Dimensional Space Research Articles

Low dimensionality of phenotypic space as an emergent property of coordinated teams in biological regulatory networks

Low dimensionality of phenotypic space as an emergent property of coordinated teams in biological regulatory networks

Uncertainty analysis method for diagnosing multi-point defects in urban drainage systems

Urban drainage system (UDS) plays a key role in city urbanization, where defective pipes can lead to seepage. Previous studies have identified the locations of defects in UDS using inverse optimization models. However, the unique optimal solution neglects uncertainty analysis, which may lead to misdiagnosis. In addition, the multi-point defect diagnosis has heavy computational burden due to high dimensional parameters space. To address these issues, this paper proposes a hybrid method that leverages the genetic algorithm (GA) to identify probable space, and then utilizes the adaptive Metropolis (AM) to provide an estimation of the posterior probability distribution (PPD). Firstly, a multi-population GA is employed for the maximum exploration within the model space. Then, AM algorithm is used to explore the final PPD of each pipe defect parameter. The metrics accuracy (ACC), Matthews correlation coefficient (MCC) and mean absolute error (MAE) are used to evaluate the diagnosis performance. A synthetic UDS case with randomized multi-point seepage scenarios is used to validate the method. Results indicate that the proposed hybrid method is effective in diagnosing multi-point defect, with 0.91, 0.78 of the hybrid method and 0.87, 0.69 of the DiffeRential Evolution Adaptive Metropolis method for the ACC and MCC, respectively. Meanwhile, the diagnosis speed has increased by 32%. The result PPD passes the 90% confidence interval validation. The proposed method can provide effective uncertainty analysis to reduce misdiagnosis of the traditional method.

Intrinsic-dimension analysis for guiding dimensionality reduction and data fusion in multi-omics data processing.

Multi-omics data have revolutionized biomedical research by providing a comprehensive understanding of biological systems and the molecular mechanisms of disease development. However, analyzing multi-omics data is challenging due to high dimensionality and limited sample sizes, necessitating proper data-reduction pipelines to ensure reliable analyses. Additionally, its multimodal nature requires effective data-integration pipelines. While several dimensionality reduction and data fusion algorithms have been proposed, crucial aspects are often overlooked. Specifically, the choice of projection space dimension is typically heuristic and uniformly applied across all omics, neglecting the unique high dimension small sample size challenges faced by individual omics. This paper introduces a novel multi-modal dimensionality reduction pipeline tailored to individual views. By leveraging intrinsic dimensionality estimators, we assess the curse-of-dimensionality impact on each view and propose a two-step reduction strategy for significantly affected views, combining feature selection with feature extraction. Compared to traditional uniform reduction pipelines in a crucial and supervised multi-omics analysis setting, our approach shows significant improvement. Additionally, we explore three effective unsupervised multi-omics data fusion methods rooted in the main data fusion strategies to gain insights into their performance under crucial, yet overlooked, settings.

Connection of the Theory of Time with the Friedmann Equation

The proposed work shows a new approach to deriving the Friedmann equation. The approach is based on the fact that the primary medium from which the universe could arise is a time substance consisting of primary tiny particles. This medium is described by a scalar field. The mathematical apparatus used for its study allowed obtaining dual equations, which were interpreted by the author as waves of direct and reverse time directed towards each other. When the waves contacted, an inversion of the reverse wave occurred. It took the direction of the direct wave. As a result of the inversion, dynamic processes arose that led to the appearance of acceleration in 4-dimensional space. Analysis of the formulas for velocity and acceleration led to the derivation of Friedmann equations for a flat universe, obtained by him from Einstein's gravitational equation. Introduction. The concept of a continuous space-time continuum has become firmly established in modern physics. It was introduced by A. Einstein in the special and then General Theory of Relativity (GTR). By tacit agreement, it is generally accepted that the continuum is filled with matter that is in continuous motion, moving at speeds not exceeding the speed of light. Matter has mass, which leads to the curvature of space-time. GTR interprets this curvature as the presence of a gravitational field in the continuum. To describe it, A. Einstein's tensor gravitational equation is used. It is used to analyze curved 4-dimensional space-time. With this approach, the dimension consists of three spatial and one time coordinate. The result is a mathematically complex theory, lacking clarity and poorly understood. In 1922, A.A. Friedman solved the equations of GTR after modifying the second cosmological postulate. This led to a result that meant a change in the size of the Metagalaxy over time, i.e. to its non-stationarity. The solutions obtained formed the basis of the theoretical basis of cosmology. No other approaches to deriving Friedman's equations, except on the basis of GTR, were undertaken. But there is another approach. And the author talks about it in this article. It is based on the theory of time developed by him.

