Search

Combinatorial spread libraries offer a unique approach to explore evolution of materials properties over the broad concentration, temperature, and growth parameter spaces. However, the traditional limitation of this approach is the requirement for the read-out of functional properties across the library. Here we demonstrate the application of automated Piezoresponse Force Microscopy (PFM) for the exploration of the physics in the SmxBi1-xFeO3 system with the ferroelectric-antiferroelectric morphotropic phase boundary. This approach relies on the synergy of the quantitative nature of PFM and the implementation of automated experiments that allows PFM-based gird sampling over macroscopic samples. The concentration dependence of pertinent ferroelectric parameters has been determined and used to develop the mathematical framework based on Ginzburg-Landau theory describing the evolution of these properties across the concentration space. We pose that combination of automated scanning probe microscope and combinatorial spread library approach will emerge as an efficient research paradigm to close the characterization gap in the high-throughput materials discovery. We make the data sets open to the community and hope that will stimulate other efforts to interpret and understand the physics of these systems., Comment: 19 pages; 5 figures

In recent years, several industrial solutions for the problem of multi-token code completion appeared, each making a great advance in the area but mostly focusing on cloud-based runtime and avoiding working on the end user's device. In this work, we describe our approach for building a multi-token code completion feature for the JetBrains' IntelliJ Platform, which we call Full Line Code Completion. The feature suggests only syntactically correct code and works fully locally, i.e., data querying and the generation of suggestions happens on the end user's machine. We share important time and memory-consumption restrictions, as well as design principles that a code completion engine should satisfy. Working entirely on the end user's device, our code completion engine enriches user experience while being not only fast and compact but also secure. We share a number of useful techniques to meet the stated development constraints and also describe offline and online evaluation pipelines that allowed us to make better decisions. Our online evaluation shows that the usage of the tool leads to 1.3 times more Python code in the IDE being produced by code completion. The described solution was initially started with a help of researchers and was then bundled into all JetBrains IDEs where it is now used by millions of users. Thus, we believe that this work is useful for bridging academia and industry, providing researchers with the knowledge of what happens when complex research-based solutions are integrated into real products., Comment: 12 pages, 4 figures

This work collects some methodological insights for numerical solution of a "minimum-dispersion" control problem for nonlinear stochastic differential equations, a particular relaxation of the covariance steering task. The main ingredient of our approach is the theoretical foundation called $\infty$-order variational analysis. This framework consists in establishing an exact representation of the increment ($\infty$-order variation) of the objective functional using the duality, implied by the transformation of the nonlinear stochastic control problem to a linear deterministic control of the Fokker-Planck equation. The resulting formula for the cost increment analytically represents a "law-feedback" control for the diffusion process. This control mechanism enables us to learn time-dependent coefficients for a predefined Markovian control structure using Monte Carlo simulations with a modest population of samples. Numerical experiments prove the vitality of our approach.

Holographic dark energy models have proven to be a very interesting way to study various aspects of late-time acceleration of the universe. In this work we extensively study HDE models with the Granda-Oliveros cutoff with an ansatz based approach. We consider the Tsallis, Barrow and PLEC HDE models in this regard and consdier simple power law, emergent universe, intermediate and logamediate forms of for the universe. Studying various cosmologically interesting parameters alongside the thermodynamical aspects in these models, we show that the Logamediate models are the best fit out of the other possibilites, followed by the emergent universe model, intermediate model and the simple power law models at the very last in terms of feasibility., Comment: 19 pages, 23 figures, comments very welcome ! arXiv admin note: text overlap with arXiv:2004.01593 by other authors

Quantum states of light play a key role in modern quantum science, but creating hybrid quantum light-matter states remains a challenge. A promising basis for the creation of hybrid states is the interaction of free electrons with photons, which has so far been largely implemented without taking into account electron quantum recoil effects. We provide an analytical quantum electrodynamics-based framework for quantum optics with recoiled electrons and introduce a single recoil parameter $\sigma$. With this framework, we show how to generate photon and electron-photon Bell, Greenberger-Horne-Zeilinger (GHZ) and NOON states, coherent states, squeezed vacuum (including bright squeezed vacuum) and twin beams. We analyze the transition between these states and predict a new class of photon and electron-photon quantum states shaped with the photon recoil effect (recoil-induced shaping). These results have wide potential applications including quantum computing and communication with photons and free electrons, and open up a novel avenue for ultrafast electron microscopy and next-generation free-electron sources.

Methods of local topology are introduced to the field of protein physics. This is achieved by explaining how the folding and unfolding processes of a globular protein alter the local topology of the protein's C-alpha backbone through conformational bifurcations. The mathematical formulation builds on the concept of Arnol'd's perestroikas, by extending it to piecewise linear chains using the discrete Frenet frame formalism. In the low-temperature folded phase, the backbone geometry generalizes the concept of a Peano curve, with its modular building blocks modeled by soliton solutions of a discretized nonlinear Schroedinger equation. The onset of thermal unfolding begins when perestroikas change the flattening and branch points that determine the centers of solitons. When temperature increases, the perestroikas cascade, which leads to a progressive disintegration of the modular structures. The folding and unfolding processes are quantitatively characterized by a correlation function that describes the evolution of perestroikas under temperature changes. The approach provides a comprehensive framework for understanding the Physics of protein folding and unfolding transitions, contributing to the broader field of protein structure and dynamics., Comment: 18 pages, 11 figures

We consider primordial nucleosynthesis in the presence of hypothetical quasi-stable doubly charged particles. Existence of $X^{--}$ with macroscopic lifetimes will lead to the formation of its bound states with $^4$He and other light elements, significantly facilitating the subsequent formation of lithium nuclei. From observational constraints on maximum allowable amount of lithium, that we update in this work, we derive strong constraints on the abundance and lifetime of $X^{--}$. In a likely cosmological freeze-out scenario with temperatures initially exceeding the mass of $X^{--}$, the BBN constrains the lifetime of these particles to be less than about 100 seconds. For parametrically long lifetimes, lithium abundance data constrain $X^{--}$ abundance to be less than $10^{-9}$ relative to protons, regardless of whether these particles decay or remain stable. Stable particles could saturate the dark matter density only if their mass is comparable to or in excess of $10^{10}$ GeV, and most of $X^{--}$ will be found in bound states with beryllium nuclei, so that chemically they would appear as abnormally heavy helium isotopes., Comment: LaTeX 24 pages, 1 table, 4 figures. v2: minor typo corrected. v3: minor textual changes. Version to be published in JCAP

