Dimensional Space Research Articles

Application of support vector machines and genetic algorithms to fluid identification in Offshore Granitic subduction hill reservoirs

YL8 area granite submarine is located in the Songnan low uplift of Qiongdongnan Basin, submarine reservoir fracture development, non-homogeneous strong. Geophysical logging and gas logging do not show a clear pattern of response to the fluid properties of submarine reservoirs, and it is difficult to use logging information to linearly classify granite submarine reservoir fluids in two dimensions. Support Vector Machines (SVM) can map multi-dimensional data into high-dimensional space and construct hyperplanes in high-dimensional space to categorize the samples, which meets the need to incorporate logging curves and mud gas parameters that show complex response relationships with the fluid types of subducted reservoirs into the model.Therefore, in this paper, a support vector machine (GA-SVM) granite subduction reservoir fluid prediction model based on genetic algorithm optimisation is constructed. Firstly, the petrophysical characteristics of different reservoirs in the granite subduction hill were analysed in detail, acquisition and standardisation of logging and mud gas logging multi-dimensional parameters sensitive to reservoir fluids, inputting sensitive parameters into GA-SVM mapping multi-dimensional parameters to higher dimensional space using Gaussian radial kernel functions, using genetic algorithms to perform crossover and mutation operations on the kernel parameter g and the penalty parameter C to obtain the optimal parameter combinations, optimising the number of GA-SVM iterations and model accuracy. The GA-SVM predictions were compared with two other machine learning predictions. As demonstrated through actual case studies in the YL8 area, fluid type recognition compliance rate of 88.2% by GA-SVM, GA-SVM effectively improve the compliance rate of fluid identification in granite subduction reservoirs, provides a new idea for logging interpretation of complex reservoirs in granite subduction reservoirs.

Exploring evolutionary-tuned autoencoder-based architectures for fault diagnosis in a wind turbine gearbox

ABSTRACT Vibration-based fault diagnosis from rotary machinery requires prior feature extraction, feature selection, or dimensionality reduction. Feature extraction is tedious, and computationally expensive. Feature selection presents unique challenges intrinsic to the method adopted. Nonlinear dimensionality reduction may be achieved through kernel transformations, however there is often a trade-off in information to achieve this. Given the above, this study proposes a novel autoencoder (AE) pre-processing framework for vibration-based fault diagnosis in wind turbine (WT) gearboxes. In this study, AEs are used to learn the features of WT gearbox vibration data while simultaneously compressing the data, obviating the need for costly feature engineering and dimensionality reduction. The effectiveness of the proposed framework was evaluated by training genetically optimized linear discriminant analysis (LDA), multilayer perceptron (MLP), and random forest (RF) models, with the AE’s latent space features. The models were evaluated using known classification metrics. The results showed that the performance of the models depends on the size of the AE’s latent space. As the size of the AE’s latent space increased, the quality of features extracted improved until a plateau was observed at a latent space dimension of 10. The AE pre-processed genetically optimized RF, MLP, and LDA models, designated AE-Pre-GO-RF, AE-Pre-GO-MLP, and AE-Pre-GO-LDA, were evaluated for accuracy, sensitivity, and specificity in the classification of seven (7) gearbox fault conditions. The AE-Pre-GO-RF model outperformed its counterparts, scoring 100% for all evaluated metrics, though with the longest training time (239.50 sec). Comparable results were found comparing this study with similar investigations involving traditional vibration processing techniques. More so, it was established that effective fault diagnosis of the WT gearbox can be achieved through manifold learning with AEs without expensive feature engineering.

Black hole firewalls and quantum mechanics *

Firewalls in black holes are easiest to understand by imposing time reversal invariance, together with a unitary evolution law. The best approach seems to be to split up the time span of a black hole into short periods, during which no firewalls can be detected by any observer. Then, gluing together subsequent time periods, firewalls seem to appear, but they can always be transformed away. At all times we need a Hilbert space of a finite dimension, as long as particles far separated from the black hole are ignored. Our conclusion contradicts other findings, as these assume that information that entered into a black hole, cannot re-emerge. But re-emergence of that information is exactly what our version of firewalls is supposed to ensure. Indeed, the firewall transformation removes the problems caused by entanglement between very early and very late in- and out-particles, in a far from trivial way.

