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The H\'enon-Heiles system, initially introduced as a simplified model of galactic dynamics, has become a paradigmatic example in the study of nonlinear systems. Despite its simplicity, it exhibits remarkably rich dynamical behavior, including the interplay between regular and chaotic orbital dynamics, resonances, and stochastic regions in phase space, which have inspired extensive research in nonlinear dynamics. In this work, we investigate the system's solutions at small energy levels, deriving asymptotic constants of motion that remain valid over remarkably long timescales -- far exceeding the range of validity of conventional perturbation techniques. Our approach leverages the system's inherent two-scale dynamics, employing a novel analytical framework to uncover these long-lived invariants. The derived formulas exhibit excellent agreement with numerical simulations, providing a deeper understanding of the system's long-term behavior., Comment: 22 pages, 6 figures

While transformers have been at the core of most recent advancements in sequence generative models, their computational cost remains quadratic in sequence length. Several subquadratic architectures have been proposed to address this computational issue. Some of them, including long convolution sequence models (LCSMs), such as Hyena, address this issue at training time but remain quadratic during inference. We propose a method for speeding up LCSMs' exact inference to quasilinear $O(L\log^2L)$ time, identify the key properties that make this possible, and propose a general framework that exploits these. Our approach, inspired by previous work on relaxed polynomial interpolation, is based on a tiling which helps decrease memory movement and share computation. It has the added benefit of allowing for almost complete parallelization across layers of the position-mixing part of the architecture. Empirically, we provide a proof of concept implementation for Hyena, which gets up to $1.6\times$ end-to-end improvement over standard inference by improving $50\times$ within the position-mixing part., Comment: 15 pages, 9 figures, 5 algorithms

This paper introduces the Hamiltonian-Adaptive Ternary Tree (HATT) framework to compile optimized Fermion-to-qubit mapping for specific Fermionic Hamiltonians. In the simulation of Fermionic quantum systems, efficient Fermion-to-qubit mapping plays a critical role in transforming the Fermionic system into a qubit system. HATT utilizes ternary tree mapping and a bottom-up construction procedure to generate Hamiltonian aware Fermion-to-qubit mapping to reduce the Pauli weight of the qubit Hamiltonian, resulting in lower quantum simulation circuit overhead. Additionally, our optimizations retain the important vacuum state preservation property in our Fermion-to-qubit mapping and reduce the complexity of our algorithm from $O(N^4)$ to $O(N^3)$. Evaluations and simulations of various Fermionic systems demonstrate $5\sim20\%$ reduction in Pauli weight, gate count, and circuit depth, alongside excellent scalability to larger systems. Experiments on the Ionq quantum computer also show the advantages of our approach in noise resistance in quantum simulations.

Resource efficient and high precision compilation of programs into quantum circuits expressed in Fault-Tolerant gate sets, such as the Clifford+T gate set, is vital for the success of quantum computing. Optimal analytical compilation methods are known for restricted classes of unitaries, otherwise the problem is intractable. Empirical search-based synthesis methods, including Reinforcement Learning and simulated annealing, can generate good implementations for a more extensive set of unitaries, but require trade-offs in approximation precision and resource use. We leverage search-based methods to reduce the general unitary synthesis problem to one of synthesizing diagonal unitaries; a problem solvable efficiently in general and optimally in the single-qubit case. We demonstrate how our approach improves the implementation precision attainable by Fault-Tolerant synthesis algorithms on an array of unitaries taken from real quantum algorithms. On these benchmarks, many of which cannot be handled by existing approaches, we observe an average of 95% fewer resource-intensive non-Clifford gates compared to the more general Quantum Shannon Decomposition. On a subset of algorithms of interest for future term applications, diagonalization can reduce T gate counts by up to 16.8% compared to other methods., Comment: 22 pages, 11 figures

In this paper we gather and extend classical results for parabolic cylinder functions, namely solutions of the Weber differential equations, using a systematic approach by Borel-Laplace methods. We revisit the definition and construction of the standard solutions $U,V$ of the Weber differential equation \begin{equation*} w''(z)-\left(\frac{z^2}{4}+a\right)w(z)=0 \end{equation*} and provide representations by Laplace integrals extended to include all values of the complex parameter $a$; we find an integral integral representation for the function $V$; none was previously available. For the Weber equation in the form \begin{equation*} u''(x)+\left(\frac{x^2}{4}-a\right)u(x)=0, \end{equation*} we define a new fundamental system $E_\pm$ which is analytic in $a\in\mathbb{C}$, based on asymptotic behavior; they appropriately extend and modify the classical solutions $E,E^*$ of the real Weber equation to the complex domain. The techniques used are general and we include details and motivations for the approach.

Research in the field of language models is rapidly evolving, with many open models being released to the public. Openly available pretraining corpora usually focus on only a handful of languages, with many others either missing completely or extremely underrepresented. In this report, we introduce FuLG, a hundred-fifty-billion-token Romanian corpus extracted from CommonCrawl. We present our methodology for filtering FuLG and compare it via ablation studies against existing Romanian corpora.

