Choice Of Parameters Research Articles

Detecting geodesic circles in hyperbolic surfaces with persistent homology

In this paper we provide conditions under which a geodesic circle on a hyperbolic surface admits arbitrarily small geodesically convex neighborhoods. This implies that persistent homology using selective Rips complexes detects the length and the position of such a loop via persistent homology in dimensions one, two, or three. In particular, if a surface has a unique systole, then the systole can always be detected with persistent homology. The existential results of the paper are complemented by the corresponding quantitative treatments which explain the choice of parameters of selective Rips complexes as well as conditions, under which the detection occurs via the standard Rips complexes. In particular, if a surface has a unique systole, then the parameters depend on the first spectral gap in the length spectrum.

Wannabe Bounded Treewidth Graphs Admit a Polynomial Kernel for Directed Feedback Vertex Set

In the Directed Feedback Vertex Set (DFVS) problem, given a digraph D and a positive integer k , the goal is to check if there exists a set of at most k vertices whose deletion from D results in a directed acyclic graph. The existence of a polynomial kernel for DFVS , parameterized by the solution size k , is a central open problem in Kernelization. In this paper, we give a polynomial kernel for DFVS parameterized by k plus the size of a treewidth- η modulator (of the underlying undirected graph), where η is any fixed positive integer. Since the status of the existence of a polynomial kernel for DFVS (parameterized by the solution size) is open for a very long time now, and it is known to not admit a polynomial kernel when the parameter is the size of a treewidth-2 modulator, solution size plus the size of the treewidth- η modulator makes for an interesting choice of parameter to study. In fact, the polynomial kernelization complexity of DFVS parameterized by the size of the undirected feedback vertex set (treewidth-1 modulator) in the underlying undirected graph, has already been studied in literature. Our choice of parameter strictly encompasses previous positive kernelization results on DFVS . Our result is based on a novel application of the tool of important separators embedded in state-of-the-art machinery such as protrusion decompositions.

Learning with Errors from Nonassociative Algebras

We construct a provably-secure structured variant of Learning with Errors (LWE) using nonassociative cyclic division algebras, assuming the hardness of worst-case structured lattice problems, for which we are able to give a full search-to-decision reduction, improving upon the construction of Grover et al. named `Cyclic Learning with Errors' (CLWE). We are thus able to create structured LWE over cyclic algebras without any restriction on the size of secret spaces, which was required for CLWE as a result of its restricted security proof. We reduce the shortest independent vectors problem in ideal lattices, obtained from ideals in orders of such algebras, to the decision variant of LWE defined for nonassociative CDAs. We believe this variant has greater security and greater freedom with parameter choices than CLWE, and greater asymptotic efficiency of multiplication than module LWE. Our reduction requires new results in the ideal theory of such nonassociative algebras, which may be of independent interest. We then adapt an LPR-like PKE scheme to hold for nonassociative spaces, and discuss the efficiency and security of our construction, showing that it is immune to certain subfield attacks. Finally, we give example parameters to construct algebras for cryptographic use.

Tow-parameter quasi-boundary value method for a backward abstract time-degenerate fractional parabolic problem

Abstract In this article, for a time-degenerate fractional parabolic equation, we study an inverse problem for restoration of the initial condition from the information of the final temperature profile. We show that the considered problem is ill-posed in the sense of Hadamard, i.e., small errors in the measurement data may lead to indefinitely large errors in the solutions. This ill-posed problem is regularized using a modified quasi-boundary value method, and some convergence estimates for the regularized solution are obtained using a priori and posteriori parameter choice rules. Finally, several numerical experiments are presented to demonstrate the accuracy and efficiency of the regularization method.

An analytic study of a novel algebraic public key encryption scheme based on polynomials over noncommutative matrix ring

Different public key exchange protocols can be employed to design a cryptosystem. The most famous example is the ElGamal cryptosystem which is based on the Diffie–Hellman key establishment to do encryption and decryption. In the same fashion, we propose a public key cryptosystem using a public key exchange protocol. This variant uses the polynomials over noncommutative matrix ring as underlying work structure. The useful feature of the proposed cryptosystem is that it provides favorable security because of use of the generalized decomposition problem over the noncommutative ring of matrices. The issues regarding the choice of parameters and platform are discussed. Further, a brief note on security analysis of the proposed cryptosystem is also presented.

