Synthesis Behavior Research Articles

A data-driven framework for agent-based modeling of vehicular travel using publicly available data

This study presents a methodology for creating a synthetic travel demand, encompassing households and individuals and their daily activities, to support agent-based modeling (ABM) in urban planning and travel analysis. Unlike previous studies, which often rely on proprietary data, our approach is entirely based on open data, ensuring replicability by the broader research community. The research is among the first to propose the entire framework for travel demand synthesis and ABM. Results are validated against ground truth from the Census and other public data sources. The ABM results are compared to an Information Minimization (IM) model, which is an aggregated model capturing commuting patterns by race. The study contributes to the field by offering a comprehensive and replicable data foundation for ABM, serving as a valuable resource for evaluating population and travel demand synthesis algorithms.

Broadband Ground-Motion Synthesis via Generative Adversarial Neural Operators: Development and Validation

ABSTRACT We present a data-driven framework for ground-motion synthesis that generates three-component acceleration time histories conditioned on moment magnitude (M), rupture distance (Rrup), time-average shear-wave velocity at the top 30 m (VS30), and style of faulting. We use a Generative Adversarial Neural Operator (GANO)—a resolution invariant architecture that guarantees model training independent of the data sampling frequency. We first present the conditional ground-motion synthesis algorithm (cGM-GANO) and discuss its advantages compared to the previous work. We next train cGM-GANO on simulated ground motions generated by the Southern California Earthquake Center Broadband Platform (BBP) and on recorded the Kiban–Kyoshin network (KiK-net) data, and show that the model can learn the overall magnitude, distance, and VS30 scaling of effective amplitude spectra (EAS) ordinates and pseudospectral accelerations (PSA). Results specifically show that cGM-GANO produces consistent median scaling with the training data for the corresponding tectonic environments over a wide range of frequencies for scenarios with sufficient data coverage. For the BBP dataset, cGM-GANO cannot learn the ground-motion scaling of the stochastic frequency components (f > 1 Hz); for the KiK-net dataset, the largest misfit is observed at short distances (Rrup<50 km) and for soft-soil conditions (VS30<200 m/s) due to the scarcity of such data. Except for these conditions, the aleatory variability of EAS and PSA are captured reasonably well. Finally, cGM-GANO produces similar median scaling to traditional ground-motion models (GMMs) for frequencies greater than 1 Hz for both PSA and EAS but underestimates the aleatory variability of EAS. Discrepancies in the comparisons between the synthetic ground motions and GMMs are attributed to inconsistencies between the training dataset and the datasets used in GMM development. Our pilot study demonstrates GANO’s potential for efficient synthesis of broadband ground motions.

Edge Detection on Field Programmable Gate Array (FPGA)

Edges are significant local changes in the image and are very important features for analysing images. Edges typically occur on the boundary between two different regions in an image. An edge in an image is a significant local change in the image intensity, usually associated with a discontinuity in either the image intensity or the first derivative of the image intensity. Edge detection is one of the tools that can be used in many image processing applications for withdrawing information from image. Sobel edge detection is one of the operators that operate on gradient based edge selection methods to find edge pixels in the image. This report proposed an implementation of Sobel edge Detection algorithm to find the pixels in grayscale images. We present a video streaming architecture and IP implementation using high level synthesis. A video with 720p resolution streamed from the HDMI source and real time edge detected video captured on another monitor. For implementation, ZYBO board or kit is used with Vivado software with 2018.3 V, which has provided adequate peripherals for implementation.

