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Autonomous Environment-Monitoring Networks

Autonomous environment-monitoring networks (AEMNs) are artificial neural networks that are specialized for recognizing familiarity and, conversely, novelty. Like a biological neural network, an AEMN receives a constant stream of inputs. For purposes of computational implementation, the inputs are vector representations of the information of interest. As long as the most recent input vector is similar to the previous input vectors, no action is taken. Action is taken only when a novel vector is encountered. Whether a given input vector is regarded as novel depends on the previous vectors; hence, the same input vector could be regarded as familiar or novel, depending on the context of previous input vectors. AEMNs have been proposed as means to enable exploratory robots on remote planets to recognize novel features that could merit closer scientific attention. AEMNs could also be useful for processing data from medical instrumentation for automated monitoring or diagnosis. The primary substructure of an AEMN is called a spindle. In its simplest form, a spindle consists of a central vector (C), a scalar (r), and algorithms for changing C and r. The vector C is constructed from all the vectors in a given continuous stream of inputs, such that it is minimally distant from those vectors. The scalar r is the distance between C and the most remote vector in the same set. The construction of a spindle involves four vital parameters: setup size, spindle-population size, and the radii of two novelty boundaries. The setup size is the number of vectors that are taken into account before computing C. The spindle-population size is the total number of input vectors used in constructing the spindle counting both those that arrive before and those that arrive after the computation of C. The novelty-boundary radii are distances from C that partition the neighborhood around C into three concentric regions (see Figure 1). During construction of the spindle, the changing spindle radius is denoted by h. It is the final value of h, reached before beginning construction on the next spindle, that is denoted by r. During construction of a spindle, if a new vector falls between C and the inner boundary, the vector is regarded as completely familiar and no action is taken. If the new vector falls into the region between the inner and outer boundaries, it is considered unusual enough to warrant the adjustment of C and r by use of the aforementioned algorithms, but not unusual enough to be considered novel. If a vector falls outside the outer boundary, it is considered novel, in which case one of several appropriate responses could be initiation of construction of a new spindle.

Hand, Charles↗

High-performance ultra-low power VLSI analog processor for data compression

An apparatus for data compression employing a parallel analog processor. The apparatus includes an array of processor cells with N columns and M rows wherein the processor cells have an input device, memory device, and processor device. The input device is used for inputting a series of input vectors. Each input vector is simultaneously input into each column of the array of processor cells in a pre-determined sequential order. An input vector is made up of M components, ones of which are input into ones of M processor cells making up a column of the array. The memory device is used for providing ones of M components of a codebook vector to ones of the processor cells making up a column of the array. A different codebook vector is provided to each of the N columns of the array. The processor device is used for simultaneously comparing the components of each input vector to corresponding components of each codebook vector, and for outputting a signal representative of the closeness between the compared vector components. A combination device is used to combine the signal output from each processor cell in each column of the array and to output a combined signal. A closeness determination device is then used for determining which codebook vector is closest to an input vector from the combined signals, and for outputting a codebook vector index indicating which of the N codebook vectors was the closest to each input vector input into the array.

Tawel, Raoul↗

Choice of gauge in 2-photon 1s-2s transition in atomic hydrogen and pseudostate expansions

The problem of gauge choice in multiphoton transitions in connection with the proper choice of the unperturbed wave functions require to insure gauge invariance was considered. J. Bassani, J. J. Forney, and A. Quattropani considered the case of 2-photon 1s-2s transition rate for hydrogen, using gauges vector E x vector r and vector A x vector p. Exactly the same results were obtained for the two gauges, but the findings indicate that the vector E x vector r interaction tends to the final result with a small number of intermediate states and is therefore the one to be used in any approximate calculation. Whether the so-called pseudostate expansion method works equally well with either gauge was tested. To accomplish this task, in addition to researching the problem, the FORTRAN programming was learned and a FORTRAN program was constructed for the calculation of the dimensionless 2-photon transition probability amplitude D(v) for 1s-2s transition in Hydrogen as a function as a function of the incident photon frequency v in gauge vector E x vector p at certain values of v, using the pseudostate method. However, some puzzling unresolved difficulties were experienced in the calculation. Then should the pseudostate calculations prove successful for gauge vector E x vector r the method will be applied to gauge vector A x vector p. If successful, then the problem is complete.

