Dimensional Space Research Articles

Holography of broken U(1) symmetry

We examine the Abelian Higgs model in (d + 1)-dimensional anti-de Sitter space with an ultraviolet brane. The gauge symmetry is broken by a bulk Higgs vacuum expectation value triggered on the brane. We propose two separate Goldstone boson equivalence theorems for the boundary and bulk degrees of freedom. We compute the holographic self-energy of the gauge field and show that its spectrum is either a continuum, gapped continuum, or a discretuum as a function of the Higgs bulk mass. When the Higgs has no bulk mass, the AdS isometries are unbroken. We find in that case that the dual CFT has a non-conserved U(1) current whose anomalous dimension is proportional to the square of the Higgs vacuum expectation value. When the Higgs background weakly breaks the AdS isometries, we present an adapted WKB method to solve the gauge field equations. We show that the U(1) current dimension runs logarithmically with the energy scale in accordance with a nearly-marginal U(1)-breaking deformation of the CFT.

Analysis of Manifold and its Application

Manifold learning is a field of study in machine learning and statistics that is closely associated with dimensionality reduction algorithmic techniques is gaining popularity these days. There are two types of manifold learning approaches: linear and nonlinear. Principal component analysis (PCA) and multidimensional scaling (MDS) are two examples of linear techniques that have long been staples in the statistician's arsenal for evaluating multivariate data. Nonlinear manifold learning, which encompasses diffusion maps, Laplacian Eigenmaps, Hessian Eigenmaps, Isomap, and local linear embedding, has seen a surge in research effort recently. A few of these methods are nonlinear extensions of linear approaches. A nearest search, the definition of distances or affinities between points (a crucial component of these methods' effectiveness), and an Eigen problem for embedding high-dimensional points into a lower dimensional space make up the algorithmic process of the majority of these techniques. The strengths and weaknesses of the new method are briefly reviewed in this article. In the field of computer graphics, we utilize a particular manifold learning method was first presented in statistics and machine learning to create a global, Spectral-based shape descriptor.

Enhancement of Reflood Test Prediction by Integrating Machine Learning and Data Assimilation Technique

Data assimilation (DA) was revealed as a highly efficient approach to enhance the prediction’s accuracy, demonstrating the reliability of the simulation through uncertainty quantification analysis. However, in the numerical simulations, most of the tasks are highly nonlinear relationships between the parameters that directly affect the efficiency of the DA such as the large search space dimension, resulting in significant computational costs. This limitation can be overcome by implementing machine learning (ML) predictions that can efficiently expand the DA search space. Therefore, this study is aimed at enhancing the performance of DA by integrating ML and DA (IMD), proposing a new method to overcome the stand-alone DA limitations. The approach involved implementing a stand-alone DA using the multidimensional analysis of reactor safety (MARS) code to enhance the prediction of reflood tests. The output datasets obtained from the stand-alone DA were then used to train the deep neural networks (DNNs), and the accuracy of the DNN’s prediction was thoroughly evaluated with varying dataset sizes. This DNN subsequently can predict the enormous unobserved samples, enabling the identification and investigation of the prospective candidates for the subsequent DA process. The results demonstrated that the stand-alone DA achieved an accuracy enhancement of up to 41.3% in reflood test predictions, while the IMD yielded even more significant improvements, with a performance enhancement of 47.0%. These findings reveal that the IMD approach outperformed the stand-alone DA approach, particularly in the case of high flooding rate tests. In this context, the proposed integrating system can effectively overcome the high computational cost and enhance the performance of stand-alone DA.

Compact convergence, deformation of the $L^{2}$-$\overline{\partial}$-complex and canonical $K$-homology classes

Let (X,\gamma) be a compact, irreducible Hermitian complex space of complex dimension m and with \dim(\mathrm{sing}(X))=0 . Let (F,\tau)\rightarrow X be a Hermitian holomorphic vector bundle over X , and let us denote by \overline{\eth}_{F,m,\mathrm{abs}} the rolled-up operator of the maximal L^{2} - \overline{\partial} -complex of F -valued (m,\bullet) -forms. Let \pi:M\rightarrow X be a resolution of singularities, g a metric on M , E:=\pi^{*}F and \rho:=\pi^{*}\tau . In this paper, under quite general assumptions on \tau , we prove the following equality of analytic K -homology classes [\overline{\eth}_{F,m,\mathrm{abs}}]=\pi_{*}[\overline{\eth}_{E,m}] , with \overline{\eth}_{E,m} the rolled-up operator of the L^{2} - \overline{\partial} -complex of E -valued (m,\bullet) -forms on M . Our proof is based on functional analytic techniques developed in Kuwae and Shioya (2003) and provides an explicit homotopy between the even unbounded Fredholm modules induced by \overline{\eth}_{F,m,\mathrm{abs}} and \overline{\eth}_{E,m} .

