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We develop a robust translation model for four low-resource Indic languages: Khasi, Mizo, Manipuri, and Assamese. Our approach includes a comprehensive pipeline from data collection and preprocessing to training and evaluation, leveraging data from WMT task datasets, BPCC, PMIndia, and OpenLanguageData. To address the scarcity of bilingual data, we use back-translation techniques on monolingual datasets for Mizo and Khasi, significantly expanding our training corpus. We fine-tune the pre-trained NLLB 3.3B model for Assamese, Mizo, and Manipuri, achieving improved performance over the baseline. For Khasi, which is not supported by the NLLB model, we introduce special tokens and train the model on our Khasi corpus. Our training involves masked language modelling, followed by fine-tuning for English-to-Indic and Indic-to-English translations., Comment: Published in WMT 2024. Low-Resource Indic Language Translation Shared Task

Partial-differential-equation (PDE)-constrained optimization is a well-worn technique for acquiring optimal parameters of systems governed by PDEs. However, this approach is limited to providing a single set of optimal parameters per optimization. Given a differentiable PDE solver, if the free parameters are reparameterized as the output of a neural network, that neural network can be trained to learn a map from a probability distribution to the distribution of optimal parameters. This proves useful in the case where there are many well performing local minima for the PDE. We apply this technique to train a neural network that generates optimal parameters that minimize laser-plasma instabilities relevant to laser fusion and show that the neural network generates many well performing and diverse minima., Comment: Accepted to D3S3: Data-driven and Differentiable Simulations, Surrogates, and Solvers - Workshop @ NeurIPS 2024

Training neural networks is computationally heavy and energy-intensive. Many methodologies were developed to save computational requirements and energy by reducing the precision of network weights at inference time and introducing techniques such as rounding, stochastic rounding, and quantization. However, most of these techniques still require full gradient precision at training time, which makes training such models prohibitive on edge devices. This work presents a novel technique for training neural networks without needing gradients. This enables a training process where all the weights are one or two bits, without any hidden full precision computations. We show that it is possible to train models without gradient-based optimization techniques by identifying erroneous contributions of each neuron towards the expected classification and flipping the relevant bits using logical operations. We tested our method on several standard datasets and achieved performance comparable to corresponding gradient-based baselines with a fraction of the compute power.

Contrary to on-road autonomous navigation, off-road autonomy is complicated by various factors ranging from sensing challenges to terrain variability. In such a milieu, data-driven approaches have been commonly employed to capture intricate vehicle-environment interactions effectively. However, the success of data-driven methods depends crucially on the quality and quantity of data, which can be compromised by large variability in off-road environments. To address these concerns, we present a novel workflow to recreate the exact vehicle and its target operating conditions digitally for domain-specific data generation. This enables us to effectively model off-road vehicle dynamics from simulation data using the Koopman operator theory, and employ the obtained models for local motion planning and optimal vehicle control. The capabilities of the proposed methodology are demonstrated through an autonomous navigation problem of a 1:5 scale vehicle, where a terrain-informed planner is employed for global mission planning. Results indicate a substantial improvement in off-road navigation performance with the proposed algorithm (5.84x) and underscore the efficacy of digital twinning in terms of improving the sample efficiency (3.2x) and reducing the sim2real gap (5.2%).

Advances in CAD and CAM have enabled engineers and design teams to digitally design parts with unprecedented ease. Software solutions now come with a range of modules for optimizing designs for performance requirements, generating instructions for manufacturing, and digitally tracking the entire process from design to procurement in the form of product life-cycle management tools. However, existing solutions force design teams and corporations to take a primarily serial approach where manufacturing and procurement decisions are largely contingent on design, rather than being an integral part of the design process. In this work, we propose a new approach to part making where design, manufacturing, and supply chain requirements and resources can be jointly considered and optimized. We present the Generative Manufacturing compiler that accepts as input the following: 1) An engineering part requirements specification that includes quantities such as loads, domain envelope, mass, and compliance, 2) A business part requirements specification that includes production volume, cost, and lead time, 3) Contextual knowledge about the current manufacturing state such as availability of relevant manufacturing equipment, materials, and workforce, both locally and through the supply chain. Based on these factors, the compiler generates and evaluates manufacturing process alternatives and the optimal derivative designs that are implied by each process, and enables a user guided iterative exploration of the design space. As part of our initial implementation of this compiler, we demonstrate the effectiveness of our approach on examples of a cantilever beam problem and a rocket engine mount problem and showcase its utility in creating and selecting optimal solutions according to the requirements and resources.

