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Continuous-time measurements are instrumental for a multitude of tasks in quantum engineering and quantum control, including the estimation of dynamical parameters of open quantum systems monitored through the environment. However, such measurements do not extract the maximum amount of information available in the output state, so finding alternative optimal measurement strategies is a major open problem. In this paper we solve this problem in the setting of discrete-time input-output quantum Markov chains. We present an efficient algorithm for optimal estimation of one-dimensional dynamical parameters which consists of an iterative procedure for updating a `measurement filter' operator and determining successive measurement bases for the output units. A key ingredient of the scheme is the use of a coherent quantum absorber as a way to post-process the output after the interaction with the system. This is designed adaptively such that the joint system and absorber stationary state is pure at a reference parameter value. The scheme offers an exciting prospect for optimal continuous-time adaptive measurements, but more work is needed to find realistic practical implementations.

In this paper we generalize Dillon's switching method to characterize the exact $c$-differential uniformity of functions constructed via this method. More precisely, we modify some PcN/APcN and other functions with known $c$-differential uniformity in a controllable number of coordinates to render more such functions. We present several applications of the method in constructing PcN and APcN functions with respect to all $c\neq 1$. As a byproduct, we generalize some result of [Y. Wu, N. Li, X. Zeng, {\em New PcN and APcN functions over finite fields}, Designs Codes Crypt. 89 (2021), 2637--2651]. Computational results rendering functions with low differential uniformity, as well as, other good cryptographic properties are sprinkled throughout the paper.

Hashing-based Recommender Systems (RSs) are widely studied to provide scalable services. The existing methods for the systems combine three modules to achieve efficiency: feature extraction, interaction modeling, and binarization. In this paper, we study an unexplored module combination for the hashing-based recommender systems, namely Compact Cross-Similarity Recommender (CCSR). Inspired by cross-modal retrieval, CCSR utilizes Maximum a Posteriori similarity instead of matrix factorization and rating reconstruction to model interactions between users and items. We conducted experiments on MovieLens1M, Amazon product review, Ichiba purchase dataset and confirmed CCSR outperformed the existing matrix factorization-based methods. On the Movielens1M dataset, the absolute performance improvements are up to 15.69% in NDCG and 4.29% in Recall. In addition, we extensively studied three binarization modules: $sign$, scaled tanh, and sign-scaled tanh. The result demonstrated that although differentiable scaled tanh is popular in recent discrete feature learning literature, a huge performance drop occurs when outputs of scaled $tanh$ are forced to be binary.

In this work, we introduce a novel approach to formulating an artificial viscosity for shock capturing in nonlinear hyperbolic systems by utilizing the property that the solutions of hyperbolic conservation laws are not reversible in time in the vicinity of shocks. The proposed approach does not require any additional governing equations or a priori knowledge of the hyperbolic system in question, is independent of the mesh and approximation order, and requires the use of only one tunable parameter. The primary novelty is that the resulting artificial viscosity is unique for each component of the conservation law which is advantageous for systems in which some components exhibit discontinuities while others do not. The efficacy of the method is shown in numerical experiments of multi-dimensional hyperbolic conservation laws such as nonlinear transport, Euler equations, and ideal magnetohydrodynamics using a high-order discontinuous spectral element method on unstructured grids.

We consider the problem of nonparametric estimation of the drift and diffusion coefficients of a Stochastic Differential Equation (SDE), based on $n$ independent replicates $\left\{X_i(t)\::\: t\in [0,1]\right\}_{1 \leq i \leq n}$, observed sparsely and irregularly on the unit interval, and subject to additive noise corruption. By \textit{sparse} we intend to mean that the number of measurements per path can be arbitrary (as small as two), and remain constant with respect to $n$. We focus on time-inhomogeneous SDE of the form $dX_t = \mu(t)X_t^{\alpha}dt + \sigma(t)X_t^{\beta}dW_t$, where $\alpha \in \{0,1\}$ and $\beta \in \{0,1/2,1\}$, which includes prominent examples such as Brownian motion, Ornstein-Uhlenbeck process, geometric Brownian motion, and Brownian bridge. Our estimators are constructed by relating the local (drift/diffusion) parameters of the diffusion to their global parameters (mean/covariance, and their derivatives) by means of an apparently novel PDE. This allows us to use methods inspired by functional data analysis, and pool information across the sparsely measured paths. The methodology we develop is fully non-parametric and avoids any functional form specification on the time-dependency of either the drift function or the diffusion function. We establish almost sure uniform asymptotic convergence rates of the proposed estimators as the number of observed curves $n$ grows to infinity. Our rates are non-asymptotic in the number of measurements per path, explicitly reflecting how different sampling frequency might affect the speed of convergence. Our framework suggests possible further fruitful interactions between FDA and SDE methods in problems with replication.

