Limits Of Computation Research Articles

Quantum Neural Networks in Machine Learning: Problems and Prospects

Despite rapid theoretical and practical progress, machine learning algorithms require large computational resources. However, new opportunities are opening up due to the advent of quantum computing devices that directly use the laws of quantum mechanics to bypass the technological and thermodynamic limitations of classical computing. Taking into account that artificial neural networks are actively used in solving a number of practical problems, with the advent of quantum computing technologies, the development of quantum neural networks for the implementation of quantum machine learning is very relevant. The article considers a quantum analogue of classical neurons that form quantum neural networks capable of performing universal quantum computations.

Mitigating Computer Limitations in Replicating Numerical Simulations of a Neural Network Model With Hodgkin-Huxley-Type Neurons.

Computational experiments have been very important to numerically simulate real phenomena in several areas. Many studies in computational biology discuss the necessity to obtain numerical replicability to accomplish new investigations. However, even following well-established rules in the literature, numerical replicability is unsuccessful when it takes the computer's limitations for representing real numbers into consideration. In this study, we used a previous published recurrent network model composed by Hodgkin-Huxley-type neurons to simulate the neural activity during development. The original source code in C/C++ was carefully refactored to mitigate the lack of replicability; moreover, it was re-implemented to other programming languages/software (XPP/XPPAUT, Python and Matlab) and executed under two operating systems (Windows and Linux). The commutation and association of the input current values during the summation of the pre-synaptic activity were also analyzed. A total of 72 simulations which must obtain the same result were executed to cover these scenarios. The results were replicated when the high floating-point precision (supplied by third-party libraries) was used. However, using the default floating-point precision type, none of the results were replicated when compared with previous results. Several new procedures were proposed during the source code refactorization; they allowed replicating only a few scenarios, regardless of the language and operating system. Thus, the generated computational “errors” were the same. Even using a simple computational model, the numerical replicability was very difficult to be achieved, requiring people with computational expertise to be performed. After all, the research community must be aware that conducting analyses with numerical simulations that use real number operations can lead to different conclusions.

Interconnects for DNA, Quantum, In-Memory, and Optical Computing: Insights From a Panel Discussion

The computing world is witnessing a proverbial Cambrian explosion of emerging paradigms propelled by applications, such as artificial intelligence, big data, and cybersecurity. The recent advances in technology to store digital data inside a deoxyribonucleic acid (DNA) strand, manipulate quantum bits (qubits), perform logical operations with photons, and perform computations inside memory systems are ushering in the era of emerging paradigms of DNA computing, quantum computing, optical computing, and in-memory computing. In an orthogonal direction, research on interconnect design using advanced electro-optic, wireless, and microfluidic technologies has shown promising solutions to the architectural limitations of traditional von-Neumann computers. In this article, experts present their comments on the role of interconnects in the emerging computing paradigms, and discuss the potential use of chiplet-based architectures for the heterogeneous integration of such technologies.

Workload Balancing in Mobile Edge Computing for Internet of Things: A Population Game Approach

Mobile edge computing (MEC) is an emerging paradigm that provides radio access networks with augmented resources to meet the requirements of Internet of Things (IoT) services. MEC allows IoT devices to offload delay sensitive and computation intensive tasks to edge clouds deployed at base stations (BSs). Offloading tasks to edge clouds can alleviate the computing and battery limitations of IoT devices. However, task offloading in MEC for IoT may face serious transmission latency and computation latency problems with massive number of IoT devices. Moreover, some edge clouds can be overloaded due to the spatially inhomogeneous distributions of IoT tasks. To solve these problems, we investigate the workload balancing problems to minimize the transmission latency and computation latency in task offloading process while considering the limited bandwidth resources of BSs and computation resources in edge clouds. We formulate the workload balancing problem as a population game in order to analyze the aggregate offloading decisions. We analyze the aggregate offloading decisions of mobile users through evolutionary game dynamics and show that the game always achieves a Nash equilibrium (NE). We further propose two workload balancing algorithms based on evolutionary dynamics and revision protocols. Simulation results show that our proposed workload balancing algorithms can achieve better performance than existing solutions.

