Unknown Order Research Articles

Efficient Verifiable Delay Functions

We construct a verifiable delay function (VDF). A VDF is a function whose evaluation requires running a given number of sequential steps, yet the result can be efficiently verified. They have applications in decentralised systems, such as the generation of trustworthy public randomness in a trustless environment, or resource-efficient blockchains. To construct our VDF, we actually build a trapdoor VDF. A trapdoor VDF is essentially a VDF which can be evaluated efficiently by parties who know a secret (the trapdoor). By setting up this scheme in a way that the trapdoor is unknown (not even by the party running the setup, so that there is no need for a trusted setup environment), we obtain a simple VDF. Our construction is based on groups of unknown order such as an RSA group or the class group of an imaginary quadratic field. The output of our construction is very short (the result and the proof of correctness are each a single element of the group), and the verification of correctness is very efficient.

Fuzzy Adaptive Containment Control for Nonlinear Nonaffine Pure-Feedback Multiagent Systems

This article addresses the containment control problem of multiagent systems under directed topologies, where the model of each agent is an unknown nonlinear nonaffine pure-feedback dynamic, and at the same time, the outputs and their derivatives of the leaders are unknown. To avoid the complex design process with the recursive methods (i.e., backstepping and dynamic surface), each unknown higher order nonlinear dynamic is transformed into a simple high-order integral model with unknown affine nonlinear terms in the last-order dynamic at first. Then, the fuzzy logic systems and the fuzzy state observers are constructed to approximate the unknown affine nonlinear terms and the unknown transformed states. Finally, a novel fully distributed fuzzy adaptive containment control law is generated according to the state observers and the supervised control. The stability of the closed-loop system is analyzed in the Lyapunov sense and the containment errors converge to a small neighborhood of the origin. Simulation results show the feasibility and effectiveness of the proposed scheme.

The uniqueness of inverse problems for a fractional equation with a single measurement

This article is concerned with an inverse problem on simultaneously determining some unknown coefficients and/or an order of derivative in a multidimensional time-fractional evolution equation either in a Euclidean domain or on a Riemannian manifold. Based on a special choice of the Dirichlet boundary input, we prove the unique recovery of at most two out of four $$\varvec{x}$$ -dependent coefficients (possibly with an extra unknown fractional order) by a single measurement of the partial Neumann boundary output. Especially, both a vector-valued velocity field of a convection term and a density can also be uniquely determined. The key ingredient turns out to be the time-analyticity of the decomposed solution, which enables the construction of Dirichlet-to-Neumann maps in the frequency domain and thus the application of inverse spectral results.

Multi-model estimation using neural network and fault detection in unknown time continuous fractional order nonlinear systems

In this paper, multi-model estimation and fault detection using neural network is proposed for an unknown time continuous fractional order nonlinear system. Fractional differentiation is considered based on Caputo concept and the fractional order is considered to be between 0 and 1. In order to estimate a time continuous fractional order nonlinear system with unknown term in its dynamic, single-layer and double-layer RBF neural network is used. First, a parallel-series neural network observer is designed for state estimation. Weights of the neural network are updated adaptively and updating laws are presented in fractional order form. Using Lyapunov method, it is proved that state estimation error and weight estimation error of the neural network are bounded. Parameters of the neural estimator converge to ideal parameters which satisfy excitation condition stability. Then, multi-model estimation structure of fractional order nonlinear systems is presented and its application in fault detection is investigated. Finally, simulation results are presented to show efficiency of the proposed method.

Whole-body Magnetic Resonance Imaging in Psoriatic Arthritis, Rheumatoid Arthritis, and Healthy Controls: Interscan, Intrareader, and Interreader Agreement and Distribution of Lesions.

