In disaster scenarios, establishing robust emergency communication networks is critical, and unmanned aerial vehicles (UAVs) offer a promising solution to rapidly restore connectivity. However, organizing UAVs to form multi-hop networks in large-scale dynamic environments presents significant challenges, including limitations in algorithmic scalability and the vast exploration space required for coordinated decision-making. To address these issues, we propose MRLMN, a novel framework that integrates multi-agent reinforcement learning (MARL) and large language models (LLMs) to jointly optimize UAV agents toward achieving optimal networking performance. The framework incorporates a grouping strategy with reward decomposition to enhance algorithmic scalability and balance decision-making across UAVs. In addition, behavioral constraints are applied to selected key UAVs to improve the robustness of the network. Furthermore, the framework integrates LLM agents, leveraging knowledge distillation to transfer their high-level decision-making capabilities to MARL agents. This enhances both the efficiency of exploration and the overall training process. In the distillation module, a Hungarian algorithm-based matching scheme is applied to align the decision outputs of the LLM and MARL agents and define the distillation loss. Extensive simulation results validate the effectiveness of our approach, demonstrating significant improvements in network performance over the MAPPO baseline and other comparison methods, including enhanced coverage and communication quality.

The combination of independent cosmological datasets is a route towards precise and accurate inference of cosmological parameters if these observations are free from systematic effects. However, unknown systematics in different datasets can lead to biased inference of cosmological parameters. In this work, we test the consistency of two independent tracers of low-redshift cosmic expansion, namely the supernova dataset from Pantheon$+$ and the BAO dataset from DESI DR2, using the distance duality relation, a cornerstone of cosmology within General Relativity. We find that these datasets violate the distance duality relation and show a redshift-dependent signature, hinting at unaccounted physical effects or observational artifacts. This effect mimics a redshift-evolving dark energy scenario when Pantheon$+$ and DESI datasets are combined without accounting for this inconsistency. Accounting for this effect in the likelihood refutes the previous claim of evidence for non-cosmological constant dark energy from DESI DR2, yielding results consistent with a cosmological constant with $w_0= -0.92\pm 0.08$ and $w_a= -0.49^{+0.33}_{-0.36}$. This is further supported by an increased Bayes factor at ($w_0 = -1$, $w_a = 0$) when the inconsistency is accounted for. This indicates that current conclusions from DESI DR2 combined with Pantheon$+$ likely arise from combining inconsistent datasets, leading to precise but inaccurate inference of cosmological parameters. Future tests of consistency between cosmological datasets will be essential for robust inference and for identifying unaccounted physical effects or observational artifacts.[Abridged]

We present a comprehensive study on $SIM(2)$ and $ISIM(2)$ groups, their representations and algebraic aspects. These groups, together with $HOM(2)$, arise as the symmetry groups of Very Special Relativity (VSR), where full Lorentz invariance is reduced while retaining many relativistic consequences. After obtaining $SIM(2)$ through the Inönü-Wigner contraction procedure, a complete four-dimensional algebraic representation is shown for $\mathfrak{sim(2)}$ and $\mathfrak{isim(2)}$. Besides that, we apply Bargmann's formalism to investigate the (projective) representations for both cases, keeping track of the source of phase factors. We complete the study by presenting a particularly simple analysis to probe the existence of local phase factors, which is useful when dealing with non-abelian groups.

We measured the relaxation and decoherence rates of a superconducting transmon qubit in a resonator-free setting. In our experiments, the qubit is coupled to an open coplanar waveguide such that the transmission of microwaves through this line depends on the qubit's state. To determine the occupation of the first excited qubit energy level, we introduced a two-pulse technique. The first applied pulse, at a frequency close to the eigenfrequency of the qubit, serves to excite the qubit. A second pulse is then used for probing the transition between the first and second excited energy levels. Utilizing this measurement technique allowed for the reconstruction of the relaxation dynamics and Rabi oscillations. Furthermore, we demonstrate the consistency between the extracted parameters and the corresponding estimations from frequency-domain measurements.

