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In this paper, we propose a method for estimating model parameters using Small-Angle Scattering (SAS) data based on the Bayesian inference. Conventional SAS data analyses involve processes of manual parameter adjustment by analysts or optimization using gradient methods. These analysis processes tend to involve heuristic approaches and may lead to local solutions.Furthermore, it is difficult to evaluate the reliability of the results obtained by conventional analysis methods. Our method solves these problems by estimating model parameters as probability distributions from SAS data using the framework of the Bayesian inference. We evaluate the performance of our method through numerical experiments using artificial data of representative measurement target models.From the results of the numerical experiments, we show that our method provides not only high accuracy and reliability of estimation, but also perspectives on the transition point of estimability with respect to the measurement time and the lower bound of the angular domain of the measured data.

This paper investigates the problem of efficient constrained global optimization of hybrid models that are a composition of a known white-box function and an expensive multi-output black-box function subject to noisy observations, which often arises in real-world science and engineering applications. We propose a novel method, Constrained Upper Quantile Bound (CUQB), to solve such problems that directly exploits the composite structure of the objective and constraint functions that we show leads substantially improved sampling efficiency. CUQB is a conceptually simple, deterministic approach that avoid constraint approximations used by previous methods. Although the CUQB acquisition function is not available in closed form, we propose a novel differentiable sample average approximation that enables it to be efficiently maximized. We further derive bounds on the cumulative regret and constraint violation under a non-parametric Bayesian representation of the black-box function. Since these bounds depend sublinearly on the number of iterations under some regularity assumptions, we establis bounds on the convergence rate to the optimal solution of the original constrained problem. In contrast to most existing methods, CUQB further incorporates a simple infeasibility detection scheme, which we prove triggers in a finite number of iterations when the original problem is infeasible (with high probability given the Bayesian model). Numerical experiments on several test problems, including environmental model calibration and real-time optimization of a reactor system, show that CUQB significantly outperforms traditional Bayesian optimization in both constrained and unconstrained cases. Furthermore, compared to other state-of-the-art methods that exploit composite structure, CUQB achieves competitive empirical performance while also providing substantially improved theoretical guarantees.

Existing error-bounded lossy compression techniques control the pointwise error during compression to guarantee the integrity of the decompressed data. However, they typically do not explicitly preserve the topological features in data. When performing post hoc analysis with decompressed data using topological methods, preserving topology in the compression process to obtain topologically consistent and correct scientific insights is desirable. In this paper, we introduce TopoSZ, an error-bounded lossy compression method that preserves the topological features in 2D and 3D scalar fields. Specifically, we aim to preserve the types and locations of local extrema as well as the level set relations among critical points captured by contour trees in the decompressed data. The main idea is to derive topological constraints from contour-tree-induced segmentation from the data domain, and incorporate such constraints with a customized error-controlled quantization strategy from the classic SZ compressor.Our method allows users to control the pointwise error and the loss of topological features during the compression process with a global error bound and a persistence threshold.

The research detailed in this paper scrutinizes Principal Component Analysis (PCA), a seminal method employed in statistics and machine learning for the purpose of reducing data dimensionality. Singular Value Decomposition (SVD) is often employed as the primary means for computing PCA, a process that indispensably includes the step of centering - the subtraction of the mean location from the data set. In our study, we delve into a detailed exploration of the influence of this critical yet often ignored or downplayed data centering step. Our research meticulously investigates the conditions under which two PCA embeddings, one derived from SVD with centering and the other without, can be viewed as aligned. As part of this exploration, we analyze the relationship between the first singular vector and the mean direction, subsequently linking this observation to the congruity between two SVDs of centered and uncentered matrices. Furthermore, we explore the potential implications arising from the absence of centering in the context of performing PCA via SVD from a spectral analysis standpoint. Our investigation emphasizes the importance of a comprehensive understanding and acknowledgment of the subtleties involved in the computation of PCA. As such, we believe this paper offers a crucial contribution to the nuanced understanding of this foundational statistical method and stands as a valuable addition to the academic literature in the field of statistics.

Coded distributed computing, proposed by Li et al., offers significant potential for reducing the communication load in MapReduce computing systems. In the setting of the \emph{cascaded} coded distributed computing that consisting of $K$ nodes, $N$ input files, and $Q$ output functions, the objective is to compute each output function through $s\geq 1$ nodes with a computation load $r\geq 1$, enabling the application of coding techniques during the Shuffle phase to achieve minimum communication load. However, for most existing coded distributed computing schemes, a major limitation lies in their demand for splitting the original data into an exponentially growing number of input files in terms of $N/\binom{K}{r} \in\mathbb{N}$ and requiring an exponentially large number of output functions $Q/\binom{K}{s} \in\mathbb{N}$, which imposes stringent requirements for implementation and results in significant coding complexity when $K$ is large. In this paper, we focus on the cascaded case of $K/s\in\mathbb{N} $, deliberately designing the strategy of input files store and output functions assignment based on a grouping method, such that a low-complexity two-round Shuffle phase is available. The main advantages of our proposed scheme contains: 1) the communication load is quilt close to or surprisingly better than the optimal state-of-the-art scheme proposed by Li et al.; 2) our scheme requires significantly less number of input files and output functions; 3) all the operations are implemented over the minimum binary field $\mathbb{F}_2$.

