Dual Representation Research Articles

Semi-supervised feature selection based on pairwise constraint-guided dual space latent representation learning and double sparse graphs discriminant

Semi-supervised feature selection based on pairwise constraint-guided dual space latent representation learning and double sparse graphs discriminant

Stable Vectors in Dual Vinberg Representations of F4

AbstractThis paper gives a classification of stable vectors in dual Vinberg representations coming from a graded Lie algebra of type F4 in a way that is independent of the field of definition. Relating these gradings to Moy–Prasad filtrations, we obtain the input for Reeder–Yu’s construction of epipelagic supercuspidal representations. As a corollary, this construction gives new supercuspidal representations of $F_{4}(\mathbb {Q}_{p})$ F 4 ( ℚ p ) when p is small.

Local pottery, hybrid identities: Exploring the Zapo-Teotihuacáno community at El Tesoro, Hidalgo through ceramic compositional analysis

Understanding cultural identity has been a critical aspect of archaeology since its inception. The Bordes-Binford debate famously tackled the issue of cultural identity based upon material culture in the 1960 s. Since then, the issue of cultural affiliation has been addressed in a variety of ways. Critical to this is the understanding of colonization, diasporas, and immigration. In this study, we consider the topic of cultural identity at the site of El Tesoro, Hidalgo, which exhibits cultural elements related to both Teotihuacán and the Valley of Oaxaca. Given the presence of both cultural styles, El Tesoro has previously been suspected to be a Zapotec enclave, perhaps founded by people who emigrated from the Oaxaca Barrio of Teotihuacán. One important example of the dual cultural representations is in the ceramic assemblage at El Tesoro. In this study, we have used Neutron Activation Analysis to assess provenance for a number of sherds which feature distinct Zapotec or Teotihuacán styles. Our results indicate that these ceramics were not the product of importation, but they were presumably made locally, even using the same recipes across both cultural traditions. Given these results and other mixed cultural expressions such as burials, we suggest that this indicates hybridization between the two cultures. Rather than affiliating themselves with one culture or the other, we propose that the Classic period community at El Tesoro can more accurately be described as “Zapo-Teotihuacáno”, as a creolization of both cultures. In contrast with a colonization or enclave model, El Tesoro may instead be thought of as the product of a trade diaspora in which individuals/groups moved to frontier locations as a way to facilitate trade between disparate locales. In doing so, they were incentivized to take on traits of both cultures.

Cooperative investment problem with an authoritative risk determined by Central Bank

In this paper, we are interested to provide an analytic solution for cooperative investment risk with an authoritative risk determined by the central Bank. This problem plays an important role in solving cooperative investment problems in an investment sector such as insurance companies or banks etc and keeping in our mind the effect of a risk determined by the central Bank which has not been done before. We reformulate cooperative investment risk by writing dual representation for each risk preference (Coherent risk measure) for each agent (investor). Finding an analytic solution for this problem for both cases individual and cooperative investment problem by using dual representation for each risk preference has a strong effect on the financial market. Moreover, we find the equilibrium allocation in terms of an equilibrium price by formulating the optimization problem in the case of equilibrium with an initial endowment for each agent’s ’investor’. In addition, formulate a problem that covers the risk minimization problem with an expected return constraint and expected return maximization problem with risk constraint, in both individual and cooperative investment cases, for the general case of an arbitrary joint distribution for the asset return under certain conditions and assuming that all coherent risk measure is continuous from below. Thus, the optimal portfolio is written as the optimal Lagrange multiplier associated with an equality-constrained dual problem. Furthermore, a unique equilibrium allocation as a fair optimal allocation solution in terms of equilibrium price density function for each agent (investor) is also shown.

Adjusted Rényi entropic Value-at-Risk

Entropy is a measure of self information or uncertainty. Using different concepts of entropy, we may get different risk measures by dual representation. In this paper, we introduce and study the main properties of a class of convex risk measures, called as adjusted Rényi entropic Value-at-Risk (VaR). The adjusted risk measure quantifies risk as the minimum amount of capital that has to be raised and injected into a financial position to ensure that its Rényi entropic-VaR does not exceed a pre-specified threshold for every probability level. When p∈[1,∞), the adjusted Rényi entropic-VaR of order p is intimately linked to the (p+1)-increasing convex order by choosing the risk threshold to be the Rényi entropic-VaR of a benchmark random loss.

