Dimensional Space Research Articles

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.

Bayesian analysis of the molecular emission and dust continuum of protoplanetary disks

The MIRI instrument on board the James Webb Space Telescope probes the chemistry and dust mineralogy of the inner regions of protoplanetary disks. The observed spectra are unprecedented in their detail and reveal a rich chemistry with strong diversity between objects. This complicates interpretations that are mainly based on manual continuum subtraction and 0D slab models. We investigate the physical conditions under which the gas emits in protoplanetary disks. Based on MIRI spectra, we apply a full Bayesian analysis that provides the posterior distributions of dust and molecular properties, such as column densities and emission temperatures. To do so, we introduced the Dust Continuum Kit with Line emission from Gas (DuCKLinG), a Python-based model simultaneously describing the molecular line emission and the dust continuum of protoplanetary disks without large computational cost. The model describes the dust continuum emission by dust models with precomputed dust opacities. The molecular emission is based on LTE slab models but from extended radial ranges with gradients in column densities and emission temperatures. We compare the model to observations using Bayesian analysis with linear regression techniques to reduce the dimension of the parameter space. We benchmarked this model to a complex thermo-chemical ProDiMo model of AA\,Tau and fit the MIRI spectrum of GW\,Lup. The latter allowed for a comparison to the previous results obtained with single slab models and hand-fitted continuum. We successfully decrease the computational time of the fitting method by a factor of $80$ by eliminating linear parameters, such as the emission areas, from the Bayesian run. This approach does not significantly change the retrieved molecular parameters, and only the calculated errors on the optically thin dust masses slightly decrease. For an AA\,Tau ProDiMo mock observation, we find that the retrieved molecular conditions from DuCKLinG (column densities from $3 cm^ $ to $4 cm^ $, radial range from $0.2\ au $ to $1.2\ au $, and temperature range from about $200\ K $ to $400\ K $) fall within the true values from ProDiMo (column densities between $4 cm^ $ to $5 cm^ $, radial extent $0.1\ au $ to $6.6\ au $, and temperature range from about $120\ K $ to $1000\ K $). The smaller DuCKLinG ranges can be explained by the relative flux contributions of the different parts of ProDiMo. The parameter posterior of GW\,Lup reinforces previously found results. The previously determined column densities fall within the retrieved ranges in this study for all examined molecules ( CO2 H2O HCN and C2H2 ). Similar overlap is found for the temperatures with only the temperature range of HCN (from $570^ K$ to K$) not including the previously found value ($875\ K$). This discrepancy may be due to the simultaneous fitting of all molecules compared to the step-by-step fitting of the previous study. There is statistically significant evidence for radial temperature and column density gradients for H2O and CO2 compared to the constant temperature and column density assumed in the 0D slab models. Additionally HCN and C2H2 emit from a small region with near constant conditions. Due to the small selected wavelength range $13.6\ m$ to $16.3\ m$, the dust properties are not well constrained for GW\,Lup. DuCKLinG can become an important tool to analyse the molecular emission and dust mineralogy of large samples based on JWST/MIRI spectra in an automated way.

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.

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.

Using autoencoders and deep transfer learning to determine the stellar parameters of 286 CARMENES M dwarfs

Deep learning (DL) techniques are a promising approach among the set of methods used in the ever-challenging determination of stellar parameters in M dwarfs. In this context, transfer learning could play an important role in mitigating uncertainties in the results due to the synthetic gap (i.e. difference in feature distributions between observed and synthetic data). We propose a feature-based deep transfer learning (DTL) approach based on autoencoders to determine stellar parameters from high-resolution spectra. Using this methodology, we provide new estimations for the effective temperature, surface gravity, metallicity, and projected rotational velocity for 286 M dwarfs observed by the CARMENES survey. Using autoencoder architectures, we projected synthetic PHOENIX-ACES spectra and observed CARMENES spectra onto a new feature space of lower dimensionality in which the differences between the two domains are reduced. We used this low-dimensional new feature space as input for a convolutional neural network to obtain the stellar parameter determinations. We performed an extensive analysis of our estimated stellar parameters, ranging from 3050 to 4300\,K, 4.7 to 5.1\,dex, and $-$0.53 to 0.25\,dex for eff $, log g and Fe/H respectively. Our results are broadly consistent with those of recent studies using CARMENES data, with a systematic deviation in our $T_ eff $ scale towards hotter values for estimations above 3\,750\,K. Furthermore, our methodology mitigates the deviations in metallicity found in previous DL techniques due to the synthetic gap. We consolidated a DTL-based methodology to determine stellar parameters in M dwarfs from synthetic spectra, with no need for high-quality measurements involved in the knowledge transfer. These results suggest the great potential of DTL to mitigate the differences in feature distributions between the observations and the PHOENIX-ACES spectra.

