Representation Of Properties Research Articles

Special irreducible representations of Leavitt path algebras

Several descriptions of irreducible representations of both Leavitt and hence Cohn path algebras of an arbitrary digraph with coefficients in a commutative field introduced by Chen and Rangaswamy are presented, using both infinite paths on the right and vertices as well as direct limits or factors of cyclic projective ideals of the ordinary quiver algebra. Specific properties of these irreducible representations become immediate when they are viewed as modules over the commutative subalgebras generated by symmetric idempotents of paths, thereby providing a unified way to treat them. Furthermore, their defining relations are read off, whence criteria are easily given when they are finitely presented or finite dimensional. Their endomorphism rings, and annihilator primitive ideals are also computed directly.

Analysis of Hue Circle Perception of Congenital Red-green Congenital Color Deficiencies Based on Color Vision Model

To investigate individual property of internal color representation of congenital red-green color-deficient observers (CDOs) and color-normal observers (CNOs) precisely, difference scaling experiment using pairs of primary colors was carried out for protans, deutans, and normal trichromats, and the results were analyzed using multi-dimensional Scaling (MDS). MDS configuration of CNOs showed circular shape similar to hue circle, whereas that of CNO showed large individual differences from circular to U- shape. Distortion index, DI, is proposed to express the shape variation of MDS configuration. All color chips were plotted in the color vision space, (L, r/g, y/b), and the MDS using a non-linear conversion from the distance in the color vision space to perceptual difference scaling was successful to obtain U-shape configuration that reflects internal color representation of CDOs.

On a linear autonomous descriptor equation with discrete time. II. Canonical representation and structural properties

We consider a linear homogeneous autonomous descriptor equation with discrete time B0g(k+1)+∑mi=1Big(k+1−i)=0,k=m,m+1,…, with rectangular (in general case) matrices Bi. Such an equation arises in the study of the most important control problems for systems with many commensurate delays in control: the 0-controllability problem, the synthesis problem of the feedback-type regulator, which provides calming to the solution of the original system, the modal controllability problem (controllability to the coefficients of characteristic quasipolynomial), the spectral reduction problem and the synthesis problem observers for dual surveillance system. The main method of the presented study is based on replacing the original equation with an equivalent equation in the “expanded” state space, which allows one to match the new equation of the beam of matrices. This made it possible to study a number of structural properties of the original equation by using the canonical form of the beam of matrices, and express the results in terms of minimal indices and elementary divisors. In the article, a criterion is obtained for the existence of a nontrivial admissible initial condition for the original equation, the verification of which is based on the calculation of the minimum indices and elementary divisors of the beam of matrices. The following problem was studied: it is required to construct a solution to the original equation in the form g(k+1)=Tψ(k+1), k=1,2…, where T is some matrix, the sequence of vectors ψ(k+1), k=1,2,…, satisfies the equation ψ(k+1)=Sψ(k), k=1,2,…, and the square matrix S has a predetermined spectrum (or part of the spectrum). The results obtained make it possible to construct solutions of the initial descriptor equation with predetermined asymptotic properties, for example, uniformly asymptotically stable.

How the forest interacts with the trees: Multiscale shape integration explains global and local processing.

Hierarchical stimuli have been widely used to study global and local processing. Two classic phenomena have been observed using these stimuli: the global advantage effect (we identify the global shape faster) and an interference effect (we identify shape slower when the global and local shapes are different). Because these phenomena have been observed during shape categorization tasks, it is unclear whether they reflect the categorical judgment or the underlying shape representation. Understanding the underlying shape representation is also critical because both global and local processing are modulated by stimulus properties.We performed two experiments to investigate these issues. In Experiment 1, we show that these phenomena can be observed in a same-different task, and that participants show systematic variation in response times across image pairs. We show that the response times to any pair of images can be accurately predicted using two factors: their dissimilarity and their distinctiveness relative to other images. In Experiment 2, we show that these phenomena can also be observed in a visual search task where participant did not have to make any categorical shape judgments. Here too, participants showed highly systematic variations in response time that could be explained as a linear sum of shape comparisons across global and local scales. Finally, the dissimilarity and distinctiveness factors estimated from the same-different task were systematically related to the search dissimilarities observed during visual search.In sum, our results show that global and local processing phenomena are properties of a systematic shape representation governed by simple rules.