Shabazz, Abdulalim A.↗

Optical implementation of inner product neural associative memory

An optical implementation of an inner-product neural associative memory is realized with a first spatial light modulator for entering an initial two-dimensional N-tuple vector and for entering a thresholded output vector image after each iteration until convergence is reached, and a second spatial light modulator for entering M weighted vectors of inner-product scalars multiplied with each of the M stored vectors, where the inner-product scalars are produced by multiplication of the initial input vector in the first iterative cycle (and thresholded vectors in subsequent iterative cycles) with each of the M stored vectors, and the weighted vectors are produced by multiplication of the scalars with corresponding ones of the stored vectors. A Hughes liquid crystal light valve is used for the dual function of summing the weighted vectors and thresholding the sum vector. The thresholded vector is then entered through the first spatial light modulator for reiteration of the process cycle until convergence is reached.

Liu, Hua-Kuang↗

Optimization methods, flux conserving methods for steady state Navier-Stokes equation

Navier-Stokes equation as discretized by new flux conserving method proposed by Chang and Scott results in the system: vector F(vector x) = 0, where F is a vector valued function. The Optimization method we use is based on Quasi-Newton methods: given a nonlinear function vector F(vector x) = 0, we solve, Delta(vector x) = -BF(vector x), where Delta(vector x) is the correction term and B is the inverse Jacobian of F(x). Then, iteratively, vector(x(sub (i+1))) = vector(x (sub i)) + alpha.Delta(vector x(sub i)), where alpha is a line search correction term determined by a line search routine. We use the BFCG's update the Jacobian matrix B(sub k) at each iteration. It is well known that B(sub k) approaches B(*) at the solution X(*). This algorithm has several advantages over the Newton-Raphson method. For example, we do not need to calculate the Jacobian matrix at each iteration which is computationally very expensive.

Adeyeye, John↗

Definition of Contravariant Velocity Components

In this paper we have reviewed the basics of tensor analysis in an attempt to clarify some misconceptions regarding contravariant and covariant vector components as used in fluid dynamics. We have indicated that contravariant components are components of a given vector expressed as a unique combination of the covariant base vector system and, vice versa, that the covariant components are components of a vector expressed with the contravariant base vector system. Mathematically, expressing a vector with a combination of base vector is a decomposition process for a specific base vector system. Hence, the contravariant velocity components are decomposed components of velocity vector along the directions of coordinate lines, with respect to the covariant base vector system. However, the contravariant (and covariant) components are not physical quantities. Their magnitudes and dimensions are controlled by their corresponding covariant (and contravariant) base vectors.

Hung, Ching-moa↗

Viral‐mediated delivery of morphogenic regulators enables leaf transformation in Sorghum bicolor (L.)

Recent advancements in monocot transformation, using leaf tissue as explant material, have expanded the number of grass species capable of transgenesis. However, the complexity of vectors and reliance on inducible excision of essential morphogenic regulators have so far limited widespread application. Plant RNA viruses, such as Foxtail Mosaic Virus (FoMV), present a unique opportunity to express morphogenic regulator genes, such as Babyboom (Bbm), Wuschel2 (Wus2), Wuschel-like homeobox protein 2a (Wox2a) and the GROWTH-REGULATING FACTOR 4 (GRF4) GRF-INTERACTING FACTOR 1 (GIF1) fusion protein transiently in leaf explant tissues. Furthermore, altruistic delivery of conventional and viral vectors could provide opportunities to simplify vectors used for leaf transformation—facilitating vector optimization and reducing reliance on morphogenic regulator gene integration. In this study, both viral and conventional T-DNA vectors were tested for their ability to promote the formation of embryonic calli, a critical step in leaf transformation protocols, using Sorghum bicolor leaf explants. Although conventional leaf transformation vectors yielded viable embryonic calli (43.2 ± 2.9%: GRF4-GIF1, 50.2 ± 3%: Bbm/Wus2), altruistic conventional vectors employing the GRF4-GIF1 morphogenic regulator resulted in improved efficiencies (61.3 ± 4.7%). Altruistic delivery was further enhanced with the use of viral vectors employing both GRF4-GIF1 and Bbm/Wus2 regulators, resulting in 75.1 ± 2.3% and 79.2 ± 2.5% embryonic calli formation, respectively. Embryonic calli generated from both conventional and viral vectors produced shoots expressing fluorescent reporters, which were confirmed using molecular analysis. This work provides an important proof-of-concept for the use of both altruistic vectors and viral-expressed morphogenic regulators for improving plant transformation.

