Runtime verification is a lightweight verification technique that complements model checking by analyzing system executions at runtime rather than exploring a complete system model in advance. It is particularly useful for partially observable or black-box systems, where uncertainty can only be resolved through observation. These lecture notes present automata-theoretic, temporal-logical, and epistemic foundations of runtime verification. They cover specification formalisms, diagnosis, opacity, and monitorability, and explain how offline analysis can be used to construct monitors that operate online on observed executions. The notes also discuss timed extensions and the additional algorithmic and semantic challenges that arise in the real-time setting.

Ultrafast scintillators are indispensable for precise timing in high-energy physics and medical diagnostics. Fundamentally constrained by the trade-off between emission rate and light yield, conventional scintillators remain kinetically trapped in the sub-nanosecond regime, failing to break 50-picosecond limit. Here, we demonstrate a strategy to bypass this limitation by harnessing the coherent radiative acceleration in weakly confined CsPbCl3 perovskite nanocrystals to generate an ultrafast photon burst. This effect originates from the giant oscillator strength, which we unlock by suppressing exciton-phonon scattering at mild cryogenic temperatures. Consequently, our scintillator achieves an unprecedented dominant lifetime of 13.11 ps alongside a high light yield of 21,851 ph/MeV. The resulting prompt photon emission rate more than 100 times higher than that of state-of-the-art ultrafast scintillators. We validate this breakthrough in realistic detection scenarios, achieving a coincidence time resolution of 30.8 ps and accurately resolving 13.5 ps electron bunches and 16.6 ps single-shot gamma-ray pulses. Our findings establish a robust coherent framework for next-generation ultrafast scintillators, pushing extreme radiation diagnostics into the picosecond frontier.

Recent JWST observations have revealed that some galaxies at $z \gtrsim 7$ generally exhibit relatively flat ultraviolet (UV) attenuation curves and a weak UV bump. These features suggest that the first dust grains formed rapidly, possibly originating from core-collapse supernovae (SNe). We investigate the time evolution of grain size distributions and extinction curves in the early phase of dust enrichment for different parameters of progenitor stars, rotation velocities, metallicity, and interstellar medium densities, including the effect of the reverse shock. We model a single starburst system assuming an initial mass function. Extinction curves are calculated from the grain size distribution for each dust species. The total dust-to-stellar mass ratio at $30 \,\mathrm{Myr}$ is $M_\mathrm{dust}/M_\star \sim 10^{-3}$ before the passage of the reverse shock, but we find it to be at most $M_\mathrm{dust}/M_\star \sim 10^{-5}$ due to the destruction effect of the reverse shock. This effect destroys grains smaller than $\sim 10\,\mathrm{nm}$ and makes amorphous carbon the dominant species, resulting in a flatter extinction curve with a wide bump at $2500\,\mathrm{\mathring{A}}$ compared to the no-reverse shock models. We find that our models are consistent with the observed attenuation curve and emissivity of high-redshift galaxies and show that the reverse shock processing significantly affects dust enrichment and grain properties such as extinction curves and emissivity in supernova yields for high-redshift galaxies.

Robust Markov decision processes (RMDPs) extend standard Markov decision processes (MDPs) to account for uncertainty in the transition probabilities. RMDPs have an uncertainty set that defines a set of possible transition functions, each of which induces a standard MDP. The natural objective in an RMDP is to optimize the discounted cumulative reward under the worst-case transition function in the uncertainty set. We study the complexity of the associated threshold problem for RMDPs with polytopic uncertainty sets in halfspace representation. Previous results focused on approximating the optimum or restricted attention to specific subclasses of RMDPs, such as interval MDPs or $L_\infty$-RMDPs. Our contributions are threefold: (1) For (s,a)-rectangular RMDPs, we prove that robust policy evaluation is in P via robust linear programming, and that the threshold problem is in NP. As a corollary, robust policy iteration is a polynomial-time algorithm for these RMDPs when the discount factor is fixed. (2) For $s$-rectangular RMDPs, we show that the threshold problem is in PSPACE via the first-order theory of the reals. (3) We establish lower bounds by reducing both parity games and bisimulation metrics between MDP states to the RMDP threshold problem. A polynomial-time algorithm for the threshold problem would resolve the long-standing open question of whether parity games can be solved in polynomial time. The reduction from bisimulation metrics also yields a practical benefit: it allows us to apply robust policy iteration as a more efficient alternative to the standard fixed-point iteration, as our empirical evaluation demonstrates.

