Relative Invariants Research Articles

Manipulating the consequences of tests: how Shanghai teens react to different consequences

ABSTRACT Students’ test-taking motivation has been found to be a predictor of performance. This study tests whether Shanghai students’ conceptions of tests and test-taking motivation differ when the consequence of tests have different foci (i.e., none, country, or personal). A between-subjects experiment with vignette instructions systematically assigned 1,003 Shanghai senior secondary school students to one of the three vignettes. Students’ conceptions of tests and test-taking motivation scales were evaluated using factor analyses. Invariance testing suggested invariant relationships between the two constructs across the three groups. Students’ general conception of tests meaningfully predicted their reported effort (β = .18). Latent mean analyses suggested that students’ reported effort, anxiety, and importance were not significantly different between country at stakes and personal stakes groups, but higher than when no consequences were attached. This study suggests that Shanghai students’ test-taking attitudes may contribute to high effort and consequently high performance on international large-scale assessments.

Parameter Estimation for Two-Dimensional Incoherently Distributed Source with Double Cross Arrays.

A direction of arrival (DOA) estimator for two-dimensional (2D) incoherently distributed (ID) sources is presented under proposed double cross arrays, satisfying both the small interval of parallel linear arrays and the aperture equalization in the elevation and azimuth dimensions. First, by virtue of a first-order Taylor expansion for array manifold vectors of parallel linear arrays, the received signal of arrays can be reconstructed by the products of generalized manifold matrices and extended signal vectors. Then, the rotating invariant relations concerning the nominal elevation and azimuth are derived. According to the rotating invariant relationships, the rotating operators are obtained through the subspace of the covariance matrix of the received vectors. Last, the angle matching approach and angular spreads are explored based on the Capon principle. The proposed method for estimating the DOA of 2D ID sources does not require a spectral search and prior knowledge of the angular power density function. The proposed DOA estimation has a significant advantage in terms of computational cost. Investigating the influence of experimental conditions and angular spreads on estimation, numerical simulations are carried out to validate the effectiveness of the proposed method. The experimental results show that the algorithm proposed in this paper has advantages in terms of estimation accuracy, with a similar number of sensors and the same experimental conditions when compared with existing methods, and that it shows a robustness in cases of model mismatch.

The education-chasing labor rush in China identified by a heterogeneous migration-network game

Despite persistent efforts in understanding the motives and patterns of human migration behaviors, little is known about the microscopic mechanism that drives migration and its association with migrant types. To fill the gap, we develop a population game model in which migrants are allowed to be heterogeneous and decide interactively on their destination, the resulting migration network emerges naturally as an Nash equilibrium and depends continuously on migrant features. We apply the model to Chinese labor migration data at the current and expected stages, aiming to quantify migration behavior and decision mode for different migrant groups and at different stages. We find the type-specific migration network differs significantly for migrants with different age, income and education level, and also differs from the aggregated network at both stages. However, a deep analysis on model performance suggests a different picture, stability exists for the decision mechanism behind the “as-if” unstable migration behavior, which also explains the relative invariance of low migration efficiency in different settings. Finally, by a classification of cities from the estimated game, we find the richness of education resources is the most critical determinant of city attractiveness for migrants, which gives hint to city managers in migration policy design.

On the Paradoxical Impact of Blending by Red Clump Giants

Abstract The impact of blending by red clump giants (RCGs; or relatively metal-rich red horizontal branch stars) is discussed as it relates to RRab and classical Cepheids, and invariably establishing an improved distance scale. An analysis of Magellanic Cloud variables reaffirms that blending with RCGs may advantageously thrust remote extragalactic stars into the range of detectability. Specifically, simulations of Magellanic Cloud RRab and RCG blends partly reproduce bright non-canonical trends readily observed in amplitude–magnitude space (I c versus A I c ). Conversely, the larger magnitude offset between classical Cepheids and RCGs causes the latter’s influence to be challenging to address. The relative invariance of a Wesenheit function’s slope to metallicity (e.g., W VI c ) implies that a deviation from the trend could reveal blending and photometric inaccuracies (e.g., standardization), as blending by RCGs (a proxy of an evolved red stellar demographic) can flatten period-Wesenehit relations owing to the increased impact on less-luminous shorter-period Cepheids. That could partly explain both a shallower inferred Wesenheit function and overestimated H 0 values. A consensus framework to identify and exploit blending is desirable, as presently H 0 estimates from diverse teams are unwittingly leveraged without homogenizing the disparate approaches (e.g., no blending correction to a sizable ≃ 0 .ͫ 3 ).

