Continuous Set Research Articles

Refining tomography with generative neural networks trained from geodynamics

SUMMARY Inverse problems occur in many fields of geophysics, wherein surface observations are used to infer the internal structure of the Earth. Given the non-linearity and non-uniqueness inherent in these problems, a standard strategy is to incorporate a priori information regarding the unknown model. Sometimes a solution is obtained by imposing that the inverted model remains close to a reference model and with smooth lateral variations (e.g. a correlation length or a minimal wavelength are imposed). This approach forbids the presence of strong gradients or discontinuities in the recovered model. Admittedly, discontinuities, such as interfaces between layers, or shapes of geological provinces or of geological objects such as slabs can be a priori imposed or even suggested by the data themselves. This is however limited to a small set of possible constraints. For example, it would be very challenging and computationally expensive to perform a tomographic inversion where the subducting slabs would have possible top discontinuities with unknown shapes. The problem seems formidable because one cannot even imagine how to sample the prior space: is each specific slab continuous or broken into different portions having their own interfaces? No continuous set of parameters seems to describe all the possible interfaces that we could consider. To circumvent these questions, we propose to train a Generative Adversarial neural Network (GAN) to generate models from a geologically plausible prior distribution obtained from geodynamic simulations. In a Bayesian framework, a Markov chain Monte Carlo algorithm is used to sample the low-dimensional model space depicting the ensemble of potential geological models. This enables the integration of intricate a priori information, parametrized within a low-dimensional model space conducive to efficient sampling. The application of this approach is demonstrated in the context of a downscaling problem, where the objective is to infer small-scale geological structures from a smooth seismic tomographic image.

Unmanned aerial vehicle variable radius set covering problem for emergency wireless network

The utilization of unmanned aerial vehicles (UAVs) has garnered increasing interest across various disciplines. The idea of smart cities led to the exploration of using UAVs in the public service industry, with a focus on integrating all aspects of the system through information and physical items. In this paper, we introduce and model the operational problem of using UAVs to construct an emergency wireless network in a disaster situation using the set covering approach. Unique to our study is the consideration that UAVs do not require predetermined positioning or altitude specifications. Consequently, the problem described in this paper can be classified as a planar variable radius covering problem, which involves a nonconvex continuous relaxation feasible set. We introduce the application of the Dantzig–Wolfe decomposition alongside a branch-and-price algorithm to tackle this problem. Additionally, the pricing subproblem’s solvable equivalent formulation is ingeniously derived from existing theories on the minimum covering circle. For large-scale instances, we propose a heuristic derived from an extended formulation. Comparative computational experiments demonstrate that our proposed algorithms significantly surpass the efficiency of the benchmark genetic algorithm previously reported in the literature.

Group theoretical classification of SIC-POVMs

The Symmetric Informationally Complete Positive Operator-Valued Measures (SIC-POVMs) are known to exist in all dimensions ⩽ 151 and many larger dimensions as high as 39604 . All known solutions with the exception of the Hoggar solutions are covariant with respect to the Weyl-Heisenberg group and in the case of dimension 3, it has been proven that all SIC-POVMs are Weyl-Heisenberg group covariant. In this work, we explore this by SIC-POVMs in dimensions 4–7 without the assumption of group covariance. We introduce two functions with which SIC-POVM Gram matrices can be generated without the group covariance constraint, and analytically show that the SIC-POVM Gram matrices exist on critical points of the surfaces defined by the two functions on a subspace of Hermitian matrices. In dimensions 4–7, all known SIC-POVM Gram matrices lie in disjoint continuous sets of solution. Thus, we define an equivalent class that relates Gram matrices based on the trivial symmetries of the two functions. In dimensions 4–7, we generated {1.7×106,1.1×105,169,50} Gram matrices, respectively. For each of the Gram matrices, we generate the symmetry group of their respective disjoint sets. In all cases, the symmetry group was isomorphic to a subgroup of the Clifford group containing the Weyl-Heisenberg group matrices and the order-3 unitaries. In dimensions 4–6, All constructed solutions belonged to a single equivalence class of Gram matrices whereas in dimension 7, we find two distinct families of SIC-POVMs. In dimensions 4 and 5, the absence of new classes of SIC-POVM strongly suggests that the functions do not have a non-trivial symmetry. Furthermore, in all the dimensions tested, the only equivalence classes found correspond to the distinct stabilizers of fiducial vectors of each dimension.