LLM agents are promising tools for empirical discovery, but their flexibility can also turn discovery into uncontrolled search. We study how to use agents under a reproducible protocol through cryptocurrency factor discovery. Our framework casts the task as sequential hypothesis search: an agent reads an append-only experiment trace, proposes falsifiable factor hypotheses, and maps them to executable recipes, while a deterministic engine enforces fixed data splits, selection gates, transaction costs, and portfolio tests. Candidate actions are restricted to a point-in-time factor DSL, making both successful and failed hypotheses auditable. A ridge-combined portfolio trained only on 2020--2022 data achieves a 44.55% annualized return and Sharpe ratio of 1.55 in the 2024--2026 pure out-of-sample period after a 5 basis point one-way trading cost.

Existing methods for learning Stackelberg equilibria typically assume that the followers' (variational, generalized) Nash equilibrium is unique. However, in the presence of multiple equilibria, without a selection convention, the problem may become ill-posed, thus leading standard algorithms to potentially fail to converge. This paper addresses this issue by introducing an optimal selection at the lower-level game, hereby defining a Stackelberg game with induced equilibrium selection. To this end, we enable the leader to augment the followers' game with an additional vanishing term that acts as an incentive. We then propose a follower-agnostic zeroth-order method, whereby the leader converges to a solution of the resulting problem by iteratively probing the followers and jointly updating its decision variable and the incentive term.

Passive Gamma Emission Tomography (PGET) is an IAEA-approved technique for verifying spent nuclear fuel assemblies prior to geological disposal. Reconstructing the emission and attenuation maps from PGET measurements is a nonlinear ill-posed inverse problem, currently solved with a Levenberg-Marquardt (LM) scheme that requires 10-20 iterations to achieve sufficient accuracy. We propose an accelerated iterative solver that combines the LM algorithm with a Deep Gauss-Newton step, in which a learned operator refines the update proposed by the deterministic algorithm at each iteration. A safeguard condition based on the trust-region model ensures that the accelerated iterates perform no worse than LM and retain convergence to a critical point of the regularized objective. Within this framework we compare three architectures for the learned component: an encoder-decoder-style convolutional neural network, Fourier Neural Operators, and Wavelet Neural Operators. Each is trained on a small set of coarsely simulated 9x9 assemblies. Experiments on simulated and real measurements from Finnish nuclear power plants show that the proposed scheme reaches LM-quality reconstructions in roughly one third of the iterations, while revealing architecture-dependent trade-offs in robustness against out-of-distribution inputs.

We show that if the conditional distribution p(C | T) factors through a sufficient statistic ϕ(T), then the Information Bottleneck (IB) problem for (T, C) is exactly equivalent to the IB problem for (ϕ(T), C). The reduction is loss-free: it preserves the full IB curve, the Lagrangian optimum at every trade-off parameter \b{eta}, and the optimal representations up to pullback through ϕ. As a result, the computational complexity of solving the IB problem is governed by the dimension of the sufficient statistic rather than the ambient dimension of the source. This identifies an exact structural condition under which the generic IB problem becomes tractable, and gives a formal bridge between the discrete and linear-Gaussian regimes. We then show that the classical Gaussian IB solution of Chechik, Globerson, Tishby and Weiss is an immediate corollary of this reduction, and we state a nonlinear-Gaussian generalisation. A small numerical example illustrates the practical consequence: when a low-dimensional sufficient statistic is available, the exact IB curve can be computed on the reduced problem at a cost determined by the statistic rather than by the ambient source dimension.

