Coefficient Space Research Articles

The space of transport coefficients allowed by causality

The space of transport coefficients allowed by causality

Optimal procurement decisions based on smoothing strategy for dual sourcing with different lead times

This study establishes a discrete-time inventory model with a smoothing procurement strategy in dual sourcing. Specifically, an assembly manufacturer purchases components from two suppliers: one overseas supplier with a long lead time but a low price, and one local supplier with a short lead time but a high price. A smoothing procurement approach taking into account previous ordering record and current demand is adopted by the assembly manufacturer. We start by exploring the scenario where storage space is not a constraint. The cost-minimization conditions for single sourcing and dual sourcing are studied. Assuming demand follows a normal distribution, the optimal order quantities and inventory levels are subsequently derived and shown to follow the same distribution. By comparing the inventory costs, it is found that dual sourcing is superior to single sourcing. Then, we examine the scenario where an assembly manufacturer with limited storage space collaborates with a third-party logistics company. The optimal order quantities, inventory levels, smoothing procurement coefficient and storage space are derived for the assembly manufacturer. Finally, numerical experiments with practical data are constructed to verify our findings.

Automated Search Strategy for Novel Ordered Structures of Block Copolymers.

Block copolymers with different architectures can possibly generate innumerable stable or metastable structures and thus provide an irreplaceable platform for theoretically exploring novel structures. Self-consistent field theory (SCFT) is a powerful tool to predict the ordered structures of block copolymers; however, it is sensitively dependent on its initial condition. Here we propose to use multiple symmetry-adapted basis functions to generate the initial conditions of SCFT and then apply Bayesian optimization to search for ordered structures by navigating the coefficient space of these basis functions. Without any prior knowledge, our scheme can automatically recover hundreds of ordered structures for two simple block copolymers, including most of the common structures and complex Frank-Kasper structures, together with many novel structures. By applying the automated scheme to various block copolymers, a huge number of novel structures can be obtained to expand the structural library, which may create new opportunities for the scientific community.

Six types of spin solitons in three-component Bose–Einstein condensates

Exact analytical solutions are good candidates for studying and explaining the dynamics of solitons in nonlinear systems. We further extend the region of existence of spin solitons in the nonlinearity coefficient space for the spin-1 Bose–Einstein condensate. Six types of spin soliton solutions can be obtained, and they exist in different regions. Stability analysis and numerical simulation results indicate that three types of spin solitons are stable against weak noise. The non-integrable properties of the model can induce shape oscillation and increase in speed after the collision between two spin solitons. These results further enrich the soliton family for non-integrable models and can provide theoretical references for experimental studies.

Turbulence Closure With Small, Local Neural Networks: Forced Two‐Dimensional and β‐Plane Flows

AbstractWe parameterize sub‐grid scale (SGS) fluxes in sinusoidally forced two‐dimensional turbulence on the β‐plane at high Reynolds numbers (Re ∼25,000) using simple 2‐layer convolutional neural networks (CNN) having only O(1000) parameters, two orders of magnitude smaller than recent studies employing deeper CNNs with 8–10 layers; we obtain stable, accurate, and long‐term online or a posteriori solutions at 16× downscaling factors. Our methodology significantly improves training efficiency and speed of online large eddy simulations runs, while offering insights into the physics of closure in such turbulent flows. Our approach benefits from extensive hyperparameter searching in learning rate and weight decay coefficient space, as well as the use of cyclical learning rate annealing, which leads to more robust and accurate online solutions compared to fixed learning rates. Our CNNs use either the coarse velocity or the vorticity and strain fields as inputs, and output the two components of the deviatoric stress tensor, Sd. We minimize a loss between the SGS vorticity flux divergence (computed from the high‐resolution solver) and that obtained from the CNN‐modeled Sd, without requiring energy or enstrophy preserving constraints. The success of shallow CNNs in accurately parameterizing this class of turbulent flows implies that the SGS stresses have a weak non‐local dependence on coarse fields; it also aligns with our physical conception that small‐scales are locally controlled by larger scales such as vortices and their strained filaments. Furthermore, 2‐layer CNN‐parameterizations are more likely to be interpretable.

