Search

Let $(x_k)_{k=1}^n$ be positive elements in the noncommutative Lebesgue space $L_p(\mathcal{M})$, and let $(\mathcal{E}_k)_{k=1}^n$ be a sequence of conditional expectations with respect to an increasing subalgebras $(\mathcal{M}_n)_{k\geq1}$ of the finite von Neumann algebra $\mathcal{M}$. We establish the following sharp noncommutative dual Doob inequalities: \begin{equation*} \Big\| \sum_{k=1}^nx_k\Big\|_{L_p(\mathcal{M})}\leq \frac{1}{p} \Big\| \sum_{k=1}^n\mathcal{E}_k(x_k)\Big\|_{L_p(\mathcal{M})},\quad 0

Matching objects across partially overlapping camera views is crucial in multi-camera systems and requires a view-invariant feature extraction network. Training such a network with cycle-consistency circumvents the need for labor-intensive labeling. In this paper, we extend the mathematical formulation of cycle-consistency to handle partial overlap. We then introduce a pseudo-mask which directs the training loss to take partial overlap into account. We additionally present several new cycle variants that complement each other and present a time-divergent scene sampling scheme that improves the data input for this self-supervised setting. Cross-camera matching experiments on the challenging DIVOTrack dataset show the merits of our approach. Compared to the self-supervised state-of-the-art, we achieve a 4.3 percentage point higher F1 score with our combined contributions. Our improvements are robust to reduced overlap in the training data, with substantial improvements in challenging scenes that need to make few matches between many people. Self-supervised feature networks trained with our method are effective at matching objects in a range of multi-camera settings, providing opportunities for complex tasks like large-scale multi-camera scene understanding., Comment: Accepted to VISAPP 2025

Despite the success of metaheuristic algorithms in solving complex network optimization problems, they often struggle with adaptation, especially in dynamic or high-dimensional search spaces. Traditional approaches can become stuck in local optima, leading to inefficient exploration and suboptimal solutions. Most of the widely accepted advanced algorithms do well either on highly complex or smaller search spaces due to the lack of adaptation. To address these limitations, we present ELENA (Epigenetic Learning through Evolved Neural Adaptation), a new evolutionary framework that incorporates epigenetic mechanisms to enhance the adaptability of the core evolutionary approach. ELENA leverages compressed representation of learning parameters improved dynamically through epigenetic tags that serve as adaptive memory. Three epigenetic tags (mutation resistance, crossover affinity, and stability score) assist with guiding solution space search, facilitating a more intelligent hypothesis landscape exploration. To assess the framework performance, we conduct experiments on three critical network optimization problems: the Traveling Salesman Problem (TSP), the Vehicle Routing Problem (VRP), and the Maximum Clique Problem (MCP). Experiments indicate that ELENA achieves competitive results, often surpassing state-of-the-art methods on network optimization tasks., Comment: 15 pages, 6 figures, 4 tables, 2 algorithms

Let $G$ be a weighted graph embedded in a metric space $(M, d_M )$. The vertices of $G$ correspond to the points in $M$ , with the weight of each edge $uv$ being the distance $d_M (u, v)$ between their respective points in $M$ . The dilation (or stretch) of $G$ is defined as the minimum factor $t$ such that, for any pair of vertices $u, v$, the distance between $u$ and $v$-represented by the weight of a shortest $u$, $v$-path is at most $ t \cdot d_M (u, v)$. We study Dilation t-Augmentation, where the objective is, given a metric $M $, a graph $G$, and numerical values $k$ and $t$, to determine whether $G$ can be transformed into a graph with dilation $t$ by adding at most $k$ edges. Our primary focus is on the scenario where the metric $M$ is the shortest path metric of an unweighted graph $\Gamma$. Even in this specific case, Dilation $t$-Augmentation remains computationally challenging. In particular, the problem is W[2]-hard parameterized by $k$ when $\Gamma$ is a complete graph, already for $t=2$. Our main contribution lies in providing new insights into the impact of combinations of various parameters on the computational complexity of the problem. We establish the following. -- The parameterized dichotomy of the problem with respect to dilation $t$, when the graph $G$ is sparse: Parameterized by $k$, the problem is FPT for graphs excluding a biclique $K_{d,d}$ as a subgraph for $t\leq 2$ and the problem is W[1]-hard for $t\geq 3$ even if $G$ is a forest consisting of disjoint stars. -- The problem is FPT parameterized by the combined parameter $k+t+\Delta$, where $\Delta$ is the maximum degree of the graph $G$ or $\Gamma$., Comment: To appear in STACS 2025

Single-molecule technology stands as a powerful tool, enabling the characterization of intricate structural and dynamic information that would otherwise remain concealed within the averaged behaviors of numerous molecules. This technology finds extensive application across diverse fields including physics, chemistry, biology, and medicine. Quantum sensing, particularly leveraging nitrogen-vacancy (NV) centers within diamond structures, presents a promising avenue for single-molecule magnetic resonance, offering prospects for sensing and imaging technology at the single-molecule level. Notably, while significant strides have been made in single-molecule scale magnetic resonance using NV centers over the past two decades, current approaches still exhibit limitations in magnetic sensitivity, spectral resolution, and spatial resolution. Particularly, the full reconstruction of three-dimensional positions of nuclear spins within single molecules remains an unattained goal. This review provides a comprehensive overview of the current state-of-the-art in single-molecule scale magnetic resonance, encompassing an analysis of various relevant techniques involving NV centers. Additionally, it explores the optimization of technical parameters associated with these methods. This detailed analysis serves as a foundation for the development of new technologies and the exploration of potential applications., Comment: 68 pages, 46 figures, 7 figures

This paper is devoted to the variational inequality problems. We consider two classes of problems, the first is classical constrained variational inequality and the second is the same problem with functional (inequality type) constraints. To solve these problems, we propose mirror descent-type methods with a weighting scheme for the generated points in each iteration of the algorithms. This scheme assigns smaller weights to the initial points and larger weights to the most recent points, thus it improves the convergence rate of the proposed methods. For the variational inequality problem with functional constraints, the proposed method switches between adaptive and non-adaptive steps in the dependence on the values of the functional constraints at iterations. We analyze the proposed methods for the time-varying step sizes and prove the optimal convergence rate for variational inequality problems with bounded and monotone operators. The results of numerical experiments of the proposed methods for classical constrained variational inequality problems show a significant improvement over the modified projection method., Comment: arXiv admin note: text overlap with arXiv:2401.04754

