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It remains an open problem to find the optimal configuration of phase shifts under the discrete constraint for intelligent reflecting surface (IRS) in polynomial time. The above problem is widely believed to be difficult because it is not linked to any known combinatorial problems that can be solved efficiently. The branch-and-bound algorithms and the approximation algorithms constitute the best results in this area. Nevertheless, this work shows that the global optimum can actually be reached in linear time on average in terms of the number of reflective elements (REs) of IRS. The main idea is to geometrically interpret the discrete beamforming problem as choosing the optimal point on the unit circle. Although the number of possible combinations of phase shifts grows exponentially with the number of REs, it turns out that there are only a linear number of circular arcs that possibly contain the optimal point. Furthermore, the proposed algorithm can be viewed as a novel approach to a special case of the discrete quadratic program (QP).

Online Food Recommendation Service (OFRS) has remarkable spatiotemporal characteristics and the advantage of being able to conveniently satisfy users' needs in a timely manner. There have been a variety of studies that have begun to explore its spatiotemporal properties, but a comprehensive and in-depth analysis of the OFRS spatiotemporal features is yet to be conducted. Therefore, this paper studies the OFRS based on three questions: how spatiotemporal features play a role; why self-attention cannot be used to model the spatiotemporal sequences of OFRS; and how to combine spatiotemporal features to improve the efficiency of OFRS. Firstly, through experimental analysis, we systemically extracted the spatiotemporal features of OFRS, identified the most valuable features and designed an effective combination method. Secondly, we conducted a detailed analysis of the spatiotemporal sequences, which revealed the shortcomings of self-attention in OFRS, and proposed a more optimized spatiotemporal sequence method for replacing self-attention. In addition, we also designed a Dynamic Context Adaptation Model to further improve the efficiency and performance of OFRS. Through the offline experiments on two large datasets and online experiments for a week, the feasibility and superiority of our model were proven.

An experimental comparison of two or more optimization algorithms requires the same computational resources to be assigned to each algorithm. When a maximum runtime is set as the stopping criterion, all algorithms need to be executed in the same machine if they are to use the same resources. Unfortunately, the implementation code of the algorithms is not always available, which means that running the algorithms to be compared in the same machine is not always possible. And even if they are available, some optimization algorithms might be costly to run, such as training large neural-networks in the cloud. In this paper, we consider the following problem: how do we compare the performance of a new optimization algorithm B with a known algorithm A in the literature if we only have the results (the objective values) and the runtime in each instance of algorithm A? Particularly, we present a methodology that enables a statistical analysis of the performance of algorithms executed in different machines. The proposed methodology has two parts. First, we propose a model that, given the runtime of an algorithm in a machine, estimates the runtime of the same algorithm in another machine. This model can be adjusted so that the probability of estimating a runtime longer than what it should be is arbitrarily low. Second, we introduce an adaptation of the one-sided sign test that uses a modified p-value and takes into account that probability. Such adaptation avoids increasing the probability of type I error associated with executing algorithms A and B in different machines.

Poor performance of quantitative analysis in histopathological Whole Slide Images (WSI) has been a significant obstacle in clinical practice. Annotating large-scale WSIs manually is a demanding and time-consuming task, unlikely to yield the expected results when used for fully supervised learning systems. Rarely observed disease patterns and large differences in object scales are difficult to model through conventional patient intake. Prior methods either fall back to direct disease classification, which only requires learning a few factors per image, or report on average image segmentation performance, which is highly biased towards majority observations. Geometric image augmentation is commonly used to improve robustness for average case predictions and to enrich limited datasets. So far no method provided sampling of a realistic posterior distribution to improve stability, e.g. for the segmentation of imbalanced objects within images. Therefore, we propose a new approach, based on diffusion models, which can enrich an imbalanced dataset with plausible examples from underrepresented groups by conditioning on segmentation maps. Our method can simply expand limited clinical datasets making them suitable to train machine learning pipelines, and provides an interpretable and human-controllable way of generating histopathology images that are indistinguishable from real ones to human experts. We validate our findings on two datasets, one from the public domain and one from a Kidney Transplant study.

The curse-of-dimensionality (CoD) taxes computational resources heavily with exponentially increasing computational cost as the dimension increases. This poses great challenges in solving high-dimensional PDEs as Richard Bellman first pointed out over 60 years ago. While there has been some recent success in solving numerically partial differential equations (PDEs) in high dimensions, such computations are prohibitively expensive, and true scaling of general nonlinear PDEs to high dimensions has never been achieved. In this paper, we develop a new method of scaling up physics-informed neural networks (PINNs) to solve arbitrary high-dimensional PDEs. The new method, called Stochastic Dimension Gradient Descent (SDGD), decomposes a gradient of PDEs into pieces corresponding to different dimensions and samples randomly a subset of these dimensional pieces in each iteration of training PINNs. We theoretically prove the convergence guarantee and other desired properties of the proposed method. We experimentally demonstrate that the proposed method allows us to solve many notoriously hard high-dimensional PDEs, including the Hamilton-Jacobi-Bellman (HJB) and the Schr\"{o}dinger equations in thousands of dimensions very fast on a single GPU using the PINNs mesh-free approach. For instance, we solve nontrivial nonlinear PDEs (one HJB equation and one Black-Scholes equation) in 100,000 dimensions in 6 hours on a single GPU using SDGD with PINNs. Since SDGD is a general training methodology of PINNs, SDGD can be applied to any current and future variants of PINNs to scale them up for arbitrary high-dimensional PDEs.

