Discrete Representation Research Articles

Effects of unit cell parameters on the thermal shock resistance of auxetic honeycomb sandwich structures: Combining discrete and continuum model

The influence of unit cell geometric parameters on the thermal fracture behavior and thermal shock resistance of honeycomb ceramics sandwich structures is revealed for the first time. The present study establishes a continuum model for the thermal fracture of sandwich structures, and a discrete numerical representation model for the equivalent fracture toughness of honeycombs, respectively. A novel evaluation approach for the thermal shock resistance of porous material structures has been provided by combining the two models. The effects of temperature dependence, face sheet thickness, honeycomb orientation and honeycomb geometrical parameters on thermal shock resistance are studied. Results indicate that changing the inclined angle of honeycomb can effectively increase the critical thermal shock temperature rise. Auxetic honeycomb sandwich structures with the inclined angle of −9° can reach the peak of the critical temperature rise. The results would contribute to the application of honeycomb sandwich structures in thermal protection systems.

Super-localization of spatial network models

Spatial network models are used as a simplified discrete representation in a wide range of applications, e.g., flow in blood vessels, elasticity of fiber based materials, and pore network models of porous materials. Nevertheless, the resulting linear systems are typically large and poorly conditioned and their numerical solution is challenging. This paper proposes a numerical homogenization technique for spatial network models which is based on the super-localized orthogonal decomposition (SLOD), recently introduced for elliptic multiscale partial differential equations. It provides accurate coarse solution spaces with approximation properties independent of the smoothness of the material data. A unique selling point of the SLOD is that it constructs an almost local basis of these coarse spaces, requiring less computations on the fine scale and achieving improved sparsity on the coarse scale compared to other state-of-the-art methods. We provide an a posteriori analysis of the proposed method and numerically confirm the method’s unique localization properties. In addition, we show its applicability also for high-contrast channeled material data.

Robust prostate disease classification using transformers with discrete representations.

Automated prostate disease classification on multi-parametric MRI has recently shown promising results with the use of convolutional neural networks (CNNs). The vision transformer (ViT) is a convolutional free architecture which only exploits the self-attention mechanism and has surpassed CNNs in some natural imaging classification tasks. However, these models are not very robust to textural shifts in the input space. In MRI, we often have to deal with textural shift arising from varying acquisition protocols. Here, we focus on the ability of models to generalise well to new magnet strengths for MRI. We propose a new framework to improve the robustness of vision transformer-based models for disease classification by constructing discrete representations of the data using vector quantisation. We sample a subset of the discrete representations to form the input into a transformer-based model. We use cross-attention in our transformer model to combine the discrete representations of T2-weighted and apparent diffusion coefficient (ADC) images. We analyse the robustness of our model by training on a 1.5 T scanner and test on a 3 T scanner and vice versa. Our approach achieves SOTA performance for classification of lesions on prostate MRI and outperforms various other CNN and transformer-based models in terms of robustness to domain shift and perturbations in the input space. We develop a method to improve the robustness of transformer-based disease classification of prostate lesions on MRI using discrete representations of the T2-weighted and ADC images.

Multivariate Meixner polynomials related to holomorphic discrete series representations of [formula omitted]

We show that Griffiths’ multivariate Meixner polynomials occur as matrix coefficients of holomorphic discrete series representations of the group SU(1,d). Using this interpretation we derive several fundamental properties of the multivariate Meixner polynomials, such as orthogonality relations and difference equations. Furthermore, we also show that matrix coefficients for specific group elements lead to degenerate versions of the multivariate Meixner polynomials and their properties.

Classification-Driven Discrete Neural Representation Learning for Semantic Communications

Classification-Driven Discrete Neural Representation Learning for Semantic Communications

An approach to calculate Franck-Condon factors involving anharmonic potentials using harmonic oscillator bases

In this contribution a discrete variable representation (DVR) approach to calculate Franck-Condon factors (FCFs) is presented. The method is illustrated using a harmonic oscillator basis. The advantage of this approach is that it is possible to calculate FCFs associated with general potentials based on the knowledge of the harmonic oscillator theory. First the coordinate and momentum representations are introduced. Based on this concept, the DVR is proposed, which allows the Franck-Condon factors to be calculated in a simple form. This method takes advantage of the momentum as generator of translations to include the displacement of the potentials. The calculation of the FCFs is exemplified for transitions involving the ground state X1Σg+ and the excited state a 1Π g of the diatomic molecule 14N2 both modelled with Morse potentials.