Dwarf spheroidal galaxies (dSphs) are recognized as being highly dominated by Dark Matter (DM), making them excellent targets for testing DM models through astrophysical observations. One effective method involves estimating the coarse-grained phase-space density (PSD) of the galactic DM component. By comparing this PSD with that of DM particles produced in the early Universe, it is possible to establish lower bounds on the DM particle mass. These constraints are particularly relevant for models of warm DM, such as those involving sterile neutrinos. Utilizing the GravSphere code, we obtain a fit of the DM PSD based on the latest reliable stellar dynamics data for twenty of the darkest dSphs, refining earlier lower bounds on sterile neutrino masses in non-resonant production scenarios. Additionally, we introduce an alternative approach involving the Excess Mass Function (EMF), which yields even tighter constraints. Specifically, using the maximum PSD, we derive a lower bound of $m>1.02$ keV at 95% confidence level, while the EMF method provides a stronger limit of $m>1.98$ keV at 95% CL. Both methods are versatile and can be extended to more complex DM production mechanisms in the early Universe. For the first time, we also constrain parameters of models involving non-standard cosmologies during the epoch of neutrino production. Our analysis yields $m>2.54$ keV for models with kination domination and $m>4.71$ keV for scenarios with extremely low reheating temperature., Comment: 22 pages, 3 figures. Prepared for IJMPA Memorial Issue: V.A. Rubakov

The kernel of the natural projection of a graph product of groups onto their direct product is called the Cartesian subgroup. This construction generalises commutator subgroups of right-angled Coxeter and Artin groups. Using theory of polyhedral products, we give a lower and an upper bound on the number of relations in presentations of Cartesian groups and on their deficiency. The bounds are related to the fundamental groups of full subcomplexes in the clique complex, and the lower bound coincide with the upper bound if these fundamental groups are free or free abelian. Following Li Cai's approach, we also describe an algorithm that computes "small" presentations of Cartesian subgroups., Comment: 26 pages, 6 figures

We study the differential equations that follow from Yangian symmetry which was recently observed for a large class of conformal Feynman graphs, originating from integrable `fishnet' theories. We derive, for the first time, the explicit general form of these equations in the most useful conformal cross-ratio variables, valid for any spacetime dimension. This allows us to explore their properties in detail. In particular, we observe that for general Feynman graphs a large set of terms in the Yangian equations can be identified with famous GKZ (Gelfand-Kapranov-Zelevinsky) hypergeometric operators. We also show that for certain nontrivial graphs the relation with GKZ systems is exact, opening the way to using new powerful solution methods. As a side result, we also elucidate the constraints on the topology and parameter space of Feynman graphs stemming from Yangian invariance., Comment: 35 pages

We present an open-source tool for manipulating Boolean circuits. It implements efficient algorithms, both existing and novel, for a rich variety of frequently used circuit tasks such as satisfiability, synthesis, and minimization. We tested the tool on a wide range of practically relevant circuits (computing, in particular, symmetric and arithmetic functions) that have been optimized intensively by the community for the last three years. The tool helped us to win the IWLS 2024 Programming Contest. In 2023, it was Google DeepMind who took the first place in the competition. We were able to reduce the size of the best circuits from 2023 by 12\% on average, whereas for some individual circuits, our size reduction was as large as 83\%., Comment: To appear in AAAI 2025

A remarkable characteristic of quantum computing is the potential for reliable computation despite faulty qubits. This can be achieved through quantum error correction, which is typically implemented by repeatedly applying static syndrome checks, permitting correction of logical information. Recently, the development of time-dynamic approaches to error correction has uncovered new codes and new code implementations. In this work, we experimentally demonstrate three time-dynamic implementations of the surface code, each offering a unique solution to hardware design challenges and introducing flexibility in surface code realization. First, we embed the surface code on a hexagonal lattice, reducing the necessary couplings per qubit from four to three. Second, we walk a surface code, swapping the role of data and measure qubits each round, achieving error correction with built-in removal of accumulated non-computational errors. Finally, we realize the surface code using iSWAP gates instead of the traditional CNOT, extending the set of viable gates for error correction without additional overhead. We measure the error suppression factor when scaling from distance-3 to distance-5 codes of $\Lambda_{35,\text{hex}} = 2.15(2)$, $\Lambda_{35,\text{walk}} = 1.69(6)$, and $\Lambda_{35,\text{iSWAP}} = 1.56(2)$, achieving state-of-the-art error suppression for each. With detailed error budgeting, we explore their performance trade-offs and implications for hardware design. This work demonstrates that dynamic circuit approaches satisfy the demands for fault-tolerance and opens new alternative avenues for scalable hardware design., Comment: 11 pages, 5 figures, Supplementary Information

Quantum error correction is essential for bridging the gap between the error rates of physical devices and the extremely low logical error rates required for quantum algorithms. Recent error-correction demonstrations on superconducting processors have focused primarily on the surface code, which offers a high error threshold but poses limitations for logical operations. In contrast, the color code enables much more efficient logic, although it requires more complex stabilizer measurements and decoding techniques. Measuring these stabilizers in planar architectures such as superconducting qubits is challenging, and so far, realizations of color codes have not addressed performance scaling with code size on any platform. Here, we present a comprehensive demonstration of the color code on a superconducting processor, achieving logical error suppression and performing logical operations. Scaling the code distance from three to five suppresses logical errors by a factor of $\Lambda_{3/5}$ = 1.56(4). Simulations indicate this performance is below the threshold of the color code, and furthermore that the color code may be more efficient than the surface code with modest device improvements. Using logical randomized benchmarking, we find that transversal Clifford gates add an error of only 0.0027(3), which is substantially less than the error of an idling error correction cycle. We inject magic states, a key resource for universal computation, achieving fidelities exceeding 99% with post-selection (retaining about 75% of the data). Finally, we successfully teleport logical states between distance-three color codes using lattice surgery, with teleported state fidelities between 86.5(1)% and 90.7(1)%. This work establishes the color code as a compelling research direction to realize fault-tolerant quantum computation on superconducting processors in the near future.