We report a detailed analysis of GAMA 376183, a powerful, heavily obscured active galactic nucleus (AGN) hosted by a low-mass galaxy ($M_\star \approx 10^{10}~M_{\odot}$) likely experiencing a galaxy merger. The source was initially identified due to its remarkably strong [Ne v] $\lambda3426$ emission, exhibiting a rest-frame equivalent width (EW) of $\approx 48$ A. We present $\sim100$ ks Nuclear Spectroscopic Telescope Array follow-up observations, confirming its heavily obscured nature with a column density (in $\mathrm{cm^{-2}}$) of $\log N_\mathrm{H} = 23.3^{+0.4}_{-1.2}$ and an intrinsic $2$--$10$ keV luminosity (in $\mathrm{erg~s^{-1}}$) of $\log L_\mathrm{X,int} = 42.92^{+0.24}_{-0.20}$. GAMA 376183 thus represents one of the few known heavily obscured AGNs in low-mass galaxies. Its estimated Eddington ratio is $λ_\mathrm{Edd}\approx0.8$, indicative of rapid black-hole growth. High-resolution optical images reveal a disturbed, likely merging morphology, while its multiwavelength spectral energy distribution indicates a recent starburst in its host galaxy. These pieces of evidence suggest that the ongoing merger has triggered both the heavily obscured, Eddington-limited accretion and the starburst, making GAMA 376183 a rare observed case in low-mass galaxies. Overall, this unique source demonstrates that (i) [Ne v] can help identify heavily obscured low-mass AGNs, and (ii) the merger-driven coevolution framework established for massive galaxies may also extend to low-mass galaxies.

We investigate the dynamical origin and kinematic signatures of spiral structure in an N-body simulation of an isolated barred galaxy, assessing whether invariant manifold theory provides a consistent dynamical framework to disentangle the disc particle populations and to identify those that genuinely build, trace, and sustain the spiral arms. We compute the Jacobi energy of disc particles and classify them relative to the energies of the equilibrium points, thereby isolating manifold-compatible orbits. We analyse their spatial distribution and velocity structure to characterise spiral-related streaming motions. The Jacobi constant provides a physically motivated dynamical separator that reveals three distinct kinematic populations: (i) low-energy particles on nearly circular orbits populating most of the disc, (ii) high-energy particles associated with banana orbits, and (iii) manifold-compatible particles originating near the bar and following transit orbits along the spiral arms. Only the manifold-compatible population generates the prominent outward-migrating ridge observed in the R - v_phi plane and reproduces the characteristic spiral streaming pattern. In contrast, the low-energy population exhibits a global quasi-circular motion with small perturbations induced by the self-gravity of the spiral structure. Our results demonstrate that the spiral arms are dynamically traced by the manifold-compatible population, which forms the backbone of the structure and drives effective radial transport. The bulk of low-energy disc particles responds to the spiral perturbation similarly to the traditional density wave picture, enhancing the density contrast caused by the invariant-manifold compatible particles. In this framework, barred spiral arms emerge as material structures sustained by manifold-guided transport, with the surrounding disc behaving as a system of material density waves.

In the Internet-of-Things (IoT) era, efficient functionality integration is essential to address the growing demands of communication, computation, and sensing. Signal-level integrated sensing, computing, and communication (Sig-ISCC) is envisioned, where a single waveform simultaneously supports sensing, computing and communication via over-the-air computation (AirComp). Meanwhile, federated learning (FL) is widely regarded as a promising distributed machine learning framework that enables network intelligence in a privacy-preserving and secure manner, and exhibits strong synergy with AirComp, which alleviates the communication bottleneck of FL. In this paper, we study uplink Sig-ISCC design for AirComp-FL with joint target detection. We formulate the joint power and receive-scaling control problem, where edge devices' transmitted signals should serve both sensing and AirComp purposes. The goal is to minimize the AirComp aggregation distortion subject to a joint target-detection requirement. Although the resulting problem is non-convex in the original variables, we show that it admits an equivalent convex reformulation after a suitable variable transformation. By exploiting analytical optimality properties, we develop a robust, optimal, and polynomial-time-complexity algorithm that efficiently achieves the optimal transmit powers and receive scaling factor. Simulation results validate the optimality and numerical robustness of the proposed algorithm and show its superior FL performance compared to baseline methods.

We investigate electronic transport across a junction between a Weyl semimetal (WSM) and a layered Chern insulator (LCI) in the presence of a magnetic field perpendicular to the interface. The topological mismatch between the gapless Weyl semimetal and the momentum-resolved chiral edge modes of the layered Chern insulator leads to interface Fermi-arc states with a qualitatively distinct connectivity: unlike WSM-WSM junctions, the interface Fermi arcs are forced to reconnect through the Brillouin-zone boundary rather than terminating at the projections of the Weyl nodes. We analyze the spectrum and compute the magneto tunnel conductance mediated by the interface-localized states. We find that the conductance increases linearly with magnetic field at low fields and saturates beyond a critical field to a constant value that is independent of microscopic details such as interface coupling, arc geometry, and lattice-scale parameters. This universal saturation reflects a transport mechanism governed by the topological charge pumping associated with the Chern layers, rather than magnetic breakdown between Fermi arcs. We further show that, under specific conditions, a junction between two distinct Weyl semimetals can exhibit a similar saturation behavior, thereby clarifying the topological origin of the observed universality.