Gravitational decoupling allows to obtain new solutions of general relativity. In this paper, we obtain new solutions of the Einstein field equations which describe non-singular black holes. We consider Hayward and Bardeen regular black holes as seed spacetimes and apply gravitational decoupling to obtain a new non-singular solution. We show that anisotropic energy-momentum tensor can spoil the regularity condition in the centre of a black hole. We solve the Einstein field equation and obtain new solutions that possess a de Sitter core and have Schwarzschild behaviour in infinity. We also analyse the thermodynamic properties of the obtained solutions., Comment: 23 pages, 32 figures

Measuring the similarity between motions and established motion models is crucial for motion analysis, recognition, generation, and adaptation. To enhance similarity measurement across diverse contexts, invariant motion descriptors have been proposed. However, for rigid-body motion, few invariant descriptors exist that are bi-invariant, meaning invariant to both the body and world reference frames used to describe the motion. Moreover, their robustness to singularities is limited. This paper introduces a novel Bi-Invariant Local Trajectory-Shape descriptor (BILTS) and a corresponding dissimilarity measure. Mathematical relationships between BILTS and existing descriptors are derived, providing new insights into their properties. The paper also includes an algorithm to reproduce the motion from the BILTS descriptor, demonstrating its bidirectionality and usefulness for trajectory generation. Experimental validation using datasets of daily-life activities shows the higher robustness of the BILTS descriptor compared to the bi-invariant ISA descriptor. This higher robustness supports the further application of bi-invariant descriptors for motion recognition and generalization., Comment: This work has been submitted as a regular research paper for consideration in the IEEE Transactions on Robotics

This paper extends a low-rank tensor decomposition (LRTD) reduced order model (ROM) methodology to simulate viscous flows and in particular to predict a smooth branch of solutions for the incompressible Navier-Stokes equations. Additionally, it enhances the LRTD-ROM methodology by introducing a non-interpolatory variant, which demonstrates improved accuracy compared to the interpolatory method utilized in previous LRTD-ROM studies. After presenting both the interpolatory and non-interpolatory LRTD-ROM, we demonstrate that with snapshots from a few different viscosities, the proposed method is able to accurately predict flow statistics in the Reynolds number range $[25,400]$. This is a significantly wider and higher range than state of the art (and similar size) ROMs built for use on varying Reynolds number have been successful on. The paper also discusses how LRTD may offer new insights into the properties of parametric solutions.

We give a $K$-theoretic and geometric interpretation for a generalized weighted Ehrhart theory of a full-dimensional lattice polytope $P$, depending on a given homogeneous polynomial function $\varphi$ on $P$, and with Laurent polynomial weights $f_Q(y)\in \mathbb{Z}[y^{\pm 1}]$ associated to the faces $Q \preceq P$ of the polytope. For this purpose, we calculate equivariant $K$-theoretic Hodge-Chern classes of an equivariant mixed Hodge module $\mathcal{M}$ on the toric variety $X_P$ associated to $P$ (defined via an equivariant embedding of $X_P$ into an ambient smooth variety). For any integer $\ell$, we introduce a corresponding equivariant Hodge $\chi_y$-polynomial $\chi_y(X_P, \ell D_P; [\mathcal{M}])$, with $D_P$ the corresponding ample Cartier divisor on $X_P$ (defined by the facet presentation of $P$). Motivic properties of the Hodge-Chern classes are used to express this equivariant Hodge polynomial in terms of weighted character sums fitting with a generalized weighted Ehrhart theory. The equivariant Hodge polynomials are shown to satisfy a reciprocity and purity formula fitting with the duality for equivariant mixed Hodge modules, and implying the corresponding properties for the generalized weighted Ehrhart polynomials. In the special case of the equivariant intersection cohomology mixed Hodge module, with the weight function corresponding to Stanley's $g$-function of the polar polytope of $P$, we recover in geometric terms a recent combinatorial formula of Beck--Gunnells--Materov., Comment: comments are welcome! arXiv admin note: text overlap with arXiv:2403.17747

The vast collection of Holocaust survivor testimonies presents invaluable historical insights but poses challenges for manual analysis. This paper leverages advanced Natural Language Processing (NLP) techniques to explore the USC Shoah Foundation Holocaust testimony corpus. By treating testimonies as structured question-and-answer sections, we apply topic modeling to identify key themes. We experiment with BERTopic, which leverages recent advances in language modeling technology. We align testimony sections into fixed parts, revealing the evolution of topics across the corpus of testimonies. This highlights both a common narrative schema and divergences between subgroups based on age and gender. We introduce a novel method to identify testimonies within groups that exhibit atypical topic distributions resembling those of other groups. This study offers unique insights into the complex narratives of Holocaust survivors, demonstrating the power of NLP to illuminate historical discourse and identify potential deviations in survivor experiences., Comment: 9 pages, 7 figures, LREC-COLING 2024

Single photon emitters (SPEs) hosted in hexagonal boron nitride (hBN) are essential elementary building blocks for enabling future on-chip quantum photonic technologies that operate at room temperature. However, fundamental challenges, such as managing non-radiative decay, competing incoherent processes, as well as engineering difficulties in achieving deterministic placement and scaling of the emitters, limit their full potential. In this work, we experimentally demonstrate large-area arrays of plasmonic nanoresonators for Purcell-induced site-controlled SPEs by engineering emitter-cavity coupling and enhancing radiative emission at room temperature. The plasmonic nanoresonator architecture consists of gold-coated silicon pillars capped with an alumina spacer layer, enabling a 10-fold local field enhancement in the emission band of native hBN defects. Confocal photoluminescence and second-order autocorrelation measurements show bright SPEs with sub-30 meV bandwidth and a saturated emission rate of more than 3.8 million counts per second. We measure a Purcell factor of 4.9, enabling average SPE lifetimes of 480 ps, a five-fold reduction as compared to emission from gold-free devices, along with an overall SPE yield of 21%. Density functional theory calculations further reveal the beneficial role of an alumina spacer between defected hBN and gold, as an insulating layer can mitigate the electronic broadening of emission from defects proximal to gold. Our results offer arrays of bright, heterogeneously integrated quantum light sources, paving the way for robust and scalable quantum information systems., Comment: 41 pages, 18 figures, supplementary information