Whole-body MRI (WBMRI) is a promising technique for monitoring patients' global disease activity in inflammatory joint diseases. The validation of WBMRI is limited; no studies have evaluated the test-retest agreement (interscan agreement) and only a few have assessed the intra- and interreader agreement. Therefore, we first examined the interscan agreement of WBMRI in patients with psoriatic arthritis (PsA), rheumatoid arthritis (RA), and healthy controls (HC); and second, we evaluated the intra- and interreader agreement and agreement with conventional hand MRI and determined the distribution of lesions. WBMRI was performed twice at a 1-week interval in 14 patients with PsA, 10 with RA, and 16 HC. Images were anonymized and read in pairs with unknown chronological order by experienced readers according to the Outcome Measures in Rheumatology (OMERACT) WBMRI, Canada-Denmark MRI, and the RA MRI scoring system (RAMRIS) and the PsA MRI scoring system (PsAMRIS). Ten image sets were reanonymized for assessment of intra- and interreader agreement. Agreement was calculated on lesion level by percentage exact agreement (PEA) and Cohen κ, and for sum scores by absolute agreement, single-measure intraclass correlation coefficient (ICC). WBMRI of the spine and peripheral joints and entheses generally showed moderate to almost perfect interscan agreement with PEA ranging from 95% to 100%, κ 0.71-1.00, and ICC 0.95 to 1.00. Intra- and interreader data generally showed moderate to almost perfect agreement. Agreement with conventional MRI varied. More lesions were found in patients than in HC. WBMRI showed good interscan agreement, implying that repositioning of the patient between examinations does not markedly affect scoring of lesions. Intra- and interreader agreement were moderate to almost perfect.

Constructions of pairs of orthogonal latin cubes

AbstractA pair of orthogonal latin cubes of order is equivalent to a maximum distance separable code with distance 3 or to an orthogonal array. We construct pairs of orthogonal latin cubes for sequences of previously unknown orders and . The minimal new obtained parameters of orthogonal arrays are .

Research Of The Blind Equalization Technology In The Non-Cooperative Communication Receiving System

Convergence rate and steady-state mean square error are the main parameters to evaluate the performance of blind equalization algorithm. In order to improve the blind equalization performance of non-cooperative communication reception under multipath fading channel, a modified super-exponential iterative blind equalization algorithm is adopted, which converges faster than the traditional constant modulus algorithm and achieves the same steady-state mean square error. Aiming at the MPSK non-cooperative signal with unknown modulation order, a two-mode blind equalization method based on fractional interval is proposed. The method makes full use of the robustness and fast convergence of the super-exponential iterative algorithm, and combines the low steady-state mean square error of the recursive least squares algorithm. The effectiveness of the method is proved by simulation and experiment.

Modify adaptive combined synchronization of fractional order chaotic systems with fully unknown parameters

This article presents a modify adaptive combined synchronization for a class of different unknown fractional order chaotic systems. A combination of different states of the drive systems asymptotically synchronizes with the desired states of the response system. Hence, increases the complexity of the communication channel in secrete communications. The Lyapunov stability theory proves the asymptotic stability of the error system at the origin. The design of a suitable adaptive controller assures the target synchronization. This work provides parameters update laws that estimate the true values of unknown parameters. This paper also presents two numerical examples of unknown different fractional order chaotic systems and simulation results that validate the efficiency and performance of the proposed adaptive combined synchronization strategy. The presented adaptive combined synchronization strategy can be applied to multiple synchronization strategies. The paper suggests some future problems related to this work.

Reply to Comment by Jie Qin and Teng Wu on “A Modified Particle Filter‐Based Data Assimilation Method for a High‐Precision 2‐D Hydrodynamic Model Considering Spatial‐Temporal Variability of Roughness: Simulation of Dam‐Break Flood Inundation”

Key Points The MPFDA‐LW could offset the unknown model errors by only adjusting the Manning's roughness coefficient The observation error in the MPFDA‐LW was determined by sensitivity analysis due to unknown truth observation error In order to improve the prediction of whole flood process, water stages observed in a regional scale should be assimilated

Momentum-resolved superconducting energy gaps of Sr2RuO4 from quasiparticle interference imaging

