Operator Research Articles

Dual-wavelength sub-Nyquist sampling scheme for clipping-avoidance photonic ADC

We propose a dual-wavelength scheme for a clipping-avoidance photonic analog-to-digital converter (PADC) operating at the sub-Nyquist sampling rate. The scheme utilizes two characteristics, the phase-wrapping feature of a PADC and the wavelength-sensitive feature of a phase modulator, equivalently performing a dual-modulus (DM) modulo operation to avoid clipping. Coupled with an unwrapping algorithm based on the Chinese remainder theorem (CRT), the proposed scheme enables signal reconstruction from the processed signals independent of the sampling rate. We demonstrated proof-of-concept experiments on a PADC chip fabricated on an LNOI platform. Experimental results show that 1G/2G/4G-baud 10-level pulse amplitude modulation (PAM-10) waveforms were successfully reconstructed at the sub-Nyquist sampling rate of 1/2/4Gs/s, respectively. Our work provides a potential solution to achieve on-chip clipping-avoidance PADCs operating at the sub-Nyquist sampling.

A Review on Modular Multi-level Converter Based HVDC Systems

Modular Multilevel Converters (MMCs) have emerged as a promising technology for High Voltage Direct Current (HVDC) transmission systems, offering several advantages such as reduced harmonic distortion, high voltage capability and modularity. This paper presents a comprehensive review of MMC-based HVDC systems, focusing on their applications, control strategies and challenges. The paper begins by discussing the basic principles and structure of MMCs, highlighting their modular design and operation. The paper delves into the control strategies employed in MMC-HVDC systems, emphasizing the importance of coordinated control between the AC and DC sides to ensure stable and efficient operation. Furthermore, the paper addresses the challenges associated with MMC-HVDC systems, such as fault ride-through capability, harmonic interactions and grid integration. It highlights recent advancements in control techniques and technologies that are being developed to address these challenges. The paper provides a valuable overview of MMC-based HVDC systems, highlighting their potential benefits and the ongoing research efforts to overcome their challenges. As the demand for renewable energy sources and long-distance power transmission increases, MMC-HVDC systems are poised to play a crucial role in shaping the future of the power grid

JumpBackHash: Say Goodbye to the Modulo Operation to Distribute Keys Uniformly to Buckets

ABSTRACTIntroductionDistributed data processing and storage systems require efficient methods to distribute keys across buckets. While simple and fast, the traditional modulo‐based mapping is unstable when the number of buckets changes, leading to spikes in system resource utilization, such as network or database requests. Consistent hash algorithms minimize remappings but are either significantly slower, require floating‐point arithmetic, or are based on a family of hash functions rarely available in standard libraries. This work introduces JumpBackHash, a consistent hash algorithm that overcomes those shortcomings.MethodologyJumpBackHash applies the concept of active indices borrowed from consistent weighted sampling, which inherently leads to consistency. It generates the active indices in reverse order, which avoids floating‐point operations, enables the minimization of consumed random values and the use of a standard pseudorandom generator, and finally leads to a very efficient algorithm.ResultsTheoretical analysis shows that JumpBackHash has an expected constant runtime. The expected value and the variance of the number of consumed random values perfectly agree with the experiments. Empirical tests also confirm the consistency.ConclusionJumpBackHash offers a fast and efficient solution for uniformly distributing keys across buckets in distributed systems. Its simplicity, performance, and the availability of a production‐ready Java implementation as part of the Hash4j open source library make it a viable replacement for the modulo‐based approach for improving assignment and system stability.

Integrated photonic modular arithmetic processor

Integrated photonic computing has emerged as a promising approach to overcome the limitations of electronic processors in the post-Moore era. However, present integrated photonic computing systems face challenges in achieving high-precision calculations, consequently limiting their potential applications, and their heavy reliance on analog-to-digital (AD) and digital-to-analog (DA) conversion interfaces undermines their performance. Here we propose an innovative photonic computing architecture featuring scalable calculation precision and, to our knowledge, a novel photonic conversion interface. By leveraging the residue number system (RNS) theory, the high-precision calculation is decomposed into multiple low-precision modular arithmetic operations executed through optical phase manipulation. Those operations directly interact with the digital system via our proposed optical digital-to-phase converter (ODPC) and phase-to-digital converter (OPDC). Through experimental demonstrations, we showcase a calculation precision of 9 bits and verify the feasibility of the ODPC/OPDC photonic interface. This approach paves the path towards liberating photonic computing from the constraints imposed by limited precision and AD/DA converters.