Neural network approach to quasiparticle dispersions in doped antiferromagnets

Numerically simulating large, spinful, fermionic systems is of great interest in condensed matter physics. However, the exponential growth of the Hilbert space dimension with system size renders exact quantum state parameterizations impractical. Owing to their representative power, neural networks often allow to overcome this exponential scaling. Here, we investigate the ability of neural quantum states (NQS) to represent the bosonic and fermionic t − J model – the high interaction limit of the Hubbard model – on various 1D and 2D lattices. Using autoregressive, tensorized recurrent neural networks (RNNs), we study ground state representations upon hole doping the half-filled system. Additionally, we propose a method to calculate quasiparticle dispersions, applicable to any network architecture or lattice geometry, and allowing to infer the low-energy physics from NQS. By analyzing the strengths and weaknesses of the RNN ansatz we shed light on the challenges and promises of NQS for simulating bosonic and fermionic systems.

Moduli Spaces of Quadratic Maps: Arithmetic and Geometry

Abstract We establish an implication between two long-standing open problems in complex dynamics. The roots of the $n$th Gleason polynomial $G_{n}\in{\mathbb{Q}}[c]$ comprise the $0$-dimensional moduli space of quadratic polynomials with an $n$-periodic critical point. $\operatorname{Per}_{n}(0)$ is the $1$-dimensional moduli space of quadratic rational maps on ${\mathbb{P}}^{1}$ with an $n$-periodic critical point. We show that if $G_{n}$ is irreducible over ${\mathbb{Q}}$, then $\operatorname{Per}_{n}(0)$ is irreducible over ${\mathbb{C}}$. To do this, we exhibit a ${\mathbb{Q}}$-rational smooth point on a projective completion of $\operatorname{Per}_{n}(0)$, using the admissible covers completion of a Hurwitz space. In contrast, the Uniform Boundedness Conjecture in arithmetic dynamics would imply that for sufficiently large $n$, $\operatorname{Per}_{n}(0)$ itself has no ${\mathbb{Q}}$-rational points.

Randomized complexity of mean computation and the adaption problem

Recently the adaption problem of Information-Based Complexity (IBC) for linear problems in the randomized setting was solved in Heinrich (2024) [8]. Several papers treating further aspects of this problem followed. However, all examples obtained so far were vector-valued. In this paper we settle the scalar-valued case. We study the complexity of mean computation in finite dimensional sequence spaces with mixed LpN norms. We determine the n-th minimal errors in the randomized adaptive and non-adaptive settings. It turns out that among the problems considered there are examples where adaptive and non-adaptive n-th minimal errors deviate by a power of n. The gap can be (up to log factors) of the order n1/4. We also show how to turn such results into infinite dimensional examples with suitable deviation for all n simultaneously.

Strong blocking sets and minimal codes from expander graphs

A strong blocking set in a finite projective space is a set of points that intersects each hyperplane in a spanning set. We provide a new graph theoretic construction of such sets: combining constant-degree expanders with asymptotically good codes, we explicitly construct strong blocking sets in the ( k − 1 ) (k-1) -dimensional projective space over F q \mathbb {F}_q that have size at most c q k c q k for some universal constant c c . Since strong blocking sets have recently been shown to be equivalent to minimal linear codes, our construction gives the first explicit construction of F q \mathbb {F}_q -linear minimal codes of length n n and dimension k k , for every prime power q q , for which n ≤ c q k n \leq c q k . This solves one of the main open problems on minimal codes.