LL-GNN: Low Latency Graph Neural Networks on FPGAs for High Energy Physics

This work presents a novel reconfigurable architecture for Low Latency Graph Neural Network (LL-GNN) designs for particle detectors, delivering unprecedented low latency performance. Incorporating FPGA-based GNNs into particle detectors presents a unique challenge since it requires sub-microsecond latency to deploy the networks for online event selection with a data rate of hundreds of terabytes per second in the Level-1 triggers at the CERN Large Hadron Collider experiments. This article proposes a novel outer-product based matrix multiplication approach, which is enhanced by exploiting the structured adjacency matrix and a column-major data layout. In addition, we propose a custom code transformation for the matrix multiplication operations, which leverages the structured sparsity patterns and binary features of adjacency matrices to reduce latency and improve hardware efficiency. Moreover, a fusion step is introduced to further reduce the end-to-end design latency by eliminating unnecessary boundaries. Furthermore, a GNN-specific algorithm-hardware co-design approach is presented which not only finds a design with a much better latency but also finds a high accuracy design under given latency constraints. To facilitate this, a customizable template for this low latency GNN hardware architecture has been designed and open-sourced, which enables the generation of low-latency FPGA designs with efficient resource utilization using a high-level synthesis tool. Evaluation results show that our FPGA implementation is up to 9.0 times faster and achieves up to 13.1 times higher power efficiency than a GPU implementation. Compared to the previous FPGA implementations, this work achieves 6.51 to 16.7 times lower latency. Moreover, the latency of our FPGA design is sufficiently low to enable deployment of GNNs in a sub-microsecond, real-time collider trigger system, enabling it to benefit from improved accuracy. The proposed LL-GNN design advances the next generation of trigger systems by enabling sophisticated algorithms to process experimental data efficiently.

Enhancing Embedded Object Tracking: A Hardware Acceleration Approach for Real-Time Predictability.

While Siamese object tracking has witnessed significant advancements, its hard real-time behaviour on embedded devices remains inadequately addressed. In many application cases, an embedded implementation should not only have a minimal execution latency, but this latency should ideally also have zero variance, i.e., be predictable. This study aims to address this issue by meticulously analysing real-time predictability across different components of a deep-learning-based video object tracking system. Our detailed experiments not only indicate the superiority of Field-Programmable Gate Array (FPGA) implementations in terms of hard real-time behaviour but also unveil important time predictability bottlenecks. We introduce dedicated hardware accelerators for key processes, focusing on depth-wise cross-correlation and padding operations, utilizing high-level synthesis (HLS). Implemented on a KV260 board, our enhanced tracker exhibits not only a speed up, with a factor of 6.6, in mean execution time but also significant improvements in hard real-time predictability by yielding 11 times less latency variation as compared to our baseline. A subsequent analysis of power consumption reveals our approach's contribution to enhanced power efficiency. These advancements underscore the crucial role of hardware acceleration in realizing time-predictable object tracking on embedded systems, setting new standards for future hardware-software co-design endeavours in this domain.

Time-optimal multi-qubit gates: Complexity, efficient heuristic and gate-time bounds

Multi-qubit entangling interactions arise naturally in several quantum computing platforms and promise advantages over traditional two-qubit gates. In particular, a fixed multi-qubit Ising-type interaction together with single-qubit X-gates can be used to synthesize global ZZ-gates (GZZ gates). In this work, we first show that the synthesis of such quantum gates that are time-optimal is NP-hard. Second, we provide explicit constructions of special time-optimal multi-qubit gates. They have constant gate times and can be implemented with linearly many X-gate layers. Third, we develop a heuristic algorithm with polynomial runtime for synthesizing fast multi-qubit gates. Fourth, we derive lower and upper bounds on the optimal GZZ gate-time. Based on explicit constructions of GZZ gates and numerical studies, we conjecture that any GZZ gate can be executed in a time O(n) for n qubits. Our heuristic synthesis algorithm leads to GZZ gate-times with a similar scaling, which is optimal in this sense. We expect that our efficient synthesis of fast multi-qubit gates allows for faster and, hence, also more error-robust execution of quantum algorithms.

