Dimensional Space Research Articles

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.

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 Handwriting using AI and ML

Shaping an evanescent focus of light for high spatial resolution optogenetic activations in live cells

Confining light illumination in the three dimensions of space is a challenge for various applications. Among these, optogenetic methods developed for live experiments in cell biology would benefit from such a localized illumination as it would improve the spatial resolution of diffusive photosensitive proteins leading to spatially constrained biological responses in specific subcellular organelles. Here, we describe a method to create and move a focused evanescent spot, at the interface between a glass substrate and an aqueous sample, across the field of view of a high numerical aperture microscope objective, using a digital micro-mirror device (DMD). We show that, after correcting the optical aberrations, light is confined within a spot of sub-micron lateral size and ∼100 nm axial depth above the coverslip, resulting in a volume of illumination drastically smaller than the one generated by a standard propagative focus. This evanescent focus is sufficient to induce a more intense and localized recruitment compared to a propagative focus on the optogenetic system CRY2-CIBN, improving the resolution of its pattern of activation.

Entropy pelican optimization algorithm (epoa) based feature selection and deep autoencoder (dae) of heart failure status prediction

Introduction: Heart Failure (HF) is a complicated condition as well as a significant public health issue. Data processing is now required for machine and statistical learning techniques while it helps to identify key features and eliminates unimportant, redundant, or noisy characteristics, hence minimizing the feature space's dimensions. A common cause of mortality in cases of heart disease is Dilated Cardiomyopathy (DCM). Methods: The feature selection in this work depends on the Entropy Pelican Optimization Algorithm (EPOA). It is a recreation of pelicans' typical hunting behaviour. This is comparable to certain characteristics that lead to better approaches for solving high-dimensional datasets. Then Deep Autoencoder (DAE) classifier has been introduced for the prediction of patients. DAE classifier is employed to compute the system's nonlinear function through data from the normal and failure state. Results: DAE was discovered to not only considerably increase accuracy but also to be beneficial when there is a limited amount of labelled data.Performance metrics like recall, precision, accuracy, f-measure, and error rate has been used for results analysis. Conclusion: Publicly available benchmark dataset has been collected from Gene Expression Omnibus (GEO) repository to evaluate and contrast the suitability of the suggested classifier with other existing methods.

Uniform large deviations for stochastic Burgers–Huxley equation driven by multiplicative noise

In this paper, we establish a Freidlin–Wentzell type large deviation principle uniformly with respect to initial condition in bounded subsets of an infinite dimensional Banach space for stochastic Burgers–Huxley equation driven by multiplicative small noise. The proof is based on the weak convergence approach obtained by Salins, Budhiraja, Dupuis (Trans. Amer. Math. Soc., 2019).

Remaining useful lifetime prediction for milling blades using a fused data prediction model (FDPM)

AbstractIn various industry sectors, predicting the real-life availability of milling applications poses a significant challenge. This challenge arises from the need to prevent inefficient blade resource utilization and the risk of machine breakdowns due to natural wear. To ensure timely and accurate adjustments to milling processes based on the machine's cutting blade condition without disrupting ongoing production, we introduce the Fused Data Prediction Model (FDPM), a novel temporal hybrid prediction model. The FDPM combines the static and dynamic features of the machines to generate simulated outputs, including average cutting force, material removal rate, and peripheral milling machine torque. These outputs are correlated with real blade wear measurements, creating a simulation model that provides insights into predicting the wear progression in the machine when associated with real machine operational parameters. The FDPM also considers data preprocessing, reducing the dimensional space to an advanced recurrent neural network prediction algorithm for forecasting blade wear levels in milling. The validation of the physics-based simulation model indicates the highest fidelity in replicating wear progression with the average cutting force variable, demonstrating an average relative error of 2.38% when compared to the measured mean of rake wear during the milling cycle. These findings illustrate the effectiveness of the FDPM approach, showcasing an impressive prediction accuracy exceeding 93% when the model is trained with only 50% of the available data. These results highlight the potential of the FDPM model as a robust and versatile method for assessing wear levels in milling operations precisely, without disrupting ongoing production.