Automating suturing during robotically-assisted surgery reduces the burden on the operating surgeon, enabling them to focus on making higher-level decisions rather than fatiguing themselves in the numerous intricacies of a surgical procedure. Accurate suture thread reconstruction and grasping are vital prerequisites for suturing, particularly for avoiding entanglement with surgical tools and performing complex thread manipulation. However, such methods must be robust to heavy perceptual degradation resulting from heavy noise and thread feature sparsity from endoscopic images. We develop a reconstruction algorithm that utilizes quadratic programming optimization to fit smooth splines to thread observations, satisfying reliability bounds estimated from measured observation noise. Additionally, we craft a grasping policy that generates gripper trajectories that maximize the probability of a successful grasp. Our full image-to-grasp pipeline is rigorously evaluated with over 400 grasping trials, exhibiting state-of-the-art accuracy. We show that this strategy can be applied to the various techniques in autonomous suture needle manipulation to achieve autonomous surgery in a generalizable way., Comment: 8 pages, 6 figures, Submitted to RAL

Large Language Models (LLMs) and strong vision models have enabled rapid research and development in the field of Vision-Language-Action models that enable robotic control. The main objective of these methods is to develop a generalist policy that can control robots with various embodiments. However, in industrial robotic applications such as automated assembly and disassembly, some tasks, such as insertion, demand greater accuracy and involve intricate factors like contact engagement, friction handling, and refined motor skills. Implementing these skills using a generalist policy is challenging because these policies might integrate further sensory data, including force or torque measurements, for enhanced precision. In our method, we present a global control policy based on LLMs that can transfer the control policy to a finite set of skills that are specifically trained to perform high-precision tasks through dynamic context switching. The integration of LLMs into this framework underscores their significance in not only interpreting and processing language inputs but also in enriching the control mechanisms for diverse and intricate robotic operations.

We study the noncommutative rank problem, ncRANK, of computing the rank of matrices with linear entries in $n$ noncommuting variables and the problem of noncommutative Rational Identity Testing, RIT, which is to decide if a given rational formula in $n$ noncommuting variables is zero on its domain of definition. Motivated by the question whether these problems have deterministic NC algorithms, we revisit their interrelationship from a parallel complexity point of view. We show the following results: 1. Based on Cohn's embedding theorem \cite{Co90,Cohnfir} we show deterministic NC reductions from multivariate ncRANK to bivariate ncRANK and from multivariate RIT to bivariate RIT. 2. We obtain a deterministic NC-Turing reduction from bivariate $\RIT$ to bivariate ncRANK, thereby proving that a deterministic NC algorithm for bivariate ncRANK would imply that both multivariate RIT and multivariate ncRANK are in deterministic NC., Comment: 31 pages

With the increasing emphasis on machine learning and artificial intelligence to drive knowledge discovery in the agricultural sciences, spatial internet of things (IoT) technologies have become increasingly important for collecting real-time, high resolution data for these models. However, managing large fleets of devices while maintaining high data quality remains an ongoing challenge as scientists iterate from prototype to mature end-to-end applications. Here, we provide a set of case studies using the framework of technology readiness levels for an open source spatial IoT system. The spatial IoT systems underwent 3 major and 14 minor system versions, had over 2,727 devices manufactured both in academic and commercial contexts, and are either in active or planned deployment across four continents. Our results show the evolution of a generalizable, open source spatial IoT system designed for agricultural scientists, and provide a model for academic researchers to overcome the challenges that exist in going from one-off prototypes to thousands of internet-connected devices., Comment: 20 pages, 5 figures, 1 table