Dynamical non-locality in the near-horizon region of a black hole with quantum time

The formalization of the modular energy operator within the curved spacetime is achieved through the timeless approach proposed by Page and Wootters. The investigation is motivated by the peculiar behavior of the near horizon region of a black hole and its quantum effects, leading to a restriction of the study to the immediate vicinity. The focus lies on the perspective of a static observer positioned close to the horizon. This paper highlights the alteration of the modular energy's behavior in this region compared to flat spacetime. Furthermore, it is observed that the geometry of the spacetime influences the non-local properties of the modular energy. Moreover, within the event horizon of the black hole, the modular energy exhibits a completely distinct behavior, rendering its modular behavior imperceptible in this specific region.

Tolerance to asynchrony in algorithms for multiplication and modulo

In this article, we study some parallel processing algorithms for multiplication and modulo operations. We demonstrate that the state transitions that are formed under these algorithms satisfy lattice-linearity, where these algorithms induce a lattice among the global states. Lattice-linearity implies that these algorithms can be implemented in asynchronous environments, where the nodes are allowed to read old information from each other. It means that these algorithms are guaranteed to converge correctly without any synchronization overhead. These algorithms also exhibit snap-stabilizing properties, i.e., starting from an arbitrary state, the sequence of state transitions made by the system strictly follows its specification.

RSD-based high-performance radix-4 Montgomery Modular Multiplication for Elliptic Curve Cryptography

This paper proposes a high-performance radix-4 Montgomery Modular Multiplication (MMM) algorithm and its corresponding hardware architecture for Elliptic Curve Cryptography (ECC), in which the quotient and the partial product accumulation are computed in parallel in each iteration. Additionally, in this MMM, the Redundant Signed Digit (RSD) representation and the Signed Digit Adder (SDA) are used to eliminate the long carry chain and achieve parallel computation, as well as remove pre-computation and integrate modular reduction operations. Our MMM algorithm is implemented in 256-bit and 1024-bit versions on Xilinx Virtex-6 and Virtex-7 FPGAs, respectively. It consumes only 1.55k/10.18k Look-Up Tables (LUTs), takes 133/517 clock cycles, and runs at maximum frequencies of 558.8/641.7 MHz. According to the comparison in terms of Area Time Product (ATP), our design can achieve the ATP of 0.369 over the 256-bit NIST prime domain, which is approximately half of that of the state-of-the-art works. The Scalar Point Multiplication (SPM) scheme using this MMM algorithm consumes 14.19k LUTs and completes a single Scalar Point Multiplication (SPM) operation in 0.217 ms, and it also has a lower ATP than most other SPM algorithms currently in existence.

Truncated multiplication and batch software SIMD AVX512 implementation for faster Montgomery multiplications and modular exponentiation

This paper presents software implementations of batch computations, dealing with multi-precision integer operations. In this work, we use the Single Instruction Multiple Data (SIMD) AVX512 instruction set of the x86-64 processors, in particular the vectorized fused multiplier-adder VPMADD52. We focus on batch multiplications, squarings, modular multiplications, modular squarings and constant time modular exponentiations of 8 values using a word-slicing storage. We explore the use of Schoolbook and Karatsuba approaches with operands up to 4108 and 4154 bits respectively. We also introduce a truncated multiplication that speeds up the computation of the Montgomery modular reduction in the context of software implementation. Our Truncated Montgomery modular multiplication improvement offers speed gains of almost 20 % over the conventional non-truncated versions. Compared to the state-of-the-art GMP and OpenSSL libraries, our speedup modular operations are more than 4 times faster. Compared to OpenSSL BN_mod_exp_mont_consttimex2 using AVX512 and madd52* (madd52hi or madd52lo) in 256-bit registers, in fixed-window exponentiations of sizes 1024 and 2048 , our 512-bit implementation provides speedups of respectively 1.75 and 1.38, while the 256-bit version speedups are 1.51 and 1.05 for 1024 and 2048 -bit sizes (batch of 4 values in this case).