Multidimensional primate niche space sheds light on interspecific competition in primate evolution

Characterising how the totality of primate diversity is distributed across the order, and how it evolved, is challenging because diversity in individual traits often show opposing phylogenetic patterns. A species’ combination of traits can be conceptualised as its ‘niche’. Here, we describe and analyse seven-dimensional niche space, comprising 11 traits, for 191 primate species. Multifaceted diversity is distributed unequally among taxonomic groups. Cercopithecoidea and Hominidae occupy the largest areas of niche space, and are the most diverse families; platyrrhine families occupy small areas, and this space overlaps with strepsirrhines. The evolution of species’ locations in niche space is regulated by selection for adaptive optima in trait combinations. Given that niche similarity results in interspecific competition, we quantify two measures of species’ niche locations relative to others. We find that omnivores, frugivores, and species tolerating higher temperatures experience stronger interspecific competition. Hominidae occupation of niche space suggests competitive exclusion from niches by Cercopithecoidea over evolutionary time; but living great apes experience the lowest levels of interspecific competition. Callitrichids experience the highest levels of interspecific competition. Our results provide a standardised measure of primate niches that sheds light on the partitioning and evolution of primate diversity, and how this is driven by interspecific competition.

INTRUDER DETECTION SYSTEM USING MACHINE LEARNING

The face is one of the easiest ways to distinguish the individual identity of each other. Face recognition is a personal identification system that uses personal characteristics of a person to identify the person's identity. Human face recognition procedure basically consists of two phases, namely face detection, where this process takes place very rapidly in humans, except under conditions where the object is located at a short distance away, the next is the introduction, which recognize a face as individuals. Stage is then replicated and developed as a model for facial image recognition (face recognition) is one of the much-studied biometrics technology and developed by experts. There are two kinds of methods that are currently popular in developed face recognition pattern namely, Eigenface method and Fisher face method. Facial image recognition Eigenface method is based on the reduction of face dimensional space using Principal Component Analysis (PCA) for facial features. The main purpose of the use of PCA on face recognition using Eigen faces was formed (face space) by finding the eigenvector corresponding to the largest eigenvalue of the face image. The area of this project face detection system with face recognition is Image processing. The software requirements for this project is MATLAB software. Keywords: Digital Image Processing, Face Detection, Face Recognition, Motion Detection

Olfactory EEG induced by odor: Used for food identification and pleasure analysis

As the need for food authenticity verification increases, sensory evaluation of food odors has become widely recognized. This study presents a theory based on electroencephalography (EEG) to create an Olfactory Perception Dimensional Space (EEG-OPDS), using feature engineering and ensemble learning to establish material and emotional spaces based on odor perception and pleasure. The study examines the intrinsic connection between these two spaces and explores the mechanisms of integration and differentiation in constructing the OPDS. This method effectively visualizes various types of food odors while identifying their perceptual intensity and pleasantness. The average classification accuracy for odor recognition in an eight-category experiment is 96.1%. Conversely, the average classification accuracy for sensory pleasantness recognition in a two-category experiment is 98.8%. The theoretical approach proposed in this study, based on olfactory EEG signals to construct an OPDS, captures the subtle perceptual differences and individualized pleasantness responses to food odors.

Scattering model of scintillation arcs in pulsar secondary spectra

ABSTRACT The dynamic spectra of pulsars frequently exhibit diverse interference patterns, often associated with parabolic arcs in the Fourier-transformed (secondary) spectra. Our approach differs from previous ones in two ways: first, we extend beyond the traditional Fresnel–Kirchhoff method by using the Green’s function of the Helmholtz equation, i.e. we consider spherical waves originating from three-dimensional space, not from a two-dimensional screen. Secondly, the discrete structures observed in the secondary spectrum result from discrete scatterer configurations, namely plasma concentrations in the interstellar medium, and not from the selection of points by the stationary phase approximation. Through advanced numerical techniques, we model both the dynamic and secondary spectra, providing a comprehensive framework that describes all components of the latter spectra in terms of physical quantities. Additionally, we provide a thorough analytical explanation of the secondary spectrum.

Entropy Production of Run-and-Tumble Particles.

We analyze the entropy production in run-and-tumble models. After presenting the general formalism in the framework of the Fokker-Planck equations in one space dimension, we derive some known exact results in simple physical situations (free run-and-tumble particles and harmonic confinement). We then extend the calculation to the case of anisotropic motion (different speeds and tumbling rates for right- and left-oriented particles), obtaining exact expressions of the entropy production rate. We conclude by discussing the general case of heterogeneous run-and-tumble motion described by space-dependent parameters and extending the analysis to the case of d-dimensional motions.