59 BASIC BIOLOGICAL SCIENCES↗

Data for "Viral-mediated Delivery of Morphogenic Regulators Enables Leaf Transformation in Sorghum bicolor (L.)"

Recent advancements in monocot transformation, using leaf tissue as explant material, have expanded the number of grass species capable of transgenesis. However, the complexity of vectors and reliance on inducible excision of essential morphogenic regulators have so far limited widespread application. Plant RNA viruses, such as Foxtail Mosaic Virus (FoMV), present a unique opportunity to express morphogenic regulator genes, such as Babyboom ( Bbm ), Wuschel2 ( Wus2 ), Wuschel-like homeobox protein 2a ( Wox2a ) and the GROWTH-REGULATING FACTOR 4 (GRF4) GRF-INTERACTING FACTOR 1 (GIF1) fusion protein transiently in leaf explant tissues. Furthermore, altruistic delivery of conventional and viral vectors could provide opportunities to simplify vectors used for leaf transformation—facilitating vector optimization and reducing reliance on morphogenic regulator gene integration. In this study, both viral and conventional T-DNA vectors were tested for their ability to promote the formation of embryonic calli, a critical step in leaf transformation protocols, using Sorghum bicolor leaf explants. Although conventional leaf transformation vectors yielded viable embryonic calli (43.2 ± 2.9%: GRF4-GIF1, 50.2 ± 3%: Bbm/Wus2), altruistic conventional vectors employing the GRF4-GIF1 morphogenic regulator resulted in improved efficiencies (61.3 ± 4.7%). Altruistic delivery was further enhanced with the use of viral vectors employing both GRF4-GIF1 and Bbm/Wus2 regulators, resulting in 75.1 ± 2.3% and 79.2 ± 2.5% embryonic calli formation, respectively. Embryonic calli generated from both conventional and viral vectors produced shoots expressing fluorescent reporters, which were confirmed using molecular analysis. This work provides an important proof-of-concept for the use of both altruistic vectors and viral-expressed morphogenic regulators for improving plant transformation.

gene editing↗

A comparison of model-based VQ compression with other VQ approaches

In our previous work on Model-Based Vector Quantization (MVQ), we presented some performance comparisons (both rate distortion and decompression time) with VQ and JPEG/DCT. In this paper, we compare the MVQ's rate distortion performance with Mean Removed Vector Quantization (MRVQ) and include our previous comparison with VQ. MVQ is similar to MRVQ in many ways. Both of these techniques extract means of the vectors (raster-scanned image blocks) and reduce them to mean removed residuals by subtracting block means from the elements of the vectors. In the case of MRVQ, a codebook of residual vectors is generated using a training set. For every vector from the input image, the block mean and address of the codevector from the codebook that matches the input vector closest are transmitted to the decoder. The codebook is generated using generalized Lloyd algorithm on training set of residual vectors. For MVQ the pairs consist of vector means and address of the closest matching vector from codebook generated by models based on statistical properties of the residuals and Human Visual System (HVS). In our experiments, we found that MVQ performance in rate distortion sense is almost always better than VQ and is comparable to MRVQ. Further, MVQ is much easier to use than either VQ or MRVQ, since the training and managing of explicit codebooks is not required.

