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The $\ell$-matroid intersection ($\ell$-MI) problem asks if $\ell$ given matroids share a common basis. Already for $\ell = 3$, notable canonical NP-complete special cases are $3$-Dimensional Matching and Hamiltonian Path on directed graphs. However, while these problems admit exponential-time algorithms that improve the simple brute force, the fastest known algorithm for $3$-MI is exactly brute force with runtime $2^{n}/poly(n)$, where $n$ is the number of elements. Our first result shows that in fact, brute force cannot be significantly improved, by ruling out an algorithm for $\ell$-MI with runtime $o\left(2^{n-5 \cdot n^{\frac{1}{\ell-1}} \cdot \log (n)}\right)$, for any fixed $\ell\geq 3$. The complexity gap between $3$-MI and the polynomially solvable $2$-matroid intersection calls for a better understanding of the complexity of intermediate problems. One such prominent problem is exact matroid intersection (EMI). Given two matroids whose elements are either red or blue and a number $k$, decide if there is a common basis which contains exactly $k$ red elements. We show that EMI does not admit a randomized polynomial time algorithm. This bound implies that the parameterized algorithm of Eisenbrand et al. (FOCS'24) for exact weight matroid cannot be generalized to matroid intersection. We further obtain: (i) an algorithm that solves $\ell$-MI faster than brute force in time $2^{n-\Omega\left(\log^2 (n)\right)} $ (ii) a parameterized running time lower bound of $2^{(\ell-2) \cdot k \cdot \log k} \cdot poly(n)$ for $\ell$-MI, where the parameter $k$ is the rank of the matroids. We obtain these two results by generalizing the Monotone Local Search technique of Fomin et al. (J. ACM'19). Broadly speaking, our generalization converts any parameterized algorithm for a subset problem into an exponential-time algorithm which is faster than brute-force.

Many problems in navigation and tracking require increasingly accurate characterizations of the evolution of uncertainty in nonlinear systems. Nonlinear uncertainty propagation approaches based on Gaussian mixture density approximations offer distinct advantages over sampling based methods in their computational cost and continuous representation. State-of-the-art Gaussian mixture approaches are adaptive in that individual Gaussian mixands are selectively split into mixtures to yield better approximations of the true propagated distribution. Despite the importance of the splitting process to accuracy and computational efficiency, relatively little work has been devoted to mixand selection and splitting direction optimization. The first part of this work presents splitting methods that preserve the mean and covariance of the original distribution. Then, we present and compare a number of novel heuristics for selecting the splitting direction. The choice of splitting direction is informed by the initial uncertainty distribution, properties of the nonlinear function through which the original distribution is propagated, and a whitening based natural scaling method to avoid dependence of the splitting direction on the scaling of coordinates. We compare these novel heuristics to existing techniques in three distinct examples involving Cartesian to polar coordinate transformation, Keplerian orbital element propagation, and uncertainty propagation in the circular restricted three-body problem.

In this work, we investigate trajectories that require thrust to maintain periodic structure in the circular restricted three-body problem (CR3BP). We produce bounds in position and velocity space for the energy-constrained reachable set of initial conditions. Our trajectories are energy-optimal and analyzed via linear analysis. We provide validation for our technique and analyze the cost of deviating in various directions to the reference. For our given reference, we find that it is relatively expensive to decrease perilune distance for orbits in the Earth-Moon system., Comment: Submitted to 2024 AAS/AIAA Astrodynamics Specialist Conference Proceedings

We present an experimental platform for linear-optical quantum information processing. Our setup utilizes multiphoton generation using a high-quality single-photon source, which is demultiplexed across multiple spatial channels, a custom-designed, programmable, low-loss photonic chip, and paired with high-efficiency single-photon detectors. We demonstrate the platform's capability in producing heralded arbitrary two-qubit dual-rail encoded states, a crucial building block for large-scale photonic quantum computers. The programmable chip was fully characterized through a calibration process that allowed us to create a numerical model accounting for fabrication imperfections and measurement errors. As a result, using on-chip quantum state tomography (QST), we achieved high-fidelity quantum state preparation, with a fidelity of 98.5\% specifically for the Bell state., Comment: 11 pages, 11 figures

