Series Of Transformations Research Articles

Toward Precise Localization of Abnormal Brain Activity: 1D CNN on Single Voxel fMRI Time-Series.

Functional magnetic resonance imaging (fMRI) is one of the best techniques for precise localization of abnormal brain activity non-invasively. Machine-learning approaches have been widely used in neuroimaging studies; however, few studies have investigated the single-voxel modeling of fMRI data under cognitive tasks. We proposed a hybrid one-dimensional (1D) convolutional neural network (1D-CNN) based on the temporal dynamics of single-voxel fMRI time-series and successfully differentiated two continuous task states, namely, self-initiated (SI) and visually guided (VG) motor tasks. First, 25 activation peaks were identified from the contrast maps of SI and VG tasks in a blocked design. Then, the fMRI time-series of each peak voxel was transformed into a temporal-frequency domain by using continuous wavelet transform across a broader frequency range (0.003–0.313 Hz, with a step of 0.01 Hz). The transformed time-series was inputted into a 1D-CNN model for the binary classification of SI and VG continuous tasks. Compared with the univariate analysis, e.g., amplitude of low-frequency fluctuation (ALFF) at each frequency band, including, wavelet-ALFF, the 1D-CNN model highly outperformed wavelet-ALFF, with more efficient decoding models [46% of 800 models showing area under the curve (AUC) > 0.61] and higher decoding accuracies (94% of the efficient models), especially on the high-frequency bands (>0.1 Hz). Moreover, our results also demonstrated the advantages of wavelet decompositions over the original fMRI series by showing higher decoding performance on all peak voxels. Overall, this study suggests a great potential of single-voxel analysis using 1D-CNN and wavelet transformation of fMRI series with continuous, naturalistic, steady-state task design or resting-state design. It opens new avenues to precise localization of abnormal brain activity and fMRI-guided precision brain stimulation therapy.

A Time Series Transformer based method for the rotating machinery fault diagnosis

Fault diagnosis of rotating machinery is a significant engineering problem. In recent years, fault diagnosis methods have matured based on the Convolutional Neural Network (CNN) and Recurrent Neural Network (RNN). However, these traditional models have the problem of Long-Term Dependencies, leading to their feature extraction ability defect. To address these issues, we proposed a new method based on the Time Series Transformer (TST) to recognize the fault modes of the various rotating machinery. In this paper, firstly, we design a new tokens sequences generation method that can handle data in 1D format, namely time series tokenizer. Then the TST combining time series tokenizer and Transformer is presented. The test results on the given datasets show that the proposed method has better fault identification capability than traditional CNN and RNN models. Secondly, the effect of structural hyperparameters on fault diagnosis performance, computational complexity, and parameters number of the TST is analyzed in detail through experiments. The influence laws of some hyperparameters are obtained as well. Finally, the feature vectors in the embedding space are visualized via the t-Distributed Stochastic Neighbor Embedding (t-SNE) dimensionality reduction method. On this basis, the working pattern of TST is explained to a certain extent. Moreover, we find that the feature vectors extracted by the proposed method show the best intra-class compactness and inter-class separability compared with CNN and RNN models by analyzing their distribution form, which further demonstrates the effectiveness of the proposed method.

Bm$(1-xy,y-x)$-expansion formula and its applications

In this paper, we first show a $(1-xy,y-x)$-expansion formula for an arbitrary analytic function $F(x)$ with respect to the basis <disp-formula><tex-math><![CDATA[$$\bigg\{\prod_{k=0}^{n-1}\frac{x-b_k}{1-x_kx}\,\bigg|\, n\geq 0\bigg\},$$]]></tex-math></disp-formula> which is mainly based on the $(f,g)$-inversion formula. Subsequently, by specializing $F(x)$, $x_n$ and $b_n$, we not only find the corresponding proofs of many classical results such as the Rogers-Fine identity, Andrews' four parametric reciprocal theorem, and Ramanujan's ${~}_1\psi_1$ summation formula, but also construct a lot of $q$-series transformations and summation formulas, including a generalization of Andrews' WP Bailey lemma.

Interpretable wind speed prediction with multivariate time series and temporal fusion transformers

Wind power has been utilized well in power systems, so steady and successful wind speed forecasting is crucial to security management power grid market economy. To date, most researchers have often discounted the interpretability of prediction models, leading to obscure forecasts. This study puts forward a unique forecasting methodology that incorporates notable decomposition techniques, multifactor interpretable forecasting models, and optimization algorithms. In the proposed model, variational mode decomposition is employed to break down the raw wind speed sequence into a set of intrinsic mode functions. Adaptive differential evolution is then used for optimizing several parameters of temporal fusion transformers (TFT) to achieve satisfactory forecasting performance. TFT is a new attention-based deep learning model that puts together high-performance multi-horizon prediction and interpretable insights into temporal dynamics. Empirical studies using eight real-world 1-h wind speed data sets in Albert, Canada, and Five Points, USA demonstrate that the system using the proposed model outperforms those employing other comparable models in nearly all performance metrics. Examples of TFT's interpretable outputs are the importance ranking of the decomposed wind speed sub-sequences and meteorological data and attention analysis of different step lengths. The findings signify substantial progress for wind speed prediction and aid policymakers.

