We present an extension to the two-dimensional functional renormalization group to efficiently treat interactions on the surface or at interfaces of three-dimensional systems. As an application, we consider a semi-infinite stack of two-dimensional square lattices, including a Hubbard interaction on the surface layer and an alternating interlayer coupling. We investigate how strongly correlated states of the decoupled two-dimensional Hubbard model on the surface evolve under inclusion of such an SSH-like interlayer coupling. For large parts of the phase diagram as a function of the interlayer hopping parameters, the physics of the two-dimensional system prevails, with antiferromagnetic, superconducting $d$-wave, and ferromagnetic correlations taking center stage. However, for intermediate interlayer couplings the superconducting state at intermediate interaction strengths separates into two regimes by a small region of incommensurate spin-density-wave and spin-bond order, enabling the potential realization of chiral spin-bond order.

The active impedance is a fundamental parameter for characterizing the behavior of large, uniform phased array antennas. However, its conventional calculation via the mutual impedance matrix (or the scattering matrix) offers limited physical intuition and can be computationally intensive. This paper presents a novel derivation of the active impedance directly from the radiated beam pattern of such arrays. This approach maps the scan-angle variation of the active impedance directly to the intrinsic angular variation of the beam, providing a more intuitive physical interpretation. The theoretical derivation is straightforward and rigorous. The validity of the proposed equation is conclusively confirmed through full-wave simulations of a prototype array. This work establishes a new and more intuitive framework for understanding, analyzing and accurately measuring the scan-dependent variations in phased arrays, which is one of the main challenges in modern phased array designs. Consequently, this novel formalism is expected to expedite and simplify the overall design and optimization process for next-generation, large-scale uniform phased arrays.

Count-compositional data arise in many different fields, including high-throughput sequencing experiments, ecological surveys, and palaeoclimate studies, where a common, important goal is to understand how covariates relate to the observed compositions. Existing methods often fail to simultaneously address key challenges inherent in such data, namely: overdispersion, an excess of zeros, cross-sample heterogeneity, and complex covariate effects. To address these concerns, we propose two novel Bayesian models based on ensembles of regression trees. Specifically, we leverage the recently introduced zero-and-$N$-inflated multinomial distribution and assign independent nonparametric Bayesian additive regression tree (BART) priors to both the compositional and structural zero probability components of the model, to flexibly capture covariate effects. We further extend this by adding latent random effects to capture overdispersion and more general dependence structures among the categories. We develop an efficient inferential algorithm combining recent data augmentation schemes with established BART sampling routines. We evaluate our proposed models in simulation studies and illustrate their applicability through a case study of palaeoclimate modelling.

Since its inception, Bohmian mechanics has been surrounded by a halo of controversy. Originally proposed to bypass the limitations imposed by von Neumann's theorem on the impossibility of hidden-variable models in quantum mechanics, it faced strong opposition from the outset. Over time, however, its use in tackling specific problems across various branches of physics has led to a gradual shift in attitude, turning the early resistance into a more moderate acceptance. A plausible explanation for this change may be that, since the late 1990s and early 2000s, Bohmian mechanics has been taking on a more operational and practical role. The original hidden-variable idea has gradually faded from its framework, giving way to a more pragmatic approach that treats it as a suitable analytical and computational tool. This discussion explores how and why such a shift in perspective has occurred and, therefore, answers questions such as whether Bohmian mechanics should be considered once and for all a legitimate quantum representation (i.e., worth being taught in elementary quantum mechanics courses) or, by extension, whether these ideas can be transferred to and benefit other fields. Here, the Schrödinger equation and several specific numerical examples are re-examined in the light of a less restrictive view than the standard one usually adopted in quantum mechanics.