Industrial control systems are becoming more distributed and interconnected to allow for interaction with modern computing infrastructures. Furthermore, the amount of data generated by these systems is increasing due to integration of more sensors and the need to increase the reliability of the system based on predictive data models. One challenge in accommodating this data and interconnectivity increase is the change of the architecture of these systems from monolithic to component based, distributed systems. Questions such as how to deploy and operate such distributed system with many sub-components arise. One approach is the use of kubernetes to orchestrate the different components as containers. The critical nature of the industrial control systems however often requires strict component isolation and network segmentation to satisfy security requirements. Cilium is a popular network overlay for kubernetes that enables definition of network policies between different components running as kubernetes pods. The network policies are crucial for maintaining the secure operation of the system, however analysis of deployed policies is often lacking. In this paper, we explore the use of a formal analysis of Cilium network policies using VDM-SL. We provide examples of Cilium policies, an approach how they could be formalised using VDM-SL and analyse several scenarios to validate the policies against a model of simple real-life system.

Graph-based machine learning models for materials properties show great potential to accelerate virtual high-throughput screening of large chemical spaces. However, in their simplest forms, graph-based models do not include any 3D information and are unable to distinguish stereoisomers such as those arising from different orderings of ligands around a metal center in coordination complexes. In this work we present a modification to revised autocorrelation descriptors, our molecular graph featurization method for machine learning various spin state dependent properties of octahedral transition metal complexes (TMCs). Inspired by analytical semi-empirical models for TMCs, the new modeling strategy is based on the many-body expansion (MBE) and allows one to tune the captured stereoisomer information by changing the truncation order of the MBE. We present the necessary modifications to include this approach in two commonly used machine learning methods, kernel ridge regression and feed-forward neural networks. On a test set composed of all possible isomers of binary transition metal complexes, the best MBE models achieve mean absolute errors of 2.75 kcal/mol on spin-splitting energies and 0.26 eV on frontier orbital energy gaps, a 30-40% reduction in error compared to models based on our previous approach. We also observe improved generalization to previously unseen ligands where the best-performing models exhibit mean absolute errors of 4.00 kcal/mol (i.e., a 0.73 kcal/mol reduction) on the spin-splitting energies and 0.53 eV (i.e., a 0.10 eV reduction) on the frontier orbital energy gaps. Because the new approach incorporates insights from electronic structure theory, such as ligand additivity relationships, these models exhibit systematic generalization from homoleptic to heteroleptic complexes, allowing for efficient screening of TMC search spaces.

Parametrized quantum circuits are essential components of variational quantum algorithms. Until now, optical implementations of these circuits have relied solely on adjustable linear optical units. In this study, we demonstrate that using programmable nonlinearities, rather than linear optics, offers a more efficient method for constructing quantum optical circuits -- especially quantum neural networks. This approach significantly reduces the number of adjustable parameters needed to achieve high-fidelity operation. Specifically, we explored a quantum optical neural network (QONN) architecture composed of meshes of two-mode interferometers programmable by adjustable Kerr-like nonlinearities. We assessed the capabilities of our quantum optical neural network architecture and compared its performance to previously studied architectures that use multimode linear optics units. Additionally, we suggest future research directions for improving programmable quantum optical circuits., Comment: 14 pages, 13 figures