Causal treatment effects in time series: CO2 emissions and energy consumption effect on GDP

This study broadens the research on the use of neural networks in conjunction with causality techniques for economic policy development. Empirical evidence is presented on the effects of energy consumption and carbon emissions on per capita economic growth with unbalanced panel data for 94 countries between 1971 and 2018. We present a methodological framework that employs the transformation of time series into a set of treatment intervals according to potential policies that a country may adopt. Based on treatment intervals, a two-stage model based on recurrent neural networks (Long Short-Term Memory) is proposed together with a multiclass classifier to obtain propensity scores. We then estimate the effects using the dynamic potential outcomes under a framework of treatment-based causality. The results indicate that for both energy consumption and carbon emissions policies, the treatment range that generates the best performance is between −2% and 0.4%; moreover, in both cases, extreme policies such as drastically reducing or increasing energy consumption generates the worst results for economic development. We find that when grouping countries according to income level, mid-low and low levels of income have better development under moderate growth policy with respect to levels of carbon emissions and energy consumption, supporting the Environmental Kuznets Curve hypothesis. This finding could be related to the fact that these countries do not have the level of infrastructure to sustain growth. However, the impact of this growth on pollution would not be comparable to the reduction effect of high-income countries, given that they make the largest overall contribution to global emissions.

Analytic Solvability of the H¨ormander Problem and the Borel Transformation of Multiple Laurent Series

In this paper, the initial-boundary value problem of Hormander is formulated in the class of functions representable by Laurent series supported in rational cones. Using the Borel transformation of Laurent series we establish a connection between a differential and a difference problems and prove its global analytic solvability

Predicting Thailand Electricity Load Demand with Modified Fourier Series and Seasonal-Trend Decomposition Methods Using LOESS Transformation

Accurate long-term and midterm electricity load forecasting play an essential role in electric power system planning. Drawing on the seasonal-trend forecasting capacity of Fourier series and LOESS transformation, this paper applies modified Fourier series transformation (MFST) and modified seasonal-trend decomposition using LOESS transformation (MSTLT) to electricity load forecasting and compares the performance of two alternative models: the ARIMA(p,d,q) SARIMA(P,D,Q) model and the support vector regression (SVR) model. The data comprise monthly electricity consumption volumes between 2002 and 2019. The data between 2002 and 2018 are utilized to construct the forecasting model, while those in 2019 are employed to test the accuracy of the predicted values. The results confirm the validity of the proposed model in terms of forecasting accuracy and interpretability.

Analysis and Simulation of a Typical Two Winding Transformer

In this study, we show how input power, terminal voltage, and efficiency changes as a function of load current. In this situation, we've chosen three scenarios they are- Coil connection in Parallel Coil connection in Series Two Winding Transformer Here, we have connected the coils of a single-phase transformer in series and parallel, then observed the transformer's loading as an autotransformer and as a two-winding transformer. It is essential to comprehend the instant polarities of the secondary terminals in relation to the primary in order to properly connect the winding.

In-Field Detection of American Foulbrood (AFB) by Electric Nose Using Classical Classification Techniques and Sequential Neural Networks.

American foulbrood is a dangerous bee disease that attacks the sealed brood. It quickly leads to the death of bee colonies. Efficient diagnosis of this disease is essential. As specific odours are produced when larvae rot, it was investigated whether an electronic nose can distinguish between colonies affected by American foulbrood and healthy ones. The experiment was conducted in an apiary with 18 bee families, 9 of which showed symptoms of the disease confirmed by laboratory diagnostics. Three units of the Beesensor V.2 device based on an array of six semiconductor TGS gas sensors, manufactured by Figaro, were tested. Each copy of the device was tested in all bee colonies: sick and healthy. The measurement session per bee colony lasted 40 min and yielded results from four 10 min measurements. One 10-min measurement consisted of a 5 min regeneration phase and a 5 min object-measurement phase. For the experiments, we used both classical classification methods such as k-nearest neighbour, Naive Bayes, Support Vector Machine, discretized logistic regression, random forests, and committee of classifiers, that is, methods based on extracted representative data fragments. We also used methods based on the entire 600 s series, in this study of sequential neural networks. We considered, in this study, six options for data preparation as part of the transformation of data series into representative results. Among others, we used single stabilised sensor readings as well as average values from stable areas. For verifying the quality of the classical classifiers, we used the 25-fold train-and-test method. The effectiveness of the tested methods reached a threshold of 75 per cent, with results stable between 65 and 70 per cent. As an element to confirm the possibility of class separation using an artificial nose, we used applied visualisations of classes. It is clear from the experiments conducted that the artificial nose tested has practical potential. Our experiments show that the approach to the problem under study by sequential network learning on a sequence of data is comparable to the best classical methods based on discrete data samples. The results of the experiment showed that the Beesensor V.2 along with properly selected classification techniques can become a tool to facilitate rapid diagnosis of American foulbrood under field conditions.