A New Framework Containing Convolution and Pooling Circuits for Image Processing and Deep Learning Applications with Quantum Computing Implementation

The resource need for deep learning and quantum computers' high computing power potential encourage collaboration between the two fields. Today, variational quantum circuits are used to perform the convolution operation with quantum computing. However, the results produced by variational circuits do not show a direct resemblance to the classical convolution operation. Because classical data is encoded into quantum data with their exact values in value-encoded methods, in contrast to variational quantum circuits, arithmetical operations can be applied with high accuracy. In this study, value-encoded quantum circuits for convolution and pooling operations are proposed to apply deep learning in quantum computers in a traditional and proven way. To construct the convolution and pooling operations, some modules such as addition, multiplication, division, and comparison are created. In addition, a window-based framework for quantum image processing applications is proposed. The generated convolution and pooling circuits are simulated on the IBM QISKIT simulator in parallel thanks to the proposed framework. The obtained results are verified by the expected results. Due to the limitations of quantum simulators and computers in the NISQ era, the used grayscale images are resized to 8x8 and the resolution of the images is reduced to 3 qubits. With developing the quantum technologies, the proposed approach can be applied for bigger and higher resolution images. Although the proposed method causes more qubit usage and circuit depth compared to variational convolutional circuits, the results they produce are exactly the same as the classical convolution process.

Software engineering for quantum programming: How far are we?

Quantum computing is no longer only a scientific interest but is rapidly becoming an industrially available technology that can potentially overcome the limits of classical computation. Over the last years, all major companies have provided frameworks and programming languages that allow developers to create their quantum applications. This shift has led to the definition of a new discipline called quantum software engineering, which is demanded to define novel methods for engineering large-scale quantum applications. While the research community is successfully embracing this call, we notice a lack of systematic investigations into the state of the practice of quantum programming. Understanding the challenges that quantum developers face is vital to precisely define the aims of quantum software engineering. Hence, in this paper, we first mine all the GitHub repositories that make use of the most used quantum programming frameworks currently on the market and then conduct coding analysis sessions to produce a taxonomy of the purposes for which quantum technologies are used. In the second place, we conduct a survey study that involves the contributors of the considered repositories, which aims to elicit the developers’ opinions on the current adoption and challenges of quantum programming. On the one hand, the results highlight that the current adoption of quantum programming is still limited. On the other hand, there are many challenges that the software engineering community should carefully consider: these do not strictly pertain to technical concerns but also socio-technical matters.

Turing Meets Shannon: On the Algorithmic Construction of Channel-Aware Codes

A capacity result involves two parts: achievability and converse. The achievability proof is usually non-constructive and only the existence of capacity-achieving codes is shown invoking probabilistic techniques. Recently, capacity-achieving codes have been found for several channels demonstrating that such codes can actually be constructed algorithmically. To this end, each construction is designed for a pre-specified channel so that the corresponding algorithm is specifically tailored to it. This paper addresses the general question of whether or not it is possible to find algorithms that can construct capacity-achieving codes for a whole class of channels. To do so, the concept of Turing machines is used which provides the fundamental performance limits of digital computers and therewith fully specifies which tasks are algorithmically feasible in principle. It is shown that there exists no Turing machine that is able to construct capacity-achieving codes for a whole class of channels, where the channel realization from this class is given as an input to the Turing machine. It is further shown that such an algorithmic construction remains impossible when the optimality condition is dropped and codes only need to achieve a fraction of the capacity. Finally, implications on channel-aware transmission, link adaptation, and cross-layer optimization are discussed.

The stress function basis of the upper bound theorem of plasticity

The discontinuous slip-line form of upper bound plasticity analysis is considered using an equilibrium of forces approach. It is demonstrated that the underlying basis of the approach can be written in terms of stress functions that provide a continuum stress state interpretation of the upper bound solution. An alternative proof of the upper bound theorem, applicable to both associative and non-associative materials, using stress functions is presented. The broader nature of the equilibrium form and the strict conditions under which it is valid are discussed, including examination of the apparent omission of moment equilibrium and associativity in many equilibrium form solutions. Finally, the relationship of the stress function formulation to the output of the computational limit analysis method discontinuity layout optimisation (DLO) and the potential to use the stress function formulation to derive a form of lower bound solution from an upper bound analysis are demonstrated.

A retrospective on hydrological catchment modelling based on half a century with the HBV model

Abstract. Hydrological catchment models are important tools that are commonly used as the basis for water resource management planning. In the 1960s and 1970s, the development of several relatively simple models to simulate catchment runoff started, and a number of so-called conceptual (or bucket-type) models were suggested. In these models, the complex and heterogeneous hydrological processes in a catchment are represented by a limited number of storage elements and the fluxes between them. While computer limitations were a major motivation for such relatively simple models in the early days, some of these models are still used frequently despite the vast increase in computational opportunities. The HBV (Hydrologiska Byråns Vattenbalansavdelning) model, which was first applied about 50 years ago in Sweden, is a typical example of a conceptual catchment model and has gained large popularity since its inception. During several model intercomparisons, the HBV model performed well despite (or because of) its relatively simple model structure. Here, the history of model development, from thoughtful considerations of different model structures to modelling studies using hundreds of catchments and cloud computing facilities, is described. Furthermore, the wide range of model applications is discussed. The aim is to provide an understanding of the background of model development and a basis for addressing the balance between model complexity and data availability that will also face hydrologists in the coming decades.

