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The FAIR principles are globally accepted guidelines for improved data management practices with the potential to align data spaces on a global scale. In practice, this is only marginally achieved through the different ways in which organizations interpret and implement these principles. The concept of FAIR Digital Objects provides a way to realize a domain-independent abstraction layer that could solve this problem, but its specifications are currently diverse, contradictory, and restricted to semantic models. In this work, we introduce a rigorously formalized data model with a set of assertions using formal expressions to provide a common baseline for the implementation of FAIR Digital Objects. The model defines how these objects enable machine-actionable decisions based on the principles of abstraction, encapsulation, and entity relationship to fulfill FAIR criteria for the digital resources they represent. We provide implementation examples in the context of two use cases and explain how our model can facilitate the (re)use of data across domains. We also compare how our model assertions are met by FAIR Digital Objects as they have been described in other projects. Finally, we discuss our results' adoption criteria, limitations, and perspectives in the big data context. Overall, our work represents an important milestone for various communities working towards globally aligned data spaces through FAIRification., Comment: Accepted at the 2024 IEEE International Conference on Big Data (IEEE BigData 2024)

The greedoid is a significant abstraction of the matroid allowing for a more flexible analysis of structures in which the greedy algorithm "works." However, their diverse structure imposes difficulties towards their application in combinatorial optimization [Sze21]. In response, we revisit the polymatroid greedoid [KL85a] to characterize it by properties approximating those of matroids, by using the submodularity of its polymatroid representation in particular. Towards doing so, our main contribution is a full description of this class. Specifically, we show that a greedoid is a polymatroid greedoid if and only if it is an optimistic interval greedoid whose kernels are closed under intersection. This constitutes the first necessary and sufficient characterization of the polymatroid greedoid in terms of its combinatorial attributes, thereby resolving a central open question of Korte and Lov\'asz [KL85a]. Here, we introduce the optimism property to approximate properties of a matroid's continuations which are implied by the closure axioms of its span, which no longer hold for greedoids. And, because the kernels of an interval greedoid are in many ways an extension of a matroid's closed sets, our direction of necessity is a direct generalization of Birkhoff and Edmond's characterization of the meet in the lattice of a matroid's closed sets [Bir35, Edm03]. Towards achieving this result, our main technical insights arise from relating the lattice of flats of a polymatroid greedoid to that of the closed sets of its representation through order preserving mappings. Specifically, we will show the novel insight that the notion of polymatroid representation considered in [KL85a] is equivalent to the existence of a certain Galois connection. As a consequence, the representation of a greedoid via a polymatroid is an order theoretic concept in disguise., Comment: 26 pages, 4 figures

The gradients used to train neural networks are typically computed using backpropagation. While an efficient way to obtain exact gradients, backpropagation is computationally expensive, hinders parallelization, and is biologically implausible. Forward gradients are an approach to approximate the gradients from directional derivatives along random tangents computed by forward-mode automatic differentiation. So far, research has focused on using a single tangent per step. This paper provides an in-depth analysis of multi-tangent forward gradients and introduces an improved approach to combining the forward gradients from multiple tangents based on orthogonal projections. We demonstrate that increasing the number of tangents improves both approximation quality and optimization performance across various tasks.

Matroids provide one of the most elegant structures for algorithm design. This is best identified by the Edmonds-Rado theorem relating the success of the simple greedy algorithm to the anatomy of the optimal basis of a matroid [Edm71; Rad57]. As a response, much energy has been devoted to understanding a matroid's computational properties. Yet, less is understood where parallel algorithms are concerned. In response, we initiate the study of parallel matroid optimization in the adaptive complexity model [BS18]. First, we reexamine Bor\r{u}vka's classical minimum weight spanning tree algorithm [Bor26b; Bor26a] in the abstract language of matroid theory, and identify a new certificate of optimality for the basis of any matroid as a result. In particular, a basis is optimal if and only if it contains the points of minimum weight in every circuit of the dual matroid. Hence, we can witnesses whether any specific point belongs to the optimal basis via a test for local optimality in a circuit of the dual matroid, thereby revealing a general design paradigm towards parallel matroid optimization. To instantiate this paradigm, we use the special structure of a binary matroid to identify an optimization scheme with low adaptivity. Here, our key technical step is reducing optimization to the simpler task of basis search in the binary matroid, using only logarithmic overhead of adaptive rounds of queries to independence oracles. Consequentially, we compose our reduction with the parallel basis search method of [KUW88] to obtain an algorithm for finding the optimal basis of a binary matroid terminating in sublinearly many adaptive rounds of queries to an independence oracle. To the authors' knowledge, this is the first algorithm for matroid optimization to outperform the greedy algorithm in terms of adaptive complexity in the independence query model without assuming the matroid is encoded by a graph., Comment: 45 pages, 7 figures, 3 algorithms

