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It is well-known that Resolution proofs can be efficiently simulated by Sherali-Adams (SA) proofs. We show, however, that any such simulation needs to exploit huge coefficients: Resolution cannot be efficiently simulated by SA when the coefficients are written in unary. We also show that Reversible Resolution (a variant of MaxSAT Resolution) cannot be efficiently simulated by Nullstellensatz (NS). These results have consequences for total NP search problems. First, we characterise the classes PPADS, PPAD, SOPL by unary-SA, unary-NS, and Reversible Resolution, respectively. Second, we show that, relative to an oracle, PLS $\not\subseteq$ PPP, SOPL $\not\subseteq$ PPA, and EOPL $\not\subseteq$ UEOPL. In particular, together with prior work, this gives a complete picture of the black-box relationships between all classical TFNP classes introduced in the 1990s.

Event cameras are bio-inspired sensors that perform well in challenging illumination conditions and have high temporal resolution. However, their concept is fundamentally different from traditional frame-based cameras. The pixels of an event camera operate independently and asynchronously. They measure changes of the logarithmic brightness and return them in the highly discretised form of time-stamped events indicating a relative change of a certain quantity since the last event. New models and algorithms are needed to process this kind of measurements. The present work looks at several motion estimation problems with event cameras. The flow of the events is modelled by a general homographic warping in a space-time volume, and the objective is formulated as a maximisation of contrast within the image of warped events. Our core contribution consists of deriving globally optimal solutions to these generally non-convex problems, which removes the dependency on a good initial guess plaguing existing methods. Our methods rely on branch-and-bound optimisation and employ novel and efficient, recursive upper and lower bounds derived for six different contrast estimation functions. The practical validity of our approach is demonstrated by a successful application to three different event camera motion estimation problems.

Due to its communication efficiency and privacy-preserving capability, federated learning (FL) has emerged as a promising framework for machine learning in 5G-and-beyond wireless networks. Of great interest is the design and optimization of new wireless network structures that support the stable and fast operation of FL. Cell-free massive multiple-input multiple-output (CFmMIMO) turns out to be a suitable candidate, which allows each communication round in the iterative FL process to be stably executed within a large-scale coherence time. Aiming to reduce the total execution time of the FL process in CFmMIMO, this paper proposes choosing only a subset of available users to participate in FL. An optimal selection of users with favorable link conditions would minimize the execution time of each communication round, while limiting the total number of communication rounds required. Toward this end, we formulate a joint optimization problem of user selection, transmit power, and processing frequency, subject to a predefined minimum number of participating users to guarantee the quality of learning. We then develop a new algorithm that is proven to converge to the neighbourhood of the stationary points of the formulated problem. Numerical results confirm that our proposed approach significantly reduces the FL total execution time over baseline schemes. The time reduction is more pronounced when the density of access point deployments is moderately low.

Cross-validation is a widely-used technique to estimate prediction error, but its behavior is complex and not fully understood. Ideally, one would like to think that cross-validation estimates the prediction error for the model at hand, fit to the training data. We prove that this is not the case for the linear model fit by ordinary least squares; rather it estimates the average prediction error of models fit on other unseen training sets drawn from the same population. We further show that this phenomenon occurs for most popular estimates of prediction error, including data splitting, bootstrapping, and Mallow's Cp. Next, the standard confidence intervals for prediction error derived from cross-validation may have coverage far below the desired level. Because each data point is used for both training and testing, there are correlations among the measured accuracies for each fold, and so the usual estimate of variance is too small. We introduce a nested cross-validation scheme to estimate this variance more accurately, and we show empirically that this modification leads to intervals with approximately correct coverage in many examples where traditional cross-validation intervals fail.

Electric Vehicles are increasingly common, with inductive chargepads being considered a convenient and efficient means of charging electric vehicles. However, drivers are typically poor at aligning the vehicle to the necessary accuracy for efficient inductive charging, making the automated alignment of the two charging plates desirable. In parallel to the electrification of the vehicular fleet, automated parking systems that make use of surround-view camera systems are becoming increasingly popular. In this work, we propose a system based on the surround-view camera architecture to detect, localize, and automatically align the vehicle with the inductive chargepad. The visual design of the chargepads is not standardized and not necessarily known beforehand. Therefore, a system that relies on offline training will fail in some situations. Thus, we propose a self-supervised online learning method that leverages the driver's actions when manually aligning the vehicle with the chargepad and combine it with weak supervision from semantic segmentation and depth to learn a classifier to auto-annotate the chargepad in the video for further training. In this way, when faced with a previously unseen chargepad, the driver needs only manually align the vehicle a single time. As the chargepad is flat on the ground, it is not easy to detect it from a distance. Thus, we propose using a Visual SLAM pipeline to learn landmarks relative to the chargepad to enable alignment from a greater range. We demonstrate the working system on an automated vehicle as illustrated in the video at //youtu.be/_cLCmkW4UYo. To encourage further research, we will share a chargepad dataset used in this work.

