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In this paper, we address a longstanding challenge in self-organized criticality (SOC) systems: establishing a connection between sandpiles and complex networks. Our approach employs a similarity-based transfer function characterized by two parameters, $\mathcal{R}=(r_1, r_2)$. Here, $r_1$ quantifies the similarity of local activities, while $r_2$ governs the filtration process used to convert a weighted network into a binary one. We reveal that the degree centrality distribution of the resulting network follows a generalized Gamma distribution (GGD), which transitions to a power-law distribution under specific conditions. The GGD exponents, estimated numerically, exhibit a dependency on $\mathcal{R}$. Notably, while both decreasing $r_1$ and $r_2$ lead to denser networks, $r_2$ plays a more significant role in influencing network density. Furthermore, the Shannon entropy is observed to decrease linearly with increasing $r_2$, whereas its variation with $r_1$ is more gradual. An analytical expression for the Shannon entropy is proposed. To characterize the network structure, we investigate the clustering coefficient ($cc$), eigenvalue centrality ($e$), closeness centrality ($c$), and betweenness centrality ($b$). The distributions of $cc$, $e$, and $c$ exhibit peaked profiles, while $b$ displays a power-law distribution over a finite interval of $k$. Additionally, we explore correlations between the exponents and identify a specific parameter regime of $\mathcal{R}$ and $k$ where the $e-k$, $c-k$, and $b-k$ correlations become negative.

Context. Supernova remnants are one potential source class considered a PeVatron (i.e. capable of accelerating cosmic rays above PeV energies). The shock fronts produced after the explosion of the supernova are ideal regions for particle acceleration. IC 443 is a supernova remnant that has been studied extensively at different wavelengths. We study this region using very-high-energy gamma-ray data. Aims. We explore the region of IC 443 using 2966 days of gamma-ray data from the HAWC observatory. We study the emission of this supernova remnant and search for signatures that would show acceleration of (hadronic) cosmic rays at the PeV range. Methods. We use the maximum likelihood estimation and a likelihood ratio test to perform a multi-source fitting search. We find the best-fit morphology and spectrum of the IC 443 region above $\sim$300 GeV that best describes the HAWC data. Results. We observe a point source located at ($\alpha$=94.42$^{\circ}$, $\delta$=22.35$^{\circ}$) that we associate with IC 443. The measured spectrum is a simple power law with an index of -3.14$\pm$0.18, which is consistent with previous TeV observations. We also find a new extended component in the region whose emission is described by a simple power law with an index of -2.49$\pm$0.08 and which we call HAWC J0615+2213. Conclusions. Although we cannot confirm that IC 443 is a hadronic PeVatron, we do not find any sign that the spectrum has a cut off at tens of TeV energies, with the spectrum extending to $\sim$30 TeV. Furthermore, we find a new extended source in the region. While we show evidence that this new source might be a new TeV halo, we defer a detailed analysis of this new source to another publication.

Data encoding is a fundamental step in emerging computing paradigms, particularly in stochastic computing (SC) and hyperdimensional computing (HDC), where it plays a crucial role in determining the overall system performance and hardware cost efficiency. This study presents an advanced encoding strategy that leverages a hardware-friendly class of low-discrepancy (LD) sequences, specifically powers-of-2 bases of Van der Corput (VDC) sequences (VDC-2^n), as sources for random number generation. Our approach significantly enhances the accuracy and efficiency of SC and HDC systems by addressing challenges associated with randomness. By employing LD sequences, we improve correlation properties and reduce hardware complexity. Experimental results demonstrate significant improvements in accuracy and energy savings for SC and HDC systems. Our solution provides a robust framework for integrating SC and HDC in resource-constrained environments, paving the way for efficient and scalable AI implementations., Comment: 5 pages, 3 figures, 4 tables

