Dimensional Space Research Articles

GAN-Generated Face Detection Based on Multiple Attention Mechanism and Relational Embedding

The rapid development of the Generative Adversarial Network (GAN) makes generated face images more and more visually indistinguishable, and the detection performance of previous methods will degrade seriously when the testing samples are out-of-sample datasets or have been post-processed. To address the above problems, we propose a new relational embedding network based on “what to observe” and “where to attend” from a relational perspective for the task of generated face detection. In addition, we designed two attention modules to effectively utilize global and local features. Specifically, the dual-self attention module selectively enhances the representation of local features through both image space and channel dimensions. The cross-correlation attention module computes similarity between images to capture the global information of the output in the image. We conducted extensive experiments to validate our method, and the proposed algorithm can effectively extract the correlations between features and achieve satisfactory generalization and robustness in generating face detection. In addition, we also explored the design of the model structure and the inspection performance on more categories of generated images (not limited to faces). The results show that RENet also has good detection performance on datasets other than faces.

Statistical analysis of trends in Battery Electric Vehicles: Special reference to vehicle weight reduction, electric motor, battery, and interior space dimensions

Electric vehicles (EVs) are increasingly being used, as they are more environmentally friendly than conventional vehicles with internal combustion engines (ICE). Battery electric vehicles (BEVs) can be said to have zero exhaust emissions only if the electricity used to drive these vehicles is obtained in an environmentally friendly way. It is common knowledge that BEVs have a significantly higher overall mass than conventional vehicles. The significantly higher total vehicle weight of BEVs can have various adverse effects on energy consumption during movement and the vehicle's dynamics. In contrast to the negative aspects of BEVs, there are also positive aspects that are primarily related to the comfort of drivers and passengers, considering the main fact that they do not require the presence of a floor tunnel. In this paper, trends related to BEVs in the previous five years were statistically analysed. Changes in average sizes related to BEVs are shown, primarily internal dimensions that can be of crucial importance when deciding between BEVs and conventional vehicles. In the paper itself, other important trends are presented, both for the electric motor itself and for the batteries used in BEVs.

Parameter identification method of information propagation models based on different network structures

In this paper, we create the rumor propagation model with diffusion behavior by considering the state of the rumor in both the time dimension and the space dimension comprehensively. Meanwhile, we demonstrate the reaction–diffusion model using Turing patterns after determining the prerequisites for their occurrence. In order to achieve the purpose of predicting and controlling rumors in time, we choose to utilize the parameter identification technique based on the Barzilai–Borwein (BB) algorithm and the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm. In the numerical simulation section, we first investigate how the rumor avoidance rate and cross-diffusion coefficients affect the propagation of rumors. Then, based on a continuous spatio-temporal system and complex network system, respectively, we perform parameter identification for the propagation model. We thoroughly examine how the type of algorithm, the quantity of unknown parameters, and the network structure affect the identification outcomes in terms of the cost function, error curve, and program function time. When the model constructed in this paper is used for parameter identification on different network structures, the error gap between the final value and the target value is not significant. However, the cost function and time consumption for parameter identification on complex networks are much smaller than on the continuous medium.

Kinetically anisotropic Hamiltonians: plane waves, Madelung streamlines and superpositions

A Hamiltonian in two space dimensions whose kinetic-energy contributions have opposite signs is studied in detail. Solutions of the time-independent Schrödinger equation for fixed energy are superpositions of plane waves, with wavevectors on hyperbolas rather than circles. The local velocity (e.g. in the Madelung representation) is proportional to the kinetic momentum, i.e. local particle velocity, not the more familiar canonical momentum (phase gradient). The patterns of the associated streamlines are different, especially near phase singularities and phase saddles where the kinetic and canonical streamline patterns have opposite indices. Contrasting with the superficially analogous circular smooth solutions of kinetically isotropic Hamiltonians are wave modes that are anisotropic in position and also discontinuous. Pictures illustrating these phenomena are included. The occurrence of familiar concepts in unfamiliar guises could be useful for teaching quantum or wave physics at graduate level.

