Invariance Properties Research Articles

Single-pixel imaging robust to arbitrary translational motion

Single-pixel imaging (SPI) stands out in computational imaging for its simplicity and adaptability, yet its performance has been hampered by artifacts from translational motion. Existing solutions heavily rely on accurate motion modeling, requiring additional hardware and computational costs. In this Letter, we propose translational motion-agnostic SPI (TMA-SPI), a novel, to the best of our knowledge, single-object SPI framework agnostic to arbitrary translational motion. Our dual-domain optimization method leverages the translation invariance property of the amplitude spectrum in the Fourier domain, combined with the spatially finite and nonnegative constraints in the image domain, to produce a clear image of the moving object without any motion estimation or compensation. Through both simulation and the deployment of a real imaging prototype, we demonstrate its superior performance over the conventional SPI method. Our framework is expected to extend the applicability of SPI, offering significant improvements for dynamic sensing applications.

Barycentric and pairwise Rényi quantum leakage with application to privacy-utility trade-off

Barycentric and pairwise quantum Rényi leakages are proposed as two measures of information leakage for privacy and security analysis in quantum computing and communication systems. These quantities both require minimal assumptions on the eavesdropper, i.e. they do not make any assumptions on the eavesdropper’s attack strategy or the statistical prior on the secret or private classical data encoded in the quantum system. They also satisfy important properties of positivity, independence, post-processing inequality and unitary invariance. The barycentric quantum Rényi leakage can be computed by solving a semi-definite program; the pairwise quantum Rényi leakage possesses an explicit formula. The barycentric and pairwise quantum Rényi leakages form upper bounds on the maximal quantum leakage, the sandwiched quantum α -mutual information, the accessible information and the Holevo’s information. Furthermore, differentially private quantum channels are shown to bound these measures of information leakage. Global and local depolarizing channels, that are common models of noise in quantum computing and communication, restrict private or secure information leakage. Finally, a privacy-utility trade-off formula in quantum machine learning using variational circuits is developed. The privacy guarantees can only be strengthened, i.e. information leakage can only be reduced, if the performance degradation grows larger and vice versa .

Beyond the Blackwell order in dichotomies

I establish a translation invariance property of the Blackwell order for dichotomies and show that the norm of the distance from the identity matrix may be interpreted as a measure of informativeness. The better experiment is closer to the fully revealing experiment; this measure extends the Blackwell order, is complete, and prior-independent.

Phosphorylation Enables Nano‐Graphene for Tunable Artificial Synapses

AbstractFlexible and robust memristors with controllable resistance‐switching characteristics are important to neuromorphic computing. However, the nanomaterials‐based, solution‐processed resistance switching layer usually has poor reliability and tunability due to uneven morphology and invariable surface properties. Herein, phosphorylated graphene nanoflakes (phos‐GPs) are synthesized for high‐performance solution‐processed flexible memristors. In situ conductive atomic force microscopy reveals that the tightly stacked uniform nanoflakes and modified phosphorate groups jointly reduce the formation barrier of the conductive filaments. Furthermore, phosphorylation gives rise to surface silver ion coordination leading to enhanced radial growth of the conductive filaments. The memristor shows volatile characteristics in the Ag/phos‐GPs/ITO architecture and exhibits non‐volatile properties in the Ag/Ag+‐(phos‐GPs)/ITO structure. Both types of memristors display consistent I‐‐V curves during long‐term cycling and under repetitive mechanical bending, in addition to excellent synaptic plasticity. Moreover, ultrasmall nonlinearity is observed from non‐volatile long‐term synaptic potentiation and depression. By utilizing the tunable artificial synapses, the processes of memory‐forgetting and re‐recognition are simulated, and the image recognition tasks are accomplished by the artificial neural networks.

Assessing the Foreign Direct Investment Performance of Middle-Income Countries Using Data Envelopment Analysis with Translation Invariance

Foreign direct investment (FDI) is a primary vehicle for manufacturing transfer. Middle-income countries can benefit by effectively utilizing FDI to achieve technological development and economic equality and possibly address the middle-income trap issue. This study assessed the FDI performance of ten middle-income countries and examined the statistical relationships between their performance and their contexts: technological development, economic equality, and during the COVID-19 pandemic. For the former, we employed non-radial data envelopment analysis, taking advantage of its translation invariance property to derive efficiency scores; for the latter, we conducted a series of Kruskal–Wallis tests to examine the statistical relationships. According to the analysis results, we found that (a) most countries, except China and India, showed stable efficiency scores over time, (b) their efficiency scores were statistically significantly associated with the level of technological development (indicated by their technology lifecycle-based sigmoid curves) and economic equality (represented by Gini index and poverty indicator); and (c) their efficiency scores were not associated with the COVID-19 pandemic. The results imply that to improve their foreign direct investment performance, host countries may need to enhance their absorptive capacity in both the technological and economic domains.