We consider a classical First-order Vector AutoRegressive (VAR(1)) model, where we interpret the autoregressive interaction matrix as influence relationships among the components of the VAR(1) process that can be encoded by a weighted directed graph. A majority of previous work studies the structural identifiability of the graph based on time series observations and therefore relies on dynamical information. In this work we assume that an equilibrium exists, and study instead the identifiability of the graph from the stationary distribution, meaning that we seek a way to reconstruct the influence graph underlying the dynamic network using only static information. We use an approach from algebraic statistics that characterizes models using the Jacobian matroids associated with the parametrization of the models, and we introduce sufficient graphical conditions under which different graphs yield distinct steady-state distributions. Additionally, we illustrate how our results could be applied to characterize networks inspired by ecological research.

The construction of stable, conservative, and accurate volume dissipation is extended to discretizations that possess a generalized summation-by-parts (SBP) property within a tensor-product framework. The dissipation operators can be applied to any finite-difference or spectral-element scheme that uses the SBP framework, including high-order entropy-stable schemes. Additionally, we clarify the incorporation of a variable coefficient within the operator structure and analyze the impact of a boundary correction matrix on operator structure and accuracy. Following the theoretical development and construction of novel dissipation operators, we relate the presented volume dissipation to the use of upwind SBP operators. When applied to spectral-element methods, the presented approach yields unique dissipation operators that can also be derived through alternative approaches involving orthogonal polynomials. Numerical examples featuring the linear convection, Burgers, and Euler equations verify the properties of the constructed dissipation operators and assess their performance compared to existing upwind SBP schemes, including linear stability behaviour. When applied to entropy-stable schemes, the presented approach results in accurate and robust methods that can solve a broader range of problems where comparable existing methods fail.

Current performance bounds for randomized iterative methods are often considered tight under per-iteration analyses, yet they are notoriously loose in practice. We derive asymptotic performance bounds that narrow this theory-practice gap, leveraging a new technique for bounding the spectral radii of operators arising in randomized iterations and a connection we establish to Perron-Frobenius theory for noncommutative algebras. The asymptotic analysis also uncovers and quantifies the previously unexplained role of relaxation in improving performance, thereby resolving an open problem posed by Strohmer and Vershynin in 2007.

In the context of clinical research, computational models have received increasing attention over the past decades. In this systematic review, we aimed to provide an overview of the role of so-called in silico clinical trials (ISCTs) in medical applications. Exemplary for the broad field of clinical medicine, we focused on in silico (IS) methods applied in drug development, sometimes also referred to as model informed drug development (MIDD). We searched PubMed and ClinicalTrials.gov for published articles and registered clinical trials related to ISCTs. We identified 202 articles and 48 trials, and of these, 76 articles and 19 trials were directly linked to drug development. We extracted information from all 202 articles and 48 clinical trials and conducted a more detailed review of the methods used in the 76 articles that are connected to drug development. Regarding application, most articles and trials focused on cancer and imaging-related research while rare and pediatric diseases were only addressed in 14 articles and 5 trials, respectively. While some models were informed combining mechanistic knowledge with clinical or preclinical (in-vivo or in-vitro) data, the majority of models were fully data-driven, illustrating that clinical data is a crucial part in the process of generating synthetic data in ISCTs. Regarding reproducibility, a more detailed analysis revealed that only 24% (18 out of 76) of the articles provided an open-source implementation of the applied models, and in only 20% of the articles the generated synthetic data were publicly available. Despite the widely raised interest, we also found that it is still uncommon for ISCTs to be part of a registered clinical trial and their application is restricted to specific diseases leaving potential benefits of ISCTs not fully exploited.

