We investigate gauge dependence of one-graviton-loop corrections to the effective field equation of the massless, minimally coupled scalar in de Sitter, obtained by including source and observer corrections to the effective self-mass correcting the equation. Using the $Δα$ variation of the de Sitter-breaking graviton propagator in a one-parameter family of gauges, we compute the gauge-dependent contributions to the effective self-mass of a massless minimally coupled scalar mediating interactions between heavy scalars. We show that gauge dependence cancels provided the contributions from all diagram classes are collected, including one-loop corrections to external mode functions, which play a qualitatively new role relative to flat space. The resulting cancellation supports the construction of graviton gauge-independent cosmological quantum-gravitational observables from quantum-corrected effective equations.

As fundamental one-dimensional defects, screw dislocations profoundly reshape the energy landscape and carrier dynamics of crystalline materials. By restoring the exact algebra of the screw dislocation group, we unveil the latent symmetry constraints that govern the electronic structure, providing a more rigorous physical picture than the conventional treatments. When applied to GaN, the method yields a band-connectivity constraint and rigorous dipole selection rules for polarization-resolved transitions. Combined with computed Hamiltonian matrix, the approach gives symmetry-filtered radiative and dielectric calculations and reveals a piezoelectrical effect at the dislocation core that strongly suppresses radiative recombination. The pronounced dominance of non-radiative capture over radiative recombination highlights the detrimental impact of screw dislocations on the luminous efficiency of GaN, providing a theoretical foundation for optimizing dislocation-limited optoelectronic devices.

Most existing secure neural network inference protocols based on secure multi-party computation (MPC) typically support at most four participants, demonstrating severely limited scalability. Liu et al. (USENIX Security'24) presented the first relatively practical approach by utilizing Shamir secret sharing with Mersenne prime fields. However, when processing deeper neural networks such as VGG16, their protocols incur substantial communication overhead, resulting in particularly significant latency in wide-area network (WAN) environments. In this paper, we propose a high-throughput and scalable MPC protocol for neural network inference against semi-honest adversaries in the honest-majority setting. The core of our approach lies in leveraging packed Shamir secret sharing (PSS) to enable parallel computation and reduce communication complexity. The main contributions are three-fold: i) We present a communication-efficient protocol for vector-matrix multiplication, based on our newly defined notion of vector-matrix multiplication-friendly random share tuples. ii) We design the filter packing approach that enables parallel convolution. iii) We further extend all non-linear protocols based on Shamir secret sharing to the PSS-based protocols for achieving parallel non-linear operations. Extensive experiments across various datasets and neural networks demonstrate the superiority of our approach in WAN. Compared to Liu et al. (USENIX Security'24), our scheme reduces the communication upto 5.85x, 11.17x, and 6.83x in offline, online and total communication overhead, respectively. In addition, our scheme is upto 1.59x, 2.61x, and 1.75x faster in offline, online and total running time, respectively.

Astrometric jitter noise arises when starspots on a rotating stellar surface move in and out of view, shifting the photocenter. This noise may limit our ability to detect and weigh small, sub-Neptune-sized planets around active stars. By deriving a linear forward model for the astrometric jitter signal of a rotating star in a spherical-harmonic coordinate system, we show that jitter noise can be used to reconstruct surface-brightness maps and, in principle, disentangle jitter from stellar reflex motion due to an orbiting planet. Furthermore, we show that astrometry and photometry probe complementary surface information: photometry measures even-degree spherical harmonic surfaces that are symmetric about the equator, while astrometry measures odd-degree modes. Their joint use, therefore, breaks degeneracies in surface mapping. Our model further quantifies the variation in the astrometric signal with inclination angle, which is foundational for studies of worst-case configurations of astrometric star-spot noise. For example, we show that pole-on stellar inclinations lead to poorly constrained inversions, as any stellar surface produces a purely circular astrometric jitter signal. We characterize the degeneracy in jointly identifying the stellar surface and stellar inclination, and develop a surface estimation approach. Using this approach, we present example simulations and reconstructions that demonstrate the use of astrometry data alongside light-curve data to improve stellar surface mapping and localize spot positions in latitude and longitude. With forthcoming high-precision Gaia astrometry, astrometric surface mapping provides a promising new approach to probe stellar activity.