Sr2RuO4 has long been the focus of intense research interest because of conjectures that it is a correlated topological superconductor. It is the momentum space (k-space) structure of the superconducting energy gap [Formula: see text] on each band i that encodes its unknown superconducting order parameter. However, because the energy scales are so low, it has never been possible to directly measure the [Formula: see text] of Sr2RuO4 Here, we implement Bogoliubov quasiparticle interference (BQPI) imaging, a technique capable of high-precision measurement of multiband [Formula: see text] At T = 90 mK, we visualize a set of Bogoliubov scattering interference wavevectors [Formula: see text] consistent with eight gap nodes/minima that are all closely aligned to the [Formula: see text] crystal lattice directions on both the α and β bands. Taking these observations in combination with other very recent advances in directional thermal conductivity [E. Hassinger et al., Phys. Rev. X 7, 011032 (2017)], temperature-dependent Knight shift [A. Pustogow et al., Nature 574, 72-75 (2019)], time-reversal symmetry conservation [S. Kashiwaya et al., Phys. Rev B, 100, 094530 (2019)], and theory [A. T. Rømer et al., Phys. Rev. Lett. 123, 247001 (2019); H. S. Roising, T. Scaffidi, F. Flicker, G. F. Lange, S. H. Simon, Phys. Rev. Res. 1, 033108 (2019); and O. Gingras, R. Nourafkan, A. S. Tremblay, M. Côté, Phys. Rev. Lett. 123, 217005 (2019)], the BQPI signature of Sr2RuO4 appears most consistent with [Formula: see text] having [Formula: see text] [Formula: see text] symmetry.

Assessment of Bacterial Diversity of Sandy-Loam Soil Polluted by Hydrocarbons Using 454 Pyrosequencing

The study was conducted on polluted soil from a refitting oil station at Pointe-Noire in Congo. The aim of the work was to study the composition of the soil microbial community. Microbial diversity was assessed using the 454 pyrosequencing. The results showed that microbial diversity was represented by 1986 OTUs assigned to the Bacteria domain with 97% of similarity. However, only 246 OTUs were affiliated with 12 Phyla, 24 Classes, 56 Orders and 85 Families. The Proteobacteria (73%), Chloroflexi (16.85%), Bacteroidetes (2.68%) and Actinobacteria (2.65%) were the most representative bacterial phyla. The dominant classes were Alphaproteobacteria, Betaproteobacteria, Gammaproteobacteria, Actinobacteria, Sphingobacteria. The most abundant orders are represented by Rhizobiales (22.94%), Sphingomodales (7.07%), Caulobacterales (6.68%) and three unknown orders corresponding to 28.96%. Bradyrhizobiaceae (14.10%), Sphingomonadaceae (7.05%) and Caulobacteraceae (6.68%) were the best distributed families in the microbial community. This soil could serve for isolation of microorganism consortia for bioremediation.

Several structure pool based identification algorithms for ARX models: order and parameter estimation

Several structure pool based identification algorithms are proposed for autoregressive exogenous (ARX) models with unknown order in this study. Since the order of the ARX model is unknown, a struct...

On the Edge of the Unknown

The present paper intends to discuss the process of design and its peculiar location at the threshold between the unknown (the insecure place with unknown order) and already established, well-accepted knowledge. The process of design is known for its catalyzing possibilities, often suggesting connections between conceptions, ideas, and solutions to problems by linking an initial formulation with the innovative and upcoming development of a project within a given design context. Thus, the process of design has the power to provide a space for playing, where experiments of thought, the testing of conceptions, the assembling of elements of these conceptions, and the serendipitous conflation of different parts of ideas can take place. Charles S. Peirce’s theory of inquiry—with especial emphasis on the systemic character of semiotics in relation to phaneroscopy, esthetics, logic of abduction and pragmatism—informs the chosen theoretical framework of this paper. Because it also emphasizes the process of discovery, Peirce’s theory of inquiry will be here mobilized to analyze, within the theory of the design process, the transition between critical predicament and an undecided—still to be formed—future. This task consists of stating in futuro the unthinkable in order to render any design project feasible.

Human Intention Estimation using Fusion of Pupil and Hand Motion

Abstract This paper addresses the problem of human intention inference in the context of human-robot collaboration by fusing information from both hand motion obtained using skeletal tracking and eye gaze obtained using pupil tracking to predict a human’s current intention. Intention is modeled as a motion profile that converges to a goal location. A Kalman filter is used on eye gaze data to obtain gaze point estimates. The gaze estimates are transformed into a reference frame common to the hand data. An IMM filter that tracks hand motion is designed which takes advantage of the gaze filter’s model probabilities by fusing them with its own. The fusion is performed with user chosen parameters that determine the degree to which each filter’s predictions are weighed over time. An experiment is designed to show the utility of the proposed algorithm in a setting in which multiple reaching tasks are completed in an unknown order. The results show that the proposed algorithm can accurately predict the human’s intention before the tasks are completed.