We experimentally study the transient dynamics of a dissipative superconducting qubit under periodic drive towards its nonequilibrium steady states. The corresponding stroboscopic evolution, given by the qubit states at times equal to integer multiples of the drive period, is determined by a (generically non-Hermitian) Floquet Liouvillian. The drive period controls both the transients across its non-Hermitian degeneracies and the resulting nonequilibrium steady states. These steady states can exhibit higher purity compared to those achieved with a constant drive. We further study the dependence of the steady states on the direction of parameter variation and relate these findings to the recent studies of dynamically encircling exceptional points. Our work provides a new approach to control non-Hermiticity in dissipative quantum systems and presents a new paradigm in quantum state preparation and stabilization., Comment: 9 pages, 8 figures

In the field of robotics and automation, conventional object recognition and instance segmentation methods face a formidable challenge when it comes to perceiving Deformable Linear Objects (DLOs) like wires, cables, and flexible tubes. This challenge arises primarily from the lack of distinct attributes such as shape, color, and texture, which calls for tailored solutions to achieve precise identification. In this work, we propose a foundation model-based DLO instance segmentation technique that is text-promptable and user-friendly. Specifically, our approach combines the text-conditioned semantic segmentation capabilities of CLIPSeg model with the zero-shot generalization capabilities of Segment Anything Model (SAM). We show that our method exceeds SOTA performance on DLO instance segmentation, achieving a mIoU of $91.21\%$. We also introduce a rich and diverse DLO-specific dataset for instance segmentation.

We explore the undamped response of step-voltage driven parallel plates and fixed-fixed microbeams. We consider a third order correction in the parallel plate system as a reduced order system to model mid-plane stretching in fixed-fixed beams. In both cases, we employ energy methods to determine the threshold values displacement and voltage. This is the point beyond which there is no oscillatory motion. The dynamic pull-in parameters of the corresponding microactuator model are identified as these critical values. We thoroughly analyze the effects of mid-plane stretching in fixed-fixed microbeams. Additionally, the phase portraits for these actuators are also thoroughly examined. Empirical relations for the oscillation period/switching time for these microactuators are also developed. These results correlate to a high accuracy to previously published results., Comment: 6 pages, 10 figures

Widely used alignment techniques, such as reinforcement learning from human feedback (RLHF), rely on the ability of humans to supervise model behavior - for example, to evaluate whether a model faithfully followed instructions or generated safe outputs. However, future superhuman models will behave in complex ways too difficult for humans to reliably evaluate; humans will only be able to weakly supervise superhuman models. We study an analogy to this problem: can weak model supervision elicit the full capabilities of a much stronger model? We test this using a range of pretrained language models in the GPT-4 family on natural language processing (NLP), chess, and reward modeling tasks. We find that when we naively finetune strong pretrained models on labels generated by a weak model, they consistently perform better than their weak supervisors, a phenomenon we call weak-to-strong generalization. However, we are still far from recovering the full capabilities of strong models with naive finetuning alone, suggesting that techniques like RLHF may scale poorly to superhuman models without further work. We find that simple methods can often significantly improve weak-to-strong generalization: for example, when finetuning GPT-4 with a GPT-2-level supervisor and an auxiliary confidence loss, we can recover close to GPT-3.5-level performance on NLP tasks. Our results suggest that it is feasible to make empirical progress today on a fundamental challenge of aligning superhuman models.

Spin waves (magnons) can enable wave-based neuromorphic computing by which one aims at overcoming limitations inherent to conventional electronics and the von Neumann architecture. In this study, we explore the storage of magnon signals and the magnetization switching of periodic and aperiodic arrays of Ni81Fe19 (Py) nanostripes with widths (w) between 50 nm and 200 nm. Spin waves excited with low microwave power in yttrium iron garnet induce the reversal of the nanostripes of different w in a small opposing field. Exploiting microwave-to-magnon transducers for magnon modes with ultrashort wavelengths, we demonstrate the reversal of 50-nm-wide Py nanostripes by magnons with wavelength ~ 100 nm after they have propagated over 25 micrometer in YIG. The findings are important for designing a magnon-based in-memory computing device.