Properties of familiar face representations: No evidence for qualitative differences between personal and media-based familiarity

Properties of familiar face representations: No evidence for qualitative differences between personal and media-based familiarity

Properties of Switch-List Representations of Boolean Functions

In this paper, we focus on a less usual way to represent Boolean functions, namely on representations by switch-lists, which are closely related to interval representations. Given a truth table representation of a Boolean function f the switch-list representation of f is a list of Boolean vectors from the truth table which have a different function value than the preceding Boolean vector in the truth table. The main aim of this paper is to include this type of representation in the Knowledge Compilation Map by Darwiche and Marquis and to argue that switch-lists may in certain situations constitute a reasonable choice for a target language in knowledge compilation. First, we compare switch-list representations with a number of standard representations (such as CNF, DNF, and OBDD) with respect to their relative succinctness. As a by-product of this analysis, we also give a short proof of a longstanding open question proposed by Darwiche and Marquis, namely the incomparability of MODS (models) and PI (prime implicates) representations. Next, using the succinctness result between switch-lists and OBDDs, we develop a polynomial time compilation algorithm from switch-lists to OBDDs. Finally, we analyze which standard transformations and queries (those considered by Darwiche and Marquis) can be performed in polynomial time with respect to the size of the input if the input knowledge is represented by a switch-list. We show that this collection is very broad and the combination of polynomial time transformations and queries is quite unique. Some of the queries can be answered directly using the switch-list input, others require a compilation of the input to OBDD representations which are then used to answer the queries.

An End-to-End Deep Fusion Model for Mapping Forests at Tree Species Levels with High Spatial Resolution Satellite Imagery

Mapping the distribution of forest resources at tree species levels is important due to their strong association with many quantitative and qualitative indicators. With the ongoing development of artificial intelligence technologies, the effectiveness of deep-learning classification models for high spatial resolution (HSR) remote sensing images has been proved. However, due to the poor statistical separability and complex scenarios, it is still challenging to realize fully automated and highly accurate forest types at tree species level mapping. To solve the problem, a novel end-to-end deep learning fusion method for HSR remote sensing images was developed by combining the advantageous properties of multi-modality representations and the powerful features of post-processing step to optimize the forest classification performance refined to the dominant tree species level in an automated way. The structure of the proposed model consisted of a two-branch fully convolutional network (dual-FCN8s) and a conditional random field as recurrent neural network (CRFasRNN), which named dual-FCN8s-CRFasRNN in the paper. By constructing a dual-FCN8s network, the dual-FCN8s-CRFasRNN extracted and fused multi-modality features to recover a high-resolution and strong semantic feature representation. By imbedding the CRFasRNN module into the network as post-processing step, the dual-FCN8s-CRFasRNN optimized the classification result in an automatic manner and generated the result with explicit category information. Quantitative evaluations on China’s Gaofen-2 (GF-2) HSR satellite data showed that the dual-FCN8s-CRFasRNN provided a competitive performance with an overall classification accuracy (OA) of 90.10%, a Kappa coefficient of 0.8872 in the Wangyedian forest farm, and an OA of 74.39%, a Kappa coefficient of 0.6973 in the GaoFeng forest farm, respectively. Experiment results also showed that the proposed model got higher OA and Kappa coefficient metrics than other four recently developed deep learning methods and achieved a better trade-off between automaticity and accuracy, which further confirmed the applicability and superiority of the dual-FCN8s-CRFasRNN in forest types at tree species level mapping tasks.