Classifying missing persons cases: an analysis of police risk assessments using multi-dimensional scaling

ABSTRACT Missing persons cases present a complex challenge for law enforcement globally and require a nuanced understanding of their typologies. This study provides a comprehensive analysis of cases from the United Kingdom, from within a single police service, focusing on the alignment of police missing person risk assessment (RA) factors with existing typologies. Utilizing data exclusively from nearly 5000 police RAs, the study undertakes a multi-stage analysis, examining RA factors for congruence with established typologies and exploring data subsets based on gender, case outcomes, and risk gradings. Using Jaccard’s similarity coefficient and smallest space analysis (SSA), the study interprets and visualizes the cases to explore relationships. Results are reported using visual and descriptive statistics. Key findings include confirmation of alignment to existing typologies and research that has identified ‘unintentional – accidental/drift’ as the dominant missing person typology, identifying it in 65% of the cases. Notably, the typology was also the dominant theme in 45% of the cases resulting in a harmful outcome and 42% graded as high-risk. Categorical nuances are identified within subsets, with 47% of long-term missing and 63% involving men relating to the intentional – dysfunctional typology. 31% of the cases involving females, and 30% and 45% of the cases graded as medium and no apparent risk, respectively, were dominated by the ‘intentional – escape’ typology. We discuss how these findings can be used to improve the police RA process and guide initial risk grading and case prioritization enhancing the understanding and response to missing person cases.

Probing muon g-2 at a future muon collider

The 4.2\sigma4.2σ discrepancy in the (g-2)(g−2) of the muon provides a hint that may indicate that physics beyond the standard model is at play. A multi-TeV scale muon collider provides a natural testing ground for this physics. In this paper, we discuss the potential to probe the BSM parameter space that is consistent with solving the (g-2)_{\mu}(g−2)μ discrepancy in the language of the SMEFT, utilizing the statistical power provided by fitting event rates collected running at multiple energies. Our results indicate the importance of including interference between the BSM and the SM amplitudes, and illustrates how a muon collider running at a handful of lower energies and with less total collected luminosity can better significantly constrain the space of relevant SMEFT coefficients than would be possible for a single high energy run.

Reconstructing robust background integral field unit spectra using machine learning

ABSTRACT In astronomy, spectroscopy consists of observing an astrophysical source and extracting its spectrum of electromagnetic radiation. Once extracted, a model is fit to the spectra to measure the observables, leading to an understanding of the underlying physics of the emission mechanism. One crucial, and often overlooked, aspect of this model is the background emission, which contains foreground and background astrophysical sources, intervening atmospheric emission, and artefacts related to the instrument such as noise. This paper proposes an algorithmic approach to constructing a background model for SITELLE observations using statistical tools and supervised machine learning algorithms. SITELLE is an imaging Fourier transform spectrometer located at the Canada-France-Hawaii Telescope, which produces a three-dimensional data cube containing the position of the emission (two dimensions) and the spectrum of the emission. SITELLE has a wide field of view (11 arcmin × 11 arcmin), which makes the background emission particularly challenging to model. We apply a segmentation algorithm implemented in photutils to divide the data cube into background and source spaxels. After applying a principal component analysis (PCA) on the background spaxels, we train an artificial neural network to interpolate from the background to the source spaxels in the PCA coefficient space, which allows us to generate a local background model over the entire data cube. We highlight the performance of this methodology by applying it to SITELLE observations obtained of a Star-formation, Ionized Gas and Nebular Abundances Legacy Survey galaxy, NGC 4449, and the Perseus galaxy cluster of galaxies, NGC 1275. We discuss the physical interpretation of the principal components and noise reduction in the resulting PCA-based reconstructions. Additionally, we compare the fit results using our new background modelling approach with standard methods used in the literature and find that our method better captures the emission from H ii regions in NGC 4449 and the faint emission regions in NGC 1275. These methods also demonstrate that the background does change as a function of the position of the data cube. While the approach is applied explicitly to SITELLE data in this study, we argue that it can be readily adapted to any integral field unit style data, enabling the user to obtain more robust measurements on the flux of the emission lines.

Adaptive optimal ℓ∞‐induced robust stabilization of minimum phase SISO plant under bounded disturbance and coprime factor perturbations

AbstractThis paper addresses the problem of optimal robust stabilization of a discrete‐time minimum‐phase plant in the framework of robust control theory in the setup and under poor a priori information. Coefficients of the transfer function of the plant nominal model with stable zeros are unknown and belong to a known bounded polyhedron in the space of coefficients. The gains of coprime factor perturbations of the plant and the upper bound of external disturbance are also unknown. The problem under consideration is to design adaptive controller that minimizes, with the prescribed accuracy, the worst‐case asymptotic upper bound of the output. Solution of the problem is based on set‐membership estimation of unknown parameters and treating the control criterion as the identification criterion. A hard nonconvex problem of on‐line computation of optimal estimates is reduced, under additional nonrestrictive assumption, to a linear‐fractional programming via a nonlinear transformation of estimated parameters. Despite the non‐identifiability of the unknown parameters, the proposed adaptive controller guarantees, with the prescribed accuracy, the same optimal asymptotic upper bound of the output of adaptive system as the optimal controller for the plant with known parameters. In addition to the optimality of adaptive control, the proposed solution provides on‐line verification/validation of current estimates and a priori assumptions.