Detection and Type Recognition of SAR Artificial Modulation Targets Based on Multi-Scale Amplitude-Phase Features

With respect to the detection and recognition of an Artificial Modulation Target (AMT) with different modulated types, the state-of-the-art methods generally suffer the deficiencies of overfitting and insufficient generalization of existing neural network solutions. To address these problems, this paper proposes a multi-scale amplitude-phase feature discrimination method for AMTs in SAR images. First, a multi-type modulated AMT Dataset is generated (AMT Detection and Modulation Type Recognition Dataset, ADMTR Dataset), wherein the factors of jamming position, jamming-to-signal ratio (JSR), and the modulated parameter are considered to enhance the generalization. Second, a Multi-Input Multi-Output Fusion Wavelet Neural Network (MIMOFWTNN) is established, which not only uses the amplitude information of the scene but also adequately makes use of the phase and high-frequency information. This empowers us to detect the AMT in a higher dimensional feature space such that the type recognition can be implemented with more certainty. Analysis and discussions conducted on comparison experiments and ablation experiments demonstrate that the proposed network can achieve an average accuracy of 96.96% on the cross-validation set and a correct rate of 99.0% on the completely independent test set, which outperforms the compared methods.

Optimization investigation on variable-density multi-layer insulation coupled with vapor-cooled shield for liquid hydrogen tank based on sequential quadratic programming

The MLI (multi-layer insulation), commonly used in liquid hydrogen tank, acts to reduce HLF (heat leakage flux) into the tank and slow down tank pressurization. It is usually optimally designed into three or four regions, with the same RS spacing in every region, which is regarded as the discontinuous variable density and called VDMLI (variable-density multi-layer insulation). However, the VCS (vapor-cooled shield) and P-O (para-to-ortho hydrogen conversion) in VDMLI are not considered in the optimal design of VDMLI. Therefore, a kind of nonlinear programming algorithm named SQP (sequential quadratic programming), in which HLF solver of liquid hydrogen tank is embedded, is firstly introduced to obtain the optimized distribution of RS (radiative shield) spacing to minimize HLF of liquid hydrogen storage tank. The HLF solver is a numerical model of VDMLI coupled with VCS and P-O, and SQP can be regarded as the optimization process of searching for an optimal solution in high dimensional space, under inequality constraints. The calculation results show that the best SN (serial number) of RS for SVCS (single vapor-cooled shield) setting to minimize HLF, in three cases of before optimization with P-O, after optimization with P-O, and after optimization without P-O is 16, 11, and 14 respectively. With P-O, the minimum HLF after optimization is reduced by 8.45% compared with the minimum HLF before optimization. When SVCS is set at the 4th RS, P-O leads to the most decreasing range of HLF, which is 28.3%, while the optimization process leads to the most decreasing range of 48.1% under condition that SVCS is set at the 2nd RS and P-O is coupled. Under condition of no P-O, after optimization, the minimum HLF occurs when the SN of RS where DVCS (double vapor-cooled shield) is set is (8,21), and the minimum HLF is reduced by 9.0%, compared to that before optimization with DVCS, and is reduced by 50.43% compared to that after optimization with SVCS.

The MIMO Data Transfer Line with Seven-Frequency Octonion Carrier

Currently, with the development of public relations and production systems, there is a need to increase the capacity of communication systems and information transmission. It has been shown theoretically that it is possible to increase throughput by using multidimensional signals in space instead of real signals on a plane. It is now accepted that a multidimensional space, MultipleInput Multiple-Output (MIMO), can be formed using multiple antennas to transmit and receive in physical space. However, as physicists point out, such space is three-dimensional, and with the addition of time it is four-dimensional. It is clear that in such a physical space, when using more than 2 antennas for transmission and 2 for reception, it is impossible to obtain a gain in throughput of more than 4 times, since according to the laws of cybernetics, the diversity at the channel input will not be transmitted to the exit. It follows that it is necessary to reconsider existing views on the dimension of physical space. Previously, in the work the MIMO data transfer line with three-frequency quaternion carrier, it was shown that it is possible to use a hypercomplex quaternion number as a model of physical space. In this case, the dimension of space will be equal to 4 with 3 imaginary (spatial) axes and one scalar axis. In addition, combinations of three quaternion angular frequencies on the imaginary axes formed 4 single-frequency channels. Accordingly, the gain in throughput compared to real signals reached 4 in orthogonal axes and 4 in frequencies. In this work, an octonion with 7 imaginary (spatial) axes and one scalar is used as a mathematical model of physical space. It is shown that the dimension of physical space will be 8 with 64 single-frequency channels in the form of combinations of 7 angular frequencies. Hence, the gain in throughput will be 8 in orthogonal axes and 64 in frequencies.