In this paper, we explore the higher- and lower-order connectivity aspects of the visibility graph representation of sandpile models, focusing on the Bak-Tang-Wiesenfeld (BTW) model. By converting the time series of avalanche events into visibility graphs, we investigate the structural properties that emerge at different scales of connectivity. Specifically, we utilize persistent homology and simplicial complex theory to identify higher-order topological features. Analyzing the statistics of degree and betweenness centralities reveal that the resulting graph is a scale-free network with the degree exponent of $\gamma_k=2.50\pm 0.02$ and betweenness exponent of $\gamma_b=1.585\pm 0.008$. The analysis of the simplexes show that the distribution function of one, two and three dimensional simplexes are power-law with the exponents of $\gamma_{\sigma_1}=0.795\pm 0.006$, $\gamma_{\sigma_2}=0.602\pm 0.009$ and $\gamma_{\sigma_3}=0.422\pm 0.008$ respectively. This power-law behavior is also seen in the homology group analysis, for the Betti numbers, the exponents of which are reported in the paper. The persistent entropy of life time of $d$ dimensional holes is analyzed indicating that it increases logarithmically in terms of the network size $N$ for $d=0,1$ and $2$.

Neuro-symbolic Artificial Intelligence (AI) models, blending neural networks with symbolic AI, have facilitated transparent reasoning and context understanding without the need for explicit rule-based programming. However, implementing such models in the Internet of Things (IoT) sensor nodes presents hurdles due to computational constraints and intricacies. In this work, for the first time, we propose a near-sensor neuro-symbolic AI computing accelerator named Neuro-Photonix for vision applications. Neuro-photonix processes neural dynamic computations on analog data while inherently supporting granularity-controllable convolution operations through the efficient use of photonic devices. Additionally, the creation of an innovative, low-cost ADC that works seamlessly with photonic technology removes the necessity for costly ADCs. Moreover, Neuro-Photonix facilitates the generation of HyperDimensional (HD) vectors for HD-based symbolic AI computing. This approach allows the proposed design to substantially diminish the energy consumption and latency of conversion, transmission, and processing within the established cloud-centric architecture and recently designed accelerators. Our device-to-architecture results show that Neuro-Photonix achieves 30 GOPS/W and reduces power consumption by a factor of 20.8 and 4.1 on average on neural dynamics compared to ASIC baselines and photonic accelerators while preserving accuracy., Comment: 12 pages, 15 figures

Accurate and timely regional weather prediction is vital for sectors dependent on weather-related decisions. Traditional prediction methods, based on atmospheric equations, often struggle with coarse temporal resolutions and inaccuracies. This paper presents a novel machine learning (ML) model, called MiMa (short for Micro-Macro), that integrates both near-surface observational data from Kentucky Mesonet stations (collected every five minutes, known as Micro data) and hourly atmospheric numerical outputs (termed as Macro data) for fine-resolution weather forecasting. The MiMa model employs an encoder-decoder transformer structure, with two encoders for processing multivariate data from both datasets and a decoder for forecasting weather variables over short time horizons. Each instance of the MiMa model, called a modelet, predicts the values of a specific weather parameter at an individual Mesonet station. The approach is extended with Re-MiMa modelets, which are designed to predict weather variables at ungauged locations by training on multivariate data from a few representative stations in a region, tagged with their elevations. Re-MiMa (short for Regional-MiMa) can provide highly accurate predictions across an entire region, even in areas without observational stations. Experimental results show that MiMa significantly outperforms current models, with Re-MiMa offering precise short-term forecasts for ungauged locations, marking a significant advancement in weather forecasting accuracy and applicability.

We propose a novel paradigm for modeling real-world scale-free networks, where the integration of new nodes is driven by the combined attractiveness of degree and betweenness centralities, the competition of which (expressed by a parameter $0\le p\le 1$) shapes the structure of the evolving network. We reveal the ability to seamlessly explore a vast landscape of scale-free networks, unlocking an entirely new class of complex networks that we call \textit{stars-with-filament} structure. Remarkably, the average degree $\bar k$ of these networks grows like $\log t$ to some power, where $t$ is time and the average shortest path length grows logarithmically with the system size for intermediate $p$ values, offering fresh insights into the structural dynamics of scale-free systems. Our approach is backed by a robust mean-field theory, which nicely captures the dynamics of $\bar{k}$. We further unveil a rich, $p$-dependent phase diagram, encompassing 47 real-world scale-free networks, shedding light on previously hidden patterns. This work opens exciting new avenues for understanding the universal properties of complex networks.