Investigating the analytical relationship between pore geometry and other pore space properties in carbonate rocks

Although pore geometry plays an important role in carbonate rock physics modelling, few studies have been carried out on its analytic relationship with other pore space properties such as pore space stiffness. We propose an analytical workflow based on the differential effective medium (DEM) to estimate the elastic properties of carbonate rocks. The validity of our results is then cross-checked with the Xu and Payne model on a real carbonate dataset. This workflow establishes a direct and quantitative link between the pore geometry of carbonate rock and its other pore space properties such as the Biot coefficient and pore space stiffness. This relationship can, furthermore, be utilized in defining rock physics templates (RPTs) to investigate the role of pore geometry on the rock elastic properties. Furthermore, we extended the Biot–Gassmann–Krief (BGK) model through our proposed workflow by establishing a theoretical framework to relate the main components of the BGK model to the pore geometry usually estimated in the laboratory or empirically. This can help to investigate the impact of fluid substitution on each of these main components. Our investigation suggests that the higher the Biot and Gassmann coefficients, the more sensitive the rock is to fluid substitution. Moreover, this analytical workflow has been employed to examine the role of selecting different rotational spheroids (i.e. oblate and prolate) on the modelled velocities. Our results show that the modelled velocities depend on this selection in such a way that prolate pores are less sensitive to the variations in their pore aspect ratio compared with oblate pores.

Distinguishing models with μ → e observables

Upcoming experiments will improve the reach for the lepton flavour violating (LFV) processes μ → eγ, μ → ee¯e\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ e\\overline{e}e $$\\end{document} and μA → eA by orders of magnitude. We investigate whether this upcoming data could rule out some popular TeV-scale LFV models (the type II seesaw, the inverse seesaw and a scalar leptoquark) using a bottom-up EFT approach. We take the data to be the twelve Wilson coefficients that experiments can constrain and in principle determine independently. In this 12-dimensional coefficient space, each model can only predict points in a specific subspace; for instance, flavour change involving singlet electrons is suppressed in the seesaw models, and the leptoquark induces negligible coefficients for 4-lepton scalar operators. Using the fact that none of these models can populate the whole region accessible to upcoming experiments, we show that μ → e experiments have the ability to rule them out.

Spectra of quotient modules

We determine the Taylor spectra of quotient tuples of the d-shift on Drury-Arveson spaces with finite-dimensional coefficient spaces. We show that the Taylor spectrum can be described in terms of the approximate zero set of the annihilator ideal, and in terms of the pointwise behavior of the inner multiplier associated with the quotient tuple.

Lasso regression method for a compositional covariate regularised by the norm L1 pairwise logratio

Lasso regression methods include a penalty function expressed in terms of a norm defined in the space of model coefficients. The norm plays a key role as regards the way coefficients can become irrelevant in the model. For models with a compositional covariate, the norm should be coherent with the Aitchison geometry. The proposed method is based on a newly-defined compositional norm called L1 pairwise logratio. The novel approach allows one to construct an appropriate basis through a sequential binary partition for discriminating between balances that influence the response variable and those that have no effect. This generalised Lasso regression scheme is illustrated with the analysis of a geochemical data set.

A High-Resolution Spatial Distribution-Based Integration Machine Learning Algorithm for Urban Fire Risk Assessment: A Case Study in Chengdu, China

The development and functional perfection of urban areas have led to increasingly severe fire risks in recent decades. Previous urban fire risk assessment methods relied on subjective judgment, rough data collection, simple linear statistical methods, etc. These drawbacks can lead to low robustness of evaluation and inadequate generalization ability. To resolve these problems, this paper selects the indicator and regression models based on the high-resolution data of the spatial distribution characteristics of Longquanyi distinct in Chengdu, China. and proposes an integrated machine learning algorithm for fire risk assessment. Firstly, the kernel density analysis is used to map the fourteen urban characteristics related to fire risks. The contributions of these indicators (characteristics) to fire risk and its corresponding index are determined by Random Forest (RF), Gradient Boosting Decision Tree (GBDT), and eXtreme Gradient Boosting (XGBoost). Then, the spatial correlation of fire risks is determined through Moran’s I, and the spatial distribution pattern of indicator weights is clarified through the raster coefficient space analysis. Finally, with these selected indicators, we test the regression performance with a backpropagation neural network (BPNN) algorithm and a geographically weighted regression (GWR) model. The results indicate that numerical variables are more suitable than dummy variables for estimating micro-scale fire risks. The main factors with a high contribution are all numerical variables, including roads, gas pipelines, GDP, hazardous chemical enterprises, petrol and charging stations, cultural heritage protection units, assembly occupancies, and high-rise buildings. The machine learning algorithm integrating RF and BPNN shows the best performance (R2 = 0.97), followed by the RF-GWR integrated algorithm (R2 = 0.87). Compared with previous methods, this algorithm reduces the subjectivity of the traditional assessment models and shows the ability to automatically obtain the key indicators of urban fire risks. Hence, this new approach provides us with a more robust tool for assessing the future fire safety level in urban areas.

