space of complex reflection coefficients of its loads, which facilitates their selection in the simulation of amplifiers and oscillators.

Matrix Relevance Learning From Spectral Data for Diagnosing Cassava Diseases

We discuss the use of matrix relevance learning, a popular extension to prototype learning algorithms, applied to a three-class classification task of diagnosing cassava diseases from spectral data. Previously this diagnosis has been done using plant image data taken with a smartphone. However for this method disease symptoms need to be visible. Unfortunately for some cassava diseases, once symptoms have manifested on the aerial part of the plant, the root which is the edible part of the plant has been totally destroyed. This research is premised on the hypothesis that diseased crops without visible symptoms can be detected using spectral information, allowing for early interventions. In this paper, we analyze visible and near-infrared spectra captured from leaves infected with two common cassava diseases (cassava brown streak disease and cassava mosaic virus disease) found in Sub-Saharan Africa. We also take spectra from leaves of healthy plants. The spectral data come with thousands of dimensions, therefore different wavelengths are analyzed in order to identify the most relevant spectral bands for diagnosing these disease. To cope with the nominally high number of input dimensions of data, functional decomposition of the spectra is applied. The classification task is addressed using Generalized Matrix Relevance Learning Vector Quantization and compared with the standard classification techniques performed in the space of expansion coefficients.

The system ErNiAl–ZrNiAl at 600 °С and the high-temperature high-pressure modification of ErNiAl

A series of samples along the line ErNiAl–ZrNiAl was synthesized by arc-melting, and annealed at 600 °C or at 1400 °C / 8 GPa. Phase and structural analyses were performed based on X-ray powder diffraction data collected at room temperature on a diffractometer STOE Stadi P (Cu K α 1 radiation, angular range 6° ≤ 2 θ ≤ 110°, scan step 0.015°). The structures were refined by the Rietveld method, using the program DBWS. The formation of limited solid solutions Er 1-0.79(4) Zr 0-0.21(4) NiAl and Zr 1-0.77(3) Er 0-0.23(3) NiAl, which both crystallize with ZrNiAl-type structures, was observed. It was found that high-temperature high-pressure annealing of the three-component (ErNiAl) and four-component (Er 2 ZrNi 3 Al 3 ) samples caused a transformation from the low-temperature modification of the compound ErNiAl with ZrNiAl-type structure to its high-temperature high-pressure modification with MgZn 2 -type structure. The latter showed low solubility of Zr (Er 0.91(3) Zr 0.09(3) NiAl). The structure of ht-hp ErNiAl (MgZn 2 -type) belongs to the family of Friauf-Laves phases: the coordination polyhedra of the Er atoms are 16-vertex Friauf polyhedra, and those of the Ni and Al atoms are 12-vertex icosahedra. The structure of the solid solutions Er 1- x Zr x NiAl and Zr 1- x Er x NiAl (ZrNiAl-type structure) belongs to the family of structures with trigonal prismatic coordination of the smallest atoms (Ni). The structures of the investigated compounds contain similar nets of atoms, in particular nets of triangles and pentagons. They are characterized by high packing coefficients (space filling), which reach 82 %. The highest value was observed for the compound ErNiAl in the sample annealed at 1400 °C / 8 GPa. It may be noted that high pressures generally increase the density, whereas high temperatures have the opposite effect. Key words : aluminide, X-ray powder diffraction, solid solution, crystal structure.

Elastic positivity vs extremal positivity bounds in SMEFT: a case study in transversal electroweak gauge-boson scatterings

The positivity bounds, derived from the axiomatic principles of quantum field theory (QFT), constrain the signs of Wilson coefficients and their linear combinations in the Standard Model Effective Field Theory (SMEFT). The precise determination of these bounds, however, can become increasingly difficult as more and more SM modes and oper- ators are taken into account. We study two approaches that aim at obtaining the full set of bounds for a given set of SM fields: 1) the traditional elastic positivity approach, which exploits the elastic scattering amplitudes of states with arbitrarily superposed helicities as well as other quantum numbers, and 2) the newly proposed extremal positivity approach, which constructs the allowed coefficient space directly by using the extremal representation of convex cones. Considering the electroweak gauge-bosons as an example, we demonstrate how the best analytical and numerical positivity bounds can be obtained in several ways. We further compare the constraining power and the efficiency of various approaches, as well as their applicability to more complex problems. While the new extremal approach is more constraining by construction, we also find that it is analytically easier to use, nu- merically much faster than the elastic approach, and much more applicable when more SM particle states and operators are taken into account. As a byproduct, we provide the best positivity bounds on the transversal quartic-gauge-boson couplings, required by the axiomatic principles of QFT, and show that they exclude ≈ 99.3% of the parameter space currently being searched at the LHC.