The stable-regenerative multiple-stable model has been shown recently to have distinct candidate extremal index and extremal index. To understand further this rare phenomenon, two more results are established here for the double-stable model. The first is the convergence of point processes for the clusters of extremes, enhancing the previous result on the weak convergence of random sup-measures. Most interestingly, the second result reveals a new phase transition at the mesoscopic level when computing the asymptotic exceedance probability over a block, $\mathbb P(\max_{k=1,\dots,d_n} X_k>b_n)$, as $n\to\infty$. Here, the mesoscopic level is referred to the fact that the block size $d_n$ is allowed to grow at the rate $n^\rho$ with $\rho\in[0,1]$, while the threshold $b_n$ is such that $\mathbb P(X_1>b_n)\sim 1/n$. The recently discovered discrepancy between the candidate extremal index and the extremal index is shown to be just a reflection of this phase transition that is prohibited by the anticlustering condition., Comment: 38 pages; corrected a few typos and implemented some minor edits

A search for the $K^{+} \to \pi^{0}\pi^{0}\pi^{0}e^+\nu$ decay is performed by the OKA collaboration. The search is based on $3.65 \times 10^9 ~ K^+$ decays. No signal is observed. The upper limit set is $BR(K^{+} \to \pi^{0}\pi^{0}\pi^{0}e^+\nu) < 5.4\times 10^{-8} ~ 90\%$ CL, 65 times lower than the one currently listed by PDG.

Linear methods are ubiquitous for control and estimation problems. In this work, we present a number of tensor operator norms as a means to approximately bound the error associated with linear methods and determine the situations in which that maximum error is encountered. An emphasis is placed on induced norms that can be computed in terms of matrix or tensor eigenvalues associated with coefficient tensors from higher-order Taylor series. These operator norms can be used to understand the performance and range of applicability of an algorithm exploiting linear approximations in different sets of coordinates. We examine uses of tensor operator norms in the context of linear and higher-order rendezvous guidance, coordinate selection for a filtering measurement model, and to present a unified treatment of nonlinearity indices for dynamical systems. Tensor norm computations can offer insights into these problems in one to two orders of magnitude less time than similarly accurate sampling methods while providing more general understanding of the error performance of linear or higher-order approximations.

We report low-loss multiscan waveguides fabricated in fused silica using femtosecond laser writing technology. The multiscan principle allows to tailor the writing regime to excel at key features of any integrated photonic platform: coupling losses and propagation losses. We optimized the writing parameters for different sizes of square-shaped waveguides and reached the mode overlap value with a standard single-mode optical fiber of above 98.8\% and demonstrated very low coupling losses of 0.2 dB/facet on average. Propagation losses in the fabricated waveguides amounted to 0.07 dB/cm. We applied the developed recipe to the fabrication of a fiber-coupled 25-channel interferometer with total insertion losses below 1 dB. The findings of this work are of interest for broad range of applications and in particular for optical information processing and quantum photonics., Comment: 12 pages, 9 figures

In this paper we introduce Sampling with a Black Box, a generic technique for the design of parameterized approximation algorithms for vertex deletion problems (e.g., Vertex Cover, Feedback Vertex Set, etc.). The technique relies on two components: $\bullet$ A Sampling Step. A polynomial time randomized algorithm which given a graph $G$ returns a random vertex $v$ such that the optimum of $G\setminus \{v\}$ is smaller by $1$ than the optimum of $G$ with some prescribed probability $q$. We show such algorithms exists for multiple vertex deletion problems. $\bullet$ A Black Box algorithm which is either an exact parameterized algorithm or a polynomial time approximation algorithm. Our technique combines these two components together. The sampling step is applied iteratively to remove vertices from the input graph, and then the solution is extended using the black box algorithm. The process is repeated sufficiently many times so that the target approximation ratio is attained with a constant probability. The main novelty of our work lies in the analysis of the framework and the optimization of the parameters it uses. We use the technique to derive parameterized approximation algorithm for several vertex deletion problems, including Feedback Vertex Set, $d$-Hitting Set and $\ell$-Path Vertex Cover. In particular, for every approximation ratio $1<\beta<2$, we attain a parameterized $\beta$-approximation for Feedback Vertex Set which is faster than the parameterized $\beta$-approximation of [Jana, Lokshtanov, Mandal, Rai and Saurabh, MFCS 23']. Furthermore, our algorithms are always faster than the algorithms attained using Fidelity Preserving Transformations [Fellows, Kulik, Rosamond, and Shachnai, JCSS 18'].

