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In this paper we propose two new subclasses of Petri nets with resets, for which the reachability and coverability problems become tractable. Namely, we add an acyclicity condition that only applies to the consumptions and productions, not the resets. The first class is acyclic Petri nets with resets, and we show that coverability is PSPACE-complete for them. This contrasts the known Ackermann-hardness for coverability in (not necessarily acyclic) Petri nets with resets. We prove that the reachability problem remains undecidable for acyclic Petri nets with resets. The second class concerns workflow nets, a practically motivated and natural subclass of Petri nets. Here, we show that both coverability and reachability in acyclic workflow nets with resets are PSPACE-complete. Without the acyclicity condition, reachability and coverability in workflow nets with resets are known to be equally hard as for Petri nets with resets, that being Ackermann-hard and undecidable, respectively.

In this paper, we consider a model reduction technique for stabilizable and detectable stochastic systems. It is based on a pair of Gramians that we analyze in terms of well-posedness. Subsequently, dominant subspaces of the stochastic systems are identified exploiting these Gramians. An associated balancing related scheme is proposed that removes unimportant information from the stochastic dynamics in order to obtain a reduced system. We show that this reduced model preserves important features like stabilizability and detectability. Additionally, a comprehensive error analysis based on eigenvalues of the Gramian pair product is conducted. This provides an a-priori criterion for the reduction quality which we illustrate in numerical experiments.

This paper explores the connections between optimal transport and variational inference, with a focus on forward and reverse time stochastic differential equations and Girsanov transformations.We present a principled and systematic framework for sampling and generative modelling centred around divergences on path space. Our work culminates in the development of a novel score-based annealed flow technique (with connections to Jarzynski and Crooks identities from statistical physics) and a regularised iterative proportional fitting (IPF)-type objective, departing from the sequential nature of standard IPF. Through a series of generative modelling examples and a double-well-based rare event task, we showcase the potential of the proposed methods.

Randomized algorithms are important for solving large-scale optimization problems. In this paper, we propose a fast sketching algorithm for least square problems regularized by convex or nonconvex regularization functions, Sketching for Regularized Optimization (SRO). Our SRO algorithm first generates a sketch of the original data matrix, then solves the sketched problem. Different from existing randomized algorithms, our algorithm handles general Frechet subdifferentiable regularization functions in an unified framework. We present general theoretical result for the approximation error between the optimization results of the original problem and the sketched problem for regularized least square problems which can be convex or nonconvex. For arbitrary convex regularizer, relative-error bound is proved for the approximation error. Importantly, minimax rates for sparse signal estimation by solving the sketched sparse convex or nonconvex learning problems are also obtained using our general theoretical result under mild conditions. To the best of our knowledge, our results are among the first to demonstrate minimax rates for convex or nonconvex sparse learning problem by sketching under a unified theoretical framework. We further propose an iterative sketching algorithm which reduces the approximation error exponentially by iteratively invoking the sketching algorithm. Experimental results demonstrate the effectiveness of the proposed SRO and Iterative SRO algorithms.

This paper presents a unified approach for maximizing continuous DR-submodular functions that encompasses a range of settings and oracle access types. Our approach includes a Frank-Wolfe type offline algorithm for both monotone and non-monotone functions, with different restrictions on the general convex set. We consider settings where the oracle provides access to either the gradient of the function or only the function value, and where the oracle access is either deterministic or stochastic. We determine the number of required oracle accesses in all cases. Our approach gives new/improved results for nine out of the sixteen considered cases, avoids computationally expensive projections in two cases, with the proposed framework matching performance of state-of-the-art approaches in the remaining five cases. Notably, our approach for the stochastic function value-based oracle enables the first regret bounds with bandit feedback for stochastic DR-submodular functions.

Diffusion models have been recently used for anomaly detection (AD) in images. In this paper we investigate whether they can also be leveraged for AD on multivariate time series (MTS). We test two diffusion-based models and compare them to several strong neural baselines. We also extend the PA%K protocol, by computing a ROCK-AUC metric, which is agnostic to both the detection threshold and the ratio K of correctly detected points. Our models outperform the baselines on synthetic datasets and are competitive on real-world datasets, illustrating the potential of diffusion-based methods for AD in multivariate time series.

In this paper, we propose an approach to address the problem of 3D reconstruction of scenes from a single image captured by a light-field camera equipped with a rolling shutter sensor. Our method leverages the 3D information cues present in the light-field and the motion information provided by the rolling shutter effect. We present a generic model for the imaging process of this sensor and a two-stage algorithm that minimizes the re-projection error while considering the position and motion of the camera in a motion-shape bundle adjustment estimation strategy. Thereby, we provide an instantaneous 3D shape-and-pose-and-velocity sensing paradigm. To the best of our knowledge, this is the first study to leverage this type of sensor for this purpose. We also present a new benchmark dataset composed of different light-fields showing rolling shutter effects, which can be used as a common base to improve the evaluation and tracking the progress in the field. We demonstrate the effectiveness and advantages of our approach through several experiments conducted for different scenes and types of motions. The source code and dataset are publicly available at: //github.com/ICB-Vision-AI/RSLF

This paper explores the development of UniFolding, a sample-efficient, scalable, and generalizable robotic system for unfolding and folding various garments. UniFolding employs the proposed UFONet neural network to integrate unfolding and folding decisions into a single policy model that is adaptable to different garment types and states. The design of UniFolding is based on a garment's partial point cloud, which aids in generalization and reduces sensitivity to variations in texture and shape. The training pipeline prioritizes low-cost, sample-efficient data collection. Training data is collected via a human-centric process with offline and online stages. The offline stage involves human unfolding and folding actions via Virtual Reality, while the online stage utilizes human-in-the-loop learning to fine-tune the model in a real-world setting. The system is tested on two garment types: long-sleeve and short-sleeve shirts. Performance is evaluated on 20 shirts with significant variations in textures, shapes, and materials. More experiments and videos can be found in the supplementary materials and on the website: //unifolding.robotflow.ai

Coin selection algorithms are a fundamental component of blockchain technology. In this paper, we present a comprehensive review of the existing coin selection algorithms utilized in unspent transaction output (UTXO)-based blockchains. We provide a list of the desired objectives and categorize existing algorithms into three types: primitive, basic, and advanced algorithms. This allows for a structured understanding of their functionalities and limitations. We also evaluate the performance of existing coin selection algorithms. The aim of this paper is to provide system researchers and developers with a concrete view of the current design landscape.

This paper describes a purely functional library for computing level-$p$-complexity of Boolean functions, and applies it to two-level iterated majority. Boolean functions are simply functions from $n$ bits to one bit, and they can describe digital circuits, voting systems, etc. An example of a Boolean function is majority, which returns the value that has majority among the $n$ input bits for odd $n$. The complexity of a Boolean function $f$ measures the cost of evaluating it: how many bits of the input are needed to be certain about the result of $f$. There are many competing complexity measures but we focus on level-$p$-complexity -- a function of the probability $p$ that a bit is 1. The level-$p$-complexity $D_p(f)$ is the minimum expected cost when the input bits are independent and identically distributed with Bernoulli($p$) distribution. We specify the problem as choosing the minimum expected cost of all possible decision trees -- which directly translates to a clearly correct, but very inefficient implementation. The library uses thinning and memoization for efficiency and type classes for separation of concerns. The complexity is represented using (sets of) polynomials, and the order relation used for thinning is implemented using polynomial factorisation and root-counting. Finally we compute the complexity for two-level iterated majority and improve on an earlier result by J.~Jansson.