Quantum thermometry aims to measure temperature in nanoscale quantum systems, paralleling classical thermometry. However, temperature is not a quantum observable, and most theoretical studies have therefore concentrated on analyzing fundamental precision limits set by the quantum Fisher information through the quantum Cramer-Rao bound. In contrast, whether a direct temperature readout can be achieved in quantum thermometry remains largely unexplored, particularly under the nonequilibrium conditions prevalent in real-world applications. To address this, we develop a direct temperature readout scheme based on a thermodynamic inference strategy. The scheme integrates two conceptual developments: (i) By applying the maximum entropy principle with the thermometer's mean energy as a constraint, we assign a reference temperature to the nonequilibrium thermometer. We demonstrate that this reference temperature outperforms a commonly used effective temperature defined through equilibrium analogy. (ii) We obtain positive semi-definite error functions that lower-bound the deviation of the reference temperature from the true temperature-in analogy to the quantum Cramer-Rao bound for the mean squared error-and vanish upon thermalization with the sample. Combining the reference temperature with these error functions, we introduce a notion of corrected dynamical temperature which furnishes a postprocessed temperature readout under nonequilibrium conditions. This corrected dynamical temperature can be evaluated adaptively without prior knowledge of the actual temperature. We validate the corrected dynamical temperature in a qubit-based thermometer under a range of nonequilibrium initial states, confirming its capability to estimate the true temperature. Importantly, we find that increasing quantum coherence can enhance the precision of this readout.

Determining whether two graphs are structurally identical is a fundamental problem with applications spanning mathematics, computer science, chemistry, and network science. Despite decades of study, graph isomorphism remains a challenging algorithmic task, particularly for highly regular structures. Here we introduce a new algorithmic approach based on ideas from spectral graph theory and geometry that constructs candidate correspondences between vertices using their curvatures. Any correspondence produced by the algorithm is explicitly verified, ensuring that non-isomorphic graphs are never incorrectly identified as isomorphic. Although the method does not yet guarantee success on all inputs, we find that it correctly resolves every instance tested in deterministic polynomial time, including a broad collection of graphs known to be difficult for classical techniques. These results demonstrate that enriched spectral methods can be far more powerful than previously understood, and suggest a promising direction for the practical resolution of the complexity of the graph isomorphism problem.

We develop an operator-based framework to coarse-grain interacting particle systems that exhibit clustering dynamics. Starting from the particle-based transfer operator, we first construct a sequence of reduced representations: the operator is projected onto concentrations and then further reduced by representing the concentration dynamics on a geometric low-dimensional manifold and an adapted finite-state discretization. The resulting coarse-grained transfer operator is finally estimated from dynamical simulation data by inferring the transition probabilities between the Markov states. Applied to systems with multichromatic and Morse interaction potentials, the reduced model reproduces key features of the clustering process, including transitions between cluster configurations and the emergence of metastable states. Spectral analysis and transition-path analysis of the estimated operator reveal implied time scales and dominant transition pathways, providing an interpretable and efficient description of particle-clustering dynamics.

We introduce an operator-theoretic framework for analyzing directional dependence in multivariate time series based on order-constrained spectral non-invariance. Directional influence is defined as the sensitivity of second-order dependence operators to admissible, order-preserving temporal deformations of a designated source component, summarized through orthogonally invariant spectral functionals. We show that the resulting supremum--infimum dispersion functional is the unique diagnostic within this class satisfying order consistency, orthogonal invariance, Loewner monotonicity, second-order sufficiency, and continuity, and that classical Granger causality, directed coherence, and Geweke frequency-domain causality arise as special cases under appropriate restrictions. An information-theoretic impossibility result establishes that entrywise-stable edge-based tests require quadratic sample size scaling in distributed (non-sparse) regimes, whereas spectral tests detect at the optimal linear scale. We establish uniform consistency and valid shift-based randomization inference under weak dependence. Simulations confirm correct size and strong power across distributed and nonlinear alternatives, and an empirical application illustrates system-level directional causal structure in financial markets.

Discrete random probability measures are central to Bayesian inference, particularly as priors for mixture modeling and clustering. A broad and unifying class is that of proper species sampling processes (SSPs), encompassing many Bayesian nonparametric priors. We show that any proper SSP admits an exact two-stage finite-mixture representation built from a latent truncation index and a simple reweighting of the atoms. For each realized truncation index, the representation has finitely many atoms, and averaging over the induced law of that index recovers the original SSP setwise. This yields at least two consequences: (i) an exact two-stage finite construction for arbitrary SSPs, without user-chosen truncation levels; and (ii) posterior inference in SSP mixture models via standard finite-mixture machinery, leading to tractable MCMC algorithms without ad hoc truncations. We explore these consequences by deriving explicit total-variation bounds for the approximation error when the truncation level is fixed, and by studying practical performance in mixture modeling, with emphasis on Dirichlet and geometric SSPs.