A new weighted means of failure rate and associated quantile versions

Abstract In this paper, we define weighted failure rate and their means from the stand point of an application. We begin by emphasizing that the formation of n independent component series system having weighted failure rates with sum of weight functions being unity is same as a mixture of n distributions. We derive some parametric and non-parametric characterization results. We discuss on the form invariance property of baseline failure rate for a specific choice of weight function. Some bounds on means of aging functions are obtained. Here, we establish that weighted increasing failure rate average (IFRA) class is not closed under formation of coherent systems unlike the IFRA class. An interesting application of the present work is credited to the fact that the quantile version of means of failure rate is obtained as a special case of weighted means of failure rate.

Adaptive fuzzy gain-scheduling robust control for stability of quadrotors

To solve the instability problem in quadrotor control system subject to parametric uncertainties and external disturbances, an attitude control approach integrated with adaptive fuzzy gain-scheduling desired model compensation robust integral of the sign of the error is proposed. Firstly, the original cascade model of attitude motion is transformed into a strict feedback form with lumped disturbances. Secondly, a desired model compensation robust integral of the sign of the error controller is designed to regulate attitude motion for its invariant properties to lumped disturbances, replacing the velocity state in model-based feedforward control with expected value to ensure the robustness of the system against uncertainties without velocity information. To mitigate the chattering caused by continuous switching control, the fuzzy logic system is used to construct the proposed robust control algorithm, in which robust integral feedback gains associated with the sign function based on fuzzy rules are adaptive scheduled, with the filter tracking error and its derivative as inputs to the fuzzy logic system and robust integral feedback gains as outputs. The stability of the designed closed-loop system is verified by analyzing the convergence of output errors. Finally, the effectiveness and robustness of the proposed method in dealing with the stability of the control system are fully demonstrated by extensive simulations and platform experiments.

Melody transposition tolerance in the human cortex: An fMRI adaptation and MVPA investigation

Abstract Melody perception involves constant relational representations, enabling most people to recognize the melodies after being transposed. This invariant property of melody transposition has been supported in many previous behavioral studies, and we hypothesize that there are brain regions showing tolerance toward melody transposition when processing melodies. To test the hypothesis, we adopted an event-related adaptation approach and a multivariate pattern cross-classification (MVCC) analysis approach. Consistent with our prediction, we discovered clusters in the right superior temporal gyrus (STG) and the left middle temporal gyrus (MTG) that exhibited adaptation when participants listened to both the same and transposed-same melodies after the original ones. An ROI and searchlight-based cross-classification analysis also revealed that BOLD pattern in the bilateral precentral gyrus (PreCG), the left inferior frontal gyrus (IFG), the left inferior parietal lobule (IPL), the right angular gyrus (AG), and the right superior temporal gyrus (STG) showed tolerance to melody transposition. These findings suggest that tolerance to melody transposition exists throughout the music processing pathway from auditory to motor cortices.

Invariant Checking for SMT-Based Systems with Quantifiers

This article addresses the problem of checking invariant properties for a large class of symbolic transition systems defined by a combination of SMT theories and quantifiers. State variables can be functions from an uninterpreted sort (finite but unbounded) to an interpreted sort, such as the integers under the theory of linear arithmetic. This formalism is very expressive and can be used for modeling parameterized systems, array-manipulating programs, and more. We propose two algorithms for finding universal inductive invariants for such systems. The first algorithm combines an IC3-style loop with a form of implicit predicate abstraction to construct an invariant in an incremental manner. The second algorithm constructs an under-approximation of the original problem and searches for a formula which is an inductive invariant for this case; then, the invariant is generalized to the original case and checked with a portfolio of techniques. We have implemented the two algorithms and conducted an extensive experimental evaluation, considering various benchmarks and different tools from the literature. As far as we know, our method is the first capable of handling in a large class of systems in a uniform way. The experiment shows that both algorithms are competitive with the state of the art.

