Pinching antenna (PA) systems have recently gained significant attention. While their physical-layer security (PLS) is being explored, most studies rely on idealized lossless models, ignoring practical waveguide attenuation. In this paper, we investigate the PLS performance of PA systems under a more realistic attenuation-incorporated waveguide model. Specifically, we investigate a PA system-based secure communication scenario consisting of a base station (BS), a legitimate user, and a passive eavesdropper. We derive expressions for closed-form upper and lower bounds on both the secrecy outage probability (SOP) and ergodic secrecy capacity (ESC). The results indicate that the PA system outperforms conventional fixed-antenna systems.

Non-parametric approaches to test for trends in time series make use of the Mann-Kendall statistic. Based on asymptotic arguments, these tests assume that its distribution follows a Gaussian distribution, even for autocorrelated time series. Recent results on the lack of validity of this assumption urge a robustness analysis of these approaches. While the issue is relevant across a wide range of applications, we illustrate it here in the context of detecting early warning signals (EWS) of critical transitions, which are used across a variety of research domains, and where commonly applied methods generate autocorrelation. We present a broad analysis, covering all types of critical transitions commonly investigated in EWS studies. We compare empirical distributions of the Mann-Kendall statistic computed from classical EWS indicators preceding critical transitions to the theoretical distributions hypothesized by Mann-Kendall tests. We detect mismatches leading to inflated type I error rates, which would routinely lead to announcing a critical transition while it is not occurring. In contrast to a recent recommendation, we conclude that the use of Mann-Kendall tests for trend detection in the context of forecasting critical transitions should be avoided. We point out several alternative methods available instead.

``Behind every limit theorem, there is an inequality'' said Kolmogorov. We say ``for every inequality, there is an approximate inequality under approximate regularity conditions.'' Suppose $X, X'$ are independent and identically distributed random variables. Then $X \le X'$ with a probability of at least $1/2$, irrespective of the underlying (common) distribution. One can ask what happens to the probability if $X, X'$ are independent but not identically distributed. It should be approximately $1/2$ if the distributions are approximately equal. Similarly, what if the random variables are dependent? It should, again, be approximately $1/2$ if the random variables are approximately independent. We explore an extension of this probability inequality involving order statistics and develop approximate versions of such an inequality under violations of independence and identical distribution assumptions. We further show that this inequality can be used as a basis to prove asymptotic validity of bootstrap/subsampling, finite-sample validity of conformal prediction, permutation tests, and asymptotic validity of rank tests without group invariance. Specifically, in the context of resampling inference, our results can be seen as a finite-sample instantiation of some results by Peter Hall and yield an alternative ``cheap bootstrap'' that applies to high-dimensional data.

Quantum state purification, which operates not by identifying and correcting specific errors but by repeatedly projecting multiple noisy copies onto special subspaces, provides a syndrome-free alternative to quantum error correction. Existing purification protocols, however, generally assume unconstrained operations and thus overlook the energetic restrictions inherent in realistic quantum devices. Here, we establish a general framework for universal state purification under energy-conservation constraints for depolarizing noise. We derive a necessary and sufficient condition for the nonexistence of universal energy-preserving purification and, whenever such purification is feasible, analytically determine the optimal performance and the corresponding protocols. We further show how the optimal protocols can be systematically implemented using only energy-preserving operations. Numerical results confirm the effectiveness of the proposed scheme. Our framework recovers the standard purification setting as a special case and naturally extends to scenarios assisted by external energy resources. These results identify fundamental physical limits on state distillation and provide an energy-efficient route to quantum error mitigation.

Optimized charging of electric vehicles (EVs) at public locations consists of two decisions: how much energy to deliver at what times, which is continuous, and where to plug in, which is binary. This makes optimizing EV charging a mixed-integer linear program (MILP). This discreteness undermines traditional marginal pricing methods. In this paper, we develop the first marginal-price-based mechanism for pricing EV charging with binary station access constraints. Using the result of Burer (2009), we express the EV charging as a completely positive program (CPP), whose dual is a copositive program (COP). This convex dual admits valid shadow prices even though the original allocation problem is discrete and nonconvex. By interpreting the COP dual variables as marginal prices, we construct a pricing mechanism that captures EV supply equipment (EVSE) congestion as well as charging-capacity limits. We prove that the resulting mechanism is revenue-adequate for the operator and individually rational for every EV user, in the strong sense that each user maximizes their own welfare by accepting their assigned charging plan rather than deviating to any alternative option. We further develop problem-specific inner-approximation and dimension-reduction techniques that substantially improve the computational tractability of solving the COP in our setting. Numerical experiments on both small and large scale charging instances demonstrate that our pricing mechanism captures discrete congestion effects and aligns user incentives with the system-optimal assignment, outperforming time-of-use (TOU) and convex relaxation benchmarks.