Continuous Control Set Model Predictive Torque Control With Minimum Current Magnitude Criterion for Synchronous Motor Drives

Continuous Control Set Model Predictive Torque Control With Minimum Current Magnitude Criterion for Synchronous Motor Drives

Regularized quantum motion in a bounded set: Hilbertian aspects

It is known that the momentum operator canonically conjugated to the position operator for a particle moving in some bounded interval of the line (with Dirichlet boundary conditions) is not essentially self-adjoint: it has a continuous set of self-adjoint extensions. We prove that essential self-adjointness can be recovered by symmetrically weighting the momentum operator with a positive bounded function approximating the indicator function of the considered interval. This weighted momentum operator is consistently obtained from a similarly weighted classical momentum through the so-called Weyl-Heisenberg covariant integral quantization of functions or distributions.

DYNAMICS OF DEFORMATION FORCES IN SINGLE-PARTICLE SPECTRA OF ODD 2s1d-SHELL NUCLEI

With help of our newly-developed evolutionary model-independent approach we have found that with the increase in mass number of all studied odd 2s1d-shell nuclei 23Na, 27Al, 31P, and 35,37Cl the dominant deformation of the shape of these nuclei in low-laying single-particle states changes from quadrupole to hexadecapole and further to hexacontatetrapole. The single states and the continuous sets of states with abnormally weak deformation are found. The points of shape phase transitions with a change in the multipolity of deformation are found in the single-particle spectrum of 37Cl nucleus.

Optimization of Time-Ordered Processes in the Finite and Asymptotic Regimes

Many problems in quantum information theory can be formulated as optimizations over the sequential outcomes of dynamical systems subject to unpredictable external influences. Such problems include many-body entanglement detection through adaptive measurements, computing the maximum average score of a preparation game over a continuous set of target states, and limiting the behavior of a (quantum) finite-state automaton. In this work, we introduce tractable relaxations of this class of optimization problems. To illustrate their performance, we use them to: (a) compute the probability that a finite-state automaton outputs a given sequence of bits; (b) develop a new many-body entanglement-detection protocol; and (c) let the computer an adaptive protocol for magic state detection. As we further show, the maximum score of a sequential problem in the limit of infinitely many time steps is in general incomputable. Nonetheless, we provide general heuristics to bound this quantity and show that they provide useful estimates in relevant scenarios. Published by the American Physical Society 2024

The 2019 Marine Heatwave at Ocean Station Papa: A Multi‐Disciplinary Assessment of Ocean Conditions and Impacts on Marine Ecosystems

AbstractIn the past decade, two large marine heatwaves (MHWs) formed in the northeast Pacific near Ocean Station Papa (OSP), one of the oldest oceanic time series stations. Physical, biogeochemical, and biological parameters observed at OSP from 2013 to 2020 are used to assess ocean response and potential impacts on marine life from the 2019 northeast Pacific MHW. The 2019 MHW reached peak surface and subsurface temperature anomalies in the summertime and had both coastal, impacting fisheries, and offshore consequences that could potentially affect multiple trophic levels in the Gulf of Alaska. In the Gulf of Alaska, the 2019 MHW was preceded by calm and stratified upper ocean conditions, which preconditioned the enhanced surface warming in late spring and early summer. The MHW coincided with lower dissolved inorganic carbon and higher pH of surface waters relative to the 2013–2020 period. A spike in the summertime chlorophyll followed by a decrease in surface macronutrients suggests increased productivity in the well‐lit stratified upper ocean during summer 2019. More blue whale calls were recorded at OSP in 2019 compared to the prior year. This study shows how the utility of long‐term, continuous oceanographic data sets and analysis with an interdisciplinary lens is necessary to understand the potential impact of MHWs on marine ecosystems.