Quadruple-active-bridge based unified power quality conditioner-L with fault current limiting capability

This study presents a quadruple-active-bridge (QAB) based unified power quality conditioner (UPQC) to improve the power quality and limit the fault currents simultaneously. Compared with conventional UPQC-L, the proposed UPQC-L-QAB has a better performance because the effect on the series transformers caused by the nonlinear load is suppressed. Since the series converter is located at load side of the UPQC-L-QAB, it could also function as a fault current limiter (FCL) by being controlled as a controllable current source. Model predictive control schemes are proposed to control the series converter and shunt converter, which are convenient for smooth mode switching between UPQC and FCL modes. Finally, the simulation and experimental results (OPAL-RT) verify the effectiveness of the proposed topology and control scheme.

2-adic morphogenesis as a metaphorical model of biological growth

The article proposes a mathematical model of morphogenesis which is based on 2-adic arithmetic. In this model, the process of morphogenesis is separated from its genetic coding and genetic control, and is considered abstractly as a transformation of complex biomorphic structures resulting from the process of sequential geometric cell division. The concept of cellular structure is introduced and the analogies that exist between the transformation of organisms and the transformation of the corresponding cellular structures generated by numerical series are considered, in particular, an analogy is drawn between the transformation of series depending on a complex parameter and the growth of biological organisms. The article also introduces some mathematical formalism used to compare different morphological pathways.

Quantum q-series identities

As analytic statements, classical $q$-series identities are equalities between power series for $|q|&lt;1$. This paper concerns a different kind of identity, which we call a quantum $q$-series identity. By a quantum $q$-series identity we mean an identity which does not hold as an equality between power series inside the unit disk in the classical sense, but does hold on a dense subset of the boundary -- namely, at roots of unity. Prototypical examples were given over thirty years ago by Cohen and more recently by Bryson-Ono-Pitman-Rhoades and Folsom-Ki-Vu-Yang. We show how these and numerous other quantum $q$-series identities can all be easily deduced from one simple classical $q$-series transformation. We then use other results from the theory of $q$-hypergeometric series to find many more such identities. Some of these involve Ramanujan's false theta functions and/or mock theta functions.

A finite-discrete element based appoach for modelling the hydraulic fracturing of rocks with irregular inclusions

A systematic hybrid approach for modelling the hydraulic fracturing process of heterogeneous rocks with irregular inclusions is developed. This approach is based on a series of computational algorithms, including Fourier series transformation, level-set-based overlapping detection, and the finite-discrete element method. Three major steps are included: (1) circular parameterization and Fourier transformation are employed to reproduce realistic inclusion contours with arbitrary irregular shapes; (2) a novel overlapping detection method based on a level-set function is employed to allocate irregular inclusions effectively and efficiently; and (3) the finite-discrete element model is established by integrating cohesive elements with pore pressure nodes into the solid mesh to simulate the progressive hydraulic fracture and interface crack of heterogeneous rocks. To validate the proposed hybrid approach, modelling results by the established model are compared with numerical simulations in the literature. In addition, the influences of injection speed and interface strength on the mechanical and fracturing responses of heterogeneous rocks are discussed. The results demonstrate that the proposed hybrid approach is capable of simulating the hydraulic fracturing process of heterogeneous rocks.

ANDREWS’ TYPE WP-BAILEY LEMMA AND ITS APPLICATIONS

ver the years, the study of Bailey transform, Bailey lemma, Bailey pair, their variants and their applications are the major subjects of interest. Of course, it is due to the efficiency of the Bailey transform and lemma in producing many ordinary and q-hypergeometric identities, multiple series summation and transformation formulas, and the Rogers-Ramanujan type identities. Andrews investigated a WP-Bailey lemma and the pairs with the help of Bailey transform and used it to derive well-known summations and multiple series transformations. In this research paper, we investigate an Andrews’ type WP-Bailey lemma and the pairs with the help of First Bailey Type Transform due to Joshi and Vyas. The investigated Andrews’ type WP-Bailey lemma is then applied to obtain terminating multiple q-hypergeometric identities and construct the WP-Bailey type chains and a binary tree. The paper is motivated by the observation that the basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) gamma and q-hypergeometric functions and basic (or q-) hypergeometric polynomials, are applicable particularly in several diverse areas including number theory, theory of partitions and combinatorial analysis as well as in the study of combinatorial generating functions.