We define a properad $Y^{(n)}_\infty$ that encodes $n$-pre-Calabi--Yau algebras with vanishing copairing. These algebras include chains on the based loop space of any space $X$ endowed with a fundamental class $[X]$ such that $(X,[X])$ satisfies Poincaré duality of degree $n \geqslant 1$ with local system coefficients, such as an oriented manifold. Extending the notion of coformality of spaces, we define coformality of such a pair $(X,[X])$ in terms of properadic formality of $Y^{(n)}_\infty$-algebra structures on $C_*(ΩX)$. Using a refined version of properadic Kaledin classes, we establish the intrinsic coformality of all spheres in characteristic zero.

We investigate the entanglement properties of the Quantum Six-Vertex Model on a cylinder, focusing on the Shannon-Renyi entropy in the limit of Renyi order $n = \infty$. This entropy, calculated from the ground state amplitudes of the equivalent XXZ spin-1/2 chain, allows us to determine the Renyi entanglement entropy of the corresponding Rokhsar-Kivelson wavefunctions, which describe the ground states of certain conformal quantum critical points. Our analysis reveals a novel logarithmic correction to the expected entanglement scaling when the system size is odd. This anomaly arises from the geometric frustration of spin configurations imposed by periodic boundary conditions on odd-sized chains. We demonstrate that the scaling prefactor of this logarithmic term is directly related to the compactification radius of the low-energy bosonic field theory description, or equivalently, the Luttinger parameter. Thus, this correction provides a direct probe of the underlying Conformal Field Theory (CFT) describing the critical point. Our findings highlight the crucial role of system size parity in determining the entanglement properties of this model and offer insights into the interplay between geometry, frustration, and criticality.

We compute the K-theory of the C*-category generated by order zero, equivariant, properly supported, classical pseudodifferential operators acting on sections of homogeneous bundles over the symmetric space of a real reductive Lie group G. Our result uses the Connes-Kasparov isomorphism for G, and in fact is equivalent to the Connes-Kasparov isomorphism. We relate our computation to David Vogan's well-known parametrization of the tempered irreducible representations of G with real infinitesimal character. When the reductive group G has real rank one, we formulate and prove a Fourier isomorphism theorem for equivariant order zero pseudodifferential operators on the symmetric space, and use it to prove a K-theoretic version of Vogan's theorem.

Photonic technologies offer promising solutions to the power consumption, bandwidth constraints and latency limits of electronic hardware used in high-performance computing and artificial intelligence. Recently, many studies have proposed and successfully demonstrated photonic accelerators based on integrated meshes of Mach-Zehnder interferometers (MZIs), enabling matrix-vector multiplications directly in the optical domain. While being fast and energy efficient, these photonic architectures still struggle to get the required precision for such applications, because setting the complex coefficients of MZI tunable gates with a high accuracy is still an unsolved problem. This work demonstrates high-precision automated setting and stabilization of MZI-based optical gates with a resolution of 7.01 and 8.04 bits for the output power and phase, respectively. Demonstration is achieved on a multistage silicon photonic circuit comprising a coherent input vector generator, an MZI matrix-vector multiplier, and a coherent receiver for phase measurement. The proposed control strategy can configure the MZIs to any desired working point, without any prior calibration or complex algorithm for the correction of hardware non-idealities, and prevents the propagation of programming errors, thus allowing scalability towards optical processors of large size.

Can stochastic gradient methods track a moving target? We study the problem of tracking multidimensional time-varying parameters under noisy observations and possible model misspecification. Gradient-based filters update the time-varying parameters using the gradient of a postulated objective function. A natural filtering objective is the logarithm of the postulated observation density, which gives rise to the widely used class of score-driven filters. As in the optimization literature, these filters come in two forms: explicit filters evaluate the gradient at the predicted parameter, whereas implicit filters evaluate it at the updated parameter. For both filter types, we derive novel sufficient conditions for exponential stability of the filtered parameter path, showing that stability can be guaranteed independently of the data-generating process. Under mild additional moment conditions on the data-generating process, we also obtain finite-sample and asymptotic mean squared error bounds relative to the pseudo-true parameter path. For implicit filters, these guarantees hold under weak parameter restrictions. For explicit filters, they additionally require Lipschitz continuity of the score and a sufficiently small learning rate. Simulation studies support our theoretical findings and show that implicit gradient filters outperform explicit ones in both accuracy and stability.