We study the $d$-dimensional knapsack problem. We are given a set of items, each with a $d$-dimensional cost vector and a profit, along with a $d$-dimensional budget vector. The goal is to select a set of items that do not exceed the budget in all dimensions and maximize the total profit. A PTAS with running time $n^{\Theta(d/\varepsilon)}$ has long been known for this problem, where $\varepsilon$ is the error parameter and $n$ is the encoding size. Despite decades of active research, the best running time of a PTAS has remained $O(n^{\lceil d/\varepsilon \rceil - d})$. Unfortunately, existing lower bounds only cover the special case with two dimensions $d = 2$, and do not answer whether there is a $n^{o(d/\varepsilon)}$-time PTAS for larger values of $d$. The status of exact algorithms is similar: there is a simple $O(n \cdot W^d)$-time (exact) dynamic programming algorithm, where $W$ is the maximum budget, but there is no lower bound which explains the strong exponential dependence on $d$. In this work, we show that the running times of the best-known PTAS and exact algorithm cannot be improved up to a polylogarithmic factor assuming Gap-ETH. Our techniques are based on a robust reduction from 2-CSP, which embeds 2-CSP constraints into a desired number of dimensions, exhibiting tight trade-off between $d$ and $\varepsilon$ for most regimes of the parameters. Informally, we obtain the following main results for $d$-dimensional knapsack. No $n^{o(d/\varepsilon \cdot 1/(\log(d/\varepsilon))^2)}$-time $(1-\varepsilon)$-approximation for every $\varepsilon = O(1/\log d)$. No $(n+W)^{o(d/\log d)}$-time exact algorithm (assuming ETH). No $n^{o(\sqrt{d})}$-time $(1-\varepsilon)$-approximation for constant $\varepsilon$. $(d \cdot \log W)^{O(d^2)} + n^{O(1)}$-time $\Omega(1/\sqrt{d})$-approximation and a matching $n^{O(1)}$-time lower~bound.

In the Unsplittable Flow on a Path problem UFP, we are given a path graph with edge capacities and a collection of tasks. Each task is characterized by a demand, a profit, and a subpath. Our goal is to select a maximum profit subset of tasks such that the total demand of the selected tasks that use each edge $e$ is at most the capacity of $e$. Bag-UFP is the generalization of UFP where tasks are partitioned into bags, and we are allowed to select at most one task per bag. UFP admits a PTAS [Grandoni,M{\"o}mke,Wiese'22] but not an EPTAS [Wiese'17]. Bag-UFP is APX-hard [Spieksma'99] and the current best approximation is $O(\log n/\log\log n)$ [Grandoni,Ingala,Uniyal'15], where $n$ is the number of tasks. In this paper, we study the mentioned two problems when parameterized by the number $m$ of edges in the graph, with the goal of designing faster parameterized approximation algorithms. We present a parameterized EPTAS for Bag-UFP, and a substantially faster parameterized EPTAS for UFP (which is an FPTAS for $m=O(1)$). We also show that a parameterized FPTAS for UFP (hence for BagUFP) does not exist, therefore our results are qualitatively tight.

Transition states (TSs) are transient structures that are key in understanding reaction mechanisms and designing catalysts but challenging to be captured in experiments. Alternatively, many optimization algorithms have been developed to search for TSs computationally. Yet the cost of these algorithms driven by quantum chemistry methods (usually density functional theory) is still high, posing challenges for their applications in building large reaction networks for reaction exploration. Here we developed React-OT, an optimal transport approach for generating unique TS structures from reactants and products. React-OT generates highly accurate TS structures with a median structural root mean square deviation (RMSD) of 0.053{\AA} and median barrier height error of 1.06 kcal/mol requiring only 0.4 second per reaction. The RMSD and barrier height error is further improved by roughly 25\% through pretraining React-OT on a large reaction dataset obtained with a lower level of theory, GFN2-xTB. We envision that the remarkable accuracy and rapid inference of React-OT will be highly useful when integrated with the current high-throughput TS search workflow. This integration will facilitate the exploration of chemical reactions with unknown mechanisms.

