Representation Of Moments Research Articles

Digital Models and 3D Biomechanics Analysis in Orthodontics. Part 1: Vector Calculations

Biomechanics is essential for optimizing orthodontic appliances and controlling dental movement. Charles J. Burstone pioneered a three-dimensional (3D) approach in orthodontics, advocating for a shift beyond appliance-focused methods. Initially, biomechanics studies were constrained to two-dimensional (2D) analysis due to the complexities of 3D evaluation. Despite progress in computational tools and digital modeling, orthodontic biomechanics has largely maintained a 2D orientation. This paper advances orthodontic biomechanics into 3D, re-evaluating concepts previously limited to 2D frameworks. A dedicated software, DDP-Ortho (Ortolab, Poland), is introduced to enable orthodontists to analyze and resolve biomechanical challenges in 3D, facilitating appliance designs with precise 3D force systems. The representation and calculation of force vectors and moments in 3D are detailed, emphasizing the inherent complexity absent computational support. Key processes such as vector subtraction and addition, fundamental for assessing and refining orthodontic force systems, are explained. Additionally, the vector split (couple replacement) method, previously described in 2D, is extended to 3D, addressing the unique constraints and challenges of this approach. These tools promise to refine the accuracy and effectiveness of orthodontic treatments, setting the stage to examine the interactions between 3D force systems and dental movement, which will be addressed in a subsequent paper, to broaden the potential of contemporary orthodontic therapy.

Flora Tristán and María Nieves Y Bustamante, Two Moments In 19th Century Peruvian Literature

Peruvian literature of the 19th century has important representatives that have been studied by critics. Its contextual conditions are highlighted, especially with two transcendental historical events: the independence of Peru and the War of the Pacific. Flora Tristán published Peregrinaciones de una paria at a time when independence was being consolidated in Peru. Later, María Nieves y Bustamante published Jorge o el hijo del pueblo after the war with Chile. Both writers constitute two creative representations of historical moments of Peruvian society. The first based on a hybrid text: a mix of personal diary, travel chronicle and adventure novel; and the second, as a historical and romantic novel from the late 19th century in Peru. The objective of this essay is to explore the historical representation in the literature carried out by these two writers.

On the eigenstructure of the q-Stancu operator

The main goal of this research is to find the eigenvalues and the corresponding eigenfunctions of the q-Stancu operator, $L_{n,s,q}$, introduced by $L$. Yun and R. Wang. In this work, an explicit representation for moments of all orders has been derived. Further, it has been proved that $L_{n,s,q}$ possesses $n − s + 1$ linearly independent eigenfunctions whose explicit expression and the corresponding eigenvalues are derived. In addition, for special choices of parameters, several eigenfunctions are depicted.

Measure-valued affine and polynomial diffusions

We introduce a class of measure-valued processes, which – in analogy to their finite dimensional counterparts – will be called measure-valued polynomial diffusions. We show the so-called moment formula, i.e. a representation of the conditional marginal moments via a system of finite dimensional linear PDEs. Furthermore, we characterize the corresponding infinitesimal generators obtaining a representation analogous to polynomial diffusions on R+m, in cases where their domain is large enough. In general the infinite dimensional setting allows for richer specifications strictly beyond this representation. As a special case, we recover measure-valued affine diffusions, sometimes also called Dawson–Watanabe superprocesses. From a mathematical finance point of view, the polynomial framework is especially attractive since it allows to transfer many famous finite dimensional models and their tractability properties to an infinite dimensional measure-valued setting.

The journeys of Orpheus

AbstractThe figure of Orpheus has been and continues to be the subject of in-depth studies focusing mainly on the historical, religious (relative especially to Orphism), and then iconographic aspects (the representation of Orpheus and typical moments of mythical imagination that concern him). It may be interesting here to draw a precise map of places visited by Orpheus, alive but also once killed, through his prophetic head and lyre. This paper also aims to present the iconographic itinerary of the journeys of the Thracian singer between Ancient and Modern times.

