Invertible Maps Research Articles

Assessing the Accuracy and Efficiency of Free Energy Differences Obtained from Reweighted Flow-Based Probabilistic Generative Models.

Computing free energy differences between metastable states characterized by nonoverlapping Boltzmann distributions is often a computationally intensive endeavor, usually requiring chains of intermediate states to connect them. Targeted free energy perturbation (TFEP) can significantly lower the computational cost of FEP calculations by choosing a set of invertible maps used to directly connect the distributions of interest, achieving the necessary statistically significant overlaps without sampling any intermediate states. Probabilistic generative models (PGMs) based on normalizing flow architectures can make it much easier via machine learning to train invertible maps needed for TFEP. However, the accuracy and applicability of approaches based on empirically learned maps depend crucially on the choice of reweighting method adopted to estimate the free energy differences. In this work, we assess the accuracy, rate of convergence, and data efficiency of different free energy estimators, including exponential averaging, Bennett acceptance ratio (BAR), and multistate Bennett acceptance ratio (MBAR), in reweighting PGMs trained by maximum likelihood on limited amounts of molecular dynamics data sampled only from end-states of interest. We carry out the comparisons on a set of simple but representative case studies, including conformational ensembles of alanine dipeptide and ibuprofen. Our results indicate that BAR and MBAR are both data efficient and robust, even in the presence of significant model overfitting in the generation of invertible maps. This analysis can serve as a stepping stone for the deployment of efficient and quantitatively accurate ML-based free energy calculation methods in complex systems.

A Natural Sonification Mapping for Handwriting

The sonification of handwriting has been shown effective in various learning tasks. In this paper, the authors investigate the sound design used for handwriting interaction based on a simple and cost-efficient prototype. The authentic interaction sound is compared with physically informed sonification designs that employ either natural or inverted mapping. In an experiment, participants copied text and drawings. The authors found simple measures of the structure-borne audio signal that showed how participants were affected in their movements, but only when drawing. In contrast, participants rated the sound features differently only for writing. The authentic interaction sound generally scored best, followed by a natural sonification mapping.

A false trigger pulse elimination circuit for low-frequency energy harvesting active rectifiers

Abstract In this article, a false trigger pulse elimination circuit is proposed to be used for a low-frequency energy harvesting active rectifier. It is divided into two-stage circuits, each stage almost including a switching signal generation circuit, a switching inverter, and an inverter to eliminate false triggering pulses on the rising edge and falling edge respectively. There is an edge detection circuit in each switching signal generation circuit, generating a switching signal that controls the switching inverter’s on-off behavior. This allows the inverter to achieve inverter output voltage clamping by turning off its inverter function and turning it into a switch that is only turned on at the high or low level. At the same time, a thyristor delay element is used to determine and adjust the effective level time of the switching signal, which can reach over 150 μs, completely covering the rising or falling edge false trigger pulse so that no GΩ-level resistors are needed in the low-frequency field. The results show that the low-frequency false trigger pulse elimination circuit proposed in this article can better eliminate false trigger pulses on both rising and falling edges. It can also achieve on-chip integration, reduce the power consumption of the self-adaptive delay compensation loop, and enhance the stability of the circuit.

GaN monolithic digital units on P-GaN platform

Gallium nitride (GaN)-based digital integrated circuits (ICs) are constructed on the commercially available GaN-on-Si wafer designed for pGaN gate HEMT. The functions of inverter, NAND, AND, NOR, and OR logic circuits are successfully realized based on direct-coupled field-effect transistor logic (DCFL) structure. Under a drive voltage of 5V and a load ratio of 20, the low output (VOL) can reach as low as 0.1V. Additionally, a functional-oriented driver, a SR flipflop, and a NOR gate D flipflop are constructed. All the transient tests at a frequency of 100 kHz and temperatures up to 200 °C exhibit satisfying performance characteristics.

Power Hardware-in-the-Loop Smart Inverter Testing with Distributed Energy Resource Management Systems

The increasing integration of grid-connected photovoltaic (PV) inverters and inverter-based resource (IBR) systems into the power grid emphasizes the critical need for standardized procedures to ensure their reliability and effective grid support functions. This research is driven by the gap in standardized testing methodologies for smart inverters, which are pivotal for the stability and quality of power in distributed energy systems. We used a Power Hardware-in-the-Loop (PHIL) laboratory setup to conduct a comprehensive analysis of smart inverters within a simulated real-world grid environment. Our approach integrates a Distributed Energy Resource Management System (DERMS) with PHIL testing to evaluate the smart inverter’s performance across various operational modes. The detailed test protocols mimic real-world grid conditions, enabling the examination of the inverter’s dynamic response to grid disturbances, control strategies, and communication protocols. The primary aim of this study is to rigorously test and validate the primary functions of smart inverters, focusing on their impact on overall grid stability and power quality management. This includes advanced features like Volt–VAR, Volt–Watt, dynamic power factor control, and the seamless integration of smart inverters into DERMSs and Advanced Distribution Management Systems (ADMSs). Furthermore, we aim to bridge the current gap in standardized testing procedures, contributing to the establishment of robust standards and operating protocols for smart inverter integration into the grid.