Surgery on links of linking number zero and the Heegaard Floer $d$-invariant

We study Heegaard Floer homology and various related invariants (such as the h -function) for two-component L-space links with linking number zero. For such links, we explicitly describe the relationship between the h -function, the Sato–Levine invariant and the Casson invariant. We give a formula for the Heegaard Floer d -invariants of integral surgeries on two-component L-space links of linking number zero in terms of the h -function, generalizing a formula of Ni and Wu. As a consequence, for such links with unknotted components, we characterize L-space surgery slopes in terms of the \nu^{+} -invariants of the knots obtained from blowing down the components. We give a proof of a skein inequality for the d -invariants of +1 surgeries along linking number zero links that differ by a crossing change. We also describe bounds on the smooth four-genus of links in terms of the h -function, expanding on previous work of the second author, and use these bounds to calculate the four-genus in several examples of links.

Problematic Internet Use Questionnaire-Short Form-6 (PIUQ-SF-6): Dimensionality, validity, reliability, measurement invariance and mean differences across genders and age categories among Nigerian adolescents

The objectives of this study were to evaluate the psychometric properties, measurement invariance and mean differences in relation to the genders and age categories of the 6-item PIUQ-SF in a non-clinical sample of Nigerian adolescents (n = 1222; Mage = 15.77; Range = 12–18). There were 622 (50.9%) females. Most (79.1%) were in the middle adolescent age bracket. The respondents completed the PIUQ-SF-6 in addition to the Hospital Anxiety and Depression Scale (HADS) and the Drug Abuse Screening Test (DAST). We applied confirmatory factor analysis (CFA) to examine the fit indices of the three-factor a priori PIUQ-SF-6 model described in literature. Measurement invariances across genders and age categories were evaluated with nested multiple-group CFA (MGCFA). The three-dimensional model of the PIUQ-SF-6 appears to satisfactorily evaluate problematic usage of the internet among Nigerian adolescents (CFI = 0.985, SRMR = 0.0214, RMSEA = 0.055/90% CI = 0.036–0.077). The internal consistencies (α) of the PIUQ-SF-6 and its three subscales were modestly satisfactory. The concurrent validity of this model was also modestly supported via significant correlations with the other study measures. MGCFA supported the configural, metric and scalar measurement invariances of the PIUQ-SF-6 across genders and age categories. Males and those in the late adolescent age category have significant higher scores on the total PIUQ-SF-6. The PIUQ-SF-6 will be a useful instrument for the quantitative evaluation and comparisons of problematic usage of the internet among Nigerian adolescents.

An Exploration of Link Functions Used in Ordinal Regression

The purpose of this study is to examine issues involved with choice of a link function in generalized linear models with ordinal outcomes, including distributional appropriateness, link specificity, and palindromic invariance are discussed and an exemplar analysis provided using the Pew Research Center 25th anniversary of the Web Omnibus Survey data. Simulated data are used to compare the relative palindromic invariance of four distinct indices of determination/discrimination, including a newly proposed index by Smith et al. (2017).

Symplectic cohomology rings of affine varieties in the topological limit

We construct a multiplicative spectral sequence converging to the symplectic cohomology ring of any affine variety X, with first page built out of topological invariants associated to strata of any fixed normal crossings compactification $$(M,{\mathbf {D}})$$ of X. We exhibit a broad class of pairs $$(M,{\mathbf {D}})$$ (characterized by the absence of relative holomorphic spheres or vanishing of certain relative GW invariants) for which the spectral sequence degenerates, and a broad subclass of pairs (similarly characterized) for which the ring structure on symplectic cohomology can also be described topologically. Sample applications include: (a) a complete topological description of the symplectic cohomology ring of the complement, in any projective M, of the union of sufficiently many generic ample divisors whose homology classes span a rank one subspace, (b) complete additive and partial multiplicative computations of degree zero symplectic cohomology rings of many log Calabi-Yau varieties, and (c) a proof in many cases that symplectic cohomology is finitely generated as a ring. A key technical ingredient in our results is a logarithmic version of the PSS morphism, introduced in our earlier work Ganatra and Pomerleano, arXiv:1611.06849.