Metal-organic frameworks (MOFs) are promising materials for gas sensing but are often limited to single-use detection. We demonstrate a hybridization strategy synergistically deploying conductive MOFs (cMOFs) and conductive polymers (cPs) as two complementary mixed ionic-electronic conductors in high-performing stand-alone chemiresistors. Our work presents significant improvement in i) sensor recovery kinetics, ii) cycling stability, and iii) dynamic range at room temperature. We demonstrate the effect of hybridization across well-studied cMOFs based on 2,3,6,7,10,11-hexahydroxytriphenylene (HHTP) and 2,3,6,7,10,11-hexaiminotripphenylene (HITP) ligands with varied metal nodes (Co, Cu, Ni). We conduct a comprehensive mechanistic study to relate energy band alignments at the heterojunctions between the MOFs and the polymer with sensing thermodynamics and binding kinetics. Our findings reveal that hole enrichment of the cMOF component upon hybridization leads to selective enhancement in desorption kinetics, enabling significantly improved sensor recovery at room temperature, and thus long-term response retention. This mechanism was further supported by density functional theory calculations on sorbate-analyte interactions. We also find that alloying cPs and cMOFs enables facile thin film co-processing and device integration, potentially unlocking the use of these hybrid conductors in diverse electronic applications.

Higher-order topological insulators (HOTIs) are unique materials hosting topologically protected states, whose dimensionality is at least by a factor of 2 lower than that of the bulk. Topological states in such insulators may be strongly confined in their corners that leads to considerable enhancement of nonlinear processes involving such states. However, all nonlinear HOTIs demonstrated so far were built on periodic bulk lattice materials. Here we demonstrate first \textit{nonlinear photonic} HOTI with the fractal origin. Despite their fractional effective dimensionality, the HOTIs constructed here on two different types of the Sierpi\'nski gasket waveguide arrays, may support topological corner states for unexpectedly wide range of coupling strengths, even in parameter regions where conventional HOTIs become trivial. We demonstrate thresholdless solitons bifurcating from corner states in nonlinear fractal HOTIs and show that their localization can be efficiently controlled by the input beam power. We observe sharp differences in nonlinear light localization on outer and multiple inner corners and edges representative for these fractal materials. Our findings not only represent a new paradigm for nonlinear topological insulators, but also open new avenues for potential applications of fractal materials to control the light flow., Comment: 10 pages, 5 figures

Broadband correlated photon pairs (biphotons) are valuable in quantum metrology, but current generation methods either involve complex nonlinear structures or lack sufficient bandwidth and brightness. In this work, we theoretically describe and experimentally demonstrate a novel technique for generation of a bright collinear biphoton field with a broad spectrum, achieved by using a tightly focused pump in a bulk nonlinear crystal. As the most straightforward application of the source, we employ Michelson interferometer-based quantum optical coherence tomography (QOCT). Utilizing the source enables the demonstration of record resolution and dispersion cancellation for this QOCT scheme., Comment: 7 pages, 4 figures

A space-filling curve (SFC) maps points in a multi-dimensional space to one-dimensional points by discretizing the multi-dimensional space into cells and imposing a linear order on the cells. This way, an SFC enables the indexing of multi-dimensional data using a one-dimensional index such as a B+-tree. Choosing an appropriate SFC is crucial, as different SFCs have different effects on query performance. Currently, there are two primary strategies: 1) deterministic schemes, which are computationally efficient but often yield suboptimal query performance, and 2) dynamic schemes, which consider a broad range of candidate SFCs based on cost functions but incur significant computational overhead. Despite these strategies, existing methods cannot efficiently measure the effectiveness of SFCs under heavy query workloads and numerous SFC options. To address this problem, we propose means of constant-time cost estimations that can enhance existing SFC selection algorithms, enabling them to learn more effective SFCs. Additionally, we propose an SFC learning method that leverages reinforcement learning and our cost estimation to choose an SFC pattern efficiently. Experimental studies offer evidence of the effectiveness and efficiency of the proposed means of cost estimation and SFC learning.