Existing learning analytics approaches, which often model learning processes as sequences of learner actions or homogeneous relationships, are limited in capturing the distributed, multi-faceted nature of interactions in contemporary learning environments. To address this, we propose Heterogeneous Interaction Network Analysis (HINA), a novel multi-level learning analytics framework for modeling complex learning processes across diverse entities (e.g., learners, behaviours, AI agents, and task designs). HINA integrates a set of original methods, including summative measures and a new non-parametric clustering technique, with established practices for statistical testing and interactive visualization to provide a flexible and powerful analytical toolkit. In this paper, we first detail the theoretical and mathematical foundations of HINA for individual, dyadic, and meso-level analysis. We then demonstrate HINA's utility through a case study on AI-mediated small-group collaborative learning, revealing students' interaction profiles with peers versus AI; distinct engagement patterns that emerge from these interactions; and specific types of learning behaviors (e.g., asking questions, planning) directed to AI versus peers. By transforming process data into Heterogeneous Interaction Networks (HINs), HINA introduces a new paradigm for modeling learning processes and provides the dedicated, multi-level analytical methods required to extract meaning from them. It thereby moves beyond a single process data type to quantify and visualize how different elements in a learning environment interact and co-influence each other, opening new avenues for understanding complex educational dynamics.

We present a numerical investigation of nonlinear cluster lens reconstruction using weak lensing mass mapping. Recent advances in imaging and shear estimation have pushed reliable reduced shear measurements closer to cluster cores, making mass reconstruction accessible in the nonlinear regime. However, the Kaiser-Squires based algorithm becomes unstable in cluster cores, where convergence $κ$ significantly deviates from zero and the linear approximation breaks down. To address this limitation, we develop a reconstruction framework with two key modifications: applying smooth masks to these regions and using a model-derived analytical solution as the initial guess, rather than assuming $κ= 0$. We validate our framework using simulated cluster lensing data with known mass distributions, incorporating realistic masks that arise from limitations in reduced shear measurements. We show that in the absence of shape noise, our framework yields high-fidelity mass reconstruction in regions of large reduced shear, with the best-performing method achieving residuals below $0.02 σ$ in the unmasked regions. This pushes mass reconstruction to higher accuracy in the nonlinear regime.

We establish an exact identity for overdamped Langevin dynamics: the total entropy production rate equals four times the mutual information rate between an infinitesimal displacement and its time midpoint, plus a mean flow term. This yields a forward-only characterization of irreversibility. As a corollary, for additive bipartite systems, the chain rule directly yields a canonical nonnegative decomposition of subsystem entropy production into self and interaction components. The self term coincides with apparent entropy production, while the interaction term captures the dissipative cost of dependence and sharpens the learning rate bound. In a proof-of-concept application to red blood cell flickering, the decomposition reveals the thermodynamic structure of mechanical irreversibility. Overall, our results recast entropy production as a decomposable information-theoretic structure.

We investigate temperature fluctuations in hot QCD matter using a 3-flavor Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model. The high-order cumulant ratios $R_{n2}$ ($n>2$) exhibit non-monotonic variations across the chiral phase transition, characterized by slight fluctuations in the chiral crossover region and significant oscillations around the critical point. In contrast, distinct peak and dip structures are observed in the cumulant ratios at low baryon chemical potential. These structures gradually weaken and eventually vanish at high chemical potential as they compete with the sharpening of the chiral phase transition, particularly near the critical point and the first-order phase transition. Our results indicate that these non-monotonic peak and dip structures in high-order cumulant ratios are associated with the deconfinement phase transition. This study quantitatively analyzes temperature fluctuation behavior across different phase transition regions, and the findings are expected to be observed and validated in heavy-ion collision experiments through measurements of event-by-event mean transverse momentum fluctuations.