New double-sum expansions for certain Mock theta functions

&lt;abstract&gt;&lt;p&gt;The study of expansions of certain mock theta functions in special functions theory has a long and quite significant history. Motivated by recent correlations between $ q $-series and mock theta functions, we establish a new $ q $-series transformation formula and derive the double-sum expansions for mock theta functions. As an application, we state new double-sum representations for certain mock theta functions.&lt;/p&gt;&lt;/abstract&gt;

Driver Steering Behaviour Modelling Based on Neuromuscular Dynamics and Multi Task Time Series Transformer

Driver Steering Behaviour Modelling Based on Neuromuscular Dynamics and Multi Task Time Series Transformer

Fault identification scheme for UPFC compensated transmission line based on characteristic voltage active injection

When a fault occurs at Unified Power Flow Controller (UPFC) compensated transmission line, the traditional auto reclosing scheme cannot identify the fault characteristics, and thus reclosing on a permanent fault would cause the second strike on the power system within a short period. To solve this problem, this paper proposes a fault identification scheme based on the active injection of the characteristic voltage by the control of UPFC. Firstly, after the circuit breakers on both sides of the faulty line have tripped, the converter on the series side of the UPFC is switched to the additional control mode. Then, the characteristic voltage is actively injected into the faulty line through the series transformer. Based on the active injection, the fault characteristics can be identified through the difference of characteristic voltages and currents under different faults. Therefore, this scheme could prevent the circuit breaker from reclosing on permanent faults and thus enhance the stability and safety of the system. Finally, the simulation results in PSCAD/EMTDC verify the robustness and effectiveness of the proposed scheme.

An air insulated linear pulse transformer for electrodischarge technology

A linear pulse transformer with air insulation at atmospheric pressure was created and tested under both constant resistance and non linear loads. The maximum power of the transformer output pulse reached ∼500 MW at a matched load with a charge voltage 50 kV. The transformer transferred ∼60% of the stored energy to the load over a characteristic time of about 1 μs. The scalability the generator was studied by connecting two identical transformers in series which gave a power output of ∼850 MW with doubled output voltage and reduced current. The frequency mode of operation was studied using one and two transformers with a charge voltage of 50 kV and a load that was, close to matched. In both cases, the power maximum and jitter showed no significant changes at any of the frequencies tested (up to 5 Hz). These results mean that the use of this generator can be recommended for a wide field of applications due to its scalability and low internal impedance.

Research on Time Series Anomaly Detection: Based on Deep Learning Methods

Time series anomaly detection has always been an important research direction. The early time series anomaly detection methods are mainly statistical methods and machine learning methods. With the powerful functions of deep neural network being continuously mined by researchers, the effect of deep neural network in anomaly detection task has been significantly better than the traditional methods. In view of the continuous development and application of deep neural networks such as transformer and graph neural network (GNN) in time series anomaly detection in recent years, the body of research lacks a comparative evaluation of deep learning methods in recent years. This paper studies various deep neural networks suitable for time series, which are divided into three categories according to anomaly detection methods. The evaluation is conducted on public datasets. By analyzing the evaluation criteria, this paper discusses the performance of each model, as well as the problems and development direction in the field of time series anomaly detection in the future. This study found that in the time series anomaly detection task, transformer is suitable for dealing with long-time series prediction, and studying the graph structure of time series may be the best way to deal with time series anomaly detection in the future

Normal forms and near-axis expansions for Beltrami magnetic fields

A formal series transformation to Birkhoff–Gustavson normal form is obtained for toroidal magnetic field configurations in the neighborhood of a magnetic axis. Bishop's rotation minimizing coordinates are used to obtain a local orthogonal frame near the axis in which the metric is diagonal, even if the curvature has zeros. We treat the cases of vacuum and force-free (Beltrami) fields in a unified way, noting that the vector potential is essentially the Poincaré–Liouville one-form of Hamiltonian dynamics, and the resulting magnetic field corresponds to the canonical two-form of a non-autonomous one-degree-of-freedom system. Canonical coordinates are obtained and Floquet theory is used to transform to a frame in which the lowest order Hamiltonian is autonomous. The resulting magnetic axis can be elliptic or hyperbolic, and resonant elliptic cases are treated. The resulting expansion for the field is shown to be well-defined to all orders, and is explicitly computed to degree four. An example is given for an axis with constant torsion near a 1:3 resonance.