Animals, especially insects, navigate their environments using complex strategies that integrate responses to chemical signals such as pheromones. The relative importance an insect places on foraging, finding a mate or other tasks can significantly influence its movement patterns. This study uncovers the distinct exploration strategies that emerge when these priorities vary. A new model is introduced that explicitly treats a pair of insects and their response to each other's pheromones. The strategy results in dynamics that exhibit characteristic anomalous scaling in displacement and non-Gaussian distributions of position; specifically, compressed exponential distributions for the number of encounters and the total duration of encounters. Our model not only elucidates these emergent behaviours but also provides insight into optimizing encounter frequencies. These strategies can be inverted to design pheromone-based traps for luring target species to specific areas for removal. The model is also applicable more broadly to pairs of agents that both respond to the paths traced by themselves and each other., Comment: 22 pages including 7 figures and 2 tables; and 7 additional pages of supplementary information

Classical optimization of parameterized quantum circuits is a widely studied methodology for the preparation of complex quantum states, as well as the solution of machine learning and optimization problems. However, it is well known that many proposed parameterized quantum circuit architectures suffer from drawbacks which limit their utility, such as their classical simulability or the hardness of optimization due to a problem known as "barren plateaus". We propose and study a class of dynamic parameterized quantum circuit architectures. These are parameterized circuits containing intermediate measurements and feedforward operations. In particular, we show that these architectures: 1. Provably do not suffer from barren plateaus. 2. Are expressive enough to describe arbitrarily deep unitary quantum circuits. 3. Are competitive with state of the art methods for the preparation of ground states and facilitate the representation of nontrivial thermal states. These features make the proposed architectures promising candidates for a variety of applications., Comment: 50 pages, 11 figures

In this paper, we address the challenge of certifying the performance of a machine learning model on an unseen target network, using measurements from an available source network. We focus on a scenario where heterogeneous datasets are distributed across a source network of clients, all connected to a central server. Specifically, consider a source network "A" composed of $K$ clients, each holding private data from unique and heterogeneous distributions, which are assumed to be independent samples from a broader meta-distribution $\mu$. Our goal is to provide certified guarantees for the model's performance on a different, unseen target network "B," governed by another meta-distribution $\mu'$, assuming the deviation between $\mu$ and $\mu'$ is bounded by either the Wasserstein distance or an $f$-divergence. We derive theoretical guarantees for the model's empirical average loss and provide uniform bounds on the risk CDF, where the latter correspond to novel and adversarially robust versions of the Glivenko-Cantelli theorem and the Dvoretzky-Kiefer-Wolfowitz (DKW) inequality. Our bounds are computable in polynomial time with a polynomial number of queries to the $K$ clients, preserving client privacy by querying only the model's (potentially adversarial) loss on private data. We also establish non-asymptotic generalization bounds that consistently converge to zero as both $K$ and the minimum client sample size grow. Extensive empirical evaluations validate the robustness and practicality of our bounds across real-world tasks., Comment: 40 pages

The aim of this paper is to address the challenge of gradual domain adaptation within a class of manifold-constrained data distributions. In particular, we consider a sequence of $T\ge2$ data distributions $P_1,\ldots,P_T$ undergoing a gradual shift, where each pair of consecutive measures $P_i,P_{i+1}$ are close to each other in Wasserstein distance. We have a supervised dataset of size $n$ sampled from $P_0$, while for the subsequent distributions in the sequence, only unlabeled i.i.d. samples are available. Moreover, we assume that all distributions exhibit a known favorable attribute, such as (but not limited to) having intra-class soft/hard margins. In this context, we propose a methodology rooted in Distributionally Robust Optimization (DRO) with an adaptive Wasserstein radius. We theoretically show that this method guarantees the classification error across all $P_i$s can be suitably bounded. Our bounds rely on a newly introduced {\it {compatibility}} measure, which fully characterizes the error propagation dynamics along the sequence. Specifically, for inadequately constrained distributions, the error can exponentially escalate as we progress through the gradual shifts. Conversely, for appropriately constrained distributions, the error can be demonstrated to be linear or even entirely eradicated. We have substantiated our theoretical findings through several experimental results., Comment: Published at Proceedings of Neural Information Processing Systems (NeurIPS) 2024