Analysis of a diffusive chemical reaction model in three space dimensions

This article proposes an implicit operator splitting nonstandard finite difference (OS-NSFD) scheme for numerical treatment of two species in three space dimensions reaction-diffusion glycolysis model. Since, the unknown state variables exhibiting the concentrations of species in glycolysis models and they cannot be negative and obtaining their positive solutions is a challenging task. The established theoretical result ensures that our proposed OS-NSFD scheme is unconditionally convergent at equilibrium point and fulfills the condition of positivity of solutions on contrary to other methods. Further, we analyze the existence and uniqueness of the solution obtained for the underlying system. To highlight the effectiveness of OS-NSFD scheme we compare the simulation results of OS-NSFD scheme with three well-known existing operators splitting finite difference (FD) schemes, namely, forward Euler explicit, backward Euler implicit and Crank Nicolson splitting schemes. Many existing techniques provide with the restricted positive solutions which do not work always. These techniques are only applicable if certain conditions on the discretized parameters are considered otherwise; they produce negative solutions, which is not the physical feature of the real system. The current work bridges this gap by catering the unconditional positive solutions to the reaction diffusion models.

SpaDE: Semantic Locality Preserving Biclustering for Neuroimaging Data.

The most discriminative and revealing patterns in the neuroimaging population are often confined to smaller subdivisions of the samples and features. Especially in neuropsychiatric conditions, symptoms are expressed within micro subgroups of individuals and may only underly a subset of neurological mechanisms. As such, running a whole-population analysis yields suboptimal outcomes leading to reduced specificity and interpretability. Biclustering is a potential solution since subject heterogeneity makes one-dimensional clustering less effective in this realm. Yet, high dimensional sparse input space and semantically incoherent grouping of attributes make post hoc analysis challenging. Therefore, we propose a deep neural network called semantic locality preserving auto decoder (SpaDE), for unsupervised feature learning and biclustering. SpaDE produces coherent subgroups of subjects and neural features preserving semantic locality and enhancing neurobiological interpretability. Also, it regularizes for sparsity to improve representation learning. We employ SpaDE on human brain connectome collected from schizophrenia (SZ) and healthy control (HC) subjects. The model outperforms several state-of-the-art biclustering methods. Our method extracts modular neural communities showing significant (HC/SZ) group differences in distinct brain networks including visual, sensorimotor, and subcortical. Moreover, these bi-clustered connectivity substructures exhibit substantial relations with various cognitive measures such as attention, working memory, and visual learning.

Noisy qudit vs multiple qubits: conditions on gate efficiency for enhancing fidelity

As qubit-based platforms face near-term technical challenges in terms of scalability, qudits, d-level bases of quantum information, are being implemented in multiple platforms as an alternative for Quantum Information Processing (QIP). We compare the infidelity scalings of single qudit and multiqubit systems within identical Hilbert space dimensions and noisy environments in the Lindblad formalism. We find them to be gate-independent to first-order and present an analytically-derived critical curve (d2−1)/3log2(d)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$({d}^{2}-1)/3{\\log }_{2}(d)$$\\end{document} that benchmarks the operational time efficiency of qudits and qubits relative to their decoherence times. This comparison reveals conditions under which qudits offer competitive gate efficiencies compared to leading qubit platforms. Our findings, supported by numerical simulations testing the applicability and limits of the linear response formalism, highlight the relevance of qudits in near-term QIP. This provides a benchmark for evaluating qudit platforms, specifically those with lower dimensionality, in terms of their operational efficiency relative to the qubit state-of-the-art.