Variable selection and basis learning for ordinal classification

We propose a method for variable selection and basis learning for high-dimensional classification with ordinal responses. The proposed method extends sparse multiclass linear discriminant analysis, with the aim of identifying not only the variables relevant to discrimination but also the variables that are order-concordant with the responses. For this purpose, we compute for each variable an ordinal weight, where larger weights are given to variables with ordered group-means, and penalize the variables with smaller weights more severely. A two-step construction for ordinal weights is developed, and we show that the ordinal weights correctly separate ordinal variables from non-ordinal variables with high probability. The resulting sparse ordinal basis learning method is shown to consistently select either the discriminant variables or the ordinal and discriminant variables, depending on the choice of a tunable parameter. Such asymptotic guarantees are given under a high-dimensional asymptotic regime where the dimension grows much faster than the sample size. We also discuss a two-step procedure of post-screening ordinal variables among the selected discriminant variables. Simulated and real data analyses confirm that the proposed basis learning provides sparse and interpretable basis, as it mostly consists of ordinal variables. Supplementary materials for this article are available online.

CSI-GEP: A GPU-based unsupervised machine learning approach for recovering gene expression programs in atlas-scale single-cell RNA-seq data.

Exploratory analysis of single-cell RNA sequencing (scRNA-seq) typically relies on hard clustering over two-dimensional projections like uniform manifold approximation and projection (UMAP). However, such methods can severely distort the data and have many arbitrary parameter choices. Methods that can model scRNA-seq data as non-discrete "gene expression programs" (GEPs) can better preserve the data's structure, but currently, they are often not scalable, not consistent across repeated runs, and lack an established method for choosing key parameters. Here, we developed a GPU-based unsupervised learning approach, "consensus and scalable inference of gene expression programs" (CSI-GEP). We show that CSI-GEP can recover ground truth GEPs in real and simulated atlas-scale scRNA-seq datasets, significantly outperforming cutting-edge methods, including GPT-based neural networks. We applied CSI-GEP to a whole mouse brain atlas of 2.2 million cells, disentangling endothelial cell types missed by other methods, and to an integrated scRNA-seq atlas of human tumors and cell lines, discovering mesenchymal-like GEPs unique to cancer cells growing in culture.

The EFG Rosetta Stone: translating between DFT calculations and solid state NMR experiments.

We present a comprehensive study on the best practices for integrating first principles simulations in experimental quadrupolar solid-state nuclear magnetic resonance (SS-NMR), exploiting the synergies between theory and experiment for achieving the optimal interpretation of both. Most high performance materials (HPMs), such as battery electrodes, exhibit complex SS-NMR spectra due to dynamic effects or amorphous phases. NMR crystallography for such challenging materials requires reliable, accurate, efficient computational methods for calculating NMR observables from first principles for the transfer between theoretical material structure models and the interpretation of their experimental SS-NMR spectra. NMR-active nuclei within HPMs are routinely probed by their chemical shielding anisotropy (CSA). However, several nuclear isotopes of interest, e.g.7Li and 27Al, have a nuclear quadrupole and experience additional interactions with the surrounding electric field gradient (EFG). The quadrupolar interaction is a valuable source of information about atomistic structure, and in particular, local symmetry, complementing the CSA. As such, there is a range of different methods and codes to choose from for calculating EFGs, from all-electron to plane wave methods. We benchmark the accuracy of different simulation strategies for computing the EFG tensor of quadrupolar nuclei with plane wave density functional theory (DFT) and study the impact of the material structure as well as the details of the simulation strategy. Especially for small nuclei with few electrons, such as 7Li, we show that the choice of physical approximations and simulation parameters has a large effect on the transferability of the simulation results. To the best of our knowledge, we present the first comprehensive reference scale and literature survey for 7Li quadrupolar couplings. The results allow us to establish practical guidelines for developing the best simulation strategy for correlating DFT to experimental data extracting the maximum benefit and information from both, thereby advancing further research into HPMs.

