Asynchronous Byzantine Atomic Broadcast (ABAB) promises, in comparison to partially synchronous approaches, simplicity in implementation, increased performance, and increased robustness. For partially synchronous approaches, it is well-known that small Trusted Execution Environments (TEE), e.g., MinBFT's unique sequential identifier generator (USIG), are capable of reducing the communication effort while increasing the fault tolerance. For ABAB, the research community assumes that the use of TEEs increases performance and robustness. However, despite the existence of a fault-model compiler, a concrete TEE-based approach is not directly available yet. In this brief announcement, we show that the recently proposed DAG-Rider approach can be transformed to provide ABAB with $n\geq 2f+1$ processes, of which $f$ are faulty. We leverage MinBFT's USIG to implement Reliable Broadcast with $n>f$ processes and show that the quorum-critical proofs of DAG-Rider still hold when adapting the quorum size to $\lfloor \frac{n}{2} \rfloor + 1$.
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Schistosomiasis mansoni is an endemic parasitic disease in more than seventy countries, whose diagnosis is commonly performed by visually counting the parasite eggs in microscopy images of fecal samples. State-of-the-art (SOTA) object detection algorithms are based on heavyweight neural networks, unsuitable for automating the diagnosis in the laboratory routine. We circumvent the problem by presenting a flyweight Convolutional Neural Network (CNN) that weighs thousands of times less than SOTA object detectors. The kernels in our approach are learned layer-by-layer from attention regions indicated by user-drawn scribbles on very few training images. Representative kernels are visually identified and selected to improve performance with reduced computational cost. Another innovation is a single-layer adaptive decoder whose convolutional weights are automatically defined for each image on-the-fly. The experiments show that our CNN can outperform three SOTA baselines according to five measures, being also suitable for CPU execution in the laboratory routine, processing approximately four images a second for each available thread.
Entropy coding is essential to data compression, image and video coding, etc. The Range variant of Asymmetric Numeral Systems (rANS) is a modern entropy coder, featuring superior speed and compression rate. As rANS is not designed for parallel execution, the conventional approach to parallel rANS partitions the input symbol sequence and encodes partitions with independent codecs, and more partitions bring extra overhead. This approach is found in state-of-the-art implementations such as DietGPU. It is unsuitable for content-delivery applications, as the parallelism is wasted if the decoder cannot decode all the partitions in parallel, but all the overhead is still transferred. To solve this, we propose Recoil, a parallel rANS decoding approach with decoder-adaptive scalability. We discover that a single rANS-encoded bitstream can be decoded from any arbitrary position if the intermediate states are known. After renormalization, these states also have a smaller upper bound, which can be stored efficiently. We then split the encoded bitstream using a heuristic to evenly distribute the workload, and store the intermediate states and corresponding symbol indices as metadata. The splits can then be combined simply by eliminating extra metadata entries. The main contribution of Recoil is reducing unnecessary data transfer by adaptively scaling parallelism overhead to match the decoder capability. The experiments show that Recoil decoding throughput is comparable to the conventional approach, scaling massively on CPUs and GPUs and greatly outperforming various other ANS-based codecs.
Predictive black-box models can exhibit high accuracy but their opaque nature hinders their uptake in safety-critical deployment environments. Explanation methods (XAI) can provide confidence for decision-making through increased transparency. However, existing XAI methods are not tailored towards models in sensitive domains where one predictor is of special interest, such as a treatment effect in a clinical model, or ethnicity in policy models. We introduce Path-Wise Shapley effects (PWSHAP), a framework for assessing the targeted effect of a binary (e.g.~treatment) variable from a complex outcome model. Our approach augments the predictive model with a user-defined directed acyclic graph (DAG). The method then uses the graph alongside on-manifold Shapley values to identify effects along causal pathways whilst maintaining robustness to adversarial attacks. We establish error bounds for the identified path-wise Shapley effects and for Shapley values. We show PWSHAP can perform local bias and mediation analyses with faithfulness to the model. Further, if the targeted variable is randomised we can quantify local effect modification. We demonstrate the resolution, interpretability, and true locality of our approach on examples and a real-world experiment.