We describe algebraic curves $ X : F(x, y) = 0 $ defined over $\overline{\mathbb{Q}}$ that satisfy the following property: there exist a number field $k$ and an infinite set $S \subset k$ such that, for every $y \in S$, the roots of the polynomial $F(x, y)$ belong to $k$.

High temperatures are typically thought to increase disorder. Here we examine this idea in Quantum Field Theory in 2+1 dimensions. For this sake we explore a novel class of tractable models, consisting of nearly-mean-field scalars interacting with critical scalars. We identify UV-complete, local, unitary models in this class and show that symmetry breaking $\mathbb{Z}_2 \to \emptyset$ occurs at any temperature in some regions of the phase diagram. This phenomenon, previously observed in models with fractional dimensions, or in the strict planar limits, or with non-local interactions, is now exhibited in a local, unitary 2+1 dimensional model with a finite number of fields., Comment: 8 pages, 1 figure

We study user history modeling via Transformer encoders in deep learning recommendation models (DLRM). Such architectures can significantly improve recommendation quality, but usually incur high latency cost necessitating infrastructure upgrades or very small Transformer models. An important part of user history modeling is early fusion of the candidate item and various methods have been studied. We revisit early fusion and compare concatenation of the candidate to each history item against appending it to the end of the list as a separate item. Using the latter method, allows us to reformulate the recently proposed amortized history inference algorithm M-FALCON \cite{zhai2024actions} for the case of DLRM models. We show via experimental results that appending with cross-attention performs on par with concatenation and that amortization significantly reduces inference costs. We conclude with results from deploying this model on the LinkedIn Feed and Ads surfaces, where amortization reduces latency by 30\% compared to non-amortized inference., Comment: 5 pages, 3 figures, WWW 2025

Capability evaluations play a critical role in ensuring the safe deployment of frontier AI systems, but this role may be undermined by intentional underperformance or ``sandbagging.'' We present a novel model-agnostic method for detecting sandbagging behavior using noise injection. Our approach is founded on the observation that introducing Gaussian noise into the weights of models either prompted or fine-tuned to sandbag can considerably improve their performance. We test this technique across a range of model sizes and multiple-choice question benchmarks (MMLU, AI2, WMDP). Our results demonstrate that noise injected sandbagging models show performance improvements compared to standard models. Leveraging this effect, we develop a classifier that consistently identifies sandbagging behavior. Our unsupervised technique can be immediately implemented by frontier labs or regulatory bodies with access to weights to improve the trustworthiness of capability evaluations., Comment: Published at NeurIPS 2024, SATA and SoLaR workshop, 6 pages, 4 figures, 1 table, code available at https://github.com/camtice/SandbagDetect

A thorough account of electromagnetic interactions of massive Dirac neutrinos as well as their spin-flavor state in the theoretical formulation of elastic neutrino-nucleon scattering is given. The formalism of neutrino charge, magnetic, electric, and anapole form factors defined as matrices in the mass basis is employed under the assumption of three-neutrino mixing. The flavor and spin change of neutrinos propagating from the source to the detector is taken into account in the form of a spin-flavor density matrix of the neutrino arriving at the detector. The potential effects of the neutrino charge radii, magnetic moments, and spin polarization in the neutrino-nucleon scattering experiments are outlined., Comment: 25 pages, 4 figures

One of the main applications of electromagnetic metasurfaces (MSs) is to tailor spatial field distributions. The radiation pattern of a given source can be desirably modified upon reflection on an MS having proper spatial modulation of its local macroscopic parameters. At the microscopic level, spatial modulation requires individually engineered meta-atoms at different points. In contrast, the present research demonstrates the opportunity for radiation pattern engineering in the reflection regime without using any spatial modulation. The principle consists in the deliberate tailoring of the surface impedance of an unmodulated but spatially dispersive (nonlocal) MS. A 2D synthesis problem with a magnetic line current source is solved analytically by finding a required form of the surface impedance as a function of the tangential wave vector in both visible and evanescent parts of the spatial spectrum. To prove the principle, three different pattern shapes are implemented via full-wave numerical simulations by tuning the spatial dispersion in a realistic mushroom-type high-impedance electromagnetic surface with loaded vias. This work extends the synthesis methods and the application area of spatially dispersive MSs, showing the latter as a promising platform for new types of antennas.

Notable progress has been made in generalist medical large language models across various healthcare areas. However, large-scale modeling of in-hospital time series data - such as vital signs, lab results, and treatments in critical care - remains underexplored. Existing datasets are relatively small, but combining them can enhance patient diversity and improve model robustness. To effectively utilize these combined datasets for large-scale modeling, it is essential to address the distribution shifts caused by varying treatment policies, necessitating the harmonization of treatment variables across the different datasets. This work aims to establish a foundation for training large-scale multi-variate time series models on critical care data and to provide a benchmark for machine learning models in transfer learning across hospitals to study and address distribution shift challenges. We introduce a harmonized dataset for sequence modeling and transfer learning research, representing the first large-scale collection to include core treatment variables. Future plans involve expanding this dataset to support further advancements in transfer learning and the development of scalable, generalizable models for critical healthcare applications., Comment: Accepted for Oral Presentation at AIM-FM Workshop at NeurIPS 2024

Let $R_{\lambda,j}$ be the $j$-th Bessel--Riesz transform, where $n\geq 1$, $\lambda>0$, and $j=1,\ldots,n+1$. In this article, we establish a Weyl type asymptotic for $[M_f,R_{\lambda,j}]$, the commutator of $R_{\lambda,j}$ with multiplication operator $M_f$, based on building a preliminary result that the endpoint weak Schatten norm of $[M_f,R_{\lambda,j}]$ can be characterised via homogeneous Sobolev norm $\dot{W}^{1,n+1}(\mathbb{R}_+^{n+1})$ of the symbol $f$. Specifically, the asymptotic coefficient is equivalent to $\|f\|_{\dot{W}^{1,n+1}(\mathbb{R}_+^{n+1})}.$ Our main strategy is to relate Bessel--Riesz commutator to classical Riesz commutator via Schur multipliers, and then to establish the boundedness of Schur multipliers., Comment: 37 pages