Manipulating Dynamic Light-Driven Solid-Liquid Transition and Static Reversible Photochromism via Organic Cocrystal Strategy.

Developing of molecular crystalline materials with light-induced multiple dynamic deformation in space dimension and photochromism on time scales has attracted much attention for its potential applications in actuators, sensoring and information storage. Nevertheless, organic crystals capable of both photoinduced dynamic effects and static color change are rare, particularly for multi-component cocrystals system. In this study, we first report the construction of charge transfer co-crystals allows their light-induced solid-to-liquid transition and photochromic behaviors to be controlled by trans-stilbene (TSB) as an electron donor and 3,4,5,6-Tetrafluorophthalonitrile (TFP) as an electron acceptor. In this case, the dynamic photo-responsive solid-to-liquid phase transition is due to the photoisomerization of TSB under UV irradiation, while the accumulation of melted droplets during solid-state photochemical process causes mechanical deformation of TSB-TFP cocrystals. The subsequent reversible photochromic behavior is attributed to the emergence of free radicals through a photo-induced electron transfer. Moreover, TSB-TFP microcrystals present typical excitation wavelength dependent emission (EWDE) fluorescence by surfactant-mediated method. This work realizes the dynamic-static photochemical cascade processes in response to light irradiation in an organic cocrystal system, providing the effective method for a new type of smart photo-responsive materials.

SOME CLASSIFICATIONS FOR GAUSS MAP OF TUBULAR HYPERSURFACES IN E^4_1 CONCERNING LINEARIZED OPERATORS L_k

In this study, we deal with the Gauss map of tubular hypersurfaces in 4-dimensional Lorentz-Minkowski space concerning the linearized operators L_1 (Cheng-Yau) and L_2. We obtain the L_1 (Cheng-Yau) operator of the Gauss map of tubular hypersurfaces that are formed as the envelope of a family of pseudo hyperspheres or pseudo hyperbolic hyperspheres whose centers lie on timelike or spacelike curves with non-null Frenet vectors in E^4_1 and give some classifications for these hypersurfaces which have generalized L_k 1-type Gauss map, first kind L_k-pointwise 1-type Gauss map, second kind L_k-pointwise 1-type Gauss map and L_k-harmonic Gauss map, k ∈ {1,2}.

Spectral submanifolds in time delay systems

Abstract The concept of spectral submanifolds, a powerful method of model order reduction of nonlinear systems, is extended to time delay systems that have infinite dimensional phase space representation. The proposed sun-star calculus based algorithm results in system reduction to manifolds which are constructed corresponding to either a real eigenvalue or to a pair of complex conjugate eigenvalues of the linearized system. Furthermore, it allows an improved approximation of self-excited oscillations exactly at the parameter point of interest, which could be further away from the corresponding Hopf bifurcation point. The paper includes case studies that demonstrate the capabilities of the algorithm.

The (1+3)-dimensional ‘quantum principle of relativity’ is Einstein’s principle of relativity

We show that the (1+3)-dimensional ‘superboost’ operators, proposed in Dragan and Ekert’s most recent work on superluminal reference frames (Dragan et al. in Class Quantum Gravity 40(2): 025013, 2023), are simply the canonical Lorentz boosts, expressed in nonstandard notation. Their (1+3)-dimensional ‘superflip’, which is claimed to interchange time and space dimensions for a superluminal observer, travelling with infinite speed, is equivalent to applying the identity operator together with an arbitrary relabeling. Physically, it corresponds to staying put within the canonical rest frame, then renaming space as ‘time’ and time as ‘space’. We conclude that their extension of the ‘quantum principle of relativity’, proposed in earlier work on (1+1)-dimensional spacetimes (Dragan and Ekert in New J Phys 22(3): 033038, 2020), to ordinary Minkowski space, is simply Einstein’s principle of relativity, proposed in 1905.