Multi-Robot-Arm Motion Planning (M-RAMP) is a challenging problem featuring complex single-agent planning and multi-agent coordination. Recent advancements in extending the popular Conflict-Based Search (CBS) algorithm have made large strides in solving Multi-Agent Path Finding (MAPF) problems. However, fundamental challenges remain in applying CBS to M-RAMP. A core challenge is the existing reliance of the CBS framework on conservative "complete" constraints. These constraints ensure solution guarantees but often result in slow pruning of the search space -- causing repeated expensive single-agent planning calls. Therefore, even though it is possible to leverage domain knowledge and design incomplete M-RAMP-specific CBS constraints to more efficiently prune the search, using these constraints would render the algorithm itself incomplete. This forces practitioners to choose between efficiency and completeness. In light of these challenges, we propose a novel algorithm, Generalized ECBS, aimed at removing the burden of choice between completeness and efficiency in MAPF algorithms. Our approach enables the use of arbitrary constraints in conflict-based algorithms while preserving completeness and bounding sub-optimality. This enables practitioners to capitalize on the benefits of arbitrary constraints and opens a new space for constraint design in MAPF that has not been explored. We provide a theoretical analysis of our algorithms, propose new "incomplete" constraints, and demonstrate their effectiveness through experiments in M-RAMP., Comment: The first two authors contributed equally. Accepted to SoCS 2024

We revisit the work of Mitter and Newton on an information-theoretic interpretation of Bayes' formula through the Gibbs variational principle. This formulation allowed them to pose nonlinear estimation for diffusion processes as a problem in stochastic optimal control, so that the posterior density of the signal given the observation path could be sampled by adding a drift to the signal process. We show that this control-theoretic approach to sampling provides a common mechanism underlying several distinct problems involving diffusion processes, specifically importance sampling using Feynman-Kac averages, time reversal, and Schr\"odinger bridges., Comment: 22 pages; dedicated to the memory of Sanjoy K. Mitter (1933-2023)

Silicon is a key semiconducting material for electrical devices and hybrid quantum systems where low temperatures and zero-spin isotopic purity can enhance quantum coherence. Electrical conductivity in Si is characterised by carrier freeze out at around 40 K allowing microwave transmission which is a key component for addressing spins efficiently in silicon quantum technologies. In this work, we report an additional sharp transition of the electrical conductivity in a Si-28 cylindrical cavity at around 1 Kelvin. This is observed by measuring microwave resonator Whispering Gallery Mode frequencies and Q factors with changing temperature and comparing these results with finite element models. We attribute this change to a transition from a relaxation mechanism-dominated to a resonant phonon-less absorption-dominated hopping conduction regime. Characterising this regime change represents a deeper understanding of a physical phenomenon in a material of high interest to the quantum technology and semiconductor device community and the impact of these results is discussed., Comment: 13 pages, 16 figures

We take a fresh look at the relation between generalised K\"ahler geometry and $N=(2,2)$ supersymmetric sigma models in two dimensions formulated in terms of $(2,2)$ superfields. Dual formulations in terms of different kinds of superfield are combined to give a formulation with a doubled target space and both the original superfield and the dual superfield. For K\"ahler geometry, we show that this doubled geometry is Donaldson's deformation of the holomorphic cotangent bundle of the original K\"ahler manifold. This doubled formulation gives an elegant geometric reformulation of the equations of motion. We interpret the equations of motion as the intersection of two Lagrangian submanifolds (or of a Lagrangian submanifold with an isotropic one) in the infinite dimensional symplectic supermanifold which is the analogue of phase space. We then consider further extensions of this formalism, including one in which the geometry is quadrupled, and discuss their geometry., Comment: 44 pages, final published version

In the era of the Internet of Things (IoT), objects connect through a dynamic network, empowered by technologies like 5G, enabling real-time data sharing. However, smart objects, notably autonomous vehicles, face challenges in critical local computations due to limited resources. Lightweight AI models offer a solution but struggle with diverse data distributions. To address this limitation, we propose a novel Multi-Stream Cellular Test-Time Adaptation (MSC-TTA) setup where models adapt on the fly to a dynamic environment divided into cells. Then, we propose a real-time adaptive student-teacher method that leverages the multiple streams available in each cell to quickly adapt to changing data distributions. We validate our methodology in the context of autonomous vehicles navigating across cells defined based on location and weather conditions. To facilitate future benchmarking, we release a new multi-stream large-scale synthetic semantic segmentation dataset, called DADE, and show that our multi-stream approach outperforms a single-stream baseline. We believe that our work will open research opportunities in the IoT and 5G eras, offering solutions for real-time model adaptation.

The Four color problem is closely related to other branches of mathematics and practical applications. More than 20 of its reformulations are known, which connect this problem with problems of algebra, statistical mechanics and planning. And this is also typical for mathematics: the solution to a problem studied out of pure curiosity turns out to be useful in representing real objects and processes that are completely different in nature. Despite the published machine methods for combinatorial proof of the Four color conjecture, there is still no clear description of the mechanism for coloring a planar graph with four colors, its natural essence and its connection with the phenomenon of graph planarity. It is necessary not only to prove (preferably by deductive methods) that any planar graph can be colored with four colors, but also to show how to color it. The paper considers an approach based on the possibility of reducing a maximally flat graph to a regular flat cubic graph with its further coloring. Based on the Tate-Volynsky theorem, the vertices of a maximally flat graph can be colored with four colors, if the edges of its dual cubic graph can be colored with three colors. Considering the properties of a colored cubic graph, it can be shown that the addition of colors obeys the transformation laws of the fourth order Klein group. Using this property, it is possible to create algorithms for coloring planar graphs., Comment: 123 pages, in Ukrainian language, 140 figures, a preprint of monography