Quantum computing is an emerging technology that has seen significant software and hardware improvements in recent years. Executing a quantum program requires the compilation of its quantum circuit for a target Quantum Processing Unit (QPU). Various methods for qubit mapping, gate synthesis, and optimization of quantum circuits have been proposed and implemented in compilers. These compilers try to generate a quantum circuit that leads to the best execution quality - a criterion that is usually approximated by figures of merit such as the number of (two-qubit) gates, the circuit depth, expected fidelity, or estimated success probability. However, it is often unclear how well these figures of merit represent the actual execution quality on a QPU. In this work, we investigate the correlation between established figures of merit and actual execution quality on real machines - revealing that the correlation is weaker than anticipated and that more complex figures of merit are not necessarily more accurate. Motivated by this finding, we propose an improved figure of merit (based on a machine learning approach) that can be used to predict the expected execution quality of a quantum circuit for a chosen QPU without actually executing it. The employed machine learning model reveals the influence of various circuit features on generating high correlation scores. The proposed figure of merit demonstrates a strong correlation and outperforms all previous ones in a case study - achieving an average correlation improvement of 49%.

Chemically realistic quasi-one-dimensional (1D) materials in which Dirac fermions and highly degenerate flat bands coexist intrinsically at the Fermi level are exceedingly rare, while representing a highly desirable platform for correlated and topological quantum phenomena. Here, using specialized symmetry-adapted first-principles calculations we predict a new class of nanomaterials -- phosphorus carbide nanotubes ($\text{P}_2\text{C}_3$NTs) -- obtained by rolling monolayer $\text{P}_2\text{C}_3$, a two-dimensional material shown in a previous letter to host "double Kagome bands". Both armchair and zigzag $\text{P}_2\text{C}_3$NTs are stable at room temperature and feature the rare coexistence of Dirac crossings and multiple flat bands at the Fermi level inherited from the underlying honeycomb-Kagome lattice, with the flat bands resilient to elastic deformations. Under large strain, the structure transforms from honeycomb-Kagome to "brick-wall," accompanied by multiple coupled structural and quantum phase transitions. We also uncover localized edge states, spin splitting from vacancies and dopants, and strain-tunable magnetism. Together, these results establish $\text{P}_2\text{C}_3$NTs as a chemically specific and mechanically tunable 1D material platform with potential applications in quantum hardware and spintronics.

We propose a novel framework where MeV-scale Dirac Dark Matter annihilates into axion-like particles, providing a natural explanation for the 511 keV gamma-ray line observed in the Galactic Center. The relic abundance is determined by p-wave annihilation into two axion-like particles, while s-wave annihilation into three axion-like particles, decaying into $e^+ e^-$ pairs, accounts for the line intensity. Remarkably, this model, assuming a standard Navarro-Frenk-White profile, reproduces the observed emission morphology, satisfies in-flight annihilation and cosmological bounds, and achieves the correct relic density, offering a compelling resolution to this longstanding anomaly.

Consider a university assigning students to courses and dorms. While many mechanisms are available, they each have their own drawbacks. Running serial dictatorship once for all goods is highly unfair, but running serial dictatorship separately for each matching problem is inefficient-Pareto improvements can be found via students jointly trading their allocated course and dorm. Alternatively, competitive equilibrium from equal incomes scales combinatorially in the number of items, making implementation and preference elicitation difficult. This paper considers paired serial dictatorship: a novel mechanism where agents signal relative preferences that determine their priority in each market. Any deterministic allocation that arises in equilibrium is Pareto efficient and envy-free, highlighting how seemingly innocuous tie-breaking is the key barrier to optimality and fairness. When agents differ only in relative preferences, paired serial dictatorship ex-ante Pareto dominates running random serial dictatorship independently in each market. Such gains exist even when agents behave simplistically.