‘All brilliant gloss’: the liminal visual in Softley’s The Wings of the Dove

Abstract This article examines Ian Softley’s 1997 adaptation of Henry James’s 1902 novel The Wings of the Dove as a study in the representation of liminal sociocultural moments, specifically through its infusive representation of the character of Aunt Maud, played in the film by Charlotte Rampling. James’s Maud is the financial centre of the narrative, a complex and contradictory weaponization of philistine convention and vulgar immorality, a collage of surfaces repeatedly described as gloss on a double-sided coin. James felt that the diffusiveness of Maud’s power was the novel’s structural problem, because it inhabited a liminal space where the desires of the individual coextend with the desires of the market, and thereby dislocated the centre of critique and control in the text, moving the reader further and further away from the commercial trappings of their cultural moment. The filmmakers claimed that eliminating Maud allowed them to update the novel’s language, costumes, etiquette, and environment for a younger audience, but the film was dismissed as a pandering cash grab, an attempt to make Henry James a brand. In this way, the film diminishes Maud’s presence but empowers her narrative agency; resituating James’s brand of displacement, alienation, and loss into a liminal environment makes Maud’s commercial influence so inescapable and self-reflexive that it makes the film look like one of her many enterprises.

Duality of Ensemble Systems through Moment Representations

Duality of Ensemble Systems through Moment Representations

Faster than FFT: Conformal accelerations method

Fourier-Laplace transform technique allows one to represent several classes of important probability distributions and solutions of basic boundary problems for wide classes of fractional differential equations as integrals of functions enjoying two key properties: analytic continuation to a cone or the union of a cone and tube domain, and regular decay at infinity. Integral representations for Wiener-Hopf factors, fractional moments and special functions enjoy these properties as well. In the paper, we present the general methodology which allows one to evaluate the integrals enjoying these properties very fast and accurately. Among applications, we derive new efficient realizations of the Fourier, Laplace and Z-transforms, representations for probability distributions in Levy models, stable ones including, and algorithms for pricing contingent claims, Monte-Carlo simulations and evaluation of special functions.

A Closer Look at Debiased Temporal Sentence Grounding in Videos: Dataset, Metric, and Approach

Temporal Sentence Grounding in Videos (TSGV) , which aims to ground a natural language sentence that indicates complex human activities in an untrimmed video, has drawn widespread attention over the past few years. However, recent studies have found that current benchmark datasets may have obvious moment annotation biases, enabling several simple baselines even without training to achieve state-of-the-art (SOTA) performance. In this paper, we take a closer look at existing evaluation protocols for TSGV, and find that both the prevailing dataset splits and evaluation metrics are the devils that lead to untrustworthy benchmarking. Therefore, we propose to re-organize the two widely-used datasets, making the ground-truth moment distributions different in the training and test splits, i.e., out-of-distribution (OOD) test. Meanwhile, we introduce a new evaluation metric “dR@ n ,IoU= m ” that discounts the basic recall scores especially with small IoU thresholds, so as to alleviate the inflating evaluation caused by biased datasets with a large proportion of long ground-truth moments. New benchmarking results indicate that our proposed evaluation protocols can better monitor the research progress in TSGV. Furthermore, we propose a novel causality-based Multi-branch Deconfounding Debiasing (MDD) framework for unbiased moment prediction. Specifically, we design a multi-branch deconfounder to eliminate the effects caused by multiple confounders with causal intervention. In order to help the model better align the semantics between sentence queries and video moments, we enhance the representations during feature encoding. Specifically, for textual information, the query is parsed into several verb-centered phrases to obtain a more fine-grained textual feature. For visual information, the positional information has been decomposed from the moment features to enhance the representations of moments with diverse locations. Extensive experiments demonstrate that our proposed approach can achieve competitive results among existing SOTA approaches and outperform the base model with great gains.