Manohar, Mareboyana↗

Method and System for Temporal Filtering in Video Compression Systems

Three related innovations combine improved non-linear motion estimation, video coding, and video compression. The first system comprises a method in which side information is generated using an adaptive, non-linear motion model. This method enables extrapolating and interpolating a visual signal, including determining the first motion vector between the first pixel position in a first image to a second pixel position in a second image; determining a second motion vector between the second pixel position in the second image and a third pixel position in a third image; determining a third motion vector between the first pixel position in the first image and the second pixel position in the second image, the second pixel position in the second image, and the third pixel position in the third image using a non-linear model; and determining a position of the fourth pixel in a fourth image based upon the third motion vector. For the video compression element, the video encoder has low computational complexity and high compression efficiency. The disclosed system comprises a video encoder and a decoder. The encoder converts the source frame into a space-frequency representation, estimates the conditional statistics of at least one vector of space-frequency coefficients with similar frequencies, and is conditioned on previously encoded data. It estimates an encoding rate based on the conditional statistics and applies a Slepian-Wolf code with the computed encoding rate. The method for decoding includes generating a side-information vector of frequency coefficients based on previously decoded source data and encoder statistics and previous reconstructions of the source frequency vector. It also performs Slepian-Wolf decoding of a source frequency vector based on the generated side-information and the Slepian-Wolf code bits. The video coding element includes receiving a first reference frame having a first pixel value at a first pixel position, a second reference frame having a second pixel value at a second pixel position, and a third reference frame having a third pixel value at a third pixel position. It determines a first motion vector between the first pixel position and the second pixel position, a second motion vector between the second pixel position and the third pixel position, and a fourth pixel value for a fourth frame based upon a linear or nonlinear combination of the first pixel value, the second pixel value, and the third pixel value. A stationary filtering process determines the estimated pixel values. The parameters of the filter may be predetermined constants.

Lu, Ligang↗

A comparison of model-based VQ compression with other VQ approaches

In our previous work on Model-Based Vector Quantization (MVQ), we presented some performance comparisons (both rate distortion and decompression time) with VQ and JPED/DCT. In this paper, we compare the MVQ's rate distortion performance with Mean Removed Vector Quantization (MRVQ) and include our previous comparison with VQ. Both MVQ and MRVQ compute the mean of each vector (raster-scanned image block) and produce mean removed residual vectors by subtracting the block mean from the elements of each vector. In the case of MRVQ, a codebook of residual vectors is generated using a training set. For MVQ, an internal codebook is generated based on the statistical properties of the residual vectors, and upon correlations derived from a Human Visual System (HVS) model. In both MVQ and MRVQ, the block mean and address of the codevector from the codebook that most closely matches each input vector are transmitted to the decoder. MVQ, a single additional statistical parameter is transmitted to the decoder. For MRVQ, we assume that the codebook of residual vectors is available to the decoder. In our experiments, we found that the rate of distortion performance of MVQ is almost always better than VQ, and is comparable to MRVQ. Further, MVQ is much easier to use than either VQ or MRVQ, since the training and management of codebooks is not required.

Manohar, Mareboyana↗

Imer-product array processor for retrieval of stored images represented by bipolar binary (+1,-1) pixels using partial input trinary pixels represented by (+1,-1)

An inner-product array processor is provided with thresholding of the inner product during each iteration to make more significant the inner product employed in estimating a vector to be used as the input vector for the next iteration. While stored vectors and estimated vectors are represented in bipolar binary (1,-1), only those elements of an initial partial input vector that are believed to be common with those of a stored vector are represented in bipolar binary; the remaining elements of a partial input vector are set to 0. This mode of representation, in which the known elements of a partial input vector are in bipolar binary form and the remaining elements are set equal to 0, is referred to as trinary representation. The initial inner products corresponding to the partial input vector will then be equal to the number of known elements. Inner-product thresholding is applied to accelerate convergence and to avoid convergence to a negative input product.

