Recursive Scheme Research Articles

Curve counting in genus one: Elliptic singularities and relative geometry

We construct and study the reduced, relative, genus one Gromov--Witten theory of very ample pairs. These invariants form the principal component contribution to relative Gromov--Witten theory in genus one and are relative versions of Zinger's reduced Gromov--Witten invariants. We relate the relative and absolute theories by degeneration of the tangency conditions, and the resulting formulas generalise a well-known recursive calculation scheme put forward by Gathmann in genus zero. The geometric input is a desingularisation of the principal component of the moduli space of genus one logarithmic stable maps to a very ample pair, using the geometry of elliptic singularities. Our study passes through general techniques for calculating integrals on logarithmic blowups of moduli spaces of stable maps, which may be of independent interest.

Automatic Detection of K-Complexes Using the Cohen Class Recursiveness and Reallocation Method and Deep Neural Networks with EEG Signals.

Evoked and spontaneous K-complexes are thought to be involved in sleep protection, but their role as biomarkers is still under debate. K-complexes have two major functions: first, they suppress cortical arousal in response to stimuli that the sleeping brain evaluates to avoid signaling danger; and second, they help strengthen memory. K-complexes also play an important role in the analysis of sleep quality, in the detection of diseases associated with sleep disorders, and as biomarkers for the detection of Alzheimer’s and Parkinson’s diseases. Detecting K-complexes is relatively difficult, as reliable methods of identifying this complex cannot be found in the literature. In this paper, we propose a new method for the automatic detection of K-complexes combining the method of recursion and reallocation of the Cohen class and the deep neural networks, obtaining a recursive strategy aimed at increasing the percentage of classification and reducing the computation time required to detect K-complexes by applying the proposed methods.

A recursive sparse representation strategy for bearing fault diagnosis

Partial faults of bearings trigger periodic vibration features, but the interference makes fault diagnosis more difficult. A recursive sparse representation (RSR) algorithm is proposed to solve the fault diagnosis of bearings from sparse representation in the time and frequency domains. The tunable Q-factor wavelet transform (TQWT) filtering strategy is used to adaptively obtain the best wavelet with the signal vibration features. The optimal wavelet data is used as a fragment of each basic atom to obtain an optimal atomic complete dictionary (OACD) by Toeplitz's complementary zero expansion. The sparse representation based on the OACD obtains sparse coefficients with time domain features. The sparse group lasso (SGL) based on Majorize-Minimization (MM) optimization solves the sparse coefficients and extracts the primary vibration information in the frequency domain. Simulation experiments, signal experiments, and a comparative analysis of spectral kurtosis (SK) prove that RSR can effectively extract the vibration characteristics of faulty bearings.

Under the same (Chole)sky: DNK models, timing restrictions and recursive identification of monetary policy shocks

Recent structural VAR studies of the monetary transmission mechanism have voiced concerns about the use of recursive identification schemes based on short-run exclusion restrictions. This paper characterizes the effects on impulse propagation of informational constraints embodying classical Cholesky-type timing restrictions in otherwise standard DSGE models. We formally show that timing restrictions can produce non-trivial moving average components of rational expectations solutions, or even serve as an independent source of model-based nonfundamentalness, thereby hampering impulse response analysis via VAR procedures. We then derive population conditions for existence of VAR representations of DSGE economies exhibiting timing restrictions, and numerically explore their bearing on shock identification in a range of monetary models of the business cycle. Our analysis reveals that dynamic New Keynesian models admit invertible equilibrium representations as well as fast-converging VAR coefficient matrices under empirically tenable parameterizations. This alleviates concerns about identification and lag truncation bias: low-order Cholesky-VARs do well at retrieving the true aggregate effects of monetary policy shocks in a Cholesky world.