Validation of the Warwick-Edinburgh Mental Well-Being Scale for the Mental Health Surveillance (MHS) of German adults

BackgroundMental health encompasses more than just the absence of mental disorders. Thus, a Mental Health Surveillance (MHS) and reporting system for Germany should monitor mental well-being in addition to psychopathology to capture a more complete picture of population mental health. The Warwick-Edinburgh Mental Well-Being Scale (WEMWBS) is an internationally established inventory for the integrated assessment of different aspects of mental well-being (i.e., hedonic and eudaimonic) in population samples that has not yet been validated for Germany.MethodsUsing data from a cross-sectional online survey of a convenience sample of N = 1.048 adults aged 18–79 years (51% female) living in Germany, the factorial structure, measurement invariance (age, sex) and psychometric properties of the WEMWBS in its long (14 items) and short (7 items) versions were analyzed. Additionally, correlations to relevant factors (e.g., health-related quality of life, psychological distress) were investigated as indicators of criterion validity.ResultsMeans of model fit indices did not confirm a unidimensional factor structure for either version. The three-factor-correlative models showed moderate to good fit while the bifactor model with one general mental well-being factor and three grouping factors fitted the data best. The full range of possible responses was used for all items, and the distribution of both scales was approximately normal. Moreover, the results revealed measurement invariance across sex and age groups. Initial evidence of criterion validity was obtained. Internal consistencies were α = 0.95 and α = 0.89, respectively. Average mental well-being was comparable to that of other European countries at 3.74 for the long version and 3.84 for the short version. While there were no differences by sex, comparisons between age groups revealed higher mental well-being among the older age groups.ConclusionsBoth versions of the WEMWBS showed sound psychometric characteristics in the present German sample. The findings indicate that the instrument is suitable for measuring mental well-being at the population level due to its distributional properties. These results are promising, suggesting that the scale is suitable for use in a national MHS that aims to capture positive mental health in the population as a foundation for prevention and promotion efforts within public mental health.

An Algebraic Approach to Light–Matter Interactions

AbstractA theoretical and computational framework for the study and engineering of light–matter interactions is reviewed in here. The framework rests on the invariance properties of electromagnetism, and is formalized in a Hilbert space whose conformally invariant scalar product provides connections to physical quantities, such as the energy or momentum of a given field, or the outcome of measurements. The light–matter interaction is modeled by the polychromatic scattering operator, which establishes a natural connection to a popular computational formalism, the transition matrix, or T‐matrix. This review contains a succinct yet comprehensive description of the main theoretical ideas, and illustrates some of the practical benefits of the approach.

Dynamic Sliding Mode Control of Spherical Bubble for Cavitation Suppression

Cavitation is a disadvantageous phenomenon that occurs when fluid pressure drops below its vapor pressure. Under these conditions, bubbles form in the fluid. When these bubbles flow into a high-pressure area or tube, they erupt, causing harm to mechanical parts such as centrifugal pumps. The difference in pressure in a fluid is the result of varying temperatures. One way to eliminate cavitation is to reduce the radius of the bubbles to zero before they reach high-pressure areas, using a robust approach. In this paper, sliding mode control is used for this purpose due to its invariance property. To force the radius of the bubbles toward zero and prevent chattering, a new dynamic sliding mode control approach is used. In dynamic sliding mode control, chattering is removed by passing the input control through a low-pass filter, such as an integrator. A general model of the spherical bubble is used, transferred to the state space, and then a state proportional-integral feedback is applied to obtain a linear system with a new input control signal. A comparison is also made with traditional sliding mode control using state feedback, providing a trusted comparison.

Rugged magneto-hydrodynamic invariants in weakly collisional plasma turbulence: Two-dimensional hybrid simulation results