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.

Homotopical characterization of strongly contextual simplicial distributions on cone spaces

This paper offers a novel homotopical characterization of strongly contextual simplicial distributions with binary outcomes, specifically those defined on the cone of a 1-dimensional space. In the sheaf-theoretic framework, such distributions correspond to non-signaling distributions on measurement scenarios where each context contains 2 measurements with binary outcomes. To establish our results, we employ a homotopical approach that includes collapsing measurement spaces and introduce categories associated with simplicial distributions that can detect strong contextuality.

Higher rank (𝑞,𝑡)-Catalan polynomials, affine Springer fibers, and a finite rational shuffle theorem

We introduce the higher rank ( q , t ) (q,t) -Catalan polynomials and prove they equal truncations of the Hikita polynomial to a finite number of variables. Using affine compositions and a certain standardization map, we define a d i n v \mathtt {dinv} statistic on rank r r semistandard ( m , n ) (m,n) -parking functions and prove c o d i n v \mathtt {codinv} counts the dimension of an affine space in an affine paving of a parabolic affine Springer fiber. Combining these results, we give a finite analogue of the Rational Shuffle Theorem in the context of double affine Hecke algebras. Lastly, we also give a Bizley-type formula for the higher rank Catalan numbers in the non-coprime case.

Proactive Resource Allocation for Cloud Manufacturing: A Dynamic Approach with DNN-Based Hybrid Many Objective Leopard Seal Algorithm

In the domain of cloud manufacturing, diverse services and the escalating demand for efficient and cost-effective service composition selection in cloud manufacturing have spurred day by day. Traditional methods face several challenges such as the risk of convergence issues and suboptimal solutions, high dimensionality of decision space, increased computational complexity, and scalability issues. To overcome these complexities, this paper proposed a novel method named the Deep Neural Network (DNN) based Hybrid Many Objective Leopard Seal (HMOLS) algorithm. In this study, DNN is employed to predict future Quality of Service (QoS) for each service based on historical data and integrated features. These predictions are fed back into the optimization model, influencing the dynamic weight calculation for each objective function. In this work, the Leopard Seal Optimization is implemented for hyperparameter optimization to enhance the performance of the HMOLS algorithm. Various evaluation metrics namely accuracy, throughput, reliability, resource utilization, and scalability are utilized to evaluate the performance of the HMOLS method and compare its performance with existing methods. The experimental outcomes depict the effectiveness of the HMOLS approach for the effective selection of services and fusion for cloud manufacturing. DNN-based predictions utilize deep neural networks to predict resource demand or utilization patterns and enable more accurate allocation decisions. These predictions optimize resource allocation by reallocating resources accordingly and address the challenges of resource utilization. Meanwhile, this method is required to overcome the computational overhead for applicability in cloud manufacturing.

Finite dimension of the ion pathway networks in conducting glasses

In disordered materials, the ordinary understanding is that charge carriers tend to occupy energetically favorable sites known as ion-conducting channels. Many studies have revealed that the inherent fractal properties of such pathways lead to a sub-diffusive behavior. The linearity or branching of these pathways is crucial for determining how the charge carriers move. It can be thought that as the space dimensionality decreases, the average distance between the highest energy barriers along the conduction paths increases. In this study the finite dimension of those pathways is computed using an extended version of the classical Hausdorff dimension. Also, the Arrhenius behavior of the most mobile lithium ions is proved, confirming that such are responsible for conductivity behavior. The lithium ions mobility behavior in response to temperature changes and the finite dimension allowed to identify the ion diffusion regions fractal features. The reported results demonstrate that as the temperature increases the conducting channels become broadener, facilitating the transfer of electrical charge through the glassy matrix, below the transition temperature. The pathways behavior confirms the increase of the ionic conductivity when the temperature increases as it is experimentally observed.

