Recent JWST observations have revealed a large population of quiescent galaxies (QGs) at high redshift ($z \sim 4-8$), challenging current models of early galaxy formation and quenching. Accurate number density estimates are crucial but remain uncertain. We present a systematic study of QGs at $0.5 < z < 8$ using a mass-complete sample from the JWST/PRIMER survey with deep NIRCam and MIRI imaging. We demonstrate that MIRI photometry is essential for refining the QG sample: it helps to mitigate contamination from dusty star-forming galaxies in the high-mass regime at $z \sim 3-5$ and aids in recovering lower-mass QG candidates at $z > 5$ that are often missed without including MIRI data. We find that the evolution of the QG number density is strongly mass-dependent. The density of massive QGs ($\log (M_{\star}/M_{\odot}) > 10.6$) declines rapidly, falling from $n \approx 1.32\times10^{-5}~~\mathrm{Mpc^{-3}}$ at $z \sim 3-4$ to $n < 1 \times10^{-6}~~\mathrm{Mpc^{-3}}$ at $z \sim 6$, and becomes negligible at $z > 6$. In contrast, low-mass QGs ($9.5 < \log (M_{\star}/M_{\odot}) < 10.6$) exhibit a remarkably constant number density of $n \sim 3\times10^{-6}~\mathrm{Mpc^{-3}}$ across the redshift range $z = 4-8$. This plateau suggests that these high-redshift, low-mass QGs may be galaxies undergoing temporary quenching episodes, likely subject to rejuvenation upon future gas accretion. Comparisons with leading galaxy formation models reveal significant tensions: most models underestimate the abundance of massive QGs at $z > 4$ and fail to reproduce the flat density evolution observed for the low-mass population.

We address the fluid-structure interaction between a viscous incompressible fluid and an elastic plate forming its moving upper boundary in three dimensions. The fluid is described by the incompressible Navier-Stokes equations with a free upper boundary that evolves according to the motion of the structure, coupled via the velocity- and stress-matching conditions. Under the natural energy bounds and additional regularity assumptions on the weak solutions, we prove a non-contact property with a uniform separation of the plate from the rigid boundary. The result does not require damping in the plate equation.

Measurements that can be implemented via local operations and classical communication (LOCC) constitute a class of operations that is available in future quantum networks in which parties share entangled resource states. We characterise the different classes of measurements implementable with LOCC, where communication is restricted to a single round with a fixed direction. In particular, using the framework of constrained separability problems, we provide a complete characterisation of the class of LOCC measurements that require one round of classical communication with a limit on the transmitted information. Furthermore, we show how to distinguish between adaptive and non-adaptive measurements strategies. Using our techniques we present examples where the success probability of state discrimination depends on the direction of communication as well as on the message size. We also discuss explicit instances of state ensembles where non-projective measurements provide an advantage and where adaptive measurement strategies lead to improved success rates when compared to all non-adaptive strategies.

We extend the canonical Gibbs distribution, originally formulated for systems at equilibrium, to systems driven out of equilibrium. The stochastic dynamics of a small system are described by a probability distribution over discrete energy levels. Within this framework, we derive a microscopic expression for work and introduce a microscopic definition of entropy production (defined here in terms of the uncompensated heat of Clausius) during a nonequilibrium stochastic process. Work and entropy production share a common origin arising from variations of the system energy. The proposed framework allows us to recover the nonequilibrium work relation and to establish a new equivalent identity for the heat exchanged during a work protocol. Finally, we show that the fluctuations of work and heat governed by the extended canonical distribution follow directly from the fluctuation theorem for entropy production.

In the type-I two-Higgs-doublet model, the pseudoscalar $A$ can act as a long-lived particle (LLP) for sufficiently large values of $\tanβ$. At the LHC, the $A$ particles are predominantly produced in pairs through $pp \to W^*/Z^* \to H^\pm/H \, A$, with subsequent decays $H^{\pm}/H \to W^\pm/Z\, A$. For the mass range of our interest, $10~\text{GeV}\lesssim m_A \lesssim 100~\text{GeV}$, the pseudoscalar $A$ typically decays into a pair of bottom quarks after traveling a macroscopic distance from its production point, giving rise to displaced-vertex (DV) signatures inside the inner detector. We perform Monte Carlo simulations of signal events with DVs plus jets, and assess the discovery prospects of $A$ as an LLP at the ATLAS and CMS experiments. Our findings show that a substantial portion of the parameter space with $m_A>10$ GeV has already been excluded by LHC Run-2 data, while the high-luminosity LHC will be able to probe broader regions.