We give a fast(er), communication-free, parallel construction of optimal communication schedules that allow broadcasting of $n$ distinct blocks of data from a root processor to all other processors in $1$-ported, $p$-processor networks with fully bidirectional communication. For any $p$ and $n$, broadcasting in this model requires $n-1+\lceil\log_2 p\rceil$ communication rounds. In contrast to other constructions, all processors follow the same, circulant graph communication pattern, which makes it possible to use the schedules for the allgather (all-to-all-broadcast) operation as well. The new construction takes $O(\log^3 p)$ time steps per processor, each of which can compute its part of the schedule independently of the other processors in $O(\log p)$ space. The result is a significant improvement over the sequential $O(p \log^2 p)$ time and $O(p\log p)$ space construction of Tr\"aff and Ripke (2009) with considerable practical import. The round-optimal schedule construction is then used to implement communication optimal algorithms for the broadcast and (irregular) allgather collective operations as found in MPI (the \emph{Message-Passing Interface}), and significantly and practically improves over the implementations in standard MPI libraries (\texttt{mpich}, OpenMPI, Intel MPI) for certain problem ranges. The application to the irregular allgather operation is entirely new.
With delayed and imperfect current channel state information at the transmitter (CSIT), namely mixed CSIT, the sum degrees-of-freedom (sum-DoF) in the two-user multiple-input multiple-output (MIMO) broadcast channel and the $K$-user multiple-input single-output (MISO) broadcast channel with not-less-than-$K$ transmit antennas have been obtained. However, the case of the three-user broadcast channel with two transmit antennas and mixed CSIT is still unexplored. In this paper, we investigate the sum-DoF upper bound of three-user MISO broadcast channel with two transmit antennas and mixed CSIT. By exploiting genie-aided signaling and extremal inequalities, we derive the sum-DoF upper bound as $(1-\alpha)3/2 + 9\alpha/4$, which is at most $12.5\%$ larger than the expected sum-DoF, given by $(1-\alpha)3/2 + 2\alpha$. This indicates that the gap may mitigate by better bounding the imperfect current CSIT counterpart.
This paper introduces general methodologies for constructing closed-form solutions to several important partial differential equations (PDEs) with polynomial right-hand sides in two and three spatial dimensions. The covered equations include the isotropic and anisotropic Poisson, Helmholtz, Stokes, and elastostatic equations, as well as the time-harmonic linear elastodynamic and Maxwell equations. Polynomial solutions have recently regained significance in the development of numerical techniques for evaluating volume integral operators and have potential applications in certain kinds of Trefftz finite element methods. Our approach to all of these PDEs relates the particular solution to polynomial solutions of the Poisson and Helmholtz polynomial particular solutions, solutions that can in turn be obtained, respectively, from expansions using homogeneous polynomials and the Neumann series expansion of the operator $(k^2+\Delta)^{-1}$. No matrix inversion is required to compute the solution. The method naturally incorporates divergence constraints on the solution, such as in the case of Maxwell and Stokes flow equations. This work is accompanied by a freely available Julia library, \texttt{PolynomialSolutions.jl}, which implements the proposed methodology in a non-symbolic format and efficiently constructs and provides access to rapid evaluation of the desired solution.
The performance of distributed storage systems deployed on wide-area networks can be improved using weighted (majority) quorum systems instead of their regular variants due to the heterogeneous performance of the nodes. A significant limitation of weighted majority quorum systems lies in their dependence on static weights, which are inappropriate for systems subject to the dynamic nature of networked environments. To overcome this limitation, such quorum systems require mechanisms for reassigning weights over time according to the performance variations. We study the problem of node weight reassignment in asynchronous systems with a static set of servers and static fault threshold. We prove that solving such a problem is as hard as solving consensus, i.e., it cannot be implemented in asynchronous failure-prone distributed systems. This result is somewhat counter-intuitive, given the recent results showing that two related problems -- replica set reconfiguration and asset transfer -- can be solved in asynchronous systems. Inspired by these problems, we present two versions of the problem that contain restrictions on the weights of servers and the way they are reassigned. We propose a protocol to implement one of the restricted problems in asynchronous systems. As a case study, we construct a dynamic-weighted atomic storage based on such a protocol. We also discuss the relationship between weight reassignment and asset transfer problems and compare our dynamic-weighted atomic storage with reconfigurable atomic storage.