Two-component mixture models have proved to be a powerful tool for modeling heterogeneity in several cluster analysis contexts. However, most methods based on these models assume a constant behavior for the mixture weights, which can be restrictive and unsuitable for some applications. In this paper, we relax this assumption and allow the mixture weights to vary according to the index (e.g., time) to make the model more adaptive to a broader range of data sets. We propose an efficient MCMC algorithm to jointly estimate both component parameters and dynamic weights from their posterior samples. We evaluate the method's performance by running Monte Carlo simulation studies under different scenarios for the dynamic weights. In addition, we apply the algorithm to a time series that records the level reached by a river in southern Brazil. The Taquari River is a water body whose frequent flood inundations have caused various damage to riverside communities. Implementing a dynamic mixture model allows us to properly describe the flood regimes for the areas most affected by these phenomena.

In this paper, we consider a full-duplex (FD) space shift keying (SSK) communication system, where information exchange between two users is assisted only by a reconfigurable intelligent surface (RIS). In particular, the impact of loop interference (LI) between the transmit and receive antennas as well as residual self-interference (SI) from the RIS is considered. Based on the maximum likelihood detector, we derive the conditional pairwise error probability and the numerical integration expression for the unconditional pairwise error probability (UPEP). Since it is difficult to find a closed-form solution, we perform accurate estimation by the Gauss-Chebyshev quadrature (GCQ) method. To gain more useful insights, we derive an expression for UPEP in the high signal-to-noise ratio region and further give the average bit error probability (ABEP) expression. Monte Carlo simulations were performed to validate the derived results. It is found that SI and LI have severe impacts on system performance. Fortunately, these two disturbances can be well counteracted by increasing the number of RIS units.

We study the fundamental problem of sampling independent events, called subset sampling. Specifically, consider a set of $n$ events $S=\{x_1, \ldots, x_n\}$, where each event $x_i$ has an associated probability $p(x_i)$. The subset sampling problem aims to sample a subset $T \subseteq S$, such that every $x_i$ is independently included in $S$ with probability $p_i$. A naive solution is to flip a coin for each event, which takes $O(n)$ time. However, the specific goal is to develop data structures that allow drawing a sample in time proportional to the expected output size $\mu=\sum_{i=1}^n p(x_i)$, which can be significantly smaller than $n$ in many applications. The subset sampling problem serves as an important building block in many tasks and has been the subject of various research for more than a decade. However, most of the existing subset sampling approaches are conducted in a static setting, where the events or their associated probability in set $S$ is not allowed to be changed over time. These algorithms incur either large query time or update time in a dynamic setting despite the ubiquitous time-evolving events with changing probability in real life. Therefore, it is a pressing need, but still, an open problem, to design efficient dynamic subset sampling algorithms. In this paper, we propose ODSS, the first optimal dynamic subset sampling algorithm. The expected query time and update time of ODSS are both optimal, matching the lower bounds of the subset sampling problem. We present a nontrivial theoretical analysis to demonstrate the superiority of ODSS. We also conduct comprehensive experiments to empirically evaluate the performance of ODSS. Moreover, we apply ODSS to a concrete application: influence maximization. We empirically show that our ODSS can improve the complexities of existing influence maximization algorithms on large real-world evolving social networks.

Lattice-based cryptographic algorithms built on ring learning with error theory are gaining importance due to their potential for providing post-quantum security. However, these algorithms involve complex polynomial operations, such as polynomial modular multiplication (PMM), which is the most time-consuming part of these algorithms. Accelerating PMM is crucial to make lattice-based cryptographic algorithms widely adopted by more applications. This work introduces a novel high-throughput and compact PMM accelerator, X-Poly, based on the crossbar (XB)-type compute-in-memory (CIM). We identify the most appropriate PMM algorithm for XB-CIM. We then propose a novel bit-mapping technique to reduce the area and energy of the XB-CIM fabric, and conduct processing engine (PE)-level optimization to increase memory utilization and support different problem sizes with a fixed number of XB arrays. X-Poly design achieves 3.1X10^6 PMM operations/s throughput and offers 200X latency improvement compared to the CPU-based implementation. It also achieves 3.9X throughput per area improvement compared with the state-of-the-art CIM accelerators.

Relay-enabled backscatter communication (BC) is an intriguing paradigm to alleviate energy shortage and improve throughput of Internet-of-Things (IoT) devices. Most of the existing works focus on the resource allocation that considered the unequal and continuous time allocation for both source-relay and relay-destination links. However, the continuous time allocation may be infeasible since in practice, the time allocation shall be carried out in integral multiple of the subframe duration unit. In this article, we study a discrete time scheme from the perspective of frame structure, where one transmission block is divided into two phases and the linear mapping is employed as a re-encoding method to determine the number of subframes for both phases and the power allocation for each subframe in a relay-enabled BC system. Based on this, we derive an accurate system-throughput expression and formulate a mixed-integral non-convex optimization problem to maximize the system throughput by jointly optimizing the power reflection coefficient (PRC) of the IoT node, the power allocation of the hybrid access point (HAP) and the linear mapping matrix, and solve it via a three-step approach. Accordingly, we propose a low complexity iterative algorithm to obtain the throughput maximization-based resource allocation solution. Numerical results analyze the performance of our proposed algorithm, verify the superiority of our proposed scheme, and evaluate the impacts of network parameters on the system throughput.