There are no weak scale triggers in the SMEFT up to dimension six that can solve the hierarchy problem far above the weak scale. Our arguments can be used to show that the same is true at dimension eight. Weak scale triggers are local operators sensitive to the Higgs mass squared and they are needed in a large number of qualitatively different cosmological solutions to the hierarchy problem. These solutions have little in common besides the use of a trigger operator. We argue that focusing on the signatures of the three already-known trigger operators can lead to discover or exclude this class of solutions to the hierarchy problem.

Using $4.5\, fb^{-1}$ of $e^+e^-$ collision data collected by the BESIII detector at center-of-mass energies between $4.600$ and $4.699\,GeV$, we search for the semileptonic decays $Λ_c^{+} \to Σ^{+} π^{-} e^+ ν_e$ and $Λ_c^{+} \to Σ^{-} π^{+} e^+ ν_e$ for the first time. Assuming their branching fractions are equal under isospin symmetry, evidence for $Λ_c^{+} \to Σ^{\pm} π^{\mp} e^+ ν_e$ is reported with a significance of $3.6σ$. The corresponding branching fraction is measured to be $\mathcal{B}(Λ_c^{+} \to Σ^\pmπ^\mp e^+ν_e) = (7.7^{+2.5}_{-2.3_{\rm stat.}}\pm1.3_{\rm syst.})\times 10^{-4}$, which is consistent with quark model predictions within two standard deviations.

Stochastic unravelings allow to efficiently simulate open system dynamics, yet their application has traditionally been restricted to master equations that preserve both Hermiticity and trace. In this work, we introduce a general framework that extends piecewise-deterministic unravelings to arbitrary trace-nonpreserving master equations, requiring only positivity and Hermiticity of the dynamics. Our approach includes, as special cases, unravelings of arbitrary dynamics in the Heisenberg picture, evolutions interpolating between fully Lindblad and non-Hermitian Hamiltonian generators, and equations employed in the derivation of full counting statistics, for which we show it can be used to obtain the moments of the associated probability distribution. The framework is suitable for both trace-decreasing and trace-increasing processes through stochastic disappearance and replication of the stochastic realizations, and it is compatible with different unraveling schemes and with reverse jumps in the non-Markovian regime. Thereby, our approach provides a powerful and versatile simulation method that significantly broadens the applicability of stochastic techniques for open system dynamics.

Weak lensing mass-mapping from shear catalogs faces systematic challenges from survey masks and spatially varying noise. To overcome these issues and reconstruct unbiased convergence $κ$ maps, we have constructed the AKRA (Accurate Kappa Reconstruction Algorithm), a prior-free and maximum-likelihood based analytical method. It has been validated for mock shear catalogs with a variety of survey masks. In this work, we present the first real-data application of the AKRA on the Subaru Hyper Suprime-Cam Year 1 (HSC Y1) data. We first validate AKRA using mock shear catalogs from the \texttt{Kun} simulation suite, with masks corresponding to the six HSC Y1 regions (\texttt{GAMA09H}, \texttt{GAMA15H}, \texttt{HECTOMAP}, \texttt{VVDS}, \texttt{WIDE12H}, and \texttt{XMMLSS}). The investigated statistics, including the lensing power spectrum, $\langle κ^2\rangle$, $\langle κ^3\rangle$, and the one-point probability distribution function of $κ$, are all unbiased. We then apply AKRA to the HSC Y1 shear catalog and provide reconstructed $κ$ maps ready for subsequent scientific analyses.

Encoding static images into spike trains is a fundamental step for enabling Spiking Neural Networks (SNNs) to process visual information. However, widely used methods such as rate coding, Poisson encoding, and time-to-first-spike (TTFS) often neglect spatial correlations and produce temporally inconsistent spike patterns, limiting both efficiency and interpretability. In this work, we propose a novel cluster-based encoding framework that explicitly preserves semantic structure across both spatial and temporal domains. The method first introduces a 2D spatial clustering mechanism, which leverages connected component analysis and local density estimation to identify salient foreground regions. Building upon this, we extend the approach to a 3D spatio-temporal (ST3D) encoding scheme that incorporates temporal neighborhood information, generating spike trains with enhanced temporal coherence. Experiments on the N-MNIST dataset demonstrate that the proposed ST3D encoder achieves 98.17% classification accuracy using a simple single-layer SNN, outperforming conventional TTFS encoding (97.58%). Notably, this performance is achieved with significantly fewer spikes (3800 vs. 5000 per sample), highlighting improved efficiency without sacrificing accuracy. These results indicate that the proposed method provides an interpretable, structure-aware, and computationally efficient encoding strategy, offering strong potential for neuromorphic computing applications.