We show that for every first-order logic (FO) formula $\varphi$, and every graph class $\mathcal{G}$ of bounded expansion, there exists a distributed (deterministic) algorithm that, for every $n$-node graph $G\in\mathcal{G}$ of diameter $D$, decides whether $G\models \varphi$ in $O(D+\log n)$ rounds under the standard CONGEST model. Graphs of bounded expansion encompass many classes of sparse graphs such as planar graphs, bounded-treedepth graphs, bounded-treewidth graphs, bounded-degree graphs, and graphs excluding a fixed graph $H$ as a minor or topological minor. Note that our algorithm is optimal up to a logarithmic additional term, as even a simple FO formula such as "there are two vertices of degree 3" already on trees requires $\Omega(D)$ rounds in CONGEST. Our result extends to solving optimization problems expressed in FO (e.g., $k$-vertex cover of minimum weight), as well as to counting the number of solutions of a problem expressible in a fragment of FO (e.g., counting triangles), still running in $O(D+\log n)$ rounds under the CONGEST model. This exemplifies the contrast between sparse graphs and general graphs as far as CONGEST algorithms are concerned. For instance, Drucker, Kuhn, and Oshman [PODC 2014] showed that the problem of deciding whether a general graph contains a 4-cycle requires $\Theta(\sqrt{n}/\log n)$ rounds in CONGEST. For counting triangles, the best known algorithm of Chang, Pettie, and Zhang [SODA 2019] takes $\tilde{O}(\sqrt{n})$ rounds. Finally, our result extends to distributed certification. We show that, for every FO formula~$\varphi$, and every graph class of bounded expansion, there exists a certification scheme for $\varphi$ using certificates on $O(\log n)$ bits. This significantly generalizes the recent result of Feuilloley, Bousquet, and Pierron [PODC 2022], which held solely for graphs of bounded treedepth.

Van der Waals (vdW) materials are becoming increasingly popular in scientific and industrial applications because of their unique mixture of record electronic, optical, and mechanical properties. However, nanostructuring of vdW materials is still in its infancy and strongly depends on the specific vdW crystal. As a result, the universal self-assembled technology of vdW materials nanostructuring opens vast technological prospects. This work demonstrates an express and universal synthesis method of vdW nanoparticles with well-defined geometry using femtosecond laser ablation and fragmentation. The disarming simplicity of the technique allows us to create nanoparticles from over 50 vdW precursor materials covering transition metal chalcogenides, MXenes, and other vdW materials. Obtained nanoparticles manifest perfectly defined crystalline structures and diverse shapes, from nanospheres to nanocubes and nanotetrahedrons. Thus, our work provides a new paradigm for vdW nanostructuring with a vast potential of tunability for size, shape, and materials specific to the particular application., Comment: 24 pages, 6 figures

The parameterized analysis of graph modification problems represents the most extensively studied area within Parameterized Complexity. Given a graph $G$ and an integer $k\in\mathbb{N}$ as input, the goal is to determine whether we can perform at most $k$ operations on $G$ to transform it into a graph belonging to a specified graph class $\mathcal{F}$. Typical operations are combinatorial and include vertex deletions and edge deletions, insertions, and contractions. However, in many real-world scenarios, when the input graph is constrained to be a geometric intersection graph, the modification of the graph is influenced by changes in the geometric properties of the underlying objects themselves, rather than by combinatorial modifications. It raises the question of whether vertex deletions or adjacency modifications are necessarily the most appropriate modification operations for studying modifications of geometric graphs. We propose the study of the disk intersection graph modification through the scaling of disks. This operation is typical in the realm of topology control but has not yet been explored in the context of Parameterized Complexity. We design parameterized algorithms and kernels for modifying to the most basic graph classes: edgeless, connected, and acyclic. Our technical contributions encompass a novel combination of linear programming, branching, and kernelization techniques, along with a fresh application of bidimensionality theory to analyze the area covered by disks, which may have broader applicability., Comment: To appear in ITCS 2025

Let $G$ be a compact, connected metric graph and let $X\subseteq G$ be a subset. If $X$ is sufficiently dense in $G$, we show that the Gromov--Hausdorff distance matches the Hausdorff distance, namely $d_{GH}(G,X)=d_{H}(G,X)$. In a recent study, when the metric graph is the circle $G=S^1$ with circumference $2\pi$, the equality $d_{GH}(S^1,X)=d_{H}(S^1,X)$ was established whenever $d_{GH}(S^1,X)<\frac{\pi}{6}$. Our result for general metric graphs relaxes this hypothesis in the circle case to $d_{GH}(S^1,X)<\frac{\pi}{3}$, and furthermore, we give an example showing that the constant $\frac{\pi}{3}$ is the best possible. We lower bound the Gromov--Hausdorff distance $d_{GH}(G,X)$ by the Hausdorff distance $d_{H}(G,X)$ via a simple topological obstruction: showing a correspondence with too small distortion contradicts the connectedness of $G$. Moreover, for two sufficiently dense subsets $X,Y\subseteq G$, we provide new lower bounds on $d_{GH}(X,Y)$ in terms of the Hausdorff distance $d_{H}(X,Y)$, which is $O(n^2)$-time computable if the subsets have at most $n$ points.