This paper presents Auriga Robotics' autonomous vehicle, developed at Shahid Beheshti University's Robotics and Intelligent Automation Lab, as part of the team's entry for the 2024 RoboCup IranOpen competition. The vehicle is a 1:10 scale car equipped with a custom-designed chassis, a stepper motor for precision, and a range of sensors for autonomous navigation. Key hardware includes ESP32 microcontrollers that manage motor control and sensor data acquisition. The software system integrates computer vision, including YOLOv8 for sign detection and PiNet for lane detection, combined with control algorithms such as the Stanley, PID, and Pure Pursuit controllers. The vehicle's design emphasizes real-time decision-making, environmental mapping, and efficient localization, ensuring its ability to navigate complex driving scenarios.

This paper proposes an observer-based event-driven approach to decrease the overuse of communication networks. The suggested approach aims to estimate the required data for sharing between units in line with as much communication reduction as possible. In other words, the proposed approach effectively determines which state variables should be shared (observer concept) among the units during specific time intervals (event-triggered concept). This strategy significantly reduces the overall communication load. It is shown that the estimation error remains bounded and Zeno behavior, characterized by an endless number of transmissions occurring within a limited time frame, does not occur. The proposed methodology can be systematically applied to any communication-based secondary controller in alternating current (AC) microgrids. Simulation results demonstrate a high degree of precision in estimating the states under the proposed approach. Also, the secondary controller performance under the proposed method is evaluated in MATLAB/Simulink environment., Comment: 2024 IEEE PES Innovative Smart Grid Technologies Europe (ISGT Europe)

Recent advancements in deep learning, particularly in medical imaging, have significantly propelled the progress of healthcare systems. However, examining the robustness of medical images against adversarial attacks is crucial due to their real-world applications and profound impact on individuals' health. These attacks can result in misclassifications in disease diagnosis, potentially leading to severe consequences. Numerous studies have explored both the implementation of adversarial attacks on medical images and the development of defense mechanisms against these threats, highlighting the vulnerabilities of deep neural networks to such adversarial activities. In this study, we investigate adversarial attacks on images associated with Alzheimer's disease and propose a defensive method to counteract these attacks. Specifically, we examine adversarial attacks that employ frequency domain transformations on Alzheimer's disease images, along with other well-known adversarial attacks. Our approach utilizes a convolutional neural network (CNN)-based autoencoder architecture in conjunction with the two-dimensional Fourier transform of images for detection purposes. The simulation results demonstrate that our detection and defense mechanism effectively mitigates several adversarial attacks, thereby enhancing the robustness of deep neural networks against such vulnerabilities., Comment: 10 pages, 4 figures, conference

Central charge is a fundamental quantity in conformal field theories (CFT), and plays a crucial role in determining universality classes of critical points in two-dimensional systems. Despite its significance, the measurement of central charge has remained elusive thus far. In this work, we present the first experimental determination of the central charge using a universal quantum processor. Using a classically optimized variational quantum circuit and employing advanced error mitigation techniques, we successfully prepare ground states of various $1+1D$ quantum spin chain models at their critical point. Leveraging the heavy-hex structure of IBM quantum processors, we are able to implement periodic boundary conditions and mitigate boundary effects. We then extract the central charge from the scaling behavior of the sub-leading term of R{\'{e}}nyi generalizations of classical Shannon entropy, computed for local Pauli measurements in the conformal bases ($\sigma^{z}$ and $\sigma^x$). The experimental results are consistent with the known central charge values for the transverse field Ising (TFI) chain ($c=0.5$) and the XXZ chain ($c=1$), achieving relative errors as low as 5 percent., Comment: 7 + 13 pages, 4 + 11 figures

Quantum phase transitions reveal deep insights into the behavior of many-body quantum systems, but identifying these transitions without well-defined order parameters remains a significant challenge. In this work, we introduce a novel approach to constructing phase diagrams using the vector field of the reduced fidelity susceptibility (RFS). This method maps quantum phases and formulates an optimization problem to discover observables corresponding to order parameters. We demonstrate the effectiveness of our approach by applying it to well-established models, including the Axial Next Nearest Neighbour Interaction (ANNNI) model, a cluster state model, and a chain of Rydberg atoms. By analyzing observable decompositions into eigen-projectors and finite-size scaling, our method successfully identifies order parameters and characterizes quantum phase transitions with high precision. Our results provide a powerful tool for exploring quantum phases in systems where conventional order parameters are not readily available.