We propose a Schrödinger equation of arbitrary order for modeling charge transport in semiconductors operating in the ballistic regime. This formulation incorporates non-parabolic effects through the Kane dispersion relation, thereby extending beyond the conventional effective mass approximation. Building upon the framework introduced in G.E. Aliffi, G. Nastasi, V. Romano, {ZAMP} {76}, 155 (2025), we derive a hierarchy of models, each governed by a Schrödinger equation of increasing order. As in the standard second-order case, the problem is formulated on a finite spatial domain with suitable transparent boundary conditions. These conditions are designed to simulate charge transport in a quantum coupler where an active region -- representing the electron device -- is connected to leads acting as reservoirs. We investigate several analytical properties of the proposed models and derive a generalized expression for the current, valid for any order. This formula includes additional terms that account for interference effects arising from the richer wave structure inherent in higher-order Schrödinger equations, which are absent in the effective mass approximation. Numerical simulations of a resonant tunneling diode (RTD) illustrate the key features of the solutions and highlight the impact of the generalized formulation on device behavior.

Spoofing-robust speaker verification (SASV) combines the tasks of speaker and spoof detection to authenticate speakers under adversarial settings. Many SASV systems rely on fusion of speaker and spoof cues at embedding, score or decision levels, based on independently trained subsystems. In this study, we respect similar modularity of the two subsystems, by integrating their outputs using trainable back-end classifiers. In particular, we explore various approaches for directly optimizing the back-end for the recently-proposed SASV performance metric (a-DCF) as a training objective. Our experiments on the ASVspoof 5 dataset demonstrate two important findings: (i) nonlinear score fusion consistently improves a-DCF over linear fusion, and (ii) the combination of weighted cosine scoring for speaker detection with SSL-AASIST for spoof detection achieves state-of-the-art performance, reducing min a-DCF to 0.196 and SPF-EER to 7.6%. These contributions highlight the importance of modular design, calibrated integration, and task-aligned optimization for advancing robust and interpretable SASV systems.

We study the problem of learning exponential distributions under differential privacy. Given $n$ i.i.d.\ samples from $\mathrm{Exp}(λ)$, the goal is to privately estimate $λ$ so that the learned distribution is close in total variation distance to the truth. We present a simple pure $ε$-differentially private algorithm that avoids the classical dependence on the true value of $λ$. Our method leverages a structural property of the exponential distribution: its $(1-1/e)$-quantile equals $1/λ$, allowing us to estimate the rate parameter directly via private quantile estimation. The resulting learner is both conceptually simple and sample-efficient, achieving near-optimal guarantees. We further extend the method to Pareto distributions via a logarithmic reduction, prove nearly matching lower bounds using group privacy arguments, and show how approximate $(ε,δ)$-DP removes the need for externally supplied parameter bounds. Together, these results give the first tight characterization of exponential distribution learning under differential privacy using a simple $λ$-free approach.

Spiking Neural Networks (SNNs), with their temporal processing capabilities and biologically plausible dynamics, offer a natural platform for unsupervised representation learning. However, current unsupervised SNNs predominantly employ shallow architectures or localized plasticity rules, limiting their ability to model long-range temporal dependencies and maintain temporal feature consistency. This results in semantically unstable representations, thereby impeding the development of deep unsupervised SNNs for large-scale temporal video data. We propose PredNext, which explicitly models temporal relationships through cross-view future Step Prediction and Clip Prediction. This plug-and-play module seamlessly integrates with diverse self-supervised objectives. We firstly establish standard benchmarks for SNN self-supervised learning on UCF101, HMDB51, and MiniKinetics, which are substantially larger than conventional DVS datasets. PredNext delivers significant performance improvements across different tasks and self-supervised methods. PredNext achieves performance comparable to ImageNet-pretrained supervised weights, through unsupervised training solely on UCF101. Additional experiments demonstrate that PredNext, distinct from forced consistency constraints, substantially improves temporal feature consistency while enhancing network generalization capabilities. This work provides a effective foundation for unsupervised deep SNNs on large-scale temporal video data.