Hadronic resonances emerge from strong interactions encoding the dynamics of quarks and gluons. The structure of these resonances can be probed by virtual photons parameterized in transition form factors. In this study, twelve $N^*$ and $\Delta$ transition form factors at the pole are extracted from data with the center-of-mass energy from $\pi N$ threshold to $1.8\,{\rm GeV}$, and the photon virtuality $0\leq Q^2/{\rm GeV}^2\leq 8$. For the first time, these results are determined from a simultaneous analysis of more than one state, i.e., $\sim 10^5$ $\pi N$, $\eta N$, and $K\Lambda$ electroproduction data. In addition, about $ 5\cdot 10^4$ data in the hadronic sector as well as photoproduction serve as boundary conditions. For the $\Delta(1232)$ and $N(1440)$ states our results are in qualitative agreement with previous studies, while the transition form factors at the poles of some higher excited states are estimated for the first time. Realistic uncertainties are determined by further exploring the parameter space., Comment: Text: 6 pages, 4 figures. Supplemental Material: 3 pages, 2 figures

To derive the best oscillator phase noise when implementing a high-Q resonator, the spectral line-shape must have high contrast and symmetry. Ideally, this line-shape is Lorentzian, however, in a high mode density spectral region, low-Q background spurious modes interact and distort the resonance. For a sapphire-loaded cavity resonator operating with whispering gallery modes we show that this high contrast and symmetry can be achieved by changing the dimensions of the surrounding cavity shield to tune the background low-Q structures into anti-resonance. This works because the high-Q resonances are primarily defined by the sapphire while the background modes are defined by the cavity shield. Alternatively, it was shown that a similar result can be achieved by exciting the high-Q resonator with a balanced microwave dipole probe in a Mach Zehnder interferometric configuration. The probe was constructed from two separate coaxial electric field probes symmetrically inserted into a cylindrical cavity resonator, from opposite sides with a small gap between them, so they can behave like an active wire dipole antenna. The power into the two separate probes may be matched with an external variable attenuator in one of the arms of the interferometer. Conversely, the phase between the two electric field probes may be changed with an external variable phase shifter, which changes the nature of the field components the probe couples to. The probe couples to the high-Q resonant modes as well as low-Q background modes, which can be made resonant or anti-resonant for the high-Q modes by changing this external phase. When the background modes are in anti-resonance the line shape of the high-Q mode can be made symmetric and with higher contrast. This technique was applied to both whispering gallery sapphire modes, as well as hollow cavity resonators, without changing the dimensions of the cavity., Comment: accepted version

In this work, we explore the generalities of the supercurrent diode effect. As an illustrative example, we examine a model of a two-dimensional superconductor with Rashba-type spin-orbit coupling under an in-plane magnetic field and in the clean limit, which realizes a helical phase. First, we utilize Ginzburg-Landau phenomenology to derive a general formula for the diode efficiency. This is achieved by incorporating higher gradient terms in the Lifshitz invariants, which are responsible for the nonreciprocal superflow. Subsequently, we validate these results through microscopic diagrammatic computation and further estimate correction terms arising from interband pairing correlations. We provide a detailed comparison to prior investigations of this problem conducted within the framework of the quasiclassical approximation based on the Eilenberger equation., Comment: 19 pages, 14 figures

Enhancement of methane emission measurement techniques is necessary to address the need for greenhouse gas emissions monitoring. Here we introduce a gas analyzer designed for remote sensing of atmospheric methane aboard unmanned aerial vehicles. This device employs the wavelength modulation spectroscopy approach and quadrature detection of laser radiation scattered from the underlying surface. Our results demonstrate that the observed correlation between various signal attributes and the distance to the surface, where laser radiation scatters, aligns with analytical expectations. Calibrations proved that the instrument provides reliable methane measurements up to 120 meters while being lightweight and power efficient. Notably, this device outperforms its competitors at altitudes exceeding 50 meters, which is safer for piloting.

The majority of multi-agent path finding (MAPF) methods compute collision-free space-time paths which require agents to be at a specific location at a specific discretized timestep. However, executing these space-time paths directly on robotic systems is infeasible due to real-time execution differences (e.g. delays) which can lead to collisions. To combat this, current methods translate the space-time paths into a temporal plan graph (TPG) that only requires that agents observe the order in which they navigate through locations where their paths cross. However, planning space-time paths and then post-processing them into a TPG does not reduce the required agent-to-agent coordination, which is fixed once the space-time paths are computed. To that end, we propose a novel algorithm Space-Order CBS that can directly plan a TPG and explicitly minimize coordination. Our main theoretical insight is our novel perspective on viewing a TPG as a set of space-visitation order paths where agents visit locations in relative orders (e.g. 1st vs 2nd) as opposed to specific timesteps. We redefine unique conflicts and constraints for adapting CBS for space-order planning. We experimentally validate how Space-Order CBS can return TPGs which significantly reduce coordination, thus subsequently reducing the amount of agent-agent communication and leading to more robustness to delays during execution.

We revisit the work of Roger Brockett on controllability of the Liouville equation, with a particular focus on the following problem: Given a smooth controlled dynamical system of the form $\dot{x} = f(x,u)$ and a state-space diffeomorphism $\psi$, design a feedback control $u(t,x)$ to steer an arbitrary initial state $x_0$ to $\psi(x_0)$ in finite time. This formulation of the problem makes contact with the theory of optimal transportation and with nonlinear controllability. For controllable linear systems, Brockett showed that this is possible under a fairly restrictive condition on $\psi$. We prove that controllability suffices for a much larger class of diffeomorphisms. For nonlinear systems defined on smooth manifolds, we review a recent result of Agrachev and Caponigro regarding controllability on the group of diffeomorphisms. A corollary of this result states that, for control-affine systems satisfying a bracket generating condition, any $\psi$ in a neighborhood of the identity can be implemented using a time-varying feedback control law that switches between finitely many time-invariant flows. We prove a quantitative version which allows us to describe the implementation complexity of the Agrachev-Caponigro construction in terms of a lower bound on the number of switchings., Comment: 15 pages; final version to appear in M.A. Belabbas, editor, Geometry and Topology in Control System Design, American Institute of Mathematical Sciences, 2024

We show that Claude 3 Opus, a large language model (LLM) released by Anthropic in March 2024, exhibits stronger machine translation competence than other LLMs. Though we find evidence of data contamination with Claude on FLORES-200, we curate new benchmarks that corroborate the effectiveness of Claude for low-resource machine translation into English. We find that Claude has remarkable \textit{resource efficiency} -- the degree to which the quality of the translation model depends on a language pair's resource level. Finally, we show that advancements in LLM translation can be compressed into traditional neural machine translation (NMT) models. Using Claude to generate synthetic data, we demonstrate that knowledge distillation advances the state-of-the-art in Yoruba-English translation, meeting or surpassing strong baselines like NLLB-54B and Google Translate., Comment: 17 pages, 15 figures

Lavrentiev curves form a special class of rectifiable curves which includes cusp-free piecewise smooth curves. We call a Lavrentiev curve Legendrian if the integral of the contact form equals zero on any its subarc. We define Legendrian isotopies of such curves and prove that the equivalence classes of Legendrian Lavrentiev links with respect to Legendrian isotopies coincide with smooth classes.