A moment kernel machine for clinical data mining to inform medical decision making

Machine learning-aided medical decision making presents three major challenges: achieving model parsimony, ensuring credible predictions, and providing real-time recommendations with high computational efficiency. In this paper, we formulate medical decision making as a classification problem and develop a moment kernel machine (MKM) to tackle these challenges. The main idea of our approach is to treat the clinical data of each patient as a probability distribution and leverage moment representations of these distributions to build the MKM, which transforms the high-dimensional clinical data to low-dimensional representations while retaining essential information. We then apply this machine to various pre-surgical clinical datasets to predict surgical outcomes and inform medical decision making, which requires significantly less computational power and time for classification while yielding favorable performance compared to existing methods. Moreover, we utilize synthetic datasets to demonstrate that the developed moment-based data mining framework is robust to noise and missing data, and achieves model parsimony giving an efficient way to generate satisfactory predictions to aid personalized medical decision making.

An object‐oriented approach toward two‐dimensional engineering mechanics

AbstractThe present work proposes an object‐oriented approach for the solution of problems in two‐dimensional engineering mechanics. New classes (in the terminology of object‐oriented programming) are proposed and implemented in the popular programming language ‘Python.’ These classes, along with the symbolic computation module of Python ‘sympy,’ enable one to reduce the solution of a large class of problems in undergraduate engineering mechanics to a set of Python statements. These statements are definitions of objects as instances of the proposed classes and calling of their relevant methods. If the thought process in the manual solution is represented by a flowchart, the present work can be viewed as a flowchart translator. As all the calculations are automatically performed, the present work relieves the student from the burden and fear of lengthy calculations. Different diagrammatic representations of velocity, acceleration, shear force, and bending moments are included for better physical understanding. It is believed that the proposed simple implementation would make problem‐solving and the learning process more enjoyable. Apart from a standard PC, the proposed work runs on a single‐board computer (tested in raspberry pi 4) and on an Android mobile device. A student feedback study ascertains the acceptability of the proposed method.

Spanish Culture from Romanticism to the Present: Structures of Feeling by Jo Labanyi

Reviewed by: Spanish Culture from Romanticism to the Present: Structures of Feeling by Jo Labanyi Richard Cleminson Spanish Culture from Romanticism to the Present: Structures of Feeling. By Jo Labanyi. (Selected Essay, 11) Cambridge: Legenda. 2019. xii+349 pp. £80. ISBN 978–1–78188–932–9. The great advantage of the Legenda 'Selected Essays' series is the combination in one volume of a set of prodigious works by highly influential authors such as Jo Labanyi. The task for the reviewer is, consequently, a somewhat daunting one, however satisfying the reading of the individual chapters may be. This book, set out in six parts and containing previously published essays, constitutes a key contribution to Spanish Cultural and Literary Studies. Running through the collection is the author's attention to 'structures of feeling', drawing on Raymond Williams's notion, as a driver and explanatory resource for the comprehension of a diverse array of cultural production primarily from the nineteenth and twentieth centuries. Part I focuses on romanticism; Part II on the realist novel and art; and the remaining parts centre on the twentieth century, with the final sections on historical memory. The first chapter, originally published in the Hispanic Research Journal in 2004, addresses the understudied (and nowadays rarely taught, at least in British universities) eighteenth and first half of the nineteenth century in order to reconsider the contribution made to European discourses on modernization and romantic love by literary production from the period. In a deft reappraisal of works by the Spanish Romantics who turned to the medieval period, Labanyi argues for the interconnectedness of Spain with European representations of love, thereby disrupting the [End Page 269] 'primitive' and anti-modern stereotypes foisted on Spain by less careful observers. Rather than rigid categories and set characteristics, Labanyi invites the reader to consider the unruly influence of alternative expressions of subjectivity by engaging in a kind of historical 'border studies' 'that tries to think across the historical "divides" produced by established schemes of periodization' (p. 11). Coupled with the identification of the structures of feeling manifested in alternative stories and readings, this borderland subjectivity perused against the grain forms the hilo conductor of Labanyi's book. The romanticized versions of love, drawn on an Arabic past, provide 'the basis for future models of the nation' (p. 15). Nation-forming was also influenced by the representation of important moments from the past or instances of daily life as events around which to coalesce and expose 'the public to representations of the past organized in a particular way', thereby schooling the public 'in modes of viewing appropriate to modern citizens' (p. 88) and emphasizing the generative force of painting in constructions of feeling and identity in the present (Chapter 8 in Part II). Novels and films are other sources of (re)presentation of images in the early twentieth century and under the Franco regime. Drawing on work by Klaus Theweleit on the genesis of the 'fascist character' in men, the chapter on Giménez Caballero's Genio de España (1932) shows how the author drew on a version of modernism that was defined by an appeal to the irrational, 'allowing it to reach the masses by speaking to the unconscious' (p. 122). Such an interpretation permits Labanyi to complicate the acceptance of certain traits of modernism by both left and right rather than assume an implicit anti-modernism on the part of Spanish fascists. Caballero's writings and speeches were ingrained with gendered aspects and the fear of the loss of unity, whether by means of the republican divorce law of 1932 or the separation of Catalonia from Spain. Rather than rejecting or eschewing the Jewish contribution to Hispanic civilization, his desire was to incorporate said contribution(s) into Spain's imperial history just as other races had been dissolved by Spanish males into the broader imperial project begun centuries before. The wide-ranging Chapter 11 on commonalities and differences between Maeztu, Giménez Caballero, and Madariaga as well as their usages of Don Juan and romantic love to prop up their own political visions is, alongside the first chapter on Arabic love and the last chapters on the intricacies of...