We explicitly show that certain 4-dimensional infinitesimal group actions with 3-dimensional orbits are related by double Wick rotations. In particular, starting with the symmetries of the spherical/hyperbolic/planar Taub-NUT spacetimes, one can obtain symmetries of the near-horizon extreme Kerr (NHEK) geometry or swirling universe by complex analytic continuations of coordinates. Similarly, the static spherical/hyperbolic/planar symmetries (i.e., symmetries of the Schwarzschild spacetime and other A-metrics) are mapped to symmetries of the B-metrics (or Melvin spacetime). All these mappings are theory-independent -- they constitute relations among symmetries themselves, and, hence among the classes of symmetry-invariant metrics and electromagnetic field strengths, rather than among specific solutions. Consequently, finding, e.g., vacuum Taub-NUT-type solutions in a given gravitational theory automatically yields vacuum NHEK- or swirling-type solutions of that theory, with a possible extension to the electromagnetic case.

Motivated by recent work on majority edge-colourings of graphs, we initiate the study of the corresponding problem for hypergraphs. First, sharpening the probabilistic argument by a $KL$ large-deviation estimate, we obtain a sufficient minimum-degree condition of order $k^3\log(kr)$ with the sharp large-deviation constant $ I_k:=D\!\left(\frac1k\middle\|\frac1{k+1}\right)=Θ(k^{-3}), $ where $D(\cdot\|\cdot)$ denotes the binary relative entropy. Our main constructive result shows that every hypergraph of rank at most $r$ and minimum degree at least $2rk^2$ admits a $1/k$-majority $(k+1)$-edge-colouring. The proof is based on a hypergraph extension of the key discrepancy lemma used in the graph case. We also show that the logarithmic dependence on the rank can be determined asymptotically. If $μ_k(r)$ denotes the least minimum-degree threshold that guarantees a $1/k$-majority $(k+1)$-edge-colouring for all hypergraphs of rank at most $r$, then for every fixed $k\ge2$, $ μ_k(r)=\frac{\log r}{I_k}+O_k(\log\log r). $ In particular, the correct logarithmic threshold is of order $k^3\log r$. Finally, we determine the correct order of the degree--colour trade-off. For integers $k\ge2$, $p\ge1$, and $r\ge2$, let $ν_{k,p}(r)$ denote the least integer $q$ such that every hypergraph of rank at most $r$ and minimum degree at least $kp$ admits a $1/k$-majority $q$-edge-colouring. Then $ ν_{k,p}(r)=Θ_{k,p}(r^{1/p}). $ In particular, minimum degree at least $k^2-k$ guarantees a $1/k$-majority $O_k(r^{1/(k-1)})$-edge-colouring, and this exponent is best possible.

Massive stars regulate galaxy evolution and star formation through their physical and chemical feedback, but their formation remains poorly understood. Accretion-powered outflows provide important diagnostics of massive star formation. We present first results from the SOMA Atomic Outflow Survey, a far-infrared massive star formation survey using the FIFI-LS instrument on SOFIA. We report detection of \OIII\ $^3P_2\rightarrow^3P_1$ emission at 52 \micron\ from the massive protostar G11.94-0.62, tracing highly ionized gas. We also detect \OI\ $^3P_2\rightarrow^3P_1$ and $^3P_1\rightarrow^3P_0$ at 63 and 145 \micron\ tracing atomic gas, as well as CO $J=14\rightarrow13$ at 186 \micron\ from highly excited molecular gas. The \OIII\ and \OI\ lines exhibit large line widths ($\sim200$ and $\sim40-80$ \kms, respectively) and their morphologies are consistent with a wide-angle bipolar outflow. The properties of molecular tracers ($^{12}$CO, $^{13}$CO, C$^{18}$O, H$_2$CO, and CH$_3$OH) observed with ALMA support this interpretation. Ionized nebula and PDR modeling imply an ionized outflow mass flux of $\sim8\times10^{-5}\:M_\odot$ yr$^{-1}$ and an atomic outflow mass flux of $\sim5\times10^{-6}\:M_\odot$ yr$^{-1}$, while the molecular outflow traced by CO has an implied mass flux of $\sim3\times10^{-4}\:M_\odot$ yr$^{-1}$. The mass and momentum flux in the ionized outflow are consistent with the primary disk wind, while the molecular component is mainly swept-up, secondary outflow gas. We also observe G11.94-0.62 with the LBT in the near-infrared, potentially tracing the base of wide-angle outflow cavities. SED modeling implies a protostellar mass $m_* = 22.4^{+21}_{-11}\:M_\odot$, while the \OIII\ emission implies $m_*\gtrsim30\:M_\odot$ and that the protostar is in the final stages of its accretion.