NAS-BNN: Neural Architecture Search for Binary Neural Networks

Binary Neural Networks (BNNs) have gained extensive attention for their superior inferencing efficiency and compression ratio compared to traditional full-precision networks. However, due to the unique characteristics of BNNs, designing a powerful binary architecture is challenging and often requires significant manpower. A promising solution is to utilize Neural Architecture Search (NAS) to assist in designing BNNs, but current NAS methods for BNNs are relatively straightforward and leave a performance gap between the searched models and manually designed ones. To address this gap, we propose a novel neural architecture search scheme for binary neural networks, named NAS-BNN. We first carefully design a search space based on the unique characteristics of BNNs. Then, we present three training strategies, which significantly enhance the training of supernet and boost the performance of all subnets. Our discovered binary model family outperforms previous BNNs for a wide range of operations (OPs) from 20M to 200M. For instance, we achieve 68.20% top-1 accuracy on ImageNet with only 57M OPs. In addition, we validate the transferability of these searched BNNs on the object detection task, and our binary detectors with the searched BNNs achieve a novel state-of-the-art result, e.g., 31.6% mAP with 370M OPs, on MS COCO dataset. The source code and models will be released at https://github.com/VDIGPKU/NAS-BNN.

Mesh Convolution With Continuous Filters for 3-D Surface Parsing.

Geometric feature learning for 3-D surfaces is critical for many applications in computer graphics and 3-D vision. However, deep learning currently lags in hierarchical modeling of 3-D surfaces due to the lack of required operations and/or their efficient implementations. In this article, we propose a series of modular operations for effective geometric feature learning from 3-D triangle meshes. These operations include novel mesh convolutions, efficient mesh decimation, and associated mesh (un)poolings. Our mesh convolutions exploit spherical harmonics as orthonormal bases to create continuous convolutional filters. The mesh decimation module is graphics processing unit (GPU)-accelerated and able to process batched meshes on-the-fly, while the (un)pooling operations compute features for upsampled/downsampled meshes. We provide an open-source implementation of these operations, collectively termed Picasso. Picasso supports heterogeneous mesh batching and processing. Leveraging its modular operations, we further contribute a novel hierarchical neural network for perceptual parsing of 3-D surfaces, named PicassoNet++. It achieves highly competitive performance for shape analysis and scene segmentation on prominent 3-D benchmarks. The code, data, and trained models are available at https://github.com/EnyaHermite/Picasso.

CSAIL2019 Crypto-Puzzle Solver Architecture

tThe CSAIL2019 time-lock puzzle is an unsolved cryptographic challenge introduced by Ron Rivest in 2019, replacing the solved LCS35 puzzle. Solving these types of puzzles requires large amounts of intrinsically sequential computations, with each iteration performing a very large (3,072-bit for CSAIL2019) modular multiplication operation. The complexity of each iteration is several times greater than known field-programmable gate array (FPGA) implementations, and the number of iterations has been increased by about 1,000x compared with LCS35. Because of the high complexity of this new puzzle, a number of intermediate, or milestone, versions of the puzzle have been specified. In this article, we present several FPGA architectures for the CSAIL2019 solver, which we implement on a medium-sized Intel Agilex device. We develop a new multi-cycle modular multiplication method, which is flexible and can fit on a wide variety of sizes of current FPGAs. We introduce a class of multi-cycle squarer-based architectures that allow for better resource and area trade-offs. We also demonstrate a new approach for improving the fitting and timing closure of large, chip-filling arithmetic designs. We used the solver to compute the first 23 out of 28 milestone solutions of the puzzle, which are the first reported results for this problem.