Scientific advancement is universally based on the dynamic interplay between theoretical insights, modelling, and experimental discoveries. However, this feedback loop is often slow, including delayed community interactions and the gradual integration of experimental data into theoretical frameworks. This challenge is particularly exacerbated in domains dealing with high-dimensional object spaces, such as molecules and complex microstructures. Hence, the integration of theory within automated and autonomous experimental setups, or theory in the loop automated experiment, is emerging as a crucial objective for accelerating scientific research. The critical aspect is not only to use theory but also on-the-fly theory updates during the experiment. Here, we introduce a method for integrating theory into the loop through Bayesian co-navigation of theoretical model space and experimentation. Our approach leverages the concurrent development of surrogate models for both simulation and experimental domains at the rates determined by latencies and costs of experiments and computation, alongside the adjustment of control parameters within theoretical models to minimize epistemic uncertainty over the experimental object spaces. This methodology facilitates the creation of digital twins of material structures, encompassing both the surrogate model of behavior that includes the correlative part and the theoretical model itself. While demonstrated here within the context of functional responses in ferroelectric materials, our approach holds promise for broader applications, the exploration of optical properties in nanoclusters, microstructure-dependent properties in complex materials, and properties of molecular systems. The analysis code that supports the funding is publicly available at https://github.com/Slautin/2024_Co-navigation/tree/main, Comment: 23 pages, 10 figures

In this paper, first we revisit the formal integration of Lie algebras, which give rise to braces in some special cases. Then we establish the formal integration theory for complete Rota-Baxter Lie algebras, that is, we show that there is a Rota-Baxter group with the underlying group structure given by the Baker-Campbell-Hausdorff formula, associated to any complete Rota-Baxter Lie algebra. In particular, we use the post-Lie Magnus expansion to give the explicit formula of the Rota-Baxter operator. Finally we show that one can obtain a graded Rota-Baxter Lie ring from a filtered Rota-Baxter group., Comment: 23 pages. Compare to the previous version: 1. we give the formal integration formula using Magnus expansion, which is very surprised (the second half of Section 4); 2. we show that conversely one can obtain a Rota-Baxter Lie ring from a filtered Rota-Baxter group (Section 5)

Many physically interesting quantities of the electromagnetic field can be computed using the electromagnetic scalar product. However, none of the existing expressions for such scalar product are directly applicable when the fields are only known in a spatially-bounded domain, as is the case for many numerical Maxwell solvers. In here, we derive an expression for the electromagnetic scalar product between radiation fields that only involves integrals over closed spatial surfaces. The expression readily leads to formulas for the number of photons, energy, and helicity of generic polychromatic light pulses of incoming or outgoing character. The capabilities of popular Maxwell solvers in spatially-bounded computational domains are thereby augmented, for example, by a straightforward method for normalizing emitted fields so that they contain a single photon.

Exploring the structural, chemical, and physical properties of matter on the nano- and atomic scales has become possible with the recent advances in aberration-corrected electron energy-loss spectroscopy (EELS) in scanning transmission electron microscopy (STEM). However, the current paradigm of STEM-EELS relies on the classical rectangular grid sampling, in which all surface regions are assumed to be of equal a priori interest. This is typically not the case for real-world scenarios, where phenomena of interest are concentrated in a small number of spatial locations. One of foundational problems is the discovery of nanometer- or atomic scale structures having specific signatures in EELS spectra. Here we systematically explore the hyperparameters controlling deep kernel learning (DKL) discovery workflows for STEM-EELS and identify the role of the local structural descriptors and acquisition functions on the experiment progression. In agreement with actual experiment, we observe that for certain parameter combinations the experiment path can be trapped in the local minima. We demonstrate the approaches for monitoring automated experiment in the real and feature space of the system and monitor knowledge acquisition of the DKL model. Based on these, we construct intervention strategies, thus defining human-in the loop automated experiment (hAE). This approach can be further extended to other techniques including 4D STEM and other forms of spectroscopic imaging.

The paper introduces a finite element method for an Eulerian formulation of partial differential equations governing the transport and diffusion of a scalar quantity in a time-dependent domain. The method follows the idea from Lehrenfeld & Olshanskii [ESAIM: M2AN, 53(2): 585-614, 2019] of a solution extension to realise the Eulearian time-stepping scheme. However, a reformulation of the partial differential equation is suggested to derive a scheme which conserves the quantity under consideration exactly on the discrete level. For the spatial discretisation, the paper considers an unfitted finite element method. Ghost-penalty stabilisation is used to release the discrete solution extension and gives a scheme robust against arbitrary intersections between the mesh and geometry interface. The stability is analysed for both first- and second-order backward differentiation formula versions of the scheme. Several numerical examples in two and three spatial dimensions are included to illustrate the potential of this method.