We investigate the impact of radiative and atomic exchange corrections in the two-neutrino double-beta ($2\nu\beta\beta$)-decay of $^{100}$Mo. In the calculation of the exchange correction, the electron wave functions are obtained from a modified Dirac-Hartree-Fock-Slater self-consistent framework that ensures orthogonality between continuum and bound states. The atomic exchange correction causes a steep increase in the low-energy region of the single-electron spectrum, consistent with previous studies on $\beta$-decay, while the radiative correction primarily accounts for a 5\% increase in the decay rate of $^{100}$Mo. When combined, the radiative and exchange effects cause a leftward shift of approximately 10 keV in the maximum of the summed electron spectrum. This shift may impact current constraints on parameters governing potential new physics scenarios in $2\nu\beta\beta$-decay. The exchange and radiative corrections are introduced on top of our previous description of $2\nu\beta\beta$-decay, where we used a Taylor expansion for the lepton energy parameters within the nuclear matrix elements denominators. This approach results in multiple components for each observable, controlled by the measurable $\xi_{31}$ and $\xi_{51}$ parameters. We explore the effects of different $\xi_{31}$ and $\xi_{51}$ values, including their experimental measurements, on the total corrected spectra. These refined theoretical predictions can serve as precise inputs for double-beta decay experiments investigating standard and new physics scenarios within $2\nu\beta\beta$-decay., Comment: 12 pages, 5 figures

Decoherence is a major challenge for quantum technologies. A way to mitigate its negative impact is by employing quantum optimal control. The decoherence dynamics varies significantly based on the characteristics of the surrounding environment of qubits, consequently affecting the outcome of the control optimization. In this work, we investigate the dependence of the shape of a spin inversion control pulse on the correlation time of the environment noise. Furthermore, we analyze the effects of constraints and optimization options on the optimization outcome and identify a set of strategies that improve the optimization performance. Finally, we present an experimental realization of the numerically-optimized pulses validating the optimization feasibility. Our work serves as a generic yet essential guide to implementing optimal control in the presence of realistic noise, e.g., in nitrogen-vacancy centers in diamond., Comment: 20 pages, 9 figures

We analyze the real-time dynamics of the large $N$ vector model, focusing on heavy states with energies of the order $N$. In this regime, we demonstrate that interactions become sufficiently strong to produce non-zero condensate of the Hubbard-Stratonovich field $\sigma$, which, in turn, induces particle production. This process leads to a significant transformation of the initial state and potential thermalization. For homogeneous perturbations, our results show that the equations become integrable, yet can still lead to thermalization in the continuum limit. Furthermore, we calculate the energies of these heavy states and their contributions to the thermal free energy, thereby determining the free energy of the critical $O(N)$ model by operator counting., Comment: 6 pages, 2 figures

We present the results of Phase I of an ongoing review of Monte Carlo tools relevant for low-energy hadronic cross sections. This includes a detailed comparison of Monte Carlo codes for electron-positron scattering into a muon pair, pion pair, and electron pair, for scan and radiative-return experiments. After discussing the various approaches that are used and effects that are included, we show differential cross sections obtained with AfkQed, BabaYaga@NLO, KKMC, MCGPJ, McMule, Phokhara, and Sherpa, for scenarios that are inspired by experiments providing input for the dispersive evaluation of the hadronic vacuum polarisation., Comment: RadioMonteCarLow 2 Working Group report Phase I, 67 pages, 34 figures; references added and other minor modifications

From the viewpoint of $*$-homomorphism on $C^{*}$-algebras, we establish the principal symbol mapping for filtered manifolds which are locally isomorphic to stratified Lie groups. Let $\mathbb{G}$ be a stratified Lie group, and let $M$ be a filtered manifold with a $\mathbb{G}$-atlas and a smooth positive density $\nu$. For the $C^{*}$-algebra bundle $E_{hom}$ of $M$ constructed from quasi-Riesz transforms on $\mathbb{G}$, we show that there exists a surjective $*$-homomorphism $${\rm sym}_{M}:\Pi_{M}\to C_{b}(E_{hom})$$ such that $${\rm ker}({\rm sym}_{M})=\mathcal{K}(L_{2}(M,\nu))\subset \Pi_{M}$$ where the domain $\Pi_{M}\subset\mathcal{B}(L_{2}(M,\nu))$ is a $C^{*}$-algebra and $C_{b}(E_{hom})$ is the $C^{*}$-algebra of bounded continuous sections of $E_{hom}$. Especially, we do not make any assumptions on the lattice of the osculating group of $M$ or the assumption of compactness on manifolds in \cite{DAO3,DAO4}.

Two-dimensional (2D) superconductors that reside on substrates must be influenced by Rashba spin-orbit coupling (SOC). The intriguing effect of Rashba-type SOCs on iron-based superconductors (IBSs) has remained largely a mystery. In this work, we unveil modified Landau-level spectroscopy and the intricate band splitting of FeSe monolayers through the precision of scanning tunneling spectroscopy, which unequivocally demonstrates the presence of Rashba SOC. The discovery sheds light on a nonparabolic electron band at the X/Y point, displaying a distinctive Landau quantization behavior characterized by $E_n\propto(nB)^{4/3}$. The theoretical model aligns with our experimental insights, positing that the k$^4$-term of the electron band becomes predominant and profoundly reshapes the band structure. Our research underscores the pivotal role of the Rashba SOC effect on 2D superconductors and sets the stage to probe new quantum states in systems with remarkably low carrier concentrations., Comment: 21 pages, 5 figures

In his book "Metric structures for Riemannian and non-Riemannian spaces", Gromov defined two properties of Riemannian manifolds, ellipticity and quasiregular ellipticity, and suggested that there may be a connection between the two. Since then, groups of researchers working independently have proved strikingly similar results about these two concepts. We obtain new topological obstructions to the two properties: most notably, we show that closed manifolds of both types must have virtually abelian fundamental group. We also give the first examples of open manifolds which are elliptic but not quasireguarly elliptic and vice versa. Whether there is a direct connection between these properties -- and, in particular, whether they are equivalent for closed manifolds -- remains elusive., Comment: 25 pages, 2 figures. Minor additions and corrections in v2