Contact instantons with Legendrian boundary condition: A priori estimates, asymptotic convergence and index formula

In this paper, we establish nonlinear ellipticity of the equation of contact instantons with Legendrian boundary condition on punctured Riemann surfaces by proving the a priori elliptic coercive estimates for the contact instantons with Legendrian boundary condition, and prove an asymptotic exponential [Formula: see text]-convergence result at a puncture under the uniform [Formula: see text] bound. We prove that the asymptotic charge of contact instantons at the punctures under the Legendrian boundary condition vanishes. This eliminates the phenomenon of the appearance of spiraling cusp instanton along a Reeb core, which removes the only remaining obstacle towards the compactification and the Fredholm theory of the moduli space of contact instantons in the open string case, which plagues the closed string case. Leaving the study of [Formula: see text]-estimates and details of Gromov-Floer-Hofer style compactification of contact instantons to [27], we also derive an index formula which computes the virtual dimension of the moduli space. These results are the analytic basis for the sequels [27]–[29] and [36] containing applications to contact topology and contact Hamiltonian dynamics.

On some pre-orders and partial orders of linear operators on infinite dimensional vector spaces

AbstractThis article is devoted to the generalization of the Drazin pre-order and the G-Drazin partial order to Core-Nilpotent endomorphisms over arbitrary k-vector spaces, namely, infinite dimensional ones. The main properties of this orders are described, such as their respective characterizations and the relations between these orders and other existing ones, generalizing the existing theory for finite matrices. In order to do so, G-Drazin inverses are also studied in this framework. Also, it includes a generalization of the space pre-order to linear operators over arbitrary k-vector spaces.

On polling directions for randomized direct-search approaches: application to beam angle optimization in intensity-modulated proton therapy

AbstractDeterministic direct-search methods have been successfully used to address real-world challenging optimization problems, including the beam angle optimization (BAO) problem in radiation therapy treatment planning. BAO is a highly non-convex optimization problem typically treated as the optimization of an expensive multi-modal black-box function which results in a computationally time consuming procedure. For the recently available modalities of radiation therapy with protons (instead of photons) further efficiency in terms of computational time is required despite the success of the different strategies developed to accelerate BAO approaches. Introducing randomization into otherwise deterministic direct-search approaches has been shown to lead to excellent computational performance, particularly when considering a reduced number (as low as two) of random poll directions at each iteration. In this study several randomized direct-search strategies are tested considering different sets of polling directions. Results obtained using a prostate and a head-and-neck cancer cases confirmed the high-quality results obtained by deterministic direct-search methods. Randomized strategies using a reduced number of polling directions showed difficulties for the higher dimensional search space (head-and-neck) and, despite the excellent mean results for the prostate cancer case, outliers were observed, a result that is often ignored in the literature. While, for general global optimization problems, mean results (or obtaining the global optimum once) might be enough for assessing the performance of the randomized method, in real-world problems one should not disregard the worst-case scenario and beware of the possibility of poor results since, many times, it is only possible to run the optimization problem once. This is even more important in healthcare applications where the mean patient does not exist and the best treatment possible must be assured for every patient.

Gauge-Optimal Approximate Learning for Small Data Classification.

Small data learning problems are characterized by a significant discrepancy between the limited number of response variable observations and the large feature space dimension. In this setting, the common learning tools struggle to identify the features important for the classification task from those that bear no relevant information and cannot derive an appropriate learning rule that allows discriminating among different classes. As a potential solution to this problem, here we exploit the idea of reducing and rotating the feature space in a lower-dimensional gauge and propose the gauge-optimal approximate learning (GOAL) algorithm, which provides an analytically tractable joint solution to the dimension reduction, feature segmentation, and classification problems for small data learning problems. We prove that the optimal solution of the GOAL algorithm consists in piecewise-linear functions in the Euclidean space and that it can be approximated through a monotonically convergent algorithm that presents-under the assumption of a discrete segmentation of the feature space-a closed-form solution for each optimization substep and an overall linear iteration cost scaling. The GOAL algorithm has been compared to other state-of-the-art machine learning tools on both synthetic data and challenging real-world applications from climate science and bioinformatics (i.e., prediction of the El Niño Southern Oscillation and inference of epigenetically induced gene-activity networks from limited experimental data). The experimental results show that the proposed algorithm outperforms the reported best competitors for these problems in both learning performance and computational cost.