The possibility of using axial spin color centers with $S=3/2$, oriented along the hexagonal $c$ axis in a silicon carbide (SiC) wafer, has been demonstrated for all-optical measurement of projection of the external magnetic field coinciding with the $c$ axis of the crystal, and the polar and azimuthal angles of the external measured magnetic field at room and significantly higher temperatures. A distinctive feature of spin centers in SiC, in which optically induced spin alignment is carried out, is the presence of a unique system of spin levels in a magnetic field, caused by fine structure interaction and hyperfine interaction with the $^{29}$Si nuclei and there is a wide range of level anticrossings (LACs), leading to an exceptionally strong change in photoluminescence in the region of LAC and the dependence of the LAC spectrum on the orientation of the external measured magnetic field, which made it possible to develop the all-optical vector magnetometry method. Such measurements do not require microwave radiation, it is possible to use single spin center for the all-optical vector magnetometry. The proposed magnetometer is based on an external magnetic field cancellation scheme, which leads to a LAC spectrum observed in a zero external magnetic field, called its reference spectrum, by maintaining a local region of zero magnetic field at the site of optical excitation of spin centers. 4H-SiC plate is placed on the scanning stage of a confocal microscope inside the Helmholtz coils. Sensitivity to a constant magnetic field for $z$ component of the magnetic field ${B}_{z}$ is better than $0.1\mu$T$/\sqrt{\text{Hz}}$ in a volume of $1\times10^{-8}$mm$^{3}$ at room temperature. The sensitivity of determining the angles polar and azimuthal is determined by the sensitivity to determining the perpendicular component of the magnetic field, which is better than $5~\mu$T$/\sqrt{\text{Hz}}$.

Atomic arrangements and local sub-structures fundamentally influence emergent material functionalities. The local structures are conventionally probed using spatially resolved studies and the property correlations are usually deciphered by a researcher based on sequential explorations and auxiliary information, thus limiting the throughput efficiency. Here we demonstrate a Bayesian deep learning based framework that automatically correlates material structure with its electronic properties using scanning tunneling microscopy (STM) measurements in real-time. Its predictions are used to autonomously direct exploration toward regions of the sample that optimize a given material property. This autonomous method is deployed on the low-temperature ultra-high vacuum STM to understand the structure-property relationship in a europium-based semimetal, EuZn2As2, one of the promising candidates for studying the magnetism-driven topological properties. The framework employs a sparse sampling approach to efficiently construct the scalar-property space using a minimal number of measurements, about 1 - 10 % of the data required in standard hyperspectral imaging methods. We further demonstrate a target-property-guided active learning of structures within a multiscale framework. This is implemented across length scales in a hierarchical fashion for the autonomous discovery of structural origins for an observed material property. This framework offers the choice to select and derive a suitable scalar property from the spectroscopic data to steer exploration across the sample space. Our findings reveal correlations of the electronic properties unique to surface terminations, local defect density, and point defects.

With the advent of machine learning, there have been several recent attempts to learn effective and generalizable heuristics. Local Heuristic A* (LoHA*) is one recent method that instead of learning the entire heuristic estimate, learns a "local" residual heuristic that estimates the cost to escape a region (Veerapaneni et al 2023). LoHA*, like other supervised learning methods, collects a dataset of target values by querying an oracle on many planning problems (in this case, local planning problems). This data collection process can become slow as the size of the local region increases or if the domain requires expensive collision checks. Our main insight is that when an A* search solves a start-goal planning problem it inherently ends up solving multiple local planning problems. We exploit this observation to propose an efficient data collection framework that does <1/10th the amount of work (measured by expansions) to collect the same amount of data in comparison to baselines. This idea also enables us to run LoHA* in an online manner where we can iteratively collect data and improve our model while solving relevant start-goal tasks. We demonstrate the performance of our data collection and online framework on a 4D $(x, y, \theta, v)$ navigation domain., Comment: Accepted in the 17th International Symposium on Combinatorial Search (SoCS 2024)

Last year, multimodal architectures served up a revolution in AI-based approaches and solutions, extending the capabilities of large language models (LLM). We propose an \textit{OmniFusion} model based on a pretrained LLM and adapters for visual modality. We evaluated and compared several architecture design principles for better text and visual data coupling: MLP and transformer adapters, various CLIP ViT-based encoders (SigLIP, InternVIT, etc.), and their fusing approach, image encoding method (whole image or tiles encoding) and two 7B LLMs (the proprietary one and open-source Mistral). Experiments on 8 visual-language benchmarks show the top score for the best OmniFusion setup in terms of different VQA tasks in comparison with open-source LLaVA-like solutions: VizWiz, Pope, MM-Vet, ScienceQA, MMBench, TextVQA, VQAv2, MMMU. We also propose a variety of situations, where OmniFusion provides highly-detailed answers in different domains: housekeeping, sightseeing, culture, medicine, handwritten and scanned equations recognition, etc. Mistral-based OmniFusion model is an open-source solution with weights, training and inference scripts available at https://github.com/AIRI-Institute/OmniFusion., Comment: 17 pages, 4 figures, 9 tables, 2 appendices

The interaction of light with short light pulses is relevant in optical traps, optical tweezers, and many other applications. The theoretical description of such polychromatic light-matter interaction is challenging, and more so when the object is moving with respect to the light source, albeit with constant speed. Light sails are futuristic examples where such speed should reach the relativistic regime. In here, we provide a methodology for the theoretical and numerical analysis of the interaction of light pulses with objects moving with constant speed. The methodology allows one, in particular, to readily compute the transfer of fundamental quantities such as energy and momentum from the light pulse to the object. As an example, we compute the transfer of energy and momentum between a given pulse and a silicon sphere moving at relativistic speeds. The methodology, however, is valid for generic pulses and objects. Particularizing the equations to the case of zero speed allows one to treat static or quasi-static objects. The method is based on the polychromatic T-matrix formalism, which leverages the many publicly available resources for computing T-matrices.

Weak Arthur packets have long been instrumental in the study of the unitary dual and automorphic spectrum of reductive Lie groups, and were recently introduced in the p-adic setting by Ciubotaru - Mason-Brown - Okada. For split odd orthogonal and symplectic p-adic groups, we explicitly determine the decomposition of weak Arthur packets into Arthur packets that arise from endoscopic transfer. We establish a characterization of the Arthur packets that partake in such decompositions by means of ramification properties of their constituents. A notion of weak sphericity for an irreducible representation is introduced: The property of containing fixed vectors with respect to a (not necessarily hyperspecial) maximal compact subgroup. We show that this property determines the weak Arthur packets in a precise sense. As steps towards this description, we explore alignments between Langlands-type reciprocities for finite and p-adic groups, and their dependence on the geometry of the unipotent locus of the dual Langlands group. Weak sphericity is shown to match with Lusztig's canonical quotient spaces that feature in the geometric theory for Weyl group representations, while the fine composition of weak Arthur packets is found to be governed by the partition of the unipotent locus into special pieces., Comment: 77 pages

