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Density Functional Tight-Binding (DFTB), an approximative approach derived from Density Functional Theory (DFT), has the potential to pave the way for simulations of large periodic or non-periodic systems. We have specifically tailored DFTB parameters to enhance the accuracy of electronic band gap calculations in both 3D and 2D lead-iodide perovskites, at a significantly reduced computational cost relative to state-of-the-art ab initio calculations. Our electronic DFTB parameters allow computing not only the band gap but also effective masses of perovskite materials with reasonable accuracy compared to existing experimental data and state-of-the-art DFT calculations. The electronic band structures of vacancy-ordered and, lead- and iodide- deficient perovskites are also explored. Additionally, we demonstrate the efficiency of DFTB in computing electronic band alignments in perovskite heterostructures. The DFTB-based approach is anticipated to be beneficial for studying large-scale systems such as heterostructures and nanocrystals., Comment: 44 pages, 9 figures

This paper addresses the problem of long-context linear system identification, where the state $x_t$ of a dynamical system at time $t$ depends linearly on previous states $x_s$ over a fixed context window of length $p$. We establish a sample complexity bound that matches the i.i.d. parametric rate up to logarithmic factors for a broad class of systems, extending previous works that considered only first-order dependencies. Our findings reveal a learning-without-mixing phenomenon, indicating that learning long-context linear autoregressive models is not hindered by slow mixing properties potentially associated with extended context windows. Additionally, we extend these results to (i) shared low-rank representations, where rank-regularized estimators improve rates with respect to dimensionality, and (ii) misspecified context lengths in strictly stable systems, where shorter contexts offer statistical advantages., Comment: 30 pages, 4 figures

Quantitative Relative Judgment Aggregation (QRJA) is a new research topic in (computational) social choice. In the QRJA model, agents provide judgments on the relative quality of different candidates, and the goal is to aggregate these judgments across all agents. In this work, our main conceptual contribution is to explore the interplay between QRJA in a social choice context and its application to ranking prediction. We observe that in QRJA, judges do not have to be people with subjective opinions; for example, a race can be viewed as a "judgment" on the contestants' relative abilities. This allows us to aggregate results from multiple races to evaluate the contestants' true qualities. At a technical level, we introduce new aggregation rules for QRJA and study their structural and computational properties. We evaluate the proposed methods on data from various real races and show that QRJA-based methods offer effective and interpretable ranking predictions., Comment: 25 pages, 11 figures, neurips 2024

With the rapid advancement of Natural Language Processing in recent years, numerous studies have shown that generic summaries generated by Large Language Models (LLMs) can sometimes surpass those annotated by experts, such as journalists, according to human evaluations. However, there is limited research on whether these generic summaries meet the individual needs of ordinary people. The biggest obstacle is the lack of human-annotated datasets from the general public. Existing work on personalized summarization often relies on pseudo datasets created from generic summarization datasets or controllable tasks that focus on specific named entities or other aspects, such as the length and specificity of generated summaries, collected from hypothetical tasks without the annotators' initiative. To bridge this gap, we propose a high-quality, personalized, manually annotated abstractive summarization dataset called PersonalSum. This dataset is the first to investigate whether the focus of public readers differs from the generic summaries generated by LLMs. It includes user profiles, personalized summaries accompanied by source sentences from given articles, and machine-generated generic summaries along with their sources. We investigate several personal signals - entities/topics, plot, and structure of articles - that may affect the generation of personalized summaries using LLMs in a few-shot in-context learning scenario. Our preliminary results and analysis indicate that entities/topics are merely one of the key factors that impact the diverse preferences of users, and personalized summarization remains a significant challenge for existing LLMs., Comment: Accepted at NeurIPS 2024 Track on Datasets and Benchmarks. Code available at https://github.com/SmartmediaAI/PersonalSum