Cycle packing is a fundamental problem in optimization, graph theory, and algorithms. Motivated by recent advancements in finding vertex-disjoint paths between a specified set of vertices that either minimize the total length of the paths [Bj\"orklund, Husfeldt, ICALP 2014; Mari, Mukherjee, Pilipczuk, and Sankowski, SODA 2024] or request the paths to be shortest [Lochet, SODA 2021], we consider the following cycle packing problems: Min-Sum Cycle Packing and Shortest Cycle Packing. In Min-Sum Cycle Packing, we try to find, in a weighted undirected graph, $k$ vertex-disjoint cycles of minimum total weight. Our first main result is an algorithm that, for any fixed $k$, solves the problem in polynomial time. We complement this result by establishing the W[1]-hardness of Min-Sum Cycle Packing parameterized by $k$. The same results hold for the version of the problem where the task is to find $k$ edge-disjoint cycles. Our second main result concerns Shortest Cycle Packing, which is a special case of Min-Sum Cycle Packing that asks to find a packing of $k$ shortest cycles in a graph. We prove this problem to be fixed-parameter tractable (FPT) when parameterized by $k$ on weighted planar graphs. We also obtain a polynomial kernel for the edge-disjoint variant of the problem on planar graphs. Deciding whether Min-Sum Cycle Packing is FPT on planar graphs and whether Shortest Cycle Packing is FPT on general graphs remain challenging open questions.

In the Hedge Cut problem, the edges of a graph are partitioned into groups called hedges, and the question is what is the minimum number of hedges to delete to disconnect the graph. Ghaffari, Karger, and Panigrahi [SODA 2017] showed that Hedge Cut can be solved in quasipolynomial-time, raising the hope for a polynomial time algorithm. Jaffke, Lima, Masar\'ik, Pilipczuk, and Souza [SODA 2023] complemented this result by showing that assuming the Exponential Time Hypothesis (ETH), no polynomial-time algorithm exists. In this paper, we show that Hedge Cut is fixed-parameter tractable parameterized by the solution size $\ell$ by providing an algorithm with running time $\binom{O(\log n) + \ell}{\ell} \cdot m^{O(1)}$, which can be upper bounded by $c^{\ell} \cdot (n+m)^{O(1)}$ for any constant $c>1$. This running time captures at the same time the fact that the problem is quasipolynomial-time solvable, and that it is fixed-parameter tractable parameterized by $\ell$. We further generalize this algorithm to an algorithm with running time $\binom{O(k \log n) + \ell}{\ell} \cdot n^{O(k)} \cdot m^{O(1)}$ for Hedge $k$-Cut., Comment: 12 pages, 1 figure, to appear in SODA 2025

We propose and demonstrate experimentally continuous phased dynamical decoupling (CPDD), where we apply a continuous field with discrete phase changes for quantum sensing and robust compensation of environmental and amplitude noise. CPDD does not use short pulses, making it particularly suitable for experiments with limited driving power or nuclear magnetic resonance at high magnetic fields. It requires control of the timing of the phase changes, offering much greater precision than the Rabi frequency control needed in standard continuous sensing schemes. We successfully apply our method to nanoscale nuclear magnetic resonance and combine it with quantum heterodyne detection, achieving $\mu$Hz uncertainty in the estimated signal frequency for a 120 s measurement. Our work expands significantly the applicability of dynamical decoupling and opens the door for a wide range of experiments, e.g., in Nitrogen-Vacancy centers, trapped ions or trapped atoms., Comment: The main text includes 4 figures, 6 pages. The supplemental material includes 6 more figures and provides more details on the theory, numerical simulation, as well as additional experimental results

One of the most challenging problems in the computational study of localization in quantum manybody systems is to capture the effects of rare events, which requires sampling over exponentially many disorder realizations. We implement an efficient procedure on a quantum processor, leveraging quantum parallelism, to efficiently sample over all disorder realizations. We observe localization without disorder in quantum many-body dynamics in one and two dimensions: perturbations do not diffuse even though both the generator of evolution and the initial states are fully translationally invariant. The disorder strength as well as its density can be readily tuned using the initial state. Furthermore, we demonstrate the versatility of our platform by measuring Renyi entropies. Our method could also be extended to higher moments of the physical observables and disorder learning.

We call a family of $s$ sets $\{F_1, \ldots, F_s\}$ a \textit{sunflower with $s$ petals} if, for any distinct $i, j \in [s]$, one has $F_i \cap F_j = \cap_{u = 1}^s F_u$. The set $C = \cap_{u = 1}^s F_u$ is called the {\it core} of the sunflower. It is a classical result of Erd\H os and Rado that there is a function $\phi(s,k)$ such that any family of $k$-element sets contains a sunflower with $s$ petals. In 1977, Duke and Erd\H os asked for the size of the largest family $\ff\subset{[n]\choose k}$ that contains no sunflower with $s$ petals and core of size $t-1$. In 1987, Frankl and F\" uredi asymptotically solved this problem for $k\ge 2t+1$ and $n>n_0(s,k)$. This paper is one of the pinnacles of the so-called Delta-system method. In this paper, we extend the result of Frankl and F\"uredi to a much broader range of parameters: $n>f_0(s,t) k$ with $f_0(s,t)$ polynomial in $s$ and $t$. We also extend this result to other domains, such as $[n]^k$ and ${n\choose k/w}^w$ and obtain even stronger and more general results for forbidden sunflowers with core at most $t-1$ (including results for families of permutations and subfamilies of the $k$-th layer in a simplicial complex). The methods of the paper, among other things, combine the spread approximation technique, introduced by Zakharov and the first author, with the Delta-system approach of Frankl and F\"uredi and the hypercontractivity approach for global functions, developed by Keller, Lifshitz and coauthors. Previous works in extremal set theory relied on at most one of these methods. Creating such a unified approach was one of the goals for the paper.

Despite an artificial intelligence-assisted modeling of disordered crystals is a widely used and well-tried method of new materials design, the issues of its robustness, reliability, and stability are still not resolved and even not discussed enough. To highlight it, in this work we composed a series of nested intermetallic approximants of quasicrystals datasets and trained various machine learning models on them correspondingly. Our qualitative and, what is more important, quantitative assessment of the difference in the predictions clearly shows that different reasonable changes in the training sample can lead to the completely different set of the predicted potentially new materials. We also showed the advantage of pre-training and proposed a simple yet effective trick of sequential training to increase stability.