Performance evaluation of whey flux in dead-end and cross-flow modes via convolutional neural networks

Effluent originating from cheese production puts pressure onto environment due to its high organic load. Therefore, the main objective of this work was to compare the influence of different process variables (transmembrane pressure (TMP), Reynolds number and feed pH) on whey protein recovery from synthetic and industrial cheese whey using polyethersulfone (PES 30 kDa) membrane in dead-end and cross-flow modes. Analysis on the fouling mechanistic model indicates that cake layer formation is dominant as compared to other pore blocking phenomena evaluated. Among the input variables, pH of whey protein solution has the biggest influence towards membrane flux and protein rejection performances. At pH 4, electrostatic attraction experienced by whey protein molecules prompted a decline in flux. Cross-flow filtration system exhibited a whey rejection value of 0.97 with an average flux of 69.40 L/m2h and at an experimental condition of 250 kPa and 8 for TMP and pH, respectively. The dynamic behavior of whey effluent flux was modeled using machine learning (ML) tool convolutional neural networks (CNN) and recursive one-step prediction scheme was utilized. Linear and non-linear correlation indicated that CNN model (R2 – 0.99) correlated well with the dynamic flux experimental data. PES 30 kDa membrane displayed a total protein rejection coefficient of 0.96 with 55% of water recovery for the industrial cheese whey effluent. Overall, these filtration studies revealed that this dynamic whey flux data studies using the CNN modeling also has a wider scope as it can be applied in sensor tuning to monitor flux online by means of enhancing whey recovery efficiency.

Partial Discharge Signal Denoising with Recursive Continuous S-Shaped Algorithm in Cables

Partial discharge (PD) detection plays a vital role in on-line condition monitoring of electrical apparatus in the power systems. However, the noise of PD measurements significantly degrades the performance of detection algorithms. In this paper, we focus on developing an adaptive filtering technique for the PD denoising problem. Heretofore, there are just a few literature reviews addressing the PD denoising based on such a method. The proposed recursive continuous S-shaped (RCSS) algorithm integrates the advantages of recursive strategy and continuous S-shaped function into adaptive noise cancellation (ANC) system, yielding enhanced filtering performance. The proposed algorithm can tackle PD noises in both Gaussian and impulsive scenarios, which is easy to implement in practical applications. The convergence behavior is also analyzed. Extensive simulation and experimental results confirm that the proposed algorithm can address polluted PD pulses, even in excessively noisy conditions, resulting in smaller mean square error (MSE) as compared to other state-of-the-art algorithms.

Entropy dissipation estimates for inhomogeneous zero-range processes

Introduced by Lu and Yau (Comm. Math. Phys. 156 (1993) 399–433), the martingale decomposition method is a powerful recursive strategy that has produced sharp log-Sobolev inequalities for homogeneous particle systems. However, the intractability of certain covariance terms has so far precluded applications to heterogeneous models. Here we demonstrate that the existence of an appropriate coupling can be exploited to bypass this limitation effortlessly. Our main result is a dimension-free modified log-Sobolev inequality for zero-range processes on the complete graph, under the only requirement that all rate increments lie in a compact subset of (0,∞). This settles an open problem raised by Caputo and Posta (Probab. Theory Related Fields 139 (2007) 65–87) and reiterated by Caputo, Dai Pra and Posta (Ann. Inst. Henri Poincaré Probab. Stat. 45 (2009) 734–753). We believe that our approach is simple enough to be applicable to many systems.

Computable structural formulas for the distribution of the $$\beta $$-Jacobi edge eigenvalues

The Jacobi ensemble is one of the classical ensembles of random matrix theory. Prominent in applications are properties of the eigenvalues at the spectrum edge, specifically the distribution of the largest (e.g. Roy’s largest root test in multivariate statistics) and smallest (e.g. condition numbers of linear systems) eigenvalues. We identify three ranges of parameter values for which the gap probability determining these distributions is a finite sum with respect to particular bases, and moreover make use of a certain differential–difference system fundamental in the theory of the Selberg integral to provide a recursive scheme to compute the corresponding coefficients.

Time‐Varying Dynamics of the German Business Cycle: A Comprehensive Investigation*

AbstractThis paper provides insights into the time‐varying dynamics of the German business cycle over the last five decades. To do so, I employ an open‐economy time‐varying parameter VAR with stochastic volatility, which I estimate by quasi‐Bayesian techniques. The reduced‐form analysis reveals substantial shifts in the variables’ long‐run growth rates and shock volatilities over time. German trend inflation has strongly decreased and settled at a historically low level. GDP growth volatility exhibits marked fluctuations over time and has dropped to historically low levels only after the global financial crisis. The structural analysis employs externally identified oil supply shocks along with a recursive identification scheme to identify key macroeconomic shocks. The analysis reveals strong fluctuations in both the impact responses of macroeconomic aggregates to these shocks and the shock propagation processes. Thus, I conclude that business cycle stabilization in Germany is driven by both good policy and good luck.