We consider the problem of approximate counting of triangles and longer fixed length cycles in directed graphs. For triangles, T\v{e}tek [ICALP'22] gave an algorithm that returns a $(1 \pm \eps)$-approximation in $\tilde{O}(n^\omega/t^{\omega-2})$ time, where $t$ is the unknown number of triangles in the given $n$ node graph and $\omega<2.372$ is the matrix multiplication exponent. We obtain an improved algorithm whose running time is, within polylogarithmic factors the same as that for multiplying an $n\times n/t$ matrix by an $n/t \times n$ matrix. We then extend our framework to obtain the first nontrivial $(1 \pm \eps)$-approximation algorithms for the number of $h$-cycles in a graph, for any constant $h\geq 3$. Our running time is \[\tilde{O}(\mathsf{MM}(n,n/t^{1/(h-2)},n)), \textrm{the time to multiply } n\times \frac{n}{t^{1/(h-2)}} \textrm{ by } \frac{n}{t^{1/(h-2)}}\times n \textrm{ matrices}.\] Finally, we show that under popular fine-grained hypotheses, this running time is optimal., Comment: Appeared in proceedings of ICALP 2024

High-harmonic generation (HHG) is a nonlinear process in which a material sample is irradiated by intense laser pulses, causing the emission of high harmonics of the incident light. HHG has historically been explained by theories employing a classical electromagnetic field, successfully capturing its spectral and temporal characteristics. However, recent research indicates that quantum-optical effects naturally exist, or can be artificially induced, in HHG. Even though the fundamental equations of motion for quantum electrodynamics (QED) are well-known, a unifying framework for solving them to explore HHG is missing. So far, numerical solutions employed a wide range of basis-sets and untested approximations. Based on methods originally developed for cavity polaritonics, here we formulate a numerically accurate QED model consisting of a single active electron and a single quantized photon mode. Our framework can in principle be extended to higher electronic dimensions and multiple photon modes to be employed in ab initio codes. We employ it as a model of an atom interacting with a photon mode and predict a characteristic minimum structure in the HHG yield vs. phase-squeezing. We find that this phenomenon, which can be used for novel ultrafast quantum spectroscopies, is partially captured by a multi-trajectory Ehrenfest dynamics approach, with the exact minima position sensitive to the level of theory. On the one hand, this motivates using multi-trajectory approaches as an alternative for costly exact calculations. On the other hand, it suggests an inherent limitation of the multi-trajectory formalism, indicating the presence of entanglement. Our work creates a road-map for a universal formalism of QED-HHG that can be employed for benchmarking approximate theories, predicting novel phenomena for advancing quantum applications, and for the measurements of entanglement and entropy., Comment: 10 pages, 7 figures

In this paper, we explore accelerating Hamiltonian ground state energy calculation on NISQ devices. We suggest using search-based methods together with machine learning to accelerate quantum algorithms, exemplified in the Quantum Eigensolver use case. We trained two small models on classically mined data from systems with up to 16 qubits, using XGBoost's Python regressor. We evaluated our preliminary approach on 20-, 24- and 28-qubit systems by optimising the Eigensolver's hyperparameters. These models predict hyperparameter values, leading to a 0.13\%-0.15\% reduction in error when tested on 28-qubit systems. However, due to inconclusive results with 20- and 24-qubit systems, we suggest further examination of the training data based on Hamiltonian characteristics. In future work, we plan to train machine learning models to optimise other aspects or subroutines of quantum algorithm execution beyond its hyperparameters.

Limbless organisms of all sizes use undulating patterns of self-deformation to locomote. Geometric mechanics, which maps deformations to motions, provides a powerful framework to formalize and investigate the theoretical properties and limitations of such modes of locomotion. However, the inherent level of abstraction poses a challenge when bridging the gap between theory or simulations and laboratory experiments. We investigate the challenges of modeling motion trajectories of an undulating robotic locomotor by comparing experiments and simulations performed with a variational integrator. Despite the extensive simplifications that the model based on a geometric variation principle entails, the simulations show good agreement on average. Notably, our approach merely requires the knowledge of the \emph{dissipation metric} -- a Riemannian metric on the configuration space, which can in practice be approximated by means closely resembling \emph{resistive force theory}.