Cyclic 2-spreads in V(6,q) and flag-transitive linear spaces

In this paper we completely classify spreads of 2-dimensional subspaces of a 6-dimensional vector space over a finite field of characteristic not two or three upon which a cyclic group acts transitively. This addresses one of the remaining open cases in the classification of flag-transitive linear spaces. We utilise the polynomial approach innovated by Pauley and Bamberg to obtain our results.

Left-invariant almost complex structures on the higher dimensional Kodaira–Thurston manifolds

We develop computational techniques which allow us to calculate the Kodaira dimension as well as the dimension of spaces of Dolbeault harmonic forms for left-invariant almost complex structures on the generalised Kodaira–Thurston manifolds.

Determining the time before or after a galaxy merger event

Aims. This work aims to reproduce the time before or after a merger event of merging galaxies from the IllustrisTNG cosmological simulation using machine learning. Methods. Images of merging galaxies were created in the u, g, r, and i bands from IllustrisTNG. The merger times were determined using the time difference between the last simulation snapshot where the merging galaxies were tracked as two galaxies and the first snapshot where the merging galaxies were tracked as a single galaxy. This time was then further refined using simple gravity simulations. These data were then used to train a residual network (ResNet50), a Swin Transformer (Swin), a convolutional neural network (CNN), and an autoencoder (using a single latent neuron) to reproduce the merger time. The full latent space of the autoencoder was also studied to see if it reproduces the merger time better than the other methods. This was done by reducing the latent space dimensions using Isomap, linear discriminant analysis (LDA), neighbourhood components analysis, sparse random projection, truncated singular value decomposition, and uniform manifold approximation and projection. Results. The CNN is the best of all the neural networks. The performance of the autoencoder was close to the CNN, with Swin close behind the autoencoder. ResNet50 performed the worst. The LDA dimensionality reduction performed the best of the six methods used. The exploration of the full latent space produced worse results than the single latent neuron of the autoencoder. For the test data set, we found a median error of 190 Myr, comparable to the time separation between snapshots in IllustrisTNG. Galaxies more than ≈625 Myr before a merger have poorly recovered merger times, as well as galaxies more than ≈125 Myr after a merger event.

Prediction of lower limb discomfort of elderly drivers based on key dimensions in the leg space

Significant difference exists in spatial fitness and perception between elderly and non-elderly drivers. However, due to dynamic and real-time changes in human subjective feelings and joint movements, two-dimensional human body templates and human-machine simulation software are not enough to obtain necessary space parameters. In this study, seven key dimensions of the legroom were measured thrice and averaged, in the situation that the seat and posture are comfortable. Such anthropometric data can reflect dynamic perception that may change due to personal emotions and environmental influences. Extreme learning machine (ELM) was adopted to build a prediction model of leg space discomfort degree, and the influence of the activation function and the number of hidden layer neurons on the prediction accuracy of the model were analyzed. In addition, a multiple linear regression (MLR) model was established with the discomfort score as the dependent variable and the seven key dimensions as the independent variables. The results indicated that the ELM model could effectively predict elderly drivers’ discomfort degree (MSE = 0.182, MRE = 9.364, R2 = 0.869) by learning the dimensions of the seven key positions. The MLR model (R2 = 0.861) did not perform as well as ELM. However, the regression coefficients could reflect the degree to which each dimension affects the discomfort degree of leg space for elderly drivers. The conclusions could function in elderly-oriented in-vehicle space arrangement and driving risk assessment of elderly people.