Optimizing laser and plasma parameters is crucial for enhancing accelerated proton energy in laser-driven proton acceleration with finite laser energy for applications such as cancer therapy. Tight focusing plays a significant role in improving laser-driven proton acceleration, which is generally believed as a result of the enhancement of laser intensity. However, we find that even at a fixed laser intensity, reducing the focal spot size still enhances the proton energy. Through particle-in-cell simulations and theoretical modeling, we find that at a small spot size (0.8 μm), the maximum proton energy is enhanced by 56.3% compared to that obtained at a conventional spot size (3 μm). This improvement is attributed to the dominance of ponderomotive-force-driven electrons at reduced spot sizes, which generate stronger charge-separation fields that propagate at higher velocities. Furthermore, to optimize proton acceleration, we analytically derive an ideal plasma density profile that promotes phase-stable proton acceleration, yielding an additional energy increase of 61.3% over the case of a tightly focused laser interacting with a planar target of uniform density. These findings remain robust under parameter variations, indicating that advanced focusing techniques combined with optimized plasma profiles could relax the demand for high laser energies, thereby reducing the reliance on large-scale laser facilities in medical and scientific applications.

We present a comprehensive theoretical study of linear wave scattering from magnetic domain walls with varied twist angles $Θ$ in spin-$1/2$ Bose-Einstein condensates (BECs). Using a gauge transformation, we show that scattering observables depend solely on the total twist $Θ$, independent of chirality. Within the Bogoliubov-de Gennes (BdG) framework, we develop a transfer-matrix method to compute reflection and transmission coefficients for incident phonons and free particles. Our results reveal a scattering threshold at the Zeeman energy $E = \hbarΩ_0$, separating a pure phonon regime from multi-channel scattering involving both collective and single-particle excitations above threshold. For large twist angles, competition between kinetic and Zeeman energies reduces the effective spin rotation, leading to comb-like density modulations and Fano-like resonances below threshold. The transition probability between phonon and particle channels is strongly tunable with $Θ$, enhanced for odd multiples of $π$ but suppressed for even multiples. These findings establish twist-engineered domain walls as a versatile platform for controlling quantum transport, with implications for atomtronic devices and quantum simulation.

Nelson's stochastic mechanics formulates quantum dynamics as a real-time conservative diffusion process in which a particle undergoes Brownian-like motion with a fluctuation amplitude fixed by Planck's constant. While being mathematically equivalent to the Schrödinger formulation, this approach provides an alternative dynamical framework that enables the study of time-resolved quantities that are not straightforwardly defined within the standard operator-based approach. In the present work, Nelson's stochastic mechanics is employed to investigate tunneling-time statistics for bound states in double-well potentials. Using first-passage time theory within this framework, both the mean tunneling time, $\barτ$, and the full probability distribution, $p(τ)$, are computed. The theoretical predictions are validated through extensive numerical simulations of stochastic trajectories for two representative potentials. For the square double-well potential, analytical expressions for $\barτ$ are derived and are shown to be in excellent agreement with simulations. In the high-barrier limit, the results reveal a direct relation between the stochastic-mechanical and quantum-mechanical tunneling times, expressed as $τ_{\mathrm{QM}} = (π/2)\barτ$, where $τ_{\mathrm{QM}}$ corresponds to half the oscillation period of the probability of finding the particle in either well. This relation is further confirmed for generic double-well systems through a WKB analysis. As a concrete application, the inversion dynamics of the ammonia molecule is analyzed, yielding an inversion frequency of approximately 24 GHz, in close agreement with experimental observations. These results highlight the potential of stochastic mechanics as a conceptually coherent and quantitatively consistent framework for analyzing tunneling phenomena in quantum systems.

LoRa is one of the most widely used low-power wide-area network technology for the Internet of Things. To achieve long-range communication with low power consumption at a low cost, LoRa uses a chirp spread spectrum modulation and transmits in the sub-GHz unlicensed industrial, scientific, and medical (ISM) frequency bands. Due to the rapid densification of IoT networks, it is crucial to obtain tailored channel models to evaluate the performance of LoRa networks. While channel models for cellular technologies have been investigated extensively, specific characteristics of LoRa transmissions operating at long range with a rather small (~ 250kHz) bandwidth require dedicated measurement campaigns and modeling efforts. In this work, we leverage an SDR-based testbed to gather and publish a dataset of LoRa frames transmitted in a campus environment. The dataset includes IQ samples of the received frames at multiple locations and allows for the evaluation of channel variations with high time resolution. Using the gathered data, we derive empirical propagation channel models for LoRa that include receiver correlation over distance for three scenarios: unmanned aerial vehicle (UAV) line-of-sight (LoS), UAV non-LoS, and pedestrian non-LoS. Furthermore, the dataset is annotated with synchronization information, enabling the evaluation of receiver algorithms using experimental data.