For many graph-related problems, it can be essential to have a set of structurally diverse graphs. For instance, such graphs can be used for testing graph algorithms or their neural approximations. However, to the best of our knowledge, the problem of generating structurally diverse graphs has not been explored in the literature. In this paper, we fill this gap. First, we discuss how to define diversity for a set of graphs, why this task is non-trivial, and how one can choose a proper diversity measure. Then, for a given diversity measure, we propose and compare several algorithms optimizing it: we consider approaches based on standard random graph models, local graph optimization, genetic algorithms, and neural generative models. We show that it is possible to significantly improve diversity over basic random graph generators. Additionally, our analysis of generated graphs allows us to better understand the properties of graph distances: depending on which diversity measure is used for optimization, the obtained graphs may possess very different structural properties which gives a better understanding of the graph distance underlying the diversity measure.

We give new formulas for reconstructions from band-limited Hankel transform of integer or half-integer order. Our formulas rely on the PSWF-Radon approach to super-resolution in multidimensional Fourier analysis. This approach consists of combining the theory of classical one-dimensional prolate spheroidal wave functions with the Radon transform theory. We also use the relation between Fourier and Hankel transforms and Cormack-type inversion of the Radon transform. Finally, we investigate numerically the capabilities of our approach to super-resolution for band-limited Hankel inversion in relation to varying levels of noise.

Lattice gauge theories (LGTs) can be employed to understand a wide range of phenomena, from elementary particle scattering in high-energy physics to effective descriptions of many-body interactions in materials. Studying dynamical properties of emergent phases can be challenging as it requires solving many-body problems that are generally beyond perturbative limits. We investigate the dynamics of local excitations in a $\mathbb{Z}_2$ LGT using a two-dimensional lattice of superconducting qubits. We first construct a simple variational circuit which prepares low-energy states that have a large overlap with the ground state; then we create particles with local gates and simulate their quantum dynamics via a discretized time evolution. As the effective magnetic field is increased, our measurements show signatures of transitioning from deconfined to confined dynamics. For confined excitations, the magnetic field induces a tension in the string connecting them. Our method allows us to experimentally image string dynamics in a (2+1)D LGT from which we uncover two distinct regimes inside the confining phase: for weak confinement the string fluctuates strongly in the transverse direction, while for strong confinement transverse fluctuations are effectively frozen. In addition, we demonstrate a resonance condition at which dynamical string breaking is facilitated. Our LGT implementation on a quantum processor presents a novel set of techniques for investigating emergent particle and string dynamics.

Let $\mathcal{M}$ be a semifinite von Neumann algebra and let $E$ be a symmetric function space on $(0,\infty)$. Denote by $E(\mathcal{M})$ the non-commutative symmetric space of measurable operators affiliated with $\mathcal{M}$ and associated with $E.$ Suppose $n\in \mathbb{N}$ and $E\cap L_{\infty}\not\subset L_{n,1}$, where $L_{n,1}$ is the Lorentz function space with the fundamental function $\varphi(t)=t^{1/n}$. We prove that for every $\varepsilon>0$ and every commuting self-adjoint $n$-tuple $(\alpha(j))_{j=1}^n,$ where $\alpha(j)$ is affiliated with $\mathcal{M}$ for each $1\leq j\leq n,$ there exists a commuting $n$-tuple $(\delta(j))_{j=1}^n$ of diagonal operators affiliated with $\mathcal{M}$ such that $\max\{\|\alpha(j)-\delta(j)\|_{E(\mathcal{M})},\|\alpha(j)-\delta(j)\|_{\infty}\}<\varepsilon$ for each $1\le j\le n$. In the special case when $\mathcal{M}=B(H)$, our results yield the classical Kuroda and Bercovici-Voiculescu theorems.

Variational Quantum Imaginary Time Evolution (VQITE) is a leading technique for ground state preparation on quantum computers. A significant computational challenge of VQITE is the determination of the quantum geometric tensor. We show that requiring the imaginary-time evolution to be correct only when projected onto a chosen set of operators allows to achieve a twofold reduction in circuit depth by bypassing fidelity estimations, and reduces measurement complexity from quadratic to linear in the number of parameters. We demonstrate by a simulation of the transverse-field Ising model that our algorithm achieves a several orders of magnitude improvement in the number of measurements required for the same accuracy.

We establish the phase diagram of the Hubbard model on a cubic lattice for a wide range of temperatures, dopings and interaction strengths, considering both commensurate and incommensurate magnetic orders. We use the dynamical mean-field theory together with an efficient method to compute the free energy which enable the determination of the correct ordering vectors. Besides an antiferromagnetic state close to half-filling, we identify a number of different magnetic spiral phases with ordering vectors $(q,\pi,\pi)$, $(q,q,\pi)$ and $(q,q,q)$ as well as a region with close competition between them, hinting at spatial phase separation or at the onset of a stripe phase. Additionally, we extensively study several thermodynamic properties with direct relevance to cold-atom experiments: the entropy, energy and double-occupancy.

The ability to process and store information on surrounding nuclear spins is a major requirement for group-IV color center-based repeater nodes. We demonstrate coherent control of a ${}^{13}$C nuclear spin strongly coupled to a negatively charged germanium-vacancy center in diamond with coherence times beyond 2.5s at mK temperatures, which is the longest reported for group-IV defects. Detailed analysis allows us to model the system's dynamics, extract the coupling parameters, and characterize noise. We estimate an achievable memory time of 18.1s with heating limitations considered, paving the way to successful applications as a quantum repeater node.