In this paper, we prove existence and uniqueness of energy solutions for nonlinear Schrödinger equations with a multiplicative white noise on $R^d$ with $d\le3$. We rely on an exponential trans-form and conserved quantities for existence of energy solutions. Using paracontrolled calculus, we prove Strichartz inequalities which encode the dispersive properties of the solutions. This allows to obtain local well-posedness for low regularity solutions and uniqueness of energy solutions for various equations. In particular, our results are the first results of propagation without loss of both regularity and localization for such equations in full space as well as the first results on $R^3$ for such singular dispersive SPDEs. We are also obtain local well-posedness in two dimensions for deterministic initial data.

Extracting actionable insights from long-duration urban videos is often labor-intensive: analysts must manually sift through raw footage to pinpoint target events or uncover broader behavioral trends. In this work, we present URBANCLIPATLAS, a visual analytics system for exploring long urban videos recorded at street intersections. URBANCLIPATLAS combines retrieval-augmented generation (RAG), taxonomy-aware entity extraction, and video grounding to support event retrieval and interpretation. The system segments extended recordings into short clips, generates textual descriptions with a vision-language model, and indexes them for semantic retrieval. A knowledge graph maps entities and relations from LLM answers onto a domain-specific taxonomy and aligns them with detected objects and trajectories to support visual grounding and verification. URBANCLIPATLAS supports scene retrieval through an augmented chat-based interface and improves scene interpretation by tightly aligning textual outputs with video evidence. This design strengthens the connection between textual reasoning and visual evidence, reducing the effort required to validate model outputs and refine hypotheses. We demonstrate the usefulness of URBANCLIPATLAS on the StreetAware dataset through two case studies involving hazardous scenarios and crossing dynamics at street intersections. URBANCLIPATLAS helps analysts reason about safety- and mobility-related patterns across large urban video collections.

Objective. Decoding visual attention from brain signals during naturalistic video viewing has emerged as a new direction in brain-computer interface research. Current methods assume that stronger coupling between object motion and neural activity indicates higher attention, but this can be confounded by eye movement artifacts and stimulus properties. This study investigates how visual eccentricity (the distance between a visual object and the fixation point) affects neural responses when eye movement artifacts are controlled. Approach. EEG signals were recorded across three tasks that manipulated object eccentricity and attention conditions while participants maintained gaze fixation. Correlation analysis and match-mismatch decoding were performed to quantify the neural tracking of object motion. Main results. The analysis supports three conclusions: (1) neural tracking of object motion in natural videos works under gaze fixation; (2) the strength of neural tracking under gaze fixation is predictive of attention; and (3) there exists a significant eccentricity confound in the EEG responses, with poorer neural tracking of motion at larger eccentricities. Significance. These results provide critical evidence that findings from previous free-viewing studies reflect genuine neural processing rather than mere oculomotor artifacts. However, the identified eccentricity effect highlights a major limitation for current decoding approaches that assume coupling strength reflects attention levels alone.

We present a mathematical model of a market with $m$ shares traded across $n$ investor groups, each one with similar motivations and trading strategies. The market of each asset consists of a fixed amount of cash and shares (no additions are allowed over time, so the system is closed), and the trading groups are influenced by trend and valuation motivations when buying or selling each asset, but follow a strategy where the purchase of one asset depends on the price of another, while the sale does not. Using these assumptions and basic microeconomic principles, the mathematical model is derived using a dynamic systems approach. We analyze the stability of the model's equilibrium points and determine the parameter conditions for such stability. First, we show that all equilibria are stable in the absence of a clear emphasis on trend-based valuation for each share. Secondly, for systems where the trading group prioritizes the valuation of each stock and the trend of the other for trading purposes, we establish stability conditions and demonstrate with numerical examples that when instability occurs, it manifests as price oscillations in the stocks. Furthermore, we argue for the existence of periodic solutions via a Hopf bifurcation, taking the momentum coefficient as the bifurcation parameter. Finally, we present examples and numerical simulations to support and expand upon the analytical results. One finding in economics and finance is the existence of cyclical behavior in the absence of exogenous factors, as determined by the momentum coefficient. In particular, a stable equilibrium price becomes unstable as trend-based trading increases.