Polymer Coatings Affect Transport and Remobilization of Colloidal Activated Carbon in Saturated Sand Columns: Implications for In Situ Groundwater Remediation.

Colloidal activated carbon (CAC) is an emerging technology for the in situ remediation of groundwater impacted by per- and polyfluoroalkyl substances (PFAS). In assessing the long-term effectiveness of a CAC barrier, it is crucial to evaluate the potential of emplaced CAC particles to be remobilized and migrate away from the sorptive barrier. We examine the effect of two polymer stabilizers, carboxymethyl cellulose (CMC) and polydiallyldimethylammonium chloride (PolyDM), on CAC deposition and remobilization in saturated sand columns. CMC-modified CAC showed high mobility in a wide ionic strength (IS) range from 0.1 to 100 mM, which is favorable for CAC delivery at a sufficient scale. Interestingly, the mobility of PolyDM-modified CAC was high at low IS (0.1 mM) but greatly reduced at high IS (100 mM). Notably, significant remobilization (release) of deposited CMC-CAC particles occurred upon the introduction of solution with low IS following deposition at high IS. In contrast, PolyDM-CAC did not undergo any remobilization following deposition due to its favorable interactions with the quartz sand. We further elucidated the CAC deposition and remobilization behaviors by analyzing colloid-collector interactions through the application of Derjaguin-Landau-Verwey-Overbeek theory, and the inclusion of a discrete representation of charge heterogeneity on the quartz sand surface. The classical colloid filtration theory was also employed to estimate the travel distance of CAC in saturated columns. Our results underscore the roles of polymer coatings and solution chemistry in CAC transport, providing valuable guidelines for the design of in situ CAC remediation with maximized delivery efficiency and barrier longevity.

Real-time collision detection between general SDFs

Signed Distance Fields (SDFs) have found widespread utility in collision detection applications due to their superior query efficiency and ability to represent continuous geometries. However, little attention has been paid to calculating the intersection of two arbitrary SDFs. In this paper, we propose a novel, accurate, and real-time approach for SDF-based collision detection between two solids, both represented as SDFs. Our primary strategy entails using interval calculations and the SDF gradient to guide the search for intersection points within the geometry. For arbitrary objects, we take inspiration from existing collision detection pipelines and segment the two SDFs into multiple parts with bounding volumes. Once potential collisions between two parts are identified, our method quickly computes comprehensive intersection information such as penetration depth, contact points, and contact normals. Our method is general in that it accepts both continuous and discrete SDF representations. Experiment results show that our method can detect collisions in high-precision models in real time, highlighting its potential for a wide range of applications in computer graphics and virtual reality.

Discrete model for discontinuous dynamic recrystallisation applied to grain structure evolution inside adiabatic shear bands

Discontinuous dynamic recrystallisation (DDRX) is a well-known phenomenon playing a significant role in the high-temperature processing of metals, including industrial forming and severe plastic deformations. The ongoing discussion on the Zener–Hollomon (Z–H) parameter as a descriptor of materials’ propensity to DDRX and a measure of microstructure homogeneity leaves more questions than answers and prevents its practical application. Most of the existing DDRX models are continuous, and so the geometry and topology of real grain microstructures cannot be considered. The present study uses a fully discrete representation of polycrystalline aluminium alloys as 2D/3D Voronoi space tessellations corresponding to EBSD maps. Such tessellations are geometric realisations of combinatorial structures referred to as polytopal cell complexes. Combining discrete models with FEM LS-Dyna simulations of shock-wave propagation in AA1050 and AW5083 aluminium alloys makes it possible to estimate for the first time the contribution of DDRX to the final material microstructure inside adiabatic shear bands. It is shown that the increase of the initial fraction of high-angle grain boundaries, caused by preliminary deformation, significantly increases the spatial homogeneity and decreases the clustering of DDRX grains. The obtained results contradict the conventional assumption that the microstructures obtained by severe plastic deformation under quasi-static and dynamic deformation conditions are similar due to the similar value of the Z–H parameter: competition between the two recrystallisation mechanisms leads to almost unpredictable final grain structures inside share bands that require further comprehensive experimental studies. This agrees with experimental evidence for high material sensitivity to the Z–H parameter.