Types of proportional reasoning of seventh grade junior high school students in Jombang

This research is a descriptive qualitative research that aims to describe the type of proportional reasoning of students. The research subjects were seventh grade students of SMP in Jombang Regency. The subject selection procedure is by purposive sampling. Data collection is done by means of tests, think aloud methods and semi-structured interviews. Data validity uses time triangulation. Data analysis techniques are carried out by: (1) grouping data in 4 categories, then reducing data not included in the 4 categories, (2) presenting data in narrative texts, and (3) concluding the type of proportional reasoning students then comparing subjects that are on the same type of proportional reasoning. Based on research conducted on 150 subjects of class VII SMP in Jombang regency, there were 62 students using cross multiplication, 30 students used additive reasoning, 45 students used multiplicative reasoning and 13 students used a mix of additive and multiplicative reasoning. Additive reasoning, the way the subject does it is to add one by one to many caterpillars associated with many leaves. In determining the missing value, the subject uses multiplicative reasoning by determining the scalar number first. Subjects with a mix of additive and multiplicative reasoning use numerical calculations and use images to reason problems. Cross multiplication, Subjects use the concept of comparable value by specifying unknown elements with a variable. Although not all subjects use formal reasoning (cross multiplication) in completing, but the reasoning of class VII students shows that it includes relative reasoning. They don’t just pair numbers with numbers. Although, there are subjects who do not fully understand invariant and covariant relationships

Relative Quasimaps and Mirror Formulae

Abstract We construct and study the theory of relative quasimaps in genus zero, in the spirit of Gathmann. When $X$ is a smooth toric variety and $Y$ is a smooth very ample hypersurface in $X$, we produce a virtual class on the moduli space of relative quasimaps to $(X,Y)$, which we use to define relative quasimap invariants. We obtain a recursion formula which expresses each relative invariant in terms of invariants of lower tangency, and apply this formula to derive a quantum Lefschetz theorem for quasimaps, expressing the restricted quasimap invariants of $Y$ in terms of those of $X$. Finally, we show that the relative $I$-function of Fan–Tseng–You coincides with a natural generating function for relative quasimap invariants, providing mirror-symmetric motivation for the theory.

Relative spectral invariants of elliptic operators on manifolds

We introduce and study new relative spectral invariants of two elliptic partial differential operators of Laplace and Dirac type on compact smooth manifolds without boundary that depend on both the eigenvalues and the eigensections of these operators and contain much more information about geometry. We prove the existence of the homogeneous short time asymptotics of the new invariants with the coefficients of the asymptotic expansion being integrals of some invariants that depend on the symbols of both operators. The first two coefficients of the asymptotic expansion are computed explicitly.

A real-time semantic visual SLAM approach with points and objects

Visual simultaneously localization and mapping (SLAM) is important for self-localization and environment perception of service robots, where semantic SLAM can provide a more accurate localization result and a map with abundant semantic information. In this article, we propose a real-time PO-SLAM approach with the combination of both point and object measurements. With point–point association in ORB-SLAM2, we also consider point–object association based on object segmentation and object–object association, where the object segmentation is employed by combining object detection with depth histogram. Also, besides the constraint of feature points belonging to an object, a semantic constraint of relative position invariance among objects is introduced. Accordingly, two semantic loss functions with point and object information are designed and added to the bundle adjustment optimization. The effectiveness of the proposed approach is verified by experiments.

