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In this paper, we study an intelligent reflecting surface (IRS)-aided communication system with single-antenna transmitter and receiver, under imperfect channel state information (CSI). More specifically, we deal with the robust selection of binary (on/off) states of the IRS elements in order to maximize the worst-case energy efficiency (EE), given a bounded CSI uncertainty, while satisfying a minimum signal-to-noise ratio (SNR). In addition, we consider not only continuous but also discrete IRS phase shifts. First, we derive closed-form expressions of the worst-case SNRs, and then formulate the robust (discrete) optimization problems for each case. In the case of continuous phase shifts, we design a dynamic programming (DP) algorithm that is theoretically guaranteed to achieve the global maximum with polynomial complexity $O(L\,{\log L})$, where $L$ is the number of IRS elements. In the case of discrete phase shifts, we develop a convex-relaxation-based method (CRBM) to obtain a feasible (sub-optimal) solution in polynomial time $O(L^{3.5})$, with a posteriori performance guarantee. Furthermore, numerical simulations provide useful insights and confirm the theoretical results. In particular, the proposed algorithms are several orders of magnitude faster than the exhaustive search when $L$ is large, thus being highly scalable and suitable for practical applications. Moreover, both algorithms outperform a baseline scheme, namely, the activation of all IRS elements.

In this work, we develop a novel efficient quadrature and sparse grid based polynomial interpolation method to price American options with multiple underlying assets. The approach is based on first formulating the pricing of American options using dynamic programming, and then employing static sparse grids to interpolate the continuation value function at each time step. To achieve high efficiency, we first transform the domain from $\mathbb{R}^d$ to $(-1,1)^d$ via a scaled tanh map, and then remove the boundary singularity of the resulting multivariate function over $(-1,1)^d$ by a bubble function and simultaneously, to significantly reduce the number of interpolation points. We rigorously establish that with a proper choice of the bubble function, the resulting function has bounded mixed derivatives up to a certain order, which provides theoretical underpinnings for the use of sparse grids. Numerical experiments for American arithmetic and geometric basket put options with the number of underlying assets up to 16 are presented to validate the effectiveness of the approach.

In this paper, we study a sampling and transmission scheduling problem for multi-source remote estimation, where a scheduler determines when to take samples from multiple continuous-time Gauss-Markov processes and send the samples over multiple channels to remote estimators. The sample transmission times are i.i.d. across samples and channels. The objective of the scheduler is to minimize the weighted sum of the time-average expected estimation errors of these Gauss-Markov sources. This problem is a continuous-time Restless Multi-arm Bandit (RMAB) problem with a continuous state space. We prove that the arms are indexable and derive an exact expression of the Whittle index. To the extent of our knowledge, this is the first Whittle index policy for multi-source signal-aware remote estimation. This result has two degenerated cases of interest: (i) In the single-source case, the Whittle index policy reproduces earlier threshold-based sampling policies for the remote estimation of Wiener and Ornstein-Uhlenbeck processes. When the instantaneous estimation error of the Gauss-Markov process crosses the optimal threshold, the Whittle index is precisely equal to 0. In addition, a new optimal sampling policy for the remote estimation of the unstable Ornstein-Uhlenbeck process is obtained. (ii) In the signal-agnostic case, we find an exact expression of the Whittle index for Age of Information (AoI)-based remote estimation, which complements earlier results by allowing for random transmission times. Our numerical results show that the proposed policy performs better than the signal-agnostic AoI-based Whittle index policy and the Maximum-Age-First, Zero-Wait (MAF-ZW) policy. The performance gain of the proposed policy is high when some of the Gauss-Markov processes are highly unstable or when the sample transmission times follow a heavy-tail distribution.

In this paper, we propose a blind source separation of a linear mixture of dependent sources based on copula statistics that measure the non-linear dependence between source component signals structured as copula density functions. The source signals are assumed to be stationary. The method minimizes the Kullback-Leibler divergence between the copula density functions of the estimated sources and of the dependency structure. The proposed method is applied to data obtained from the time-domain analysis of the classical 11-Bus 4-Machine system. Extensive simulation results demonstrate that the proposed method based on copula statistics converges faster and outperforms the state-of-the-art blind source separation method for dependent sources in terms of interference-to-signal ratio.