Constructing a Nondegenerate m-Dimensional Integer-Domain Chaotic Map Model over GF(2n) with Application in PRNG

To address the problem of dynamic degradation over a finite-precision platform of chaotic maps and the reversibility of linear chaotic maps, we propose an improved model over GF([Formula: see text]) that is called the nondegenerate m-Dimensional [Formula: see text] Integer-Domain Chaotic Maps (mD-IDCMs). This model incorporates modular exponentiation operation, and is capable of constructing nondegenerate IDCMs of any dimension. Moreover, we prove the irreversibility of mD-IDCM and analyze its chaotic behaviors in terms of positive Lyapunov Exponents (LEs). The results of theoretical analysis show that the proposed mD-IDCM model can obtain the desired positive LEs by appropriately configuring its coefficient matrix. Then, we present two instances, and analyze their LEs, Kolmogorov entropy, Sample entropy, Correlation dimension, and the dynamic analysis indicates that the chaotic map constructed by mD-IDCM has ergodicity within a sufficiently large chaotic range. Finally, we design a Pseudo-Random Number Generator (PRNG) with a key to verify the practicability of the mD-IDCM.

U-DeepONet: U-Net enhanced deep operator network for geologic carbon sequestration

Learning operators with deep neural networks is an emerging paradigm for scientific computing. Deep Operator Network (DeepONet) is a modular operator learning framework that allows for flexibility in choosing the kind of neural network to be used in the trunk and/or branch of the DeepONet. This is beneficial as it has been shown many times that different types of problems require different kinds of network architectures for effective learning. In this work, we design an efficient neural operator based on the DeepONet architecture. We introduce U-Net enhanced DeepONet (U-DeepONet) for learning the solution operator of highly complex CO2-water two-phase flow in heterogeneous porous media. The U-DeepONet is more accurate in predicting gas saturation and pressure buildup than the state-of-the-art U-Net based Fourier Neural Operator (U-FNO) and the Fourier-enhanced Multiple-Input Operator (Fourier-MIONet) trained on the same dataset. Moreover, our U-DeepONet is significantly more efficient in training times than both the U-FNO (more than 18 times faster) and the Fourier-MIONet (more than 5 times faster), while consuming less computational resources. We also show that the U-DeepONet is more data efficient and better at generalization than both the U-FNO and the Fourier-MIONet.

Modular linear differential operators and generalized Rankin-Cohen brackets

The aim of this paper is to give expressions for modular linear differential operators (MLDOs) of any order. In particular, we show that they can all be described in terms of Rankin-Cohen brackets and a modified Rankin-Cohen bracket found by Kaneko and Koike. We also give more uniform descriptions of MLDOs in terms of canonically defined higher Serre derivatives and an extension of Rankin-Cohen brackets, as well as in terms of quasimodular forms and almost holomorphic modular forms. The last of these descriptions involves the holomorphic projection map. The paper also includes some general results on the theory of quasimodular forms on both cocompact and non-cocompact subgroups of S L 2 ( R ) SL_2(\mathbb {R}) , as well as a slight sharpening of a theorem of Martin and Royer on Rankin-Cohen brackets of quasimodular forms.

A multi-objective decision-making method for small modular reactor operation based on A3C algorithm

Small modular reactors (SMRs) are ideal energy sources for remote areas, but they still require operators to make decisions. Due to the harsh working environment, it is difficult to resume operation of small modular reactors once an accident occurs in unmanned application scenarios. Therefore, a multi-objective operation scheme that ensures safety and takes into account the operational task requirements is particularly important. We proposed an artificial intelligence approach for multi-objective optimization and decision-making for SMRs. We used a multi-objective extension of the Asynchronous Advantage Actor-Critic (A3C) algorithm to learn a comprehensive optimization function reflecting the importance of each objective under different tasks. We also used a proxy deep neural network (DNN) simulating the reactor dynamics and speeding up the training process. We tested our approach on a simulated SMR under different scenarios, such as normal operation and fault occurrence. The results showed that our approach can perform well under different conditions and avoid local optima. The verification results showed that the operation limits are not violated in the transient process. Our approach solves a challenging problem and provides a valuable insight for the field of SMRs. It can also be applied to other complex systems that require multi-objective optimization and decision-making.