The subspace design property for additive codes is a higher-dimensional generalization of the minimum distance property. As shown recently by Brakensiek, Chen, Dhar and Zhang, it implies that the code has similar performance as random linear codes with respect to all "local properties". Explicit algebraic codes, such as folded Reed-Solomon and multiplicity codes, are known to have the subspace design property, but they need alphabet sizes that grow as a large polynomial in the block length. Constructing explicit constant-alphabet subspace design codes was subsequently posed as an open question in Brakensiek, Chen, Dhar and Zhang. In this work, we answer their question and give explicit constructions of subspace design codes over constant-sized alphabets, using the expander-based Alon-Edmonds-Luby (AEL) framework. This generalizes the recent work of Jeronimo and Shagrithaya, which showed that such codes share local properties of random linear codes. Our work obtains this consequence in a unified manner via the subspace design property. In addition, our approach yields some improvements in parameters for list-recovery.

The American Community Survey (ACS) Public Use Microdata Sample (PUMS) provides access to a wide range of unit-level survey data consisting of correlated Gaussian and binomial distributed survey responses along with associated survey weights. As such, we propose a Bayesian hierarchical framework for jointly modeling unit-level Gaussian and binomial survey data. The model introduces a shared area-level random effect to capture dependence across responses. Informative sampling is addressed using a pseudo-likelihood construction, and Polya-Gamma data augmentation provides an efficient conjugate Gibbs sampler, enabling scalable inference for large survey datasets. Through empirical simulations based on ACS PUMS data, we show that the joint model achieves notable reductions in mean squared error and improved interval scores compared to univariate and design-based estimators. Applying the method to the 2023 Illinois PUMS data, we find that the joint model yields small-area estimates similar to those from the univariate model and the Horvitz-Thompson estimator, but with smaller posterior variances. The computational cost associated with the joint model is also comparable to that of the univariate binomial model. Combined with the empirical simulation results, these findings demonstrate the practical advantages of the proposed approach.

We explore the expected performance of a semiconducting spin cQED quantum processor for Multiple Hypothesis Tracking (MHT) algorithm via a quantum annealing procedure. From two different benchmarking scenarios we evaluate this type of quantum annealer on a quantum emulator in which we incorporated both dynamical coherent errors and incoherent errors. From estimate of the reset, measurement and annealing time of the processor, we find that cQED-spin processors could reach a total run time of around 50 ms. This makes this technology promising for potential real time application such as radar tracking.

We study the orientational dynamics of superparamagnetic colloidal dimers that carry both an induced magnetic moment, proportional to the applied field, and an effective permanent moment. In a static, uniform magnetic field, dimers that are permanently fixed together hop between two preferred in-plane angles, developing a bimodal steady-state orientation distribution. When the same field is periodically reversed, we observe a sharp, field-controlled change in the dynamical response from small hopping events with $Δθ\ll π$ to full $Δθ\approx π$ rotations on each field flip. We show that both the static bistability and the switching bifurcation can be rationalised by a magnetic response in the dimer that consists of both a strong induced and weak body-fixed component. This leads to a complex orientational energy/potential landscape, with coupled roll-yaw rotations of the dimer responsible for the bistable dynamics. By combining the misorientation between dimer axis and field, bifurcation field strength and short-time orientational variance, we determine the magnitude and orientation of the net permanent dipole, thereby characterising details of the internal magnetic structure of the particles via microscopy.

Shape adaptive shape memory alloy hybrid composites (SMAHCs) are composites that incorporate shape memory alloys (SMAs) to realize shape transformation. Despite the availability of numerous analytical and finite element models for predicting the transient response of SMAHCs, many approaches exhibit limitations with respect to the thermomechanical coupling and comprehensive experimental validation. Therefore, this paper presents a coupled, multiphysics, 3D finite element approach for the simulation of a SMAHC actuator, integrating mechanical, thermal and electromagnetic solvers in the Finite Element Code ANSYS LS-DYNA. The proposed approach employs a micromechanical constitutive model implemented in ANSYS LS-DYNA, to accurately capture the complex thermomechanical phase transformation of SMAs. A key feature of the model is the ability to prescribe a defined martensitic pre-strain through a preceding simulation step, in which an initially scaled SMA wire is mechanically loaded and stretched to its nominal length. This procedure enables partial detwinning of the martensitic microstructure and provides a physically motivated initialization of the material state. Joule heating of the SMA wires, as well as varying mechanical loads and ambient temperature conditions, are explicitly considered. The simulation results are validated against experimental data and a fully coupled transient staggered scheme model to assess the predictive capability of the 3D approach. The results show good qualitative agreement, reproducing the characteristic hysteresis of actuator deflection as a function of temperature. Quantitatively, the predicted deflections are of the correct order of magnitude, although marginally outside the 95 % experimental confidence interval. Overall, a consistent trend between simulation and experiment is observed, giving rise to possibility of simulating more complex SMAHC systems.