Liu, Hua-Kuang↗

Water Across Synthetic Aperture Radar Data (WASARD): SAR Water Body Classification for the Open Data Cube

The detection of inland water bodies from Synthetic Aperture Radar (SAR) data provides a great advantage over water detection with optical data, since SAR imaging is not impeded by cloud cover. Traditional methods of detecting water from SAR data involves using thresholding methods that can be labor intensive and imprecise. This paper describes Water Across Synthetic Aperture Radar Data (WASARD): a method of water detection from SAR data which automates and simplifies the thresholding process using machine learning on training data created from Geoscience Australia’s WOFS algorithm. Of the machine learning models tested, the Linear Support Vector Machine was determined to be optimal, with the option of training using solely the VH polarization or a combination of the VH and VV polarizations. WASARD was able to identify water in the target area with a correlation of 97% with WOFS. Sentinel-1, Open Data Cube, Earth Observations, Machine Learning, Water Detection 1. INTRODUCTION Water classification is an important function of Earth imaging satellites, as accurate remote classification of land and water can assist in land use analysis, flood prediction, climate change research, as well as a variety of agricultural applications [2]. The ability to identify bodies of water remotely via satellite is immensely cheaper than contracting surveys of the areas in question, meaning that an application that can accurately use satellite data towards this function can make valuable information available to nations which would not be able to afford it otherwise. Highly reliable applications for the remote detection of water currently exist for use with optical satellite data such as that provided by LANDSAT. One such application, Geoscience Australia’s Water Observations from Space (WOFS) has already been ported for use with the Open Data Cube [6]. However, water detection using optical data from Landsat is constrained by its relatively long revisit cycle of 16 days [5], and water detection using any optical data is constrained in that it lacks the ability to make accurate classifications through cloud cover [2]. The alternative solution which solves these problems is water detection using SAR data, which images the Earth using cloud-penetrating microwaves. Because of its advantages over optical data, much research has been done into water detection using SAR data. Traditionally, this has been done using the thresholding method, which involves picking a polarization band and labeling all pixels for which this band’s value is below a certain threshold as containing water. The thresholding method works since water tends to return a much lower backscatter value to the satellite than land [1]. However, this method can be flawed since estimating the proper threshold is often imprecise, complicated, and labor intensive for the end user. Thresholding also tends to use data from only one SAR polarization, when a combination of polarizations can provide insight into whether water is present. [2] In order to alleviate these problems, this paper presents an application for the Open Data Cube to detect water from SAR data using support vector machine (SVM) classification. 2. PLATFORM WASARD is an application for the Open Data Cube, a mechanism which provides a simple yet efficient means of ingesting, storing, and retrieving remote sensing data. Data can be ingested and made analysis ready according to whatever specifications the researcher chooses, and easily resampled to artificially alter a scene’s resolution. Currently WASARD supports water detection on scenes from ESA’s Sentinel-1 and JAXA’s ALOS. When testing WASARD, Sentinel-1 was most commonly used due to its relatively high spatial resolution and its rapid 6 day revisit cycle [5]. With minor alterations to the application's code, however, it could support data from other satellites. 3. METHODOLOGY Using supervised classification, WASARD compares SAR data to a dataset pre-classified by WOFS in order to train an SVM classifier. This classifier is then used to detect water in other SAR scenes outside the training set. Accuracy was measured according to the following metrics:  Precision: a measure of what percentage of the points WASARD labels as water are truly water  Recall: a measure of what percentage of the total water cover WASARD was able to identify.  