Molecular communication (MC) enables information transfer using particles inspired by biological systems. Volatile Organic Compounds (VOCs) are one of the most abundant and diverse classes of signaling molecules used by living or non-living objects. VOC-based MC holds great promise in developing long-range, bio-compatible communication systems capable of interfacing nano- and micro-scale devices. In this paper, we present a comprehensive end-to-end framework for VOC-based interplant MC from an ICT perspective. The communication process is divided into three stages: transmission (VOC biosynthesis and emission from leaves), channel propagation (advection-diffusion in turbulent wind via Gaussian puff for stress-induced VOC release and Gaussian plume for constitutive VOC release), and reception (VOC uptake and physiological response in the receiver plant). Each stage is analyzed by its attenuation and delay. Numerical results demonstrate that VOC-based channels exhibit low-pass behavior, with bandwidth and capacity heavily influenced by distance, wind velocity, and noise. Though the physical channel supports moderate frequencies, biological constraints at the transmitter restrict the end-to-end channel to slow-varying signals.

We analyze a cosmological solution to the field equations of a modified gravity model where curvature and matter are nonminimally coupled. The current Universe's accelerated expansion is driven by a cosmological constant while the impact of the nonminimal coupling on the expansion history is recast as an effective equation of state for evolving dark energy. The model is analyzed under a tracking solution that follows the minimum of the effective potential for a scalar field that captures the modified theory's effects. We determine the conditions for the existence of this minimum and for the validity of the tracking solution. Cosmological constraints on the parameters of the model are obtained by resorting to recent outcomes of data from the DESI collaboration in combination with the Pantheon+ and Dark Energy Survey supernovae compilations, which give compatible results that point to the presence of a dynamical behavior for dark energy. The gravity model violates the equivalence principle since it gives rise to a fifth force that implies the Earth and Moon fall differently towards the Sun. The cosmological constraints are intersected with limits resulting from a test of the equivalence principle in the Earth-Moon system based on lunar laser ranging data. We find that a variety of model parameters are consistent with both of these constraints, all while producing a dynamical evolution of dark energy with similarities to that found in recent DESI results.

Spontaneous symmetry breaking is a cornerstone of modern physics, defining a wealth of phenomena in condensed-matter and high-energy physics, and beyond. It requires an infinite number of degrees of freedom, and even then, for continuous symmetries, it only works if the spatial dimension is not too low, following the classic results of Coleman, Hohenberg, Mermin and Wagner. While usually discussed in the context of quantum and statistical field theories, and in particular, effective field theories, there are advantages in addressing the same kind of phenomena on discrete geometric structures rather than conventional manifolds. When the space is discretized into a lattice, a lucid picture of conventional spontaneous symmetry breaking springs up, with the ultraviolet issues of continuum quantum field theory out-of-sight, and the key effect, which is infrared in nature, revealed through elementary harmonic oscillator networks. From there, it is natural to generalize lattices to other graphs/networks. In this setting, the presence of spontaneous symmetry breaking is controlled by fractional generalizations of resistance distance and the Kirchhoff index, and most broadly by the spectral dimension. Predictably, because of the richness of discrete geometric structures in comparison with continuous manifolds, a broader array of geometries emerge where spontaneous breaking of continuous symmetries is blocked by large fluctuations.