An adaptive anti-noise network with recursive attention mechanism for gear fault diagnosis in real-industrial noise environment condition

Acoustic-based diagnosis (ABD) is a promising method for machinery fault detection due to its ability of non-contact measurement by air-couple. However, most of the ABD methods are constrained by strong and highly non-stationary background noise interference in practical industrial application. To address the shortcoming, a novel anti-noise ABD method based on recursive attention mechanism (RAM) is proposed in this paper. In proposed method, a multi-stage attention module (MSAM) is firstly designed as fundament of RAM to automatically estimate the noise interference probability within time–frequency (T-F) unit of each signal sample. Simultaneously, a recursive learning strategy is introduced to construct RAM by reusing the MSAM for multiple blocks to gradually refine the estimated probability and adaptively simulated noise interference in diagnosis model for enhancing anti-noise diagnosis ability. Then, based on RAM, a domain adaption method is established to endow the model with good cross-domain ability for further improving the anti-noise performance of the diagnosis model. The experiment result in both real-industrial noise condition and stimulated noise conditions with different SNRs indicate that the proposed method has stronger robustness and better generalization ability than other popular methods in dealing with gear fault diagnosis task under noise condition.

Reducing Higher-order Recursion Scheme Equivalence to Coinductive Higher-order Constrained Horn Clauses

Higher-order constrained Horn clauses (HoCHC) are a semantically-invariant system of higher-order logic modulo theories. With semi-decidable unsolvability over a semi-decidable background theory, HoCHC is suitable for safety verification. Less is known about its relation to larger classes of higher-order verification problems. Motivated by program equivalence, we introduce a coinductive version of HoCHC that enjoys a greatest model property. We define an encoding of higher-order recursion schemes (HoRS) into HoCHC logic programs. Correctness of this encoding reduces decidability of the open HoRS equivalence problem -- and, thus, the LambdaY-calculus B\"ohm tree equivalence problem -- to semi-decidability of coinductive HoCHC over a complete and decidable theory of trees.

A cost‐efficient joint target location and clock bias estimation technique using multiple time step measurements in mobile bistatic sonar

Active localization of a stationary target is one key issue in applications of bistatic sonar based on bistatic range (BR) measurement. However, the complex underwater environment makes achieving the synchronization between the transmitted station and the received station difficult. For solving the synchronization problem, this study relies on mobile bistatic sonar to acquire measurement information at multiple time steps. After that, the target location and clock bias are jointly estimated by solving a non-linear least square problem. To this end, a recursive scheme is proposed to optimise the measurement cost and reduce the impact of the initial value to achieve accurate estimation by taking full advantage of the redundant measurement information. Orthogonal transformation is used to ensure computational efficiency and numerical reliability. The Cramer–Rao Lower Bound (CRLB) is also derived as a lower bound on the error in estimating the target position and clock bias. Simulation results show that the proposed method achieves the CRLB performance and optimises the measurement cost over the small error region under Gaussian noise.

Free-surface disturbances due to the submersion of a cylindrical obstacle

We explore the initial perturbations that form on a liquid free surface as a result of the submersion of a circular cylinder beneath the surface, a scenario that arises in a number of diverse applications. The behaviour of the free surface is determined by transforming the equations of motion of the system via the Wehausen scheme, to variables for the free surface. A small-time series expansion is utilized to construct a recursive scheme that can be implemented numerically, and the time frame over which this approximation is valid is analysed. The resulting numerical model allows one to extend the results in the literature to study arbitrary cylinder sizes, including those where the cylinder is close to the free surface, and arbitrary cylinder motions. Of particular interest in this study was identifying the conditions under which strong jets would appear, and those were the free surface exhibited gravity waves. The formation of a central jet is found to be related to the growth of secondary, nonlinear waves, which rapidly merge as the obstacle is submerged. Classification maps are presented as a function of obstacle size and submersion speed, to identify the conditions which lead to jetting. Furthermore, the acceleration profile of the cylinder is shown to significantly affect the conditions under which jets form, which we argue is due to the rate at which energy is injected into the system.