Received Signal Strength Indicator (RSSI) estimation is essential for wireless link management, yet conventional feedback-based approaches incur uplink overhead, suffer from measurement instability, and are subject to inherent feedback loop latency, rendering proactive adaptation infeasible. Although vision-based approaches have been explored, existing methods remain limited by hardware dependency or auxiliary inputs, and lack the spatial diversity needed to resolve camera-side NLoS conditions. To address these limitations, we propose MulViT-TF, a vision-only RSSI estimation framework that exploits distributed multi-view observations through Transformer-based fusion, achieving complementary spatial coverage without any auxiliary sensing inputs. Experimental results across two distinct indoor scenes demonstrate that MulViT-TF achieves RMSE reductions of up to 26.3% and improves the 3dB error coverage by up to 13.8 percentage points over the best-performing single-view baseline, while using fewer FLOPs and parameters.

We analyze the weight diagram associated with foliations on the complex projective plane through the Hilbert-Mumford criterion in Geometric Invariant Theory, focusing in particular on invariants such as the algebraic multiplicity and the existence of invariant curves.

FlyClient is a lightweight blockchain verification protocol that enables proof-of-work validation using minimal data, making it ideal for resource-constrained environments like mobile wallets, Internet-of-Things devices or cross-chain bridges implemented with smart contracts. Despite its strong potential for enabling lightweight blockchain verification, FlyClient protocol is still in the experimental stages, with limited real-world deployments and performance evaluations under diverse conditions. In this paper we bridge the gap between theory and deployment, by addressing several technical challenges to advance FlyClient to a production-ready solution. Namely, our contribution is three-fold: (i) we formally introduce an adversary model alternative to the original FlyClient one, that allows us to parametrize a verifier under a concrete economic interpretation, while also saving some proof space; (ii) we provide the first practical FlyClient prover implementation for a production blockchain (Zcash), and we estimate its performance under different configurations; (iii) we introduce and evaluate two optimizations that minimize the size of FlyClient proofs, the first of which does not require any consensus change.

We study the optimization of (strongly) quasar-convex functions, a class that arises naturally in many machine learning and data science applications due to its favorable properties. The fundamental properties of this class are first developed, including its stability under standard calculus operations, growth conditions, and the absence of spurious critical points, which together imply a benign global geometry with no saddle points. Motivated by these properties, a class of proximal-point algorithms (HiPPA) with high-order regularization of order $p>1$ is introduced. Conditions are identified under which the iterates converge globally to minimizers, and a unified convergence analysis is provided with explicit rates and iteration complexity bounds under appropriate regularity assumptions. The results reveal a sharp transition in behavior with respect to the order $p$: for $p\in(1,2)$, the method achieves local linear convergence with complexity $\mathcal{O}(\log(\varepsilon^{-1}))$ when initialized sufficiently close to a minimizer; for $p=2$, it attains global linear convergence with the same complexity; and for $p>2$, it exhibits superlinear convergence with complexity $\mathcal{O}(\log\log(\varepsilon^{-1}))$, where $\varepsilon>0$ denotes the target accuracy. The theory is complemented with preliminary numerical experiments on selected machine learning problems, which illustrate the effectiveness of the proposed methods and are consistent with the theoretical findings.

Near-Earth asteroid (469219) Kamo'oalewa is an Earth quasi-satellite, temporarily trapped in a 1:1 orbital resonance with our planet. Despite its dynamical relevance and the hypothesis that it may be a lunar ejecta fragment, its physical properties are still poorly constrained. In particular, no reliable models of its shape and spin state have been published so far. The scientific interest in this object is further enhanced by its selection as the primary target of the Chinese Tianwen-2 mission, which aims to rendezvous with this asteroid and return samples of it to Earth. The aim of this work is to determine the shape and spin axis orientation of Kamo'oalewa by means of photometric telescope observations and lightcurve inversion. We analyzed lightcurves obtained during several apparitions using the well-established algorithm, based on convex shape modeling. We derived a convex shape model and estimated the spin pole orientation. In the preferred solution, the pole is located at ecliptic coordinates λ, β = (126,-16) degrees, with a sidereal rotation period of P~0.465 h. Conclusions. Our results provide the first direct constraints on the rotational state and morphology of Kamo'oalewa, information of key importance in preparation for the upcoming Tianwen-2 sample-return mission.