Pattern Recognition of Partial Discharge Faults in Switchgear Using a Back Propagation Neural Network Optimized by an Improved Mantis Search Algorithm.

The dependable functioning of switchgear is essential to maintain the stability of power supply systems. Partial discharge (PD) is a critical phenomenon affecting the insulation of switchgear, potentially leading to equipment failure and accidents. PDs are generally grouped into metal particle discharge, suspended discharge, and creeping discharge. Different types of PDs are closely related to the severity of a PD. Partial discharge pattern recognition (PDPR) plays a vital role in the early detection of insulation defects. In this regard, a Back Propagation Neural Network (BPNN) for PDPR in switchgear is proposed in this paper. To eliminate the sensitivity to initial values of BPNN parameters and to enhance the generalized ability of the proposed BPRN, an improved Mantis Search Algorithm (MSA) is proposed to optimize the BPNN. The improved MSA employs some boundary handling strategies and adaptive parameters to enhance the algorithm's efficiency in optimizing the network parameters of BPNN. Principal Component Analysis (PCA) is introduced to reduce the dimensionality of the feature space to achieve significant time saving in comparable recognition accuracy. The initially extracted 14 feature values are reduced to 7, reducing the BPNN parameter count from 183 with 14 features to 113 with 7 features. Finally, numerical results are presented and compared with Decision Tree (DT), k-Nearest Neighbor classifiers (KNN), and Support Vector Machine (SVM). The proposed method in this paper exhibits the highest recognition accuracy in metal particle discharge and suspended discharge.

Stable blowup for focusing semilinear wave equations in all dimensions

We consider the wave equation with focusing power nonlinearity. The associated ODE in time gives rise to a self-similar solution known as the ODE blowup. We prove the nonlinear asymptotic stability of this blowup mechanism outside of radial symmetry in all space dimensions and for all superlinear powers. This result covers for the first time the whole energy-supercritical range without symmetry restrictions.

Classifications of THA-surfaces in I^3

In classical differential geometry, the problem of obtaining Gaussian and mean curvatures of a surface is one of the most important problems. A surface M2 in I3 is a THA-surface of first type if it can be parameterized by r(s, t) = (s, t, Af(s + at)g(t) + B(f(s + at) + g(t))). A surface M2 in I3 is a THA- surface of second type if it can be parameterized by r(s, t) = (s, Af(s + at)g(t) + B(f(s + at) + g(t)), t), where A and B are non-zero real numbers [16, 17, 18]. In this paper, we classify two types THA-surfaces in the 3-dimensional isotropic space I3 and study THA-surfaces with zero curvature in I3.

Air Handwriting using AI and ML

Air-writing refers to virtually writing linguistic characters through hand gestures in three dimensional space with six degrees of freedom. In this paper a generic video camera dependent convolutional neural network (CNN) based air-writing framework has been proposed. Gestures are performed using a marker of fixed color in front of a generic video camera followed by color based segmentation to identify the marker and track the trajectory of marker tip. A pre-trained CNN is then used to classify the gesture. The recognition accuracy is further improved using transfer learning with the newly acquired data. The performance of the system varies greatly on the illumi nation condition due to color based segmentation. In a less fluctuating illumination condition the system is able to recognize isolated unistroke numerals of multiple languages. The proposed framework achieved 97.7recognition rate in person inde pendent evaluation over English, Bengali and Devanagari numerals, respectively. Object tracking is considered as an important task within the field of Computer Vision. The invention of faster computers, availability of inexpensive and good quality video cameras and demands of automated video analysis has given popularity to object tracking techniques. Generally, video analysis procedure has three major steps: firstly, detecting of the object, secondly tracking its movement from frame to frame and lastly analysing the behaviour of that object. For object tracking, four different issues are taken into account; selection of suitable object representation, feature selection for tracking, object detection and object tracking. In real world, Object tracking algorithms are the primarily part of different applications such as: automatic surveillance, video indexing and vehicle navigation etc. The generated text can also be used for various purposes, such as sending messages, emails, etc. It will be a powerful means of communication for the deaf. It is an effective communication method that reduces mobile and laptop usage by eliminating the need to write. Key Words: Air Writing, Character Recognition, Object Detection, Real-Time Gesture Control System, Computer Vision , Hand tracking.