This work introduces distribution error mitigation (DEM), which mitigates the error in the output distribution of a quantum circuit. We provide a rigorous theoretical foundation. If the composite noise affecting the circuit is a Pauli channel, the ideal output distribution and noisy distribution in the standard basis are related by a stochastic matrix. This system is described by a XOR convolution (the matrix is recursive 2 by 2 block circulant) between a noise vector and the ideal distribution. The noisy output distribution can be corrected to the ideal output distribution via a Fast Walsh-Hadamard Transform. We introduce a tomography method to approximate the noise vector, which requires sampling of only one logical circuit. The quantum overhead of DEM requires sampling of only two logical circuits. We provide techniques to scale the application of DEM efficiently. Accuracy bounds are provided. The approach is tested with quantum hardware executions consisting of 20-qubit and 30-qubit GHZ state preparation, 5-qubit Grover, 6-qubit and 10-qubit quantum phase estimation, and 10-qubit and 20-qubit Dicke state preparation circuits. DEM dramatically improves the accuracies of the output distributions for all demonstrations. For 30-qubit GHZ state preparation, a corrected distribution fidelity of 97.7% is achieved from an initial raw fidelity of 23.2%.

We introduce a notion of stratification for rigidly-compactly generated tensor-triangulated categories relative to the homological spectrum and develop the fundamental features of this theory. In particular, we demonstrate that it exhibits excellent descent properties. In conjunction with Balmer's Nerves of Steel conjecture, we conclude that stratification admits a general form of descent. This gives a uniform treatment of several recent stratification results and provides a complete answer to the question: When does stratification descend? As a new application, we extend earlier work on the tensor triangular geometry of equivariant module spectra from finite groups to compact Lie groups.

Constructing cryptographic schemes with tight or almost-tight security has long been one of the central problems in theoretical cryptography. At ASIACRYPT 2016, Boyen and Li posed an open problem: whether it is possible to construct a homomorphic signature scheme with tight or almost-tight security under the Short Integer Solution (SIS) assumption in the standard model. In 2024, Chen achieved the first construction with almost-tight security under a weaker security model. To further achieve tight security in the standard model, this paper introduces a new security model whose security requirements are weaker than those of the standard adaptive model but stronger than the model adopted by Chen. Under this model, we construct a linearly homomorphic signature scheme with tight security.

Shock-generated transients, such as hot flow anomalies (HFAs), upstream of planetary bow shocks, play a critical role in electron acceleration. Using multi-mission data from NASA's Magnetospheric Multiscale (MMS) and ESA's Cluster missions, we demonstrate the transmission of HFAs through Earth's quasi-parallel bow shock, associated with acceleration of electrons up to relativistic energies. Energetic electrons, initially accelerated upstream, are shown to remain broadly confined within the transmitted transient structures downstream, where betatron acceleration further boosts their energy due to elevated compression levels. Additionally, high-speed jets form at the compressive edges of HFAs, exhibiting a significant increase in dynamic pressure and potentially contributing to driving further localized compression. Our findings emphasize the efficiency of quasi-parallel shocks in driving particle acceleration far beyond the immediate shock transition region, expanding the acceleration region to a larger spatial domain. Finally, this study underscores the importance of multi-scale observational approach in understanding the convoluted processes behind collisionless shock physics and their broader implications.