Bars play an integral role in regulating star formation (SF) in spiral galaxies, from triggering central starbursts to driving quenching. The diverse SF morphologies observed in local barred galaxies reflect different evolutionary stages of the bar, motivating studies across these stages. Here we study 12 nearby barred galaxies (z=0.01-0.06) identified as centrally quenched galaxies (having extended star-forming discs but quenched inner regions) by leveraging the differences in SFRs between the MPA-JHU and GSWLC catalogues. However, they exhibit residual central emission in the SDSS 3" fibre spectral region. Emission line analysis shows that this emission originates from either ongoing SF or LINER-like activity, suggesting diverse central ionization mechanisms. Using spatially resolved UV-optical colour maps from SDSS (r-band) and GALEX (FUV and NUV band) imaging data, we find that discs are star-forming and bluer in colour (NUV-r < 4 mag) while the bulge and bar regions are systematically redder (NUV-r > 4 mag) and dominated by older stellar populations. The NUV-r radial colour profiles show a clear transition from red to blue colours at the bar end with a corresponding median stellar age of ~ 1 Gyr. Compared to fully centrally quenched barred galaxies from our earlier work which lack SDSS fibre emission, these galaxies remain systematically bluer at similar radii, despite showing NUV-r > 4 mag inside the bar suggesting an intermediate stage in bar-driven quenching. We also estimate black hole masses associated with kinetic-mode AGN feedback and find them below the threshold (logM_BH < 8.0). Adding this with the presence of pseudo bulges, our results support bars as the primary drivers of quenching, with these galaxies representing an evolutionary phase just before their inner regions are completely quenched.

The study of Sobolev and Poincaré inequalities for differential forms in Carnot groups and in the more general sub-Riemannian setting is still an open problem in its full generality. One may conjecture that, for general Carnot groups, these inequalities are expressed in terms of suitable graded Lebesgue norms. In recent years, many results have been obtained, both in the Euclidean setting and in the Heisenberg groups, as well as for contact manifolds with bounded geometry. There are also some results for general Carnot groups; however, these do not cover the problem in its full generality. In this paper, we consider a particular Carnot group, the so-called Cartan group (a free Carnot group, of step $3$ with $2$ generators), which provides a natural testing ground for these questions, since its step-three structure already exhibits several phenomena that do not occur in the Heisenberg groups. In this setting, we are able to prove global Poincaré and Sobolev-Gaffney inequalities for differential forms. With the aim of obtaining sharp estimates, we replace the de Rham complex of differential forms with the Rumin complex. The case $p>1$ is carried out after establishing an $L^p$-Hodge decomposition with homogeneous Sobolev classes. We are able to consider also the endpoint case $p=1$; however, as in Euclidean setting, when $p=1$, the operator we deal with provides only weak-type estimates which do not yield a Hodge decomposition analogous to the case $p>1$. Therefore, in this situation the proof follows a different approach, relying on a recent result proved in \cite{BT}.

Let $S\subset \mathbb{R}^d$ $(d\geq 2)$. A set $S$ is said to be $m$-point convex, if for every $m$ distinct points in $S$, at least one of the line-segments determined by them lies in $S$. We also say that $S$ has property $P_m$. Let ${x,y,z}\in \mathbb{R}^{d}$. If $\mathrm{conv}\{x,y,z\}$ is a right triangle, then $\{x,y,z\}$ is called a {\it right triple}. A set $S$ is said to have the right-$3$-point property,if, for every right triple of $S$, at least one of the line-segments determined by them belongs to $S$. In particular, it has the double right-$3$-point property, if, for every right triple in $S$, at least two of the line-segments determined by them belong to $S$. In this paper, we further investigate $m$-point convex sets and establish the relationship between the sets with the double right-$3$-point property and convex sets in $\mathbb{R}^d$.

