Dot Product Research Articles

An Observer-Based View of Euclidean Geometry

An influence network of events is a view of the universe based on events that may be related to one another via influence. The network of events forms a partially ordered set which, when quantified consistently via a technique called chain projection, results in the emergence of spacetime and the Minkowski metric as well as the Lorentz transformation through changing an observer from one frame to another. Interestingly, using this approach, the motion of a free electron as well as the Dirac equation can be described. Indeed, the same approach can be employed to show how a discrete version of some of the features of Euclidean geometry including directions, dimensions, subspaces, Pythagorean theorem, and geometric shapes can emerge. In this paper, after reviewing the essentials of the influence network formalism, we build on some of our previous works to further develop aspects of Euclidean geometry. Specifically, we present the emergence of geometric shapes, a discrete version of the parallel postulate, the dot product, and the outer (wedge product) in 2+1 dimensions. Finally, we show that the scalar quantification of two concatenated orthogonal intervals exhibits features that are similar to those of the well-known concept of a geometric product in geometric Clifford algebras.

Deep spectral improvement for unsupervised image instance segmentation.

Recently, there has been growing interest in deep spectral methods for image localization and segmentation, influenced by traditional spectral segmentation approaches. These methods reframe the image decomposition process as a graph partitioning task by extracting features using self-supervised learning and utilizing the Laplacian of the affinity matrix to obtain eigensegments. However, instance segmentation has received less attention than other tasks within the context of deep spectral methods. This paper addresses that not all channels of the feature map extracted from a self-supervised backbone contain sufficient information for instance segmentation purposes. Some channels are noisy and hinder the accuracy of the task. To overcome this issue, this paper proposes two channel reduction modules, Noise Channel Reduction (NCR) and Deviation-based Channel Reduction (DCR). The NCR retains channels with lower entropy, as they are less likely to be noisy, while DCR prunes channels with low standard deviation, as they lack sufficient information for effective instance segmentation. Furthermore, the paper demonstrates that the dot product, commonly used in deep spectral methods, is not suitable for instance segmentation due to its sensitivity to feature map values, potentially leading to incorrect instance segments. A novel similarity metric called Bray-curtis over Chebyshev (BoC) is proposed to address this issue. This metric considers the distribution of features in addition to their values, providing a more robust similarity measure for instance segmentation. Quantitative and qualitative results on the Youtube-VIS 2019 and OVIS datasets highlight the improvements achieved by the proposed channel reduction methods and using BoC instead of the conventional dot product for creating the affinity matrix. These improvements regarding mean Intersection over Union (mIoU) and extracted instance segments are observed, demonstrating enhanced instance segmentation performance. The code is available on: https://github.com/farnooshar/SpecUnIIS.

Blue Laser for Production of Carbon Dots.

The synthesis of carbon dots (CDs) is gaining wide-ranging interest due to their broad applicability, owing to their small size and luminescence. CDs were prepared from charcoal via a one-step process using laser ablation in liquid without the use of reagents. The adopted method was based on the use of a commercially available continuous wave (CW) laser diode emitting a 450 nm wavelength and, for the liquid, a phosphate-buffered saline (PBS) solution, routinely used in the biological field. Photoluminescence analysis revealed fluorescence, at 480 nm, increasing with laser irradiation time. The atomic force microscopy (AFM) of the CDs revealed an average sphere shape with a size of about 10 nm. Biodegradable polycaprolactone (PCL), typically adopted in biomedicine applications, was used as a matrix to show the preserved luminescence, ideal for the non-invasive monitoring of implanted scaffolds in tissue engineering.

