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The relentless pursuit of miniaturization and performance enhancement in electronic devices has led to a fundamental challenge in the field of circuit design and simulation: how to accurately account for the inherent stochastic nature of certain devices. While conventional deterministic models have served as indispensable tools for circuit designers, they fall short when it comes to capture the subtle yet critical variability exhibited by many electronic components. In this paper, we present an innovative approach that transcends the limitations of traditional modeling techniques by harnessing the power of machine learning, specifically Mixture Density Networks (MDNs), to faithfully represent and simulate the stochastic behavior of electronic devices. We demonstrate our approach to model heater cryotrons, where the model is able to capture the stochastic switching dynamics observed in the experiment. Our model shows 0.82% mean absolute error for switching probability. This paper marks a significant step forward in the quest for accurate and versatile compact models, poised to drive innovation in the realm of electronic circuits.

Recent breakthroughs by deep neural networks (DNNs) in natural language processing (NLP) and computer vision have been driven by a scale-up of models and data rather than the discovery of novel computing paradigms. Here, we investigate if scale can have a similar impact for models designed to aid small molecule drug discovery. We address this question through a large-scale and systematic analysis of how DNN size, data diet, and learning routines interact to impact accuracy on our Phenotypic Chemistry Arena (Pheno-CA) benchmark: a diverse set of drug development tasks posed on image-based high content screening data. Surprisingly, we find that DNNs explicitly supervised to solve tasks in the Pheno-CA do not continuously improve as their data and model size is scaled-up. To address this issue, we introduce a novel precursor task, the Inverse Biological Process (IBP), which is designed to resemble the causal objective functions that have proven successful for NLP. We indeed find that DNNs first trained with IBP then probed for performance on the Pheno-CA significantly outperform task-supervised DNNs. More importantly, the performance of these IBP-trained DNNs monotonically improves with data and model scale. Our findings reveal that the DNN ingredients needed to accurately solve small molecule drug development tasks are already in our hands, and project how much more experimental data is needed to achieve any desired level of improvement. We release our Pheno-CA benchmark and code to encourage further study of neural scaling laws for small molecule drug discovery.

Superconducting electronics are among the most promising alternatives to conventional CMOS technology thanks to the ultra-fast speed and ultra-high energy efficiency of the superconducting devices. Having a cryogenic control processor is also a crucial requirement for scaling the existing quantum computers up to thousands of qubits. Despite showing outstanding speed and energy efficiency, Josephson junction-based circuits suffer from several challenges such as flux trapping leading to limited scalability, difficulty in driving high impedances, and so on. Three-terminal cryotron devices have been proposed to solve these issues which can drive high impedances (>100 k{\Omega}) and are free from any flux trapping issue. In this work, we develop a reconfigurable logic circuit using a heater cryotron (hTron). In conventional approaches, the number of devices to perform a logic operation typically increases with the number of inputs. However, here, we demonstrate a single hTron device-based logic circuit that can be reconfigured to perform 1-input copy and NOT, 2-input AND and OR, and 3-input majority logic operations by choosing suitable biasing conditions. Consequently, we can perform any processing task with a much smaller number of devices. Also, since we can perform different logic operations with the same circuit (same layout), we can develop a camouflaged system where all the logic gates will have the same layout. Therefore, this proposed circuit will ensure enhanced hardware security against reverse engineering attacks., Comment: 13 pages, 6 figures

For the last 50 years, superconducting detectors have offered exceptional sensitivity and speed for detecting faint electromagnetic signals in a wide range of applications. These detectors operate at very low temperatures and generate a minimum of excess noise, making them ideal for testing the non-local nature of reality, investigating dark matter, mapping the early universe, and performing quantum computation and communication. Despite their appealing properties, however, there are currently no large-scale superconducting cameras - even the largest demonstrations have never exceeded 20 thousand pixels. This is especially true for one of the most promising detector technologies, the superconducting nanowire single-photon detector (SNSPD). These detectors have been demonstrated with system detection efficiencies of 98.0%, sub-3-ps timing jitter, sensitivity from the ultraviolet (250nm) to the mid-infrared (10um), and dark count rates below 6.2e-6 counts per second (cps), but despite more than two decades of development they have never achieved an array size larger than a kilopixel. Here, we report on the implementation and characterization of a 400,000 pixel SNSPD camera, a factor of 400 improvement over the previous state-of-the-art. The array spanned an area 4x2.5 mm with a 5x5um resolution, reached unity quantum efficiency at wavelengths of 370 nm and 635 nm, counted at a rate of 1.1e5 cps, and had a dark count rate of 1e-4 cps per detector (corresponding to 0.13 cps over the whole array). The imaging area contains no ancillary circuitry and the architecture is scalable well beyond the current demonstration, paving the way for large-format superconducting cameras with 100% fill factors and near-unity detection efficiencies across a vast range of the electromagnetic spectrum.