QuickCSGModeling: Quick CSG Operations Based on Fusing Signed Distance Fields for VR Modeling

The latest advancements in Virtual Reality (VR) enable the creation of 3D models within a holographic immersive simulation environment. In this article, we create QuickCSGModeling , a user-friendly mid-air interactive modeling system. We first prepare a dataset consisting of diverse components and precompute the discrete signed distance function (SDF) for each component. During the modeling phase, users can freely design complicated shapes with a pair of VR controllers. Based on the discrete SDF representation, any CSG-like operation (union, intersection, and subtraction) can be performed voxel-wisely. Also, we maintain a single dynamic SDF for the whole scene, whose zero-level set surface exactly encodes the most recent constructed shape. Both SDF fusion and surface extraction are implemented via GPU for a smooth user experience. A total of 34 volunteers were asked to create their favorite models using QuickCSGModeling. With a simple training, most of them can create a fascinating shape or even a descriptive scene quickly. We also discuss how to extend our system to create articulated models with hinges, where an adaptive cube subdivision has to be enforced to improve the reconstruction accuracy around the hinge part, followed by a Dual Contouring-based surface extraction. 1

Nonadiabatic Conical Intersection Dynamics in the Local Diabatic Representation with Strang Splitting and Fourier Basis.

We develop and implement an exact conical intersection nonadiabatic wave packet dynamics method that combines the local diabatic representation, Strang splitting for the total molecular propagator, and discrete variable representation with uniform grids. By employing the local diabatic representation, this method captures all nonadiabatic effects, including nonadiabatic transitions, electronic coherences, and geometric phase. Moreover, it is free of singularities in the first and second derivative couplings and does not require the electronic wave function to be continuous with respect to the nuclear coordinates. We further show that in contrast to the adiabatic representation, the split-operator method can be directly applied to the full molecular propagator with the locally diabatic ansatz. The Fourier series, employed as the primitive nuclear basis functions, is universal and can be applied to all types of reactive coordinates. The combination of local diabatic representation, Strang splitting, and Fourier basis allows numerically exact modeling of conical intersection quantum dynamics directly with adiabatic electronic states that can be obtained from standard electronic structure computations.

MODELING OF ANALOG-TO-DIGITAL SIGNAL CONVERTERS FOR SENSOR MICROSYSTEMS IN THE MICROWIND SOFTWARE

For the results of simulating the operation of analog-digital converters, we chose such a converter as the serial approximation ADC (SAR ADC). A sequential approximation ADC is a type of analog-to-digital converter that converts a continuous analog waveform to a discrete digital representation by binary search through all possible quantization levels before finally converging on a digital output for each conversion. There are three important blocks in the SAR ADC architecture: the sample and hold circuit (Sample and Hold, S/H), the comparator, and the SAR block. The topology and principle of operation of which was modeled in the Micro Wind software environment.

Iterative Token Evaluation and Refinement for Real-World Super-resolution

Real-world image super-resolution (RWSR) is a long-standing problem as low-quality (LQ) images often have complex and unidentified degradations. Existing methods such as Generative Adversarial Networks (GANs) or continuous diffusion models present their own issues including GANs being difficult to train while continuous diffusion models requiring numerous inference steps. In this paper, we propose an Iterative Token Evaluation and Refinement (ITER) framework for RWSR, which utilizes a discrete diffusion model operating in the discrete token representation space, i.e., indexes of features extracted from a VQGAN codebook pre-trained with high-quality (HQ) images. We show that ITER is easier to train than GANs and more efficient than continuous diffusion models. Specifically, we divide RWSR into two sub-tasks, i.e., distortion removal and texture generation. Distortion removal involves simple HQ token prediction with LQ images, while texture generation uses a discrete diffusion model to iteratively refine the distortion removal output with a token refinement network. In particular, we propose to include a token evaluation network in the discrete diffusion process. It learns to evaluate which tokens are good restorations and helps to improve the iterative refinement results. Moreover, the evaluation network can first check status of the distortion removal output and then adaptively select total refinement steps needed, thereby maintaining a good balance between distortion removal and texture generation. Extensive experimental results show that ITER is easy to train and performs well within just 8 iterative steps.