Operation Scheme analysis of a multipurpose small modular reactor under cogeneration condition based on a once-through steam generator dynamic model

Highly flexible load requirements and cogeneration economy need to challenge the operation of a multipurpose small modular reactor cogeneration plant with once-through steam generators. Therefore, the present study develops a once-through steam generator dynamic model to analyze the multipurpose small modular reactor operation scheme under cogeneration conditions at different power levels. The once-through steam generator dynamic model is derived based on conversation equations using the moving boundary method. It is verified with RELAP5 results and open literature and the maximum relative error is 3.21 %. Three operation schemes are proposed for multipurpose small modular reactor cogeneration operation: Scheme 1 with constant steam pressure and average coolant temperature, Scheme 2 with constant steam temperature and pressure, and Scheme 3 with constant steam temperature and pure sliding steam pressure. Steady-state and dynamic characteristics with three operation schemes are simulated and investigated at three power levels: 100 %, 70 % and 30 %. The steady-state results show that Scheme 1 is more favorable for the primary loop, while Scheme 2 is beneficial to the secondary loop, and Scheme 3 can improve the thermal efficiency at low power level. The transient findings indicate that disturbances from the reactor side have a significant impact on the once-through steam generator and the minimum settling time is 3.3 s. Consequently, steam temperature control of once-through steam generator is achieved by regulating the control rods for Schemes 2 and 3, while steam pressure is suggested to be controlled by the feedwater valve for Scheme 1. For cogeneration conditions at 70 % power level, Scheme 2 can achieve the highest steam flow of turbine, the highest steam flow of steam extraction and the smallest steam specific volume, which are 87.88 kg·s−1, 28.96 kg·s−1, and 0.0503 m3·kg−1, respectively. Scheme 2 is recommended for high power levels under cogeneration operation. In contrast, Scheme 1 is more suitable for the condensing unit operation for low power levels.

Chaotic roots of the modular multiplication dynamical system in Shor's algorithm

Shor's factoring algorithm, believed to provide an exponential speedup over classical computation, relies on finding the period of an exactly periodic quantum modular multiplication operator. This exact periodicity is the hallmark of an integrable system, which is paradoxical from the viewpoint of quantum chaos, given that the classical limit of the modular multiplication operator is a highly chaotic system that occupies the “maximally random” Bernoulli level of the classical ergodic hierarchy. In this work, we approach this apparent paradox from a quantum dynamical systems viewpoint, and consider whether signatures of ergodicity and chaos may indeed be encoded in such an “integrable” quantization of a chaotic system. We show that Shor's modular multiplication operator, in specific cases, can be written as a superposition of quantized A-baker's maps exhibiting more typical signatures of quantum chaos and ergodicity. This work suggests that the integrability of Shor's modular multiplication operator may stem from the interference of other “chaotic” quantizations of the same family of maps, and paves the way for deeper studies on the interplay of integrability, ergodicity, and chaos in and via quantum algorithms. Published by the American Physical Society 2024

Tailored environments for directed mesenchymal stromal cell proliferation and differentiation using decellularized extracellular matrices in conjunction with substrate modulus