This paper investigates the influence of interfaces on the performance of finite-sized mechanical metamaterial structures for vibration damping applications. The metamaterial structures are designed in a sandwich configuration in which two homogeneous plates are connected to a metamaterial array. We test four different arrays that are obtained from the same metamaterial by differently cutting the metamaterial's unit cell at the metamaterial/plate interface. When the four unit cells are periodically repeated in space, they create the same infinitely large metamaterial with an identical mechanical response. In finite-sized structures, however, the different interfaces between the metamaterial array and the plates~--~called ``material interfaces''~--~and between the metamaterial and the air~--~called ``free interfaces''~--~strongly affect the specimen's vibration transmission characteristics. Using experimental measurements and validated finite-element (FE) models, we demonstrate a significant influence of the different types of interfaces on the global responses and local displacement fields of the structures. We also demonstrate the presence of a vibroacoustic coupling in the structures which also depends on the type of metamaterial/plate interfaces. Furthermore, we explore optimization strategies for enhancing the vibration damping performance of the metamaterial structures considering not only the metamaterial array but also the adjacent structures (the homogeneous plates). A comparison with benchmark cases illustrates the optimization potential that the interfaces' design offers for the vibration damping capability of finite-sized metamaterial structures. We show that optimizing the type of targeted interfaces can shift a metamaterial's response from underperforming to significantly outperforming compared to classical solutions for noise and vibration damping in civil engineering.

The transverse momentum spectrum of charged particles in ultra-relativistic heavy-ion collisions fluctuates event-by-event, encoding signatures of underlying collective dynamics. Such fluctuations originate from a combined effect of thermal and geometric fluctuations in the initial state. We present a direct decomposition of these spectral fluctuations through principal component analysis performed on the joint covariance structure of normalized spectrum, mean transverse momentum and elliptic flow squared. The first two leading modes explain 99.5\% of the total variance, and are orthogonally rotated by imposing physical constraints motivated by the initial state thermal and geometric response. The resulting thermal and geometric modes bear direct analogy with the vibrational normal modes of a linear triatomic molecule. The thermal mode entirely drives the experimentally measured $v_0(p_T)$, while the geometric mode contributes substantially to $v_{02}(p_T)$ in non-central collisions, providing a transparent explanation of its characteristic low-$p_T$ sign change. The study establishes the first physically motivated interpretation of principal component modes in the field of heavy-ion collisions and provides an experimental window into the thermo-geometric structure of the QGP initial state.

This paper proposes a flexible new framework for constructing Neyman-orthogonal scores in semiparametric models involving infinite-dimensional nuisance parameters. While locally estimation is vital for integrating machine learning into econometrics, deriving orthogonal scores for complex models remains a major challenge. We provide explicit construction strategies for broad classes of settings. The proposed framework ensures asymptotic normality of target parameter estimators in a way that does not depend on the method used to construct the nuisance parameter estimators, provided they are $o_p(n^{-\1/4})$-consistent. We apply the proposed methodology to causal inference with a binary instrumental variable, developing a novel, robust estimator for treatment effects. Numerical studies demonstrate that our approach significantly outperforms naive alternatives in finite samples. An empirical application to the Oregon Health Insurance Experiment illustrates the framework's utility in providing robust causal evidence.

The radial profile of binary fraction may vary with environment and is of significant importance for studying the formation mechanisms of binary stars and their dynamical evolution within globular clusters (GCs) and galaxies. However, existing studies remain limited to the Milky Way and its neighboring galaxies. Leveraging the method proposed by Zhang et al. for estimating the variation of binary fraction from integrated spectral features, we analyze a sample of 513 elliptical galaxies drawn from the Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey to measure their radial binary fraction profiles. Our results show that after accounting for the effect induced by radial variations in the stellar population (SP), the median SP-subtracted binary fraction, $r_{\rm b,sub}^{\rm med}$, becomes approximately flat. For nearly all elliptical galaxies in our sample, the variation in binary fraction relative to the galaxy center at $1R_e$ is less than 5%. No clear correlation is found between the binary fraction gradient and the gradients of SP properties. Moreover, we also compare differences between ultraviolet (UV) upturn and non-UV upturn galaxies. The overall binary fraction profiles and SP properties of the non-UV upturn galaxies in our sample are comparable to those of the UV upturn galaxies. This similarity may arise from the presence of residual star formation (RSF) in the non-UV upturn systems.