Asymptotic Stability of the Relativistic Boltzmann Equation Without Angular Cut-Off

This paper is concerned with the relativistic Boltzmann equation without angular cutoff. We establish the global-in-time existence, uniqueness and asymptotic stability for solutions nearby the relativistic Maxwellian. We work in the case of a spatially periodic box. We assume the generic hard-interaction and soft-interaction conditions on the collision kernel that were derived by Dudyński and Ekiel-Je\(\dot{\text {z}}\)ewska (Comm. Math. Phys. 115(4):607–629, 1985) in [32], and our assumptions include the case of Israel particles (J. Math. Phys. 4:1163–1181, 1963) in [56]. In this physical situation, the angular function in the collision kernel is not locally integrable, and the collision operator behaves like a fractional diffusion operator. The coercivity estimates that are needed rely crucially on the sharp asymptotics for the frequency multiplier that has not been previously established. We further derive the relativistic analogue of the Carleman dual representation for the Boltzmann collision operator. This resolves the open question of perturbative global existence and uniqueness without the Grad’s angular cut-off assumption.

Monte Carlo study of duality and the Berezinskii-Kosterlitz-Thouless phase transitions of the two-dimensional q-state clock model in flow representations.

The two-dimensional q-state clock model for q≥5 undergoes two Berezinskii-Kosterlitz-Thouless (BKT) phase transitions as temperature decreases. Here we report an extensive worm-type simulation of the square-lattice clock model for q=5-9 in a pair of flow representations, from high- and low-temperature expansions, respectively. By finite-size scaling analysis of susceptibilitylike quantities, we determine the critical points with a precision improving over the existing results. Due to the dual flow representations, each point in the critical region is observed to simultaneously exhibit a pair of anomalous dimensions, which are η_{1}=1/4 and η_{2}=4/q^{2} at the two BKT transitions. Further, the approximate self-dual points β_{sd}(L), defined by the stringent condition that the susceptibilitylike quantities in both flow representations are identical, are found to be nearly independent of system size L and behave as β_{sd}≃q/2π asymptotically at the large-q limit. The exponent η at β_{sd} is consistent with 1/q within statistical error as long as q≥5. Based on this, we further conjecture that η(β_{sd})=1/q holds exactly and is universal for systems in the q-state clock universality class. Our work provides a vivid demonstration of rich phenomena associated with the duality and self-duality of the clock model in two dimensions.

Dual collaborative representation based discriminant projection for face recognition

Collaborative representation based techniques have shown promising results for face recognition; however, most of them code the samples by taking the overall samples as a dictionary, which may contain much noise information. To tackle this problem, a new face recognition algorithm, namely dual collaborative representation based discriminant projection (DCRDP), is proposed in this paper. In DCRDP, each training sample is reconstructed via dual collaborative representation to enhance the robustness to noise information: the first collaborative representation is used to choose an appropriate dictionary with respect to the training sample, while the second collaborative representation is used to find collaborative representation relationships between samples. After dual collaborative representation, DCRDP constructs two adjacency graphs to model the similarity and dissimilarity between samples, and then finds the optimal projection matrix for dimension reduction. Experiments on ExtYaleB, AR and CMU PIE face datasets verify the superiority of DCRDP to some other state-of-the-art approaches.

Dual-Representation-Based Autoencoder for Domain Adaptation.

Domain adaptation aims to facilitate the learning task in an unlabeled target domain by leveraging the auxiliary knowledge in a well-labeled source domain from a different distribution. Almost existing autoencoder-based domain adaptation approaches focus on learning domain-invariant representations to reduce the distribution discrepancy between source and target domains. However, there is still a weakness existing in these approaches: the class-discriminative information of the two domains may be damaged while aligning the distributions of the source and target domains, which makes the samples with different classes close to each other, leading to performance degradation. To tackle this issue, we propose a novel dual-representation autoencoder (DRAE) to learn dual-domain-invariant representations for domain adaptation. Specifically, DRAE consists of three learning phases. First, DRAE learns global representations of all source and target data to maximize the interclass distance in each domain and minimize the marginal distribution and conditional distribution of both domains simultaneously. Second, DRAE extracts local representations of instances sharing the same label in both domains to maintain class-discriminative information in each class. Finally, DRAE constructs dual representations by aligning the global and local representations with different weights. Using three text and two image datasets and 12 state-of-the-art domain adaptation methods, the extensive experiments have demonstrated the effectiveness of DRAE.

Multiple Representation Ability of High School Students in Physics: A Study of Modern Response Theory

Physics education emphasizes students' ability to represent a problem and then choose alternative solutions from various perspectives. However, teachers still very rarely use this ability as the focus of assessment. The purpose of this study is to describe the results of an assessment of the ability to represent multiple physics in each of its components. This is survey research that takes a quantitative approach. This study's sample included 287 high school students from Yogyakartam using cluster sampling. The instrument used is a physics multiple representation ability test that has been tested for validity, reliability, and item quality using IRT 1 PL analysis. According to the measurement results, physics high school students' dual representation ability in all aspects, namely mathematical representation, graphic representation, image representation, and verbal representation, is in the low category. However, according to the four existing components, the mathematical component is the highest and the verbal component is the lowest. So this finding can be a reference for teachers in improving the quality of physics teaching.

