IST Austria: PubRep (Institute of Science and Technology)
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Almost optimal upper bound for the ground state energy of a dilute Fermi gas via cluster expansion
No full textWe prove an upper bound on the energy density of the dilute spin- Fermi gas capturing the leading correction to the kinetic energy with an error of size smaller than for any, where a denotes the scattering length of the interaction. The result is valid for a large class of interactions including interactions with a hard core. A central ingredient in the proof is a rigorous version of a fermionic cluster expansion adapted from the formal expansion of Gaudin et al. (Nucl Phys A 176(2):237–260, 1971. https://doi.org/10.1016/0375-9474(71)90267-3)
LIPIcs
No full textIn numerous fields, dynamic time series data require continuous updates, necessitating efficient data processing techniques for accurate analysis. This paper examines the banana tree data structure, specifically designed to efficiently maintain the multi-scale topological descriptor commonly known as persistent homology for dynamically changing time series data. We implement this data structure and conduct an experimental study to assess its properties and runtime for update operations. Our findings indicate that banana trees are highly effective with unbiased random data, outperforming state-of-the-art static algorithms in these scenarios. Additionally, our results show that real-world time series share structural properties with unbiased random walks, suggesting potential practical utility for our implementation
Scalable mechanistic neural networks
No full textWe propose Scalable Mechanistic Neural Network (S-MNN), an enhanced neural network framework designed for scientific machine learning applications involving long temporal sequences. By reformulating the original Mechanistic Neural Network (MNN) (Pervez et al., 2024), we reduce the computational time and space complexities from cubic and quadratic with respect to the sequence length, respectively, to linear. This significant improvement enables efficient modeling of long-term dynamics without sacrificing accuracy or interpretability. Extensive experiments demonstrate that S-MNN matches the original MNN in precision while substantially reducing computational resources. Consequently, S-MNN can drop-in replace the original MNN in applications, providing a practical and efficient tool for integrating mechanistic bottlenecks into neural network models of complex dynamical systems. Source code is available at https://github.com/IST-DASLab/ScalableMNN
LDAdam: Adaptive optimization from low-dimensional gradient statistics
No full textWe introduce LDAdam, a memory-efficient optimizer for training large models, that performs adaptive optimization steps within lower dimensional subspaces, while consistently exploring the full parameter space during training. This strategy keeps the optimizer's memory footprint to a fraction of the model size. LDAdam relies on a new projection-aware update rule for the optimizer states that allows for transitioning between subspaces, i.e., estimation of the statistics of the projected gradients. To mitigate the errors due to low-rank projection, LDAdam integrates a new generalized error feedback mechanism, which explicitly accounts for both gradient and optimizer state compression. We prove the convergence of LDAdam under standard assumptions, and provide empirical evidence that LDAdam allows for efficient fine-tuning and pre-training of language models
Front-biased activation of the Ras-Rab5-Rac1 loop coordinates collective cell migration
No full textCollective cell migration is coordinated by the front-to-rear intercellular propagation of EGFR-Ras-ERK pathway activation. However, the molecular mechanisms integrating front-to-rear information into this intercellular signaling cascade, particularly the determinants of cellular front-side specification, remain elusive. We visualized the activity of EGFR, Ras, Rac1 and Rab5A (hereafter Rab5) by using FRET biosensors and chemogenetic tools. Whereas EGFR activation was uniformly observed within cells, Ras activation was biased to the front side within cells. The polarized Ras activation depended on Merlin and Rac1, which also showed front-biased activation. Furthermore, Rab5, a crucial regulator of cell migration, demonstrated similar front-biased activation and was found to function downstream of Ras while being necessary for Rac1 activation. Thus, the positive feedback loop consisting of Ras, Rab5 and Rac1 is activated primarily at the front of collectively migrating cells. These findings offer new spatio-temporal insight into processing front–rear information during collective cell migration
Data of: "Quantifying the carbon footprint of conference travel: the case of NMR meetings"
No full textThis repository contains calculations of carbon footprints of NMR conferences, as described in the article by
Lucky N. Kapoor, Natalia Ruzickova, Predrag Živadinović, Valentin Leitner, Maria Anna Sisak, Cecelia Mweka, Jeroen Dobbelaere, Georgios Katsaros, and Paul Schanda
Published in Magnetic Resonance, 2025
In the search of optimal tree networks: Hardness and heuristics
No full textTraffic in datacenters may follow some pattern: some pairs of servers communicate more frequently than others. Demand-oblivious networks may perform poorly for such workloads, and demand-aware networks optimized for traffic should be used instead. Unfortunately, not all shapes of networks are feasible in real hardware. Practical limitations are usually provided in the form of a topology. For example, a network may be required to be a binary tree, a bounded-degree graph or a Fat tree.
In this work, we consider a topology of a binary tree, one of the most fundamental network topologies. We show that already finding an optimal demand-aware binary tree network is NP-hard. Then, we explore how various optimization techniques, including simple local searches, as well as deterministic mutation and crossover operators, cope with generating efficient tree networks on real-life and synthetic workloads
Burning or collapsing the medial axis is unstable
No full textThe medial axis of a set consists of the points in the ambient space without a unique closest point in the original set. Since its introduction, the medial axis has been used extensively in many applications as a method of computing a skeleton topologically equivalent to the original set. Unfortunately, one limiting factor in the use of the medial axis of a smooth manifold is that it is not necessarily topologically stable under small perturbations of the manifold. To counter these instabilities, various prunings of the medial axis have been proposed in the computational geometry community. Here, we examine one type of pruning, called burning. Because of the good experimental results it was hoped that the burning method of simplifying the medial axis would be stable. In this work, we show a simple example that dashes such hopes. Based on Bing’s house with two rooms, we demonstrate an isotopy of a shape where the medial axis goes from collapsible to non-collapsible. More precisely, we consider the standard deformation retract from the closed ball to Bing’s house with two rooms, but stop just short of the point where Bing’s house becomes two dimensional. This way we obtain an isotopy from the 3-ball to a thickened version of Bing’s house. Under this isotopy, the medial axis goes from collapsible to non-collapsible. We stress that this isotopy can be made generic, in the sense of singularity theory, as developed by Arnol’d and Thom
PMLR
No full textSimultaneously addressing multiple objectives is becoming increasingly important in modern machine learning. At the same time, data is often high-dimensional and costly to label. For a single objective such as prediction risk, conventional regularization techniques are known to improve generalization when the data exhibits low-dimensional structure like sparsity. However, it is largely unexplored how to leverage this structure in the context of multi-objective learning (MOL) with multiple competing objectives. In this work, we discuss how the application of vanilla regularization approaches can fail, and propose a two-stage MOL framework that can successfully leverage low-dimensional structure. We demonstrate its effectiveness experimentally for multi-distribution learning and fairness-risk trade-offs
PMLR
No full textA standard model that arises in several applications in sequential decision-making is partially observable Markov decision processes (POMDPs) where a decision-making agent interacts with an uncertain environment. A basic objective in POMDPs is the reachability objective, where given a target set of states, the goal is to eventually arrive at one of them.
The limit-sure problem asks whether reachability can be ensured with probability arbitrarily close to 1. In general, the limit-sure reachability problem for POMDPs is undecidable. However, in many practical cases, the most relevant question is the existence of policies with a small amount of memory. In this work, we study the limit-sure reachability problem for POMDPs with a fixed amount of memory. We establish that the computational complexity of the problem is NP-complete