We consider a general queueing model with price-sensitive customers in which the service provider seeks to balance two objectives, maximizing the average revenue rate and minimizing the average queue length. Customers arrive according to a Poisson process, observe an offered price, and decide to join the queue if their valuation exceeds the price. The queue is operated first-in first-out, and the service times are exponential. Our model represents applications in areas like make-to-order manufacturing, cloud computing, and food delivery. The optimal solution for our model is dynamic; the price changes as the state of the system changes. However, such dynamic pricing policies may be undesirable for a variety of reasons. In this work, we provide performance guarantees for a simple and natural class of static pricing policies which charge a fixed price up to a certain occupancy threshold and then allow no more customers into the system. We provide a series of results showing that such static policies can simultaneously guarantee a constant fraction of the optimal revenue with at most a constant factor increase in expected queue length. For instance, our policy for the M/M/1 setting allows bi-criteria approximations of $(0.5, 1), (0.66, 1.16), (0.75, 1.54)$ and $(0.8, 2)$ for the revenue and queue length, respectively. We also provide guarantees for settings with multiple customer classes and multiple servers, as well as the expected sojourn time objective.

In data-driven stochastic optimization, model parameters of the underlying distribution need to be estimated from data in addition to the optimization task. Recent literature considers integrating the estimation and optimization processes by selecting model parameters that lead to the best empirical objective performance. This integrated approach, which we call integrated-estimation-optimization (IEO), can be readily shown to outperform simple estimate-then-optimize (ETO) when the model is misspecified. In this paper, we show that a reverse behavior appears when the model class is well-specified and there is sufficient data. Specifically, for a general class of nonlinear stochastic optimization problems, we show that simple ETO outperforms IEO asymptotically when the model class covers the ground truth, in the strong sense of stochastic dominance of the regret. Namely, the entire distribution of the regret, not only its mean or other moments, is always better for ETO compared to IEO. Our results also apply to constrained, contextual optimization problems where the decision depends on observed features. Whenever applicable, we also demonstrate how standard sample average approximation (SAA) performs the worst when the model class is well-specified in terms of regret, and best when it is misspecified. Finally, we provide experimental results to support our theoretical comparisons and illustrate when our insights hold in finite-sample regimes and under various degrees of misspecification.

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order. The authors dedicate this paper to the 2023 Turkey/Syria earthquake victims. We sincerely hope that advances in OR will play a role towards minimising the pain and suffering caused by this and future catastrophes.

We present multiplexed gradient descent (MGD), a gradient descent framework designed to easily train analog or digital neural networks in hardware. MGD utilizes zero-order optimization techniques for online training of hardware neural networks. We demonstrate its ability to train neural networks on modern machine learning datasets, including CIFAR-10 and Fashion-MNIST, and compare its performance to backpropagation. Assuming realistic timescales and hardware parameters, our results indicate that these optimization techniques can train a network on emerging hardware platforms orders of magnitude faster than the wall-clock time of training via backpropagation on a standard GPU, even in the presence of imperfect weight updates or device-to-device variations in the hardware. We additionally describe how it can be applied to existing hardware as part of chip-in-the-loop training, or integrated directly at the hardware level. Crucially, the MGD framework is highly flexible, and its gradient descent process can be optimized to compensate for specific hardware limitations such as slow parameter-update speeds or limited input bandwidth.

We consider a personalized pricing problem in which we have data consisting of feature information, historical pricing decisions, and binary realized demand. The goal is to perform off-policy evaluation for a new personalized pricing policy that maps features to prices. Methods based on inverse propensity weighting (including doubly robust methods) for off-policy evaluation may perform poorly when the logging policy has little exploration or is deterministic, which is common in pricing applications. Building on the balanced policy evaluation framework of Kallus (2018), we propose a new approach tailored to pricing applications. The key idea is to compute an estimate that minimizes the worst-case mean squared error or maximizes a worst-case lower bound on policy performance, where in both cases the worst-case is taken with respect to a set of possible revenue functions. We establish theoretical convergence guarantees and empirically demonstrate the advantage of our approach using a real-world pricing dataset.