Dynamic Prediction of the Thermal Nonlinear Process Based on Deep Hybrid Neural Network

Nonlinear system prediction plays an important role in the practical thermal process, and deep learning algorithm is now popular in nonlinear dynamic system modeling because of its powerful learning ability. In this paper, the dynamic artificial neural networks (DANNs), which can be divided into two different types with external dynamic characteristics and internal dynamic characteristics, are analyzed. The mathematical formulations of feedforward deep neural network (DNN), traditional recurrent neural network (RNN) and Long-Short Term Memory network (LSTM) models are given. Furthermore, the structure of deep Hybrid Neural Network (DHNN) is described. Finally, the applicability of the above models in the thermal nonlinear process with different structural features is discussed. Simulation experiments reveal that DANNs with internal dynamic characteristics more suitable for solving thermal nonlinear system modeling problems with unknown order, and DHNN based on LSTM model has performed much better in approximating the dynamics of the thermal process with state parameters.

Intelligent Demand Forecasting of Smelting Process Using Data-Driven and Mechanism Model

The demand for electricity for the fused magnesia smelting process is calculated by the moving average of the energy consumption of a given period, which gives the efficiency of the smelting and indicates if the power supply should be cut off. Therefore, demand forecasting is very important for the operation of the smelting process. However, it is difficult to forecast demand since the power changes depend on the smelting process and raw materials. To obtain an accurate model, the mechanism model of the smelting process is combined with the data-driven method using artificial intelligence technology in this paper. The mechanism model is described by a linear model with unknown parameters. The uncertainties and error of the mechanism model are modeled by neural networks with unknown order. The maximal information coefficient method and the rule reasoning are combined to identify the order. To effectively combine the mechanism model and the data-driven model, a new saturated alternating identification strategy is proposed. The results of simulations and industrial applications show that the effectiveness of the proposed intelligent method of demand forecasting has been validated.

Joint convergence of sample autocovariance matrices when $p/n\to 0$ with application

Consider a high-dimensional linear time series model where the dimension $p$ and the sample size $n$ grow in such a way that $p/n\to 0$. Let $\hat{\Gamma }_{u}$ be the $u$th order sample autocovariance matrix. We first show that the LSD of any symmetric polynomial in $\{\hat{\Gamma }_{u},\hat{\Gamma }_{u}^{*},u\geq 0\}$ exists under independence and moment assumptions on the driving sequence together with weak assumptions on the coefficient matrices. This LSD result, with some additional effort, implies the asymptotic normality of the trace of any polynomial in $\{\hat{\Gamma }_{u},\hat{\Gamma }_{u}^{*},u\geq 0\}$. We also study similar results for several independent MA processes. We show applications of the above results to statistical inference problems such as in estimation of the unknown order of a high-dimensional MA process and in graphical and significance tests for hypotheses on coefficient matrices of one or several such independent processes.

Finite element implementation based on explicit, Galerkin and Crank–Nicolson methods to phase field theory for thermal- and surface- induced martensitic phase transformations