Decellularised extracellular matrix (dECM) produced by mesenchymal stromal cells (MSCs) is a promising biomaterial for improving the ex vivo expansion of MSCs. The dECMs are often deposited on high modulus surfaces such as tissue culture plastic or glass, and subsequent differentiation assays often bias towards osteogenesis. We tested the hypothesis that dECM deposited on substrates of varying modulus will produce cell culture environments that are tailored to promote the proliferation and/or lineage-specific differentiation of MSCs. dECM was produced on type I collagen-functionalised polyacrylamide hydrogels with discrete moduli (∼4, 10, and 40 kPa) or in a linear gradient of modulus that spans the same range, and the substrates were used as culture surfaces for MSCs. Fluorescence spectroscopy and mass spectrometry characterization revealed structural compositional changes in the dECM as a function of substrate modulus. Softer substrates (4 kPa) with dECM supported the largest number of MSCs after 7 days (∼1.6-fold increase compared to glass). Additionally, osteogenic differentiation was greatest on high modulus substrates (40 kPa and glass) with dECM. Nuclear translocation of YAP1 was observed on all surfaces with a modulus of 10 kPa or greater and may be a driver for the increased osteogenesis on the high modulus surfaces. These data demonstrate that dECM technology can be integrated with environmental parameters such as substrate modulus to improve/tailor MSC proliferation and differentiation during ex vivo culture. These results have potential impact in the improved expansion of MSCs for tailored therapeutic applications and in the development of advanced tissue engineering scaffolds. Statement of significanceMesenchymal stromal cells (MSCs) are extensively used in tissue engineering and regenerative medicine due to their ability to proliferate, differentiate, and modulate the immune environment. Controlling MSC behavior is critical for advances in the field. Decellularised extracellular matrix (dECM) can maintain MSC properties in culture, increase their proliferation rate and capacity, and enhance their stimulated differentiation. Substrate stiffness is another key driver of cell function, and previous reports have primarily looked at dECM deposition and function on stiff substrates such as glass. Herein, we produce dECM on substrates of varying stiffness to create tailored environments that enhance desired MSC properties such as proliferation and differentiation. Additionally, we complete mechanistic studies including quantitative mass spec of the ECM to understand the biological function.

Large-scale Multiphysics Simulations of Small Modular Reactors Operating in Natural Circulation

Thanks to the advancements in high-performance computing, advanced modeling and simulation have become crucial in driving the development and deployment of next-generation nuclear reactors, such as small modular reactors (SMRs). SMRs offer the promise of cost-effective baseload electricity production and improved safety, while addressing some of the challenges associated with large reactor designs, such as high capital costs and extended construction timelines. As part of the Exascale Computing Project, the large-scale multiphysics simulation of an entire SMR primary system has been achieved by combining computational fluid dynamics and neutronics. In addition to the successful demonstration of full-core SMR simulations, the current study integrated the impact of natural circulation into the system. Natural circulation is the primary mechanism driving coolant circulation in SMRs. The mass flow rate in the core depends on the core power, and a numerical model has been developed to predict it. The pressure drop caused by the helical coil steam generator was also accounted for by developing a pressure drop correlation based on high-fidelity large eddy simulation results, further improving prediction accuracy. The results of the study demonstrate that the implemented natural circulation model is effective in predicting the responses of SMR full-core multiphysics simulations.

Porosity estimation based on the shear modulus inversion of seismic shear wave

Reliable estimation of subsurface porosity is necessary for hydrocarbon reservoir characterization and fluid identification. Porosity estimations from seismic data can provide the lateral distribution of subsurface porosity, but the results may be highly nonunique because subsurface elastic properties (such as velocity and density) can be affected by porosity and pore fluids. Because shear modulus is insensitive to pore fluid content, it can be effectively used to estimate porosity. We develop a novel porosity estimation method using the reflected SH wave (SH-SH wave), whose propagation characteristics depend mainly on shear modulus and S-wave velocity. We derive a new analytical expression for the SH-SH-wave reflection coefficient, which acts as a function of shear modulus and S-wave velocity in its natural logarithm form. This new approximation has high accuracy, and both coefficients corresponding to shear modulus and S-wave velocity are “model-parameter independent”; thus, there is no need for prior estimation of any model parameter during inversion. Numerical analysis indicates that shear modulus inverted from the SH-SH wave has lower uncertainty, the problem is better conditioned, and the method requires data with fewer incidence angles than algorithms that invert for the shear modulus from the PP wave. Furthermore, the highly correlated rock-physics relationships between porosity and shear modulus facilitate accurate porosity estimation. A field data application indicates that high-resolution porosity of fine structures can be reliably recovered using our method.