Fusion and fission phenomena in a (2+1)-dimensional Sawada-Kotera type system

In this study, we extend the generalized multilinear variable separation approach to a fifth-order nonlinear evolution equation. By performing asymptotic analysis on the variable separation solution, which is composed of three lower-dimensional functions, we identify a resonant regime governing dromion-dromion/solitoff interactions. In the case of two-dromion interactions, elastic, inelastic, and completely inelastic collisions are possible, while for the dromion-solitoff interaction only inelastic and completely inelastic collisions are permitted. Furthermore, we derive two types of semi-rational solutions from the quadratic function ansatz. In particular, in the scenario of a completely resonant collision between a lump and a line-soliton pair, the lump separates from one line soliton and exists briefly before merging with the other soliton, forming a localized lump in both time and space dimensions. The fusion or fission phenomena between the dromion-dromion/solitoff interaction and the lump-line soliton interaction are shown graphically.

A domain wall and chiral edge currents in holographic chiral phase transitions

We investigate spatially inhomogeneous solutions in a top-down holographic model: the D3/D7 model which provides a holographic description of the chiral phase transition for a finite external magnetic field, chemical potential, and temperature. We numerically find a domain wall (or kink) solution in the three dimensional space, which incorporates between the chiral symmetry broken phase at the spatial infinity, under the homogeneous sources. Along with the inhomogeneity of the chiral condensate, the charge density is also spatially modulated. The modulated charge density and finite magnetic field lead to the chiral edge current close to the domain wall. We explore the dependences of those profiles on the chemical potential and temperature near the first and second order phase transition points. Our results indicate that the inhomogeneous solutions we found are in good agreement with those obtained by the Ginzburg-Landau theory in the vicinity of the transition points.

A shortest‐path‐aided fast‐sweeping method to improve the accuracy of traveltime calculation in vertically transverse isotropic media

AbstractThe high accuracy and efficiency of traveltime calculation are critical in seismic tomography, migration, static corrections, source locations and anisotropic parameter estimation. The fast‐sweeping method is an efficient upwind finite‐difference approach for solving the eikonal equation. However, the fast‐sweeping method is accurate only along the axis directions. In two‐dimensional or higher dimensional cases, the accuracy is severely decreased in the diagonal directions due to the numerical errors in these directions. These similar numerical errors also arose in higher order fast‐sweeping method and anisotropic fast‐sweeping method. To improve the accuracy of traveltime calculation in two‐dimensional or higher dimensional space, a shortest‐path‐aided fast‐sweeping method is proposed. The shortest‐path‐aided solution is embedded into the sweeping process of the standard fast‐sweeping method to improve the traveltime accuracy in the diagonal directions. Shortest‐path‐aided fast‐sweeping method is very easy to implement nearly without additional computational cost and memory consumption. Furthermore, this method is easy to extend from two‐dimensional to higher dimensional, from low‐order to higher‐order and from isotropic to anisotropic cases.

Active Learning of Ligands That Enhance Perovskite Nanocrystal Luminescence.

Ligands play a critical role in the optical properties and chemical stability of colloidal nanocrystals (NCs), but identifying ligands that can enhance NC properties is daunting, given the high dimensionality of chemical space. Here, we use machine learning (ML) and robotic screening to accelerate the discovery of ligands that enhance the photoluminescence quantum yield (PLQY) of CsPbBr3 perovskite NCs. We developed a ML model designed to predict the relative PL enhancement of perovskite NCs when coordinated with a ligand selected from a pool of 29,904 candidate molecules. Ligand candidates were selected using an active learning (AL) approach that accounted for uncertainty quantified by twin regressors. After eight experimental iterations of batch AL (corresponding to 21 initial and 72 model-recommended ligands), the uncertainty of the model decreased, demonstrating an increased confidence in the model predictions. Feature importance and counterfactual analyses of model predictions illustrate the potential use of ligand field strength in designing PL-enhancing ligands. Our versatile AL framework can be readily adapted to screen the effect of ligands on a wide range of colloidal nanomaterials.

Opto-magnonic reservoir computing coupling nonlinear interfered spin wave and visible light switching

Physical reservoir computing is a promising approach to realize high-performance artificial intelligence systems utilizing physical devices. Recently, it has been experimentally found that nonlinear interfered spin wave multi-detection shows excellent performance for processing nonlinear time-series data due to its outstanding features: nonlinearity, short-term memory, and the ability to map in high dimensional space. However, said performance is considerably inferior to reservoir computing utilizing an optical circuit with a large volume. Herein, we develop reservoir computing with nonlinear interfered spin wave coupled with light switching, namely opto-magnonic reservoir computing. The spin wave was modulated through a crystal field transition that occurred in two different Fe3+ sites of Y3Fe5O12 by visible light switching, and it was found that the spin wave modulated by visible light switching dramatically reduced normalized mean square errors to 4.96 × 10−3, 0.163, and 3.66 × 10−5 for NARMA2, NARMA10, and second-order nonlinear dynamical equation tasks. Said excellent performance results from the strong nonlinearity caused by chaos and large memory capacity induced by reservoir states diversified by visible light switching.

