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In Bioinformatics, the applications of flow decomposition in directed acyclic graphs are highlighted in RNA Assembly problem. However, it admits multiple solutions where exactly one solution correctly represents the underlying transcripts. The problem was addressed by Safe and Complete framework~[RECOMB16], which reports all the parts of the solution that are present in every possible solution. Khan et al.~[RECOMB22] first studied flow decomposition in the safe and complete framework. Their algorithm showed superior performance ($\approx20\%$) over the popular heuristic (greedy-width) on sufficiently complex graphs for a unified metric of precision and coverage (F-score). They presented the solution in multiple representations using simple but suboptimal algorithms, which were later optimized by Khan and Tomescu~[ESA22], who also presented an optimal representation. In this paper, we evaluate the practical significance of the optimal algorithms by Khan and Tomescu~[ESA22]. Our work highlights the significance of the theoretically optimal algorithms improving time (up to $60-70\%$) and memory (up to $76-85\%$), and the optimal representations improving output size (up to $135-170\%$) significantly. However, the impact of optimal algorithms was limited due to a large number of extremely short safe paths. We propose heuristics to improve these representations further, resulting in further improvement in time (up to $10\%$) and output size ($10-25\%$). However, in absolute terms, these improvements were limited to a few seconds on real datasets involved due to the smaller size of the graphs. We thus generated large random graphs, to demonstrate the scalability of the above results. The older algorithms [RECOMB22] were not practical on moderately large graphs ($\geq 1M$ nodes), while optimal algorithms [ESA22] were linearly scalable for much larger graphs ($\geq 100M$ nodes).

Depth first search is a fundamental graph problem having a wide range of applications. For a graph $G=(V,E)$ having $n$ vertices and $m$ edges, the DFS tree can be computed in $O(m+n)$ using $O(m)$ space where $m=O(n^2)$. In the streaming environment, most graph problems are studied in the semi-streaming model where several passes (preferably one) are allowed over the input, allowing $O(nk)$ local space for some $k=o(n)$. Trivially, using $O(m)$ space, DFS can be computed in one pass, and using $O(n)$ space, it can be computed in $O(n)$ passes. Khan and Mehta [STACS19] presented several algorithms allowing trade-offs between space and passes, where $O(nk)$ space results in $O(n/k)$ passes. They also empirically analyzed their algorithm to require only a few passes in practice for even $O(n)$ space. Chang et al. [STACS20] presented an alternate proof for the same and also presented $O(\sqrt{n})$ pass algorithm requiring $O(n~poly\log n)$ space with a finer trade-off between space and passes. However, their algorithm uses complex black box algorithms, making it impractical. We perform an experimental analysis of the practical semi-streaming DFS algorithms. Our analysis ranges from real graphs to random graphs (uniform and power-law). We also present several heuristics to improve the state-of-the-art algorithms and study their impact. Our heuristics improve state of the art by $40-90\%$, achieving optimal one pass in almost $40-50\%$ cases (improved from zero). In random graphs, they improve from $30-90\%$, again requiring optimal one pass for even very small values of $k$. Overall, our heuristics improved the relatively complex state-of-the-art algorithm significantly, requiring merely two passes in the worst case for random graphs. Additionally, our heuristics made the relatively simpler algorithm practically usable even for very small space bounds, which was impractical earlier.

In this work, we investigate the effects of H2 on the physical properties of Fe25Pd75. Broadband ferromagnetic resonance (FMR) spectroscopy revealed a significant FMR peak shift induced by H2 absorption for the FCC phased Fe25Pd75. The peak shifted towards higher applied fields, which is contrary to what was previously observed for CoPd alloys. Additionally, we conducted structural and magneto-optical Kerr ellipsometric studies on the Fe25Pd75 film and performed density functional theory calculations to explore the electronic and magnetic properties in both hydrogenated and dehydrogenated states. In the final part of this study, we deposited a Fe25Pd75 layer on top of a microscopic coplanar transmission line and investigated the FMR response of the layer while driven by a microwave current in the coplanar line. We observed a large amplitude FMR response upon hydrogen absorption, as well as desorption rates when cycling between pure N2 and a mixture of 3% H2 + 97% N2.

Genome assembly is a prominent problem studied in bioinformatics, which computes the source string using a set of its overlapping substrings. Classically, genome assembly uses assembly graphs built using this set of substrings to compute the source string efficiently, having a tradeoff between scalability and avoiding information loss. The scalable de Bruijn graphs come at the price of losing crucial overlap information. The complete overlap information is stored in overlap graphs using quadratic space. Hierarchical overlap graphs [IPL20] (HOG) overcome these limitations, avoiding information loss despite using linear space. After a series of suboptimal improvements, Khan and Park et al. simultaneously presented two optimal algorithms [CPM2021], where only the former was seemingly practical. We empirically analyze all the algorithms for computing Hierarchical overlap graphs, where the optimal algorithm~[CPM2021] outperforms the previous algorithms as expected. However, it is still based on relatively complex arguments for its formal proof and uses relatively complex data structures for its implementation. We present an intuitive algorithm, using only elementary arrays, which is also optimal. Our algorithm empirically proves even better for both time and memory over all the algorithms, highlighting its significance in both theory and practice. We further explore the applications of hierarchical overlap graphs to solve variants of suffix-prefix queries on a set of strings, recently studied by Loukides et al.~[CPM2023]. They presented state-of-the-art algorithms requiring complex black-box data structures, making them seemingly impractical. Our algorithms, despite failing to match their theoretical bounds, answer queries in $0.002$-$100~ms$ for datasets having around a billion characters.