As a distributed learning paradigm, Federated Learning (FL) faces the communication bottleneck issue due to many rounds of model synchronization and aggregation. Heterogeneous data further deteriorates the situation by causing slow convergence. Although the impact of data heterogeneity on supervised FL has been widely studied, the related investigation for Federated Reinforcement Learning (FRL) is still in its infancy. In this paper, we first define the type and level of data heterogeneity for policy gradient based FRL systems. By inspecting the connection between the global and local objective functions, we prove that local training can benefit the global objective, if the local update is properly penalized by the total variation (TV) distance between the local and global policies. A necessary condition for the global policy to be learn-able from the local policy is also derived, which is directly related to the heterogeneity level. Based on the theoretical result, a Kullback-Leibler (KL) divergence based penalty is proposed, which, different from the conventional method that penalizes the model divergence in the parameter space, directly constrains the model outputs in the distribution space. By jointly penalizing the divergence of the local policy from the global policy with a global penalty and constraining each iteration of the local training with a local penalty, the proposed method achieves a better trade-off between training speed (step size) and convergence. Experiment results on two popular RL experiment platforms demonstrate the advantage of the proposed algorithm over existing methods in accelerating and stabilizing the training process with heterogeneous data.

We present faster-than-native alternatives for the full AVX512-VP2INTERSECT instruction subset using basic AVX512F instructions. These alternatives compute only one of the output masks, which is sufficient for the typical case of computing the intersection of two sorted lists of integers, or computing the size of such an intersection. While the na\"ive implementation (compare the first input vector against all rotations of the second) is slower than the native instructions, we show that by rotating both the first and second operands at the same time there is a significant saving in the total number of vector rotations, resulting in the emulations being faster than the native instructions, for all instructions in the VP2INTERSECT subset. Additionally, the emulations can be easily extended to other types of inputs (e.g. packed vectors of 16-bit integers) for which native instructions are not available.

Recent decades, the emergence of numerous novel algorithms makes it a gimmick to propose an intelligent optimization system based on metaphor, and hinders researchers from exploring the essence of search behavior in algorithms. However, it is difficult to directly discuss the search behavior of an intelligent optimization algorithm, since there are so many kinds of intelligent schemes. To address this problem, an intelligent optimization system is regarded as a simulated physical optimization system in this paper. The dynamic search behavior of such a simplified physical optimization system are investigated with quantum theory. To achieve this goal, the Schroedinger equation is employed as the dynamics equation of the optimization algorithm, which is used to describe dynamic search behaviours in the evolution process with quantum theory. Moreover, to explore the basic behaviour of the optimization system, the optimization problem is assumed to be decomposed and approximated. Correspondingly, the basic search behaviour is derived, which constitutes the basic iterative process of a simple optimization system. The basic iterative process is compared with some classical bare-bones schemes to verify the similarity of search behavior under different metaphors. The search strategies of these bare bones algorithms are analyzed through experiments.

Most existing works of polar codes focus on the analysis of block error probability. However, in many scenarios, bit error probability is also important for evaluating the performance of channel codes. In this paper, we establish a new framework to analyze the bit error probability of polar codes. Specifically, by revisiting the error event of bit-channel, we first introduce the conditional bit error probability as a metric to evaluate the reliability of bit-channel for both systematic and non-systematic polar codes. Guided by the concept of polar subcode, we then derive an upper bound on the conditional bit error probability of each bit-channel, and accordingly, an upper bound on the bit error probability of polar codes. Based on these, two types of construction metrics aiming at minimizing the bit error probability of polar codes are proposed, which are of linear computational complexity and explicit forms. Simulation results show that the polar codes constructed by the proposed methods can outperform those constructed by the conventional methods.

In structure learning, the output is generally a structure that is used as supervision information to achieve good performance. Considering the interpretation of deep learning models has raised extended attention these years, it will be beneficial if we can learn an interpretable structure from deep learning models. In this paper, we focus on Recurrent Neural Networks (RNNs) whose inner mechanism is still not clearly understood. We find that Finite State Automaton (FSA) that processes sequential data has more interpretable inner mechanism and can be learned from RNNs as the interpretable structure. We propose two methods to learn FSA from RNN based on two different clustering methods. We first give the graphical illustration of FSA for human beings to follow, which shows the interpretability. From the FSA's point of view, we then analyze how the performance of RNNs are affected by the number of gates, as well as the semantic meaning behind the transition of numerical hidden states. Our results suggest that RNNs with simple gated structure such as Minimal Gated Unit (MGU) is more desirable and the transitions in FSA leading to specific classification result are associated with corresponding words which are understandable by human beings.