We study the penetration of an external magnetic field into a superconductor with collinear $d$-wave altermagnetic order. We demonstrate that instead of circular Abrikosov vortices, the magnetic field generates elliptical vortices with their major axis oriented along one of the crystallographic axis, along which the altermagnetic spin splitting is maximal. Upon reversing the component of the magnetic field parallel to the altermagnetic Néel vector, the vortices reorient towards the other crystallographic axis with maximal spin splitting. We demonstrate that this effect originates from an altermagnetism-induced anisotropy of the effective mass, which is controlled by the coupling between the external magnetic field and the Néel vector. As a consequence, a superconducting film hosting such altermagnetic order and containing pinning defects exhibits nonreciprocal magnetization curves under reversal of the magnetic field parallel to its Néel vector, due to the different vortex--vortex interaction energies for the two field orientations. Our results broaden the understanding of the coexistence of altermagnetism and superconductivity, both in materials hosting these orders intrinsically or in superconductor/altermagnet hybrid structures, and open new experimental avenues for exploring supercurrent vortices in these systems.

We study the question of whether a sequence of non-instanton Yang-Mills connections can limit to a bubbling configuration composed only of instantons. In the case that the Uhlenbeck limit and the bubbles are of opposite charge, we determine an obstruction coming from deformations of the Uhlenbeck limit. As an application, we prove that instantons are the only solutions of the $\mathrm{SU}(2)$ Yang-Mills equation on $\mathbb{R}^4$ with energy less than $4π^2 \left( |κ| + 2 \right) + \varepsilon_κ,$ where $κ$ is the charge. We also prove discreteness of the energy spectrum on the trivial $\mathrm{SU}(2)$-bundle in the range $\left[ 0, 16 π^2 \right).$

Rare and very rare decays of third-generation particles, including $b$-hadrons and $τ$ leptons, provide sensitive probes of physics beyond the Standard Model (SM). Unlike direct searches limited by collider energies, they probe new physics at much higher energy scales. Many of these decays have SM-predicted branching fractions below the sensitivity of current detectors. These proceedings report on recent LHCb searches, including several first searches and results setting the most stringent limits to date. In particular, searches for $b \to s τ^+τ^-$, $b \to s τ^\pm e^\mp$, $b \to s μ^\pm e^\mp$, and $τ^- \to μ^-μ^+μ^-$ are presented, alongside searches for lepton-number-violating processes and loop-suppressed annihilation decays.

We provide a comparatively simple proof of the dynamical stability of Ricci flow near a linearly stable Ricci-flat ALE metric with integrable deformations. Our proof relies on the equivalence between integrability and an "almost-orthogonality" property of the Ricci-DeTurck tensor, allowing us to analyze the latter directly. We obtain our main results in weighted Holder spaces and then show how to recover the $L^p$-stability theorems of Deruelle-Kroncke and Kroncke-Petersen.

We revisit static tidal perturbations of relativistic stars with emphasis on two technical issues in the standard quadrupolar formulation. First, we derive the regular-center Frobenius expansion of the interior even-parity master function and obtain a corrected subleading coefficient, which differs from the expression commonly used in the literature. Second, we derive the static even-parity master equation on a Schwarzschild-de Sitter background, extending the usual asymptotically flat problem to a two-horizon geometry. To place these results on a common footing, we also show how the general interior even-parity system in Regge-Wheeler gauge reduces to the standard quadrupolar equation used in Love-number calculations. Numerical integrations for polytropic equations of state show that the corrected center coefficient affects only subleading initial data and leaves the extracted Love number $k_2$ unchanged within numerical accuracy. Taken together, these results fix the regular-center input to the standard quadrupolar problem and extend the static even-parity formalism to Schwarzschild-de Sitter backgrounds.

Symplectic and complex toric quasifolds are a generalization of toric manifolds and orbifolds to the nonrational case. In this paper, we reframe these notions from the viewpoint of algebraic geometry.

In this paper, we explore quantitative stability of multi-marginal Schrödinger bridges with respect to the marginal constraints. We focus on the case where the number of marginal constraints is large (i.e. ``many-marginals"). When this number increases, we show that the Kullback--Leibler (KL) divergence between two multi-marginal Schrödinger bridges, as measures on the path space, can be asymptotically bounded by the terminal marginal KL divergence and a time-integrated squared discrepancy {that combines} Wasserstein-2 geodesic velocity fields with a log-density gradient term. Our stability upper bound is also asymptotically tight: it converges to zero as the number of marginal constraints increases with unperturbed marginal constraints. To the best of our knowledge, this is the first such stability result that addresses the many-marginal regime, giving error estimates that are asymptotically independent of the number of marginals. To achieve our result, the key step is to derive an asymptotic expansion (of order $k\ge 2$) of Schrödinger potentials with respect to a diminishing regularization coefficient. This result can also be applied to deriving asymptotic expansions of entropic Brenier maps in entropic optimal self-transport problems. As byproducts of our analyses, we also establish the asymptotic expansion of entropic optimal transport cost with respect to the diminishing regularization coefficient when two marginal constraints are sufficiently close. We also prove a stability property of the Schrödinger functional.