Asymmetric low-rank double-level cooperation for scalable discrete cross-modal hashing

As an efficient information retrieval technique, cross-modal hashing has received increasing attention. However, the remaining challenges include (1) designing effective kernelization techniques to sufficiently strengthen the connections among different samples in kernel space and improve the class separability of data; (2) learning robust compact common representations to fully extract the correlation information between different modalities; and (3) fully leveraging underlying semantic information and embedding it into optimal hash codes. To conquer these challenges, we propose a novel algorithm called Asymmetric Low-rank Double-level Cooperation Hashing (ALDCH). First, we propose a novel Nonlinear Normalized Space Kernelization submodule (NNSK) to obtain the high-quality kernelized features, which can not only capture the more powerful nonlinear structure representations but also better express the nonlinear intra-modal correlations among the original features. To learn high-quality compact representations, we further propose a novel Low-rank Double-level Cooperation Mapping submodule (LDCM) with the L21-norm constraint, which can enhance the correlation of the coefficient spaces from different modalities and enable the samples to learn constrained and compact hash representations. Besides, our proposed method fully utilizes the underlying semantic label information by introducing the Semantic Pairwise Correlation Learning submodule (SPCL). Extensive experiments conducted on benchmark datasets demonstrate the accuracy and efficiency of ALDCH, which outperforms many state-of-the-art methods.

Learning Mappings from Iced Airfoils to Aerodynamic Coefficients Using a Deep Operator Network

This study abstracted the prediction of the aerodynamic coefficients of an iced airfoil as a mapping from the iced airfoil space to the aerodynamic coefficient space. Thus, a deep network called Airfoils2AeroNet that can learn this mapping was established based on Deep Operator Network (DeepONet). The deep network consists of a branch network for encoding the iced airfoil images and a trunk network that learns a nonlinear mapping from the one-dimensional aerodynamic coefficient function input to p-dimensional outputs. The branch network consists of deep convolutional neural networks (CNNs), and the trunk network consists of fully connected neural networks (FNNs). Then the network was trained and tested on iced airfoils based on NACA 0012 airfoils. Comparing the prediction results of Airfoils2AeroNet with those of the conventional direct CNN network, the network proposed in this paper has a strong advantage for generalization. Unlike the traditional CNN, which can only predict the aerodynamic coefficients at fixed flow conditions consistent with the training data, the network can flexibly predict the aerodynamic coefficients at different flow conditions. Finally, the influence of the structure of the branch network and trunk network on the prediction results was analyzed.

Generalized Affine Equivalence Checking of Boolean Functions via Reachability Analysis

We consider the problem of checking the generalized affine equivalence of two given Boolean functions. This problem arises in various computer-aided design (CAD) and cryptographic applications, such as circuit synthesis and Reed-Muller codes. Based on the theory of affine group acting on the Boolean functions, we define the coefficient spaces and transition relations, and transform the checking problem into reachability analysis of finite state machines. Two methods are proposed to check the affine equivalence of Boolean functions using Binary Decision Diagrams (BDDs) and Property Directed Reachability (PDR), respectively. Both methods can check affine equivalence of bent and semi-bent functions, which state-of-the-art methods can hardly handle. Furthermore, existing methods only consider the case of affine equivalence, while our methods can handle the generalized affine equivalence of subspaces of Boolean functions. In the application of circuit synthesis, our methods can significantly reduce the size of the library compared to Boolean matching. To classify Boolean functions up to the generalized affine equivalence, we propose a method to obtain a complete classification based on BDDs. In the experiments, we have successfully applied our methods to some examples that can hardly be solved by using the previous methods, thus validating the effectiveness of our methods.

Co-Efficient Vector Based Differential Distributed Quasi-Orthogonal Space Time Frequency Coding.

