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When two different parties use the same learning rule on their own data, how can we test whether the distributions of the two outcomes are similar? In this paper, we study the similarity of outcomes of learning rules through the lens of the Total Variation (TV) distance of distributions. We say that a learning rule is TV indistinguishable if the expected TV distance between the posterior distributions of its outputs, executed on two training data sets drawn independently from the same distribution, is small. We first investigate the learnability of hypothesis classes using TV indistinguishable learners. Our main results are information-theoretic equivalences between TV indistinguishability and existing algorithmic stability notions such as replicability and approximate differential privacy. Then, we provide statistical amplification and boosting algorithms for TV indistinguishable learners.

The solution of computational fluid dynamics problems is one of the most computationally hard tasks, especially in the case of complex geometries and turbulent flow regimes. We propose to use Tensor Train (TT) methods, which possess logarithmic complexity in problem size and have great similarities with quantum algorithms in the structure of data representation. We develop the Tensor train Finite Element Method -- TetraFEM -- and the explicit numerical scheme for the solution of the incompressible Navier-Stokes equation via Tensor Trains. We test this approach on the simulation of liquids mixing in a T-shape mixer, which, to our knowledge, was done for the first time using tensor methods in such non-trivial geometries. As expected, we achieve exponential compression in memory of all FEM matrices and demonstrate an exponential speed-up compared to the conventional FEM implementation on dense meshes. In addition, we discuss the possibility of extending this method to a quantum computer to solve more complex problems. This paper is based on work we conducted for Evonik Industries AG.

This paper presents a novel transceiver design aimed at enabling Direct-to-Satellite Internet of Things (DtS-IoT) systems based on long range-frequency hopping spread spectrum (LR-FHSS). Our focus lies in developing an accurate transmission method through the analysis of the frame structure and key parameters outlined in Long Range Wide-Area Network (LoRaWAN) [1]. To address the Doppler effect in DtS-IoT networks and simultaneously receive numerous frequency hopping signals, a robust signal detector for the receiver is proposed. We verify the performance of the proposed LR-FHSS transceiver design through simulations conducted in a realistic satellite channel environment, assessing metrics such as miss detection probability and packet error probability.

We analyze to what extent final users can infer information about the level of protection of their data when the data obfuscation mechanism is a priori unknown to them (the so-called ''black-box'' scenario). In particular, we delve into the investigation of two notions of local differential privacy (LDP), namely {\epsilon}-LDP and R\'enyi LDP. On one hand, we prove that, without any assumption on the underlying distributions, it is not possible to have an algorithm able to infer the level of data protection with provable guarantees; this result also holds for the central versions of the two notions of DP considered. On the other hand, we demonstrate that, under reasonable assumptions (namely, Lipschitzness of the involved densities on a closed interval), such guarantees exist and can be achieved by a simple histogram-based estimator. We validate our results experimentally and we note that, on a particularly well-behaved distribution (namely, the Laplace noise), our method gives even better results than expected, in the sense that in practice the number of samples needed to achieve the desired confidence is smaller than the theoretical bound, and the estimation of {\epsilon} is more precise than predicted.

Symbiotic radio (SR) is a promising technology of spectrum- and energy-efficient wireless systems, for which the key idea is to use cognitive backscattering communication to achieve mutualistic spectrum and energy sharing with passive backscatter devices (BDs). In this paper, a reconfigurable intelligent surface (RIS) based SR system is considered, where the RIS is used not only to assist the primary active communication, but also for passive communication to transmit its own information. For the considered system, we investigate the EE trade-off between active and passive communications, by characterizing the EE region. To gain some insights, we first derive the maximum achievable individual EEs of the primary transmitter (PT) and RIS, respectively, and then analyze the asymptotic performance by exploiting the channel hardening effect. To characterize the non-trivial EE trade-off, we formulate an optimization problem to find the Pareto boundary of the EE region by jointly optimizing the transmit beamforming, power allocation and the passive beamforming of RIS. The formulated problem is non-convex, and an efficient algorithm is proposed by decomposing it into a series of subproblems by using alternating optimization (AO) and successive convex approximation (SCA) techniques. Finally, simulation results are presented to validate the effectiveness of the proposed algorithm.