Aims. We investigated plasma turbulence in the context of solar wind. We concentrated on properties of ideal second-order magneto-hydrodynamic (MHD) and Hall MHD invariants. Methods. We studied the results of a two-dimensional hybrid simulation of decaying plasma turbulence with an initial large cross helicity and a negligible magnetic helicity. We investigated the evolution of the combined energy and the cross, kinetic, mixed, and magnetic helicities. For the combined (kinetic plus magnetic) energy and the cross, kinetic, and mixed helicities, we analysed the corresponding Kármán-Howarth-Monin (KHM) equation in the hybrid (kinetic proton and fluid electron) approximation. Results. The KHM analysis shows that the combined energy decays at large scales. At intermediate scales, this energy cascades (from large to small scales) via the MHD non-linearity and this cascade partly continues via Hall coupling to sub-ion scales. The cascading combined energy is transferred (dissipated) to the internal energy at small scales via the resistive dissipation and the pressure-strain effect. The Hall term couples the cross helicity with the kinetic one, suggesting that the coupled invariant, referred to here as the mixed helicity, is a relevant turbulence quantity. However, when analysed using the KHM equations, the kinetic and mixed helicities exhibit very dissimilar behaviours to that of the combined energy. On the other hand, the cross helicity, in analogy to the energy, decays at large scales, cascades from large to small scales via the MHD+Hall non-linearity, and is dissipated at small scales via the resistive dissipation and the cross-helicity equivalent of the pressure-strain effect. In contrast to the combined energy, the Hall term is important for the cross helicity over a wide range of scales (even well above ion scales). In contrast, the magnetic helicity is scantily generated through the resistive term and does not exhibit any cascade.

Representing Noisy Image Without Denoising.

A long-standing topic in artificial intelligence is the effective recognition of patterns from noisy images. In this regard, the recent data-driven paradigm considers 1) improving the representation robustness by adding noisy samples in training phase (i.e., data augmentation) or 2) pre-processing the noisy image by learning to solve the inverse problem (i.e., image denoising). However, such methods generally exhibit inefficient process and unstable result, limiting their practical applications. In this paper, we explore a non-learning paradigm that aims to derive robust representation directly from noisy images, without the denoising as pre-processing. Here, the noise-robust representation is designed as Fractional-order Moments in Radon space (FMR), with also beneficial properties of orthogonality and rotation invariance. Unlike earlier integer-order methods, our work is a more generic design taking such classical methods as special cases, and the introduced fractional-order parameter offers time-frequency analysis capability that is not available in classical methods. Formally, both implicit and explicit paths for constructing the FMR are discussed in detail. Extensive simulation experiments and robust visual applications are provided to demonstrate the uniqueness and usefulness of our FMR, especially for noise robustness, rotation invariance, and time-frequency discriminability.

Fractional-Order Correlation between Special Functions Inspired by Bone Fractal Operators

In recent years, our research on biomechanical and biophysical problems has involved a series of symmetry issues. We found that the fundamental laws of the aforementioned problems can all be characterized by fractal operators, and each type of operator possesses rich invariant properties. Based on the invariant properties of fractal operators, we discovered that the symmetry evolution laws of functional fractal trees in the physical fractal space can reveal the intrinsic correlations between special functions. This article explores the fractional-order correlation between special functions inspired by bone fractal operators. Specifically, the following contents are included: (1) showing the intrinsic expression in the convolutional kernel function of bone fractal operators and its correlation with special functions; (2) proving the following proposition: the convolutional kernel function of bone fractal operators is still related to the special functions under different input signals (external load, external stimulus); (3) using the bone fractal operators as the background and error function as the core, deriving the fractional-order correlation between different special functions.

Structure of Multi-State Correlation in Electronic Systems.

Beyond the Hohenberg-Kohn density functional theory for the ground state, it has been established that the Hamiltonian matrix for a finite number (N) of lowest eigenstates is a matrix density functional. Its fundamental variable─the matrix density D(r)─can be represented by, or mapped to, a set of auxiliary, multiconfigurational wave functions expressed as a linear combination of no more than N2 determinant configurations. The latter defines a minimal active space (MAS), which naturally leads to the introduction of the correlation matrix functional, responsible for the electronic correlation effects outside the MAS. In this study, we report a set of rigorous conditions in the Hamiltonian matrix functional, derived by enforcing the symmetry of a Hilbert subspace, namely the subspace invariance property. We further establish a fundamental theorem on the correlation matrix functional. That is, given the correlation functional for a single state in the N-dimensional subspace, all elements of the correlation matrix functional for the entire subspace are uniquely determined. These findings reveal the intricate structure of electronic correlation within the Hilbert subspace of lowest eigenstates and suggest a promising direction for efficient simulation of excited states.