The purpose of this article is to study certain binary relations of endomorphisms over infinite dimensional vector spaces defined by GD1 and 1GD generalized inverses. In order to do so, these generalized inverses are studied over arbitrary vector spaces (namely, infinite dimensional ones) using finite potent endomorphisms. We characterize them in terms of the AST decomposition of a finite potent endomorphism and we obtain algorithms for their respective computation. This theory is then used to characterize the GD1 and 1GD binary relations for finite potent endomorphisms in terms of the AST decomposition and to prove that they define partial orders in the set of finite potent endomorphisms, thus, completing the theory of these generalized inverses for matrices.

We use a $^{87}\text{Rb}$ atomic vapor, suitable for an optically-pumped magnetometer (OPM) in Earth-field conditions, to study the noise properties of three strategies for generating pulsed optical pumping. We compare a frequency-modulated (FM) laser, amplitude modulation (AM) via an acousto-optic modulator (AOM), and amplitude modulation via a semiconductor optical amplifier (SOA). Pumping the ensemble to operate as a Bell-Bloom OPM, and with an equal degree of spin polarization, the three methods give nearly identical sensitivity, showing that the SOA, despite being an active device, can introduce negligible additional noise. Pumping the ensemble to operate as a free-induction-decay OPM, we observe longer unpumped coherence times with the SOA-AM method than with the FM method. Finally, using the higher power available from the SOA, we demonstrate an environment-limited sensitivity of $80\text{fT}/\sqrt{\text{Hz}}$ at $600\text{Hz}$ and 200fT$200\text{fT}/\sqrt{\text{Hz}}$ at $4\text{kHz}$, one to two orders of magnitude beyond what was achievable with the other pumping methods.

The coupling between light and strain gradients shows two kinds of effects: light enhanced flexoelectricity (photoflexoelectricity) and gradient enhanced photovoltage (flexophotovoltage). Although these effects originate from fundamentally different physical mechanisms (one is light enhanced electromechanical coupling, the other is a bulk photovoltaic effect), in this article we show that dynamic flexoelectric measurements of semiconductors under illumination intrinsically contain contributions from both. To allow disentangling them, we have developed a general theoretical framework for their combined response in oscillating systems, demonstrating that the two contributions can be unambiguously separated through their distinct frequency and phase dependencies. We have validated these predictions using oscillating cantilever measurements on centrosymmetric perovskite semiconductors (SrTiO3 and methylammonium lead bromide, MAPbBr3), obtaining selfconsistent values for the coefficients both effects which are in excellent agreement with independent static measurements. Our results establish a general protocol for disentangling both light strain gradient couplings using only oscillatory measurements, and clarify the interpretation of flexoelectric measurements under illumination.

This work is concerned with the probabilistic representation of solutions to the $p$-Laplace evolution equation $\frac{\partial u}{\partial t}={\rm div}(|\nabla u|^{p-2}\nabla u)$ in $(0,\infty)\times\mathbb{R}^d$, $u(0,x)=u_0(x),$ $x\in\mathbb{R}^d$. One proves that, if $p\geq 4$, and if $u_0$ is a probability density with compact support and $u_0\in L^2$, $|\nabla u_0|\in L^\infty$, then $u$ can be represented as $u(t,x)dx=\mathscr L_{X(t)}(dx)$, where $\mathscr L_{X(t)}$ denotes the time marginal law of $X$ at time $t$ with $X$ being a probabilistically weak solution to a corresponding McKean-Vlasov stochastic differential equation. This result is based on a new second order global regularity result for the weak solutions to the parabolic $p$-Laplace equation.