Variational inference for the latent shrinkage position model

AbstractThe latent position model (LPM) is a popular method used in network data analysis where nodes are assumed to be positioned in a ‐dimensional latent space. The latent shrinkage position model (LSPM) is an extension of the LPM which automatically determines the number of effective dimensions of the latent space via a Bayesian nonparametric shrinkage prior. However, the LSPM's reliance on Markov chain Monte Carlo for inference, while rigorous, is computationally expensive, making it challenging to scale to networks with large numbers of nodes. We introduce a variational inference approach for the LSPM, aiming to reduce computational demands while retaining the model's ability to intrinsically determine the number of effective latent dimensions. The performance of the variational LSPM is illustrated through simulation studies and its application to real‐world network data. To promote wider adoption and ease of implementation, we also provide open‐source code.

Redefining Public Space: The Evolution of Meaning in the Digital Era

Throughout history, public space has had a dynamic and evolving structure interacting with society and has undergone various conceptual changes and developments. This paper explores the evolving definition of public space, emphasizing the role of digitalization in this transformation. The study also seeks to delve deeply into the current meaning of public space, informed by perspectives from spatial design experts and Istanbul residents. The research employs a systematic literature review and a survey method, segmented across two distinct groups. The survey also concentrated on the spatial and digital dimensions of public space and asked participants to evaluate the personal meanings and usage patterns of these spaces. Besides, the advancement of digital technologies has led to literature that indicates an expansion in the definition of public space. The findings acquired from the research also supported this. In other words, analysis displays that public space goes beyond its traditional definition. Participants began to represent public spaces not only as physical spaces but also as digital platforms and social networks, and these findings supported the idea that the meaning and boundaries of public space augment and alter with digitalisation. This study emphasizes that the definition of public space cannot be confined solely to physical spaces but also includes digital platforms as integral components of this domain. Acquiring insight into public spaces' ever-changing and dynamic structure is essential for comprehending social and spatial dynamics in contemporary societies. This study revealed the evolution of the concept of public space and the effects of digitalization on this evolution.

Machine learning decoding of single neurons in the thalamus for speech brain-machine interfaces

Objective. Our goal is to decode firing patterns of single neurons in the left ventralis intermediate nucleus (Vim) of the thalamus, related to speech production, perception, and imagery. For realistic speech brain-machine interfaces (BMIs), we aim to characterize the amount of thalamic neurons necessary for high accuracy decoding. Approach. We intraoperatively recorded single neuron activity in the left Vim of eight neurosurgical patients undergoing implantation of deep brain stimulator or RF lesioning during production, perception and imagery of the five monophthongal vowel sounds. We utilized the Spade decoder, a machine learning algorithm that dynamically learns specific features of firing patterns and is based on sparse decomposition of the high dimensional feature space. Main results. Spade outperformed all algorithms compared with, for all three aspects of speech: production, perception and imagery, and obtained accuracies of 100%, 96%, and 92%, respectively (chance level: 20%) based on pooling together neurons across all patients. The accuracy was logarithmic in the amount of neurons for all three aspects of speech. Regardless of the amount of units employed, production gained highest accuracies, whereas perception and imagery equated with each other. Significance. Our research renders single neuron activity in the left Vim a promising source of inputs to BMIs for restoration of speech faculties for locked-in patients or patients with anarthria or dysarthria to allow them to communicate again. Our characterization of how many neurons are necessary to achieve a certain decoding accuracy is of utmost importance for planning BMI implantation.