Hydrodynamic discontinuities in an external potential and incompressible flow are investigated. Using the reaction front as an example in a 2D stream, an overdetermined system of equations is obtained that describes its motion in terms of the surface itself. Assuming that the harmonic flux approaching discontinuity is additional smooth, these equations can be used to determine the motion of this discontinuity without taking into account the influence of the flow behind the front, as well as the entire external flow. It is well known that for vanishingly low viscosity, the integral relation on the boundary (Dirichlet, Neumann problems) connects the tangential and normal components of the velocity. Knowing one of them along the boundary of the discontinuity, one can determine the entire external flow. However, assuming the external flow is smooth, this will also be the case for all derivatives of velocity with respect to coordinates and time. Then a paradox arises, knowing the position of the discontinuity and the velocity data at a point on its surface, it is possible to determine the motion of this discontinuity without taking into account the influence of the flow behind the front, as well as the entire external flow. There is no physical explanation for this mechanism. It is possible that a boundary layer is formed in front of the front, where viscosity plays a significant role and Euler equations are violated. It is argued that the classical idea of the motion of hydrodynamic discontinuities in the smooth, potential and incompressible flow in the external region should be supplemented in this case., Comment: 19 pages, 2 figures

In previous work on learning and controlling contact-rich tasks, the procedure for choosing a proper reference frame to express learned signals for the motion and the interaction wrench is often implicit, requires expert insight, or starts from proposed frame candidates. This article presents an automatic method to derive the optimal reference frame, referred to as optimal task frame, directly from the recorded motion and wrench data of the demonstration. Using screw theory, several origin and orientation candidates are generated that maximize decoupling in the data. These candidates are then processed probabilistically, without needing hyperparameters, to obtain the optimal task frame. Its origin and orientation are independently fixed to either the world or the robot tool. The method works regardless of whether the task involves translation, rotation, force, or moment, or any combination thereof. The method was validated for various tasks, including surface following and manipulation of articulated objects, showing good agreement between derived and assumed expert task frames. To validate the robot's performance, a constraint-based controller was designed based on the data expressed in the derived task frames. These experiments demonstrated the approach's effectiveness and versatility. The automatic task frame derivation approach supports learning methods to design controllers for a wide range of contact-rich tasks.

This paper was written in 1994 and has attracted a large number of citations since then. The main result was a definition of what is called the affine Brauer algebra in the present version. It is now posted to affirm this terminology., Comment: 23 pages, the proof of Theorem 3.12 includes three original figures omitted in the journal version

Our paper addresses the complex task of transferring a hairstyle from a reference image to an input photo for virtual hair try-on. This task is challenging due to the need to adapt to various photo poses, the sensitivity of hairstyles, and the lack of objective metrics. The current state of the art hairstyle transfer methods use an optimization process for different parts of the approach, making them inexcusably slow. At the same time, faster encoder-based models are of very low quality because they either operate in StyleGAN's W+ space or use other low-dimensional image generators. Additionally, both approaches have a problem with hairstyle transfer when the source pose is very different from the target pose, because they either don't consider the pose at all or deal with it inefficiently. In our paper, we present the HairFast model, which uniquely solves these problems and achieves high resolution, near real-time performance, and superior reconstruction compared to optimization problem-based methods. Our solution includes a new architecture operating in the FS latent space of StyleGAN, an enhanced inpainting approach, and improved encoders for better alignment, color transfer, and a new encoder for post-processing. The effectiveness of our approach is demonstrated on realism metrics after random hairstyle transfer and reconstruction when the original hairstyle is transferred. In the most difficult scenario of transferring both shape and color of a hairstyle from different images, our method performs in less than a second on the Nvidia V100. Our code is available at https://github.com/AIRI-Institute/HairFastGAN.

The famous Goldbach conjecture states that any even natural number $N$ greater than $2$ can be written as the sum of two prime numbers $p$ and $p'$, with $p \, , p'$ referred to as a Goldbach pair. In this article we present a quantum analogue protocol for detecting -- given a even number $N$ -- the existence of a so-called minimal Goldbach partition $N=p+p'$ with $p\equiv p_{\rm min}(N)$ being the so-called minimal Goldbach prime, i.e. the least possible value for $p$ among all the Goldbach pairs of $N$. The proposed protocol is effectively a quantum Grover algorithm with a modified final stage. Assuming that an approximate smooth upper bound $\mathcal{N}(N)$ for the number of primes less than or equal to $ p_{\rm min}(N)$ is known, our protocol will identify if the set of $\mathcal{N}(N)$ lowest primes contains the minimal Goldbach prime in approximately $\sqrt{\mathcal{N}(N)}$ steps, against the corresponding classical value $\mathcal{N}(N)$. In the larger context of a search for violations of Goldbach's conjecture, the quantum advantage provided by our scheme appears to be potentially convenient. E.g., referring to the current state-of-art numerical search for violations of the Goldbach conjecture among all even numbers up to $N_{\text{max}} = 4\times 10^{18}$ [T. O. e Silva, S. Herzog, and S. Pardi, Mathematics of Computation 83, 2033 (2013)], a quantum realization of the search would deliver a quantum advantage factor of $\sqrt{\mathcal{N}(N_{\text{max}})} \approx 37$ and it will require a Hilbert space spanning $\mathcal{N}(N_{\text{max}}) \approx 1376$ basis states.