The neutron-rich unbound fluorine isotope $^{30}$F$_{21}$ has been observed for the first time by measuring its neutron decay at the SAMURAI spectrometer (RIBF, RIKEN) in the quasi-free proton knockout reaction of $^{31}$Ne nuclei at 235 MeV/nucleon. The mass and thus one-neutron-separation energy of $^{30}$F has been determined to be $S_n = -472\pm 58 \mathrm{(stat.)} \pm 33 \mathrm{(sys.)}$ keV from the measurement of its invariant-mass spectrum. The absence of a sharp drop in $S_n$($^{30}$F) shows that the ``magic'' $N=20$ shell gap is not restored close to $^{28}$O, which is in agreement with our shell-model calculations that predict a near degeneracy between the neutron $d$ and $fp$ orbitals, with the $1p_{3/2}$ and $1p_{1/2}$ orbitals becoming more bound than the $0f_{7/2}$ one. This degeneracy and reordering of orbitals has two potential consequences: $^{28}$O behaves like a strongly superfluid nucleus with neutron pairs scattering across shells, and both $^{29,31}$F appear to be good two-neutron halo-nucleus candidates., Comment: 9 pages, 2 figures, accepted for publication in Physical Review Letters

Recent Baryon Acoustic Oscillation (BAO) measurements released by DESI, when combined with Cosmic Microwave Background (CMB) data from Planck and two different samples of Type Ia supernovae (Pantheon-Plus and DESY5) reveal a preference for Dynamical Dark Energy (DDE) characterized by a present-day quintessence-like equation of state that crossed into the phantom regime in the past. A core ansatz for this result is assuming a linear Chevallier-Polarski-Linder (CPL) parameterization $w(a) = w_0 + w_a (1-a)$ to describe the evolution of the DE equation of state (EoS). In this paper, we test if and to what extent this assumption impacts the results. To prevent broadening uncertainties in cosmological parameter inference and facilitate direct comparison with the baseline CPL case, we focus on 4 alternative well-known models that, just like CPL, consist of only two free parameters: the present-day DE EoS ($w_0$) and a parameter quantifying its dynamical evolution ($w_a$). We demonstrate that the preference for DDE remains robust regardless of the parameterization: $w_0$ consistently remains in the quintessence regime, while $w_a$ consistently indicates a preference for a dynamical evolution towards the phantom regime. This tendency is significantly strengthened by DESY5 SN measurements. By comparing the best-fit $\chi^2$ obtained within each DDE model, we notice that the linear CPL parameterization is not the best-fitting case. Among the models considered, the EoS proposed by Barboza and Alcaniz consistently leads to the most significant improvement., Comment: 44 pages, 7 figures, 7 tables. V2: additional references, more details and discussion on the results and their interpretation, added a new Appendix presenting additional constraints on interesting properties of the DE EoS across the different models analyzed. Version accepted for publication in JCAP

A spatiotemporal deep learning framework is proposed that is capable of 2D full-field prediction of fracture in concrete mesostructures. This framework not only predicts fractures but also captures the entire history of the fracture process, from the crack initiation in the interfacial transition zone to the subsequent propagation of the cracks in the mortar matrix. In addition, a convolutional neural network is developed which can predict the averaged stress-strain curve of the mesostructures. The UNet modeling framework, which comprises an encoder-decoder section with skip connections, is used as the deep learning surrogate model. Training and test data are generated from high-fidelity fracture simulations of randomly generated concrete mesostructures. These mesostructures include geometric variabilities such as different aggregate particle geometrical features, spatial distribution, and the total volume fraction of aggregates. The fracture simulations are carried out in Abaqus, utilizing the cohesive phase-field fracture modeling technique as the fracture modeling approach. In this work, to reduce the number of training datasets, the spatial distribution of three sets of material properties for three-phase concrete mesostructures, along with the spatial phase-field damage index, are fed to the UNet to predict the corresponding stress and spatial damage index at the subsequent step. It is shown that after the training process using this methodology, the UNet model is capable of accurately predicting damage on the unseen test dataset by using 470 datasets. Moreover, another novel aspect of this work is the conversion of irregular finite element data into regular grids using a developed pipeline. This approach allows for the implementation of less complex UNet architecture and facilitates the integration of phase-field fracture equations into surrogate models for future developments.