Formal method-based analysis of the 5G Wireless Communication Protocol is crucial for identifying logical vulnerabilities and facilitating an all-encompassing security assessment, especially in the design phase. Natural Language Processing (NLP) assisted techniques and most of the tools are not widely adopted by the industry and research community. Traditional formal verification through a mathematics approach heavily relied on manual logical abstraction prone to being time-consuming, and error-prone. The reason that the NLP-assisted method did not apply in industrial research may be due to the ambiguity in the natural language of the protocol designs nature is controversial to the explicitness of formal verification. To address the challenge of adopting the formal methods in protocol designs, targeting (3GPP) protocols that are written in natural language, in this study, we propose a hybrid approach to streamline the analysis of protocols. We introduce a two-step pipeline that first uses NLP tools to construct data and then uses constructed data to extract identifiers and formal properties by using the NLP model. The identifiers and formal properties are further used for formal analysis. We implemented three models that take different dependencies between identifiers and formal properties as criteria. Our results of the optimal model reach valid accuracy of 39% for identifier extraction and 42% for formal properties predictions. Our work is proof of concept for an efficient procedure in performing formal analysis for largescale complicate specification and protocol analysis, especially for 5G and nextG communications.

The concept of the federated Cloud-Edge-IoT continuum promises to alleviate many woes of current systems, improving resource use, energy efficiency, quality of service, and more. However, this continuum is still far from being realized in practice, with no comprehensive solutions for developing, deploying, and managing continuum-native applications. Breakthrough innovations and novel system architectures are needed to cope with the ever-increasing heterogeneity and the multi-stakeholder nature of computing resources. This work proposes a novel architecture for choreographing workloads in the continuum, attempting to address these challenges. The architecture that tackles this issue comprehensively, spanning from the workloads themselves, through networking and data exchange, up to the orchestration and choreography mechanisms. The concept emphasizes the use of varied AI techniques, enabling autonomous and intelligent management of resources and workloads. Open standards are also a key part of the proposition, making it possible to fully engage third parties in multi-stakeholder scenarios. Although the presented architecture is promising, much work is required to realize it in practice. To this end, the key directions for future research are outlined.

Numerical methods for Inverse Kinematics (IK) employ iterative, linear approximations of the IK until the end-effector is brought from its initial pose to the desired final pose. These methods require the computation of the Jacobian of the Forward Kinematics (FK) and its inverse in the linear approximation of the IK. Despite all the successful implementations reported in the literature, Jacobian-based IK methods can still fail to preserve certain useful properties if an improper matrix inverse, e.g. Moore-Penrose (MP), is employed for incommensurate robotic systems. In this paper, we propose a systematic, robust and accurate numerical solution for the IK problem using the Mixed (MX) Generalized Inverse (GI) applied to any type of Jacobians (e.g., analytical, numerical or geometric) derived for any commensurate and incommensurate robot. This approach is robust to whether the system is under-determined (less than 6 DoF) or over-determined (more than 6 DoF). We investigate six robotics manipulators with various Degrees of Freedom (DoF) to demonstrate that commonly used GI's fail to guarantee the same system behaviors when the units are varied for incommensurate robotics manipulators. In addition, we evaluate the proposed methodology as a global IK solver and compare against well-known IK methods for redundant manipulators. Based on the experimental results, we conclude that the right choice of GI is crucial in preserving certain properties of the system (i.e. unit-consistency).

We explore the information geometry and asymptotic behaviour of estimators for Kronecker-structured covariances, in both growing-$n$ and growing-$p$ scenarios, with a focus towards examining the quadratic form or partial trace estimator proposed by Linton and Tang. It is shown that the partial trace estimator is asymptotically inefficient An explanation for this inefficiency is that the partial trace estimator does not scale sub-blocks of the sample covariance matrix optimally. To correct for this, an asymptotically efficient, rescaled partial trace estimator is proposed. Motivated by this rescaling, we introduce an orthogonal parameterization for the set of Kronecker covariances. High-dimensional consistency results using the partial trace estimator are obtained that demonstrate a blessing of dimensionality. In settings where an array has at least order three, it is shown that as the array dimensions jointly increase, it is possible to consistently estimate the Kronecker covariance matrix, even when the sample size is one.

As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.