An exciting frontier in robotic manipulation is the use of multiple arms at once. However, planning concurrent motions is a challenging task using current methods. The high-dimensional composite state space renders many well-known motion planning algorithms intractable. Recently, Multi-Agent Path-Finding (MAPF) algorithms have shown promise in discrete 2D domains, providing rigorous guarantees. However, widely used conflict-based methods in MAPF assume an efficient single-agent motion planner. This poses challenges in adapting them to manipulation cases where this assumption does not hold, due to the high dimensionality of configuration spaces and the computational bottlenecks associated with collision checking. To this end, we propose an approach for accelerating conflict-based search algorithms by leveraging their repetitive and incremental nature -- making them tractable for use in complex scenarios involving multi-arm coordination in obstacle-laden environments. We show that our method preserves completeness and bounded sub-optimality guarantees, and demonstrate its practical efficacy through a set of experiments with up to 10 robotic arms., Comment: The first two authors contributed equally. Accepted to ICAPS 2024

Multi-agent path finding (MAPF) is the problem of finding collision-free paths for a team of agents to reach their goal locations. State-of-the-art classical MAPF solvers typically employ heuristic search to find solutions for hundreds of agents but are typically centralized and can struggle to scale when run with short timeouts. Machine learning (ML) approaches that learn policies for each agent are appealing as these could enable decentralized systems and scale well while maintaining good solution quality. Current ML approaches to MAPF have proposed methods that have started to scratch the surface of this potential. However, state-of-the-art ML approaches produce "local" policies that only plan for a single timestep and have poor success rates and scalability. Our main idea is that we can improve a ML local policy by using heuristic search methods on the output probability distribution to resolve deadlocks and enable full horizon planning. We show several model-agnostic ways to use heuristic search with learnt policies that significantly improve the policies' success rates and scalability. To our best knowledge, we demonstrate the first time ML-based MAPF approaches have scaled to high congestion scenarios (e.g. 20% agent density)., Comment: Accepted in ICAPS 2024

Due to the spin-orbit coupling, Dirac fermions, submerged in a thermal bath with finite macroscopic vorticity, exhibit a spin polarisation along the direction parallel to the vorticity vector $\boldsymbol{\Omega}$. Due to the symmetries of the Lagrangian for free massless Dirac particles, there are three independent and classically conserved currents corresponding to the vector, axial, and helical charges. The constitutive relations for the charge currents and the stress-energy tensor at thermal equilibrium, derived in the framework of quantum field theory at finite temperature, reveal vorticity-induced contributions that deviate from the perfect fluid form. In this paper, we consider the mode structure of the corresponding hydrodynamical theory and derive collective excitations associated with coherent fluctuations of all three charges. We show that the chirally imbalanced rotating fluid should possess non-reciprocal gapless waves that propagate with different velocities along and opposite to the vorticity vector. We also uncover a strictly unidirectional mode, which we call the Axial Vortical Wave, propagating in the background of the axial charge density. We point out an unexpected instability in the limit of degenerate matter and discuss possible solutions when helicity and axial charge non-conservation is taken into account., Comment: 41 pages, 6 figures, 1 table. Part 1

In this paper, we consider the effect of interactions on the local, average polarization of a quantum plasma of massless fermion particles characterized by vector, axial, and helical quantum numbers. Due to the helical and axial vortical effects, perturbations in the vector charge in a rotating plasma can lead to chiral and helical charge transfer along the direction of the vorticity vector. At the same time, interactions between the plasma constituents lead to the dissipation of the helical charge through helicity-violating pair annihilation (HVPA) processes and of the axial charge through the axial anomaly. We will discuss separately a QED-like plasma, in which we ignore background electromagnetic fields and thus the axial charge is roughly conserved, as well as a QCD-like plasma, where instanton effects lead to the violation of the axial charge conservation, even in the absence of background chromomagnetic fields. The non-conservation of helicity and chirality leads to a gapping of the Helical, Axial and mixed, Axial-Helical vortical waves that prevents their infrared modes from propagating. On the other hand, usual dissipative effects, such as charge diffusion, lead to significant damping of ultraviolet modes. We end this paper with a discussion of the regimes where these vortical waves may propagate., Comment: 56 pages, 14 figures. Part 2

We survey recent developments in the study of torus equivariant motivic Chern and Hirzebruch characteristic classes of projective toric varieties, with applications to calculating equivariant Hirzebruch genera of torus-invariant Cartier divisors in terms of torus characters, as well as to general Euler-Maclaurin type formulae for full-dimensional simple lattice polytopes. We present recent results by the authors, emphasizing the main ideas and some key examples. This includes global formulae for equivariant Hirzebruch classes in the simplicial context proved by localization at the torus fixed points, a weighted versions of a classical formula of Brion, as well as of the Molien formula of Brion-Vergne. Our Euler-Maclaurin type formulae provide generalizations to arbitrary coherent sheaf coefficients of the Euler-Maclaurin formulae of Cappell-Shaneson, Brion-Vergne, Guillemin, etc., via the equivariant Hirzebruch-Riemann-Roch formalism. Our approach, based on motivic characteristic classes, allows us, e.g., to obtain such Euler-Maclaurin formulae also for (the interior of) a face. We obtain such results also in the weighted context, and for Minkovski summands of the given full-dimensional lattice polytope., Comment: survey paper overviewing recent results by the authors from arXiv:2303.16785, emphasizing the main ideas and some key examples

We give a cohomological and geometrical interpretation for the weighted Ehrhart theory of a full-dimensional lattice polytope $P$, with Laurent polynomial weights of geometric origin. For this purpose, we calculate the motivic Chern and Hirzebruch characteristic classes of a mixed Hodge module complex $\mathcal{M}$ whose underlying cohomology sheaves are constant on the $\mathbb{T}$-orbits of the toric variety $X_P$ associated to $P$. Besides motivic coefficients, this also applies to the intersection cohomology Hodge module. We introduce a corresponding generalized Hodge $\chi_y$-polynomial of the ample divisor $D_P$ on $X_P$. Motivic properties of these characteristic classes are used to express this Hodge polynomial in terms of a very general weighed lattice point counting and the corresponding weighted Ehrhart theory. We introduce, for such a mixed Hodge modules complex $\mathcal{M}$ on $X$, an Ehrhart polynomial $E_{P,\mathcal{M}}$ generalizing the Hodge polynomial of $\mathcal{M}$ and satisfying a reciprocity formula and a purity formula fitting with the duality for mixed Hodge modules. This Ehrhart polynomial and its properties depend only on a Laurent polynomial weight function on the faces $Q$ of $P$. In the special case of the intersection cohomology mixed Hodge module, the weight function corresponds to Stanley's $g$-function of the polar polytope of $P$, hence it depends only on the combinatorics of $P$. In particular, we obtain a combinatorial formula for the intersection cohomology signature., Comment: comments are welcome! v2: corrected several typos, added one reference

We show a beyond 200Gb/s VCSEL transmission experiment. Results are based on 35GHz VCSEL and advanced DSP. We show an AIR of 245Gb/s PAM-6 back-to-back, and 200Gb/s PAM-4 over 60m OM4 fiber assuming KP4-FEC.