A Koopman–Takens Theorem: Linear Least Squares Prediction of Nonlinear Time Series

The least squares linear filter, also called the Wiener filter, is a popular tool to predict the next element(s) of time series by linear combination of time-delayed observations. We consider observation sequences of deterministic dynamics, and ask: Which pairs of observation function and dynamics are predictable? If one allows for nonlinear mappings of time-delayed observations, then Takens’ well-known theorem implies that a set of pairs, large in a specific topological sense, exists for which an exact prediction is possible. We show that a similar statement applies for the linear least squares filter in the infinite-delay limit, by considering the forecast problem for invertible measure-preserving maps and the Koopman operator on square-integrable functions.

Efficiency comparison of MCMC and Transport Map Bayesian posterior estimation for structural health monitoring

In this paper, an alternative to solving Bayesian inverse problems for structural health monitoring based on a variational formulation with so-called transport maps is examined. The Bayesian inverse formulation is a widely used tool in structural health monitoring applications. While Markov Chain Monte Carlo (MCMC) methods are often implemented in these settings, they come with the problem of using many model evaluations, which in turn can become quite costly. We focus here on recent developments in the field of transport theory, where the problem is formulated as finding a deterministic, invertible mapping between some easy to evaluate reference density and the posterior. The resulting variational formulation can be solved with integration and optimization methods. We develop a general formulation for the application of transport maps to vibration-based structural health monitoring. Further, we study influences of different integration approaches on the efficiency and accuracy of the transport map approach and compare it to the Transitional MCMC algorithm, a widely used method for structural identification. Both methods are applied to a lower-dimensional dynamic model with uni- and multi-modal properties, as well as to a higher-dimensional neural network surrogate system of an airplane structure. We find that transport maps have a significant increase in accuracy and efficiency, when used in the right circumstances.

Single Source Switched Capacitor Based Multilevel Inverter With Reduced Number of Components

Multilevel inverters find extensive use across various applications owing to their capability to generate voltage waveforms of superior quality. thereby minimizing harmonic distortion. Traditional multilevel inverters require a substantial number of power semiconductor devices and passive components, resulting in heightened costs, intricacy, and physical dimensions. These multilevel inverters play a pivotal role in the electric vehicle sector, serving as a critical component in EV power trains for converting Convert DC power from batteries into AC power to operate electric motors.. The research methodology involves the following steps: Design and configuration of a multilevel inverter utilizing switched capacitor technology from a single source.. Design proposed topologies for multilevel inverter design. Design a circuit according topologies in MATLAB. Comparative analysis with existing multilevel inverter designs. Evaluation of the inverter's performance in terms of harmonic distortion, output voltage quality, and efficiency. Rather than employing a multilevel inverter with fewer switches that operates from a single source the highest possible levels are preferred. This paper introduces an innovative 9-level multilevel inverter based on a single source and switched capacitors, which significantly reduces the number of switches required, utilizing only three capacitors and a single DC source. This design approach serves to streamline the inverter's intricacy, decrease costs, and minimize its physical footprint. Furthermore, it elevates the voltage levels by up to 96%, enhancing the overall performance and efficiency of the inverter. Additionally, this technology can be applied in electric vehicles, integrated with renewable energy sources, and utilized in industrial settings. The novelty of this research lies in the utilization of a single-source switched capacitor configuration to achieve multilevel inverter functionality. This approach reduces the number of components required, leading to potential cost savings and improved system reliability. The novel features of this study include: Integration of switched capacitors in a single-source multilevel inverter design. Achieving multilevel inverter functionality with fewer components. Improved performance and efficiency compared to traditional multilevel inverter designs.