Ranking models play a crucial role in enhancing overall accuracy of text retrieval systems. These multi-stage systems typically utilize either dense embedding models or sparse lexical indices to retrieve relevant passages based on a given query, followed by ranking models that refine the ordering of the candidate passages by its relevance to the query. This paper benchmarks various publicly available ranking models and examines their impact on ranking accuracy. We focus on text retrieval for question-answering tasks, a common use case for Retrieval-Augmented Generation systems. Our evaluation benchmarks include models some of which are commercially viable for industrial applications. We introduce a state-of-the-art ranking model, NV-RerankQA-Mistral-4B-v3, which achieves a significant accuracy increase of ~14% compared to pipelines with other rerankers. We also provide an ablation study comparing the fine-tuning of ranking models with different sizes, losses and self-attention mechanisms. Finally, we discuss challenges of text retrieval pipelines with ranking models in real-world industry applications, in particular the trade-offs among model size, ranking accuracy and system requirements like indexing and serving latency / throughput., Comment: Accepted for the 1st Workshop on GenAI and RAG Systems for Enterprise @ CIKM 2024

A data-driven model (DDM) suitable for regional weather forecasting applications is presented. The model extends the Artificial Intelligence Forecasting System by introducing a stretched-grid architecture that dedicates higher resolution over a regional area of interest and maintains a lower resolution elsewhere on the globe. The model is based on graph neural networks, which naturally affords arbitrary multi-resolution grid configurations. The model is applied to short-range weather prediction for the Nordics, producing forecasts at 2.5 km spatial and 6 h temporal resolution. The model is pre-trained on 43 years of global ERA5 data at 31 km resolution and is further refined using 3.3 years of 2.5 km resolution operational analyses from the MetCoOp Ensemble Prediction System (MEPS). The performance of the model is evaluated using surface observations from measurement stations across Norway and is compared to short-range weather forecasts from MEPS. The DDM outperforms both the control run and the ensemble mean of MEPS for 2 m temperature. The model also produces competitive precipitation and wind speed forecasts, but is shown to underestimate extreme events.

We provide a fast distributed algorithm for detecting $h$-cycles in the \textsf{Congested Clique} model, whose running time decreases as the number of $h$-cycles in the graph increases. In undirected graphs, constant-round algorithms are known for cycles of even length. Our algorithm greatly improves upon the state of the art for odd values of $h$. Moreover, our running time applies also to directed graphs, in which case the improvement is for all values of $h$. Further, our techniques allow us to obtain a triangle detection algorithm in the quantum variant of this model, which is faster than prior work. A key technical contribution we develop to obtain our fast cycle detection algorithm is a new algorithm for computing the product of many pairs of small matrices in parallel, which may be of independent interest., Comment: 37 pages. To appear in proceedings of DISC 2024

Although the existence of dark matter has been widely acknowledged in the cosmology community, it is as yet unknown in nature, despite decades of research, which questions its very existence. This never-ending search for dark matter leads to consider alternatives. Since increasing the enclosed mass is the only way to explain the flat appearance of galaxies rotation curves in a Newtonian framework, the MOND theory proposed to modify Newton's dynamics when the acceleration is around or below a threshold value, a_0. Observed rotation curves, generally flat at large distances, are then usually well reproduced by MOND with a_0 ~ 1.2 10^{-10} m/s^2. However, the recent Gaia evidence of a decline in the Milky Way rotation curve is a distinct behavior. Therefore, we examine whether LCDM and MOND can accommodate the Gaia declining rotation curve of the Milky Way. We first depict a standard model to describe the Milky Way's baryonic components. Secondly, we show that a NFW model is able to fit the decline, assuming a scale radius R_s of the order of 4 kpc. In a third step, we show that the usual MOND paradigm is not able to reproduce the declining part for a standard baryonic model. Finally, we examine whether the MOND theory can accommodate the declining part of the rotation curve when relaxing the characteristics of the baryonic components. To do so we use a MCMC method on the characteristics of the stellar and the HI disk, including their mass. We found that the stellar disk should be massive, of the order of 10^{11} M_\odot. The HI disk mass is capped at nearly 1.8 10^{11} M_\odot but could also be negligible. Finally, a_0 is consistent with 0, with an upper limit of 0.53 10^{-10} m/s^{2} (95\%), a value much lower than the above mentioned value usually advocated to explain standard flat rotation curves in MOND theory., Comment: 6 pages, 5 figures, to be submitted to The Open Journal of Astrophysics