Distributed space time frequency coding (DSTFC) schemes address problems of performance degradation encountered by cooperative broadband networks operating in highly mobile environments. Channel state information (CSI) acquisition is, however, impractical in such highly mobile environments. Therefore, to address this problem, designers focus on incorporating differential designs with DSTFC for signal recovery in environments where neither the relay nodes nor destination have CSI. Traditionally, unitary matrix-based differential designs have been used to generate the differentially encoded symbols and codeword matrices. Unitary based designs are suitable for cooperative networks that utilize the amplify-and-forward protocol where the relay nodes are typically required to forego differential decoding. In considering other scenarios where relay nodes are compelled to differentially decode and re-transmit information signals, we propose a novel co-efficient vector differential distributed quasi-orthogonal space time frequency coding (DQSTFC) scheme for decode-and-forward cooperative networks. Our proposed space time frequency coding scheme relaxes the need for constant channel gain in the temporal and frequency dimensions over long symbol periods; thus, performance degradation is reduced in frequency-selective and time-selective fading environments. Simulation results illustrate the performance of our proposed co-efficient vector differential DQSTFC scheme under different channel conditions. Through pair-wise error probability analysis, we derive the full diversity design criteria for our code.

The bifurcation diagram of the configurations of invariant lines of total multiplicity exactly three in quadratic vector fields

We denote by ${\mbox{\boldmath $QSL$}}_3$ the family of quadratic differential systems possessing invariant straight lines, finite and infinite, of total multiplicity exactly three. In a sequence of papers the complete study of quadratic systems with invariant lines of total multiplicity at least four was achieved. In addition three more families of quadratic systems possessing invariant lines of total multiplicity at least three were also studied, among them the Lotka-Volterra family. However there were still systems in ${\mbox{\boldmath ${\mbox{\boldmath $QSL$}}$}}_3$ missing from all these studies. The goals of this article are: to complete the study of the geometric configurations of invariant lines of ${\mbox{\boldmath ${\mbox{\boldmath $QSL$}}$}}_3$ by studying all the remaining cases and to give the full classification of this family modulo their configurations of invariant lines together with their bifurcation diagram. The family ${\mbox{\boldmath ${\mbox{\boldmath $QSL$}}$}}_3$ has a total of 81 distinct configurations of invariant lines. This classification is done in affine invariant terms and we also present the bifurcation diagram of these configurations in the 12-parameter space of coefficients of the systems. This diagram provides an algorithm for deciding for any given system whether it belongs to ${\mbox{\boldmath $QSL$}}_3$ and in case it does, by producing its configuration of invariant straight lines.

The structural tuning of the convolutional neural network forspeaker identification in mel frequency cepstrumcoefficients space

As a result of the literature analysis, the main methods for speaker identification from speech signals were defined. These are statistical methods based on Gaussian mixture model and a universal background model, as well as neural network methods, in particular, using convolutional or Siamese neural networks. The main characteristics of these methods are the recognition performance, a number of parameters, and the training time. High recognition performance is achieved by using convolutional neural networks, but a number of parameters of these networks are much higher than for statistical methods, although lower than for Siamese neural networks. A large number of parameters require a large training set, which is not always available for the researcher. In addition, despite the effectiveness of convolutional neural networks, model size and inference efficiency remain important fordevices with a limited source of computing power, such as peripheral or mobile devices. Therefore, the aspects of tuning of the structure of existing convolutional neural networks are relevant for research. In this work, we have performed a structural tuning of an existing convolutional neural network based on the VGGNet architecture for speaker identification in the space of mel frequency cepstrum coefficients. The aim of the work was to reduce the number of neural network parameters and, as a result, to reduce the network training time, provided that the recognition performance is sufficient (the correct recognition is above 95 %). The neural network proposed as a result of structural tuning has fewer layers than the architecture of the basic neural network. Insteadof the ReLU activation function, the related Leaky ReLU function with a parameter of 0.1 was used. The number of filters and the size of kernels in convolutional layers are changed. The size of kernels for the max pooling layer has been increased. It is proposedto use the averaging of the results of each convolution to input a two-dimensional convolution results to a fully connected layer with the Softmax activation function. The performed experiment showed that the number of parameters of the proposed neural network is 29 % less than the number of parameters of the basic neural network, provided that the speaker recognition performance is almost the same. In addition, the training time of the proposed and basic neural networks was evaluated on five datasets of audio recordings corresponding to different numbers of speakers. The training time of the proposed network was reduced by 10-39 % compared to the basic neural network. The results of the research show the advisability of the structural tuning of the convolutional neural network for devices with a limited source of computing, namely, peripheral or mobile devices.