Differential Subordination and Coefficient Functionals of Univalent Functions Related to $\cos z$

Differential subordination in the complex plane is the generalization of a differential inequality on the real line. In this paper, we consider two subclasses of univalent functions associated with the trigonometric function $\cos z$. Using some properties of the hypergeometric functions, we determine the sharp estimate on the parameter $\beta$ such that the analytic function $p(z)$ satisfying $p(0)=1$, is subordinate to $\cos z$ when the differential expression $p(z)+\beta z (dp(z)/dz)$ is subordinate to the Janowski function. We compute sharp bounds on coefficient functional Hermitian--Toeplitz determinants of the third and the fourth order with an invariance property for such functions. In addition, we estimate bound on Hankel determinants of the second and the third order.

Characterization and Exploitation of the Rotational Memory Effect in Multimode Fibers

In an ideal perfectly straight multimode fiber with a circular core, the symmetry ensures that rotating the input wave front leads to a corresponding rotation of the output wave front. This invariant property, known as the rotational memory effect (RME), remains independent of the typically unknown output profile. The RME thus offers significant potential for imaging and telecommunication applications. However, in real-life fibers, this effect is degraded by intrinsic imperfections and external perturbations, and is challenging to observe because of its acute sensitivity to misalignments and aberrations in the optical setup. Building on a previously established method for precisely estimating fiber transmission properties, we demonstrate an accurate extraction of RME properties. Additionally, we introduce a comprehensive theoretical framework for both qualitative and quantitative analysis, which specifically links the angular-dependent correlation of the RME to the core deformation’s geometrical properties and the fiber’s mode characteristics. Our theoretical predictions align well with experimental data and simulations for various amounts of fiber distorsion. Finally, we demonstrate the ability to engineer wave fronts with significantly enhanced correlation across all rotation angles. This work enables accurate characterization of distributed disorder from the fabrication process and facilitates calibration-free imaging in multimode fibers. Published by the American Physical Society 2024

Hydrogel Composition Effects on Performance as Single-Walled Carbon Nanotube Purification Media.

Hydrogel microsphere media allows for postsynthetic purification of single-walled carbon nanotubes (SWNTs), affording characterization and application of their unique (n,m) chirality-dependent properties. This work reports the characterization of five hydrogel resins, Sephacryl S-100, S-200, S-300, S-400, and S-500, and the implementation of each as a SWNT purification medium. The physiochemical properties of each resin were explored spectroscopically through elemental analyses and with both light and electron microscopy. Both surface porosity and hydrogel swelling ratio were found to increase as the concentration of component allyl dextran (aDEX) decreased, each with an increasing Sephacryl S-number. Conversely, invariant properties included a hydrogel microsphere size distribution and concentrations of components methylenebisacrylamide and ammonium persulfate. When employed within gel-based SWNT purification schemes in overloading conditions, Sephacryl formulations of larger S-number adsorbed fewer SWNTs, but the chirality dependence of SWNT adsorption and elution was approximately consistent across all resins. In underloading conditions, approximately one-third of introduced SWNTs passed through each resin unabsorbed, while the resins showed varying chirality-dependent adsorption efficiencies. These observations collectively identify aDEX-rich gel regions as being responsible for SWNT purification, along with a SWNT-exclusive parameter other than chirality (speculated as length) that convolutes the effectiveness of gel-based single-chirality purification.

Cooperative coevolution for non-separable large-scale black-box optimization: Convergence analyses and distributed accelerations

Given the ubiquity of non-separable optimization problems in real worlds, in this paper we analyze and extend the large-scale version of the well-known cooperative coevolution (CC), a divide-and-conquer black-box optimization framework, on non-separable functions. First, we reveal empirical reasons of when decomposition-based methods are preferred or not in practice on some non-separable large-scale problems, which have not been clearly pointed out in many previous CC papers. Then, we formalize CC to a continuous-game model via simplification, but without losing its essential property. Different from previous evolutionary game theory for CC, our new model provides a much simpler but useful viewpoint to analyze its convergence, since only the pure Nash equilibrium concept is needed and more general fitness landscapes can be explicitly considered. Based on convergence analyses, we propose a hierarchical decomposition strategy for better generalization, as for any decomposition, there is a risk of getting trapped into a suboptimal Nash equilibrium. Finally, we use powerful distributed computing to accelerate it under the recent multi-level learning framework, which combines the fine-tuning ability from decomposition with the invariance property of CMA-ES. Experiments on a set of high-dimensional test functions validate both its search performance and scalability (w.r.t. CPU cores) on a clustering computing platform with 400 CPU cores.