Text embedding models have been popular for information retrieval applications such as semantic search and Question-Answering systems based on Retrieval-Augmented Generation (RAG). Those models are typically Transformer models that are fine-tuned with contrastive learning objectives. Many papers introduced new embedding model architectures and training approaches, however, one of the key ingredients, the process of mining negative passages, remains poorly explored or described. One of the challenging aspects of fine-tuning embedding models is the selection of high quality hard-negative passages for contrastive learning. In this paper we propose a family of positive-aware mining methods that leverage the positive relevance score for more effective false negatives removal. We also provide a comprehensive ablation study on hard-negative mining methods over their configurations, exploring different teacher and base models. We demonstrate the efficacy of our proposed methods by introducing the NV-Retriever-v1 model, which scores 60.9 on MTEB Retrieval (BEIR) benchmark and 0.65 points higher than previous methods. The model placed 1st when it was published to MTEB Retrieval on July 07, 2024.

Metabolic models condense biochemical knowledge about organisms in a structured and standardised way. As large-scale network reconstructions are readily available for many organisms of interest, genome-scale models are being widely used among modellers and engineers. However, these large models can be difficult to analyse and visualise, and occasionally generate hard-to-interpret or even biologically unrealistic predictions. Out of the thousands of enzymatic reactions in a typical bacterial metabolism, only a few hundred comprise the metabolic pathways essential to produce energy carriers and biosynthetic precursors. These pathways carry relatively high flux, are central to maintaining and reproducing the cell, and provide precursors and energy to engineered metabolic pathways. Here, focusing on these central metabolic subsystems, we present a manually-curated medium-scale model of energy and biosynthesis metabolism for the well-studied prokaryote Escherichia coli K-12 MG1655. The model is a sub-network of the most recent genome-scale reconstruction, iML1515, and comes with an updated layer of database annotations, as well as a range of metabolic maps for visualisation. We enriched the stoichiometric network with extensive biological information and quantitative data, enhancing the scope and applicability of the model. In addition, here we assess the properties of this model in relation to its genome-scale parent and demonstrate the use of the network and supporting data in various scenarios, including enzyme-constrained flux balance analysis, elementary flux mode analysis, and thermodynamic analysis. Overall, we believe this model holds the potential to become a reference medium-scale metabolic model for E. coli., Comment: Minor stylistic changes. Extended discussion in Supplementary Information A.5

Dynamical symmetries of laser-dressed matter determine selection rules that determine its absorption spectrum. We explore selection rules for polarization-sensitive absorption in Floquet matter, using Floquet group theory in synthetic dimensions. We present comprehensive tables of selection rules that polarization-structured light impose on Floquet dark states and Floquet dark bands. Notably, our tables encompass nonlinear absorption, to all nonlinear orders, revealing that different nonlinear orders follow distinct polarization selection rules, potentially leading to polarization-tunable optical filters.