Open quantum dynamics for plant motions

Stochastic Schrödinger equations that govern the dynamics of open quantum systems are given by the equations for signal processing. In particular, the Brownian motion that drives the wave function of the system does not represent noise, but provides purely the arrival of new information. Thus the wave function is guided by the optimal signal detection about the conditions of the environments under noisy observations. This behaviour is similar to biological systems that detect environmental cues, process this information, and adapt to them optimally by minimising uncertainties about the conditions of their environments. It is postulated that information-processing capability is a fundamental law of nature, and hence that models describing open quantum systems can equally be applied to biological systems to model their dynamics. For illustration, simple stochastic models are considered to capture heliotropic and gravitropic motions of plants. The advantage of such dynamical models is that they allow for the quantification of information processed by the plants. By considering the consequence of information erasure, it is argued that biological systems can process environmental signals relatively close to the Landauer limit of computation, and that loss of information must lie at the heart of ageing in biological systems.

Structured precision skipping: Accelerating convolutional neural networks with budget-aware dynamic precision selection

Despite the remarkable advancement in various intelligence tasks achieved by Convolutional Neural Networks, the massive computation and storage consumption limit applications on resource-constrained devices. Existing works explore to reduce computation cost by leveraging the input-dependent redundancy at runtime. The irregular dynamic sparsity distribution, however, limits the real speedup for dynamic models deployed in traditional neural network accelerators. To solve this problem, we propose an algorithm-architecture co-design, named structured precision skipping (SPS), to exploit the dynamic precision redundancy in statically quantized models. SPS computes most neurons in a lower precision and only a small portion of important neurons in a higher precision to preserve performance. Specifically, we first propose the structured dynamic block to exploit the dynamic sparsity in a structured manner. Based on the block, we then apply a budget-aware training method by inducing a budget regularization to learn the precision skipping under a target resource constraint. Finally, we present an architecture design based on the bit-serial architecture with support for SPS models, where only a predict controller module with small overhead is introduced. Extensive evaluation results demonstrate that SPS can achieve up to 1.5× speedup and 1.4× energy saving on various models and datasets with marginal accuracy loss.

Analytical Nonadiabatic Couplings and Gradients within the State-Averaged Orbital-Optimized Variational Quantum Eigensolver.

We introduce several technical and analytical extensions to our recent state-averaged orbital-optimized variational quantum eigensolver (SA-OO-VQE) algorithm (see Yalouz et al. Quantum Sci. Technol. 2021, 6, 024004). Motivated by the limitations of current quantum computers, the first extension consists of an efficient state-resolution procedure to find the SA-OO-VQE eigenstates, and not just the subspace spanned by them, while remaining in the equi-ensemble framework. This approach avoids expensive intermediate resolutions of the eigenstates by postponing this problem to the very end of the full algorithm. The second extension allows for the estimation of analytical gradients and nonadiabatic couplings, which are crucial in many practical situations ranging from the search of conical intersections to the simulation of quantum dynamics, in, for example, photoisomerization reactions. The accuracy of our new implementations is demonstrated on the formaldimine molecule CH2NH (a minimal Schiff base model relevant for the study of photoisomerization in larger biomolecules), for which we also perform a geometry optimization to locate a conical intersection between the ground and first-excited electronic states of the molecule.

A mathematical theory of the computational resolution limit in one dimension

Given an image generated by the convolution of point sources with a band-limited function, the deconvolution problem involves reconstructing the source number, positions, and amplitudes. This problem is related to many important applications in imaging and signal processing. It is well known that it is impossible to resolve the sources when they are sufficiently close in practice. Rayleigh investigated this problem and formulated a resolution limit known as the Rayleigh limit for the case of two sources with identical amplitudes. However, many numerical experiments have demonstrated that stable recovery of the sources is possible even if the sources are separated below the Rayleigh limit. In this study, a mathematical theory for the deconvolution problem in one dimension is developed. The theory addresses the problem when the source number can be recovered exactly from noisy data. The key component is a new concept called the “computational resolution limit,” which is defined as the minimum separation distance between the sources such that exact recovery of the source number is possible. This new resolution limit is determined by the signal-to-noise ratio and the sparsity of sources, as well as the cutoff frequency of the image. Quantitative bounds for this limit are derived, and they demonstrate the importance of the sparsity and signal-to-noise ratio for the recovery problem. The stability of recovering the source positions is also analyzed under a condition on their separation distances. Moreover, a singular value thresholding algorithm is proposed to recover the source number for a cluster of closely spaced point sources and to verify our theoretical results regarding the computational resolution limit. The results are based on a multipole expansion method and a nonlinear approximation theory in Vandermonde space.