F1 Score: a harmonic average of the precision and recall scores Both precision and recall are calculated at the end of the training phase, when the trained classifier is compared to a testing dataset. Because the WOFS algorithm’s classifications are used as the truth values when training a WASARD classifier, when precision and recall are mentioned in this paper, they are always with respect to the values produced by WOFS on a similar scene of Landsat data, which themselves have a classification accuracy of 97% [6]. Visual representations of water identified by WASARD in this paper were produced using the function wasard_plot(), which is included in WASARD. 3.1 Algorithm Selection The machine learning model used by WASARD is the Linear Support Vector Machine (SVM). This model uses a supervised learning algorithm to develop a classifier, meaning it creates a vector which can be multiplied by the vector formed by the relevant data bands to determine whether a pixel in a SAR scene contains water. This classifier is trained by comparing data points from selected bands in a SAR scene to their respective labels, which in this case are “water” or “not water” as given by the WOFS algorithm. The SVM was selected over the Random Forest model, which outperformed the SVM in training speed, but had a greater classification time and lower accuracy, and the Multilayer Perceptron Artificial Neural Network, which had a slightly higher average accuracy than the SVM, but much greater training and classification times. Figure 1: Visual representation of the SVM Classifier. Each white point represents a pixel in a SAR scene. In Figure 1, the diagonal line separating pixels determined to be water from those determined not to be water represents the actual classification vector produced by the SVM. It is worth noting that once the model has been trained, classification of pixels is done in a similar manner as in the thresholding method. This is especially true if only one band was used to train the model. 3.1 Feature Selection Sentinel-1 collects data from two bands: the Vertical/Vertical polarization (VV) and the Vertical/Horizontal polarization (VH). When 100 SVM classifiers were created for each polarization individually, and for the combination of the two, the following results were achieved: Figure 2: Accuracy of classifiers trained using different polarization bands. Precision and Recall were measured with respect to the values produced by WOFS. Figure 2 demonstrates that using both the VV and VH bands trades slightly lower recall for significantly greater precision when compared with the VH band alone, and that using the VV band alone is inferior in both metrics. WASARD therefore defaults to using both the VV and VH bands, and includes the option to use solely the VH band. The VV polarization’s lower precision compared to the VH polarization is in contrast to results from previous research and may merit further analysis [4]. 3.2 Training a Classifier The steps in training a classifier with WASARD are 1. Selecting two scenes (one SAR, one optical) with the same spatial extents, and acquired close to each other in time, with a preference that the scenes are taken on the same day. 2. Using the WOFS algorithm to produce an array of the detected water in the scene of optical data, to be used as the labels during supervised learning 3. Data points from the selected bands from the SAR acquisition are bundled together into an array with the corresponding labels gathered from WOFS. A random sample with an equal number of points labeled “Water” and “Not Water” is selected to be partitioned into a training and a testing dataset 4. Using Scikit-Learn’s LinearSVC object, the training dataset is used to produce a classifier, which is then tested against the testing dataset to determine its precision and recall The result is a wasard_classifier object, which has the following attributes: 1. f1, recall, and precision: 3 metrics used to determine the classifier’s accuracy 2. Coefficient: Vector which the SVM uses to make its predictions. The classifier detects water when the dot product of the coefficient and the vector formed by the SAR bands is positive 3. Save(): allows a user to save a classifier to the disk in order to use it without retraining 4. wasard_classify(): Classifies an entire xarray of SAR data using the SVM classifier All of the above steps are performed automatically when the user creates a wasard_classifier object. 3.3 Classifying a Dataset Once the classifier has been created, it can be used to detect water in an xarray of SAR data using wasard_classify(). By taking the dot product of the classifier’s coefficients and the vector formed by the selected bands of SAR data, an array of predictions is constructed. A classifier can effectively be used on the same spatial extents as the ones where it was trained, or on any area with a similar landscape. While