The Procrustes-Wasserstein problem consists in matching two high-dimensional point clouds in an unsupervised setting, and has many applications in natural language processing and computer vision. We consider a planted model with two datasets $X,Y$ that consist of $n$ datapoints in $\mathbb{R}^d$, where $Y$ is a noisy version of $X$, up to an orthogonal transformation and a relabeling of the data points. This setting is related to the graph alignment problem in geometric models. In this work, we focus on the euclidean transport cost between the point clouds as a measure of performance for the alignment. We first establish information-theoretic results, in the high ($d \gg \log n$) and low ($d \ll \log n$) dimensional regimes. We then study computational aspects and propose the Ping-Pong algorithm, alternatively estimating the orthogonal transformation and the relabeling, initialized via a Franke-Wolfe convex relaxation. We give sufficient conditions for the method to retrieve the planted signal after one single step. We provide experimental results to compare the proposed approach with the state-of-the-art method of Grave et al. (2019)., Comment: 28 pages, 1 figure. Comments are most welcome!

Predicting cancer dynamics under treatment is challenging due to high inter-patient heterogeneity, lack of predictive biomarkers, and sparse and noisy longitudinal data. Mathematical models can summarize cancer dynamics by a few interpretable parameters per patient. Machine learning methods can then be trained to predict the model parameters from baseline covariates, but do not account for uncertainty in the parameter estimates. Instead, hierarchical Bayesian modeling can model the relationship between baseline covariates to longitudinal measurements via mechanistic parameters while accounting for uncertainty in every part of the model. The mapping from baseline covariates to model parameters can be modeled in several ways. A linear mapping simplifies inference but fails to capture nonlinear covariate effects and scale poorly for interaction modeling when the number of covariates is large. In contrast, Bayesian neural networks can potentially discover interactions between covariates automatically, but at a substantial cost in computational complexity. In this work, we develop a hierarchical Bayesian model of subpopulation dynamics that uses baseline covariate information to predict cancer dynamics under treatment, inspired by cancer dynamics in multiple myeloma (MM), where serum M protein is a well-known proxy of tumor burden. As a working example, we apply the model to a simulated dataset and compare its ability to predict M protein trajectories to a model with linear covariate effects. Our results show that the Bayesian neural network covariate effect model predicts cancer dynamics more accurately than a linear covariate effect model when covariate interactions are present. The framework can also be applied to other types of cancer or other time series prediction problems that can be described with a parametric model., Comment: 22 pages, 10 figures

Conditional displacement with a qubit ancilla is a critical component in continuous-variable error correction protocols. We present the generalized conditional displacement operator, conditioned on a qudit ancilla, showing how it enhances error-correction with Gottesman-Kitaev-Preskill (GKP) codes and exploring potential implementations.

We consider a two-dimensional electron gas interacting with a quantized cavity mode. We find that the coupling between the electrons and the photons in the cavity enhances the superconducting gap. Crucially, all terms in the Peierls phase are kept, in contrast to more naive approaches, which may result in spurious superradiant phase transitions. We use a mean-field theory to show that the gap increases approximately linearly with the cavity coupling strength. The effect can be observed locally as an increase in the gap size via scanning tunneling microscopy (STM) measurements for a flake of a 2D material (or for a Moir\'e system where the enhancement is expected to be more pronounced due to a large lattice constant) interacting with a locally-structured electromagnetic field formed by split-ring resonators. Our results are also relevant for quantum optics setups with cold atoms interacting with the cavity mode, where the lattice geometry and system parameters can be tuned in a vast range., Comment: 5 pages, 2 figures

We show that when a honeycomb antiferromagnetic insulator (AFMI) is sandwiched between two transition metal dichalcogenide (TMD) monolayers in a commensurate way, magnons in the AFMI can mediate an interaction between electrons in the TMDs that gives rise to interlayer Cooper pairing. This interaction opens coexisting extended $s$-wave and chiral $p$-wave superconducting gaps in the energy spectrum of the coupled system, and the latter give rise to topological Majorana edge modes., Comment: 13 pages, including 5 pages supplemental material