Kinematic modeling and control of orthogonal omnidirectional wheeled two-dimensional conveyor platform

This paper proposes an orthogonal omnidirectional wheeled two-dimensional conveyor platform and the inverse kinematic equations based on the cell model and the omnidirectional wheel model are derived, respectively. The two models use the way of the circumcircle of the cargo box and the dot product method to obtain the cell or omnidirectional wheel directly contacted under the cargo box, respectively. This paper uses YOLOV8_OBB and Strong SORT target tracking algorithms to assign tracking IDs to the cargo box and output the box position information. A feedback mechanism for faulty omnidirectional wheels or faulty cells is proposed, where the faulty area is classified as impassable during path planning and the A* path planning algorithm is used for path planning to avoid the faulty area. A visual feedback-based path tracking is adopted to enable timely correction when the cargo box deviates from the established path. The experimental results show that the omnidirectional wheel-based model improves the path-tracking accuracy by 44.52% and reduces the average power consumption by 2.6 times compared to the cell-based model.

A novel data-driven state evaluation approach for photovoltaic arrays in uncertain shading scenarios

Accurately determining the operating state of photovoltaic (PV) power-generation equipment and providing accurate support for maintenance management requires evaluation of the states of PV arrays under partial shading conditions. Results of such evaluation enable the optimization of maintenance measures to reduce maintenance costs and extend the lifespan of PV modules, thereby increasing the overall revenue of the PV power station. Therefore, this study proposes a novel state-evaluation approach based on current-voltage (I-V) curves under partial shading conditions. Based on the size of the pixel values in this curve, the proposed novel state-evaluation was performed using the proportion of the values of the normal and shaded curves under the same environmental conditions. Specifically, the feature variables (open-circuit voltage, short-circuit current) and pixel values within the I-V curve were analyzed and calculated using a sensitivity algorithm and computer vision algorithms (Canny edge-detection algorithm and Green's theorem). Based on the mapping relationship between feature variables and pixels, an improved Gaussian-process regression method with a combined kernel function (dot product and Matérn function) was proposed to predict the pixel values under the corresponding normal curve. This combined kernel function effectively captured causal relationships and handled outliers in the test dataset to improve the robustness of the model. Finally, the ratios of the pixel values were calculated using the predicted pixels within the normal curve and the calculated pixels within the shading curve. Experiments demonstrated that the root mean square error (RMSE), mean absolute error (MAE), R squared (R2) and log likelihood of the improved Gaussian-process regression method reached 0.011, 0.0086, 0.9996, and 24.7096, respectively.

Extraordinarily Time- and Memory-Efficient Large-Scale Canonical Correlation Analysis in Fourier Domain: From Shallow to Deep.

Canonical correlation analysis (CCA) is a correlation analysis technique that is widely used in statistics and the machine-learning community. However, the high complexity involved in the training process lays a heavy burden on the processing units and memory system, making CCA nearly impractical in large-scale data. To overcome this issue, a novel CCA method that tries to carry out analysis on the dataset in the Fourier domain is developed in this article. Appling Fourier transform on the data, we can convert the traditional eigenvector computation of CCA into finding some predefined discriminative Fourier bases that can be learned with only element-wise dot product and sum operations, without complex time-consuming calculations. As the eigenvalues come from the sum of individual sample products, they can be estimated in parallel. Besides, thanks to the data characteristic of pattern repeatability, the eigenvalues can be well estimated with partial samples. Accordingly, a progressive estimate scheme is proposed, in which the eigenvalues are estimated through feeding data batch by batch until the eigenvalues sequence is stable in order. As a result, the proposed method shows its characteristics of extraordinarily fast and memory efficiencies. Furthermore, we extend this idea to the nonlinear kernel and deep models and obtained satisfactory accuracy and extremely fast training time consumption as expected. An extensive discussion on the fast Fourier transform (FFT)-CCA is made in terms of time and memory efficiencies. Experimental results on several large-scale correlation datasets, such as MNIST8M, X-RAY MICROBEAM SPEECH, and Twitter Users Data, demonstrate the superiority of the proposed algorithm over state-of-the-art (SOTA) large-scale CCA methods, as our proposed method achieves almost same accuracy with the training time of our proposed method being 1000 times faster. This makes our proposed models best practice models for dealing with large-scale correlation datasets. The source code is available at https://github.com/Mrxuzhao/FFTCCA.