How Civil Societies Are Undermined

Several studies highlight the fact that the first decades of the 21st century are characterized by a resurgence of authoritarianism, which contradicts the optimistic visions of the 1990s regarding the so-called end of history. For instance, Freedom House argues, presenting relevant data, that since 2006, a process of democratic backsliding has been in place worldwide. Not only developing countries or regions are affected but also countries in Europe and Northern America, where democracy once seemed inexpugnable. This illiberal wave thrives on the weaknesses of civil societies and has the effect of further reducing the dimensions of the civic space. Although those who promote open societies are on the defensive, their cause is far from being an obsolete remnant of the second half of the 20th century. However, their endeavors can be ineffective if the causes of the antidemocratic forces’ success are not properly acknowledged. The main goal of this paper is to contribute to a better understanding of the factors that are vital for building or strengthening closed societies. To shape relevant conclusions, we analyze information from projects like People Power under Attack, realized by the CIVICUS global civil society network or V-Dem (The Varieties of Democracy), managed by an institute affiliated with the University of Gothenburg (Sweden). We focus especially on countries that experienced sharp transformations regarding the state of their civil societies in the last 3–5 years. Our findings underline, among others, the importance of the electoral process and foreign policy influencing the evolution of the civic space. Cases like the Czech Republic suggest that the decline of civil society can be stopped at the polls. The Russian Federation is an example of a successful suspension of civic freedoms under the pretext of protecting the population from toxic foreign interference.

Positive bases, cones, Helly-type theorems

Abstract Assume that k ≤ d is a positive integer and 𝓒 is a finite collection of convex bodies in ℝ d . We prove a Helly-type theorem: If for every subfamily 𝓒* ⊂ 𝓒 of size at most max{d + 1, 2(d – k + 1)} the set ⋂ 𝓒* contains a k-dimensional cone, then so does ⋂ 𝓒. One ingredient in the proof is another Helly-type theorem about the dimension of lineality spaces of convex cones.

Equality of different definitions of conformal dimension for quasiself-similar and CLP spaces

We prove that for a quasiself-similar and arcwise connected compact metric space all three known versions of the conformal dimension coincide: the conformal Hausdorff dimension, conformal Assouad dimension and Ahlfors regular conformal dimension. This answers a question posed by Murugan. Quasisimilar spaces include all approximately self-similar spaces. As an example, the standard Sierpiński carpet is quasiself-similar and thus the three notions of conformal dimension coincide for it. We also give the equality of the three dimensions for combinatorially p-Loewner (CLP) spaces. Both proofs involve using a new notion of combinatorial modulus, which lies between two notions of modulus that have appeared in the literature. The first of these is the modulus studied by Pansu and Tyson, which uses a Carathéodory construction. The second is the one used by Keith and Laakso (and later modified and used by Bourdon, Kleiner, Carrasco-Piaggio, Murugan and Shanmugalingam). By combining these approaches, we gain the flexibility of giving upper bounds for the new modulus from the Pansu–Tyson approach, and the ability of getting lower bounds using the Keith–Laakso approach. Additionally the new modulus can be iterated in self-similar spaces, which is a crucial, and novel, step in our argument.

Estimating Biogeochemical Rates Using a Computationally Efficient Lagrangian Approach

Nutrient concentrations in many estuaries have increased over the past century due to increases in wastewater discharge and increased agricultural intensity, contributing to multiple environmental problems. Numerous biogeochemical and physical processes in estuaries influence nutrient concentrations during transport, resulting in complex spatial and temporal variability and challenges identifying predominant processes and their rates. Mechanistic models which require these rates to quantify biogeochemical processes become complex and difficult to calibrate as the number of processes and parameters grows, owing to the high dimensionality of the parameter space and the computational cost of simultaneously modeling the transport and transformations of constituents. We developed a modeling approach that decouples transport from transformations, enabling fast, data-driven exploration of the parameter space. The approach extracted information including water age, cumulative exposure to specific habitats, and mean water depth exposure from a hydrodynamic model. Using this information, a biogeochemical model was implemented to predict ammonium and nitrate concentrations in a Lagrangian frame. The model performed each simulation in milliseconds on a laptop computer, allowing the fitting of rate parameters for key transformations by optimization. The optimization used fixed station nitrate observations and the model was then validated against high-resolution mapping observations of ammonium and nitrate. The results suggest that the observed spatial and temporal variation can be largely represented with five transformation processes and their associated rates. Dissolved inorganic nitrogen (DIN) losses occurred only in shallow vegetated areas in the model, highlighting that biogeochemical processes in these areas should be included in DIN models.