We propose a novel collider probe of baryogenesis at TeV scale by measuring decay asymmetries into particle and anti-particle final states. Motivated by the idea of Dirac leptogenesis, we consider an extension of the standard model with new colored and $SU(2)_L$ singlet particles in such a way that the out-of-equilibrium decay of heavy colored fermions creates equal and opposite CP asymmetries in two sectors, prevented from equilibrating with each other. While the TeV scale viability of this mechanism requires a resonantly enhanced CP asymmetry, the latter also plays a crucial role leading to observable decay asymmetries in colliders. In addition to discussing conventional signatures of such heavy colored particles, namely, mono-jet plus missing transverse energy, displaced vertex, colored track at hadron colliders, we also show the unique possibility of measuring decay asymmetries via forward-backward and charge asymmetries at future muon colliders. In addition to being a verifiable TeV-scale baryogenesis scenario, the model also predicts a singlet scalar dark matter candidate consistent with the required thermal dark matter properties near the Higgs resonance.

These lecture notes explain the classification of some simple fermionic topological phases of matter in a pedestrian manner, with an aim to be maximally pedagogical = doing things in excruciating detail. We focus on a many-body perspective, even if many of the models we work with are non-interacting. We start out with symmetry protected topological (SPT) phases of free fermions that are protected by U(1) symmetry = topological insulators. We then look at fermion topological phases that don't even need a symmetry = topological superconductors, and explain how their classification changes in presence of spinless time-reversal symmetry. We close by perturbatively checking which of the 1D topological phases we had found are stable to interactions.

A natural strengthening of an algorithm for the (promise) constraint satisfaction problem is its singleton version: we first fix a variable to an element from its domain, then run the algorithm, and remove the element from the domain if the answer is negative. Using the Hales-Jewett theorem, we characterize the power of the singleton versions of standard universal algorithms for the (promise) CSP over a fixed template in terms of the existence of polymorphisms with certain symmetries, which we call palette symmetric polymorphisms. By proving the existence of such polymorphisms we establish that the singleton version of the BLP+AIP algorithm solves all (multi-sorted) tractable CSPs over domains of size at most 7. We further show that already for domain size 8 there exists a relational structure arising from the dihedral group $\mathbf D_4$ that does not admit palette symmetric polymorphisms and cannot be solved by singleton BLP+AIP. By providing concrete CSP templates, we illustrate the limitations of linear programming, the power of the singleton versions, and the elegance of palette symmetric polymorphisms. Among tractable temporal templates, we exhibit a structure demonstrating that finiteness is crucial for the Hales-Jewett argument; nevertheless, by introducing generalized palette polymorphisms we establish tractability for each such template.

Feynman integrals with generic propagator powers in one and two spacetime dimensions are investigated from various perspectives. In particular, we argue that the class of track integrals at any loop order is fixed by the recently found $\mathrm{\widehat P}$-symmetries of Yangian type. All track integrals up to six external points (and four loops) are bootstrapped explicitly as well as the full family of one-loop integrals at any multiplicity. Moreover, the triangle tracks at generic loop order, which constitute the most generic family of track-type integrals, are bootstrapped in this way. The results are compared to the direct evaluation via a `spectral transform' from the integrability toolbox that turns out to be particularly efficient for position-space tree integrals in lower dimensions. We prove that all $\mathrm{\widehat P}$-symmetries of these integrals can be derived from the framework of Aomoto--Gelfand hypergeometric functions, which applies to integrals in one and two dimensions. Finally, we also demonstrate the method's applicability to conformal integrals by deriving the complete results for all comb-channel conformal partial waves as well as the conformal double-box integral. We explicitly go through all examples of the above integrals in 1D and then provide a straightforward recipe for how to read off their 2D counterparts.

We bound the indices of normal abelian subgroups in finite groups contained in the Cremona group of rank 2 over a field of odd characteristic.