A "moment-conserving" reformulation of GW theory.

We show how to construct an effective Hamiltonian whose dimension scales linearly with system size, and whose eigenvalues systematically approximate the excitation energies of GW theory. This is achieved by rigorously expanding the self-energy in order to exactly conserve a desired number of frequency-independent moments of the self-energy dynamics. Recasting GW in this way admits a low-scaling O[N4] approach to build and solve this Hamiltonian, with a proposal to reduce this further to O[N3]. This relies on exposing a novel recursive framework for the density response moments of the random phase approximation, where the efficient calculation of its starting point mirrors the low-scaling approaches to compute RPA correlation energies. The frequency integration of GW, which distinguishes so many different GW variants, can be performed without approximation directly in this moment representation. Furthermore, the solution to the Dyson equation can be performed exactly, avoiding analytic continuation, diagonal approximations, or iterative solutions to the quasiparticle equation, with the full-frequency spectrum obtained from the complete solution of this effective static Hamiltonian. We show how this approach converges rapidly with respect to the order of the conserved self-energy moments and is applied across the GW100 benchmark dataset to obtain accurate GW spectra in comparison to traditional implementations. We also show the ability to systematically converge all-electron full-frequency spectra and high-energy features beyond frontier excitations, as well as avoiding discontinuities in the spectrum, which afflict many other GW approaches.

A graphic processing unit implementation for the moment representation of the lattice Boltzmann method

AbstractWe implement the moment representation of the lattice Boltzmann method in a graphic processing unit (GPU) environment to study the computational performance of three‐dimensional fluid flows. The moment representation of the lattice Boltzmann method (MRLBM) uses up to second‐order moments of the particle distribution function to regularize and reconstruct it. By adopting this method, there is a reduction in memory usage and global memory transfer and, therefore, increased performance. The results show an increase of up to 40% in speed compared to population schemes. The validation results show there was no loss of accuracy when using single precision for turbulent flows. The adoption of single‐precision also enables higher processing speed for GPUs with low double‐precision capability and reduces the memory footprint, which can further increase performance. The implementation here presented provides a fast and straightforward environment for fluid simulation by combining single‐precision and the MRLBM.