Symmetric operator means

AbstractThe purpose of this paper is to extend symmetric means of multi-variable positive matrices to those of multi-variable positive operators on an infinite dimensional Hilbert space. We also consider the situations where symmetric means of operators A, B, C become linear combinations of them.

Private Query Release via the Johnson-Lindenstrauss Transform

We introduce a new method for releasing answers to statistical queries with differential privacy, based on the Johnson-Lindenstrauss lemma. The key idea is to randomly project the query answers to a lower dimensional space so that the distance between any two vectors of feasible query answers is preserved up to an additive error. Then we answer the projected queries using a simple noise-adding mechanism, and lift the answers up to the original dimension. Using this method, we give, for the first time, purely differentially private mechanisms with optimal worst case sample complexity under average error for answering a workload of $k$ queries over a universe of size $N$. As other applications, we give the first purely private efficient mechanisms with optimal sample complexity for computing the covariance of a bounded high-dimensional distribution, and for answering 2-way marginal queries. We also show that, up to the dependence on the error, a variant of our mechanism is nearly optimal for every given query workload.

Calibration-independent bound on the unitarity of a quantum channel with application to a frequency converter

We report on a method to certify a unitary operation with the help of source and measurement apparatuses whose calibration throughout the certification process needs not be trusted. As in the device-independent paradigm our certification method relies on a Bell test and requires no assumption on the underlying Hilbert space dimension, but it removes the need for high detection efficiencies by including the single additional assumption that non-detected events are independent of the measurement settings. The relevance of the proposed method is demonstrated experimentally by bounding the unitarity of a quantum frequency converter. The experiment starts with the heralded creation of a maximally entangled two-qubit state between a single 40Ca+ ion and a 854 nm photon. Entanglement preserving frequency conversion to the telecom band is then realized with a non-linear waveguide embedded in a Sagnac interferometer. The resulting ion-telecom photon entangled state is assessed by means of a Bell-CHSH test from which the quality of the frequency conversion is quantified. We demonstrate frequency conversion with an average certified fidelity of ≥84% and an efficiency ≥3.1 × 10−6 at a confidence level of 99%. This ensures the suitability of the converter for integration in quantum networks from a trustful characterization procedure.

Examining the nonlinear relationship between neighborhood environment and residents' health

Although numerous studies have revealed linear associations between the urban environment and health, the nonlinear effects of subjective and objective neighborhood environment on health have been under-researched. Using Beijing as a case study, this study employs the random forest method to investigate the nonlinear relationship between subjective/objective neighborhood environment and physical/mental health, respectively. The findings indicate that the subjective environment is the most important for both physical and mental health, and subjective air and noise pollution are the key factors. Neighborhood environmental variables have nonlinear correlations with health. Improved perception of facility accessibility is positively associated with physical health, whereas extremely high levels of accessibility may inversely decrease the probability of reporting good health. Road connectivity and bus stop density exhibit inverted U-shaped patterns with physical health and mental health, separately. Furthermore, the study highlights different dimensions of green space affect residents' health in diverse ways.

Immersions into Sasakian space forms

We study immersions of Sasakian manifolds into finite and infinite dimensional Sasakian space forms. After proving Calabi’s rigidity results in the Sasakian setting, we characterise all homogeneous Sasakian manifolds which admit a (local) Sasakian immersion into a nonelliptic Sasakian space form. Moreover, we give a characterisation of homogeneous Sasakian manifolds which can be embedded into the standard sphere both in the compact and noncompact case.