In this paper, a nonlinear finite element approach is used to solve the time-dependent phase field or Ginzburg–Landau (GL) equation for phase transformations (PTs) at the nanoscale. The utilized Helmholtz energy includes a third-degree polynomial of the phase variable which results in a nonlinear dependence on the order parameter in the GL equation. The method of weighted residuals is used to derive the corresponding finite element formulation. Using the divergence theorem, the Laplace term in the GL equation is reduced to the first-order term which can represent both the isolated and variable surface energy boundary conditions, allowing for surface-induced phenomena. In order to apply the Dirichlet boundary condition, i.e., constant phase order parameter, the penalty method is used. Quadrilateral elements have been used in the Cartesian coordinate system, and irregular elements for complex geometries are transformed to regular ones by using natural coordinates. Four-point Gaussian integral has been used for integral calculations. The alpha family and both the explicit and implicit methods (Crank–Nicolson and Galerkin methods) are used for time discretization. Thus, the Picard and Newton–Raphson methods are used to linearize the nonlinear equation and their computational efficiencies are compared. In the explicit method, in order to calculate the inverse of the stiffness matrix, the lumping technique has been used which transforms it into a modified diagonal matrix, and this significantly reduced the computation time. In the implicit methods of Picard and Newton–Raphson, both the exact and numerical approaches were used to calculate the tangential matrix for the unknown order parameter and no difference in results between them was found. The convergence for both the Picard and Newton–Raphson methods was studied and compared. Cubic to tetragonal, thermal- induced transformation in NiAl is considered. The order parameter profile and the width and velocity of austenite (A)–martensite (M) interface are calculated and verified with previous works. Examples of thermal- and surface-induced PTs in nanosized samples without hole and with it are studied, presenting planar and nonplanar interfaces. The developed algorithm and code present a proper tool to solve more advanced phase field problems for PTs at the nanoscale with complex geometries and including mechanics effects and with considering complex interactions.

High Capacity Steganography Protected using Shamir’s Threshold Scheme and Permutation Framework

This paper presents a framework that conceal large volume of secret information using distributed file system that permit implantation of decomposed secret images across multiple-cover images. The strong security is imposed utilizing Shamir’s threshold scheme and permutation generator framework. Three layers of security is being applied to protect the secret information, in first, secret image is decomposed into equal size of smaller sub-images and generate a framework of permutations from an integer for distributing and reassembling the circulated broken secret sub images among the intended participants. At the time of embedding purpose of permutation generator is to arrange the sub-images in unknown order for outsider. During the discloser stage only inverse of permutation can rearrange the distributed sub-images to reassemble into original image by authorized contributors. In second, Shamir’s threshold scheme is designed for authentication of shared associated stego-cover images before starting the extraction process. This process provides an extremely secured construction of shared secret information. In third, image is divided in 2x2 blocks of pixels and traverses it in zig-zag manner; the pixel value difference is computed for all Red, Green, and Blue (RGB) components between non-overlapping pixels of selected diagonal path with in targeted block. Secret bits are concealed inside RGB color pixels of cover image by utilizing proposed novel pixel-value differencing (PVD) scheme, furthermore varying embedding capacity may be obtained by controlling the selection of number of 2x2 block. Exploratory result displays that the proposed approach provides productive algorithms in term multilayer unbreakable security and higher payload of embedded information.

Acoustic performance of a resonating perforated liner with incident axial and circumferential acoustic modes

Perforated liners are a common form of passive damping device used in engineering applications to damp acoustic pressure fluctuations. The liner has many orifices arranged over the surface with a rear cavity, where the liner can be designed to resonate akin to an array of Helmholtz resonators in parallel. However, whilst a Helmholtz resonator is insensitive to the incident mode, the large surface area and rear cavity of a perforated liner can generate internal mode shapes that affect the acoustic performance. This paper presents a quasi-one-dimensional analytical model capable of capturing the variation in acoustic performance as the internal cavity segmentation is altered with incident higher-order acoustic modes in a narrow annular duct. Thus, the model can allow the generation of circumferential mode shapes. The model shows, when the liner is highly segmented circumferentially, the liner behaviour is akin to that with an incident axial wave. The segmentation causes the internal cavity pressure to fluctuate uniformly at a similar frequency to a Helmholtz resonator with the same effective cavity dimensions. When the cavity length is significant relative to the wavelength, circumferential mode shapes are generated within the cavity and the frequency of resonance increases based on the circumferential frequency component. The model is then compared to an example experimental data set obtained from a facility designed to allow circumferential modes to cut-on simultaneously with an axial mode. A description of the facility and the multi-microphone decomposition method applied to decompose simultaneous modes of unknown orders and relative magnitudes is presented. The model has good agreement with the experimental results for a small cavity segmentation, although there is deviation observed at high frequencies when the cavity length becomes significant relative to the circumferential wavelength.