Let X be a set definable in a sharply o-minimal structure. We consider the problem of counting the number of points where X intersects algebraic varieties V over Q of dimension k < codim X, as a function of T := deg(V) + h(V), where h(V) is the log-height of V. In particular, we conjecture that after removing a suitable "algebraic part", this number grows polynomially in T -- a generalization of Wilkie's conjecture. We show that this full conjecture implies some open problems in algebraic independence theory. We also formulate a weaker conjecture stating that all intersections above are contained in a poly(T) amount of balls of radius e^{-T}. We then consider the case where X (subset of C^n) is a (compact piece of a) trajectory of a polynomial differential equation satisfying a variant of Nesterenko's D-property. Our main theorem is a proof of the weakened conjecture for such curves when k < sqrt(n) - 1.

We investigate the asymptotic behavior of the solutions to the Neumann sieve problem for the Poisson equation in a thin, randomly perforated domain. The perforations (sieve-holes) are generated by a stationary marked point process. According to the scaling between the domain thickness and the typical hole size, three distinct limiting regimes emerge. We also identify the optimal stochastic integrability condition on the random hole radii that guarantees stochastic homogenization, even in the presence of clustering holes.

We apply Random Forest and XGBoost machine learning algorithms to determine which galaxy properties most effectively predict star formation and quenching in simulated galaxies. Using spatially-resolved data from approximately 63,000 annular bins across 6,189 TNG100 galaxies, we train classification models to predict quenching states and regression models to predict star formation rate surface densities. Despite their different algorithmic approaches, both methods produce consistent feature importance rankings, with XGBoost distributing importance more evenly among correlated features. For central galaxies and high-mass satellites, black hole mass dominates quenching predictions, consistent with quenching via active galactic nuclei (AGN) feedback. Classification of low-mass satellites shows overwhelming importance for halo mass, indicating environmental quenching. Star formation predictions are dominated by local stellar mass surface density across all star-forming galaxy types, confirming that active star formation is a local process while quenching is driven by global properties.

The Metropolis-Hastings algorithm is a cornerstone of Markov Chain Monte Carlo methods, underpinning a wide range of applications in computational physics, Bayesian inference, and machine learning. Quantum variants of Metropolis-Hastings promise accelerated mixing through quantum walks, but their practical realisation remains challenging. In this work, we construct and simulate an explicit circuit level implementation of a quantum Metropolis-Hastings algorithm based on the framework introduced by Claudon \emph{et al.} (arXiv:2506.11576). We present the full quantum workflow required to prepare a stationary distribution, including a number of modifications required to make the algorithm implementable in a realistic quantum circuit model. Our results demonstrate that these modifications are essential to recover the correct stationary behaviour and highlight both the potential and current limitations of quantum Metropolis-Hastings algorithms, which are expected to become practically relevant in the fault tolerant quantum computing regime.

In the context of waves in space time modulated materials, we ask two questions how much energy does it cost to break time reversal symmetry and transition to a PT symmetric state. and can a PT symmetric system have a ground state in the sense that no photons are present. Our model system is a periodic metamaterial set in virtual motion with velocity cg to become a space-time crystal. We find that the expectation of energy content is always increased on breaking symmetry. At the same time breaking T symmetry introduces photon-pairs even when we start from a T symmetric ground state empty of photons, except in certain pathological examples which we describe. For a range of velocities, PT symmetry is broken so that energy must be continuously invested to preserve motion, creating a trail of photon pairs. Here energy must be continuously invested to preserve motion. We make an analogy with acoustic radiation generated from breaking the sound barrier.

Fungal automata are a nature-inspired computational model, where a rule is alternatively applied verticaly and horizontaly. In this work we study the computational complexity of predicting the dynamics of all fungal freezing totalistic one-dimentional rules of radius $1$, exhibiting various behaviors. Despite efficiently predictable in most cases (with non-deterministic logspace algorithms), a non-linear rule is left open to characterize. We further explore the freezing majority rule (which is totalistic), and prove that at radius $1.5$ it becomes $\mathbf{P}$-complete to predict.