The measurements of the cosmic microwave background (CMB) have played a significant role in understanding the nature of dark energy. In this article, we investigate the dynamics of the dark energy equation of state, utilizing high-precision CMB data from multiple experiments. We begin by examining the Chevallier-Polarski-Linder (CPL) parametrization, a commonly used and recognized framework for describing the dark energy equation of state. We then explore the general Exponential parametrization, which incorporates CPL as its first-order approximation, and extensions of this parametrization that incorporate nonlinear terms. We constrain these scenarios using CMB data from various missions, including the Planck 2018 legacy release, the Wilkinson Microwave Anisotropy Probe (WMAP), the Atacama Cosmology Telescope (ACT), and the South Pole Telescope (SPT), as well as combinations with low-redshift cosmological probes such as Baryon Acoustic Oscillations (BAO) and the Pantheon sample. While the $\Lambda$CDM cosmology remains consistent within the 68\% confidence level, we observe that the extensions of the CPL parametrization are indistinguishable for Planck data. However, for ACT and SPT data, the inclusion of additional terms begins to reveal a peak in $w_{\rm a, DE}$ that was previously unconstrained., Comment: 14 pages, 6 tables and 4 captioned figures; version published in Phys. Dark. Univ

Heavy-tailed distributions are infamously difficult to estimate because their moments tend to infinity as the shape of the tail decay increases. Nevertheless, this study shows the utilization of a modified group of moments for estimating a heavy-tailed distribution. These modified moments are determined from powers of the original distribution. The nth-power distribution is guaranteed to have finite moments up to n-1. Samples from the nth-power distribution are drawn from n-tuple Independent Approximates, which are the set of independent samples grouped into n-tuples and sub-selected to be approximately equal to each other. We show that Independent Approximates are a maximum likelihood estimator for the generalized Pareto and the Student's t distributions, which are members of the family of coupled exponential distributions. We use the first (original), second, and third power distributions to estimate their zeroth (geometric mean), first, and second power-moments respectively. In turn, these power-moments are used to estimate the scale and shape of the distributions. A least absolute deviation criteria is used to select the optimal set of Independent Approximates. Estimates using higher powers and moments are possible though the number of n-tuples that are approximately equal may be limited., Comment: 23 pages, 2 figures

In neural network (NN) security, safeguarding model integrity and resilience against adversarial attacks has become paramount. This study investigates the application of stochastic computing (SC) as a novel mechanism to fortify NN models. The primary objective is to assess the efficacy of SC to mitigate the deleterious impact of attacks on NN results. Through a series of rigorous experiments and evaluations, we explore the resilience of NNs employing SC when subjected to adversarial attacks. Our findings reveal that SC introduces a robust layer of defense, significantly reducing the susceptibility of networks to attack-induced alterations in their outcomes. This research contributes novel insights into the development of more secure and reliable NN systems, essential for applications in sensitive domains where data integrity is of utmost concern., Comment: 3 pages, 1 figure, 2 tables

We report an observation of ultra-high energy (UHE) gamma rays from the Galactic Center region, using seven years of data collected by the High-Altitude Water Cherenkov (HAWC) Observatory. The HAWC data are best described as a point-like source (HAWC J1746-2856) with a power-law spectrum ($\mathrm{d}N/\mathrm{d}E=\phi(E/26 \,\text{TeV})^{\gamma}$), where $\gamma=-2.88 \pm 0.15_{\text{stat}} - 0.1_{\text{sys}} $ and $\phi=1.5 \times 10^{-15}$ (TeV cm$^{2}$s)$^{-1}$ $\pm\, 0.3_{\text{stat}}\,^{+0.08_{\text{sys}}}_{-0.13_{\text{sys}}}$ extending from 6 to 114 TeV. We find no evidence of a spectral cutoff up to $100$ TeV using HAWC data. Two known point-like gamma-ray sources are spatially coincident with the HAWC gamma-ray excess: Sgr A$^{*}$ (HESS J1745-290) and the Arc (HESS J1746-285). We subtract the known flux contribution of these point sources from the measured flux of HAWC J1746-2856 to exclude their contamination and show that the excess observed by HAWC remains significant ($>$5$\sigma$) with the spectrum extending to $>$100 TeV. Our result supports that these detected UHE gamma rays can originate via hadronic interaction of PeV cosmic-ray protons with the dense ambient gas and confirms the presence of a proton PeVatron at the Galactic Center.