Waveguide lattices offer a compact and stable platform for a range of applications, including quantum walks, topological effects, condensed matter system simulation, and classical and quantum information processing. In such lattices, the Hamiltonian's hopping and on-site terms determine the optical evolution, which can be engineered using waveguide spacing and refractive index profile. While waveguide lattices have been realized in various photonic platforms, these devices have always been static and designed for specific applications. We present a programmable waveguide array in which the Hamiltonian terms can be electro-optically tuned to implement various Hamiltonian continuous-time evolutions on a single device. We used a single array with 11 waveguides in lithium niobate, controlled via 22 electrodes, to perform a range of experiments that realized the Su-Schriffer-Heeger model, the Aubrey-Andre model, and Anderson localization, which is equivalent to over 2500 static devices. Our architecture's micron-scale local electric fields independently control waveguide coupling coefficients and effective indices, which overcomes cross-talk limitations of thermo-optic phase shifters in other platforms such as silicon, silicon-nitride, and silica. Electro-optic control allows for ultra-fast and more precise reconfigurability with lower power consumption, and with quantum input states, our platform can enable the study of multiple condensed matter quantum dynamics with a single device.

Open systems with balanced gain and loss, described by parity-time PT-symmetric Hamiltonians have been deeply explored over the past decade. Most explorations are limited to finite discrete models (in real or reciprocal spaces) or continuum problems in one dimension. As a result, these models do not leverage the complexity and variability of two-dimensional continuum problems on a compact support. Here, we investigate eigenvalues of the Schrodinger equation on a disk with zero boundary condition, in the presence of constant, PT-symmetric, gain-loss potential that is confined to two mirror-symmetric disks. We find a rich variety of exceptional points, re-entrant PT-symmetric phases, and a non-monotonic dependence of the PT-symmetry breaking threshold on the system parameters. By comparing results of two model variations, we show that this simple model of a multi-core fiber supports propagating modes in the presence of gain and loss.

Over the past decade classical optical systems with gain or loss, modelled by non-Hermitian parity-time symmetric Hamiltonians, have been deeply investigated. Yet, their applicability to the quantum domain with number-resolved photonic states is fundamentally voided by quantum-limited amplifier noise. Here, we show that second-quantised Hermitian Hamiltonians on the Fock space give rise to non-Hermitian effective Hamiltonians that generate the dynamics of corresponding creation and annihilation operators. Using this equivalence between $\mathcal{PT}$-symmetry and symplectic Bogoliubov transformations, we create a quantum optical scheme comprising squeezing, phase-shifters, and beam-splitters for simulating arbitrary non-unitary processes by way of singular value decomposition. In contrast to the post-selection scheme for non-Hermitian quantum simulation, the success probability in this approach is independent of the system size or simulation time, and can be efficiently Trotterised similar to a unitary transformation., Comment: 7 pages, 1 figure

Thermodynamics constrains changes to the energy of a system, both deliberate and random, via its first and second laws. When the system is not in equilibrium, fluctuation theorems such as the Jarzynski equality further restrict the distributions of deliberate work done. Such fluctuation theorems have been experimentally verified in small, non-equilibrium quantum systems undergoing unitary or decohering dynamics. Yet, their validity in systems governed by a non-Hermitian Hamiltonian has long been contentious, due to the false premise of the Hamiltonian's dual and equivalent roles in dynamics and energetics. Here we show that work fluctuations in a non-Hermitian qubit obey the Jarzynski equality even if its Hamiltonian has complex or purely imaginary eigenvalues. With post-selection on a dissipative superconducting circuit undergoing a cyclic parameter sweep, we experimentally quantify the work distribution using projective energy measurements and show that the fate of the Jarzynski equality is determined by the parity-time symmetry of, and the energetics that result from, the corresponding non-Hermitian, Floquet Hamiltonian. By distinguishing the energetics from non-Hermitian dynamics, our results provide the recipe for investigating the non-equilibrium quantum thermodynamics of such open systems., Comment: 7 pages, 5 figures