Conventional understandings of quantum theory hold that measurements change the state of an observed system following the Lüders update rule. Textbooks describe the application of this idea to non-relativistic systems, but extensions to relativistic and gravitating systems encounter subtleties. One consistent approach is via detector-based measurements. We study the effects of such measurements in a CFT with a holographic dual. We work out the boundary space-time regions associated to a Lüders update and how the outcome extends to modifications of the bulk gravity state. We explore information-theoretic consequences of this picture, and relate the information extracted by a measurement to updates of the semiclassical parameters of the bulk state.

We study axial gravitational perturbations of the Dymnikova regular black hole, an asymptotically flat spacetime in which the Schwarzschild singularity is replaced by a de Sitter core. Using the WKB method with Padé approximants, we compute grey-body factors, and absorption cross-sections, and test the recently proposed correspondence between quasinormal frequencies and transmission coefficients. We find that variations of the quantum parameter \(l_{\rm cr}\) affect the effective potential only near the horizon, leading to minor deviations of grey-body factors and absorption cross-sections from the Schwarzschild case. As a result, the Hawking radiation spectrum is governed mainly by the modified Hawking temperature, with grey-body factors providing only subleading corrections. Unlike higher quasinormal overtones, which are highly sensitive to near-horizon deformations, the grey-body factors remain robust, a feature explicitly confirmed for the Dymnikova geometry. The correspondence between quasinormal modes and grey-body factors holds in our case with high accuracy for multipoles $\ell \geq 2$.

Optimized control of quantum networks is essential for enabling distributed quantum applications with strict performance requirements. In near-term architectures with constrained hardware, effective control may determine the feasibility of deploying such applications. Because quantum network dynamics are suitable for being modeled as a Markov decision process, dynamic programming and reinforcement learning (RL) offer promising tools for optimizing control strategies. However, key quantum network performance measures -- such as secret key rate in quantum key distribution -- often involve a non-linear relationship between interdependent variables that describe quantum state quality and generation rate. Such objectives are not easily captured by standard RL approaches based on additive rewards. We propose a novel gradient-based RL framework that directly optimizes non-linear, differentiable objective functions, while accounting for uncertainties introduced by classical communication delays. We evaluate this framework in the context of entanglement distillation between two quantum network nodes equipped with multiplexing capability, and demonstrate up to 20-23% improvement over heuristic baselines in certain parameter regimes. Our work comprises the first step towards non-linear objective function optimization in quantum networks with RL, opening a path towards more advanced use cases.

We carry out an Effective Field Theory (EFT) study of the $pp \to \bar{t} t Zh$ process in the $4b + 3 \ell + \ge 2j + \slashed{E}_T$ final state. This process can uniquely probe the $\bar{t} t Zh$ couplings arising from higher dimensional EFT operators and can also provide bounds on $\bar{t} t Z$ coupling deviations. We highlight the importance of the proposed proton-proton Future Circular Collider (FCC-$hh$) to study this process and then perform a complete collider analysis by examining the relevant background processes. This allows us to determine the FCC-$hh$ sensitivity to probe anomalous $\bar{t} t Zh$ couplings.

The combination of solid state single-photon emitters and mechanical excitations on a common platform is a promising approach for the development of hybrid quantum technologies. In this topical review we discuss state-of-the-art platforms for emitter-based acousto-optics and their feasibility for acousto-optical Floquet engineering. To this aim we investigate theoretically the resonance fluorescence (RF) spectrum of an acoustically modulated single-photon emitter under arbitrarily strong optical driving. In the spectrum, the combination of Mollow triplet physics and phonon sidebands results in a complex structure of crossings, anti-crossings, and line suppressions. We apply Floquet theory to develop an analytical expression for the RF spectrum. Complemented with perturbative and non-perturbative techniques, this allows us to fully understand the underlying acousto-optical double dressing physics of the hybrid quantum system, explaining the observed spectral features. We use these insights to perform an experimental feasibility study of existing emitter-based acousto-optical platforms and come to the conclusion that surface and bulk acoustic waves interfaced with quantum dots as an established Mollow triplet platform represent particularly promising infrastructures for acousto-optical Floquet engineering.