We study the class of dependence models for spatial data obtained from Cauchy convolution processes based on different types of kernel functions. We show that the resulting spatial processes have appealing tail dependence properties, such as tail dependence at short distances and independence at long distances with suitable kernel functions. We derive the extreme-value limits of these processes, study their smoothness properties, and detail some interesting special cases. To get higher flexibility at sub-asymptotic levels and separately control the bulk and the tail dependence properties, we further propose spatial models constructed by mixing a Cauchy convolution process with a Gaussian process. We demonstrate that this framework indeed provides a rich class of models for the joint modeling of the bulk and the tail behaviors. Our proposed inference approach relies on matching model-based and empirical summary statistics, and an extensive simulation study shows that it yields accurate estimates. We demonstrate our new methodology by application to a temperature dataset measured at 97 monitoring stations in the state of Oklahoma, US. Our results indicate that our proposed model provides a very good fit to the data, and that it captures both the bulk and the tail dependence structures accurately.

As a prevailing collaborative filtering method for recommendation systems, one-bit matrix completion requires data collected by users to provide personalized service. Due to insidious attacks and unexpected inference, the release of users' data often raises serious privacy concerns. To address this issue, differential privacy(DP) has been widely used in standard matrix completion models. To date, however, little has been known about how to apply DP to achieve privacy protection in one-bit matrix completion. In this paper, we propose a unified framework for ensuring a strong privacy guarantee of one-bit matrix completion with DP. In our framework, we develop four different private perturbation mechanisms corresponding to different stages of one-bit matrix completion. For each mechanism, we design a privacy-preserving algorithm and provide a theoretical recovery error bound under the proper conditions. Numerical experiments on synthetic and real-world datasets demonstrate the effectiveness of our proposal. Compared to the one-bit matrix completion without privacy protection, our proposed mechanisms can maintain high-level privacy protection with marginal loss of completion accuracy.

Estimating worst-case execution times (WCET) is an important activity at early design stages of real-time systems. Based on WCET estimates, engineers make design and implementation decisions to ensure that task executions always complete before their specified deadlines. However, in practice, engineers often cannot provide precise point WCET estimates and prefer to provide plausible WCET ranges. Given a set of real-time tasks with such ranges, we provide an automated technique to determine for what WCET values the system is likely to meet its deadlines, and hence operate safely with a probabilistic guarantee. Our approach combines a search algorithm for generating worst-case scheduling scenarios with polynomial logistic regression for inferring probabilistic safe WCET ranges. We evaluated our approach by applying it to three industrial systems from different domains and several synthetic systems. Our approach efficiently and accurately estimates probabilistic safe WCET ranges within which deadlines are likely to be satisfied with a high degree of confidence.

Voting forms the most important tool for arriving at a decision in any institution. The changing needs of the civilization currently demands a practical yet secure electronic voting system, but any flaw related to the applied voting technology can lead to tampering of the results with the malicious outcomes. Currently, blockchain technology due to its transparent structure forms an emerging area of investigation for the development of voting systems with a far greater security. However, various apprehensions are yet to be conclusively resolved before using blockchain in high stakes elections. Other than this, the blockchain based voting systems are vulnerable to possible attacks by upcoming noisy intermediate scale quantum (NISQ) computer. To circumvent, most of these limitations, in this work, we propose an anonymous voting scheme based on quantum assisted blockchain by enhancing the advantages offered by blockchain with the quantum resources such as quantum random number generators and quantum key distribution. The purposed scheme is shown to satisfy the requirements of a good voting scheme. Further, the voting scheme is auditable and can be implemented using the currently available technology.

Embedded devices are increasingly ubiquitous and their importance is hard to overestimate. While they often support safety-critical functions (e.g., in medical devices and sensor-alarm combinations), they are usually implemented under strict cost/energy budgets, using low-end microcontroller units (MCUs) that lack sophisticated security mechanisms. Motivated by this issue, recent work developed architectures capable of generating Proofs of Execution (PoX) for the correct/expected software in potentially compromised low-end MCUs. In practice, this capability can be leveraged to provide "integrity from birth" to sensor data, by binding the sensed results/outputs to an unforgeable cryptographic proof of execution of the expected sensing process. Despite this significant progress, current PoX schemes for low-end MCUs ignore the real-time needs of many applications. In particular, security of current PoX schemes precludes any interrupts during the execution being proved. We argue that lack of asynchronous capabilities (i.e., interrupts within PoX) can obscure PoX usefulness, as several applications require processing real-time and asynchronous events. To bridge this gap, we propose, implement, and evaluate an Architecture for Secure Asynchronous Processing in PoX (ASAP). ASAP is secure under full software compromise, enables asynchronous PoX, and incurs less hardware overhead than prior work.