Distinct fronto-temporal substrates of distributional and taxonomic similarity among words: evidence from RSA of BOLD signals

A class of semantic theories defines concepts in terms of statistical distributions of lexical items, basing meaning on vectors of word co-occurrence frequencies. A different approach emphasizes abstract hierarchical taxonomic relationships among concepts. However, the functional relevance of these different accounts and how they capture information-encoding of lexical meaning in the brain still remains elusive.We investigated to what extent distributional and taxonomic models explained word-elicited neural responses using cross-validated representational similarity analysis (RSA) of functional magnetic resonance imaging (fMRI) and model comparisons.Our findings show that the brain encodes both types of semantic information, but in distinct cortical regions. Posterior middle temporal regions reflected lexical-semantic similarity based on hierarchical taxonomies, in coherence with the action-relatedness of specific semantic word categories. In contrast, distributional semantics best predicted the representational patterns in left inferior frontal gyrus (LIFG, BA 47). Both representations coexisted in the angular gyrus supporting semantic binding and integration. These results reveal that neuronal networks with distinct cortical distributions across higher-order association cortex encode different representational properties of word meanings. Taxonomy may shape long-term lexical-semantic representations in memory consistently with the sensorimotor details of semantic categories, whilst distributional knowledge in the LIFG (BA 47) may enable semantic combinatorics in the context of language use.Our approach helps to elucidate the nature of semantic representations essential for understanding human language.

Image Compressive Sensing via Hybrid Nonlocal Sparsity Regularization.

This paper focuses on image compressive sensing (CS). As the intrinsic properties of natural images, nonlocal self-similarity and sparse representation have been widely used in various image processing tasks. Most existing image CS methods apply either self-adaptive dictionary (e.g., principle component analysis (PCA) dictionary and singular value decomposition (SVD) dictionary) or fixed dictionary (e.g., discrete cosine transform (DCT), discrete wavelet transform (DWT), and Curvelet) as the sparse basis, while single dictionary could not fully explore the sparsity of images. In this paper, a Hybrid NonLocal Sparsity Regularization (HNLSR) is developed and applied to image compressive sensing. The proposed HNLSR measures nonlocal sparsity in 2D and 3D transform domain simultaneously, and both self-adaptive singular value decomposition (SVD) dictionary and fixed 3D transform are utilized. We use an efficient alternating minimization method to solve the optimization problem. Experimental results demonstrate that the proposed method outperforms existing methods in both objective evaluation and visual quality.

Poetic Sensorium and Aesthetic Objectification in the Middle English Pearl

ABSTRACT This article considers the ways in which sensory perception underlies the aesthetic appreciation of the Middle English Pearl. In particular it focuses on how sensory description and perception is used to interlink the different aspects of the poem’s representational properties, such as its form, its thematic content, and the narrative medium, to engage the audience. The article therefore addresses the intricate correlation between the poetic form of Pearl and the function of sensory perception within the poem as means of mediating between the external audience and what might be termed the internal poetic sensorium. Sensorium is here conceived as the entirety of the sensory realm of an individual, including the external objects, sounds or smells along with perceived sensations, perception and the cognitive processes associated with deciphering and processing the sensorial input. Poetic sensorium instead refers to the fictive description of a sensory realm and experiences that are actualized and materialized via the process of reading or listening. In the article it is argued that the haptic sense is the fulcrum on which much of the poetry turns, revealing the underlying implications of the poem’s function as a memorializing artifact.

Algebraic treatment of the Pais–Uhlenbeck oscillator and its PT-variant

The algebraic method enables one to study the properties of the spectrum of a quadratic Hamiltonian through the mathematical properties of a matrix representation called regular or adjoint. This matrix exhibits exceptional points where it becomes defective and can be written in canonical Jordan form. It is shown that any quadratic function of K coordinates and K momenta leads to a 2K differential equation for those dynamical variables. We illustrate all these features of the algebraic method by means of the Pais–Uhlenbeck oscillator and its PT-variant.