Halide perovskites have emerged in the last decade as a new important class of semiconductors for a variety of optoelectronic applications. A lot of previous studies were thus devoted to the characterisation of their point defects. Positron annihilation spectroscopy is a well recognized tool for probing vacancies in materials. Recent applications of this technique to APbX$_3$ halide perovskites are sparse, and the rare theoretical predictions of positron lifetimes in these materials, published in association with experiments, do not fully agree with each other. These works suggest that vacancies on the A site are not detected. In our theoretical study we focus on the role of the electron-positron correlation functional. We thoroughly revisit and compare several approximations when applied to methylammonium lead iodide (MAPbI$_3$) with or without vacancies, as well as inorganic perovskites CsPbI$_3$ and CsPbBr$_3$, in various phases. We show also the relationship between the size of the voids, through Voronoi volumes, and the calculated lifetimes. For the cubic phases we investigate in detail the role of polymorphism, including the distribution of vacancy formation energies and positron annihilation lifetimes. In our lifetimes calculations, apart from older and more recent semi-local approximations for the electron-positron correlation potential, we also consider the weighted density approximation (WDA), which is truly non-local and should better describe positron annihilation in regions with strong electronic density variations. We show that for this class of materials, and especially for cations vacancies, the influence of the chosen approximation is crucial, much stronger than in metals, alloys and conventional semiconductors. This influence may induce to reconsider the interpretation of experimentally determined lifetimes.

Pauli exchange-repulsion is the dominant short-range intermolecular interaction and it is an essential component of molecular force fields. Current approaches to modeling Pauli repulsion in molecular force fields often rely on over 20 atom types to achieve chemical accuracy. The number of parameters in these approaches hampers the development of force fields with quantum-chemical accuracy that are transferable across many chemical systems. We present the anisotropic valence density overlap (AVDO) model for exchange-repulsion. The model produces sub-kcal/mol accuracy for dimers of organic molecules and contains two universal parameters, which we demonstrate are transferable for molecules composed of H, C, N, O, F, P, S, Cl, and Br. The model is tested on 1,872 unique molecular pairs selected from a set of 135 molecules, and samples dissociation curves and configurations from condensed-phase molecular dynamics trajectories. Given recent progress in machine learning of the electronic density, this model offers a promising path toward high-accuracy, next-generation machine-learned force fields.

We quantify the transition between weak and strong coupling in thermal ${\cal N}=4$ supersymmetric Yang--Mills (SYM) theory in four space-time dimensions by constructing an \emph{admissible ensemble} of log-aware Padé approximants that incorporate the weak- and strong-coupling expansions through $\mathcal O(λ^2)$ and $\mathcal O(λ^{-3/2})$ ($λ$ is the 't~Hooft coupling), including the non-analytic $λ^{3/2}$ and $λ^{2}\logλ$ terms. This replaces single-curve estimates with a reproducible uncertainty band and a well-defined central curve across the intermediate regime. The framework is \emph{predictive}, setting testable benchmarks for forthcoming perturbative and holographic calculations.

In this paper, we further develop a recently proposed theory of time based on wavefunction collapse in general relativity. It is based on the postulations that quantum states, which violate the momentum and Hamiltonian constraints, represent instances of time, and stochastic fluctuations of the lapse and shift generate the time evolution under which an initial state gradually collapses toward a diffeomorphism-invariant state. Under the wavefunction collapse, the scale factor monotonically increases, thus acting as a clock. The scalar, vector, and tensor gravitons arise as physical excitations, and the arrow of time for their evolution is set by the initial state. In the long-time limit, the tensor gravitons exhibit emergent unitary dynamics. However, the extra modes are strongly damped due to the non-unitary dynamics that suppress the constraint-violating excitations. The vector mode is uniformly suppressed over all length scales, but the decay rate of the scalar is proportional to its wave vector. This makes the latter a viable candidate for dark matter; excitations with large wavelengths survive over long periods, contributing to long-range interactions, while the fast decay of short-wavelength modes renders them undetectable without sufficient temporal resolution. These are demonstrated for the cosmological constant-dominated universe through semi-classical and adiabatic approximations, which are controlled in the limit of large space dimension.