To ensure safe autonomous driving in urban environments with complex vehicle-pedestrian interactions, it is critical for Autonomous Vehicles (AVs) to have the ability to predict pedestrians' short-term and immediate actions in real-time. In recent years, various methods have been developed to study estimating pedestrian behaviors for autonomous driving scenarios, but there is a lack of clear definitions for pedestrian behaviors. In this work, the literature gaps are investigated and a taxonomy is presented for pedestrian behavior characterization. Further, a novel multi-task sequence to sequence Transformer encoders-decoders (TF-ed) architecture is proposed for pedestrian action and trajectory prediction using only ego vehicle camera observations as inputs. The proposed approach is compared against an existing LSTM encoders decoders (LSTM-ed) architecture for action and trajectory prediction. The performance of both models is evaluated on the publicly available Joint Attention Autonomous Driving (JAAD) dataset, CARLA simulation data as well as real-time self-driving shuttle data collected on university campus. Evaluation results illustrate that the proposed method reaches an accuracy of 81% on action prediction task on JAAD testing data and outperforms the LSTM-ed by 7.4%, while LSTM counterpart performs much better on trajectory prediction task for a prediction sequence length of 25 frames.

Recently, Armstrong, Guzm\'an, and Sing Long (2021), presented an optimal $O(n^2)$ time algorithm for strict circular seriation (called also the recognition of strict quasi-circular Robinson spaces). In this paper, we give a very simple $O(n\log n)$ time algorithm for computing a compatible circular order for strict circular seriation. When the input space is not known to be strict quasi-circular Robinson, our algorithm is complemented by an $O(n^2)$ time verification of compatibility of the returned order. This algorithm also works for recognition of other types of strict circular Robinson spaces known in the literature. We also prove that the circular Robinson dissimilarities (which are defined by the existence of compatible orders on one of the two arcs between each pair of points) are exactly the pre-circular Robinson dissimilarities (which are defined by a four-point condition).

This study develops an asymptotic theory for estimating the time-varying characteristics of locally stationary functional time series (LSFTS). We investigate a kernel-based method to estimate the time-varying covariance operator and the time-varying mean function of an LSFTS. In particular, we derive the convergence rate of the kernel estimator of the covariance operator and associated eigenvalue and eigenfunctions and establish a central limit theorem for the kernel-based locally weighted sample mean. As applications of our results, we discuss methods for testing the equality of time-varying mean functions in two functional samples.

Many standard linear algebra problems can be solved on a quantum computer by using recently developed quantum linear algebra algorithms that make use of block encodings and quantum eigenvalue/singular value transformations. A block encoding embeds a properly scaled matrix of interest A in a larger unitary transformation U that can be decomposed into a product of simpler unitaries and implemented efficiently on a quantum computer. Although quantum algorithms can potentially achieve exponential speedup in solving linear algebra problems compared to the best classical algorithm, such gain in efficiency ultimately hinges on our ability to construct an efficient quantum circuit for the block encoding of A, which is difficult in general, and not trivial even for well-structured sparse matrices. In this paper, we give a few examples on how efficient quantum circuits can be explicitly constructed for some well-structured sparse matrices, and discuss a few strategies used in these constructions. We also provide implementations of these quantum circuits in MATLAB.

Traditional approaches to the design of multi-agent navigation algorithms consider the environment as a fixed constraint, despite the influence of spatial constraints on agents' performance. Yet hand-designing conducive environment layouts is inefficient and potentially expensive. The goal of this paper is to consider the environment as a decision variable in a system-level optimization problem, where both agent performance and environment cost are incorporated. Towards this end, we propose novel problems of unprioritized and prioritized environment optimization, where the former considers agents unbiasedly and the latter accounts for agent priorities. We show, through formal proofs, under which conditions the environment can change while guaranteeing completeness (i.e., all agents reach goals), and analyze the role of agent priorities in the environment optimization. We proceed to impose real-world constraints on the environment optimization and formulate it mathematically as a constrained stochastic optimization problem. Since the relation between agents, environment and performance is challenging to model, we leverage reinforcement learning to develop a model-free solution and a primal-dual mechanism to handle constraints. Distinct information processing architectures are integrated for various implementation scenarios, including online/offline optimization and discrete/continuous environment. Numerical results corroborate the theory and demonstrate the validity and adaptability of our approach.