On the relativistic quantum mechanics of a photon between two electrons in 1+1 dimensions

A Lorentz-covariant system of wave equations is formulated for a quantum-mechanical three-body system in one space dimension, comprised of one photon and two identical massive spin one-half Dirac particles, which can be thought of as two electrons (or alternatively, two positrons). Manifest covariance is achieved using Dirac’s formalism of multi-time wave functions, i.e., wave functions Ψ(xph,xe1,xe2) where xph,xe1,xe2 are generic spacetime events of the photon and two electrons, respectively. Their interaction is implemented via a Lorentz-invariant no-crossing-of-paths boundary condition at the coincidence submanifolds {xph=xe1} and {xph=xe2} compatible with conservation of probability current. The corresponding initial-boundary value problem is shown to be well-posed, and it is shown that the unique solution can be represented by a convergent infinite sum of Feynman-like diagrams, each one corresponding to the photon bouncing between the two electrons a fixed number of times.

Winding topology of multifold exceptional points

Despite their ubiquity, a systematic classification of multifold exceptional points, n-fold spectral degeneracies (EPns), remains a significant unsolved problem. In this article, we characterize the Abelian eigenvalue topology of generic EPns and symmetry-protected EPns for arbitrary n. The former and the latter emerge in (2n−2)- and (n−1)-dimensional parameter spaces, respectively. By introducing topological invariants called resultant winding numbers, we elucidate that these EPns are stable due to topology of a map from a base space (momentum or parameter space) to a sphere defined by resultants. In a D-dimensional parameter space (D≥c), the resultant winding numbers topologically characterize (D−c)-dimensional manifolds of generic (symmetry-protected) EPns, whose codimension is c=2n−2 (c=n−1). Our framework implies fundamental doubling theorems for both generic EPns and symmetry-protected EPns in n-band models. Published by the American Physical Society 2025

ExoSim 2: the new exoplanet observation simulator applied to the Ariel space mission

ExoSim 2 is the next generation of the Exoplanet Observation Simulator (ExoSim) tailored for spectro-photometric observations of transiting exoplanets from space, ground, and sub-orbital platforms. This software is a complete rewrite implemented in Python 3, embracing object-oriented design principles, which allow users to replace each component with their functions when required. ExoSim 2 is publicly available on GitHub, serving as a valuable resource for the scientific community. ExoSim 2 employs a modular architecture using Task classes, encapsulating simulation algorithms and functions. This flexible design facilitates the extensibility and adaptability of ExoSim 2 to diverse instrument configurations to address the evolving needs of the scientific community. Data management within ExoSim 2 is handled by the Signal class, which represents a structured data cube incorporating time, space, and spectral dimensions. The code execution in ExoSim 2 follows a three-step workflow: the creation of focal planes, the production of Sub-Exposure blocks, and the generation of non-destructive reads (NDRs). Each step can be executed independently, optimizing time and computational resources. ExoSim 2 has been extensively validated against other tools like ArielRad and has demonstrated consistency in estimating photon conversion efficiency, saturation time, and signal generation. The simulator has also been validated independently for instantaneous read-out and jitter simulation, and for astronomical signal representation. In conclusion, ExoSim 2 offers a robust and flexible tool for exoplanet observation simulation, capable of adapting to diverse instrument configurations and evolving scientific needs. Its design principles and validation results underscore its potential as a valuable resource in the field of exoplanet research.

Stabilization of a Rigid Body in Two Fluids With Surface Tension

Abstract This paper poses and solves a stabilization problem of a rigid body governed by nonlinear differential equations in two viscous incompressible fluids governed by Navier–Stokes equations (NSEs), where surface tension of the interface between the two fluids is considered, in a bounded domain in three dimensional space. Since only weak solutions of the NSEs exist globally while global existence of their strong/smooth solutions is a millennium problem, point-wise fluid forces and moments acting on the rigid body are not able to bound. This difficulty is overcome by designing an appropriate control law and performing stability analysis of the closed-loop system including the NSEs and surface tension, where “work and power of the two fluids” instead of forces and moments on the rigid body are used. A simulation is included to illustrate the results.