We present a novel multilayer level-set method (MLSM) for eikonal-based first-arrival traveltime tomography. Unlike classical level-set approaches that rely solely on the zero-level set, the MLSM represents multiple phases through a sequence of $i_n$-level sets ($n = 0, 1, 2, \cdots$). Near each $i_n$-level set, the function is designed to behave like a local signed-distance function, enabling a single level-set formulation to capture arbitrarily many interfaces and subregions. Within this Eulerian framework, first-arrival traveltimes are computed as viscosity solutions of the eikonal equation, and Fréchet derivatives of the misfit are obtained via the adjoint state method. To stabilize the inversion, we incorporate several regularization strategies, including multilayer reinitialization, arc-length penalization, and Sobolev smoothing of model parameters. In addition, we introduce an illumination-based error measure to assess reconstruction quality. Numerical experiments demonstrate that the proposed MLSM efficiently recovers complex discontinuous slowness models with multiple phases and interfaces.

Many-body entanglement properties of quantum spin liquids (QSLs), persisting at arbitrarily long distances, have been intensely explored over the past two decades, but mostly for QSLs viewed as {\em closed} quantum systems. However, in experiments and potential quantum computing applications, candidate materials for this exotic phase of quantum matter will always interact with a dissipative environment, such as the one generated by bosonic quasiparticles in solids at finite temperature. Here we investigate both the {\em stability} and {\em spatial distribution} of entanglement for the Kitaev model of QSL, which is made {\em open} by its sudden coupling to an infinite bosonic bath of Caldeira-Leggett type and then time-evolved in both Markovian and non-Markovian regimes. From the time-dependent density matrix of QSL subregions, we extract genuine multipartite negativity (GMN), quantum Fisher information, spin-spin correlators, and the expectation value (EV) of the Wilson loop operator. In particular, time dependence of GMN offers the most penetrating insights: ({\em i}) in the Markovian regime, it remains nonzero only in hexagonal loopy subregions of QSL (as also discovered very recently for closed QSLs), eventually vanishing on the same timescale on which the EV of the Wilson loop operator vanishes; ({\em ii}) in the non-Markovian regime with pronounced memory effects, surprisingly, GMN remains nonzero up to much higher temperatures while also remaining zero in non-loopy subregions. In addition, the non-Markovian dynamics generates emergent interactions between spins, thereby opening avenues for tailoring properties of QSL via engineering of dissipation.

We extend the recently introduced strong disorder renormalization group method in real space, well suited to study bond disordered antiferromagnetic power law coupled quantum spin chains, to study excited states, and finite temperature properties. First, we apply it to a short range coupled spin chain, which is defined by the model with power law interaction, keeping only interactions between adjacent spins. We show that the distribution of the absolute value of the couplings is the infinite randomness fixed point distribution. However, the sign of the couplings becomes distributed, and the number of negative couplings increases with temperature $T.$ Next, we derive the Master equation for the power law long range interaction between all spins with power exponent $α$. While the sign of the couplings is found to be distributed, the distribution of the coupling amplitude is given by the strong disorder distribution with finite width $2α,$ with small corrections for $α>2$. Resulting finite temperature properties of both short and power law long ranged spin systems are derived, including the magnetic susceptibility, concurrence and entanglement entropy.