Quantum System Dynamics: Harnessing Constructive Resonance for Technological Advancements, Universal Matter Creation and Exploring the Paradigm of Resonance-induced Gravity

Quantum System Dynamics: Harnessing Constructive Resonance for Technological Advancements, Universal Matter Creation and Exploring the Paradigm of Resonance-induced Gravity

Weighted topological pressure revisited

Abstract Feng and Huang [Variational principle for weighted topological pressure. J. Math. Pures Appl. (9)106 (2016), 411–452] introduced weighted topological entropy and pressure for factor maps between dynamical systems and established its variational principle. Tsukamoto [New approach to weighted topological entropy and pressure. Ergod. Th. & Dynam. Sys.43 (2023), 1004–1034] redefined those invariants quite differently for the simplest case and showed via the variational principle that the two definitions coincide. We generalize Tsukamoto’s approach, redefine the weighted topological entropy and pressure for higher dimensions, and prove the variational principle. Our result allows for an elementary calculation of the Hausdorff dimension of affine-invariant sets such as self-affine sponges and certain sofic sets that reside in Euclidean space of arbitrary dimension.

SkinSwinViT: A Lightweight Transformer-Based Method for Multiclass Skin Lesion Classification with Enhanced Generalization Capabilities

In recent decades, skin cancer has emerged as a significant global health concern, demanding timely detection and effective therapeutic interventions. Automated image classification via computational algorithms holds substantial promise in significantly improving the efficacy of clinical diagnoses. This study is committed to mitigating the challenge of diagnostic accuracy in the classification of multiclass skin lesions. This endeavor is inherently formidable owing to the resemblances among various lesions and the constraints associated with extracting precise global and local image features within diverse dimensional spaces using conventional convolutional neural network methodologies. Consequently, this study introduces the SkinSwinViT methodology for skin lesion classification, a pioneering model grounded in the Swin Transformer framework featuring a global attention mechanism. Leveraging the inherent cross-window attention mechanism within the Swin Transformer architecture, the model adeptly captures local features and interdependencies within skin lesion images while additionally incorporating a global self-attention mechanism to discern overarching features and contextual information effectively. The evaluation of the model’s performance involved the ISIC2018 challenge dataset. Furthermore, data augmentation techniques augmented training dataset size and enhanced model performance. Experimental results highlight the superiority of the SkinSwinViT method, achieving notable metrics of accuracy, recall, precision, specificity, and F1 score at 97.88%, 97.55%, 97.83%, 99.36%, and 97.79%, respectively.

Stochastic evolution equations with Wick-analytic nonlinearities

We study nonlinear stochastic partial differential equations with Wick-analytic type nonlinearities set in the framework of white noise analysis. These equations include the stochastic Fisher–KPP equations, stochastic Allen–Cahn, stochastic Newell–Whitehead–Segel, and stochastic Fujita–Gelfand equations. By implementing the theory of C 0 − semigroups and evolution systems into the chaos expansion theory in infinite dimensional spaces, we prove the existence and uniqueness of solutions for this class of stochastic partial differential equations.

All-order exact solutions for non-linear Yang–Mills theory

We show that the so-called ’t Hooft–Polyakov monopole solution in D=(3,1) dimensions satisfies the field equations of a wide set of non-linear Yang–Mills (YM) actions to all orders in the parameter α that is inversely proportional to the string tension T. Here the expression D=(s,t) is for the (s+t)dimensional space–time with the signature ((+)s,(−)t), namely s positive and t negative signatures. We show that the so-called Born–Infeld (BI) action is only a special case of a general set of non-linear YM theories. We also consider BI-actions in D=(2,2) dimensions, and show that the self-dual SU(2) instanton (BPSTH) solution satisfies the field equations of BI-like actions perturbatively to all orders inα. In D=(2,2) dimensions, the usual action-principle problem for (anti)self-dual ((A)SD) YM field strengths is avoided by auxiliary-gravity lagrangians. The conditions on non-linear YM theories to have the ’t Hooft–Polyakov monopole solution to all orders in α in D=(3,1) dimensions, or similarly the BPSTH instanton solution in D=(2,2) dimensions, allow infinitely many non-linear YM actions in these dimensions.