Microwave‐Assisted Synthesis Method for the Production of Carbon Nano Dots and Its Genotoxicity Assessment

Microwave‐Assisted Synthesis Method for the Production of Carbon Nano Dots and Its Genotoxicity Assessment

Lentil Extract-Mediated Ag QD Synthesis: Predilection for Albumin Protein Interaction, Antibacterial Activity, and Its Cytotoxicity for Wi-38 and PC-3 Cell Lines.

Recent focus has been directed toward semiconductor nanocrystals owing to their unique physicochemical properties. Nevertheless, the synthesis and characterization of quantum dots (QDs) pose considerable challenges, limiting our understanding of their interactions within a biological environment. This research offers valuable insights into the environmentally friendly production of silver quantum dots (Ag QDs) using lentil extract and clarifies their distinct physicochemical characteristics, previously unexplored to our knowledge. These findings pave the path for potential practical applications. The investigation of the phytochemical-assisted Ag QDs' affinity for BSA demonstrated modest interactions, as shown by the enthalpy and entropy changes as well as the associated Gibbs free energy during their association. Steady-state and time-resolved fluorescence spectroscopy further demonstrated a transient effect involving dynamic quenching, predominantly driven by Forster resonance energy transfer. Additionally, the study highlights the potential broad-spectrum antibacterial activity of Ag QDs (<5 nm, a zeta potential of -3.04 mV), exhibiting a remarkable MIC value of 1 μg/mL against Gram-negative bacteria (E. coli) and 1.65 μg/mL against Gram-positive bacteria (S. aureus). They can readily enter cells and tissues due to their minuscule size and the right chemical environment. They cause intracellular pathway disruption, which leads to cell death. This outcome emphasizes the distinctive biocompatibility of the green-synthesized Ag QDs, which has been confirmed by their MTT assay-based cytotoxicity against the PC-3 and Wi-38 cell lines.

Multiple-base Logarithmic Quantization and Application in Reduced Precision AI Computations

The power of logarithmic quantizations and computations has been recognized as a useful tool in optimizing the performance of large ML models. There are plenty of applications of ML techniques in digital preservation. The accuracy of computations may play a crucial role in the corresponding algorithms. In this article, we provide results that demonstrate significantly better quantization signal-to-noise ratio performance thanks to multiple-base logarithmic number systems (MDLNS) in comparison with the floating point quantizations that use the same number of bits. On a hardware level, we present details about our Xilinx VCU-128 FPGA design for dot product and matrix vector computations. The MDLNS matrix-vector design significantly outperforms equivalent fixed-point binary designs in terms of area (A) and time (T) complexity and power consumption as evidenced by a 4 × scaling of AT 2 metric for VLSI performance, and 57% increase in computational throughput per watt compared to fixed-point arithmetic.

Utilizing the 2nd harmonic Nd: YAG laser ablation in liquid for the production of copper oxide quantum dots: Influence of laser fluence and ablation duration

One environmentally friendly technique for creating colloids of nanoparticles is pulsed laser ablation in liquid, which stands out for its ability to create nanoparticles free of contamination without the use of hazardous chemicals. In the present work, A Q-Switched Nanosecond Nd: YAG laser was utilized to precisely produce colloidal copper oxide nanoparticles (CuONPs) through the laser ablation of a copper target immersed in distilled water. The impact of the laser fluence and laser ablation time on the size, morphology, and concentration of the generated CuONPs was investigated experimentally. The UV–visible absorption spectra of CuONPs display surface plasmonic resonance peaks in the UV region, which are attributed to interband transitions. The energy band gaps of the colloidal CuONPs were determined using UV–visible spectroscopy, and they ranged between 3.45 and 3.72 eV at various ablation times and laser fluences. The TEM micrographs were used to assess the size and morphology of the CuONPs, while the concentration and elemental composition were determined using ICP and EDXA spectroscopy. The TEM images of the CuONPs indicate a spherical shape at various laser ablation times and laser fluences. The average size of the CuONPs decreased to the quantum size range. The experimental results show that increasing laser fluence from 28.6 to 51.5 × 103 J/cm2 while keeping laser ablation time fixed for 30 min resulted in a reduction in the average size of the nanoparticles from 8.5 to 4.6 nm, respectively. Moreover, increasing laser ablation time from 10 to 50 min at a constant incident laser fluence of 34.3 × 103 J/cm2 decreased the average size of the CuONPs from 6.8 to 4.3 nm, respectively. The concentration of the synthesized CuONPs increased as laser fluence and laser ablation time increased.