Ideational Praxis, Play, and Playfulness: A Cross-Sectional Study of Autistic Children

Abstract Importance: Assessment of praxis skills is an essential aspect of understanding autistic children’s development of play and playfulness. Objective: To assess the relationship and influence of ideational praxis skills on play skills and playfulness among autistic children. Design: A cross-sectional study. Settings: Homes, schools, and early care centers across Spain. Participants: Children ages 4 yr 6 mo to 6 yr 11 mo (45 typically developing [TP] and 45 with autism spectrum disorder [ASD]). Outcomes and Measures: Student’s t tests were used to compare means between the two groups. Pearson’s correlation and multiple linear regression were used to determine possible effects of ideational skills on play and playfulness. Results: Scores for the TP group were significantly higher than those of the ASD group on all play dimensions—space management, t(88) = 4.58; material management, t(88) = 5.86; pretense–symbolism, t(88) = 8.12; and participation, t(88) = 7.31—and on the Test of Playfulness (ToP), t(88) = 10.18, and Test of Ideational Praxis (TIP), t(88) = 4.38 (all ps < .001). Multiple linear regression revealed a statistically significant effect of TIP dimensions—space management, F(3, 41) = 4.83, p < .042; material management, F(3.41) = 8.49. p < .001; pretense–symbolism, F(3, 41) = 5.66. p < .002; and participation, F(3.41) = 7.81. p < .001—and on the ToP, F(3, 41) = 5.96. p < .002. Conclusions and Relevance: Ideational praxis skills combined with diagnostic information significantly predicted play skills and playfulness, highlighting the influence of ideation on play. Plain-Language Summary: This article provides data supporting the influence of ideational praxis skills on the play skills and playfulness of autistic children. Understanding how ideational praxis skills affect the ability to recognize and act on object affordances might promote greater possibilities for play interactions among autistic children.

Cosmographic analysis of the dynamics of universe in higher dimensional compactified space with Tachyonic field

In this work, the considered model is contained in higher dimensional compactified space in the form of M4 × M6, where M6 is compact inner space. Since, for a higher dimensional cosmological model, Tachyon matter is an automatic and fantastic choice, we have supposed that the scalar field is driven by Tachyon together with the higher dimensional cosmological constant [Formula: see text]. Our observation is that the theory provides a good solution for the cosmological scale factor of the present universe. Here, it is important that the forms of the tachyonic field ϕ and potential V are simple trigonometric hyperbolic functions. We study the cosmographical parameters like equation of state parameter, statefinder parameters, jerk, snap, and lerk parameters. The graphical representations of cosmological parameters show the overall evolution of the universe under a tachyonic field in a higher dimensional model. The classical stability of the model due to small perturbations both for dark energy and metric are examined by the study of the square speed of sound and by the linear perturbation method. We also analyzed the model in ω−ω′ and r− s cosmological plane.

A bound preserving cut discontinuous Galerkin method for one dimensional hyperbolic conservation laws