Topological vortex textures in magnetic disks have garnered great attention due to their interesting physics and diverse applications. However, up to now, the vortex state has mainly been studied in microsize ferromagnetic disks, which have oscillation frequencies confined to the GHz range. Here, we propose an experimentally feasible ultrasmall and ultrafast vortex state in an antiferromagnetic nanodot surrounded by a heavy metal, which is further harnessed to construct a highly tunable vortex network. We theoretically demonstrate that, interestingly, the interfacial Dzyaloshinskii-Moriya interaction (iDMI) induced by the heavy metal at the boundary of the dot acts as an effective chemical potential for the vortices in the interior. Mimicking the creation of a superfluid vortex by rotation, we show that a magnetic vortex state can be stabilized by this iDMI. Subjecting the system to an electric current can trigger vortex oscillations via spin-transfer torque, which reside in the THz regime and can be further modulated by external magnetic fields. Furthermore, we show that coherent coupling between vortices in different nanodisks can be achieved via an antiferromagnetic link. Remarkably, this interaction depends on the vortex polarity and topological charge and is also exceptionally tunable through the vortex resonance frequency. This opens up the possibility for controllable interconnected networks of antiferromagnetic vortices. Our proposal therefore introduces a new avenue for developing high-density memory, ultrafast logic devices, and THz signal generators, which are ideal for compact integration into microchips., Comment: 11 pages including supplemental material; 4 figures

Layered halide perovskites have emerged as potential alternatives to three-dimensional halide perovskites due to their improved stability and larger material phase space, allowing fine-tuning of structural, electronic, and optical properties. However, their charge carrier mobilities are significantly smaller than that of three-dimensional halide perovskites, which has a considerable impact on their application in optoelectronic devices. Here, we employ state-of-the-art ab initio approaches to unveil the electron-phonon mechanisms responsible for the diminished transport properties of layered halide perovskites. Starting from a prototypical ABX$_{3}$ halide perovskite, we model the case of $n=1$ and $n=2$ layered structures and compare their electronic and transport properties to the three-dimensional reference. The electronic and phononic properties are investigated within density functional theory (DFT) and density functional perturbation theory (DFPT), while transport properties are obtained via the ab initio Boltzmann transport equation. The vibrational modes contributing to charge carrier scattering are investigated and associated with polar-phonon scattering mechanisms arising from the long-range Fr\"ohlich coupling and deformation potential scattering processes. Our investigation reveals that the lower mobilities in layered systems primarily originates from the increased electronic density of states at the vicinity of the band edges, while the electron-phonon coupling strength remains similar. Such increase is caused by the dimensionality reduction and the break in octahedra connectivity along the stacking direction. Our findings provide a fundamental understanding of the electron-phonon coupling mechanisms in layered perovskites and highlight the intrinsic limitations of the charge carrier transport in these materials.

Decentralized learning (DL) enables collaborative learning without a server and without training data leaving the users' devices. However, the models shared in DL can still be used to infer training data. Conventional defenses such as differential privacy and secure aggregation fall short in effectively safeguarding user privacy in DL, either sacrificing model utility or efficiency. We introduce Shatter, a novel DL approach in which nodes create virtual nodes (VNs) to disseminate chunks of their full model on their behalf. This enhances privacy by (i) preventing attackers from collecting full models from other nodes, and (ii) hiding the identity of the original node that produced a given model chunk. We theoretically prove the convergence of Shatter and provide a formal analysis demonstrating how Shatter reduces the efficacy of attacks compared to when exchanging full models between nodes. We evaluate the convergence and attack resilience of Shatter with existing DL algorithms, with heterogeneous datasets, and against three standard privacy attacks. Our evaluation shows that Shatter not only renders these privacy attacks infeasible when each node operates 16 VNs but also exhibits a positive impact on model utility compared to standard DL. In summary, Shatter enhances the privacy of DL while maintaining the utility and efficiency of the model., Comment: Accepted at PETS 2025