Electrophysical Properties of Epoxy Composite Materials Filled with Carbon Black Nanopowder

The effect of carbon black (CB) nanopowder on the electrical properties of polymer composite systems based on the epoxy resin is investigated using the method of impedance spectroscopy. It is established that the electrical and dielectric properties of the studied systems significantly depend on the nanofiller content. It is found that electrical conductivity and dielectric constant exhibit percolation behavior when the filler’s content increases. In this case, the electrical conductivity increases exponentially, indicating the formation of filler electrically conductive mesh inside the polymer matrix. A small jump in electrical conductivity when reaching the percolation threshold indicates the formation of indirect contacts between the particles. The value of the percolation threshold of conductivity is 8%. It is shown that the dielectric constant of epoxy nanosystems is almost unchanged in the frequency range of 102–105 Hz. It is related to the structural features of the filler particles, which ensure the existence of a minimal dielectric gradient between the matrix and the filler. It is found that the dielectric constant of the studied systems also shows percolation behavior. The obtained material based on the epoxy matrix is characterized by a high value of dielectric constant, which at a carbon black nanopowder content of 29% is 4680. This material is characterized by relative frequency invariance and a high value of dielectric constant, so it has great potential for practical application.

On a micropolar theory of growing solids

Обсуждается принцип вывода граничных условий в краевых задачах механики растущих микрополярных тел. Приводится вывод уравнений динамики микрополярного континуума в терминах относительных тензоров для тел постоянного состава. Указана определяющая квадратичная форма упругого потенцила (абсолютного скаляра) для линейного гемитропного микрополярного тела. Выведены определяющие соотношения для симметричных и антисимметричных частей тензоров силовых и моментных напряжений. Получены конечные формы уравнений динамики гемитропного микрополярного континуума в терминах скоростей перемещений и микровращений. Полученные динамические уравнения для тел постоянного состава остаются справедливыми и в теориях растущих тел. Предложена процедура преобразования уравнений равновесия для получения граничных условий на поверхности наращивания в терминах относительных тензоров в форме дифференциальных ограничений. Полученные условия справедливы для весьма широкого круга материалов и метаматериалов. При выводе определяющих соотношений на поверхности наращивания активно используется аппарат алгебры рациональных относительных инвариантов. Получены полные системы совместных относительных инвариантов для тензоров силовых, моментных напряжений и единичного вектора нормали, в том числе системы инвариантов, не выдерживающие зеркальных отражений.

Identification of fingers on the basis of Hamiltonian cycles of local features

The problem of finding the lengths of Hamiltonian cycles on complex graphs is considered. The task has such practical applications as determining the optimal routes (salesman's task), identifying graph structures (recognizing the characteristics of local features of biometric objects), etc. When solving the task of verification of biometric samples, the problems of addition or disappearance of reference points, deformation of the distances between them, the appearance of linear and angular displacements of the whole sample emerges. Using the method described in the article, the problem of displacements can be eliminated, as the solution is stable when shuffling of the points is present. Moreover, it is possible to obtain reference plans with the same stability. Obtaining them requires less computational complexity and provides greater recognition accuracy. A detailed description of the problem solution based on the application of the method of branches and boundaries for symmetric matrices of graphs, which describe the distribution of local features in the images of fingerprints, has been proposed. It is known that a guaranteed solution for finding the length of the Hamiltonian cycle for an arbitrary graph of the planar distribution of points is possible only by using an exhaustive search. However, the computational complexity of such a search is not acceptable. The method of branches and boundaries, like all existing methods of directional search, does not guarantee finding a solution with an arbitrarily large dimension of the graph. Therefore, a method of decomposing graphs is proposed, which allows reducing a complex problem to a set of simpler ones. That allows for a significant reduction in computational complexity. The relative invariance of the metrics of Hamiltonian cycles to probabilistic shifts, which are characteristic of biometric pattern recognition problems, has been shown.

Property-Directed Inference of Relational Invariants

Property Directed Reachability (PDR) is an efficient and scalable approach to solving systems of symbolic constraints also known as Constrained Horn Clauses (CHC). In the case of non-linear CHCs, which may arise, e.g., from relational verification tasks, PDR aims to infer an inductive invariant for each uninterpreted predicate. However, in many practical cases this reasoning is not successful, as invariants should be derived for groups of predicates instead of individual predicates. The article describes a novel algorithm that identifies these groups automatically and complements the existing PDR technique. The key feature of the algorithm is that it does not require a possibly expensive synchronization transformation over the system of CHCs. We have implemented the algorithm on top of a up-to-date CHC solver Spacer. Our experimental evaluation shows that for some CHC systems, on which existing solvers diverge, our tool is able to discover relational invariants.