D2FE-GAN: Decoupled dual feature extraction based GAN for MRI image synthesis

Magnetic resonance imaging (MRI) technique can generate various tissue contrasts by using different pulse sequences and parameters. However, obtaining multiple different contrast images for the same patient is sometimes time-consuming and costly. In this paper, we propose a novel generative adversarial network based on decoupled dual feature representations (D2FE-GAN) for cross-modality MRI synthesis. Inspired by the previous works of image style transferring, we argue that the MRI images can be viewed as a compound of underlying information shared among the bodies of modalities (e.g., semantic information), and representative information varying with the styles of modalities (e.g., edges, contrasts). Different from the existing GAN-based methods that pay attention to either the body consistency or the style refinement, the proposed D2FE-GAN method considers both aspects for better synthesis. Specifically, our method decouples the underlying information and the representative information from the source modality and target modality, respectively, through two dissimilar encoders. In response to the invisibility of target modality in testing phase, we propose to employ a Residual Network firstly to generate an intermediate modality as the pseudo target modality. Subsequently, the decoupled two kinds of information will be integrated through a decoder. Here, we introduce the Adaptive Instance Normalization layer, in which the affine parameters are replaced by the mean and standard deviation of the representative information, thus completing the fusion processing of feature space information. Experimental results on BRATS2015 dataset and IXI dataset show that the proposed method outperforms the state-of-the-art image synthesis approaches in both qualitative and quantitative measures.

Combining multi-asset and intrinsic risk measures

The risk of a future payoff is commonly quantified by calculating the costs of a hedging portfolio such that the resulting position is acceptable, i.e., that it passes a capital adequacy test. A multi-asset risk measure describes the minimal external capital which has to be raised into multiple eligible assets to make a future position acceptable. Recently, the alternative methodology of intrinsic risk measures was introduced in the literature. These ask for the minimal proportion of the financial position which has to be reallocated to pass the capital adequacy test, i.e., only internal capital is used.We combine these two concepts and call this new type of risk measure a multi-asset intrinsic risk measure. It allows to secure the financial position by external capital as well as reallocating parts of the portfolio as an internal rebooking. We investigate several properties to demonstrate similarities and differences to the two aforementioned classical types of risk measures. We find that diversification reduces the capital requirement only in special situations depending on the financial positions. With the help of Sion's minimax theorem we also prove a dual representation for multi-asset intrinsic risk measures. Finally, we determine capital requirements in a model motivated by the Solvency II methodology.

Solving optimal stopping problems under model uncertainty via empirical dual optimisation

In this work, we consider optimal stopping problems with model uncertainty incorporated into the formulation of the underlying objective function. Typically, the robust, efficient hedging of American options in incomplete markets may be described as optimal stopping of such kind. Based on a generalisation of the additive dual representation of Rogers (Math. Financ. 12:271–286, 2002) to the case of optimal stopping under model uncertainty, we develop a novel regression-based Monte Carlo algorithm for the approximation of the corresponding value function. The algorithm involves optimising a penalised empirical dual objective functional over a class of martingales. This formulation allows us to construct upper bounds for the optimal value with reduced complexity. Finally, we carry out a convergence analysis of the proposed algorithm and illustrate its performance by several numerical examples.

OPTIMAL INVESTMENT AND CONTINGENT CLAIM VALUATION WITH EXPONENTIAL DISUTILITY UNDER PROPORTIONAL TRANSACTION COSTS

We consider indifference pricing of contingent claims consisting of payment flows in a discrete-time model with proportional transaction costs and under exponential disutility. This setting covers utility maximization of terminal wealth as a special case. A dual representation is obtained for the associated disutility minimization problem, together with a dynamic procedure for solving it. This leads to efficient and convergent numerical procedures for indifference pricing, optimal trading strategies and shadow prices that apply to a wide range of payoffs, a large range of time steps and all magnitudes of transaction costs.

A Trident Quaternion Framework for Inertial-Based Navigation Part I: Rigid Motion Representation and Computation

Strapdown inertial navigation research involves the parameterization and computation of the attitude, velocity, and position of a rigid body in a chosen reference frame. The community has long devoted to finding the most concise and efficient representation for the strapdown inertial navigation system (INS). The current work is motivated by simplifying the existing dual quaternion representation of the kinematic model. This article proposes a compact and elegant representation of the body's attitude/velocity/position, with the aid of a devised trident quaternion tool, which is an extension of dual quaternions. And the position is accounted for by adding a second dual part to the dual quaternion. Eventually, the kinematics of the strapdown INS are cohesively unified in one concise differential equation, which bears the same form as the classical attitude quaternion differential equation. In addition, the numerical solution to this trident quaternion-based kinematic equation is dealt with the recently proposed functional iterative integration approach. Numerical results are provided to verify the analysis. The new representation not only provides an elegant kinematic form of inertial navigation, but gives birth to precision inertial navigation algorithm.