Decoupled Continuous Control Set Model Predictive Control for T-Type Three-Phase Four-Leg Three-Level Inverters Driving Constant Power Loads

Decoupled Continuous Control Set Model Predictive Control for T-Type Three-Phase Four-Leg Three-Level Inverters Driving Constant Power Loads

Privacy-Preserving Synthetic Continual Semantic Segmentation for Robotic Surgery.

Deep Neural Networks (DNNs) based semantic segmentation of the robotic instruments and tissues can enhance the precision of surgical activities in robot-assisted surgery. However, in biological learning, DNNs cannot learn incremental tasks over time and exhibit catastrophic forgetting, which refers to the sharp decline in performance on previously learned tasks after learning a new one. Specifically, when data scarcity is the issue, the model shows a rapid drop in performance on previously learned instruments after learning new data with new instruments. The problem becomes worse when it limits releasing the dataset of the old instruments for the old model due to privacy concerns and the unavailability of the data for the new or updated version of the instruments for the continual learning model. For this purpose, we develop a privacy-preserving synthetic continual semantic segmentation framework by blending and harmonizing (i) open-source old instruments foreground to the synthesized background without revealing real patient data in public and (ii) new instruments foreground to extensively augmented real background. To boost the balanced logit distillation from the old model to the continual learning model, we design overlapping class-aware temperature normalization (CAT) by controlling model learning utility. We also introduce multi-scale shifted-feature distillation (SD) to maintain long and short-range spatial relationships among the semantic objects where conventional short-range spatial features with limited information reduce the power of feature distillation. We demonstrate the effectiveness of our framework on the EndoVis 2017 and 2018 instrument segmentation dataset with a generalized continual learning setting. Code is available at https://github.com/XuMengyaAmy/Synthetic_CAT_SD.

South Atlantic Anomaly Evolution Seen by the Proton Flux

AbstractThe SEM‐2 (Space Environment Monitor‐2) instrument embedded on the NOAA‐15 Low Earth Orbit satellite provides measurements of trapped protons in the Van Allen inner belt from 1998 to nowadays. This continuous set of measurements enables us to study the dynamics of the South Atlantic Anomaly (SAA) over more than two solar cycles, particularly, its temporal evolution. We observe that the area of the SAA is anti‐correlated with the solar activity. Two physical processes explain this anticorrelation. First, the more the Sun is active the more it disables the cosmic rays to reach the Earth's magnetosphere and fill in the inner radiation belt with protons. Then, when the Sun is more active, the upper atmosphere is warmer and therefore absorbs more protons from the radiation belt. Then, we investigate the protons flux centroid of the SAA. The temporal evolution of its position, latitude and, longitude is studied over the same time interval (1998–2022). We notice that the latitude of the centroid is also anti‐correlated with the solar activity whereas the longitude seems absolutely independent. The temporal evolution of the position of the centroid shows a drift of the SAA. Indeed from 1998 to 2022 the SAA drifted of about 7° West. The SEM‐2 instrument measures flux for protons of different energies (16, 36, 70, and, 140 MeV). For each energy, the SAA dynamic has a similar trend but with different values. These differences are investigated and the results are discussed.

An encoding generative modeling approach to dimension reduction and covariate adjustment in causal inference with observational studies

In this article, we develop CausalEGM, a deep learning framework for nonlinear dimension reduction and generative modeling of the dependency among covariate features affecting treatment and response. CausalEGM can be used for estimating causal effects in both binary and continuous treatment settings. By learning a bidirectional transformation between the high-dimensional covariate space and a low-dimensional latent space and then modeling the dependencies of different subsets of the latent variables on the treatment and response, CausalEGM can extract the latent covariate features that affect both treatment and response. By conditioning on these features, one can mitigate the confounding effect of the high dimensional covariate on the estimation of the causal relation between treatment and response. In a series of experiments, the proposed method is shown to achieve superior performance over existing methods in both binary and continuous treatment settings. The improvement is substantial when the sample size is large and the covariate is of high dimension. Finally, we established excess risk bounds and consistency results for our method, and discuss how our approach is related to and improves upon other dimension reduction approaches in causal inference.