We compare two methods for evaluating the cardinality of the Cartesian product $N \times N$ of the set of natural numbers $N$. The first is used to explain the thermodynamics of black body radiation by using convergent functions on $N \times N$. The cardinality of $N \times N$ enters through the partition function, internal energy and entropy for every macrostate given by a normal mode of electromagnetic wave. Here, $N \times N$ is assigned a greater cardinality than $N$. The second method was devised in analysis to count the rational numbers by using divergent functions on $N \times N$. Here, $N \times N$ is not assigned a greater cardinality than $N$. In this article, we show that the experimentally confirmed first approach is mathematically more consistent with the definition of the real line and foundations of topology. It also provides a quantitative measure of the cardinality of $N \times N$ relative to that of N. Similar arguments show that the set of rational numbers is not countable. This article suggests that the axiom of choice is a more rigorous technique to prove the existence theorems for connection and metric on the spacetime manifold than the usual application of second-countability.

We propose the Steiner Traveling Salesman Problem with Time Windows and Pickup and Delivery, an advanced and practical extension of classical routing models. This variant integrates the characteristics of the Steiner Traveling Salesman Problem with time-window constraints, pickup and delivery operations and vehicle capacity limitations. These features closely mirror the complexities of contemporary logistics challenges, including last-mile distribution, reverse logistics and on-demand service scenarios. To tackle the inherent computational difficulties of this NP-hard problem, we propose two specialized mathematical formulations: an arc-based model and a node-oriented model, each designed to capture distinct structural aspects of the problem. We further introduce a preprocessing reduction method that eliminates redundant arcs, significantly enhancing computational performance and scalability. Both formulations are implemented using classical and quantum optimization approaches. In particular, the classical models are solved with Gurobi, whereas the quantum implementation is carried out on D-Wave's LeapCQMHybrid platform, a hybrid quantum-classical environment that integrates quantum annealing with classical optimization techniques for constrained problem solving. Numerical experiments are conducted to validate the proposed formulations and the preprocessing reduction method. The analyses performed assess the structural properties of the two models, their computational behavior, and the impact of preprocessing on problem size and solution efficiency.

We demonstrate the realization and interplay of two ferromagnetic resonances in one SFS $φ_0$ Josephson junction. First resonance that is realized under microwave radiation is the famous Kittel resonance. The other is Buzdin one appearing as a result of interaction of superconducting current and ferromagnetic interlayer magnetization. Transformations of one type of resonance to another under variation of external electromagnetic radiation and the $φ_0$ junction parameters open an interesting way to manipulation both of them. The combined ferromagnetic resonance that exhibits the features of both resonances is demonstrated too. The coupling of the Josephson phase with the magnetization of the ferromagnetic layer, caused by the spin-orbit interaction, leads to double synchronization, namely, synchronization of both magnetic precession and Josephson oscillations by external radiation. The obtained results demonstrate reach physics and unique opportunities for various applications.

Data from ground-based gravitational-wave detectors like LIGO contain many types of noise. Glitches are short bursts of non-Gaussian noise that may hinder our ability to identify or analyse gravitational-wave signals. They may have instrumental or environmental origins, and new types of glitches may appear following detector changes. The Gravity Spy project studies glitches and their origins, combining insights from volunteers on the community-science Zooniverse platform with machine learning. Here, we study volunteer proposals for new glitch classes, discussing links between these glitches and the state of the detectors, and examining how new glitch classes pose a challenge for machine-learning classification. Our results demonstrate how Zooniverse empowers non-experts to make discoveries, and the importance of monitoring changes in data quality in the LIGO detectors.

Semiconductor quantum dots are a promising platform for generating single and entangled photons.Still, their use is limited even in the most advanced structures by changes in the charge state of the quantum dot and its environment. Here, we present detailed time-resolved resonance fluorescence measurements on a single charge-tunable GaAs quantum dot, shedding new light on the spectral shadows invoked by the complex impurity environment. Detuning-dependent measurements reveal the existence of multiple Stark-shifted resonances, which are associated with rare spectral jumps smaller than the homogeneous linewidth and, therefore, typically concealed in the measurement noise. We observe similar environmentally induced Stark shifts for both the neutral exciton and negatively charged trion transitions, while the positively and doubly negatively charged trions exhibit significant differences. Our investigation quantifies the underlying impurity charge dynamics over a range from well below milliseconds to seconds, revealing that the hole occupation of the positively charged trion transition is constrained by rapid hole loss and slow hole recapture dynamics. Utilizing a second non-resonant laser, we increase the hole occupancy by over an order of magnitude and identify both a prolonged hole residence time and an enhanced hole tunneling rate into the quantum dot. These findings are supported by complementary spin noise spectroscopy measurements, which offer a significantly higher bandwidth compared to the time-resolved resonance fluorescence measurements.