Optimizing realization of the terrestrial reference frame on a regional basis: A case study using the crustal movement observation network of China

It is critical in the study of crustal deformation to reduce TRF-related system errors and enhance the accuracy of GPS coordinate time series. To reduce system errors associated with the coordinate time series, which are related to the terrestrial reference frame (TRF) realization, we develop a recursive TRF realization strategy in regional GPS data processing. We have processed the whole set of CMONOC (Crustal Movement Observation Network of China) GPS data by using the Bernese 5.2 software and employed the controlled datum removal (CDR) filter to deal with the rank defect problem in the daily coordinate normal equations (NEQs). On the recursive TRF realization, we sequentially perform time series modeling with integral trajectory models, TRF realization with all continuous stations treated as “pseudo” fiducial stations, and frame alignment to the ITRF2014 with the 6-parameters Helmert transformation, in an iterative mode. We obtain the final coordinate time series through 3 times of iterations. Compared to the results derived from the conventional TRF realization strategy with the average root mean squares (RMS) being 1.98 mm, 2.62 mm and 5.39 mm for the east, north and up components, respectively, the average RMS scatters earn significant reduction up to 30%, 43% and 16% in the first loop, with their quantities being 1.41 mm, 1.51 mm and 4.57 mm for the east, north and up components, respectively, and negligible changes in the following 2 loops. In contrast to previous studies, our strategy is feasible in the processing of regional geodetic networks and concentrated on the TRF-related system errors without any pre-assumption and spatial limitation. In essence, the recursive strategy enhances the weights for the CMONOC stations and inevitably weakens the weights for stations exterior to the CMONOC to accommodate the misfits between the referential and estimated daily solutions in the least squares adjustment, thus resulting in the slightly increase of RMS scatters for the coordinate time series of globally distributed stations. For the CMONOC stations, the north component of coordinates time series has a maximum RMS reduction, revealing the identical precision for both horizontal components, thus indicating that our strategy remedies the frame defects stemming from the extremely uneven distribution of the fiducial network, and retrieves the “real” precision of GPS observations. The insignificant RMS reduction on the vertical component may be attributed to the insufficiency in the time series modeling. Our recursive TRF realization strategy can benefit the velocity estimation for campaign stations.

Dew Point Time Series Forecasting at the North Dakota

Hydrological time series forecasting is one of the hot topics in the domain of statistical hydrology. Providing accurate forecasting can contribute to diverse applications for catchment sustainability and management. Dew point temperature (Tdew) is one of the complex hydrological processes that highly essential to be quantified accurately for several catchment activities such as crops, agriculture, and others. In this study, three types of models’ recursive strategy, direct strategy, and DirRec which is the combination of recursive and direct strategies were adopted to obtain h-steps ahead predictions of Tdew. Ten years monthly scale dataset of Tdew at two meteorological stations (Beach and Cavalier) located at the North Dakota, USA, were used for the modeling development. The performance of the considered models was compared with two benchmark models: autoregressive moving average (ARIMA) and exponential smoothing (ETS). Modeling results indicated that, compared with the benchmark models, the proposed methods gave good results for the multi-ahead forecasting. For instance, for Cavalier station, the root mean squared prediction errors obtained from the proposed and benchmark methods when the forecast horizon is 12 are as follows: recursive strategy (RMSPE = 3.731) direct strategy (RMSPE = 3.385), DirRec (RMSPE = 3.141), ARIMA (RMSPE = 12.957), and ETS (RMSPE = 27.479).

CIDO ontology updates and secondary analysis of host responses to COVID-19 infection based on ImmPort reports and literature

BackgroundWith COVID-19 still in its pandemic stage, extensive research has generated increasing amounts of data and knowledge. As many studies are published within a short span of time, we often lose an integrative and comprehensive picture of host-coronavirus interaction (HCI) mechanisms. As of early April 2021, the ImmPort database has stored 7 studies (with 6 having details) that cover topics including molecular immune signatures, epitopes, and sex differences in terms of mortality in COVID-19 patients. The Coronavirus Infectious Disease Ontology (CIDO) represents basic HCI information. We hypothesize that the CIDO can be used as the platform to represent newly recorded information from ImmPort leading the reinforcement of CIDO.MethodsThe CIDO was used as the semantic platform for logically modeling and representing newly identified knowledge reported in the 6 ImmPort studies. A recursive eXtensible Ontology Development (XOD) strategy was established to support the CIDO representation and enhancement. Secondary data analysis was also performed to analyze different aspects of the HCI from these ImmPort studies and other related literature reports.ResultsThe topics covered by the 6 ImmPort papers were identified to overlap with existing CIDO representation. SARS-CoV-2 viral S protein related HCI knowledge was emphasized for CIDO modeling, including its binding with ACE2, mutations causing different variants, and epitope homology by comparison with other coronavirus S proteins. Different types of cytokine signatures were also identified and added to CIDO. Our secondary analysis of two cohort COVID-19 studies with cytokine panel detection found that a total of 11 cytokines were up-regulated in female patients after infection and 8 cytokines in male patients. These sex-specific gene responses were newly modeled and represented in CIDO. A new DL query was generated to demonstrate the benefits of such integrative ontology representation. Furthermore, IL-10 signaling pathway was found to be statistically significant for both male patients and female patients.ConclusionUsing the recursive XOD strategy, six new ImmPort COVID-19 studies were systematically reviewed, the results were modeled and represented in CIDO, leading to the enhancement of CIDO. The enhanced ontology and further seconary analysis supported more comprehensive understanding of the molecular mechanism of host responses to COVID-19 infection.