Measuring Distances in High Dimensional Spaces Why Average Group Vector Comparisons Exhibit Bias, And What to Do about it

Abstract Analysts often seek to compare representations in high-dimensional space, e.g., embedding vectors of the same word across groups. We show that the distance measures calculated in such cases can exhibit considerable statistical bias, that stems from uncertainty in the estimation of the elements of those vectors. This problem applies to Euclidean distance, cosine similarity, and other similar measures. After illustrating the severity of this problem for text-as-data applications, we provide and validate a bias correction for the squared Euclidean distance. This same correction also substantially reduces bias in ordinary Euclidean distance and cosine similarity estimates, but corrections for these measures are not quite unbiased and are (non-intuitively) bimodal when distances are close to zero. The estimators require obtaining the variance of the latent positions. We (will) implement the estimator in free software, and we offer recommendations for related work.

Traveling Front Solutions of Dimension n Generate Entire Solutions of Dimension (n-1) in Reaction–Diffusion Equations as the Speeds Go to Infinity

Multidimensional traveling front solutions and entire solutions of reaction–diffusion equations have been studied intensively. To study the relationship between multidimensional traveling front solutions and entire solutions, we study the reaction–diffusion equation with a bistable nonlinear term. It is well known that there exist multidimensional traveling front solutions with every speed that is greater than the speed of a one-dimensional traveling front solution connecting two stable equilibria. In this paper, we show that the limit of the n-dimensional multidimensional traveling front solutions as the speeds go to infinity generates an entire solution of the same reaction–diffusion equation in the (n-1)-dimensional space.

Polynomial quasi-Trefftz DG for PDEs with smooth coefficients: elliptic problems

Abstract Trefftz schemes are high-order Galerkin methods whose discrete spaces are made of elementwise exact solutions of the underlying partial differential equation (PDE). Trefftz basis functions can be easily computed for many PDEs that are linear, homogeneous and have piecewise-constant coefficients. However, if the equation has variable coefficients, exact solutions are generally unavailable. Quasi-Trefftz methods overcome this limitation relying on elementwise ‘approximate solutions’ of the PDE, in the sense of Taylor polynomials. We define polynomial quasi-Trefftz spaces for general linear PDEs with smooth coefficients and source term, describe their approximation properties and, under a nondegeneracy condition, provide a simple algorithm to compute a basis. We then focus on a quasi-Trefftz DG method for variable-coefficient elliptic diffusion–advection–reaction problems, showing stability and high-order convergence of the scheme. The main advantage over standard DG schemes is the higher accuracy for comparable numbers of degrees of freedom. For nonhomogeneous problems with piecewise-smooth source term we propose to construct a local quasi-Trefftz particular solution and then solve for the difference. Numerical experiments in two and three space dimensions show the excellent properties of the method both in diffusion-dominated and advection-dominated problems.

Slicing-free supervised dimension reduction for multivariate time series

Sufficient dimension reduction (SDR) methods have been extensively studied for regression models with independent data, but options for time series are limited, focusing mainly on scalar responses with TSIR, TSAVE, and TSSH. Although valuable, these SDR methods rely on the slice approach. Extending them to multivariate responses via marginal slicing leads to numerous slices. Furthermore, the slice approach also poses two main questions: how many slices should be chosen and how to divide all samples into different slices. To overcome these, we introduce TMDDM, a slicing-free SDR method for time series, using approximate joint diagonalization of supervised lagged martingale difference divergence matrices (MDDM) to account for the data temporal characteristics. We also discuss lag selection strategies and the dimensionality of dimension reduction space. Simulations and real data analysis demonstrate its favourable finite-sample performance.

On the hidden layer-to-layer topology of the representations of reality realised within neural networks

PurposeConsider an information processing algorithm that is designed to process an input data object onto an output data object via a number of successive internal {\it layers} and mappings between them. The possible activation state within each layer can be represented as a cube within Euclidean space of a high dimension (e.g. equal to the number of artificial neurons at that level). Multiple instances of such input objects produce a point cloud within each layer’s cube: this is the “representation of the reality” at that layer, as sampled by the set of input objects.Design/methodology/approachMost neural networks reduce the dimension of each layer’s cube from layer to successive layer. This gives the false impression of refining the inner representations of reality, distilling it down to fewer dimensions from which to discriminate or to infer outcomes (whatever is the aim). However, the representation of reality realised within each layer’s cube is a manifold, a curved subset embedded within it and of much lower dimension. Investigations show that such manifolds may not always be reducing in their local dimension. Instead, the manifold may become folded over and over, filling up further dimensions and creating non-realistic (unforeseeable) proximities.FindingsWe discuss some of the likely consequences of these relatively unforeseen characteristics and, in particular, the possible vulnerability of such algorithms to non-realistic perturbations. We consider a possible response to this issue.Practical implicationsNew forms of calibration are necessary, using geometric/topological loss functions, as opposed to simple (variation-limiting) regularisation terms.Originality/valueWe apply persistent homology methods to understand how the images of the point cloud (representing the sampled reality) change as they pass from layer to layer.