Quantum Local Area Networks (QLANs) represent a promising building block for larger scale quantum networks with the ambitious goal -- in a long time horizon -- of realizing a Quantum Internet. Surprisingly, the physical topology of a QLAN can be enriched by a set of artificial links, enabled by shared multipartite entangled states among the nodes of the network. This novel concept of artificial topology revolutionizes the possibilities of connectivity within the local network, enabling an on-demand manipulation of the artificial network topology. In this paper, we discuss the implementation of the QLAN model in SeQUeNCe, a discrete-event simulator of quantum networks. Specifically, we provide an analysis of how network nodes interact, with an emphasis on the interplay between quantum operations and classical signaling within the network. Remarkably, through the modeling of a measurement protocol and a correction protocol, our QLAN model implementation enables the simulation of the manipulation process of a shared entangled quantum state, and the subsequent engineering of the entanglement-based connectivity. Our simulations demonstrate how to obtain different virtual topologies with different manipulations of the shared resources and with all the possible measurement outcomes, with an arbitrary number of nodes within the network.

We investigate relativistic effects on the performance of a quantum battery in an open quantum framework. We consider an Unruh-DeWitt detector driven by a coherent classical pulse as a quantum battery that is interacting with a massless scalar field through a quadratic coupling. The battery follows a trajectory composed of uniform acceleration along one direction, combined with constant four-velocity components in the orthogonal plane to the acceleration. Accelerated motion degrades the performance of the quantum battery rapidly in the absence of the orthogonal velocity component. We first derive the Lindblad equation for quadratic coupling in detail. We then show that the quadratic scalar field coupling enhances coherence and stability in the presence of orthogonal velocity. We observe that decoherence is mitigated significantly, resulting in remarkable improvement in the battery capacity and efficiency compared to the case of the usual linear field coupling. This opens up the possibility of nonlinear environmental coupling enabling stored energy to be retained over longer durations, leading to more efficient operation of quantum devices.

Aluminum scandium nitride (Al$_{1-x}$Sc$_x$N) is a promising material for ferroelectric devices due to its large remanent polarization, scalability, and compatibility with semiconductor technology. By doping AlN with Sc, the bonds in the polar AlN structure are weakened, which enables ferroelectric switching below the dielectric breakdown field. However, one disadvantage of Sc doping is that it increases the material's tendency towards oxidation. In the present study, the oxidation process of tungsten-capped and uncapped Al$_{0.83}$Sc$_{0.17}$N thin films is investigated by hard X-ray photoelectron spectroscopy (HAXPES). The samples had been exposed to air for either two weeks or 6 months. HAXPES spectra indicate the replacement of nitrogen by oxygen, and the tendency of oxygen to favor oxidation with Sc rather than Al. The appearance of an N$_2$ spectral feature thus can be directly related to the oxidation process. We present an oxidation model that mimics these spectroscopic results of the element-specific oxidation processes within Al$_{1-x}$Sc$_x$N. Finally, in operando HAXPES data of uncapped and capped AlScN-capacitor stacks are interpreted using the proposed model.

Temporal fluctuations in the superconducting qubit lifetime, $T_1$, bring up additional challenges in building a fault-tolerant quantum computer. While the exact mechanisms remain unclear, $T_1$ fluctuations are generally attributed to the strong coupling between the qubit and a few near-resonant two-level systems (TLSs) that can exchange energy with an assemble of thermally fluctuating two-level fluctuators (TLFs) at low frequencies. Here, we report $T_1$ measurements on the qubits with different geometrical footprints and surface dielectrics as a function of the temperature. By analyzing the noise spectrum of the qubit depolarization rate, $Γ_1 = 1/T_1$, we can disentangle the impact of TLSs, non-equilibrium quasiparticles (QPs), and equilibrium (thermally excited) QPs on the variance in $Γ_1$. We find that $Γ_1$ variances in the qubit with a small footprint are more susceptible to the QP and TLS fluctuations than those in the large-footprint qubits. Furthermore, the QP-induced variances in all qubits are consistent with the theoretical framework of QP diffusion and fluctuation. We suggest these findings can offer valuable insights for future qubit design and engineering optimization.