Symbolic Cognitive Diagnosis via Hybrid Optimization for Intelligent Education Systems

Cognitive diagnosis assessment is a fundamental and crucial task for student learning. It models the student-exercise interaction, and discovers the students' proficiency levels on each knowledge attribute. In real-world intelligent education systems, generalization and interpretability of cognitive diagnosis methods are of equal importance. However, most existing methods can hardly make the best of both worlds due to the complicated student-exercise interaction. To this end, this paper proposes a symbolic cognitive diagnosis~(SCD) framework to simultaneously enhance generalization and interpretability. The SCD framework incorporates the symbolic tree to explicably represent the complicated student-exercise interaction function, and utilizes gradient-based optimization methods to effectively learn the student and exercise parameters. Meanwhile, the accompanying challenge is that we need to tunnel the discrete symbolic representation and continuous parameter optimization. To address this challenge, we propose to hybridly optimize the representation and parameters in an alternating manner. To fulfill SCD, it alternately learns the symbolic tree by derivative-free genetic programming and learns the student and exercise parameters via gradient-based Adam. The extensive experimental results on various real-world datasets show the superiority of SCD on both generalization and interpretability. The ablation study verifies the efficacy of each ingredient in SCD, and the case study explicitly showcases how the interpretable ability of SCD works.

G2P-DDM: Generating Sign Pose Sequence from Gloss Sequence with Discrete Diffusion Model

The Sign Language Production (SLP) project aims to automatically translate spoken languages into sign sequences. Our approach focuses on the transformation of sign gloss sequences into their corresponding sign pose sequences (G2P). In this paper, we present a novel solution for this task by converting the continuous pose space generation problem into a discrete sequence generation problem. We introduce the Pose-VQVAE framework, which combines Variational Autoencoders (VAEs) with vector quantization to produce a discrete latent representation for continuous pose sequences. Additionally, we propose the G2P-DDM model, a discrete denoising diffusion architecture for length-varied discrete sequence data, to model the latent prior. To further enhance the quality of pose sequence generation in the discrete space, we present the CodeUnet model to leverage spatial-temporal information. Lastly, we develop a heuristic sequential clustering method to predict variable lengths of pose sequences for corresponding gloss sequences. Our results show that our model outperforms state-of-the-art G2P models on the public SLP evaluation benchmark. For more generated results, please visit our project page: https://slpdiffusier.github.io/g2p-ddm.

Say Anything with Any Style

Generating stylized talking head with diverse head motions is crucial for achieving natural-looking videos but still remains challenging. Previous works either adopt a regressive method to capture the speaking style, resulting in a coarse style that is averaged across all training data, or employ a universal network to synthesize videos with different styles which causes suboptimal performance. To address these, we propose a novel dynamic-weight method, namely Say Anything with Any Style (SAAS), which queries the discrete style representation via a generative model with a learned style codebook. Specifically, we develop a multi-task VQ-VAE that incorporates three closely related tasks to learn a style codebook as a prior for style extraction. This discrete prior, along with the generative model, enhances the precision and robustness when extracting the speaking styles of the given style clips. By utilizing the extracted style, a residual architecture comprising a canonical branch and style-specific branch is employed to predict the mouth shapes conditioned on any driving audio while transferring the speaking style from the source to any desired one. To adapt to different speaking styles, we steer clear of employing a universal network by exploring an elaborate HyperStyle to produce the style-specific weights offset for the style branch. Furthermore, we construct a pose generator and a pose codebook to store the quantized pose representation, allowing us to sample diverse head motions aligned with the audio and the extracted style. Experiments demonstrate that our approach surpasses state-of-the-art methods in terms of both lip-synchronization and stylized expression. Besides, we extend our SAAS to video-driven style editing field and achieve satisfactory performance as well.