The Blind Spot of History: Colonialism in Tabu

This article looks at the film Tabu (Miguel Gomes, 2012) as an example of the negative use of cinema for realist ends. The film addresses Portugal’s tainted colonial past by means of a relentless questioning of the film medium and its representational properties, whilst the horrors of colonialism in Africa – the main issue at stake – remain conspicuous by their absence. Indeed, Tabu gravitates around an irresistible, all-consuming black hole, where the sombre legacy of colonialism makes itself felt by resisting representation. This article analyses two opposites, but complementary movements in the film: on the one hand, the foreclosure of history, and, on the other, the grounding of the story in the reality of both the objective world and the medium itself. The aim will be to define a possible truth procedure, as defined by Badiou, contained in the film’s self-defeating fantasy.

"Walk this way": specific contributions of active walking to the encoding of metric properties during spatial learning.

The effect of body-based information on spatial memory has been traditionally described as a facilitating factor for large-scale spatial learning in the field of active learning research (Chrastil & Warren, Psychonomic Bulletin and Review, 19(1):1-23; 2012). The specific contribution of body-based information to spatial representation properties is however not yet well defined and the mechanisms through which body-based information contributes to spatial learning are not clear enough. To disambiguate the effect of active spatial learning on the quality of spatial representations from the beneficial effect of physiological arousal, we compared four experimental conditions (walking on a unidirectional treadmill during learning, retrieval, both phases or no walking). Results showed no effect of the walking condition for a route perspective task, but a significant effect on a survey perspective task (landmark positioning on a map): participants who walked during encoding (encoding group and encoding + retrieval group) obtained better results than those who did not walk or walked only during retrieval. Geometrical analysis of spatial positions on maps revealed that the activity of walking during encoding improves the correlation between participants' coordinates and actual coordinates through better distance estimations and angular accuracy, even though the optic flow was not matched with individual walking speed. Control group variance in all measures was higher than that of the walking groups (regardless of the moment of walking). Taken together, these results provide arguments for the multimodal nature of spatial representations, where body-related information derived from walking is involved in metric properties accuracy and perspective switching.

DA-CapsUNet: A Dual-Attention Capsule U-Net for Road Extraction from Remote Sensing Imagery

The up-to-date and information-accurate road database plays a significant role in many applications. Recently, with the improvement in image resolutions and quality, remote sensing images have provided an important data source for road extraction tasks. However, due to the topology variations, spectral diversities, and complex scenarios, it is still challenging to realize fully automated and highly accurate road extractions from remote sensing images. This paper proposes a novel dual-attention capsule U-Net (DA-CapsUNet) for road region extraction by combining the advantageous properties of capsule representations and the powerful features of attention mechanisms. By constructing a capsule U-Net architecture, the DA-CapsUNet can extract and fuse multiscale capsule features to recover a high-resolution and semantically strong feature representation. By designing the multiscale context-augmentation and two types of feature attention modules, the DA-CapsUNet can exploit multiscale contextual properties at a high-resolution perspective and generate an informative and class-specific feature encoding. Quantitative evaluations on a large dataset showed that the DA-CapsUNet provides a competitive road extraction performance with a precision of 0.9523, a recall of 0.9486, and an F-score of 0.9504, respectively. Comparative studies with eight recently developed deep learning methods also confirmed the applicability and superiority or compatibility of the DA-CapsUNet in road extraction tasks.

Object Synthesis by Learning Part Geometry with Surface and Volumetric Representations

We propose a conditional generative model, named Part Geometry Network (PG-Net), which synthesizes realistic objects and can be used as a robust feature descriptor for object reconstruction and classification. Surface and volumetric representations of objects have complementary properties of three-dimensional objects. Combining these modalities is more informative than using one modality alone. Therefore, PG-Net utilizes complementary properties of surface and volumetric representations by estimating curvature, surface area, and occupancy in voxel grids of objects with a single decoder as a multi-task learning. Objects are combinations of multiple parts, and therefore part geometry (PG) is essential to synthesize each part of the objects. PG-Net employs a part identifier to learn the part geometry. Additionally, we augmented a dataset by interpolating individual functional parts such as wings of an airplane, which helps learning part geometry and finding local/global minima of PG-Net. To demonstrate the capability of learning object representations of PG-Net, we performed object reconstruction and classification tasks on two standard large-scale datasets. PG-Net outperformed the state-of-the-art methods in object synthesis, classification, and reconstruction in a large margin.