Desa Peduli Pendidikan melalui pendampingan penulisan Karya Ilmiah (laporan PTK)

The publication of scientific papers is an essential element in promoting educators. The problem is that the average teacher at SD Negeri 45 has not written and published independently. Some teachers are not proficient in operating computers, especially Microsoft Office Word. Even though writing scientific papers requires these skills to facilitate the work of teachers during writing. In this service, several points are trained, namely optimizing the use of Microsoft Office Word, the rules of writing scientific reports and publications, and techniques for implementing CAR. This activity was carried out on September 18, 2021. The partners of this service were all teachers at the 45 Ternate State Elementary School. The method used is demonstration, lecture, and question and answer. The results of community service activities show that teachers at SD Negeri 45 Ternate City can write CAR scientific reports even though only three people have the best writing skills. At the evaluation stage, several corrections were found, such as spelling errors, data analysis techniques, and the use of references. The obstacle in this research is the limitations of laptops and computers. It takes a long time because there are three available laptop facilities during practice, so the teacher is divided into 3 study groups. However, overall, this service can provide understanding and motivation to teachers at SD Negeri 45 Ternate City to write scientific papers

Coupled bend–twist mechanics of biomimetic scale substrate

We develop the mechanics of combined bending and twisting deformation of a one-dimensional filamentous structure with protruding stiff fish-scale-like plates embedded at an angle on the surface. We develop a Cosserat kinematic formulation along with scale contact constraints. This geometrically exact model allows us to bypass the limitations of small deflection finite element computations, thereby preserving the accuracy of scale kinematics. The derived structure–property relationships reveal, for the first time, the combined effect of bending and twisting on a slender fish-scale inspired substrate. The model subsumes previous models on pure bending and pure twisting, but also shows previously unobserved phenomena that arise due to the coupled effects of these loads. These include a new interpretation of kinematic locking behavior, multiple contact regimes, asymmetric sensitivities of one curvature over the other, and discontinuous transitions in the nonlinear moment–curvature and torque–twist behaviors, reflecting the complex scale engagement patterns.

A backprojection kernel (KRNL3D) for very-wide-aperture 3D tomography applied to PET with Multigrid for precise use of time-of-flight data

In ‘KRNL3D’ we derive a kernel function K(y 1, y 2, φ) whose backprojections from all directions (θ, φ) in the spherical band on the celestial sphere, when integrated with respect to solid angle, yield ρ, the 3D Gaussian point response function (PRF) of radius 1. This K, when convolved against line integral data from an unknown density function f, yields an integral formula for the ‘mollification’ ff = ρ ∗ f, which is a slightly blurred version of f, and which stabilizes the mild ill-posedness. Applied to positron emission tomography that backprojection reconstruction occurs stochastically and one emission event at a time, after needed data corrections. We describe Octave (≈Matlab) codes to tabulate K and to test its use with a large aperture or π/6. ‘KRNL3D- TOF’ truncates backprojection to a cylindrical patch about the TOF approximate location of each event. These ‘backplacements’ decrease the computational cost and limit noise and streaking in one region from contaminating the reconstruction in more distant regions. They also retain the ability to count emission events in an isolated blob despite very low event counts, a valuable feature for dynamic studies of metabolic processes. ‘Multigrid’ allows further reduction in the radius and lengths of the cylinders, thereby enabling even more precise use of the TOF information. This precision should be especially important as researchers decrease the TOF uncertainty in newer generation scanners. Finally, we discuss ‘further work’ that needs to be done. Our codes are being made freely available at https://github.com/keithmillerberkeley/PET-codes.

A Lightweight Proxy Re-Encryption Approach with Certificate-Based and Incremental Cryptography for Fog-Enabled E-Healthcare

Cloud computing aims to provide reliable, customized, and quality of service (QoS) guaranteed dynamic computing environments for end-users. However, there are applications such as e-health and emergency response monitoring that require quick response and low latency. Delays caused by transferring data over the cloud can seriously affect the performance and reliability of real-time applications. Before outsourcing e-health care data to the cloud, the user needs to perform encryption on these sensitive data to ensure its confidentiality. Conventionally, any modification to the user data requires encrypting the entire data and calculating the hash of the data from scratch. This data modification mechanism increases communication and computation costs over the cloud. The distributed environment of fog computing is used to overcome the limitations of cloud computing. This paper proposed a certificate-based incremental proxy re-encryption scheme (CB-PReS) for e-health data sharing in fog computing. The proposed scheme improves the file modification operations, i.e., updation, deletion, and insertion. The proposed scheme is tested on the iFogSim simulator. The iFogSim simulator facilitates the development of models for fog and IoT environments, and it also measures the impact of resource management techniques regarding network congestion and latency. Experiments depict that the proposed scheme is better than the existing schemes based on expensive bilinear pairing and elliptic curve techniques. The proposed scheme shows significant improvement in key generation and file modification time.