Constraining acyclicity of differentiable Bayesian structure learning with topological ordering

Distributional estimates in Bayesian approaches in structure learning have advantages compared to the ones performing point estimates when handling epistemic uncertainty. Differentiable methods for Bayesian structure learning have been developed to enhance the scalability of the inference process and are achieving optimistic outcomes. However, in the differentiable continuous setting, constraining the acyclicity of learned graphs emerges as another challenge. Various works utilize post-hoc penalization scores to impose this constraint which cannot assure acyclicity. The topological ordering of the variables is one type of prior knowledge that contains valuable information about the acyclicity of a directed graph. In this work, we propose a framework to guarantee the acyclicity of inferred graphs by integrating the information from the topological ordering into the inference process. Our integration framework does not interfere with the differentiable inference process while being able to strictly assure the acyclicity of learned graphs and reduce the inference complexity. Our extensive empirical experiments on both synthetic and real data have demonstrated the effectiveness of our approach with preferable results compared to related Bayesian approaches.

Energy norm error estimates and convergence analysis for a stabilized Maxwell’s equations in conductive media

The aim of this article is to investigate the well-posedness, stability of solutions to the time-dependent Maxwell’s equations for electric field in conductive media in continuous and discrete settings, and study convergence analysis of the employed numerical scheme. The situation we consider would represent a physical problem where a subdomain is emerged in a homogeneous medium, characterized by constant dielectric permittivity and conductivity functions. It is well known that in these homogeneous regions the solution to the Maxwell’s equations also solves the wave equation, which makes computations very efficient. In this way our problem can be considered as a coupling problem, for which we derive stability and convergence analysis. A number of numerical examples validate theoretical convergence rates of the proposed stabilized explicit finite element scheme.

Automated discovery of symbolic laws governing skill acquisition from naturally occurring data.

Skill acquisition is a key area of research in cognitive psychology as it encompasses multiple psychological processes. The laws discovered under experimental paradigms are controversial and lack generalizability. This paper aims to unearth the laws of skill learning from large-scale training log data. A two-stage algorithm was developed to tackle the issues of unobservable cognitive states and an algorithmic explosion in searching. A deep learning model is initially employed to determine the learner's cognitive state and assess the feature importance. Symbolic regression algorithms are then used to parse the neural network model into algebraic equations. Experimental results show that the algorithm can accurately restore preset laws within a noise range in continuous feedback settings. When applied to Lumosity training data, the method outperforms traditional and recent models in fitness terms. The study reveals two new forms of skill acquisition laws and reaffirms some previous findings.

Noise sensitivity of the minimum spanning tree of the complete graph

Abstract We study the noise sensitivity of the minimum spanning tree (MST) of the $n$ -vertex complete graph when edges are assigned independent random weights. It is known that when the graph distance is rescaled by $n^{1/3}$ and vertices are given a uniform measure, the MST converges in distribution in the Gromov–Hausdorff–Prokhorov (GHP) topology. We prove that if the weight of each edge is resampled independently with probability $\varepsilon \gg n^{-1/3}$ , then the pair of rescaled minimum spanning trees – before and after the noise – converges in distribution to independent random spaces. Conversely, if $\varepsilon \ll n^{-1/3}$ , the GHP distance between the rescaled trees goes to $0$ in probability. This implies the noise sensitivity and stability for every property of the MST that corresponds to a continuity set of the random limit. The noise threshold of $n^{-1/3}$ coincides with the critical window of the Erdős-Rényi random graphs. In fact, these results follow from an analog theorem we prove regarding the minimum spanning forest of critical random graphs.