To increase mobile user engagement, current apps employ a variety of behavioral nudges, but these engagement techniques are applied in a one-size-fits-all approach. Yet the very same techniques may be perceived differently by different individuals. To test this, we developed HarrySpotter, a location-based AR app that embedded six engagement techniques. We deployed it in a 2-week study involving 29 users who also took the Big-Five personality test. Preferences for specific engagement techniques are not only descriptive but also predictive of personality traits. The Adj. $R^2$ ranges from 0.16 for conscientious users (encouraged by competition) to 0.32 for neurotic users (self-centered and focused on their own achievements), and even up to 0.61 for extroverts (motivated by both exploration of objects and places). These findings suggest that these techniques need to be personalized in the future., Comment: 10 pages, 1 figure, 2 tables

Solving fluid dynamics equations often requires the use of closure relations that account for missing microphysics. For example, when solving equations related to fluid dynamics for systems with a large Reynolds number, sub-grid effects become important and a turbulence closure is required, and in systems with a large Knudsen number, kinetic effects become important and a kinetic closure is required. By adding an equation governing the growth and transport of the quantity requiring the closure relation, it becomes possible to capture microphysics through the introduction of ``hidden variables'' that are non-local in space and time. The behavior of the ``hidden variables'' in response to the fluid conditions can be learned from a higher fidelity or ab-initio model that contains all the microphysics. In our study, a partial differential equation simulator that is end-to-end differentiable is used to train judiciously placed neural networks against ground-truth simulations. We show that this method enables an Euler equation based approach to reproduce non-linear, large Knudsen number plasma physics that can otherwise only be modeled using Boltzmann-like equation simulators such as Vlasov or Particle-In-Cell modeling.

The next generation of high-power lasers enables repetition of experiments at orders of magnitude higher frequency than was possible using the prior generation. Facilities requiring human intervention between laser repetitions need to adapt in order to keep pace with the new laser technology. A distributed networked control system can enable laboratory-wide automation and feedback control loops. These higher-repetition-rate experiments will create enormous quantities of data. A consistent approach to managing data can increase data accessibility, reduce repetitive data-software development, and mitigate poorly organized metadata. An opportunity arises to share knowledge of improvements to control and data infrastructure currently being undertaken. We compare platforms and approaches to state-of-the-art control systems and data management at high-power laser facilities, and we illustrate these topics with case studies from our community., Comment: In press at High Power Laser Science and Engineering (2023), in special issue on "Future Control Systems and Machine Learning at High Power Laser Facilities." This Arxiv version is formatted for easy readability (single-column, 1.3x line spacing). Document navigation is available from the PDF sidebar, under "Bookmarks". 39 pages including references, 8 figures

We propose conditioning field initialization for neural network based topology optimization. In this work, we focus on (1) improving upon existing neural network based topology optimization, (2) demonstrating that by using a prior initial field on the unoptimized domain, the efficiency of neural network based topology optimization can be further improved. Our approach consists of a topology neural network that is trained on a case by case basis to represent the geometry for a single topology optimization problem. It takes in domain coordinates as input to represent the density at each coordinate where the topology is represented by a continuous density field. The displacement is solved through a finite element solver. We employ the strain energy field calculated on the initial design domain as an additional conditioning field input to the neural network throughout the optimization. The addition of the strain energy field input improves the convergence speed compared to standalone neural network based topology optimization.

We propose a direct mesh-free method for performing topology optimization by integrating a density field approximation neural network with a displacement field approximation neural network. We show that this direct integration approach can give comparable results to conventional topology optimization techniques, with an added advantage of enabling seamless integration with post-processing software, and a potential of topology optimization with objectives where meshing and Finite Element Analysis (FEA) may be expensive or not suitable. Our approach (DMF-TONN) takes in as inputs the boundary conditions and domain coordinates and finds the optimum density field for minimizing the loss function of compliance and volume fraction constraint violation. The mesh-free nature is enabled by a physics-informed displacement field approximation neural network to solve the linear elasticity partial differential equation and replace the FEA conventionally used for calculating the compliance. We show that using a suitable Fourier Features neural network architecture and hyperparameters, the density field approximation neural network can learn the weights to represent the optimal density field for the given domain and boundary conditions, by directly backpropagating the loss gradient through the displacement field approximation neural network, and unlike prior work there is no requirement of a sensitivity filter, optimality criterion method, or a separate training of density network in each topology optimization iteration.