For real-world applications of machine learning (ML), it is essential that models make predictions based on well-generalizing features rather than spurious correlations in the data. The identification of such spurious correlations, also known as shortcuts, is a challenging problem and has so far been scarcely addressed. In this work, we present a novel approach to detect shortcuts in image and audio datasets by leveraging variational autoencoders (VAEs). The disentanglement of features in the latent space of VAEs allows us to discover feature-target correlations in datasets and semi-automatically evaluate them for ML shortcuts. We demonstrate the applicability of our method on several real-world datasets and identify shortcuts that have not been discovered before., Comment: Accepted at the ICML 2023 Workshop on Spurious Correlations, Invariance and Stability

In a strongly connected graph $G = (V,E)$, a cut arc (also called strong bridge) is an arc $e \in E$ whose removal makes the graph no longer strongly connected. Equivalently, there exist $u,v \in V$, such that all $u$-$v$ walks contain $e$. Cut arcs are a fundamental graph-theoretic notion, with countless applications, especially in reachability problems. In this paper we initiate the study of cut paths, as a generalisation of cut arcs, which we naturally define as those paths $P$ for which there exist $u,v \in V$, such that all $u$-$v$ walks contain $P$ as subwalk. We first prove various properties of cut paths and define their remainder structures, which we use to present a simple $O(m)$-time verification algorithm for a cut path ($|V| = n$, $|E| = m$). Secondly, we apply cut paths and their remainder structures to improve several reachability problems from bioinformatics. A walk is called safe if it is a subwalk of every node-covering closed walk of a strongly connected graph. Multi-safety is defined analogously, by considering node-covering sets of closed walks instead. We show that cut paths provide simple $O(m)$-time algorithms verifying if a walk is safe or multi-safe. For multi-safety, we present the first linear time algorithm, while for safety, we present a simple algorithm where the state-of-the-art employed complex data structures. Finally we show that the simultaneous computation of remainder structures of all subwalks of a cut path can be performed in linear time. These properties yield an $O(mn)$ algorithm outputting all maximal multi-safe walks, improving over the state-of-the-art algorithm running in time $O(m^2+n^3)$. The results of this paper only scratch the surface in the study of cut paths, and we believe a rich structure of a graph can be revealed, considering the perspective of a path, instead of just an arc.

Minimum flow decomposition (MFD) is the NP-hard problem of finding a smallest decomposition of a network flow/circulation $X$ on a directed graph $G$ into weighted source-to-sink paths whose superposition equals $X$. We show that, for acyclic graphs, considering the \emph{width} of the graph (the minimum number of paths needed to cover all of its edges) yields advances in our understanding of its approximability. For the version of the problem that uses only non-negative weights, we identify and characterise a new class of \emph{width-stable} graphs, for which a popular heuristic is a \gwsimple-approximation ($|X|$ being the total flow of $X$), and strengthen its worst-case approximation ratio from $\Omega(\sqrt{m})$ to $\Omega(m / \log m)$ for sparse graphs, where $m$ is the number of edges in the graph. We also study a new problem on graphs with cycles, Minimum Cost Circulation Decomposition (MCCD), and show that it generalises MFD through a simple reduction. For the version allowing also negative weights, we give a $(\lceil \log \Vert X \Vert \rceil +1)$-approximation ($\Vert X \Vert$ being the maximum absolute value of $X$ on any edge) using a power-of-two approach, combined with parity fixing arguments and a decomposition of unitary circulations ($\Vert X \Vert \leq 1$), using a generalised notion of width for this problem. Finally, we disprove a conjecture about the linear independence of minimum (non-negative) flow decompositions posed by Kloster et al. [ALENEX 2018], but show that its useful implication (polynomial-time assignments of weights to a given set of paths to decompose a flow) holds for the negative version., Comment: A preliminary version was submitted to ESA 2022

Decomposing a network flow into weighted paths has numerous applications. Some applications require any decomposition that is optimal w.r.t. some property such as number of paths, robustness, or length. Many bioinformatic applications require a specific decomposition where the paths correspond to some underlying data that generated the flow. For real inputs, no optimization criteria guarantees to uniquely identify the correct decomposition. Therefore, we propose to report safe paths, i.e., subpaths of at least one path in every flow decomposition. Ma, Zheng, and Kingsford [WABI 2020] addressed the existence of multiple optimal solutions in a probabilistic framework, i.e., non-identifiability. Later [RECOMB 2021], they gave a quadratic-time algorithm based on a global criterion for solving a problem called AND-Quant, which generalizes the problem of reporting whether a given path is safe. We give the first local characterization of safe paths for flow decompositions in directed acyclic graphs (DAGs), leading to a practical algorithm for finding the complete set of safe paths. We evaluated our algorithms against the trivial safe algorithms (unitigs, extended unitigs) and the popularly used heuristic (greedy-width) for flow decomposition on RNA transcripts datasets. Despite maintaining perfect precision our algorithm reports significantly higher coverage ($\approx 50\%$ more) than trivial safe algorithms. The greedy-width algorithm though reporting a better coverage, has significantly lower precision on complex graphs. Overall, our algorithm outperforms (by $\approx 20\%$) greedy-width on a unified metric (F-Score) when the dataset has significant number of complex graphs. Moreover, it has superior time ($3-5\times$) and space efficiency ($1.2-2.2\times$), resulting in a better and more practical approach for bioinformatics applications of flow decomposition., Comment: RECOMB 2022. arXiv admin note: text overlap with arXiv:2102.06480