An accurate characterisation of the physical properties of galaxies at cosmic dawn is key to understanding the origin of the high abundance of UV-bright galaxies at z$\gtrsim$10. We exploit deep NIRSpec PRISM observations of GHZ2 to constrain the sources of ionising radiation and the properties of the ISM in this bright, compact, and highly ionising galaxy at z=12.3. We measure with high significance the prominent N IV, C IV, He II, O III, C III, O II, and Ne III emission features previously detected in shallower observations, and confirm the detection of the N III] $λ1750$ multiplet, yielding tight constraints on the N/O ratio, which is found to be $\simeq$2 times the solar value. We also detect the Mg II $λ2800$, [Fe IV] $λ2833$ and Si II $λ1812$ doublets, the H8+HeI $λλ3889$ blend, and the Si IV+O IV] $λλ1400$ absorption complex. The O III $λ3133$ fluorescence line is only detected in the first observing epoch, implying variability on a rest-frame time span of 19 days, strongly suggesting the presence of an active nucleus. Combining the NIRSpec dataset with available optical and far-infrared constraints from MIRI and ALMA, we show that the emission spectrum of GHZ2 cannot be reproduced by single-density spectro-photometric models. Multi-zone photoionisation modelling performed with the HOMERUN code demonstrates that star formation must be occurring in a strongly stratified ISM, where both low-/intermediate-density gas and high-density regions (log($n_e$/cm$^{-3}) \gtrsim 4$) coexist. The GHZ2 emission landscape is consistent with either a composite star-formation plus AGN scenario, or with star formation occurring in a combination of radiation- and matter-bounded regions. Purely radiation-bounded stellar models fail to reproduce the observed He II emission, making an additional hard ionising component unavoidable.

Topological quasiparticles, such as merons and bimerons, are characterized by non-trivial textures that exhibit remarkably robust transport against deformation, offering significant potential for information processing. While these phenomena have been explored in various systems, acoustic realizations remain challenging. Here, we report that acoustic meron topological textures were successfully realized using designed Archimedeanlike square spiral metastructures via the excitation of spoof surface acoustic waves (SSAWs). By applying mirror-symmetric combinatorial operations to the unit structures, we further construct composite chiral metastructures that enable both one-dimensional and two-dimensional stable transport of acoustic bimerons. It is further revealed that bimeron transport originates from the locked opposite phase differences of SSAWs, induced by the handedness of the cavity resonant modes. The intrinsic robustness of the meron textures against structural defects is confirmed through the calculation of their topological charge. Our findings establish stable acoustic bimeron transport as a topologically resilient foundation for future acoustic information processing and storage technologies.

The crux of understanding the superconducting mechanism in pressurized Ruddlesden-Popper nickelates hinges on elucidating their structural phases. Under ambient conditions, the trilayer nickelate La4Ni3O10 stabilizes in a twinned monoclinic structure with space group P21/c. Upon heating, it undergoes a structural transition to the tetragonal I4/mmm phase at Ts ~ 1030 K, while a second transition associated with the onset of density-weave (DW) ordering emerges upon cooling below TDW ~ 135 K. Here from pressure-temperature x-ray diffraction on high quality flux-grown single crystals we unequivocally demonstrate a direct tetragonal-to-monoclinic transition with no trace of intermediate orthorhombic Bmab phase. Ab initio density-functional theory calculations as a function of pressure fully corroborate the experimental observations. The transition unfolds as a 2-fold superstructure due to the emergence of commensurate superlattice reflections and can be progressively suppressed from 1030 K down to 20 K under 14 GPa. Notably, from XRD we establish the first observation of weak incommensurate satellite reflections associated with the DW ordering in fluxgrown samples, as previous findings were confined to only to crystals grown by the floating-zone technique. This is further reinforced by Raman spectroscopy that reveal the emergence of additional phonon modes below 130 K, implying a breaking of monoclinic P21/c symmetry.

We investigate the impact of shear viscosity on the propagation of primordial gravitational waves (pGW) after inflation. Without assuming a specific inflationary scenario we focus on the evolution of pGWs after they re-enter the horizon during a cosmological epoch characterized by the presence of shear viscosity. We show that shear viscosity introduces an additional damping term in the tensor equation, modifying both the transfer function and the energy density power spectrum. For a constant shear viscosity-to-Hubble ratio the transfer function acquires an extra red tilt, while a time-dependent viscosity leads to a running spectral index $Ω_\text{GW}\sim k^{n_\text{eff}(k)}$ controlled by the time evolution of the mean free path of the viscous fluid. Our analysis provides a general framework to analytically quantify how shear viscosity can alter the primordial gravitational wave background in standard and non-standard post-inflationary scenarios. As a case study we evaluate the effect of viscosity of the electron-photon-baryon plasma, on both the transfer function and the normalized energy density, finding a $k$-dependent blue tilt due to gravitational wave freeze-out from the viscous phase. This effect corresponds to a fractional difference of order $10^{-3}$.