Transformers have recently gained prominence in long time series forecasting by elevating accuracies in a variety of use cases. Regrettably, in the race for better predictive performance the overhead of model architectures has grown onerous, leading to models with computational demand infeasible for most practical applications. To bridge the gap between high method complexity and realistic computational resources, we introduce the Residual Cyclic Transformer, ReCycle. ReCycle utilizes primary cycle compression to address the computational complexity of the attention mechanism in long time series. By learning residuals from refined smoothing average techniques, ReCycle surpasses state-of-the-art accuracy in a variety of application use cases. The reliable and explainable fallback behavior ensured by simple, yet robust, smoothing average techniques additionally lowers the barrier for user acceptance. At the same time, our approach reduces the run time and energy consumption by more than an order of magnitude, making both training and inference feasible on low-performance, low-power and edge computing devices. Code is available at https://github.com/Helmholtz-AI-Energy/ReCycle, Comment: 9 pages, 3 figures, to be published at IEEE CAI 2024, Associated code available at https://github.com/Helmholtz-AI-Energy/ReCycle

[Context and motivation]: Understanding and interpreting regulatory norms and inferring software requirements from them is a critical step towards regulatory compliance, a matter of significant importance in various industrial sectors. [Question/ problem]: However, interpreting regulations still largely depends on individual legal expertise and experience within the respective domain, with little to no systematic methodologies and supportive tools to guide this practice. In fact, research in this area is too often detached from practitioners' experiences, rendering the proposed solutions not transferable to industrial practice. As we argue, one reason is that we still lack a profound understanding of industry- and domain-specific practices and challenges. [Principal ideas/ results]: We aim to close this gap and provide such an investigation at the example of the banking and insurance domain. We conduct an industrial multi-case study as part of a long-term academia-industry collaboration with a medium-sized software development and renovation company. We explore contemporary industrial practices and challenges when inferring requirements from regulations to support more problem-driven research. Our study investigates the complexities of requirement engineering in regulatory contexts, pinpointing various issues and discussing them in detail. We highlight the gathered insights and the practical challenges encountered and suggest avenues for future research. [Contribution]: Our contribution is a comprehensive case study focused on the FinTech domain, offering a detailed understanding of the specific needs within this sector. We have identified key practices for managing regulatory requirements in software development, and have pinpointed several challenges. We conclude by offering a set of recommendations for future problem-driven research directions.

Communication bottlenecks severely hinder the scalability of distributed neural network training, particularly in high-performance computing (HPC) environments. We introduce AB-training, a novel data-parallel method that leverages low-rank representations and independent training groups to significantly reduce communication overhead. Our experiments demonstrate an average reduction in network traffic of approximately 70.31\% across various scaling scenarios, increasing the training potential of communication-constrained systems and accelerating convergence at scale. AB-training also exhibits a pronounced regularization effect at smaller scales, leading to improved generalization while maintaining or even reducing training time. We achieve a remarkable 44.14 : 1 compression ratio on VGG16 trained on CIFAR-10 with minimal accuracy loss, and outperform traditional data parallel training by 1.55\% on ResNet-50 trained on ImageNet-2012. While AB-training is promising, our findings also reveal that large batch effects persist even in low-rank regimes, underscoring the need for further research into optimized update mechanisms for massively distributed training.

Predicting the performance of various infrastructure design options in complex federated infrastructures with computing sites distributed over a wide area network that support a plethora of users and workflows, such as the Worldwide LHC Computing Grid (WLCG), is not trivial. Due to the complexity and size of these infrastructures, it is not feasible to deploy experimental test-beds at large scales merely for the purpose of comparing and evaluating alternate designs. An alternative is to study the behaviours of these systems using simulation. This approach has been used successfully in the past to identify efficient and practical infrastructure designs for High Energy Physics (HEP). A prominent example is the Monarc simulation framework, which was used to study the initial structure of the WLCG. New simulation capabilities are needed to simulate large-scale heterogeneous computing systems with complex networks, data access and caching patterns. A modern tool to simulate HEP workloads that execute on distributed computing infrastructures based on the SimGrid and WRENCH simulation frameworks is outlined. Studies of its accuracy and scalability are presented using HEP as a case-study. Hypothetical adjustments to prevailing computing architectures in HEP are studied providing insights into the dynamics of a part of the WLCG and candidates for improvements., Comment: 26th International Conference on Computing in High Energy and Nuclear Physics (CHEP 2023)

This study explores the learning dynamics of neural networks by analyzing the singular value decomposition (SVD) of their weights throughout training. Our investigation reveals that an orthogonal basis within each multidimensional weight's SVD representation stabilizes during training. Building upon this, we introduce Orthogonality-Informed Adaptive Low-Rank (OIALR) training, a novel training method exploiting the intrinsic orthogonality of neural networks. OIALR seamlessly integrates into existing training workflows with minimal accuracy loss, as demonstrated by benchmarking on various datasets and well-established network architectures. With appropriate hyperparameter tuning, OIALR can surpass conventional training setups, including those of state-of-the-art models.

The graph polynomial for the number of independent sets of size $k$ in a general undirected graph is shown to be equal to an elementary symmetric polynomial of the vertex monomials, which are determined by the edges incident at the vertices. The edge variables that comprise the vertex monomials are shown to be nilpotent of degree two. The index of nilpotency of the algebra generated by the graph's vertex monomials is the order of a maximum independent set of the graph. Graph polynomials for the number of cliques and vertex covers are derived from the graph polynomial for independent sets. The graph polynomial for the number of bipartite cuts is given as a coefficient of a multivariate Laurent polynomial.