Lead halide perovskite quantum dots (QDs), the latest generation of colloidal QD family, exhibit outstanding optical properties which are now exploited as both classical and quantum light sources. Most of their rather exceptional properties are related to the peculiar exciton fine-structure of band-edge states which can support unique bright triplet excitons. The degeneracy of the bright triplet excitons is lifted with energetic splitting in the order of millielectronvolts, which can be resolved by the photoluminescence (PL) measurements of single QDs at cryogenic temperatures. Each bright exciton fine-structure-state (FSS) exhibits a dominantly linear polarization, in line with several theoretical models based on the sole crystal field, exchange interaction and shape anisotropy. Here, we show that in addition to a high degree of linear polarization, the individual exciton FSS can exhibit a non-negligible degree of circular polarization even without external magnetic fields by investigating the four Stokes parameters of the exciton fine-structure in individual CsPbBr3 QDs through Stokes polarimetric measurements. We observe a degree of circular polarization up to ~38%, which could not be detected by using the conventional polarimetric technique. In addition, we found a consistent transition from left- to right-hand circular polarization within the fine-structure triplet manifold, which was observed in magnetic field dependent experiments. Our optical investigation provides deeper insights into the nature of the exciton fine-structures and thereby drives the yet-incomplete understanding of the unique photophysical properties of this novel class of QDs, potentially opening new scenarios in chiral quantum optics.

We use strong-coupling Eliashberg theory to study the competition of separate superconducting orders at low temperatures. Specifically, we study magnon-mediated superconductivity in a trilayer heterostructure with a thin normal metal between two antiferromagnetic insulators. Spin-triplet $p$-wave, spin-triplet $f$-wave, and spin-singlet $d$-wave superconducting gaps have been predicted to occur close to the critical temperature for the superconducting instability. The gap symmetry with the largest critical temperature depends on parameters in the model. We confirm that the same gap symmetries appear at any temperature below the critical temperature. Furthermore, we show that the temperature can affect the competition between the different superconducting orders. In addition, we consider time-reversal-symmetry-breaking, complex linear combinations of candidate pairings, such as chiral $p$-, $f$-, and $d$-wave gaps, as well as $p_x+if_y$-wave gaps. We find indications that some of these time-reversal-symmetry-breaking, nodeless gaps offer a greater condensation energy than the time-reversal symmetric gaps. This indicates that superconducting states with spontaneously broken time-reversal symmetry and nontrivial topology may be preferred in this system., Comment: 12 pages, 7 figures, accepted in Physical Review B

We investigate the existence of a fundamental computation-information gap for the problem of clustering a mixture of isotropic Gaussian in the high-dimensional regime, where the ambient dimension $p$ is larger than the number $n$ of points. The existence of a computation-information gap in a specific Bayesian high-dimensional asymptotic regime has been conjectured by arXiv:1610.02918 based on the replica heuristic from statistical physics. We provide evidence of the existence of such a gap generically in the high-dimensional regime $p \geq n$, by (i) proving a non-asymptotic low-degree polynomials computational barrier for clustering in high-dimension, matching the performance of the best known polynomial time algorithms, and by (ii) establishing that the information barrier for clustering is smaller than the computational barrier, when the number $K$ of clusters is large enough. These results are in contrast with the (moderately) low-dimensional regime $n \geq poly(p, K)$, where there is no computation-information gap for clustering a mixture of isotropic Gaussian. In order to prove our low-degree computational barrier, we develop sophisticated combinatorial arguments to upper-bound the mixed moments of the signal under a Bernoulli Bayesian model., Comment: 53 pages

The amplituhedron is a mathematical object which was introduced to provide a geometric origin of scattering amplitudes in $\mathcal{N}=4$ super Yang Mills theory. It generalizes \emph{cyclic polytopes} and the \emph{positive Grassmannian}, and has a very rich combinatorics with connections to cluster algebras. In this article we provide a series of results about tiles and tilings of the $m=4$ amplituhedron. Firstly, we provide a full characterization of facets of BCFW tiles in terms of cluster variables for $\mbox{Gr}_{4,n}$. Secondly, we exhibit a tiling of the $m=4$ amplituhedron which involves a tile which does not come from the BCFW recurrence -- the \emph{spurion} tile, which also satisfies all cluster properties. Finally, strengthening the connection with cluster algebras, we show that each standard BCFW tile is the positive part of a cluster variety, which allows us to compute the canonical form of each such tile explicitly in terms of cluster variables for $\mbox{Gr}_{4,n}$. This paper is a companion to our previous paper ``Cluster algebras and tilings for the $m=4$ amplituhedron''., Comment: 44 pages, 20 figures. arXiv admin note: text overlap with arXiv:2310.17727