Dynamical processes can be classified in various ways as deterministic or stochastic, and continuous or discrete time. All these types can be studied by the path-spaces they generate, and stationary measures on that path-space. Such measures are called the law of the dynamics. This article presents how a general ergodic dynamical system may be approximated in terms of their law, by a simple and restricted family of deterministic continuous-time skew-product systems. In these systems, a deterministic, mixing flow intermittently drives a deterministic flow through a topological space created by gluing cylinders. The resulting orbits mimic the law of the original dynamics. This comparison is made possible by introducing a secondary intermediary approximation of the ergodic dynamics. This third system is a step-skew dynamical system, in which a finite state Markov process drives a dynamics on topological disk. Each of these three representations have their advantages. It is proved that the distribution induced on the space of paths by these three dynamics can be made arbitrarily close to each other. This analysis reconfirms the old principle that it is impossible to decide whether a general timeseries is generated by a deterministic or stochastic process, and is of continuous or discrete time.

Principal component analysis has been a main tool in multivariate analysis for estimating a low dimensional linear subspace that explains most of the variability in the data. However, in high-dimensional regimes, naive estimates of the principal loadings are not consistent and difficult to interpret. In the context of time series, principal component analysis of spectral density matrices can provide valuable, parsimonious information about the behavior of the underlying process, particularly if the principal components are interpretable in that they are sparse in coordinates and localized in frequency bands. In this paper, we introduce a formulation and consistent estimation procedure for interpretable principal component analysis for high-dimensional time series in the frequency domain. An efficient frequency-sequential algorithm is developed to compute sparse-localized estimates of the low-dimensional principal subspaces of the signal process. The method is motivated by and used to understand neurological mechanisms from high-density resting-state EEG in a study of first episode psychosis.

The note contains a short elementary proof of Cayley's formula for labeled trees.

Active fluids display spontaneous turbulent-like flows known as active turbulence. Recent work revealed that these flows have universal features, independent of the material properties and of the presence of topological defects. However, the differences between defect-laden and defect-free active turbulence remain largely unexplored. Here, by means of large-scale numerical simulations, we show that defect-free active nematic turbulence can undergo dynamical arrest. This state is characterized by an emergent network of nematic domain walls that channels coherent streams and suppresses chaotic flows. As the system evolves, the branched wall network produces a large-scale pattern with tree-like topological properties. We find that flow alignment -- the tendency of nematics to reorient under shear -- enhances large-scale chaotic jets in contractile rodlike systems while promoting dynamical arrest in extensile systems. We further show that dynamical arrest persists regardless of whether defects are prohibited by construction or simply fail to form due to a high energy cost of defect cores. Taken together, our findings reveal a striking pattern-formation mechanism, with labyrinths emerging from active turbulence, and illuminate the rich transitional regime between defect-free and defect-laden dynamics. These behaviors call for the experimental realization of active nematics at vanishing or low defect densities, and underscore that, in extensile rodlike nematics, topological defects enable turbulence by preventing dynamical arrest.

We propose a method to construct a tensor network representation of partition functions without singular value decompositions nor series expansions. The approach is demonstrated for one- and two-dimensional Ising models and we study the dependence of the tensor renormalization group (TRG) on the form of the initial tensors and their symmetries. We further introduce variants of several tensor renormalization algorithms. Our benchmarks reveal a significant dependence of various TRG algorithms on the choice of initial tensors and their symmetries. However, we show that the boundary TRG technique can eliminate the initial tensor dependence for all TRG methods. The numerical results of TRG calculations can thus be made significantly more robust with only a few changes in the code. Furthermore, we study a three-dimensional $\mathbb{Z}_2$ gauge theory without gauge-fixing and confirm the applicability of the initial tensor construction. Our method can straightforwardly be applied to systems with longer range and multi-site interactions, such as the next-nearest neighbor Ising model.