A bivariate simultaneous pollutant forecasting approach by Unified Spectro-Spatial Graph Neural Network (USSGNN) and its application in prediction of O3 and NO2 for New Delhi, India

Declining urban air quality affects socioeconomic stability, public health, and ecosystems and is demanding attention of the administration to address environmental sustainability goals. Given the effects of ozone, a greenhouse gas, on local climate and health, this study introduces a Unified Spectro-Spatial Graph Neural Network (USS-GNN) designed for simultaneous 24-hour forecasting of ozone and its precursor, nitrogen-dioxide, while addressing their chemical interactions and spatiotemporal dynamics. This model exploits the graph structure of atmospheric dynamics and mines high-level spatial, spectral, and physical features from atmospheric data through a Dot Product Edge Attention mechanism and a location-aware graph feature rewiring technique. The proposed model is developed for Indian capital city New Delhi, utilizes hourly observations for the years 2021 and 2022 and achieved R2 values of 0.650 and 0.618, RMSE of 13.950 and 16.120 μg/m3, MAE of 10.730 and 12.930 μg/m3 for ozone and nitrogen-dioxide respectively, outperforming state-of-the-art models. The model’s forecast analysis identified error-prone areas, effects of local meteorology, and pollutant interdependencies. An ablation study further detailed the impacts of graph operations on forecasts. Moreover, this study promotes the utility of bivariate modeling frameworks in improving urban pollution monitoring and supporting sustainable city management through data-driven policy implementations.

Granformer: A granular transformer net with linear complexity

Recently, transformer models have demonstrated excellent performance across various intelligent applications owing to their ability to understand global context through self-attention mechanism. However, the extensively investigated multiplicative-based attention mechanism is inadequate for capturing relationship-based feature representations, as the dot product cannot depict the intricate semantic information between objects. Moreover, it has a great computational burden with a complexity of O(n2), due to the global feature representation capability achieved by calculating the relationship between each token within the entire feature sequence. To solve the current problem, this paper proposes a granular transformer framework with linear complexity, wherein diverse granulation functions can be employed to supersede the prevailing multiplicative relationships, and an innovative linearization methodology in the form of matrix factorization is designed to reduce the computational burden. Relying on the intricate semantics information embedded within granular structures, the capacity for feature extraction is significantly more comprehensive. Then, a novel matrix factorization methodology is developed for the linearity of granulation-based attention, accomplished by implementing separate deformable convolution sampling and using an approximate iterative algorithm based on cubic equations to calculate the Moore–Penrose inverse. The mathematical proof that our method is approximate with the complete granulation-based attention matrix is investigated in detail. Finally, the performance of Granformer, an innovative reconfiguration of plug-and-play transformer block, is evaluated on representative intelligent applications, including 3D point cloud classification, emotion recognition and sentiment analysis, and object detection. The experimental results suggest that our methodologies outperform the state-of-the-art models.

An explainable MHSA enabled deep architecture with dual-scale convolutions for methane source classification using remote sensing

Methane is the second most abundant greenhouse gas after carbon dioxide. Anthropogenic sources are the dominant emitters of methane. The poor spatial resolution of satellite imagery, high interclass similarity, the multi-scalar nature of features, and the dominance of background limit the performance of the previous approaches. Further, the reliance on high-resolution imagery limits the cost-effective global application of the works introduced in the literature. To resolve this, the present work proposes a novel method for methane source classification based on open-source multi-spectral satellite imagery of Sentinel-1 and 2. The work utilizes deep dual-scale convolutions with scaled dot product self-attention calculated across the 15 composite bands of Sentinel-1 and 2 data. The incorporation of non-RGB bands along with the RGB bands further enables the model to learn the spectral differences essential for the classification. The experimental results witness the superior performance of the developed method against other considered state-of-the-art methods.