On the minimal dimension of a finite simple group

Let G be a finite group and let M be a set of maximal subgroups of G. We say that M is irredundant if the intersection of the subgroups in M is not equal to the intersection of any proper subset. The minimal dimension of G, denoted Mindim(G), is the minimal size of a maximal irredundant set of maximal subgroups of G. This invariant was recently introduced by Garonzi and Lucchini and they computed the minimal dimension of the alternating groups. In this paper, we prove that Mindim(G)⩽3 for all finite simple groups, which is best possible, and we compute the exact value for all non-classical simple groups. We also introduce and study two closely related invariants denoted by α(G) and β(G). Here α(G) (respectively β(G)) is the minimal size of a set of maximal subgroups (respectively, conjugate maximal subgroups) of G whose intersection coincides with the Frattini subgroup of G. Evidently, Mindim(G)⩽α(G)⩽β(G). For a simple group G we show that β(G)⩽4 and β(G)−α(G)⩽1, and both upper bounds are best possible.

Polarization evolution dynamics of dissipative soliton fiber lasers

Dissipative solitons emerge as stable pulse solutions of nonintegrable and nonconservative nonlinear physical systems, owing to a balance of nonlinearity, dispersion, and loss/gain. A considerable research effort has been dedicated to characterizing amplitude and phase evolutions in the spatiotemporal dynamics of dissipative solitons emerging from fiber lasers. Yet, the picture of the buildup process of dissipative solitons in fiber lasers is incomplete in the absence of corresponding information about the polarization evolution. Here, we characterize probabilistic polarization distributions in the buildup of dissipative solitons in a net-normal dispersion fiber laser system, mode-locked by single-wall carbon nanotubes. The output optical spectra under different pump powers are filtered by a tunable filter, and are detected by a polarization state analyzer. The laser system operates from random amplified spontaneous emission into a stable dissipative soliton state as the cavity gain is progressively increased. Correspondingly, the state of polarization of each spectral wavelength converges towards a fixed point. To reveal the invariant polarization relationship among the various wavelength components of the laser output field, the phase diagram of the ellipticity angle and the spherical orientation angle is introduced. We find that, within the central spectral region of the dissipative soliton, the state of polarization evolves with frequency by tracing a uniform arc on the Poincare sphere, whereas in the edges of the dissipative soliton spectrum, the state of polarization abruptly changes its path. Increasing cavity gain leads to spectral broadening, accompanied by a random scattering of the state of polarization of newly generated frequencies. Further increases of pump power result in dissipative soliton explosions, accompanied by the emergence of a new type of optical polarization rogue waves. These experimental results provide a deeper insight into the transient dynamics of dissipative soliton fiber lasers.

Coneat Injective Modules

A module is called coneat injective if it is injective with respect to all coneat exact sequences. The class of such modules is enveloping and falls properly between injectives and pure injectives. Generalizations of coneat injectivity, like relative coneat injectivity and full invariance of a module in its coneat injective envelope, are studied. Using properties of such classes of modules, we characterize certain types of rings like von Neumann regular and right SF-rings. For instance, $R$ is a right SF-ring if and only if every coneat injective left $R$-module is injective.

A lower bound and several exact results on the d-lucky number

If ℓ:V(G)→N is a vertex labeling of a graph G=(V(G),E(G)), then the d-lucky sum of a vertex u ∈ V(G) is dℓ(u)=dG(u)+∑v∈N(u)ℓ(v). The labeling ℓ is a d-lucky labeling if dℓ(u) ≠ dℓ(v) for every uv ∈ E(G). The d-lucky number ηdl(G) of G is the least positive integer k such that G has a d-lucky labeling V(G) → [k]. A general lower bound on the d-lucky number of a graph in terms of its clique number and related degree invariants is proved. The bound is sharp as demonstrated with an infinite family of corona graphs. The d-lucky number is also determined for the so-called Gm,n-web graphs and graphs obtained by attaching the same number of pendant vertices to the vertices of a generalized cocktail-party graph.