Kreiser, Zachary↗

Summer Internship Report: ARA2 Benchmarking

Over the past decade, the RISC-V Instruction Set Architecture (ISA) has emerged as a significant player in both academic and industrial processor design due to its open-source nature, modular extension system, and versatility across domains ranging from microcontrollers to high-performance computing (HPC). One of its most important recent advancements is the RISC-V Vector Extension (RVV), which enables explicit data-level parallelism through vector registers and vectorized instructions. Unlike traditional SIMD (Single Instruction, Multiple Data) architectures that fix vector lengths at design time, RVV uses the concept of VLEN (vector register length) as a hardware-independent parameter and allows software to adapt dynamically to the available vector width. This flexible approach ensures portability across implementations while enabling scalable performance. The ARA2 core is a parameterizable RISC-V vector processor developed at the Integrated Systems Lab at ETH Zürich and the University of Bologna. Designed as a tightly-coupled accelerator to a scalar RISC-V core, ARA2 implements the RVV 1.0 specification and offers tunable architectural parameters such as the number of vector lanes, VLEN, and cache sizes.

97 MATHEMATICS AND COMPUTING↗

Simplified model of statistically stationary spacecraft rotation and associated induced gravity environments

A stochastic model of spacecraft motion was developed based on the assumption that the net torque vector due to crew activity and rocket thruster firings is a statistically stationary Gaussian vector process. The process had zero ensemble mean value, and the components of the torque vector were mutually stochastically independent. The linearized rigid-body equations of motion were used to derive the autospectral density functions of the components of the spacecraft rotation vector. The cross-spectral density functions of the components of the rotation vector vanish for all frequencies so that the components of rotation were mutually stochastically independent. The autospectral and cross-spectral density functions of the induced gravity environment imparted to scientific apparatus rigidly attached to the spacecraft were calculated from the rotation rate spectral density functions via linearized inertial frame to body-fixed principal axis frame transformation formulae. The induced gravity process was a Gaussian one with zero mean value. Transformation formulae were used to rotate the principal axis body-fixed frame to which the rotation rate and induced gravity vector were referred to a body-fixed frame in which the components of the induced gravity vector were stochastically independent. Rice's theory of exceedances was used to calculate expected exceedance rates of the components of the rotation and induced gravity vector processes.

Fichtl, G. H.↗

Kinematic sensitivity of robot manipulators

Kinematic sensitivity vectors and matrices for open-loop, n degrees-of-freedom manipulators are derived. First-order sensitivity vectors are defined as partial derivatives of the manipulator's position and orientation with respect to its geometrical parameters. The four-parameter kinematic model is considered, as well as the five-parameter model in case of nominally parallel joint axes. Sensitivity vectors are expressed in terms of coordinate axes of manipulator frames. Second-order sensitivity vectors, the partial derivatives of first-order sensitivity vectors, are also considered. It is shown that second-order sensitivity vectors can be expressed as vector products of the first-order sensitivity vectors.

Vuskovic, Marko I.↗

Fast temporal neural learning using teacher forcing

A neural network is trained to output a time dependent target vector defined over a predetermined time interval in response to a time dependent input vector defined over the same time interval by applying corresponding elements of the error vector, or difference between the target vector and the actual neuron output vector, to the inputs of corresponding output neurons of the network as corrective feedback. This feedback decreases the error and quickens the learning process, so that a much smaller number of training cycles are required to complete the learning process. A conventional gradient descent algorithm is employed to update the neural network parameters at the end of the predetermined time interval. The foregoing process is repeated in repetitive cycles until the actual output vector corresponds to the target vector. In the preferred embodiment, as the overall error of the neural network output decreasing during successive training cycles, the portion of the error fed back to the output neurons is decreased accordingly, allowing the network to learn with greater freedom from teacher forcing as the network parameters converge to their optimum values. The invention may also be used to train a neural network with stationary training and target vectors.

Toomarian, Nikzad↗

Fast temporal neural learning using teacher forcing

A neural network is trained to output a time dependent target vector defined over a predetermined time interval in response to a time dependent input vector defined over the same time interval by applying corresponding elements of the error vector, or difference between the target vector and the actual neuron output vector, to the inputs of corresponding output neurons of the network as corrective feedback. This feedback decreases the error and quickens the learning process, so that a much smaller number of training cycles are required to complete the learning process. A conventional gradient descent algorithm is employed to update the neural network parameters at the end of the predetermined time interval. The foregoing process is repeated in repetitive cycles until the actual output vector corresponds to the target vector. In the preferred embodiment, as the overall error of the neural network output decreasing during successive training cycles, the portion of the error fed back to the output neurons is decreased accordingly, allowing the network to learn with greater freedom from teacher forcing as the network parameters converge to their optimum values. The invention may also be used to train a neural network with stationary training and target vectors.

Toomarian, Nikzad↗