The present bias is a well-documented behavioral trait that significantly influences human decision-making, with present-biased agents often prioritizing immediate rewards over long-term benefits, leading to suboptimal outcomes in various real-world scenarios. Kleinberg and Oren (2014) proposed a popular graph-theoretical model of inconsistent planning to capture the behavior of present-biased agents. In this model, a multi-step project is represented by a weighted directed acyclic task graph, where the agent traverses the graph based on present-biased preferences. We use the model of Kleinberg and Oren to address the principal-agent problem, where a principal, fully aware of the agent's present bias, aims to modify an existing project by adding or deleting tasks. The challenge is to create a modified project that satisfies two somewhat contradictory conditions. On one hand, the present-biased agent should select specific tasks deemed important by the principal. On the other hand, if the anticipated costs in the modified project become too high for the agent, there is a risk of the agent abandoning the entire project, which is not in the principal's interest. To tackle this issue, we leverage the tools of parameterized complexity to investigate whether the principal's strategy can be efficiently identified. We provide algorithms and complexity bounds for this problem., Comment: Accepted at ECAI 2024

In Two-Sets Cut-Uncut, we are given an undirected graph $G=(V,E)$ and two terminal sets $S$ and $T$. The task is to find a minimum cut $C$ in $G$ (if there is any) separating $S$ from $T$ under the following ``uncut'' condition. In the graph $(V,E \setminus C)$, the terminals in each terminal set remain in the same connected component. In spite of the superficial similarity to the classic problem Minimum $s$-$t$-Cut, Two-Sets Cut-Uncut is computationally challenging. In particular, even deciding whether such a cut of any size exists, is already NP-complete. We initiate a systematic study of Two-Sets Cut-Uncut within the context of parameterized complexity. By leveraging known relations between many well-studied graph parameters, we characterize the structural properties of input graphs that allow for polynomial kernels, fixed-parameter tractability (FPT), and slicewise polynomial algorithms (XP). Our main contribution is the near-complete establishment of the complexity of these algorithmic properties within the described hierarchy of graph parameters. On a technical level, our main results are fixed-parameter tractability for the (vertex-deletion) distance to cographs and an OR-cross composition excluding polynomial kernels for the vertex cover number of the input graph (under the standard complexity assumption NP is not contained in coNP/poly).

Quantum error correction provides a path to reach practical quantum computing by combining multiple physical qubits into a logical qubit, where the logical error rate is suppressed exponentially as more qubits are added. However, this exponential suppression only occurs if the physical error rate is below a critical threshold. In this work, we present two surface code memories operating below this threshold: a distance-7 code and a distance-5 code integrated with a real-time decoder. The logical error rate of our larger quantum memory is suppressed by a factor of $\Lambda$ = 2.14 $\pm$ 0.02 when increasing the code distance by two, culminating in a 101-qubit distance-7 code with 0.143% $\pm$ 0.003% error per cycle of error correction. This logical memory is also beyond break-even, exceeding its best physical qubit's lifetime by a factor of 2.4 $\pm$ 0.3. We maintain below-threshold performance when decoding in real time, achieving an average decoder latency of 63 $\mu$s at distance-5 up to a million cycles, with a cycle time of 1.1 $\mu$s. To probe the limits of our error-correction performance, we run repetition codes up to distance-29 and find that logical performance is limited by rare correlated error events occurring approximately once every hour, or 3 $\times$ 10$^9$ cycles. Our results present device performance that, if scaled, could realize the operational requirements of large scale fault-tolerant quantum algorithms., Comment: 10 pages, 4 figures, Supplementary Information

Let $E(\mathbb{T}^{d}_{\theta}),F(\mathbb{T}^{d}_{\theta})$ be two symmetric operator spaces on noncommutative torus $\mathbb{T}^{d}_{\theta}$ corresponding to symmetric function spaces $E,F$ on $(0,1)$. We obtain the Gagliardo--Nirenberg interpolation inequality with respect to $\mathbb{T}^{d}_{\theta}$: if $G=E^{1-\frac{l}{k}}F^{\frac{l}{k}}$ with $ 0\leq l\leq k$ and if the Ces\`{a}ro operator is bounded on $E$ and $F$, then \begin{align*} \|\nabla^lx\|_{G(\mathbb{T}^{d}_{\theta})}\leq 2^{3\cdot 2^{k-2}-2}(k+1)^d\|C\|_{E\to E}^{1-\frac{l}{k}}\|C\|_{F\to F}^{\frac{l}{k}}\|x\|_{E(\mathbb{T}^{d}_{\theta})}^{1-\frac{l}{k}}\|\nabla^kx\|_{F(\mathbb{T}^{d}_{\theta})}^{\frac{l}{k}},\; x\in W^{k,1}(\mathbb{T}^{d}_{\theta}), \end{align*} where $W^{k,1}(\mathbb{T}^{d}_{\theta})$ is the Sobolev space on $\mathbb{T}^{d}_{\theta}$ of order $k\in\mathbb{N}$. Our method is different from the previous settings, which is of interest in its own right.

With each holomorphic map $f: R \rightarrow \mathbb C\mathbb P^1$ between compact Riemann surfaces one can associate a combinatorial datum consisting of the genus $g$ of $R$, the degree $n$ of $f$, the number $q$ of branching points of $f$, and the $q$ partitions of $n$ given by the local degrees of $f$ at the preimages of the branching points. These quantities are related by the Riemann-Hurwitz formula, and the Hurwitz existence problem asks whether a combinatorial datum that fits this formula actually corresponds to some $f$. In this paper, using results and techniques related to fiber products of holomorphic maps between compact Riemann surfaces, we prove a number of results that enable us to uniformly explain the non-realizability of many previously known non-realizable branch data, and to construct a large amount of new such data. We also deduce from our results the theorem of Halphen, proven in 1880, concerning polynomial solutions of the equation $A(z)^a+B(z)^b=C(z)^c$, where $a,b,c$ are integers greater than one., Comment: 27 pages

Using trial wavefunctions prepared on quantum devices to reduce the bias of auxiliary-field quantum Monte Carlo (QC-AFQMC) has established itself as a promising hybrid approach to the simulation of strongly correlated many body systems. Here, we further reduce the required quantum resources by decomposing the trial wavefunction into classical and quantum parts, respectively treated by classical and quantum devices, within the contextual subspace projection formalism. Importantly, we show that our algorithm is compatible with the recently developed matchgate shadow protocol for efficient overlap calculation in QC-AFQMC. Investigating the nitrogen dimer and the reductive decomposition of ethylene carbonate in lithium-based batteries, we observe that our method outperforms a number of established algorithm for ground state energy computations, while reaching chemical accuracy with less than half of the original number of qubits., Comment: 16 pages, 7 figures