Polar duality is a well-known concept from convex geometry and analysis. In the present paper, we study two symplectically covariant versions of polar duality keeping in mind their applications to quantum mechanics. The first variant makes use of the symplectic form on phase space and allows a precise study of the covariance matrix of a density operator. The latter is a fundamental object in quantum information theory., The second variant is a symplectically covariant version of the usual polar duality highlighting the role played by Lagrangian planes. It allows us to define the notion of "geometric quantum states" with are in bijection with generalized Gaussians.

Estimating the head pose of a person is a crucial problem for numerous applications that is yet mainly addressed as a subtask of frontal pose prediction. We present a novel method for unconstrained end-to-end head pose estimation to tackle the challenging task of full range of orientation head pose prediction. We address the issue of ambiguous rotation labels by introducing the rotation matrix formalism for our ground truth data and propose a continuous 6D rotation matrix representation for efficient and robust direct regression. This allows to efficiently learn full rotation appearance and to overcome the limitations of the current state-of-the-art. Together with new accumulated training data that provides full head pose rotation data and a geodesic loss approach for stable learning, we design an advanced model that is able to predict an extended range of head orientations. An extensive evaluation on public datasets demonstrates that our method significantly outperforms other state-of-the-art methods in an efficient and robust manner, while its advanced prediction range allows the expansion of the application area. We open-source our training and testing code along with our trained models: //github.com/thohemp/6DRepNet360.

In this paper, we present methodologies for optimal selection for renewable energy sites under a different set of constraints and objectives. We consider two different models for the site-selection problem - coarse-grained and fine-grained, and analyze them to find solutions. We consider multiple different ways to measure the benefits of setting up a site. We provide approximation algorithms with a guaranteed performance bound for two different benefit metrics with the coarse-grained model. For the fine-grained model, we provide a technique utilizing Integer Linear Program to find the optimal solution. We present the results of our extensive experimentation with synthetic data generated from sparsely available real data from solar farms in Arizona.

In this paper a new optical-computational method is introduced to unveil images of targets whose visibility is severely obscured by light scattering in dense, turbid media. The targets of interest are taken to be dynamic in that their optical properties are time-varying whether stationary in space or moving. The scheme, to our knowledge the first of its kind, is human vision inspired whereby diffuse photons collected from the turbid medium are first transformed to spike trains by a dynamic vision sensor as in the retina, and image reconstruction is then performed by a neuromorphic computing approach mimicking the brain. We combine benchtop experimental data in both reflection (backscattering) and transmission geometries with support from physics-based simulations to develop a neuromorphic computational model and then apply this for image reconstruction of different MNIST characters and image sets by a dedicated deep spiking neural network algorithm. Image reconstruction is achieved under conditions of turbidity where an original image is unintelligible to the human eye or a digital video camera, yet clearly and quantifiable identifiable when using the new neuromorphic computational approach.

In this paper, we develop rotation-equivariant neural networks for 4D panoptic segmentation. 4D panoptic segmentation is a benchmark task for autonomous driving that requires recognizing semantic classes and object instances on the road based on LiDAR scans, as well as assigning temporally consistent IDs to instances across time. We observe that the driving scenario is symmetric to rotations on the ground plane. Therefore, rotation-equivariance could provide better generalization and more robust feature learning. Specifically, we review the object instance clustering strategies and restate the centerness-based approach and the offset-based approach as the prediction of invariant scalar fields and equivariant vector fields. Other sub-tasks are also unified from this perspective, and different invariant and equivariant layers are designed to facilitate their predictions. Through evaluation on the standard 4D panoptic segmentation benchmark of SemanticKITTI, we show that our equivariant models achieve higher accuracy with lower computational costs compared to their non-equivariant counterparts. Moreover, our method sets the new state-of-the-art performance and achieves 1st place on the SemanticKITTI 4D Panoptic Segmentation leaderboard.

In this paper, we study the shape reconstruction problem, when the shape we wish to reconstruct is an orientable smooth d-dimensional submanifold of the Euclidean space. Assuming we have as input a simplicial complex K that approximates the submanifold (such as the Cech complex or the Rips complex), we recast the problem of reconstucting the submanifold from K as a L1-norm minimization problem in which the optimization variable is a d-chain of K. Providing that K satisfies certain reasonable conditions, we prove that the considered minimization problem has a unique solution which triangulates the submanifold and coincides with the flat Delaunay complex introduced and studied in a companion paper. Since the objective is a weighted L1-norm and the contraints are linear, the triangulation process can thus be implemented by linear programming.