We propose integral representations and analytical solutions for the propagator of the $1+1$ dimensional Salpeter Hamiltonian, describing a relativistic quantum particle with no spin. We explore the exact Green function and an exact solution for a given initial condition, and also find the asymptotic solutions in some limiting cases. The analytical extension of the Hamiltonian in the complex plane allows us to formulate the equivalent stochastic problem, namely the B\"aumer equation. This equation describes \textit{relativistic} stochastic processes with time-changing anomalous diffusion. This B\"aumer propagator corresponds to the Green function of a relativistic diffusion process that interpolates between Cauchy distributions for small times and Gaussian diffusion for large times, providing a framework for stochastic processes where anomalous diffusion is time-dependent., Comment: 10 pages, 5 figures, five appendixes. to be submitted to PRE

Fibonacci string-net condensate, a complex topological state that supports non-Abelian anyon excitations, holds promise for fault-tolerant universal quantum computation. However, its realization by a static-lattice Hamiltonian has remained elusive due to the inherent high-order interactions demanded. Here, we introduce a scalable dynamical string-net preparation (DSNP) approach, suitable even for near-term quantum processors, that can dynamically prepare the state through reconfigurable graphs. DSNP enables the creation and manipulation of the Fibonacci string-net condensate (Fib-SNC). Using a superconducting quantum processor, we couple the DSNP approach with a composite error-mitigation strategy on deep circuits to successfully create, measure, and braid Fibonacci anyons in two spatial dimensions (2D) demonstrating their potential for universal quantum computation. To this end, we measure anyon charges for two species of anyons associated with the doubled topological quantum field theory underlying Fid-SNC, with an average experimental accuracy of 94%. We validate that a scalable 2D braiding operation on a logical qubit encoded on three anyons yields the golden ratio $\phi$ with 98% average accuracy and 8% measurement uncertainty. We further sample the Fib-SNC wavefunction to estimate the chromatic polynomial at $\phi+2$ for various graphs. Given the established computational hardness of the chromatic polynomial, the wavefunction amplitude is classically hard to evaluate. Our results establish the first proof of principle that scalable DSNP can open doors to fault-tolerant universal quantum computation and to classically-hard problems., Comment: 4 pages and 4 figures with Supplemental Materials (47 pages, 18 Figures)

Development of a two-phase incompressible solver for magnetic flows in the magnetostatic case is presented. The proposed numerical toolkit couples the Navier-Stokes equations of hydrodynamics with Maxwell's equations of electromagnetism to model the behaviour of magnetic flows in the presence of a magnetic field. To this end, a rigorous implementation of a second-order two-phase solver for incompressible nonmagnetic flows is introduced first. This solver is implemented in the finite-difference framework, where a fifth-order conservative level set method is employed to capture the evolution of the interface, along with an incompressible solver based on the projection scheme to model the fluids. The solver demonstrates excellent performance even with high density ratios across the interface (Atwood number $\approx 1$), while effectively preserving the mass conservation property. Subsequently, the numerical discretization of Maxwell's equations under the magnetostatic assumption is described in detail, utilizing the vector potential formulation. The primary second-order solver for two-phase flows is extended to the case of magnetic flows, by incorporating the Lorentz force into the momentum equation, accounting for high magnetic permeability ratios across the interface. The implemented solver is then utilized for examining the deformation of ferrofluid droplets in both quiescent and shear flow regimes across various susceptibility values of the droplets. The results suggest that increasing the susceptibility value of the ferrofluid droplet can affect its deformation and rotation in low capillary regimes. In higher capillary flows, increasing the magnetic permeability jump across the interface can further lead to droplet breakup as well. The effect of this property is also investigated for the Rayleigh-Taylor instability growth in magnetic fluids.