Endpoint carbon content and temperature prediction model in BOF steelmaking based on posterior probability and intra-cluster feature weight online dynamic feature selection

Abstract A posterior probability and intra-cluster feature weight online dynamic feature selection algorithm is proposed to address the issues of high dimensionality and high volatility of data in the basic oxygen furnace (BOF) steelmaking production process. First, a genetic algorithm with fixed feature space dimensions is introduced, which narrows the solution space by predefining the number of selected features, thereby enhancing the stability of feature selection. Second, the posterior probability of samples and intra-cluster feature weights are used to weigh and calculate the feature importance of the current sample, obtaining the optimal features that align with the current operating conditions. Finally, the dynamically selected features are used in a regression model to predict the carbon content and temperature of the BOF steelmaking process data. Simulations of actual BOF steelmaking process data showed that the prediction accuracy was 86% within a carbon content error range of 0.02, and 88% within a temperature error range of 10°C.

The clinical value and most informative threshold of polygenic risk score in the Quebec City Case-Control Asthma Cohort

Genome-wide association studies (GWAS) have identified genetic variants robustly associated with asthma. A potential near-term clinical application is to calculate polygenic risk score (PRS) to improve disease risk prediction. The value of PRS, as part of numerous multi-source variables used to define asthma, remains unclear. This study aims to evaluate PRS and define most informative thresholds in relation to conventional clinical and physiological criteria of asthma using a multivariate statistical method. Clinical and genome-wide genotyping data were obtained from the Quebec City Case-Control Asthma Cohort (QCCCAC), which is an independent cohort from previous GWAS. PRS was derived using LDpred2 and integrated with other asthma phenotypes by means of Principal Component Analysis with Optimal Scaling (PCAOS). PRS was considered using ‘ordinal level of scaling’ to account for non-linear information. In two dimensional PCAOS space, the first component delineated individuals with and without asthma, whereas the severity of asthma was discerned on the second component. The positioning of high vs. low PRS in this space matched the presence and absence of airway hyperresponsiveness, showing that PRS delineated cases and controls at the same extent as a positive bronchial challenge test. The top 10% and the bottom 5% of the PRS were the most informative thresholds to define individuals at high and low genetic risk of asthma in this cohort. PRS used in a multivariate method offers a decision-making space similar to hyperresponsiveness in this cohort and highlights the most informative and asymmetrical thresholds to define high and low genetic risk of asthma.

WeTICA: A directed search weighted ensemble based enhanced sampling method to estimate rare event kinetics in a reduced dimensional space.

Estimating rare event kinetics from molecular dynamics simulations is a non-trivial task despite the great advances in enhanced sampling methods. Weighted Ensemble (WE) simulation, a special class of enhanced sampling techniques, offers a way to directly calculate kinetic rate constants from biased trajectories without the need to modify the underlying energy landscape using bias potentials. Conventional WE algorithms use different binning schemes to partition the collective variable (CV) space separating the two metastable states of interest. In this work, we have developed a new "binless" WE simulation algorithm to bypass the hurdles of optimizing binning procedures. Our proposed protocol (WeTICA) uses a low-dimensional CV space to drive the WE simulation toward the specified target state. We have applied this new algorithm to recover the unfolding kinetics of three proteins: (A) TC5b Trp-cage mutant, (B) TC10b Trp-cage mutant, and (C) Protein G, with unfolding times spanning the range between 3and40μs using projections along predefined fixed Time-lagged Independent Component Analysis (TICA) eigenvectors as CVs. Calculated unfolding times converge to the reported values with good accuracy with more than one order of magnitude less cumulative WE simulation time than the unfolding time scales with or without a priori knowledge of the CVs that can capture unfolding. Our algorithm can be used with other linear CVs, not limited to TICA. Moreover, the new walker selection criteria for resampling employed in this algorithm can be used on more sophisticated nonlinear CV space for further improvements of binless WE methods.