Hyperscalers dominate the landscape of large network deployments, yet they rarely share data or insights about the challenges they face. In light of this supremacy, what problems can we find to solve in this space? We take an unconventional approach to find relevant research directions, starting from public plans to build a $100 billion datacenter for machine learning applications. Leveraging the language models scaling laws, we discover what workloads such a datacenter might carry and explore the challenges one may encounter in doing so, with a focus on networking research. We conclude that building the datacenter and training such models is technically possible, but this requires novel wide-area transports for inter-DC communication, a multipath transport and novel datacenter topologies for intra-datacenter communication, high speed scale-up networks and transports, outlining a rich research agenda for the networking community.

Languages such as P4 and NPL have enabled a wide and diverse range of networking applications that take advantage of programmable dataplanes. However, software development in these languages is difficult. To address this issue, high-level languages have been designed to offer programmers powerful abstractions that reduce the time, effort and domain-knowledge required for developing networking applications. These languages are then translated by a compiler into P4/NPL code. Inspired by the recent success of Large Language Models (LLMs) in the task of code generation, we propose to raise the level of abstraction even higher, employing LLMs to translate prose into high-level networking code. We analyze the problem, focusing on the motivation and opportunities, as well as the challenges involved and sketch out a roadmap for the development of a system that can generate high-level dataplane code from natural language instructions. We present some promising preliminary results on generating Lucid code from natural language.

Existing numerical optimizers deployed in quantum compilers use expensive $\mathcal{O}(4^n)$ matrix-matrix operations. Inspired by recent advances in quantum machine learning (QML), QFactor-Sample replaces matrix-matrix operations with simpler $\mathcal{O}(2^n)$ circuit simulations on a set of sample inputs. The simpler the circuit, the lower the number of required input samples. We validate QFactor-Sample on a large set of circuits and discuss its hyperparameter tuning. When incorporated in the BQSKit quantum compiler and compared against a state-of-the-art domain-specific optimizer, We demonstrate improved scalability and a reduction in compile time, achieving an average speedup factor of 69 for circuits with more than 8 qubits. We also discuss how improved numerical optimization affects the dynamics of partitioning-based compilation schemes, which allow a trade-off between compilation speed and solution quality., Comment: 15 pages, 8 figures, and 4 appendices

The increasing demand of machine learning (ML) workloads in datacenters places significant stress on current congestion control (CC) algorithms, many of which struggle to maintain performance at scale. These workloads generate bursty, synchronized traffic that requires both rapid response and fairness across flows. Unfortunately, existing CC algorithms that rely heavily on delay as a primary congestion signal often fail to react quickly enough and do not consistently ensure fairness. In this paper, we propose FASTFLOW, a streamlined sender-based CC algorithm that integrates delay, ECN signals, and optional packet trimming to achieve precise, real-time adjustments to congestion windows. Central to FASTFLOW is the QuickAdapt mechanism, which provides accurate bandwidth estimation at the receiver, enabling faster reactions to network conditions. We also show that FASTFLOW can effectively enhance receiver-based algorithms such as EQDS by improving their ability to manage in-network congestion. Our evaluation reveals that FASTFLOW outperforms cutting-edge solutions, including EQDS, Swift, BBR, and MPRDMA, delivering up to 50% performance improvements in modern datacenter networks.

The design space of current quantum computers is expansive with no obvious winning solution. This leaves practitioners with a clear question: "What is the optimal system configuration to run an algorithm?". This paper explores hardware design trade-offs across NISQ systems to guide algorithm and hardware design choices. The evaluation is driven by algorithmic workloads and algorithm fidelity models which capture architectural features such as gate expressivity, fidelity, and crosstalk. We also argue that the criteria for gate design and selection should be extended from maximizing average fidelity to a more comprehensive approach that takes into account the gate expressivity with respect to algorithmic structures. We consider native entangling gates (CNOT, ECR, CZ, ZZ, XX, Sycamore, $\sqrt{\text{iSWAP}}$), proposed gates (B Gate, $\sqrt[4]{\text{CNOT}}$, $\sqrt[8]{\text{CNOT}}$), as well as parameterized gates (FSim, XY). Our methodology is driven by a custom synthesis driven circuit compilation workflow, which is able to produce minimal circuit representations for a given system configuration. By providing a method to evaluate the suitability of algorithms for hardware platforms, this work emphasizes the importance of hardware-software co-design for quantum computing.

Coronary artery disease (CAD) is the dominant cause of death and hospitalization across the globe. Atherosclerosis, an inflammatory condition that gradually narrows arteries and has potentially fatal effects, is the most frequent cause of CAD. Nonetheless, the circulation regularly adapts in the presence of atherosclerosis, through the formation of collateral arteries, resulting in significant long-term health benefits. Therefore, timely detection of coronary collateral circulation (CCC) is crucial for CAD personalized medicine. We propose a novel deep learning based method to detect CCC in angiographic images. Our method relies on a convolutional backbone to extract spatial features from each frame of an angiography sequence. The features are then concatenated, and subsequently processed by another convolutional layer that processes embeddings temporally. Due to scarcity of data, we also experiment with pretraining the backbone on coronary artery segmentation, which improves the results consistently. Moreover, we experiment with few-shot learning to further improve performance, given our low data regime. We present our results together with subgroup analyses based on Rentrop grading, collateral flow, and collateral grading, which provide valuable insights into model performance. Overall, the proposed method shows promising results in detecting CCC, and can be further extended to perform landmark based CCC detection and CCC quantification.