Topological magnetic insulators host chiral gapless edge modes. In the presence of strong interaction effects, the spin of these modes may fractionalize. Studying a 2D array of coupled insulating spin-1/2 chains, we show how spatially modulated magnetic fields and Dzyaloshinskii-Moriya interactions can be exploited to realize chiral spin liquids or integer and fractional spin quantum Hall effect phases. These are characterized by a gapped bulk spectrum and gapless chiral edge modes with fractional spin. The spin fractionalization is manifested in the quantized spin conductance, which can be used to probe the fractional spin quantum Hall effect. We analyze the system via bosonization and perturbative renormalization group techniques that allow us to identify the most relevant terms induced by the spin-spin interactions that open gaps and render the system topological under well-specified resonance conditions. We show explicitly that the emerging phase is a genuine chiral spin liquid. We suggest that the phases can be realized experimentally in synthetic spin chains and ultracold atom systems., Comment: 22 pages, 6 figures

This Letter introduces an approach for precisely designing surface friction properties using a conditional generative machine learning model, specifically a diffusion denoising probabilistic model (DDPM). We created a dataset of synthetic surfaces with frictional properties determined by molecular dynamics simulations, which trained the DDPM to predict surface structures from desired frictional outcomes. Unlike traditional trial-and-error and numerical optimization methods, our approach directly yields surface designs meeting specified frictional criteria with high accuracy and efficiency. This advancement in material surface engineering demonstrates the potential of machine learning in reducing the iterative nature of surface design processes. Our findings not only provide a new pathway for precise surface property tailoring but also suggest broader applications in material science where surface characteristics are critical.

Bilateral trade is one of the most natural and important forms of economic interaction: A seller has a single, indivisible item for sale, and a buyer is potentially interested. The two parties typically have different, privately known valuations for the item, and ideally, they would like to trade if the buyer values the item more than the seller. The celebrated impossibility result by Myerson and Satterthwaite shows that any mechanism for this setting must violate at least one important desideratum. In this paper, we investigate a richer paradigm of bilateral trade, with many self-interested buyers and sellers on both sides of a single trade who cannot be excluded from the trade. We show that this allows for more positive results. In fact, we establish a dichotomy in the possibility of trading efficiently. If in expectation, the buyers value the item more, we can achieve efficiency in the limit. If this is not the case, then efficiency cannot be achieved in general. En route, we characterize trading mechanisms that encourage truth-telling, which may be of independent interest. We also evaluate our trading mechanisms experimentally, and the experiments align with our theoretical results., Comment: 14 pages, 2 figures, 1 table, aaai 2024

Coalitions naturally exist in many real-world systems involving multiple decision makers such as ridesharing, security, and online ad auctions, but the coalition structure among the agents is often unknown. We propose and study an important yet previously overseen problem -- Coalition Structure Learning (CSL), where we aim to carefully design a series of games for the agents and infer the underlying coalition structure by observing their interactions in those games. We establish a lower bound on the sample complexity -- defined as the number of games needed to learn the structure -- of any algorithms for CSL and propose the Iterative Grouping (IG) algorithm for designing normal-form games to achieve the lower bound. We show that IG can be extended to other succinct games such as congestion games and graphical games. Moreover, we solve CSL in a more restrictive and practical setting: auctions. We show a variant of IG to solve CSL in the auction setting even if we cannot design the bidder valuations. Finally, we conduct experiments to evaluate IG in the auction setting and the results align with our theoretical analysis., Comment: 13 pages, 4 figures, 3 tables, aaai 2024