NEW ECONOMIC REALITY AS A SUBJECT MATTER OF RESEARCH

The article reveals the trends of modern crisis processes in the economy, which more and more clearly highlight the signs of a new reality. The authors note that in recent years, political and economic contradictions have been growing at an accelerated pace, integration interactions are slowing down, social paradigm is aggravating, the environmental crisis is taking on global proportions, and the stagnation of the economy is increasing. These crisis processes alternate, intersect, are being resolved, however, the range of opportunities for solving accumulated problems and conditions for further development becomes critical. The authors explore many specific manifestations of the new economic reality, including the deepening gap between economic theory and practice, identifying the contradictions that arise here and attracting the possibilities of political economy theory, system economics, and the potential of interdisciplinary knowledge. These manifestations are considered in a continuous set of space and time of the subject matter of research. The authors demonstrate the necessity to comply fundamental developments in the field of economic theory with the need to develop the foundations of state economic policy, risk management assessment, and creative approach to human capital. Based on this, conclusions are drawn on the need for a holistic theoretical and methodological description of the new economic reality, the definition of its subject area, the use of the achievements of scientific and technological progress for the intensive development of the economy and the correct definition of methods and tools for solving the problems of the new reality. The authors believe that the new reality that emerged in the socio-economic system after the financial crisis of 2008–2009 and clearly manifested in strong shocks that hit the world community in 2020–2022 is pushing economic theory to move as quickly as possible to the level of development, meeting practical requirements. In the process of research, the authors used the possibilities of a dialectical method, systemic and evolutionary approaches, as well as such theories as: the mode of production; socio-economic transformations; creative and innovative economy; threshold measures in phenomenon development.

Sliding mode observer-based fault diagnosis and continuous control set fault tolerant control for PMSM with demagnetization fault

A fault detection, estimation and fault tolerant control scheme for demagnetization fault in the permanent magnet synchronous motor systems is proposed in this paper. When demagnetization fault occurs, the system will deviate from the normal state severely. To facilitate the calculation, the demagnetization fault is converted to the dq coordinate system for processing and the resistance change is modeled as the system uncertainty, and the effect of the uncertainty on the system is analyzed. Then a fault detection observer is designed to detect the fault occurrence time, and a sliding mode observer based fault estimation algorithm is designed to estimate the fault and disturbance information. The observer parameters are determined by linear matrix inequality. When the fault information is obtained, a continuous control set fault tolerant control scheme is presented to minimize the impact of fault as far as possible. Finally, experimental results provide evidence of the feasibility of the suggested algorithm.

Night-duty dilemmas: Health and work-life challenges for LIS professionals in Indian libraries

This study investigates the impact of 24/7 library operations on the health and work-life balance of Library and Information Science (LIS) professionals in India. Using a mixed-method approach with 52 respondents, reveals significant physical and mental health issues, sleep disruptions, and dietary challenges. Qualitative insights highlight personal and professional hurdles, gender disparities, and concerns about workload and safety. The findings underscore the need for tailored support and infrastructure improvements in continuous library settings. The study contributes to understanding the multifaceted challenges faced by LIS professionals and provides recommendations to enhance overall well-being in 24/7 operational environments.

Stability analysis for an ad-hoc model predictive control in DC/DC converters with a constant power load

This paper presents a stability analysis for a horizon-one continuous control set model predictive control (MPC) for DC/DC converters connected to a constant power loads (CPLs). Different MPC approaches have been previously presented, each tailored to a specific type of converter but without a formal stability proof, failing to ensure robust performance across various operating conditions. Unlike previous works in the scientific literature, our approach is general and applicable to any second-order DC/DC converter, including the Buck, Boost, Buck-Boost, and non-inverting Buck-Boost converters. A formal stability analysis was conducted using the proposed approach, initially for the open-loop system and subsequently for the closed-loop system. The trace-determinant or triangle criterion was employed for discrete-time systems in R2. Three analyses were conducted to evaluate the performance of the proposed MPC, showing the stability issues of DC/DC converters with CPLs in open loops. This work proposes solutions using the suggested technique. Numerical simulations utilizing the Boost and Buck-Boost converters demonstrate that, in open-loop operation, even minor perturbations in the CPL value can destabilize the behavior of electrical variables. In addition, simulations show that, for the Boost converter, the settling time was about 1.5ms. Meanwhile, in the Buck-Boost case, it was about 5ms. Standardized control indicators, such as the integral absolute error criterion (IAE), the integral of the time-multiplied absolute error criterion (ITAE), and the integral of the time-multiplied square error criterion (ITSE), confirm the effective performance of the proposed one-step MPC. The values range between 1.521×10−2 and 4.591×10−6 for the Boost converter, and between 6.607×10−3 and 3.366×10−6 for the Buck-Boost topology.