Ensemble-based approach for semisupervised learning in remote sensing

Semisupervised learning (SSL) techniques explore the progressive discovery of the hidden latent data structure by propagating supervised information on unlabeled data, which are thereafter used to reinforce learning. These schemes are beneficial in remote sensing, where thousands of new images are added every day, and manual labeling results are prohibitive. Our work introduces an ensemble-based semisupervised deep learning approach that initially takes a subset of labeled data Dl, which represents the latent structure of the data and progressively propagates labels automatically from an expanding set of unlabeled data Du. The ensemble is a set of classifiers whose predictions are collated to derive a consolidated prediction. Only those data having a high-confidence prediction are considered as newly generated labels. The proposed approach was exhaustively validated on four public datasets, achieving appreciable results compared to the state-of-the-art methods in most of the evaluated configurations. For all datasets, the proposed approach achieved a classification F1-score and recall of up to 90%, on average. The SSL and recursive scheme also demonstrated an average gain of ∼2 % at the last training stage in such large datasets.

Symmetries in porous flows: recursive solutions of the Brinkman equation in polygonal ducts

In this paper, we solve the Brinkman equation for unidirectional, steady, incompressible and Newtonian flow through a duct of uniform cross-section in the shape of a regular N-gon under no-slip boundary condition on the surface of the duct in the absence of applied forces. We calculate solutions for small values of N and by analysing them we devise a recursive scheme of generating solutions for all . We obtain approximate expressions for the vortex lines for all values of N by applying a trigonometric perturbation on circular vortex lines and graphically compare them with exact vortex lines. We also graphically compare both exact and approximate vortex lines with Schwarz-Christoffel transformation.

Reversible Stepwise Condensation Polymerization with Cyclization: Strictly Alternating Co-polymerization and Homopolymerization Based upon Two Orthogonal Reactions

In a preceding work [M. Lang, K. Kumar, A simple and general approach for reversible condensation polymerization with cyclization, Macromolecules 54 (2021) 7021], we have introduced a simple recursive scheme that allows to treat stepwise linear reversible polymerizations of any kind with cyclization. This approach is used to discuss the polymerization of linear Gaussian strands (LGS) with two different reactive groups $A$ and $B$ on either chain end that participate in two orthogonal reactions and the strictly alternating copolymerization of LGS that carry $A$ reactive groups with LGS equipped with type $B$ reactive groups. The former of these cases has not been discussed theoretically in literature, the latter only regarding some special cases. We provide either analytical expressions or exact numerical solutions for the general cases with and without cyclization. Weight distributions, averages, polydispersity, and the weight fractions of cyclic and linear species are computed. All numerical solutions were tested by Monte-Carlo simulations.

Performance analysis of LSTM model with multi-step ahead strategies for a short-term traffic flow prediction

In this study, the effect of direct and recursive multi-step forecasting strategies on the short-term traffic flow forecast performance of the Long Short-Term Memory (LSTM) model is investigated. To increase the reliability of the results, analyses are carried out with various traffic flow data sets. In addition, databases are clustered using the k-means++ algorithm to reduce the number of experiments. Analyses are performed for different time periods. Thus, the contribution of strategies to LSTM was examined in detail. The results of the recursive based strategy performances are not satisfactory. However, different versions of the direct strategy performed better at different time periods. This research makes an important contribution to clarifying the compatibility of LSTM and forecasting strategies. Thus, more efficient traffic flow prediction models will be developed and systems such as Intelligent Transportation System (ITS) will work more efficiently. A practical implication for researchers that forecasting strategies should be selected based on time periods.