We define a new class of predicates called equilevel predicates on a distributive lattice which eases the analysis of parallel algorithms. Many combinatorial problems such as the vertex cover problem, the bipartite matching problem, and the minimum spanning tree problem can be modeled as detecting an equilevel predicate. The problem of detecting an equilevel problem is NP-complete, but equilevel predicates with the helpful property can be detected in polynomial time in an online manner. An equilevel predicate has the helpful property with a polynomial time algorithm if the algorithm can return a nonempty set of indices such that advancing on any of them can be used to detect the predicate. Furthermore, the refined independently helpful property allows online parallel detection of such predicates in NC. When the independently helpful property holds, advancing on all the specified indices in parallel can be used to detect the predicate in polylogarithmic time. We also define a special class of equilevel predicates called solitary predicates. Unless NP = RP, this class of predicate also does not admit efficient algorithms. Earlier work has shown that solitary predicates with the efficient advancement can be detected in polynomial time. We introduce two properties called the antimonotone advancement and the efficient rejection which yield the detection of solitary predicates in NC. Finally, we identify the minimum spanning tree, the shortest path, and the conjunctive predicate detection as problems satisfying such properties, giving alternative certifications of their NC memberships as a result., Comment: To appear in ICDCN 2024

A large body of literature within the additive manufacturing (AM) community has focused on successfully creating stable tungsten (W) microstructures due to significant interest in its application for extreme environments. However, solidification cracking and additional embrittling features at grain boundaries have resulted in poorly performing microstructures, stymying the application of AM as a manufacturing technique for W. Several alloying strategies, such as ceramic particles and ductile elements, have emerged with the promise to eliminate solidification cracking while simultaneously enhancing stability against recrystallization. In this work, we provide new insights regarding the defects and microstructural features that result from the introduction of ZrC for grain refinement and NiFe as a ductile reinforcement phase - in addition to the resulting thermophysical and mechanical properties. ZrC is shown to promote microstructural stability with increased hardness due to the formation of ZrO2 dispersoids. Conversely, NiFe forms into micron-scale FCC phase regions within a BCC W matrix, producing enhanced toughness relative to pure AM W. A combination of these effects is realized in the WNiFe+ZrC system and demonstrates that complex chemical environments coupled with the tuning of AM microstructures provides an effective pathway for enabling laser AM W materials with enhanced stability and performance.

Given the urgency to reduce fossil fuel energy production to make climate tipping points less likely, we call for resource-aware knowledge gain in the research areas on Universe and Matter with emphasis on the digital transformation. A portfolio of measures is described in detail and then summarized according to the timescales required for their implementation. The measures will both contribute to sustainable research and accelerate scientific progress through increased awareness of resource usage. This work is based on a three-days workshop on sustainability in digital transformation held in May 2023., Comment: 20 pages, 2 figures, publication following workshop 'Sustainability in the Digital Transformation of Basic Research on Universe & Matter', 30 May to 2 June 2023, Meinerzhagen, Germany, https://indico.desy.de/event/37480

Visualization onboarding supports users in reading, interpreting, and extracting information from visual data representations. General-purpose onboarding tools and libraries are applicable for explaining a wide range of graphical user interfaces but cannot handle specific visualization requirements. This paper describes a first step towards developing an onboarding library called VisAhoi, which is easy to integrate, extend, semi-automate, reuse, and customize. VisAhoi supports the creation of onboarding elements for different visualization types and datasets. We demonstrate how to extract and describe onboarding instructions using three well-known high-level descriptive visualization grammars - Vega-Lite, Plotly.js, and ECharts. We show the applicability of our library by performing two usage scenarios that describe the integration of VisAhoi into a VA tool for the analysis of high-throughput screening (HTS) data and, second, into a Flourish template to provide an authoring tool for data journalists for a treemap visualization. We provide a supplementary website that demonstrates the applicability of VisAhoi to various visualizations, including a bar chart, a horizon graph, a change matrix or heatmap, a scatterplot, and a treemap visualization.

Segregation engineering has emerged as a promising pathway towards designing thermally stable nanocrystalline alloys with enhanced mechanical properties. However, the compositional and processing space for solute stabilized microstructures is vast, thus the application of high-throughput techniques to accelerate optimal material development is increasingly attractive. In this work, combinatorial synthesis is combined with high-throughput characterization techniques to explore microstructural transitions through annealing of a nanocrystalline ternary Al-base alloy containing a transition metal (TM=Ni) and rare earth dopant (RE=Y). A down-selected optimal composition with the highest thermal stability is annealed through in situ transmission electron microscopy, revealing that the removal of the RE species is correlated to a reduction in the microstructural stability at high temperatures as a result of variations in intermetallic phase formation. Results demonstrate the benefits of co-segregation for enhancing mechanical hardness and delaying the onset of microstructural instability., Comment: 12 pages, 4 figures