Direct Punjabi to English Speech Translation using Discrete Units

Speech-to-speech translation is yet to reach the same level of coverage as text-to-text translation systems. The current speech technology is highly limited in its coverage of over 7000 languages spoken worldwide, leaving more than half of the population deprived of such technology and shared experiences. With voice-assisted technology (such as social robots and speech-to-text apps) and auditory content (such as podcasts and lectures) on the rise, ensuring that the technology is available for all is more important than ever. Speech translation can play a vital role in mitigating technological disparity and creating a more inclusive society. With a motive to contribute towards speech translation research for low-resource languages, our work presents a direct speech-to-speech translation model for one of the Indic languages called Punjabi to English. Additionally, we explore the performance of using a discrete representation of speech called discrete acoustic units as input to the Transformer-based translation model. The model, abbreviated as Unit-to-Unit Translation (U2UT), takes a sequence of discrete units of the source language (the language being translated from) and outputs a sequence of discrete units of the target language (the language being translated to). Our results show that the U2UT model performs better than the Speechto-Unit Translation (S2UT) model by a 3.69 BLEU score.

Hierarchical graph contrastive learning of local and global presentation for multimodal sentiment analysis

Multi-modal sentiment analysis (MSA) aims to regress or classify the overall sentiment of utterances through acoustic, visual, and textual cues. However, most of the existing efforts have focused on developing the expressive ability of neural networks to learn the representation of multi-modal information within a single utterance, without considering the global co-occurrence characteristics of the dataset. To alleviate the above issue, in this paper, we propose a novel hierarchical graph contrastive learning framework for MSA, aiming to explore the local and global representations of a single utterance for multimodal sentiment extraction and the intricate relations between them. Specifically, regarding to each modality, we extract the discrete embedding representation of each modality, which includes the global co-occurrence features of each modality. Based on it, for each utterance, we build two graphs: local level graph and global level graph to account for the level-specific sentiment implications. Then, two graph contrastive learning strategies is adopted to explore the different potential presentations based on graph augmentations respectively. Furthermore, we design a cross-level comparative learning for learning local and global potential representations of complex relationships.

Commonality and variation in mental representations of music revealed by a cross-cultural comparison of rhythm priors in 15 countries

Music is present in every known society but varies from place to place. What, if anything, is universal to music cognition? We measured a signature of mental representations of rhythm in 39 participant groups in 15 countries, spanning urban societies and Indigenous populations. Listeners reproduced random ‘seed’ rhythms; their reproductions were fed back as the stimulus (as in the game of ‘telephone’), such that their biases (the prior) could be estimated from the distribution of reproductions. Every tested group showed a sparse prior with peaks at integer-ratio rhythms. However, the importance of different integer ratios varied across groups, often reflecting local musical practices. Our results suggest a common feature of music cognition: discrete rhythm ‘categories’ at small-integer ratios. These discrete representations plausibly stabilize musical systems in the face of cultural transmission but interact with culture-specific traditions to yield the diversity that is evident when mental representations are probed across many cultures.

Learning All-In Collaborative Multiview Binary Representation for Clustering.

Multiview clustering via binary representation has attracted intensive attention due to its effectiveness in handling large-scale multiple view data. However, these kind of clustering approaches usually ignore a very important potential high-order correlation in discrete representation learning. In this article, we propose a novel all-in collaborative multiview binary representation for clustering (AC-MVBC) framework, where multiview collaborative binary representation and clustering structure are learned in a joint manner. Specifically, using a new type of tensor low-rank constraint, the high-order collaborations, i.e., cross-view and inner view collaborations, can be effectively captured in our model. Moreover, by incorporating the Bregman discrepancy, the projective consistency among different views can be guaranteed to achieve a more powerful binary representation. An efficient optimization algorithm is also proposed to solve the objective function with fast convergence empirically. Experimental results on several challenge datasets demonstrate that the proposed method has achieved highly competent performance compared with the state-of-the-art multiview clustering (MVC) methods while maintaining low computational and memory requirements.