Boosting general-purpose stream processing with reconfigurable hardware

Reconfigurable devices such as field-programmable gate arrays (FPGAs) offer flexible solutions to workload acceleration with high energy efficiency. Despite such a potential advantage, they often reveal hard to program by application programmers. High-level synthesis languages have been developed to provide higher-level abstractions, allowing the developers to define the FPGA behavior using an imperative programming approach based on C/C++ languages. However, such approaches still leave the developer with the responsibility to harness the low-level optimizations required to develop efficient FPGA programs. Along this line, this paper introduces FSPX, a framework helping programmers to develop FPGA-accelerated data stream processing (DSP) applications. The approach provides a high-level Python API to develop the data-flow graph of operators, which is automatically translated into an efficient Vitis source code targeting Xilinx devices. The execution of the bitstreams implementing two benchmark applications showcases the efficiency of using FPGAs for DSP workloads. In general, FSPX provides, with a reasonable time-to-solution, higher performance compared with state-of-the-art DSP frameworks.

Design of coherent passive quantum equalizers using robust control theory

The paper develops a methodology for the design of coherent equalizing filters for quantum communication channels. Given a linear quantum system model of a quantum communication channel, the aim is to obtain another quantum system which, when coupled with the original system, mitigates degrading effects of the environment. The main result of the paper is a systematic equalizer synthesis algorithm which relies on methods of state–space robust control design via semidefinite programming.

High-resolution Si3N4 spectrometer: architecture & virtual channel synthesis and experimental demonstration.

Up-to-date network telemetry is the key enabler for resource optimization by capacity scaling, fault recovery, and network reconfiguration among other means. Reliable optical performance monitoring in general and, specifically, the monitoring of the spectral profile of WDM signals in fixed- and flex- grid architectures across the entire C-band, remains challenging. This article describes a two-stage spectrometer architecture amenable to integration on a single chip that can measure quantitatively the spectrum across the entire C-band with a resolution of ∼ 1.4 GHz. The first stage consists of a ring resonator with intra-ring phase shifter to provide a tuneable fine filter. The second stage makes use of an AWG subsystem and a novel processing algorithm to synthesize a tuneable coarse filter with a flat passband which isolates individual resonances of a multiplicity of ring resonances. The spectrometer is capable of scanning the entire C-band with high resolution using only one dynamic control. Due to its maturity and low loss, CMOS compatible Si3N4 is chosen for fabrication of the ring resonator and two cyclic AWGs. Complete spectrometer operation is demonstrated experimentally over a selected portion of the C-band. A novel virtual channel synthesis algorithm based on the weighted summation of the AWG output port powers relaxes the conventional AWG design requirement of a flat passband and sharp transition to stopband. The operation of the circuit is invariant to the optical path length between individual components and the algorithm corrects to some extent fabrication process variation impairments of the AWG channel spectra substantially improving robustness.

Sensor based Dance Coherent Action Generation Model using Deep Learning Framework

Dance Coherent Action Generation is a popular research task in recent years to generate movements and actions for computer-generated characters in a simulated environment. It is sometimes referred to as "Motion Synthesis". Motion synthesis algorithms are used to generate physically believable, visually compelling, and contextually appropriate movement using motion sensors. The Dance Coherent Action Generation Model (DCAM) is a generative framework for producing aesthetically pleasing movements using deep learning from small amounts of data. By learning an internal representation of motion dynamics, DCAM can synthesize long sequences of movements in which coherent patterns can be created through latent space interpolation. This framework provides a mechanism for varying the amplitude of the generated motion, allowing further realistic thinking and expression. The proposed model obtained 93.79% accuracy, 93.79% precision, 97.75% recall and 92.92% F1 score. DCAM exploits the balance between imitation and creativity by enabling the production of novel outputs from limited input data and can be trained in an unsupervised manner or fine-tuned with sparse supervision. Furthermore, the framework is easily extended to handle multiple layers of abstraction and can be further personalized to a particular type of movement, enabling the generation of highly individualized outputs.