Quantum theory provides rules governing much of the microscopic world, and among its counter-intuitive consequences are correlations that exceed the bounds from local, classical theories. In two-level quantum systems - qubits - unitary dynamics theoretically limit these spatiotemporal quantum correlations, called Bell/Clauser-Horn-Shimony-Holt or Leggett-Garg inequalities, to $2\sqrt{2}$ or 1.5 respectively. Experiments with state-of-the-art qubits have approached the spatial, Bell and temporal, Leggett-Garg quantum correlation bounds. Here, using a dissipative, trapped $^{40}$Ca$^+$ ion governed by a two-level, non-Hermitian Hamiltonian, we observe temporal correlation values up to 1.703(4) for the Leggett-Garg parameter $K_3$, clearly exceeding the hitherto inviolable L\"{u}der's bound of 1.5. These excesses occur across the exceptional point of the parity-time symmetric Hamiltonian responsible for the qubit's non-unitary, coherent dynamics. Distinct evolution speeds for antipodal qubit states, which violate the unified (Mendelstam-Tamm or Margolus-Levitin) bound $\tau_{\textrm{QSL}}$ for the transit time based on quantum speed limit, result in the super-quantum $K_3$ values observed over a wide parameter range. Our results demonstrate that post-selected, coherent dynamics of non-Hermitian Hamiltonians pave the way for enhanced quantum correlations that exceed protocols based on unitary or dissipative dynamics., Comment: 9 pages, 4 figures

Since the realization of quantum systems described by non-Hermitian Hamiltonians with parity-time (PT) symmetry, interest in non-Hermitian, quantum many-body models has steadily grown. Most studies to-date map to traditional quantum spin models with a non-Hermiticity that arises from making the model parameters complex or purely imaginary. Here, we present a new set of models with non-Hermiticity generated by splitting a Hermitian term into two Jordan-normal form parts, and the perturbations are confined to one or two sites. We present exact diagonalization results for the PT-threshold in such models, and provide an analytical approach for understanding the numerical results. Surprisingly, with non-Hermitian potentials confined to two or even a single site, we find a robust PT threshold that seems insensitive to the size of the quantum spin chain. Our results provide a pathway to experimentally feasible non-Hermitian quantum spin chains where the confluence of many-body effects and non-Hermiticity effects can be observed.

Based on a theorem of Bergman we show that multivariate noncommutative polynomial factorization is deterministic polynomial-time reducible to the factorization of bivariate noncommutative polynomials. More precisely, we show the following: (1) In the white-box setting, given an n-variate noncommutative polynomial f in F over a field F (either a finite field or the rationals) as an arithmetic circuit (or algebraic branching program), computing a complete factorization of f is deterministic polynomial-time reducible to white-box factorization of a noncommutative bivariate polynomial g in F; the reduction transforms f into a circuit for g (resp. ABP for g), and given a complete factorization of g the reduction recovers a complete factorization of f in polynomial time. We also obtain a similar deterministic polynomial-time reduction in the black-box setting. (2) Additionally, we show over the field of rationals that bivariate linear matrix factorization of 4 x 4 matrices is at least as hard as factoring square-free integers. This indicates that reducing noncommutative polynomial factorization to linear matrix factorization (as done in our recent work [AJ22]) is unlikely to succeed over the field of rationals even in the bivariate case. In contrast, multivariate linear matrix factorization for 3 x 3 matrices over rationals is in polynomial time.

Non-Hermitian, tight-binding $\mathcal{PT}$-symmetric models are extensively studied in the literature. Here, we investigate two forms of non-Hermitian Hamiltonians to study the $\mathcal{PT}$-symmetry breaking thresholds and features of corresponding surfaces of exceptional points (EPs). They include one-dimensional chains with uniform or 2-periodic tunnelling amplitudes, one pair of balanced gain and loss potentials $\Delta\pm\i\gamma$ at parity-symmetric sites, and periodic or open boundary conditions. By introducing a Hermitian detuning potential, we obtain the dependence of the $\mathcal{PT}$-threshold, and therefore the exceptional-point curves, in the parameter space of detuning and gain-loss strength. By considering several such examples, we show that EP curves of a given order generically have cusp-points where the order of the EP increases by one. In several cases, we obtain explicit analytical expressions for positive-definite intertwining operators that can be used to construct a complex extension of quantum theory by re-defining the inner product. Taken together, our results provide a detailed understanding of detuned tight-binding models with a pair of gain-loss potentials., Comment: 27 pages, 5 figures