Stochastic modeling of gene expression is a classic problem in theoretical biophysics, and the burst approximation is widely used to simplify gene expression models formulated via the chemical master equation. However, the approximation error has been investigated only for the simplest case. This article proposes and analyzes a general stochastic gene expression model with an arbitrary number of gene states, and quantifies the error introduced by the burst approximation. Using the standard binomial moment method, we derive recurrence relations for binomial moments in steady state. We develop an algorithm to numerically compute binomial moments in a hierarchical manner. In particular, explicit expressions for low-order moments are presented. Compared with surrogate models under the burst approximation, we conclude that the first-order moment of protein counts is preserved, whereas discrepancies generally arise in higher-order moments. By estimating the difference between two second-order moments using functional analysis, we evaluate the validity of the burst approximation.

This paper provides a complete classification of the subvarieties and subquasivarieties of pointed Abelian lattice-ordered groups ($\ell$-groups) that are generated by their totally ordered members. We present two complementary approaches to achieve this classification. First, using purely $\ell$-group-theoretic methods, we analyze the structure of lexicographic products and values to identify all join-irreducible members of the lattice of subvarieties of positively pointed Abelian $\ell$-groups. We provide a novel equational basis for each of these subvarieties, leading to a complete description of the entire subvariety lattice. As a direct application, our $\ell$-group-theoretic classification yields an alternative, self-contained proof of Komori's classification of subvarieties of MV-algebras. Second, we explore the connection to MV-algebras via Mundici's $Γ$ functor. We prove that this functor preserves universal classes, a result of independent model-theoretic interest. This allows us to lift the classification of universal classes of totally ordered MV-algebras, due to Gispert, to a complete classification of universal classes of totally ordered pointed Abelian $\ell$-groups. As a direct consequence, we obtain a full description of the corresponding lattice of subquasivarieties.

A thermodynamic description of cosmological spacetimes may provide insights into the fundamentals of the cosmic evolution that remain otherwise obscure, similar to `black hole thermodynamics'. We investigate the thermodynamic properties of late-time cosmological evolution using the dynamical systems approach, focusing on $Λ${}CDM model and scalar field models with exponential potentials. Thermodynamic quantities obtained through the Hayward-Kodama formalism are mapped onto the phase-space of these models. Specifically, we express the thermodynamic quantities as functions of the phase-space variables, allowing us to study the thermodynamic behavior across the phase space, particularly at the critical points. We focus on thermodynamic stability and phase transitions, analyzed in an initial condition-independent manner. In these models, the universe inevitably undergoes a thermodynamic phase transition, marked by diverging specific heats, irrespective of its initial configuration. We further demonstrate that the thermodynamic stability can occur only during an accelerating phase of the universe. For $Λ$CDM and quintessence models, the necessary stability conditions are never satisfied anywhere in the phase space, rendering both models thermodynamically unstable within the Hayward-Kodama framework and the canonical ensemble based stability criteria. Interestingly, the phantom models, although dynamically unstable, allow for the universe to attain thermodynamic stability in its asymptotic future. This can indicate the limitations of applying canonical ensemble based thermodynamic stability criteria to cosmological horizons. Through these archetypal descriptions of late-time cosmology, we show that the dynamical system approach is a robust framework to probe the thermodynamic aspects of cosmological evolution.

We measure the flux flow resistivity in FeSe$_{0.5}$Te$_{0.5}$ epitaxial films using a microwave dual-frequency technique (16 GHz and 27 GHz), in the range 5 K-$T_c$, in static magnetic fields up to 1.2 T. By applying a temperature scaling procedure, we extract from flux flow measurements the temperature dependence of the orbital upper critical field, that shows features of multiband superconductors. The reduced orbital upper critical field is then fitted with a two-band model with strong intraband and weak interband coupling, as expected in 11 Fe-based systems. We derive the vortex viscosity and we estimate the bands-averaged vortex core quasiparticle reduced scattering time within the Bardeen-Stephen framework. Our data suggest that, for our epitaxial FeSe$_{0.5}$Te$_{0.5}$ films, the quasiparticle scattering rate values are at the upper edge for the dirty regime. Finally, tentative numerical values of the orbital upper critical field and coherence length are provided.