A Decentralized Voltage Regulation Scheme Using Improved Volt‐Var Function of PV Smart Inverter

With the growing distributed PV installation rate in distribution systems, voltage regulation difficulties such as local voltage violations and fluctuations have become common. To solve the voltage regulation problems, the local voltage regulation method using volt‐var (VV) function is effective for its high regulation speed, high accuracy, and flexibility. However, there are still hurdles on real application, such as parameter setting difficulties, insufficient voltage fluctuation mitigation effect, and unfairness of reactive power generation between PV customers. To further improve the VV function, this paper proposes a PID closed‐loop based VV function and mode‐switching function of PV smart inverter (SI). To validate the proposed methods, numerical simulations were conducted using a 6‐feeder distribution system model based on the JST‐CREST 126 distribution feeder model. According to the simulation result, the proposed method can better mitigate the local voltage violation compared to basic VV function based on the VV curve, also improve the fairness between PV customers, while the total reactive power generation and tap operations increases for the aim of more adequate voltage regulation. © 2024 The Authors. IEEJ Transactions on Electrical and Electronic Engineering published by Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

Coupling Exponential to Linear Amplification for Endpoint Quantitative Analysis.

Exponential DNA amplification techniques are fundamental in ultrasensitive molecular diagnostics. These systems offer a wide dynamic range, but the quantification requires real-time monitoring of the amplification reaction. Linear amplification schemes, despite their limited sensitivity, can achieve quantitative measurement from a single end-point readout, suitable for low-cost, point-of-care, or massive testing. Reconciling the sensitivity of exponential amplification with the simplicity of end-point readout would thus break through a major design dilemma and open a route to a new generation of massively scalable quantitative bioassays. Here a hybrid nucleic acid-based circuit design is introduced to compute a logarithmic function, therefore providing a wide dynamic range based on a single end-point measurement. CELIA (Coupling Exponential amplification reaction to LInear Amplification) exploits a versatile biochemical circuit architecture to couple a tunable linear amplification stage - optionally embedding an inverter function - downstream of an exponential module in a one-pot format. Applied to the detection of microRNAs, CELIA provides a limit of detection in the femtomolar range and a dynamic range of six decades. This isothermal approach bypasses thermocyclers without compromising sensitivity, thereby opening the way to applications in various diagnostic assays, and providing a simplified, cost-efficient, and high throughput solution for quantitative nucleic acid analysis.

Free and forced vibration analysis over meshes with tangled (non-convex) elements

Tangled (non-convex) elements, i.e. elements with negative Jacobian determinant, can lead to erroneous results in the standard finite element method (FEM). Constructing tangle-free, well-structured meshes for complex geometries is often impossible. Hence there is a need to explore analysis methods that can directly handle such tangled meshes.In this paper, we propose the isoparametric tangled finite element method (i-TFEM) for free and forced vibration problems over tangled meshes. By employing piece-wise invertible mapping, a variational formulation is derived, leading to a simple modification of the standard FEM stiffness and mass matrices with the incorporation of additional compatibility constraints. Moreover, i-TFEM reduces to standard FEM for non-tangled (regular) meshes. The proposed method is implemented for three types of elements: 4-node quadrilateral, 9-node quadrilateral, and 8-node hexahedral elements. The numerical results demonstrate that i-TFEM is able to consistently handle general tangled (non-convex) elements, enabling convenient meshing for complex geometries.

Application of Module Level Power Electronics Technology in Distributed Photovoltaic Power Generation System

Distributed photovoltaic power generation system usually adopts series wiring scheme, which has problems such as high voltage DC electrical safety risk, power mismatch of modules and maintenance management difficulty. Three schemes of module level power electronics technology are proposed, including string inverter with rapid shutdown device, string inverter with module optimizer and micro inverter. The electrical shut-off, power generation data monitoring, power optimization and inverter function characteristics of each scheme are described and compared, and the suggested application scenarios are given. In addition, typical electrical topology schemes of module level power electronic devices including rapid shutdown device, module optimizer and micro inverter are introduced.

Variable augmentation network for invertible MR coil compression

To improve the efficiency of multi-coil data compression and recover the compressed image reversibly, increasing the possibility of applying the proposed method to medical scenarios. A deep learning algorithm is employed for MR coil compression in the presented work. The approach introduces a variable augmentation network for invertible coil compression (VAN-ICC). This network utilizes the inherent reversibility of normalizing flow-based models. The aim is to enhance the readability of the sentence and clearly convey the key components of the algorithm. By applying the variable augmentation technology to image/k-space variables from multi-coils, VAN-ICC trains the invertible network by finding an invertible and bijective function, which can map the original data to the compressed counterpart and vice versa. Experiments conducted on both fully-sampled and under-sampled data verified the effectiveness and flexibility of VAN-ICC. Quantitative and qualitative comparisons with traditional non-deep learning-based approaches demonstrated that VAN-ICC carries much higher compression effects. The proposed method trains the invertible network by finding an invertible and bijective function, which improves the defects of traditional coil compression method by utilizing inherent reversibility of normalizing flow-based models. In addition, the application of variable augmentation technology ensures the implementation of reversible networks. In short, VAN-ICC offered a competitive advantage over other traditional coil compression algorithms.