Quaternion fractional-order weighted generalized Laguerre–Fourier moments and moment invariants for color image analysis

Orthogonal moments based on Laguerre polynomials, especially the quaternion representation of fractional-order orthogonal moments have attracted interest in the imaging field. However, most of the existing quaternion fractional-order color orthogonal moments (QFr-COMs) based on Laguerre polynomials are constructed on Cartesian coordinate space and do not have direct rotation geometric invariance. Inspired by the idea of polynomial transformation, we present a weighted radial normalized fractional-order generalized Laguerre polynomials (WRNFr-GLPs) in polar coordinate space. On the basis, a new set of quaternion fractional-order weighted generalized Laguerre–Fourier moments (QFr-WGLFMs) is proposed and a fast and reliable computing method for geometric invariance of QFr-WGLFMs also is introduced in this paper. Theoretical analyses and experimental results showed that the proposed QFr-WGLFMs and moment invariants offer enhanced image reconstruction and pattern recognition compared with the existing quaternion fractional-order-based orthogonal moments and deep learning-based​ methods, especially under the conditions of image processing with noise and smooth filtering.

An integral representation for inverse moments of multivariate random variables

In this note, we derive an integral representation for inverse moments of positive integer valued multivariate random variables, generalizing a result in Shibu et al. Examples are provided to illustrate the result.

Bernstein-type bounds for beta distribution

This work obtains sharp closed-form exponential concentration inequalities of Bernstein type for the ubiquitous beta distribution, improving upon sub-Gaussian and sub-gamma bounds previously studied in this context. The proof leverages a novel handy recursion of order 2 for central moments of the beta distribution, obtained from the hypergeometric representations of moments; this recursion is useful for obtaining explicit expressions for central moments and various tail approximations.

Representation of nuclear magnetic moments via a Clifford algebra formulation of Bohm’s hidden variables

In this paper, we outline the research conducted by the first named author and his associates on the axiom-preserving, thus isotopic completion of quantum mechanics into hadronic mechanics according to the historical legacy by A. Einstein, B. Podolsky and N. Rosen that quantum mechanics is not a complete theory and review the ensuing exact representation of the magnetic moment and spin of the Deuteron in its ground state thanks to the isotopic completion of Pauli’s matrices with an explicit and concrete content of D. Bohm’s hidden variablelambda. We then outline the independent studies conducted by the second named author on the representation of the conventional Pauli’s matrices via geometric Clifford algebras. We finally show that the combination of the two studies allows a mathematically rigorous, numerically exact and time invariant geometric representation of the magnetic moment, spin and hidden variable of the Deuteron in its ground state.

Propagation pattern for moment representation of the lattice Boltzmann method.

A propagation pattern for the moment representation of the regularized lattice Boltzmann method (LBM) in three dimensions is presented. Using effectively lossless compression, the simulation state is stored as a set of moments of the lattice Boltzmann distribution function, instead of the distribution function itself. An efficient cache-aware propagation pattern for this moment representation has the effect of substantially reducing both the storage and memory bandwidth required for LBM simulations. This paper extends recent work with the moment representation by expanding the performance analysis on central processing unit (CPU) architectures, considering how boundary conditions are implemented, and demonstrating the effectiveness of the moment representation on a graphics processing unit (GPU) architecture.

Learning Video Moment Retrieval Without a Single Annotated Video

Video moment retrieval has progressed significantly over the past few years, aiming to search the moment that is most relevant to a given natural language query. Most existing methods are trained in a fully-supervised or a weakly-supervised manner, which requires a time-consuming and expensive manually labeling process. In this work, we propose an alternative approach to achieving video moment retrieval that requires no textual annotations of videos and instead leverages the existing visual concept detectors and a pre-trained image-sentence embedding space. Specifically, we design a video-conditioned sentence generator to produce a suitable sentence representation by utilizing the mined visual concepts in videos. We then design a GNN-based relation-aware moment localizer to reasonably select a portion of video clips under the guidance of the generated sentence. Finally, the pre-trained image-sentence embedding space is adopted to evaluate the matching scores between the generated sentence and moment representations with the knowledge transferred from the image domain. By maximizing these scores, the sentence generator and moment localizer can enhance and complement each other to achieve the moment retrieval task. Experimental results on the Charades-STA and ActivityNet Captions datasets demonstrate the effectiveness of our proposed method.