Exceptional Luttinger liquids from sublattice-dependent interaction

We demonstrate how exceptional points (EPs) naturally occur in the Luttinger liquid (LL) theory describing the low-energy excitations of a microscopic lattice model with sublattice-dependent electron-electron interaction. Upon bosonization, this sublattice dependence directly translates to a nonstandard sine-Gordon-type term responsible for the non-Hermitian matrix structure of the single-particle Green function (GF). As the structure in the lifetime of excitations does not commute with the underlying free Bloch Hamiltonian, non-Hermitian topological properties of the single-particle GF emerge—despite our Hermitian model Hamiltonian. Both finite temperature and a nontrivial Luttinger parameter K≠1 are required for the formation of EPs, and their topological stability in one spatial dimension is guaranteed by the chiral symmetry of our model. In the presence of the aforementioned sine-Gordon term, we resort to leading-order perturbation theory (PT) to compute the single-particle GF. All qualitative findings derived within LL theory are corroborated by comparison to both numerical simulations within the conserving second Born approximation and, for weak interactions and high temperatures, by fermionic plain PT. In certain parameter regimes, quantitative agreement can be reached by a suitable parameter choice in the effective bosonized model. Published by the American Physical Society 2024

Quantifying performance gains of DirectStorage for the visualisation of time-dependent particle datasets

Abstract Visualisation is an essential tool for analysing unstructured particle data as they are produced, for instance, in molecular dynamics or astrodynamics simulations. Such simulations often comprise multiple time steps, and scientists produce datasets with more and more particles in each step. To handle the steadily increasing size of these simulations, many solutions based on organising the data efficiently or reducing their amount using compression have been proposed over the years. Recently, a new storage API called DirectStorage has been introduced on Xbox consoles and Windows. DirectStorage promises a dramatic reduction of loading times in games by making the transfer from NVMe drives to graphics memory more efficient. That begs the question of whether DirectStorage is also beneficial for visualising time-dependent particle data that have to be streamed from disc to the GPU and whether a potential improvement in throughput enables interactive streaming of frames that traditional APIs cannot handle. For that, we implemented a benchmarking application that supports different streaming methods. We report on the results of an extensive series of tests with varying parameters that influence the streaming performance, which show that the performance of DirectStorage is highly dependent on the choice of various parameters. Graphic Abstract We provide an empirical evaluation for the performance gains to be expected when using the DirectStorage API for rendering dynamic particle data set like the one on the right side. For that, we compare the overlapping DirectStorage-based I/O scheme depicted on at the bottom with traditional methods

METHODS OF ANALYSIS OF DYNAMIC PROCESSES IN DISCRETE-CONTINUUM SYSTEMS UNDER PULSE EXCITATIONS

This paper addresses the enhancement of methods for calculating vibration-impact machines, particularly concerning adjustments to prevent potential shock resonances. This design criterion for substantiating the parameters of vibration-impact machines had not been previously considered. However, the likelihood of shock resonance increases significantly with the mass of the process load, operating frequencies of vibration excitation, and overall dimensions of the thin-walled bodies of vibrating machines. Hence, prioritizing the criterion of tuning out resonant modes through the appropriate choice of housing parameters becomes crucial for modern, heavily loaded machines. This novel approach is proposed in this paper for calculating vibration-impact machines and armored vehicles. To analyze the conditions for the onset of resonant modes under periodic shock loading, single-mass, multi-mass, and continuum dynamic systems were sequentially considered. It was shown that, in the absence of friction, shock resonance occurs when any natural frequency of the machine body oscillations matches a multiple of the excitation frequency from the drive. Additionally, numerical integration of the system of differential equations of motion was used to confirm shock resonance conditions. The numerical results were consistent with the analytical ones. It was also determined that tuning away from the resonant frequency by 5% to 10% significantly alters the steady-state mode of the vibration machine, notably reducing oscillation amplitudes. Therefore, to substantiate the parameters of vibrating machines, it is essential to maximize the adjustment of the natural frequency spectrum of their bodies, considered as elastically deformable structures, away from frequencies that are multiples of the drive frequency. To implement this algorithm, we propose adopting a generalized parametric description. Variable parameters include the thickness of housing elements, their cross-sections, reinforcement schemes, and the number of stiffeners. It was found that varying these parameters diversely affects the migration of natural frequencies in the spectrum. Specific parameters with the greatest impact on detuning from shock resonance frequencies were identified. This set of parameters is used to determine the optimal set that satisfies the criterion of maximum detuning from shock resonance. Similar developments and studies have been conducted for the armor hulls of lightly armored vehicles.