Modern information technologies rely on controlling the flow of electrons through their charge and spin. A rapidly emerging alternative is to use the orbital motion of electrons, the way they circulate around atomic sites as a new carrier of information. This orbital angular momentum (OAM) could enable more energy-efficient devices and reduce reliance on scarce heavy elements, but how orbital currents are generated and transported, especially on ultrafast timescales, remains largely unknown. In this review, we introduce terahertz optorbitronics, an approach that uses ultrafast femtosecond laser pulses and terahertz radiation to observe orbital transport in real time. On timescales of quadrillionth of a second, this technique allows us to track how orbital currents are launched, propagate, and convert into electrical signals in nanoscale thin-film materials. Surprisingly, recent experiments have revealed conflicting pictures such as orbital currents may travel over tens of nanometres like ballistic waves or instead decay within just a few atomic layers, highlighting a fundamental unresolved question in the field. We explain how these ultrafast measurements can disentangle orbital motion from conventional spin transport, and we highlight new materials from engineered graphene to altermagnets, that could act as tunable sources of orbital currents. We also discuss how light, electrical gating, strain, and interface design can be used to actively control orbital transport and improve its conversion into usable electronic signals. By revealing orbital transport as a dynamic, non-equilibrium process, terahertz optorbitronics opens a new direction for nanoscale science, the one that could lead to faster, more efficient technologies operating beyond the limits of conventional spin-based electronics.

In the Schrödinger evolution of a quantum state time enters as a real parameter representing the coordinate. In a more consistent approach time should be defined as a quantum observable, with the evolution taking place in a four-dimensional spacetime. This is possible in the projection evolution model in which the wave function is defined in both space and time. This allows to construct the time operator and discuss the temporal structure of quantum processes. In this paper we discuss a photon travelling through a Mach-Zehnder interferometer, focusing the description on the temporal profile of the wave function. We show that in this approach the delayed-choice experiments can be explained by the temporal overlap of the photon and the devices in the interferometer.

This chapter, to appear in the section on QCD under extreme conditions within the Encyclopedia of Nuclear Physics, aims to provide a pedagogical introduction to the physics of quarks and gluons in the presence of high temperature, nonzero (isospin) density and strong background electromagnetic fields. Extreme conditions of these types are relevant for the description of high-energy heavy-ion collisions, neutron stars and their mergers, as well as the evolution of the early Universe in its first microsecond. Most of the existing results on this topic have been obtained by means of first-principles simulations of the discretized theory of the strong interactions, lattice Quantum Chromodynamics (QCD). This lays the focus of this review chapter, although various calculations within effective theories of QCD -- most notably chiral perturbation theory -- are also discussed. Furthermore, we provide an outlook concerning open questions and yet uncharted parameter regions within this fascinating system.

In the Independent Set Reconfiguration problem under the Token Addition/Removal rule, given a graph $G$ and two independent sets $I$ and $J$ of $G$, we want to transform $I$ into $J$ by adding and removing vertices, such that all the sets throughout the process are independent sets. Its approximate version called MaxMin Independent Set Reconfiguration aims to maximise the minimum size of the independent sets in the process above. We study the (in)approximability of this problem for general graphs as well as restricted graph classes. Firstly, on general graphs, we obtain a polynomial-time $(n / \log n)$-factor approximation algorithm, complementing the $\mathsf{PSPACE}$-hardness of $n^{Ω(1)}$-factor approximation due to Hirahara and Ohsaka [STOC 2024, ICALP 2024] and the $\mathsf{NP}$-hardness of $n^{1-\varepsilon}$-factor approximation due to Ito, Demaine, Harvey, Papadimitriou, Sideri, Uehara, and Uno [TCS 2011]. Secondly, we present a polynomial-time approximation algorithm for degenerate graphs as well as $\mathsf{FPT}$-approximation schemes for bounded-treewidth graphs and $H$-minor-free graphs. Lastly, we extend the above inapproximability results to bounded-degree graphs, graphs of bandwidth $n^{\frac{1}{2}+Θ(1)}$, and bipartite graphs.

In this paper we propose a finite-dimensional and deterministic approach to the study of invariant sets of certain nonautonomous differential inclusions naturally arising in the context of random and control dynamical systems, as well as in systems modeling the dynamical propagation of uncertainty. In particular, to any such differential inclusion, we associate a finite-dimensional and deterministic system of nonautonomous ordinary differential equations, which we call the boundary system, due to its following characteristic property: invariant sets of the differential inclusion lift in a unique way to backward invariant unit normal cones of the associated boundary system, and these are even invariant if the boundary is smooth. We further illustrate the strength of this approach in the study of minimal attractors of nonautonomous linear differential inclusions. Under the natural assumption of exponential stability for the unperturbed problem, we establish existence and uniqueness of a minimal attractor for the differential inclusion with fiberwise strictly convex, closed, and continuously differentiable boundaries. We also show that the unit normal bundle is in fact the pullback attractor for the skew-product flow associated to the boundary system which extends to the global attractor when the underlying admits a compact base.