MOSAIC: Maximizing ResOurce Sharing in Behavioral Application SpecIfic ProCessors

This work presents a method that can quickly determine which hardware accelerators (HWaccs) should be mapped together onto an Application-Specific Instruction Set Processor (ASIP), such that the resources shared among them are maximized. This work in particular targets HWaccs generated from untimed behavioral descriptions for High-Level Synthesis (HLS). Although HLS is a single process synthesis method, our approach is able to force resource sharing among the HWaccs by combining their behavioral descriptions together into a single description based on their potential to share resources. These shared resources include functional units (FUs) like multipliers, adders, and dividers, and also registers. In particular, our proposed flow leads up to 48% in area savings and on average 30%. Because an exhaustive enumeration of all possible combinations can lead to long runtimes, we propose a fast heuristic that leads to comparable results (only 6% worse on average), while being much faster (on average 500×).

Publisher Correction: Parallel chaos-based image encryption algorithm: high-level synthesis and FPGA implementation

Publisher Correction: Parallel chaos-based image encryption algorithm: high-level synthesis and FPGA implementation

Speech recognition sensors and artificial intelligence automatic evaluation application in English oral correction system

In China, although many college students have achieved good results in English exams, their oral proficiency is relatively weak. With the rapid development of internet information technology, the use of speech recognition technology to improve English oral pronunciation learning has become a research hotspot. The goal of this article is to design a system based on speech recognition and speech synthesis to help learners improve their oral pronunciation. By automatically evaluating learners' pronunciation accuracy and providing targeted correction and training, the system aims to improve learners' pronunciation level. This article adopts the principles and algorithms of speech recognition and speech synthesis. Through speech recognition technology, the system can convert learners' oral recordings into text and evaluate accuracy. By utilizing speech synthesis technology, the system can generate corrected audio based on correction rules to assist learners in pronunciation training. By evaluating and correcting real learners' oral recordings, the system can accurately evaluate learners' pronunciation accuracy and generate targeted corrected audio. Through systematic training and practice, learners' pronunciation level has been effectively improved.

An Efficient Hybrid Deep Learning Accelerator for Compact and Heterogeneous CNNs

Resource-efficient Convolutional Neural Networks (CNNs) are gaining more attention. These CNNs have relatively low computational and memory requirements. A common denominator among such CNNs is having more heterogeneity than traditional CNNs. This heterogeneity is present at two levels: intra-layer type and inter-layer type. Generic accelerators do not capture these levels of heterogeneity, which harms their efficiency. Consequently, researchers have proposed model-specific accelerators with dedicated engines. When designing an accelerator with dedicated engines, one option is to dedicate one engine per CNN layer. We refer to accelerators designed with this approach as single-engine single-layer (SESL). This approach enables optimizing each engine for its specific layer. However, such accelerators are resource-demanding and unscalable. Another option is to design a minimal number of dedicated engines such that each engine handles all layers of one type. We refer to these accelerators as single-engine multiple-layer (SEML). SEML accelerators capture the inter-layer-type but not the intra-layer-type heterogeneity. We propose the Fixed Budget Hybrid CNN Accelerator (FiBHA), a hybrid accelerator composed of an SESL part and an SEML part, each processing a subset of CNN layers. FiBHA captures more heterogeneity than SEML while being more resource-aware and scalable than SESL. Moreover, we propose a novel module, Fused Inverted Residual Bottleneck (FIRB), a fine-grained and memory-light SESL architecture building block. The proposed architecture is implemented and evaluated using high-level synthesis (HLS) on different Field Programmable Gate Arrays representing various resource budgets. Our evaluation shows that FiBHA improves the throughput by up to 4 x and 2.5 x compared to state-of-the-art SESL and SEML accelerators, respectively. Moreover, FiBHA reduces memory and energy consumption compared to an SEML accelerator. The evaluation also shows that FIRB reduces the required memory by up to 54%, and energy requirements by up to 35% compared to traditional pipelining.