The $K^{+} \to \pi^{+}\pi^{0}\pi^{0}\gamma$ decay is observed by the OKA collaboration. The branching ratio is measured to be $(4.1 \pm 0.9(stat) \pm 0.4(syst))\times 10^{-6}$. The branching ratio and $\gamma$ energy spectrum are consistent with ChPT prediction., Comment: arXiv admin note: text overlap with arXiv:2310.16429

A high statistics data sample of the $K^{+}$ decays is recorded by the OKA collaboration. A missing mass analysis is performed to search for a light invisible pseudoscalar axion-like particle (ALP) $a$ in the decay $K^{+} \to \pi^{+} \pi^{0} a$. No signal is observed, the upper limits for the branching ratio of the decay are calculated. The $90\%$ confidence level upper limit is changing from $2.5\cdot10^{-6}$ to $2\cdot10^{-7}$ for the ALP mass from 0 to 200 MeV/$c^{2}$, except for the region of $\pi^{0}$ mass, where the upper limit is $4.4\cdot10^{-6}$., Comment: 6 pages, 6 figures

We carried out a sensitive survey of C$_2$ and C$_3$ using the EDIBLES data set. We also expanded our searches to C$_4$, C$_5$, and $^{13}$C$^{12}$C isotopologue in the most molecule-rich sightlines. We fit synthetic spectra generated following a physical excitation model to the C$_2$ (2-0) Phillips band to obtain the C$_2$ column density ($N$) as well as the kinetic temperature ($T_\textrm{kin}$) and number density ($n$) of the host cloud. The C$_3$ molecule was measured through its $\tilde{A} - \tilde{X}$ (000-000) electronic origin band system. We simulated the excitation of this band with a double-temperature Boltzmann distribution. We present the largest combined survey of C$_2$ and C$_3$ to date in which the individual transitions can be resolved. In total we detected C$_2$ in 51 velocity components along 40 sightlines, and C$_3$ in 31 velocity components along 27 sightlines. The two molecules are detected in the same velocity components. We find a very good correlation between $N$(C$_2$) and $N$(C$_3$) with Pearson $r = 0.93$ and an average $N$(C$_2$)/$N$(C$_3$) ratio of 15.5$\pm$1.4. A comparison with the behaviour of the C$_2$ DIBs shows that there are no clear differences among sightlines with and without detection of C$_2$ and C$_3$. This is in direct contrast to the better-studied non-C$_2$ DIBs who have reduced strengths in molecule-rich environments. We also identify for the first time the $Q$(2), $Q$(3), and $Q$(4) transitions of the $^{13}$C$^{12}$C (2-0) Phillips band in a stacked average spectrum, and estimate the isotopic ratio of carbon $^{12}$C/$^{13}$C as 79$\pm$8. Our search for the C$_4$ and C$_5$ optical bands was unsuccessful., Comment: 31 pages, 23 figures. To appear in A&A

We consider disjoint and sliding blocks estimators of cluster indices for multivariate, regularly varying time series in the Peak-over-Threshold framework. We aim to provide a complete description of the limiting behaviour of these estimators. This is achieved by a precise expansion for the difference between the sliding and the disjoint blocks statistics. The rates in the expansion stem from internal clusters and boundary clusters. To obtain these rates we need to extend the existing results on vague convergence of cluster measures. We reveal dichotomous behaviour between small blocks and large blocks scenario., Comment: 52 pages