A Nonparametric Model for High-Frequency Energy Prices

Abstract This paper proposes an efficient approach for modelling a high frequency continuous time diffusion process for the dynamics of crude oil. While various applications of continuous time models are considered in the literature, the results on choosing the right model are mixed. We employ a very general non-parametric approach to capture the dynamics of the crude oil market proxied by United States Oil (USO) exchange traded fund. This approach is purely data driven and does not require specification of the drift or the diffusion coefficient function. The proposed nonparametric kernel-based estimation procedure relies on the local polynomial kernel regression, where the choice of a bandwidth parameter plays a significant role. We demonstrate that besides offering a convenient way of estimating the continuous-time models for energy prices, our estimation procedure performs well when dealing with predicting USO prices out-of-sample. The analysis is extended by incorporating possible jump diffusion, where the assumption of continuity of the stochastic process is relaxed and a jump component is added to the diffusion process. In addition, we extend our model by adding possible seasonalities in the underlying dynamics, which requires decomposing the price by means of the Maximum Overlap Discrete Wavelet Transform (MODWT) algorithm and applying nonparametric kernel-based estimation procedure to modelling of the deseasonalized prices.

Application of Machine Learning Models to Multi-Parameter Maximum Magnitude Prediction

Magnitude prediction is a key focus in earthquake science research, and using machine learning models to analyze seismic data, identify pre-seismic anomalies, and improve prediction accuracy is of great scientific and practical significance. Taking the southern part of China’s North–South Seismic Belt (20° N~30° N, 96° E~106° E), where strong earthquakes frequently occur, as an example, we used the sliding time window method to calculate 11 seismicity indicators from the earthquake catalog data as the characteristic parameters of the training model, and compared six machine learning models, including the random forest (RF) and long short-term memory (LSTM) models, to select the best-performing LSTM model for predicting the maximum magnitude of an earthquake in the study area in the coming year. The experimental results show that the LSTM model performs exceptionally well in predicting earthquakes of magnitude 5 < ML ≤ 6 within the time window of the test set, with a prediction success rate of 85%. Additionally, the study explores how different time windows, spatial locations, and parameter choices affect model performance. It found that longer time windows and key seismicity parameters, such as the b-value and the square root of total seismic energy, are crucial for improving prediction accuracy. Finally, we propose a magnitude interval-based assessment method to better predict the actual impacts that different magnitudes may cause. This method demonstrates the LSTM model’s potential in predicting moderate to strong earthquakes and offers new approaches for earthquake early warning and disaster mitigation.

Modified heuristic criterion for parameter choice for one stabilization scheme of the finite element method

We consider a modi cation to a heuristic criterion for the optimal choice of the stabilization parameter in a certain nite element scheme for the singularly perturbed di usion-advectionreaction problem. This criterion is based on a minimization problem of the function of the stabilization parameter and the corresponding algorithm for nding the minimum. The function generally exhibits two extremum points: a local minimum and a local maximum. This forces the algorithm to repeatedly use an additional controlled heuristic "try-and-check" procedure, which can be ine cient in some cases. In this article, we propose simple heuristic modi cations to the criterion to eliminate the second maximum point, making ordinary bisection method applicable to the minimum- nding procedure.

Adaptive residual subsampling algorithms for kernel interpolation based on cross validation techniques

In this article we present an adaptive residual subsampling scheme designed for kernel based interpolation. For an optimal choice of the kernel shape parameter we consider some cross validation (CV) criteria, using efficient algorithms of $k$-fold CV and leave-one-out CV (LOOCV) as a special case. In this framework, the selection of the shape parameter within the residual subsampling method is totally automatic, provides highly reliable and accurate results for any kind of kernel, and guarantees existence and uniqueness of the kernel based interpolant. Numerical results show the performance of this new adaptive scheme, also giving a comparison with other computational techniques.

General regularization scheme in data-driven learning of Koopman operators

As is known, the Koopman operator is widely used in the analysis of complex dynamic systems. In this paper, we consider the problem of numerical representation of the Koopman operators on Reproducing Kernel Hilbert spaces. The main idea of the proposed approach is the use of a concept of general regularization scheme to ensure the stability of the constructed approximations. This concept allows us to simultaneously consider several well-known regularization methods, which have been previously employed for approximating the Koopman operators. We also discuss the issue of the regularization parameter choice, that has been understudied so far.