In this paper we present a family of high order cut finite element methods with bound preserving properties for hyperbolic conservation laws in one space dimension. The methods are based on the discontinuous Galerkin framework and use a regular background mesh, where interior boundaries are allowed to cut through the mesh arbitrarily. Our methods include ghost penalty stabilization to handle small cut elements and a new reconstruction of the approximation on macro-elements, which are local patches consisting of cut and un-cut neighboring elements that are connected by stabilization. We show that the reconstructed solution retains conservation and order of accuracy. Our lowest order scheme results in a piecewise constant solution that satisfies a maximum principle for scalar hyperbolic conservation laws. When the lowest order scheme is applied to the Euler equations, the scheme is positivity preserving in the sense that positivity of pressure and density are retained. For the high order schemes, suitable bound preserving limiters are applied to the reconstructed solution on macro-elements. In the scalar case, a maximum principle limiter is applied, which ensures that the limited approximation satisfies the maximum principle. Correspondingly, we use a positivity preserving limiter for the Euler equations, and show that our scheme is positivity preserving. In the presence of shocks additional limiting is needed to avoid oscillations, hence we apply a standard TVB limiter to the reconstructed solution. The time step restrictions are of the same order as for the corresponding discontinuous Galerkin methods on the background mesh. Numerical computations illustrate accuracy, bound preservation, and shock capturing capabilities of the proposed schemes.

Unification of conformal gravity and internal interactions

Based on the observation that the dimension of the tangent space is not necessarily equal to the dimension of the corresponding curved manifold and on the known fact that gravitational theories can be formulated in a gauge theoretic way, we discuss how to describe all known interactions in a unified manner. This is achieved by enlarging the tangent group of the four-dimensional manifold to SO(2, 16), which permits the inclusion of both gauge groups, the one that describes gravity as a gauge theory as well as the SO(10) describing the internal interactions. Moreover it permits the use of both Weyl and Majorana conditions imposed on the fermions, as to avoid the duplication of fermion multiplets of SO(10) appearing in previous attempts. The gravity theory discussed in the present work is the Conformal Gravity which, after a spontaneous symmetry breaking, can lead either to Weyl Gravity or to the usual Einstein Gravity.

Fidelity and entanglement of random bipartite pure states: insights and applications

We investigate the fidelity of Haar random bipartite pure states from a fixed reference quantum state and their bipartite entanglement. By plotting the fidelity and entanglement on perpendicular axes, we observe that the resulting plots exhibit non-uniform distributions. The distribution depends on the entanglement of the fixed reference quantum state used to quantify the fidelity of the random pure bipartite states. We find that the average fidelity of typical random pure bipartite qubits within a narrow entanglement range with respect to a randomly chosen fixed bipartite qubit is 14 . Extending our study to higher dimensional bipartite qudits, we find that the average fidelity of typical random pure bipartite qudits with respect to a randomly chosen fixed bipartite qudit remains constant within a narrow entanglement range. The values of these constants are 1d2 , with d being the dimension of the local Hilbert space of the bipartite qudit system, suggesting a consistent relationship between entanglement and fidelity across different dimensions. The probability distribution functions of fidelity with respect to a product state are analytically studied and used as a reference for the benchmarking of distributed quantum computing devices.

Scattering for quantum Zakharov system in two space dimensions

In this paper, we study long time behavior of solution to the quantum Zakharov system in two dimensions. We construct a small global solution to the quantum Zakharov system which scatters to a given free solution by using space-time resonance method developed by Gustafson-Nakanishi-Tsai [Commun. Contemp. Math. 11 (2009), pp. 657–707] and Germain-Masmoudi-Shatah [Int. Math. Res. Not. IMRN 3 (2009), 414–432; J. Math. Pures Appl. (9) 97 (2012), pp. 505–543] etc.

Morse–Smale complexes on convex polyhedra

AbstractMotivated by applications in geomorphology, the aim of this paper is to extend Morse–Smale theory from smooth functions to the radial distance function (measured from an internal point), defining a convex polyhedron in 3-dimensional Euclidean space. The resulting polyhedral Morse–Smale complex may be regarded, on one hand, as a generalization of the Morse–Smale complex of the smooth radial distance function defining a smooth, convex body, on the other hand, it could be also regarded as a generalization of the Morse–Smale complex of the piecewise linear parallel distance function (measured from a plane), defining a polyhedral surface. Beyond similarities, our paper also highlights the marked differences between these three problems and it also relates our theory to other methods. Our work includes the design, implementation and testing of an explicit algorithm computing the Morse–Smale complex on a convex polyhedron.