We present numerically exact inchworm quantum Monte Carlo results for the real-time dynamics of the spin polarization in the sub-Ohmic spin-boson model at finite temperature. We focus in particular on the localization and coherence behavior of the model, extending our previous study at low temperature [Phys. Rev. Lett. 134, 056502 (2025)]. As the temperature increases, the system becomes less localized and less coherent. The loss of coherence, which is controlled by two independent mechanisms -- a smooth damping-driven crossover and a sharp frequency-driven transition -- exhibits a nontrivial temperature dependence. While both types of coherence loss occur at lower coupling in the high temperature regime, the frequency exhibits a sharper drop at high temperatures and this drop is observed for all values of the sub-Ohmic exponent, in contrast to the zero-temperature case. We discuss the full temperature-dependent dynamical phase diagram of the system and the interplay between coherence and localization across a wide range of physical parameters.

We study mappings that satisfy the inverse modulus inequality of Poletsky type with respect to $p$-modulus. Given $n-1<p\leqslant n,$ we show that, the image of some ball contains a fixed ball under mappings mentioned above. This statement can be interpreted as the well-known analogue of Koebe's theorem for analytic functions. As a consequence, we obtain the openness and discreteness of the limit mapping in the class under study. The paper also studies mappings of the Orlicz-Sobolev classes, for which an analogue of the Koebe one-quarter theorem is obtained as a consequence of the main results

Internet of Things (IoT) devices constantly generate heterogeneous data streams, driving demand for continuous, decentralized intelligence. Federated Lifelong Learning (FLL) provides an ideal solution by incorporating federated learning and lifelong learning. However, the extended lifecycle of FLL in IoT systems increases their vulnerability to persistent attacks. This problem is exacerbated by the single point of failure. Furthermore, the single point of trust created by the central server hinders reliable auditing for long-term threats. Blockchain technology provides a tamper-proof foundation for trustworthy FLL. Nevertheless, directly applying blockchain to FLL significantly increases computational and retrieval costs with the expansion of the knowledge base, slowing down the training on resource-constrained IoT devices. To address these challenges, we propose LiFeChain, a lightweight blockchain for secure and efficient federated lifelong learning with minimal on-chain disclosure and bidirectional verification. LiFeChain is the first blockchain tailored for FLL. It incorporates two complementary mechanisms: the Proof-of-Model-Correlation (PoMC) consensus on the server, which couples learning and unlearning mechanisms to mitigate negative transfer; and Segmented Zero-knowledge Arbitration (Seg-ZA) at the client, which detects and arbitrates abnormal committee behavior without compromising privacy. LiFeChain is a plug-and-play component that can be seamlessly integrated into existing FLL algorithms for IoT applications. To demonstrate its practicality and performance, we implement LiFeChain in representative FLL algorithms with Hyperledger Fabric under 6 attacks. Theoretical analysis and extensive evaluations demonstrate that LiFeChain effectively mitigates long-term attacks, and significantly reduces latency and storage overhead compared to state-of-the-art blockchain solutions.

We consider bilevel optimization problems with general nonconvex lower-level objectives and show that the classical hyperfunction-based formulation is unsettled, since the global minimizer of the lower-level problem is generally unattainable. To address this issue, we propose a correspondence-driven hyperfunction $ϕ^{\text{cd}}$. In this formulation, the follower is modeled not as a rational agent always attaining a global minimizer, but as an algorithm-based bounded rational agent whose decisions are produced by a fixed algorithm with initialization and step size. Since $ϕ^{\text{cd}}$ is generally discontinuous, we apply Gaussian smoothing to obtain a smooth approximation $ϕ^{\text{cd}}_ξ$, then show that its value and gradient converge to those of $ϕ^{\text{cd}}$. In the nonconvex setting, we identify that bifurcation phenomena, which arise when $g(x,\cdot)$ has a degenerate stationary point, pose a key challenge for hyperfunction-based methods. This is especially the case when $ϕ^{\text{cd}}_ξ$ is solved using gradient methods. To overcome this challenge, we analyze the geometric structure of the bifurcation set under some weak assumptions. Building on these results, we design a biased projected SGD-based algorithm SCiNBiO to solve $ϕ^{\text{cd}}_ξ$ with a cubic-regularized Newton lower-level solver. We also provide convergence guarantees and oracle complexity bounds for the upper level. Finally, we connect bifurcation theory from dynamical systems to the bilevel setting and define the notion of fold bifurcation points in this setting. Under the assumption that all degenerate stationary points are fold bifurcation points, we establish the oracle complexity of SCiNBiO for the lower-level problem.