Exceptional points (EPs) are degeneracies of non-Hermitian systems, where both eigenvalues and eigenvectors coalesce. Classical and quantum systems exhibiting high-order EPs have recently been identified as fundamental building blocks for the development of novel, ultra-sensitive opto-electronic devices. However, arguably one of their major drawbacks is that they rely on non-linear amplification processes that could limit their potential applications, particularly in the quantum realm. In this work, we show that high-order EPs can be designed by means of linear, time-modulated, chain of inductively coupled RLC (where R stands for resistance, L for inductance, and C for capacitance) electronic circuits. With a general theory, we show that $N$ coupled circuits with $2N$ dynamical variables and time-dependent parameters can be mapped onto an $N$-site, time-dependent, non-Hermitian Hamiltonian, and obtain constraints for $\mathcal{PT}$-symmetry in such models. With numerical calculations, we obtain the Floquet exceptional contours of order $N$ by studying the energy dynamics in the circuit. Our results pave the way toward realizing robust, arbitrary-order EPs by means of synthetic gauge fields, with important implications for sensing, energy transfer, and topology.

The dense environment of neutron stars makes them an excellent target for probing dark matter interactions with the Standard Model. We study neutron star heating from capture of inelastic dark matter, which can evade direct detection constraints. We investigate kinematics of the inelastic scattering process between quasirelativistic dark matter particles and ultrarelativistic targets in neutron stars, and derive analytical expressions for the maximal mass gap allowed for the scattering to occur. We implement them into a fully relativistic formalism for calculating the capture rate and apply it to various scenarios of inelastic dark matter. The projected constraints from neutron stars can systematically surpass those from terrestrial searches, including direct detection and collider experiments. Neutron stars can also be sensitive to the parameter space of inelastic self-interacting dark matter. Our results indicate that extreme astrophysical environments, such as neutron stars, are an important target for searching dark matter., Comment: 25 pages, 6 figures

Hermitian Hamiltonians with time-periodic coefficients can be analyzed via Floquet theory, and have been extensively used for engineering Floquet Hamiltonians in standard quantum simulators. Generalized to non-Hermitian Hamiltonians, time-periodicity offers avenues to engineer the landscape of Floquet quasi-energies across the complex plane. We investigate two-level non-Hermitian Hamiltonians with coefficients that have different periodicities using Floquet theory. By analytical and numerical calculations, we obtain their regions of stability, defined by real Floquet quasi-energies, and contours of exceptional point (EP) degeneracies. We extend our analysis to study the phases that accompany the cyclic changes. Our results demonstrate that time-periodic, non-Hermitian Hamiltonians generate a rich landscape of stable and unstable regions.

The strength of social relations has been shown to affect an individual's access to opportunities. To date, however, the correspondence between tie strength and population's economic prospects has not been quantified, largely because of the inability to operationalise strength based on Granovetter's classic theory. Our work departed from the premise that tie strength is a unidimensional construct (typically operationalized with frequency or volume of contact), and used instead a validated model of ten fundamental dimensions of social relationships grounded in the literature of social psychology. We built state-of-the-art NLP tools to infer the presence of these dimensions from textual communication, and analyzed a large conversation network of 630K geo-referenced Reddit users across the entire US connected by 12.8M social ties created over the span of 7 years. We found that unidimensional tie strength is only weakly correlated with economic opportunities (R2=0.30), while multidimensional constructs are highly correlated (R2=0.62). In particular, economic opportunities are associated to the combination of: i) knowledge ties, which bridge geographically distant groups, facilitating the knowledge dissemination across communities; and ii) social support ties, which knit geographically close communities together, and represent dependable sources of social and emotional support. These results point to the importance of developing high-quality measures of tie strength in network theory., Comment: Main paper: 11 pages, 4 figures, 2 tables. Supplementary Information: 6 pages, 5 figures, 4 tables