We propose to use L\'evy {\alpha}-stable distributions for constructing priors for Bayesian inverse problems. The construction is based on Markov fields with stable-distributed increments. Special cases include the Cauchy and Gaussian distributions, with stability indices {\alpha} = 1, and {\alpha} = 2, respectively. Our target is to show that these priors provide a rich class of priors for modelling rough features. The main technical issue is that the {\alpha}-stable probability density functions do not have closed-form expressions in general, and this limits their applicability. For practical purposes, we need to approximate probability density functions through numerical integration or series expansions. Current available approximation methods are either too time-consuming or do not function within the range of stability and radius arguments needed in Bayesian inversion. To address the issue, we propose a new hybrid approximation method for symmetric univariate and bivariate {\alpha}-stable distributions, which is both fast to evaluate, and accurate enough from a practical viewpoint. Then we use approximation method in the numerical implementation of {\alpha}-stable random field priors. We demonstrate the applicability of the constructed priors on selected Bayesian inverse problems which include the deconvolution problem, and the inversion of a function governed by an elliptic partial differential equation. We also demonstrate hierarchical {\alpha}-stable priors in the one-dimensional deconvolution problem. We employ maximum-a-posterior-based estimation at all the numerical examples. To that end, we exploit the limited-memory BFGS and its bounded variant for the estimator.
A private cache-aided compression problem is studied, where a server has access to a database of $N$ files, $(Y_1,...,Y_N)$, each of size $F$ bits and is connected through a shared link to $K$ users, each equipped with a local cache of size $MF$ bits. In the placement phase, the server fills the users$'$ caches without knowing their demands, while the delivery phase takes place after the users send their demands to the server. We assume that each file $Y_i$ is arbitrarily correlated with a private attribute $X$, and an adversary is assumed to have access to the shared link. The users and the server have access to a shared key $W$. The goal is to design the cache contents and the delivered message $\cal C$ such that the average length of $\mathcal{C}$ is minimized, while satisfying: i. The response $\cal C$ does not reveal any information about $X$, i.e., $X$ and $\cal C$ are independent, which corresponds to the perfect privacy constraint; ii. User $i$ is able to decode its demand, $Y_{d_i}$, by using $\cal C$, its local cache $Z_i$, and the shared key $W$. Since the database is correlated with $X$, existing codes for cache-aided delivery do not satisfy the perfect privacy condition. Indeed, we propose a variable-length coding scheme that combines privacy-aware compression with coded caching techniques. In particular, we use two-part code construction and Functional Representation Lemma. Finally, we extend the results to the case, where $X$ and $\mathcal{C}$ can be correlated, i.e., non-zero leakage is allowed.
Deep learning methods have gained considerable interest in the numerical solution of various partial differential equations (PDEs). One particular focus is on physics-informed neural networks (PINNs), which integrate physical principles into neural networks. This transforms the process of solving PDEs into optimization problems for neural networks. In order to address a collection of advection-diffusion equations (ADE) in a range of difficult circumstances, this paper proposes a novel network structure. This architecture integrates the solver, which is a multi-scale deep neural network (MscaleDNN) utilized in the PINN method, with a hard constraint technique known as HCPINN. This method introduces a revised formulation of the desired solution for advection-diffusion equations (ADE) by utilizing a loss function that incorporates the residuals of the governing equation and penalizes any deviations from the specified boundary and initial constraints. By surpassing the boundary constraints automatically, this method improves the accuracy and efficiency of the PINN technique. To address the ``spectral bias'' phenomenon in neural networks, a subnetwork structure of MscaleDNN and a Fourier-induced activation function are incorporated into the HCPINN, resulting in a hybrid approach called SFHCPINN. The effectiveness of SFHCPINN is demonstrated through various numerical experiments involving advection-diffusion equations (ADE) in different dimensions. The numerical results indicate that SFHCPINN outperforms both standard PINN and its subnetwork version with Fourier feature embedding. It achieves remarkable accuracy and efficiency while effectively handling complex boundary conditions and high-frequency scenarios in ADE.
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