A hierarchical effective mode approach to phonon-driven multilevel vibrational relaxation dynamics at surfaces

We discuss an efficient Hierarchical Effective Mode (HEM) representation of a high-dimensional harmonic oscillator bath, which describes phonon-driven vibrational relaxation of an adsorbate-surface system, namely, deuterium adsorbed on Si(100). Starting from the original Hamiltonian of the adsorbate-surface system, the HEM representation is constructed via iterative orthogonal transformations, which are efficiently implemented with Householder matrices. The detailed description of the HEM representation and its construction are given in the second quantization representation. The hierarchical nature of this representation allows access to the exact quantum dynamics of the adsorbate-surface system over finite time intervals, controllable via the truncation order of the hierarchy. To study the convergence properties of the effective mode representation, we solve the time-dependent Schrödinger equation of the truncated system-bath HEM Hamiltonian, with the help of the multilayer extension of the Multiconfigurational Time-Dependent Hartree (ML-MCTDH) method. The results of the HEM representation are compared with those obtained with a quantum-mechanical tier-model. The convergence of the HEM representation with respect to the truncation order of the hierarchy is discussed for different initial conditions of the adsorbate-surface system. The combination of the HEM representation with the ML-MCTDH method provides information on the time evolution of the system (adsorbate) and multiple effective modes of the bath (surface). This permits insight into mechanisms of vibration-phonon coupling of the adsorbate-surface system, as well as inter-mode couplings of the effective bath.

Properties of a separable representation of optical potentials

Background: Separable interactions have a long history in nuclear physics. In the last few years, separable expansions have been used to represent the optical potential between a nucleon (proton or neutron) and a target. Purpose: We explore the non-local properties of these separable optical potentials as well as their convergence behavior. Method: For a couple of cases, we use the generalized Ersnt-Shakin-Thaler scheme to generate separable interactions starting from local optical potentials. We study the variation of the interaction with energy range and rank. Results: We find that, overall the off-diagonal behavior of the converged separable interaction deviates from the Gaussian form assumed by Perey and Buck. However, in the region surrounding the maximum depth the Gaussian form works quite well. Focusing on this region, we study potentials describing neutron elastic scattering on $^{16}$O and $^{48}$Ca for beam energies in the range of $ E=$10-50 MeV and explore several measures of non-locality of the separable interactions. Conclusions: When the energy range considered for generating the separable interaction is $0\le E_{range}\le 50$ MeV, the resulting non-locality is large and target dependent. Contrarily, the nonlocality obtained including larger energy ranges in the separable procedure is independent of the target and other details of the original local potential. We find that, even when including in the expansion many support points with energy ranges $0\le E_{range}\le 2400$ MeV, the resulting potential retains non-local behavior. Connections with microscopic optical potentials as well as other transformations used in the nucleon-nucleon domain are made.

The method of virtual copies and contractions of simple Lie algebras

Contractions of simple Lie algebras onto semidirect sums are analyzed in the context of the method of virtual copies, and various existence conditions are obtained in terms of the branching rules of representations and the properties of the characteristic representation associated to an embedding of semisimple algebras. Contractions of the Lie algebra with respect to nonmaximal symplectic subalgebras are studied in some detail. In particular, a realization of the subalgebra in terms of cubic polynomial operators is constructed.