Rock lithology classification algorithm based on improved self-attention mechanism VIT

Abstract When applying VIT to image classification, although good accuracy has been achieved, there is a limitation on the number of stacked layers. The similarity between different tokens increases as the model deepens, leading to low accuracy in shallow VIT models and wasting computational resources in deep VIT models. To address this issue, a multi-valued self-attention mechanism is proposed. By introducing an additional clue “V,” that does not vary arbitrarily, the dot product similarity observes each position in the token sequence more, reducing the depth of the attention mechanism network and avoiding the problem of similarity disappearing between deep tokens. Additionally, the loss function is improved by combining the Focal Loss function with Label Smoothing, enhancing the model’s handling of uncertain images while retaining the category focus of Focal Loss. Experiments are conducted on a rock lithology classification dataset, showing that compared to the VGG model and ResNet-18, the accuracy of the ResNet-50 model improves by 17.6%, 12%, and 4.9%, respectively. This paper also demonstrates the effectiveness of the multi-valued self-attention mechanism, which significantly reduces depth and parameter count while maintaining comparable accuracy. Finally, generalization experiments on the CIFAR-10 dataset further validate these conclusions.

Projective Peridynamic Modeling of Hyperelastic Membranes With Contact.

Real-time simulation of hyperelastic membranes like cloth still faces a lot of challenges, such as hyperplasticity modeling and contact handling. In this study, we propose projective peridynamics that uses a local-global strategy to enable fast and robust simulation of hyperelastic membranes with contact. In the global step, we propose a semi-implicit strategy to linearize the governing equation for hyperelastic materials that are modeled with peridynamics. By decomposing the first Piola-Kirchhoff stress tensor into a positive and a negative part, successive substitutions can be taken to solve the nonlinear problems. Convergence is guaranteed by further addressing the overshooting problem. Since our global step solve requires no energy summation and dot product operations over the entire problem, it fits into GPU implementation perfectly. In the local step, we further present a GPU-friendly gradient descent method to prevent interpenetration by solving an optimization problem independently. Putting the global and local solves together, experiments show that our method is robust and efficient in simulating complex models of membranes involving hyperelastic materials and contact.

Mixture-of-Rookies: Saving DNN computations by predicting ReLU outputs

Deep Neural Networks (DNNs) are widely used in many application domains. However, they require a vast amount of computations and memory accesses to deliver outstanding accuracy. In this paper, we propose a scheme to predict whether the output of each ReLu activated neuron will be a zero or a positive number in order to skip the computation of those neurons that will likely output a zero. Our predictor, named Mixture-of-Rookies, combines two inexpensive components. The first one exploits the high linear correlation between binarized (1-bit) and full-precision (8-bit) dot products, whereas the second component clusters together neurons that tend to output zero at the same time. We propose a novel clustering scheme based on analysis of angles, as the sign of the dot product of two vectors depends on the cosine of the angle between them. We implement our hybrid zero output predictor on top of a state-of-the-art DNN accelerator. Experimental results show that our scheme introduces a small area overhead of 5.3% while achieving a speedup of 1.2x and reducing energy consumption by 16.5% on average for a set of diverse DNNs.