A Comprehensive Overview of the Ulianov Theory

BThis article provides a comprehensive overview of the Ulianov Theory (UT), a pioneering model formulated by Dr. Policarpo Yoshin Ulianov. The UT offers a revolutionary approach to understanding the universe, anchored in mathematical rigor and logical scrutiny. Central to its framework is a redefined conception of time, positing it as a digital and complex variable time dimension and aligning the notion of imaginary time, with six digital spatial dimensions (three normal space dimensions an three spatial wrapped dimensions) named as General Octo-Dimension Universe (GODU), that also can see like four five-dimensions subuniverses separate by walls of space and walls of time, an original idea proposed by Issac Asimov in 1966 to explain a ”four leaf clover universe” beginning for noting, with the antimatter universes going to the negative time direction (travel to the past before the Big Bang). The Ulianov theory present a 12 basic particles model (6 particles and 6 antiparticles, like the quarks) seems as elastic holes in walls of time and space. The connections between it proposes particles properties (mass and electric charge) are familiar within our observable universe. In challenging prevailing scientific paradigms, UT beckons the scientific community to reassess foundational beliefs. The UT is based on only two fundamental forces (gravitational and eletromagnetic), replacing the Nuclear Strong add Week Forces by an Gravitational Contact Force, that becomes in play only wen two masses becomes in contact (with a Planck distance between then). Additionally, the article delves into a novel String Theory model (when photons, protons electrons and neutrons are basically the same length string, but wrapped in distinct ways). The UT also presents the ”Small Bang” hypothesis, suggesting the universe’s genesis from a small and cold space bubble (only a Planck length of diameter), with antimatter micro black hole becomes supermassive antimatter black holes and generating matter and antimatter (in the same proportion), stolen energy by the cosmic inflation field. Within the UT’s purview, seminal equations from classical physics, Einstein’s theories of relativity, and quantum mechanics are eloquently derived.

The inverse of a quantum bilinear form of the oriented braid arrangement

We follow here the results of Varchenko, who assigned to each weighted arrangement \(\mathcal{A}\) of hyperplanes in the \(n\)-dimensional real space a bilinear form, which he called the quantum bilinear form of the arrangement \(\mathcal{A}\). We briefly explain the quantum bilinear form of the oriented braid arrangement in the \(n\)-dimensional real space. The main concern of this paper is to compute the inverse of the matrix of the quantum bilinear form of the oriented braid arrangement in \(\mathbb{R}^n\), \({n\ge 2}\). To solve this problem, in [3] the authors used some special matrices and their factorizations in terms of simpler matrices. So, to simplify some matrix calculations, we first introduce a twisted group algebra \({\mathcal{A}(S_{n})}\) of the symmetric group \(S_{n}\) with coefficients in the polynomial ring in \(n^2\) commutative variables and then use a natural representation of some elements of the algebra \({\mathcal{A}(S_{n})}\) on the generic weight subspaces of the multiparametric quon algebra \({\mathcal{B}}\), which immediately gives the corresponding matrices of the quantum bilinear form.

Singular backward stochastic Volterra integral equations in infinite dimensional spaces

In this paper, the notion of singular backward stochastic Volterra integral equations (singular BSVIEs for short) in infinite dimensional space is introduced, and the corresponding well-posedness is carefully established. A class of singularity conditions are proposed, which not only cover that of fractional kernel, Volterra Heston model kernel, completely monotone kernels, to mention a few, but also happen to be used in the forward stochastic Volterra integral with new conclusions arising. Motivated by mathematical physics problem such as the viscoelasticity/thermoviscoelasticity of materials, heat conduction in materials with memory, optimal control problems of abstract stochastic Volterra integral equations (including fractional stochastic evolution equations and stochastic evolutionary integral equations) are presented. At last, our BSVIEs are surprisingly used in maximum principle of controlled stochastic delay evolution equations. One advantage of this new standpoint is that the final cost functional can naturally depend on the past state.