Reliable Event Generation With Invertible Conditional Normalizing Flow.

Event streams provide a novel paradigm to describe visual scenes by capturing intensity variations above specific thresholds along with various types of noise. Existing event generation methods usually rely on one-way mappings using hand-crafted parameters and noise rates, which may not adequately suit diverse scenarios and event cameras. To address this limitation, we propose a novel approach to learn a bidirectional mapping between the feature space of event streams and their inherent parameters, enabling the generation of reliable event streams with enhanced generalization capabilities. We first randomly generate a vast number of parameters and synthesize massive event streams using an event simulator. Subsequently, an event-based normalizing flow network is proposed to learn the invertible mapping between the representation of a synthetic event stream and its parameters. The invertible mapping is implemented by incorporating an intensity-guided conditional affine simulation mechanism, facilitating better alignment between event features and parameter spaces. Additionally, we impose constraints on event sparsity, edge distribution, and noise distribution through novel event losses, further emphasizing event priors in the bidirectional mapping. Our framework surpasses state-of-the-art methods in video reconstruction, optical flow estimation, and parameter estimation tasks on synthetic and real-world datasets, exhibiting excellent generalization across diverse scenes and cameras.

Determining the Inverse of a Matrix over Min-Plus Algebra

Linear algebra over the semiring R_ε with ⊗ (plus) and ⨁ (maximum) operations which is known as max-plus algebra. One of the isomorphic with this algebra is a min-plus algebra. Min-plus algebra that is the set R_(ε^' )=R∪{ε'}, with ⊗^' (plus) and ⨁' (minimum) operations. Given a matrix whose components are elements of R_(ε^' ) is called min-plus algebra matrices. Any matrix can be connected by an inverse. In conventional algebra, a square matrix is said an invertible matrix if the det⁡〖(A)〗≠0. In contrast to max-plus algebra, a matrix is said to have inverse condition if it meets certain conditions. Some concepts from the max-plus algebra can be transformed to the min-plus, because of their structural similarity. This means that the inverse matrix concept in max-plus can be constructed into a min-plus version. Thus, this study will explain the inverse of a matrix over the min-plus algebra, property of multiplying two invertible matrices, and connection between invertible matrix and linear mapping used the literature study method, with literature sources such as books, journals, articles, and theses. The data analysis technique used in this research is qualitative data analysis technique. Then, this article has a principal result that is matrix A∈R_(ε^')^(n×n) has a right inverse if and only if there are permutations of σ and the value of λ_i<ε', i∈{1,2,3,…,n} such that A=P_σ ⊗^' D(λ_i ) which is the inverse of matrices. Furthermore, if B is the correct inverse that satisfies A⊗^' B=E then B⊗^' A=E and B is uniquely determined by A.

Applications of vector bundle to finite elasto-plasticity

A new approach to finite elasto-plasticity of crystalline materials, with a differential geometry point of view toward the material description, is proposed. In order to define the plastic and elastic distortions, traditionally it is accepted the existence of an intermediate configuration, which is endowed with a differential manifold structure. A more restrictive but physically and mathematically well-motivated structure is assigned to the intermediate configuration, namely, a vector bundle structure. Two approaches to multiplicative decomposition of the deformation gradient can be rebuilt if on the same total space (intermediate configuration) the vector bundle structures are considered, but either the reference configuration, B (i.e., plastic assumption) or the deformed configuration, B t (i.e., elastic assumption) stands for the base space. As the base spaces are homeomorphic, a pullback vector bundle over one base space is provided by the other one through the motion diffeomorphism. Thus, the total space is endowed with different differential manifold structures. The plastic distortion and the inverse elastic distortion, respectively, are defined for any material points as linear, invertible, and non-integrable maps from the tangent vector space at their material points, with the value on the attached vector fiber. The multiplicative decompositions into their non-integrable components are derived, based on the associate inverse elastic distortion and plastic distortion, respectively. When the plastic and elastic assumptions are simultaneously accepted, then a three-term multiplicative decomposition of the deformation gradient is achieved. The transition functions, which characterize the compatibility of the overlapping charts which belong to these different structures, namely of the vector bundle and of the pullback vector bundle over the same configuration, say B define the non-uniqueness of the two-term multiplicative decomposition. The material symmetry transformation is defined for elastic-type materials. The compatibility of the models and examples of the bundle vector structures are also discussed.