The problem of implementing the concept of maximum integration of heterogeneous data in practical navigation

The topic of the work is the research of the problem of the practical realization of opportunistic navigation, which actually consists in the fact that the “signals of opportunity” are not optimized for global navigation according to their original purpose. A hypothesis about the possibility of strategic application of the navigation concept based on the principles of data integration with the objective existence of tactically surmountable difficulties is put forward. In the conditions of vulnerability of the global satellite system, an approach to use an additional source of combined signals in order to continuously ensure accurate geolocation of water transport vehicles is proposed. The comparative assessment confirms the comparability of the positioning error of alternative navigation with the data of classical satellite observations of mobile objects. An assumption about the effectiveness of spline modeling of the cartographic standard of informativeness for the practical organization of the basic principle of opportunistic positioning by analogy with the paradigm of correlation-extreme navigation is made. A computer visualization of a fixed fragment of the ocean gravitational field based on spline approximation is performed in order to optimize the problem of simultaneous localization and three-dimensional representation of the ship movement in a graphical environment unaffiliated with foreign software. A hybrid algorithm for mathematical synthesis of the navigational isosurface has been tested as a harmonized support for the navigation staff to implement the “terrain-referenced procedure” in the landscape coordinate space. The variants of the “ambiguity resolution” problem implementation in the issue of maximum integration of heterogeneous navigation data are considered. The probability of practical use of the opportunistic navigation postulates in marine applications, taking into account the “navigation gap” factor for leveling local satellite incapacity with a real possibility of countering malicious interception of ship control, is estimated. The expediency of using the factor of observational reckoning of the vessel path as an additional condition for navigation safety in the aspect of packet processing of the “signals of opportunity” slot is substantiated.

Synthesis, Characterization, and Evaluation of the Adsorption Behavior of Cellulose-Graft-Poly(Acrylonitrile-co-Acrylic Acid) and Cellulose-Graft-Poly(Acrylonitrile-co-Styrene) towards Ni(II) and Cu(II) Heavy Metals.

In this study, the synthesis and characterization of grafted cellulose fiber with binary monomers mixture obtained using a KMnO4/citric acid redox initiator were investigated. Acrylonitrile (AN) was graft copolymerized with acrylic acid (AA) and styrene (Sty) at different monomer ratios with evaluating percent graft yield (GY%). Cell-g-P(AN-co-AA) and Cell-g-P(AN-co-Sty) were characterized by SEM, FT-IR, 13C CP MAS NMR, TGA, and XRD. An AN monomer was used as principle-acceptor monomer, and GY% increases with AN ratio up to 60% of total monomers mixture volume. The adsorption behaviors of Cell-g-P(AN-co-AA) and Cell-g-P(AN-co-Sty) were studied for the adsorption of Ni(II) and Cu(II) metal ions from aqueous solution. Optimal adsorption conditions were determined, including 8 h contact time, temperature of 30 °C, and pH 5.5. Cell-g-P(AN-co-AA) showed maximum adsorption capacity of 435.07 mg/g and 375.48 mg/g for Ni(II) and Cu(II), respectively, whereas Cell-g-P(AN-co-Sty) showed a maximum adsorption capacity of 379.2 mg/g and 349.68 mg/g for Ni(II) and Cu(II), respectively. Additionally, adsorption equilibrium isotherms were studied, and the results were consistent with the Langmuir model. The Langmuir model's high determinant coefficient (R2) predicted monolayer sorption of metal ions. Consequently, Cell-g-P(AN-co-AA) and Cell-g-P(AN-co-Sty) prepared by a KMnO4/citric acid initiator were found to be efficient adsorbents for heavy metals from wastewater as an affordable and adequate alternative.

Weather-Domain Transfer-Based Attention YOLO for Multi-Domain Insulator Defect Detection and Classification in UAV Images.

Insulator defect detection of transmission line insulators is an important task for unmanned aerial vehicle (UAV) inspection, which is of immense importance in ensuring the stable operation of transmission lines. Transmission line insulators exist in complex weather scenarios, with small and inconsistent shapes. These insulators under various weather conditions could result in low-quality images captured, limited data numbers, and imbalanced sample problems. Traditional detection methods often struggle to accurately identify defect information, resulting in missed or false detections in real-world scenarios. In this paper, we propose a weather domain synthesis network for extracting cross-modality discriminative information on multi-domain insulator defect detection and classification tasks. Firstly, we design a novel weather domain synthesis (WDSt) module to convert various weather-conditioned insulator images to the uniform weather domain to decrease the existing domain gap. To further improve the detection performance, we leverage the attention mechanism to construct the Cross-modality Information Attention YOLO (CIA-YOLO) model to improve the detection capability for insulator defects. Here, we fuse both shallow and deep feature maps by adding the extra object detection layer, increasing the accuracy for detecting small targets. The experimental results prove the proposed Cross-modality Information Attention YOLO with the weather domain synthesis algorithm can achieve superior performance in multi-domain insulator datasets (MD-Insulator). Moreover, the proposed algorithm also gives a new perspective for decreasing the multi-domain insulator modality gap with weather-domain transfer, which can inspire more researchers to focus on the field.