Enabling Artistic Control Over Pattern Density and Stroke Strength

Despite the remarkable results and numerous advancements in neural style transfer, achieving artistic control is still a challenging feat, primarily since existing methodologies treat the style representation as a black-box model. This oversight significantly limits the range of possible artistic manipulations. In this paper, we propose a method to enable artistic control on any correlation-based style transfer models along with guiding intuitions. Our focus is on controlling two perceptual factors: Pattern Density and Stroke Strength. To achieve this, we introduce the centered Gram style representation and manipulate it with our variance-aware adaptive weighting and correlation-based selective masking. Through several experiments and comparisons with the state-of-the-art, we show that we can achieve artistic control with competitive stylization quality. Additionally, since our method involves manipulating style representation, it can easily be adapted to popular style transfer models. We analyze different style representation properties to propose rules that govern the style transfer process, which is critical towards achieving artistic control over pattern density and stroke strength.

LieART 2.0 – A Mathematica application for Lie Algebras and Representation Theory

We present LieART 2.0 which contains substantial extensions to the Mathematica application LieART (LieAlgebras and Representation Theory) for computations frequently encountered in Lie algebras and representation theory, such as tensor product decomposition and subalgebra branching of irreducible representations. The basic procedure is unchanged—it computes root systems of Lie algebras, weight systems and several other properties of irreducible representations, but new features and procedures have been included to allow the extensions to be seamless. The new version of LieART continues to be user friendly. New extended tables of properties, tensor products and branching rules of irreducible representations are included in the supplementary material for use without Mathematica software. LieART 2.0 now includes the branching rules to special subalgebras for all classical and exceptional Lie algebras up to and including rank 15. Program summaryProgram Title: LieART 2.0CPC Library link to program files:http://dx.doi.org/10.17632/8vm7j67bwt.1Licensing provisions: GNU Lesser General Public LicenseProgramming language: MathematicaExternal routines/libraries: Wolfram Mathematica 8–12Nature of problem: The use of Lie algebras and their representations is widespread in physics, especially in particle physics. The description of nature in terms of gauge theories requires the assignment of fields to representations of compact Lie groups and their Lie algebras. Mass and interaction terms in the Lagrangian give rise to the need for computing tensor products of representations of Lie algebras. The mechanism of spontaneous symmetry breaking leads to the application of subalgebra decomposition. This computer code was designed for the purpose of Grand Unified Theory (GUT) model building, (where compact Lie groups beyond the U(1), SU(2) and SU(3) of the Standard Model of particle physics are needed), but it has found use in a variety of other applications. Tensor product decomposition and subalgebra decomposition have been implemented for all classical Lie groups SU(N), SO(N) and Sp(2N) and all the exceptional groups E6, E7, E8, F4 and G2. This includes both regular and irregular (special) subgroup decomposition of all Lie groups up through rank 15, and many more.Solution method: LieART generates the weight system of an irreducible representation (irrep) of a Lie algebra by exploiting the Weyl reflection groups, which is inherent in all simple Lie algebras. Tensor products are computed by the application of Klimyk’s formula, except for SU(N)’s, where the Young-tableaux algorithm is used. Subalgebra decomposition of SU(N)’s are performed by projection matrices, which are generated from an algorithm to determine maximal subalgebras as originally developed by Dynkin [1,2]. We generate projection matrices by the Dynkin procedure, i.e., removing dots from the Dynkin or extended Dynkin diagram, for regular subalgebras, and we implement explicit projection matrices for special subalgebras.Restrictions: Internally irreps are represented by their unique Dynkin label. LieART’s default behavior in TraditionalForm is to print the dimensional name, which is the labeling preferred by physicist. Most Lie algebras can have more than one irrep of the same dimension and different irreps with the same dimension are usually distinguished by one or more primes (e.g. 175 and 175′ of A4). To determine the need for one or more primes of an irrep a brute-force loop over other irreps must be performed to search for irreps with the same dimensionality. Since Lie algebras have an infinite number of irreps, this loop must be cut off, which is done by limiting the maximum Dynkin digit in the loop. In rare cases for irreps of high dimensionality in high-rank algebras the used cutoff is too low and the assignment of primes is incorrect. However, this only affects the display of the irrep. All computations involving this irrep are correct, since the internal unique representation of Dynkin labels is used.