Well-synthesized carbon dots from flower of Cassia fistula and its hydrothermally grown heterojunction photocatalyst with zinc oxide (CDs@ZnO-H400) for photocatalytic degradation of ciprofloxacin and paracetamol

Pharmaceutical residues in aquatic environments have the potential to induce bacterial resistance, subsequently complicating disease treatment and posing a substantial hazard to public health. This study demonstrates the production of carbon dots from Cassia fistula flowers using a hydrothermal process. The obtained carbon dots were then mixed with zinc oxide to create CDs@ZnO-H400. This heterojunction photocatalyst exhibited notable enhancement in photocatalytic performance due to improved charge separation efficiency at the interface. The CDs@ZnO-H400 catalyst effectively removed two medications, ciprofloxacin and paracetamol. Ciprofloxacin showed maximum photocatalytic efficiency, with 99.8 % degradation, while paracetamol exhibited a degradation efficiency of 75.1 %. The stability of the synthesized photocatalyst was evaluated across four usage cycles using EDX-SEM, FTIR, and XRD techniques. The CDs@ZnO-H400 heterostructure photocatalyst maintained strong photoactivity even after the fourth cycle of usage.

Non-transverse electromagnetic fields in micro- and nano-fibers

We present an analytical and numerical study of electromagnetic modes in micro- and nano-fibers (MNFs) where the electric and magnetic fields of the modes are not necessarily orthogonal to each other. We first investigate these modes for different fiber structures including circular- and rectangular-core fibers as well as photonic crystal fibers. We then discuss two specific applications of these modes: (1) generation of hypothetical axions that are coupled to the electromagnetic fields through the dot product of electric and magnetic fields of a mode, E→⋅B→, and (2) a new type of optical trap (optical tweezers) for chiral atoms with magneto-electric cross coupling, where the confining potential again is proportional to E→⋅B→.

An In-Memory-Computing Structure with Quantum-Dot Transistor Toward Neural Network Applications: From Analog Circuits to Memory Arrays

The rapid advancements in artificial intelligence (AI) have demonstrated great success in various applications, such as cloud computing, deep learning, and neural networks, among others. However, the majority of these applications rely on fast computation and large storage, which poses significant challenges to the hardware platform. Thus, there is a growing interest in exploring new computation architectures to address these challenges. Compute-in-memory (CIM) has emerged as a promising solution to overcome the challenges posed by traditional computer architecture in terms of data transfer frequency and energy consumption. Non-volatile memory, such as Quantum-dot transistors, has been widely used in CIM to provide high-speed processing, low power consumption, and large storage capacity. Matrix-vector multiplication (MVM) or dot product operation is a primary computational kernel in neural networks. CIM offers an effective way to optimize the performance of the dot product operation by performing it through an intertwining of processing and memory elements. In this paper, we present a novel design and analysis of a Quantum-dot transistor (QDT) based CIM that offers efficient MVM or dot product operation by performing computations inside the memory array itself. Our proposed approach offers energy-efficient and high-speed data processing capabilities that are critical for implementing AI applications on resource-limited platforms such as portable devices.

Detecting localized damage in cantilevered structures under nonstationary ambient excitations via Gabor spectral mode transmissibility functions

A method based on Gabor spectral mode transmissibility functions (GSMTFs) is proposed to detect local damage in a cantilevered structure under nonstationary ambient excitations. Gabor transformation and singular value decomposition are used to reduce the influences of other vibration modes on Gabor spectral mode transmissibility functions and process nonstationary structural responses, respectively. A new state characteristic based on the fundamental structure frequency is formulated on the basis of the GSMTFs, eventually leading to the development of a new damage indicator. The probability density functions of the damage indicator for healthy and damaged states can be estimated from the measured data, and the receiver operating characteristic (ROC) curve derived from these probability distributions and the corresponding area under the ROC curve (AUC) are used to determine the damage location. A six-degree-of-freedom system and a typical transmission tower are numerically studied, and the results show that the proposed method can estimate the structural damage location under nonstationary random loads. The proposed method is further validated with a planar frame in the laboratory, which exhibits multiple damage elements via random force hammer excitations. The results show that the AUC values computed for certain parts of the structure containing the damaged elements are greater than those for other parts of the structure, indicating the effectiveness of the proposed method. Moreover, the proposed method is compared with the dot product difference (DPD) index, and the results from the laboratory planar frame demonstrate that the proposed method can better identify damage.