After the Cambridge Controversies: Reflections Old and New

Abstract Perfect foresight is a consequence of applying the Pontryagin Maximum Principle to the analysis of an intertemporal general equilibrium. For this reason, the capital theory controversy ended in an intellectual impasse. The critique of mainstream theory largely ignored the perfect foresight entailments of intertemporal equilibrium analysis, while its defenders, with notable exceptions, too often failed to acknowledge this implication of the technique of dynamic programming. From this standpoint, the long debate over the existence or non-existence of an aggregate production function is secondary. This leaves open the theoretical question of how to proceed with an analysis of the actual dynamics of capitalist development. The critique of mainstream capital theory remains a ‘prelude’, caught up in an ever deeper analysis of the implications of alternative representations of the technique of production. The first part of this paper deals with the question of how perfect foresight came to infect mainstream theory; the second part turns to a consideration of a weakness in the dual representation of the technique of production in the simplest Sraffian framework. Neither part addresses the bigger questions of how to analyze the process of uneven development under the capitalist rules of the game.

Do You Need Another Hand? Investigating Dual Body Representations During Anisomorphic 3D Manipulation.

In virtual reality, several manipulation techniques distort users' motions, for example to reach remote objects or increase precision. These techniques can become problematic when used with avatars, as they create a mismatch between the real performed action and the corresponding displayed action, which can negatively impact the sense of embodiment. In this paper, we propose to use a dual representation during anisomorphic interaction. A co-located representation serves as a spatial reference and reproduces the exact users' motion, while an interactive representation is used for distorted interaction. We conducted two experiments, investigating the use of dual representations with amplified motion (with the Go-Go technique) and decreased motion (with the PRISM technique). Two visual appearances for the interactive representation and the co-located one were explored. This exploratory study investigating dual representations in this context showed that people globally preferred having a single representation, but opinions diverged for the Go-Go technique. Also, we could not find significant differences in terms of performance. While interacting seemed more important than showing exact movements for agency during out-of-reach manipulation, people felt more in control of the realistic arm during close manipulation.

Set-valued dynamic risk measures for processes and for vectors

The relationship between set-valued risk measures for processes and vectors on the optional filtration is investigated. The equivalence of risk measures for processes and vectors and the equivalence of their penalty function formulations are provided. In contrast to scalar risk measures, this equivalence requires an augmentation of the set-valued risk measures for processes. We utilise this result to deduce a new dual representation for risk measures for processes in the set-valued framework. Finally, the equivalence of multi-portfolio time-consistency between set-valued risk measures for processes and vectors is provided. To accomplish this, an augmented definition for multi-portfolio time-consistency of set-valued risk measures for processes is proposed.

Support for Social Change Among Members of Advantaged Groups: The Role of a Dual Identity Representation and Accepting Intergroup Contact.

This preregistered research analyzed survey data from ethnic and religious advantaged groups in 12 countries (N = 2,304) to examine the interplay between two determinants of support for social change toward intergroup equality. Drawing on the needs-based model and the common-ingroup identity model, we hypothesized that the experience of accepting intergroup contact and the endorsement of a dual identity representation of intergroup relations would be associated with greater support for equality. Furthermore, integrating the logic of both models, we tested the novel hypothesis that the positive effect of accepting contact on support for equality would be stronger under a high (vs. low) dual identity representation. While the predicted main effects received empirical support, we found no evidence for the expected interaction. These findings suggest that interventions to foster support for social change among advantaged group members can promote accepting contact and a dual identity representation independently of each other.

A New Approach to Jordan D-Bialgebras via Jordan–Manin Triples

Jordan D-bialgebras were introduced by Zhelyabin. In this paper, we use a new approach to study Jordan D-bialgebras by a new notion of the dual representation of the regular representation of a Jordan algebra. Motivated by the essential connection between Lie bialgebras and Manin triples, we give an explicit proof of the equivalence between Jordan D-bialgebras and a class of special Jordan–Manin triples called double constructions of pseudo-euclidean Jordan algebras. We also show that a Jordan D-bialgebra leads to the Jordan Yang–Baxter equation under the coboundary condition and an antisymmetric nondegenerate solution of the Jordan Yang–Baxter equation corresponds to an antisymmetric bilinear form, which we call a Jordan symplectic form on Jordan algebras. Furthermore, there exists a new algebra structure called pre-Jordan algebra on Jordan algebras with a Jordan symplectic form.