Do Human Capital Value Added Impact the Risk-Based Performance of Banks? (A Review Based on the CAMEL Model)

Objective: The significance of human capital is well recognized in contemporary times, and the management of firms with a knowledge-centric approach has underscored the importance of intellectual and human capital as key competitive advantages. Among these, the banking industry holds considerable importance, necessitating the industry's focus on leveraging human capital. Methodology: This study examines the relationship between the human capital value-added coefficient, a component of intellectual capital, and bank performance. The CAMEL model is employed to determine the functional components of bank performance. Financial statement data from 12 banks for the years 2012 to 2022 were utilized. Findings: The study's findings indicate a significant relationship between the intellectual capital value-added coefficient and variables such as capital adequacy, asset quality, management, and income, with a nonlinear inverted U-shaped function. In contrast, the relationship between the human capital value-added coefficient and liquidity is nonlinear and U-shaped. Conclusion: The study reveals that human capital value-added significantly impacts bank performance indicators, exhibiting nonlinear, inverted U-shaped relationships with capital adequacy, management, and income, and a U-shaped relationship with liquidity. Strategic investment in human capital is essential for optimizing these performance metrics in the banking sector.

Sparcl: A language for partially invertible computation

Abstract Invertibility is a fundamental concept in computer science, with various manifestations in software development (serializer/deserializer, parser/printer, redo/undo, compressor/decompressor, and so on). Full invertibility necessarily requires bijectivity, but the direct approach of composing bijective functions to develop invertible programs is too restrictive to be useful. In this paper, we take a different approach by focusing on partially invertible functions—functions that become invertible if some of their arguments are fixed. The simplest example of such is addition, which becomes invertible when fixing one of the operands. More involved examples include entropy-based compression methods (e.g., Huffman coding), which carry the occurrence frequency of input symbols (in certain formats such as Huffman tree), and fixing this frequency information makes the compression methods invertible. We develop a language Sparcl for programming such functions in a natural way, where partial invertibility is the norm and bijectivity is a special case, hence gaining significant expressiveness without compromising correctness. The challenge in designing such a language is to allow ordinary programming (the “partially” part) to interact with the invertible part freely, and yet guarantee invertibility by construction. The language Sparcl is linear-typed and has a type constructor to distinguish data that are subject to invertible computation and those that are not. We present the syntax, type system, and semantics of the language and prove that Sparcl correctly guarantees invertibility for its programs. We demonstrate the expressiveness of Sparcl with examples including tree rebuilding from preorder and inorder traversals, Huffman coding, arithmetic coding, and LZ77 compression.

О подстановках, разрушающих структуру подпространств определённых размерностей

We consider the sets Pnkconsisting of invertible functions F : F2n → F2n such that any U ⊆ F2n and its image F(U) are not simultaneously k-dimensional affine subspaces of F2n, where 3 ⩽ k ⩽ n - 1. We present lower bounds for the cardinalities of all such Pkn ∩...∩ Pn-1n that improve the result of W. E. Clark, X. Hou, and A. Mihailovs, 2007, providing that these sets are not empty. We prove that almost all permutations of F2n belong to P4n∩...∩ Pn-1n. Asymptotic lower and upper bounds of |P3n| up to o(2n!) are obtained. They are correct for |P3n ∩...∩ Pn-1n| as well. The number of functions from P4n∩...∩ Pn-1n that map exactly one 3-dimensional affine subspace of F2n to an affine subspace is estimated. The connection between the restrictions of component functions of F and the case when both U and F(U) are affine subspaces of is obtained. The characterization of differentially 4-uniform permutations in the mentioned terms is provided.

Distributed adaptive sliding-mode control for 2-D plane vehicle platoon with prescribed performance and angle constraint

This paper focuses on the distributed adaptive sliding-mode control problem for two-dimensional (2-D) plane vehicle platoon with prescribed performance, angle constraints, and actuator faults. The quadratic spacing policy (QSP) is first adopted for the 2-D plane vehicle platoon to adjust the inter-vehicle spacing. The spacing error can converge within a finite time to the small region predetermined by a new finite-time performance function (FTPF). Meanwhile, a new transformed error function is introduced to convert the FTPF-constrained spacing errors into equivalent unconstrained ones. Besides, the property of the invertible nonlinear mapping function is used for the original system with the angle constraint to get a new unconstrained system. Moreover, a new controller based on hyperbolic tangent function is designed to handle actuator faults occurring multiple times over a period. Furthermore, the stability and string stability of the 2-D plane vehicle platoon are achieved through sliding-mode control. Finally, the simulation results validate the effectiveness of the proposed techniques.