Determining input factor importance in a compartmental model using screening methods

Models are used in a wide variety of scientific disciplines to mathematically and simply represent real phenomenon, to understand and explain observed behaviors, and to make predictions of future behaviors. A compartmental model is a type of model that is used to evaluate an experimental investigation concerning transport of material in a system of the real world. Sensitivity analysis (SA) of models is required to investigate the effects of changes in the inputs on the model output(s). When dealing with large, complex, computationally expensive models, screening methods are essential to reduce the dimensionality of the input space for a subsequent SA which can help to determine and quantify the change in model behavior as model factors change. In this study, our focus is on the application of screening designs to a 25-compartment global carbon cycle model, which help us identify the most important input factors that control most of the output uncertainty. We explore similarities and dissimilarities in the results from these screening methods.

General perturbations in D+1 standard and brane cosmology revisited

In this work, we generalize the theory of perturbations in a ([Formula: see text])-dimensional space–time with cosmological constant, studying scalar, vector and tensor perturbations, as well as its structure in Newtonian and Synchronous gauge. We also show the theory of perturbations in the context of brane cosmology, where branes are embedded in a set of D-spatial dimensions, a temporal dimension, and an additional spatial dimension. In both standard and brane cosmology, an unperturbed space–time is provided with a Friedmann–Lemaitre–Robertson–Walker metric and arbitrary sectional curvature, the matter content has the shape of a perfect fluid. In addition, we consider the arbitrary sectional curvature, obtaining the respective equations in the Newtonian and Synchronous gauge. We highlight that the results presented in this paper can be used to treat brane cosmology with two concentric branes or tackle the [Formula: see text] tension with a braneworld approach. Finally, as an example of the utility of all the technology presented in this paper, we show an application to the energy flux and the repercussions in the framework of the braneworlds.

Consequences of Assigning Non-Measurable Sets Imprecise Probabilities

Abstract This paper is a discussion note on Isaacs, Hájek and Hawthorne (2022), which claims to offer a new motivation for imprecise probabilities, based on the mathematical phenomenon of non-measurability. In this note, I clarify some consequences of that proposal. In particular, I show that if the proposal is applied to a bounded 3-dimensional space, then one has to reject at least one of the following: If A is at most as probable as B and B is at most as probable as C, then A is at most as probable as C. • Let A∩C=B∩C=∅. A is at most as probable as B if and only if (A∪C) is at most as probable as (B∪C). But rejecting either statement seems unattractive.

Spectrality and the Plural Body: A Comparative Study of the Works of Apichatpong Weerasethakul and Korakrit Arunanondchai

This article surveys the role of the spectral body as a device of transgression, multiplicity and entanglement, through a comparative study of the film Uncle Boonmee Who Recalls His Past Lives (2010), by the contemporary artist and filmmaker Apichatpong Weerasethakul, and short film installation by contemporary artist Korakrit Arunanondchai, titled No History in a Room Filled with People with Funny Names 5 (2018) at Serralves Contemporary Art Museum, Porto, co-produced with Alex Gjovic and boychild. The body enacts a spectral, pluralistic device in the narrative strategies devised by the authors, traversing physical and spiritual dimensions in diegetic and extra-diegetic spaces, entangling subjects, territories, esoteric and spiritual traditions, postcolonial histories, and sociological dimensions.

The isomorphism problem for oligomorphic groups with weak elimination of imaginaries

AbstractIn Kechris et al. [J. Symb. Log. 83 (2018), no. 3, 1190–1203], it was asked if equality on the reals is sharp as a lower bound for the complexity of topological isomorphism between oligomorphic groups. We prove that under the assumption of weak elimination of imaginaries, this is indeed the case. Our methods are model theoretic and they also have applications on the classical problem of reconstruction of isomorphisms of permutation groups from (topological) isomorphisms of automorphisms groups. As a concrete application, we give an explicit description of for any vector space of dimension over a finite field, in affinity with the classical description for finite‐dimensional spaces due to Schreier and van der Waerden.

Optimal control problem for higher-order non-instantaneous impulsive fractional system with non-local conditions

The purpose of this article is to study the optimal control problem of higher-order non-instantaneous impulsive fractional system with non-local conditions by virtue of cosine operator theory in the Hilbert space. Initially, the sufficient conditions for the existence of a mild solution of the proposed system are verified by applying the fixed point theorem in infinite dimensional space. Further, we formulate and prove the existence results for optimal control of the proposed system with the corresponding cost functional by using Balder's theorem. Finally, an example is provided to illustrate the main results.