Ultracold neutral atoms in optical lattices are a promising platform for simulating the behavior of complex materials and implementing quantum gates. We optimize collision gates for fermionic Lithium atoms confined in a double-well potential, controlling the laser amplitude and keeping its relative phase constant. We obtain high-fidelity gates based on a one-dimensional confinement simulation. Our approach extends beyond earlier Fermi-Hubbard simulations by capturing a momentum dependence in the interaction energy. This leads to a higher interaction strength when atoms begin in separate subwells compared to the same subwell. This momentum dependence might limit the gate fidelity under realistic experimental conditions, but also enables tailored applications in quantum chemistry and quantum simulation by optimizing gates for each of these cases separately.

Transmit Array Spatial Encoding (TRASE) is an MRI technique in which spatial encoding is achieved using phase gradients of the B1 field. This approach offers potential advantages such as hardware simplicity and reduced acoustic noise. In this study, we present an assessment of various winding patterns for twisted solenoid phase-gradient coils, including the simple twisted solenoid (with and without return wire), a double-wound twisted solenoid, and a discrete-loop twisted solenoid. We analyze the magnetic field uniformity and phase linearity of these configurations using Biot-Savart simulations. Our results show that both the double-wound and discrete loop designs offer similar improvements over the simple twisted solenoid with return wire. The discrete loop pattern requires less wire than the double-wound version, making it the preferred option for practical coil construction and operation in a TRASE MRI system.

Automated verbal deception detection using methods from Artificial Intelligence (AI) has been shown to outperform humans in disentangling lies from truths. Research suggests that transparency and interpretability of computational methods tend to increase human acceptance of using AI to support decisions. However, the extent to which humans accept AI judgments for deception detection remains unclear. We experimentally examined how an AI model's accuracy (i.e., its overall performance in deception detection) and confidence (i.e., the model's uncertainty in single-statements predictions) influence human adoption of the model's judgments. Participants (n=373) were presented with veracity judgments of an AI model with high or low overall accuracy and various degrees of prediction confidence. The results showed that humans followed predictions from a highly accurate model more than from a less accurate one. Interestingly, the more confident the model, the more people deviated from it, especially if the model predicted deception. We also found that human interaction with algorithmic predictions either worsened the machine's performance or was ineffective. While this human aversion to accept highly confident algorithmic predictions was partly explained by participants' tendency to overestimate humans' deception detection abilities, we also discuss how truth-default theory and the social costs of accusing someone of lying help explain the findings.

We present a generalization of down-up algebras, originally defined by Benkart and Roby. These quiver down-up algebras arise as quotients of the double of the extended Dynkin quiver of type A. Under a certain non-degeneracy condition, we show that quiver down-up algebras are noetherian piecewise domains, and that they are twisted Calabi--Yau. Finally, we consider the isomorphism problem for graded quiver down-up algebras.

The generation of engineered quantum states of light via nonlinear processes is fundamental for quantum technologies based on photons. Although embedding nonlinear materials within resonant structures allows for the enhancement and tailoring of photon properties, accurately modeling these quantum interactions remains a challenge. In this work, we apply the asymptotic-fields formalism, an approach based on scattering theory, to describe nonlinear optical processes within a Fabry-Pérot cavity. Unlike previous applications of this formalism, we explicitly account for reflections in the system. We derive the interaction Hamiltonian and calculate photon-pair generation rates using perturbation theory. The versatility of this model is illustrated through three examples: (i) spontaneous parametric down-conversion in an idealized cavity with flat-response mirrors; (ii) the generation of counter-propagating photon pairs in a periodically-poled material; and (iii) spontaneous four-wave mixing in a cavity built with Bragg reflectors.

Assessing whether two patient populations exhibit comparable event dynamics is essential for evaluating treatment equivalence, pooling data across cohorts, or comparing clinical pathways across hospitals or strategies. We introduce a statistical framework for formally testing the similarity of competing risks models based on transition probabilities, which represent the cumulative risk of each event over time. Our method defines a maximum-type distance between the transition probability matrices of two multistate processes and employs a novel constrained parametric bootstrap test to evaluate similarity under both administrative and random right censoring. We theoretically establish the asymptotic validity and consistency of the bootstrap test. Through extensive simulation studies, we show that our method reliably controls the type I error and achieves higher statistical power than existing intensity-based approaches. Applying the framework to routine clinical data of prostate cancer patients treated with radical prostatectomy, we identify the smallest similarity threshold at which patients with and without prior in-house fusion biopsy exhibit comparable readmission dynamics. The proposed method provides a robust and interpretable tool for quantifying similarity in event history models.