Advanced electro-optic processing combines electrical control with optical modulation and detection. For quantum photonic applications these processes must be carried out at the single photon level with high efficiency and low noise. Integrated quantum photonics has made great strides achieving single photon manipulation by combining key components on integrated chips which are operated by external driving electronics. Nevertheless, electrical interconnects between driving electronics and the electro-optic components, some of which require cryogenic operating conditions, can introduce parasitic effects. Here we show an all-optical interface which simultaneously delivers the operation power to, and extracts the measurement signal from, an advanced photonic circuit, namely, bias and readout of a superconducting nanowire single photon detector (SNSPD) on a single stage in a 1K cryostat. To do so, we supply all power for the single photon detector, output signal conditioning, and electro-optic readout using optical interconnects alone, thereby fully decoupling the cryogenic circuitry from the external environment. This removes the need to heatsink electrical connections, and potentially offers low-loss, high-bandwidth signal processing. This method opens the possibility to operate other advanced electrically decoupled photonic circuits such as optical control and readout of superconducting circuits, and feedforward for photonic quantum computing.

We consider the problem of pricing a reusable resource service system. Potential customers arrive according to a Poisson process and purchase the service if their valuation exceeds the current price. If no units are available, customers immediately leave without service. Serving a customer corresponds to using one unit of the reusable resource, where the service time has an exponential distribution. The objective is to maximize the steady-state revenue rate. This system is equivalent to the classical Erlang loss model with price-sensitive customers, which has applications in vehicle sharing, cloud computing, and spare parts management. Although an optimal pricing policy is dynamic, we provide two main results that show a simple static policy is universally near-optimal for any service rate, arrival rate, and number of units in the system. When there is one class of customers who have a monotone hazard rate (MHR) valuation distribution, we prove that a static pricing policy guarantees 90.4\% of the revenue from the optimal dynamic policy. When there are multiple classes of customers that each have their own regular valuation distribution and service rate, we prove that static pricing guarantees 78.9\% of the revenue of the optimal dynamic policy. In this case, the optimal pricing policy is exponentially large in the number of classes while the static policy requires only one price per class. Moreover, we prove that the optimal static policy can be easily computed, resulting in the first polynomial time approximation algorithm for this problem.

Newsvendor problems are an important and much-studied topic in stochastic inventory control. One strand of the literature on newsvendor problems is concerned with the fact that practitioners often make judgemental adjustments to the theoretically "optimal" order quantities. Although judgemental adjustment is sometimes beneficial, two specific kinds of adjustment are normally considered to be particularly naive: demand chasing and pull-to-centre. We discuss how these adjustments work in practice and what they imply in a variety of settings. We argue that even such naive adjustments can be useful under certain conditions. This is confirmed by experiments on simulated data. Finally, we propose a heuristic algorithm for "tuning" the adjustment parameters in practice.

Superconducting optoelectronic hardware is being explored as a path towards artificial spiking neural networks with unprecedented scales of complexity and computational ability. Such hardware combines integrated-photonic components for few-photon, light-speed communication with superconducting circuits for fast, energy-efficient computation. Monolithic integration of superconducting and photonic devices is necessary for the scaling of this technology. In the present work, superconducting-nanowire single-photon detectors are monolithically integrated with Josephson junctions for the first time, enabling the realization of superconducting optoelectronic synapses. We present circuits that perform analog weighting and temporal leaky integration of single-photon presynaptic signals. Synaptic weighting is implemented in the electronic domain so that binary, single-photon communication can be maintained. Records of recent synaptic activity are locally stored as current in superconducting loops. Dendritic and neuronal nonlinearities are implemented with a second stage of Josephson circuitry. The hardware presents great design flexibility, with demonstrated synaptic time constants spanning four orders of magnitude (hundreds of nanoseconds to milliseconds). The synapses are responsive to presynaptic spike rates exceeding 10 MHz and consume approximately 33 aJ of dynamic power per synapse event before accounting for cooling. In addition to neuromorphic hardware, these circuits introduce new avenues towards realizing large-scale single-photon-detector arrays for diverse imaging, sensing, and quantum communication applications., Comment: 23 pages, 20 figures

Although superconducting nanowire single-photon detectors (SNSPDs) are a promising technology for quantum optics, metrology, and astronomy, they currently lack a readout architecture that is scalable to the megapixel regime and beyond. In this work, we have designed and demonstrated such an architecture for SNSPDs, called the thermally-coupled imager (TCI). The TCI uses a combination of time-of-flight delay lines and thermal coupling to create a scalable architecture that can scale to large array sizes, allows neighboring detectors to operate independently, and requires only four microwave readout lines to operate no matter the size of the array. We give an overview of how the architecture functions, and demonstrate a proof-of-concept $32\times32$ imaging array. The array was able to image a free-space focused spot at 373 nm, count at 9.6 Mcps, and resolve photon location with greater than 99.83\% distinguishability.