From features to benefits: a data-driven approach for the economic design of adaptive quality control

The current economic design of control charts assumes specific quality distributions, limits parameter choices, and over-relies on historical samples, hindering companies from determining the most economical parameters accurately. Leveraging industrial big data, we propose a data-driven, mixed-integer linear programming model for the economic design of adaptive control charts. Control limits are dynamically designed as a function of features to minimise quality costs. Considering the trade-off between false alarms and penalty costs, we develop three models: a basic model incorporating big data, a model with cost-penalised features, and a model that uses regularisation to manage overfitting. We simulate the model using new performance measures. Our findings demonstrate the economic value of adaptive control limits strategies incorporating feature data compared to benchmarks. We expanded the model to an endogenous sample size and sampling interval framework, further demonstrating the superiority of our approach. We undertook a case study using real-world data from a casting company and revealed that employing our approach culminates in a 24.6% reduction in costs relative to the company's existing quality control protocols. Our approach enables manufacturers to make strategic decisions about quality control by operationalising big data, thereby proving advantageous in reducing quality costs.

Influence of single observations on the choice of the penalty parameter in ridge regression

Penalized regression methods such as ridge regression heavily rely on the choice of the penalty parameter, which is often computed via cross-validation. Discrepancies in the value of the penalty parameter may lead to substantial differences in regression coefficient estimates and predictions. This paper investigates the effect of single observations on the optimal choice of the penalty parameter, showing how the presence of influential points can change it dramatically. The points are distinguished as ‘expanders’ or ‘shrinkers’ based on their effect on the model complexity. The approach supplies a visual exploratory tool to identify influential points, naturally implementable for high-dimensional data where traditional approaches usually fail. Applications to simulated and real data examples, both low- and high-dimensional, are presented. The visual tool is implemented in the R package influridge.

Metabolic Fluxes Using Deep Learning Based on Enzyme Variations: Application to Glycolysis in Entamoeba histolytica.

Metabolic pathway modeling, essential for understanding organism metabolism, is pivotal in predicting genetic mutation effects, drug design, and biofuel development. Enhancing these modeling techniques is crucial for achieving greater prediction accuracy and reliability. However, the limited experimental data or the complexity of the pathway makes it challenging for researchers to predict phenotypes. Deep learning (DL) is known to perform better than other Machine Learning (ML) approaches if the right conditions are met (i.e., a large database and good choice of parameters). Here, we use a knowledge-based model to massively generate synthetic data and extend a small initial dataset of experimental values. The main objective is to assess if DL can perform at least as well as other ML approaches in flux prediction, using 68,950 instances. Two processing methods are used to generate DL models: cross-validation and repeated holdout evaluation. DL models predict the metabolic fluxes with high precision and slightly outperform the best-known ML approach (the Cubist model) with a lower RMSE (≤0.01) in both cases. They also outperform the PLS model (RMSE ≥ 30). This study is the first to use DL to predict the overall flux of a metabolic pathway only from variations of enzyme concentrations.

Investigating the Iron Plating and Stripping of Anolytes for All-Iron Redox-Flow Batteries

All-iron redox-flow batteries (AIRFB) are capable of addressing the needs for cost-effective long-term storage of renewable energies. Currently, a major limitation of AIRFB performance is the half-cell reaction of the anolyte utilising the redox couple Fe/Fe2+. In this work, the performance of sulphate and chloride-based iron electrolytes was investigated by combining cyclic voltammetry (CV) and electrochemical quartz crystal microbalance (EQCM). The investigations demonstrate that complexing agents exert a detrimental influence on the kinetics of plating/stripping reactions, resulting in diffusivity reduction, while favouring hydrogen evolution reaction (HER). The coulombic (plating) efficiency was found to be 87.1% at −1.2 V vs. Ag/AgCl (sat’d) at pH 3.5, while the coulombic efficiency in oxidation sweep (stripping) was observed to be 100% in an electrolyte containing 0.8 M FeCl2 and 3 M NH4Cl. In the context of iron deposition, the most crucial factors are the suppression of HER, and the influence of diffusion limitations, as well as the role of additives in this process to achieve a high reversibility. It is evident that the investigated complexing agents of glycine, malic acid and malonic acid are inadequate for battery-compatible, efficient properties, given that the overvoltages for the charge transfer reaction are too high and parasitic HER reduces coulombic efficiencies. Ultimately, the choice of deposition parameters from EQCM and electrolyte composition reduced to 0.8 M FeCl2, and 3 M NH4Cl can optimise the battery efficiencies as such.