Improving Column Generation for Vehicle Routing Problems via Random Coloring and Parallelization

We consider a variant of the vehicle routing problem (VRP) where each customer has a unit demand and the goal is to minimize the total cost of routing a fleet of capacitated vehicles from one or multiple depots to visit all customers. We propose two parallel algorithms to efficiently solve the column-generation-based linear-programming relaxation for this VRP. Specifically, we focus on algorithms for the “pricing problem,” which corresponds to the resource-constrained elementary shortest path problem. The first algorithm extends the pulse algorithm for which we derive a new bounding scheme on the maximum load of any route. The second algorithm is based on random coloring from parameterized complexity which can be also combined with other techniques in the literature for improving VRPs, including cutting planes and column enumeration. We conduct numerical studies using VRP benchmarks (with 50–957 nodes) and instances of a medical home care delivery problem using census data in Wayne County, Michigan. Using parallel computing, both pulse and random coloring can significantly improve column generation for solving the linear programming relaxations and we can obtain heuristic integer solutions with small optimality gaps. Combining random coloring with column enumeration, we can obtain improved integer solutions having less than 2% optimality gaps for most VRP benchmark instances and less than 1% optimality gaps for the medical home care delivery instances, both under a 30-minute computational time limit. The use of cutting planes (e.g., robust cuts) can further reduce optimality gaps on some hard instances, without much increase in the run time. Summary of Contribution: The vehicle routing problem (VRP) is a fundamental combinatorial problem, and its variants have been studied extensively in the literature of operations research and computer science. In this paper, we consider general-purpose algorithms for solving VRPs, including the column-generation approach for the linear programming relaxations of the integer programs of VRPs and the column-enumeration approach for seeking improved integer solutions. We revise the pulse algorithm and also propose a random-coloring algorithm that can be used for solving the elementary shortest path problem that formulates the pricing problem in the column-generation approach. We show that the parallel implementation of both algorithms can significantly improve the performance of column generation and the random coloring algorithm can improve the solution time and quality of the VRP integer solutions produced by the column-enumeration approach. We focus on algorithmic design for VRPs and conduct extensive computational tests to demonstrate the performance of various approaches.

ELECTRIC POWER BID DETERMINATION AND EVALUATION FOR PRICE TAKER UNITS UNDER PRICE UNCERTAINTY

Power companies aim to maximize their profit which is highly related to the bidding strategies used. In order to sell electricity at high prices and maximize their profit, power companies need suitable bidding models that consider power operating constraints and price uncertainty within the market. Price taker units have no power to affect the prices but need to determine their best bidding strategy to maximize their profit assuming a quadratic cost function and uncertain market prices. Price taker units also need to evaluate their bidding strategy under different price scenarios. In this paper, we first model the bidding problem for a price taker unit and then propose quadratic programming, nonlinear programming and marginal cost based bidding models under price uncertainty. We use case studies to study the computation burden and limitation to reach a solution. We also propose a simulation methodology to evaluate the performance of each bidding strategy for different market prices in an effort to help decision makers to assess their bidding decisions.Keywords: Bidding, nonlinear programming, quadratic programming, simulation, electricity marketsJEL Classifications: L94, D44, D47, E17DOI: https://doi.org/10.32479/ijeep.11382

On Preserving Scientific Integrity for Climate Model Data in the HPC Era

Over the last 30 years, the Computational Science Graduate Fellowship (CSGF) program has played an integral role in preparing a large and diverse community of computational scientists to push the limits of high-performance computing (HPC). To celebrate the CSGF program’s enduring influence, I share my perspective from the climate modeling community, which has used HPC to better understand the earth’s climate system. While the benefits of HPC in climate science have been enormous, rapid computing advances have brought new challenges. One difficulty is quality assurance—ensuring that large and complex codes running on multiple platforms are correct. A second is mitigating the increasingly large data volumes. Here, I describe our software quality assurance framework and strategies to reduce climate data volumes. In these complementary efforts, our focus has been preserving the scientific integrity of the simulation output data, a priority shared across HPC model simulation disciplines.