The dilaton, a pseudo-Nambu-Goldstone boson (pNGB) of broken scale invariance, is an appealing ultralight dark matter (DM) candidate. Its mass is protected by conformal invariance and it can be searched for in tabletop experiments. However, contrary to standard pNGBs of internal symmetries, the dilaton generically has a large non-derivative self-coupling, leading to radiative contributions to its mass of the order of its decay constant. Hence typical ultralight dilatons should also have sub-eV decay constants, which would incur significant deviations from standard DM behavior at structure formation times, in severe tension with observations. Therefore, a fine-tuning is required to generate a hierarchy between the mass and the decay constant. In this work, we consider whether supersymmetry (SUSY) can be used to protect this hierarchy from quantum corrections. To ensure an ultralight dilaton mass robust against realistic SUSY-breaking contributions, we must consider a novel dilaton stabilization mechanism. The observed DM abundance can be produced by the misalignment mechanism for dilaton masses ranging from $10^{-11}$ to $1$ eV. Unfortunately, irreducible SUSY-breaking corrections due to gravity restrict the couplings between the dilaton and the Standard Model to be extremely small, beyond the reach of any current or proposed experiments. Our work demonstrates that constructing a consistent model of ultralight dilaton DM is quite involved.

We investigate the problem of quantum heat transport, based on the quadratic fermionic systems with help of the Peschel trick of single-particle correlation functions. The efficient numerical method is applied to the particular case of a single mode heat valve and the results are compared to analytical formulae. Comparing several configurations and parameters we perform the systematic analysis of the method to most efficiently and accurately describe the simple quantum heat valve system.

We show that for a general rational function $A$ of degree $m \geq 2$, any decomposition of its iterate $A^{\circ n}$, $n \geq 1$, into a composition of indecomposable rational functions is equivalent to the decomposition $A^{\circ n}$ itself. As an application, we prove that if $(A_1, A_2)$ is a pair of general rational functions, then the endomorphism of $\mathbb C\mathbb P^1 \times \mathbb C\mathbb P^1$ given by $ (z_1, z_2) \mapsto (A_1(z_1), A_2(z_2)) $ admits a periodic curve that is neither a vertical nor a horizontal line if and only if $A_1$ and $A_2$ are conjugate.

High-speed quantum key distribution (QKD) systems have achieved repetition frequencies above gigahertz through advanced technologies and devices, laying an important foundation for the deployment of high-key-rate QKD system. Although these advanced systems may introduce potential loopholes, an eavesdropper Eve is challenging to exploit them by performing the intercept-resend attacks due to the limited time window under high repetition frequency. However, here, we propose a security analysis model of orthogonal state attacks that do not require intercept-resend operation on the key rate of a QKD system. Under this framework, we propose a muted attack and experimentally verify the feasibility of the attack using a 1 GHz single-photon avalanche detector (SPAD). By sending hundreds of photons each time, Eve can mute Bob's SPADs to control the overall detection response of the QKD receiver, allowing her to learn nearly all the keys. Furthermore, we use this security model to simulate the overestimated key rates of the QKD system under orthogonal state attacks, including both the muted attack and the dead-time attack. This work theoretically and experimentally shows a timely case of the security vulnerability in the high-speed QKD system.

The organisers of major sports competitions use different policies with respect to constraints in the group draw. Our paper aims to rationalise these choices by analysing the trade-off between attractiveness (the number of games played by teams from the same geographic zone) and fairness (the departure of the draw mechanism from a uniform distribution). A parametric optimisation model is formulated and applied to the 2018 and 2022 FIFA World Cup draws. A flaw of the draw procedure is identified: the pre-assignment of the host to a group unnecessarily increases the distortions. All Pareto efficient sets of draw constraints are determined via simulations. The proposed framework can be used to find the optimal draw rules and justify the non-uniformity of the draw procedure for the stakeholders.