Hardware Implementations of a Deep Learning Approach to Optimal Configuration of Reconfigurable Intelligence Surfaces

Reconfigurable intelligent surfaces (RIS) offer the potential to customize the radio propagation environment for wireless networks, and will be a key element for 6G communications. However, due to the unique constraints in these systems, the optimization problems associated to RIS configuration are challenging to solve. This paper illustrates a new approach to the RIS configuration problem, based on the use of artificial intelligence (AI) and deep learning (DL) algorithms. Concretely, a custom convolutional neural network (CNN) intended for edge computing is presented, and implementations on different representative edge devices are compared, including the use of commercial AI-oriented devices and a field-programmable gate array (FPGA) platform. This FPGA option provides the best performance, with ×20 performance increase over the closest FP32, GPU-accelerated option, and almost ×3 performance advantage when compared with the INT8-quantized, TPU-accelerated implementation. More noticeably, this is achieved even when high-level synthesis (HLS) tools are used and no custom accelerators are developed. At the same time, the inherent reconfigurability of FPGAs opens a new field for their use as enabler hardware in RIS applications.

Reinforcement Learning-Driven Bit-Width Optimization for the High-Level Synthesis of Transformer Designs on Field-Programmable Gate Arrays

With the rapid development of deep-learning models, especially the widespread adoption of transformer architectures, the demand for efficient hardware accelerators with field-programmable gate arrays (FPGAs) has increased owing to their flexibility and performance advantages. Although high-level synthesis can shorten the hardware design cycle, determining the optimal bit-width for various transformer designs remains challenging. Therefore, this paper proposes a novel technique based on a predesigned transformer hardware architecture tailored for various types of FPGAs. The proposed method leverages a reinforcement learning-driven mechanism to automatically adapt and optimize bit-width settings based on user-provided transformer variants during inference on an FPGA, significantly alleviating the challenges related to bit-width optimization. The effect of bit-width settings on resource utilization and performance across different FPGA types was analyzed. The efficacy of the proposed method was demonstrated by optimizing the bit-width settings for users’ transformer-based model inferences on an FPGA. The use of the predesigned hardware architecture significantly enhanced the performance. Overall, the proposed method enables effective and optimized implementations of user-provided transformer-based models on an FPGA, paving the way for edge FPGA-based deep-learning accelerators while reducing the time and effort typically required in fine-tuning bit-width settings.

P-stable abstractions of hybrid systems

Stability is a fundamental requirement of dynamical systems. Most of the works concentrate on verifying stability for a given stability region. In this paper, we tackle the problem of synthesizingP\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {P}}$$\\end{document}-stable abstractions. Intuitively, the P\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {P}}$$\\end{document}-stable abstraction of a dynamical system characterizes the transitions between stability regions in response to external inputs. The stability regions are not given—rather, they are synthesized as their most precise representation with respect to a given set of predicates P\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {P}}$$\\end{document}. A P\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {P}}$$\\end{document}-stable abstraction is enriched by timing information derived from the duration of stabilization. We implement a synthesis algorithm in the framework of Interpretation that allows different degrees of approximation. We show the representational power of P\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {P}}$$\\end{document}-stable abstractions that provide a high-level account of the behavior of the system with respect to stability, and we experimentally evaluate the effectiveness of the algorithm in synthesizing P\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {P}}$$\\end{document}-stable abstractions for significant systems.