In the presence of a strong electric field, the vacuum is unstable to the production of pairs of charged particles -- the Schwinger effect. The created pairs extract energy from the electric field, resulting in nontrivial backreaction. In this paper, we study 1+1D massive QED subject to strong external electric fields in a self-consistent and fully quantum manner. We use the bosonized version of the theory, which attains a cosine interaction term in the presence of nonzero fermion mass $m$. However, the assumption of strong electric field justifies a perturbative treatment of the cosine interaction, i.e., an expansion in $m$. We calculate the vacuum expectation value of the electric field to first order in $m$ and show that -- surprisingly -- it satisfies a classical nonlinear partial differential equation (related to the sine-Gordon equation). We show that the electric field exhibits dissipation-free oscillations (analogous to ordinary plasma oscillations) and calculate the plasma frequency analytically. We also compare to the semiclassical approximation commonly used to study backreaction, showing that it fails to capture the $O(m)$ shift in the plasma frequency.

We study the average shifted convolution sum $$ B(H,N):= \frac{1}{H} \sum_{h \sim H} \sum_{n \sim N} A_{π_1}(n)\, A_{π_2}(n+h), $$ where $A_{π_i}(n)$ denotes the Fourier coefficients of a Hecke--Maass cusp form $π_i$ for $\mathrm{SL}(d_i,\mathbb{Z})$ with $d_i\ge 4$, $i=1,2$. We establish a nontrivial power-saving bound of $B(H,N)$ for the range of the shift $H\ge N^{1-\frac{4}{d_1+d_2}+\varepsilon}$ for any $\varepsilon>0$. For the cases $d_1 = d_2 + 1$ and $d_1 = d_2$, our result extends a result that can be derived from a theorem of Friedlander and Iwaniec. In particular, when $d_1 = d_2$, we reach the critical threshold $H\ge N^{1-2/d+\varepsilon}$ such that any further improvement in this range yields a subconvexity bound for the corresponding standard $L$-function in the $t$-aspect.

While Large Language Models (LLMs) have been extensively tested in dyadic game-theoretic scenarios, their collective behavior within complex network games remains surprisingly unexplored. To bridge this gap, we present NetworkGames, a framework connecting Generative Agents and Geometric Deep Learning. By formalizing social simulation as a message-passing process governed by LLM policies, we investigate how node heterogeneity (MBTI personalities) and network topology co-determine collective welfare. We instantiate a population of LLM agents, each endowed with a distinct personality from the MBTI taxonomy, and situate them in various network structures (e.g., small-world and scale-free). Through extensive simulations of the Iterated Prisoner's Dilemma, we first establish a baseline dyadic interaction matrix, revealing nuanced cooperative preferences between all 16 personality pairs. We then demonstrate that macro-level cooperative outcomes are not predictable from dyadic interactions alone; they are co-determined by the network's connectivity and the spatial distribution of personalities. For instance, we find that small-world networks are detrimental to cooperation, while strategically placing pro-social personalities in hub positions within scale-free networks can significantly promote cooperative behavior. We validate the robustness of these findings through extensive stress tests across multiple LLM architectures, scaled network sizes, varying random seeds, and comprehensive ablation studies. Our findings offer significant implications for designing healthier online social environments and forecasting collective behavior. We open-source our framework to facilitate research into the social physics of AI societies.

In 1981 Antonyan classified the orbits of SL$(8,\mathbb{C})$ on $\bigwedge^4 \mathbb{C}^8$. This is an example of a $θ$-group action as introduced and studied by Vinberg. The orbits of a $θ$-group are divided into three classes: nilpotent, semisimple and mixed. We consider the action of SL$(8,\mathbb{R})$ on $\bigwedge^4 \mathbb{R}^8$ and classify the nilpotent and semisimple orbits as well as the Cartan subspaces. The semisimple orbits are divided into 1441 parametrized classes. Due to this high number a classification of the mixed orbits does not seem feasible. Our methods are based on Galois cohomology.