We use a simple method to derive two concentration bounds on the hypergeometric distribution. Comparison with existing results illustrates the advantage of these bounds across different regimes.

Chiral spin textures in magnetic insulators promise magneto-electric (ME) spintronics with orders-of-magnitude lower power consumption than metallic systems. However, realizing the short magnetic periods required for high-density device integration remains difficult, as conventional Dzyaloshinskii-Moriya interaction (DMI)-based mechanisms typically constrain spiral periods to tens of nanometers. While theory predicts that strong single-ion anisotropy (SIA) on frustrated lattices can stabilize complex non-coplanar textures, the potential for using this mechanism to engineer such compact textures remains largely unexplored. Here we report that a cubic chiral insulator Co$_5$TeO$_8$ provides an experimental example of this paradigm. Comprehensive neutron scattering and magnetometry reveal helimagnetic spirals with continuously tunable pitch of 5.7-10 nm embedded in a complex phase diagram spanning eight distinct phases. Capacitance anomalies throughout the phase diagram indicate magneto-electric coupling, pointing to the possibility of future $E$-field control of these textures. The temperature- and field-dependence of the helical wavevector strongly support a scenario in which site-dependent SIA provides the leading contribution to the selection of the helical period from a frustration-induced degenerate manifold. Consistent with this interpretation, $ab\,initio$ calculations place SIA approximately an order of magnitude above DMI, distinct from conventional helimagnets. Co$_5$TeO$_8$ thus offers an experimental realization of sub-10 nm helimagnetism and motivates a design principle for anisotropy-engineered correlated insulators.

Soft materials exhibit pronounced tension-compression asymmetry (TCA) in their softening and failure, a feature that conventional hyperelastic and continuum-damage formulations fail to capture in a unified framework. We present a Lode-invariant-based hyperelastic softening model for distortional-mode-dependent failure in soft materials, where mode dependence is introduced through a bi-failure construction with distinct tensile and compressive energy limiters. The proposed model extends Volokh's classical energy-limiting approach by embedding a Lode-angle-dependent weighting function, ensuring a smooth and physically consistent transition in failure across distortion modes within the constitutive description of the bulk response, without introducing internal damage variables. Agarose hydrogels (1, 2, and 3 % w/v) serve as the validation system. The framework reproduces experimental stress-stretch responses in uniaxial tension and compression, capturing concentration-dependent stiffness and failure energetics. Using parameters calibrated solely from combined uniaxial data, the model predicts pure shear behavior, including softening and failure, thereby demonstrating strong cross-mode predictive capability. To further assess thermodynamic consistency and distortion-mode sensitivity, the model's free-energy landscape is analyzed across the full Lode-invariant space, confirming a smooth and physically consistent response under diverse loading conditions. Parameter evolution with concentration follows power-law scaling, enabling interpolation and predictive validation at intermediate concentrations (evaluated at 2.5 % w/v). Overall, the proposed formulation provides a physically interpretable constitutive framework for tension-compression-asymmetric softening and distortional-mode-dependent failure, and establishes a foundation for three-dimensional failure mapping in soft materials.

The increasing reliance on software in various applications has made the problem of software vulnerability detection more critical. Software vulnerabilities can lead to security breaches, data theft, and other negative outcomes. Traditional software vulnerability detection techniques, such as static and dynamic analysis, have been shown to be ineffective at detecting multiple vulnerabilities. To address this issue, this study employed a deep learning approach, specifically Convolutional Neural Networks (CNN), to solve the software vulnerability detection problem. A 5-split cross-validation approach was used to train and evaluate the CNN model, which takes tokenized source code as input. The findings indicated that Sherlock successfully detected multiple vulnerabilities at the function level, and its performance was particularly strong for CWE-199, CWE-120, and CWE-Other, with an overall high accuracy rate and significant true positive and true negative values. However, the performance was less reliable for some vulnerabilities due to the lack of a standardized dataset which will be a future research direction. The results suggest that compared to current techniques, the proposed deep learning approach has the potential to substantially enhance the accuracy of software vulnerability detection.

Code is presented that computes and exploits orbital tori for any axisymmetric gravitational potential. The code is a development of the AGAMA software package for action-based galaxy modelling and can be downloaded as the AGAMAb code library. Although coded in C++, most of its functions can be accessed from Python. We add to the package functions that facilitate confronting models with data, which involve sky coordinates, lines of sight, distances, extinction, etc. The new torus generator can produce tori for both highly eccentric and nearly circular orbits that lie beyond the range of the earlier torus-mapping code. Tori can be created by interpolation between tori at very low cost. Tori are fundamentally devices for computing ordinary phase-space coordinates from angle-action coordinates, but AGAMAb includes an action finder that returns angle-action coordinates from any given phase-space location. This action finder yields the torus through the given point, so it includes the functionality of an orbit integrator. The action finder is more accurate and reliable but computationally more costly than the widely used Staeckel Fudge. We show how AGAMAb can be used to generate sophisticated but cheap models of tidal streams and use it to analyse data for the GD1 stream. With the most recently published distances to the stream, energy and angular momentum imply that the end that must be leading is trailing, but extremely small changes to the distances rectify the problem.

Gross-Neveu model in 2+1 dimensions exhibits a continuous transition from gapless Dirac semimetal to the gapped quantum anomalous Hall (QAH) insulator at a finite (attractive) coupling, at which the inversion and time-reversal symmetry become spontaneously broken, and the flavor O($M$) symmetry remains preserved. A unification of leading order parameters of 2+1 dimensional $N$ four-component Dirac fermions collects all Lorentz-singlet mass-like fermion bilinears, except the one condensing in the QAH state, into an irreducible representation of the O($M=4N$), and predicts another phase transition in the Gross-Neveu model to occur at a strong (repulsive) coupling. Here, a fermionic auxiliary-field quantum Monte Carlo algorithm is employed in order to study a lattice realization of the Gross-Neveu field theory in the repulsive regime, where the sign problem is absent. We indeed find the O($4N$) symmetry breaking transition out of Dirac semimetal to occur and to be weakly first-order for $N=2$, relevant to graphene. The size of the discontinuity and the magnitude of the critical coupling, however, both grow with $N$. Adding a finite chemical potential is found to break the symmetry and cause superconductivity. These results are in broad agreement with the predictions of the unified field theory. Our lattice model also displays an interesting exact O($2N$) symmetry, a subgroup of the low-energy O($4N$), and has the ordered ground state with the order parameter that belongs to its $N(2N-1)$-dimensional representation. Other order parameters are also examined, and a certain hierarchy among those that belong to different representations of the exact $O(2N)$ is observed.

Restriction categories provide a categorical framework for partiality. In this paper, we introduce three new categorical theories for partiality: local categories, partial categories, and inclusion categories. The objects of a local category are partially accessible resources, and morphisms are processes between these resources. In a partial category, partiality is addressed via two operators, restriction and contraction, which control the domain of definition of a morphism. Finally, an inclusion category is a category equipped with a family of monics which axiomatize the inclusions between sets. The main result of this paper shows that restriction categories are $2$-equivalent to local categories, that partial categories are $2$-equivalent to inclusion categories, and that both restriction/local categories are $2$-equivalent to bounded partial/inclusion categories. Our result offers four equivalent ways to describe partiality: on morphisms, via restriction categories; on objects, with local categories; operationally, with partial categories; and via inclusions, with inclusion categories. We also translate several key concepts from restriction category theory to the local category context, which allows us to show that various special kinds of restriction categories, such as inverse categories, are $2$-equivalent to their analogous kind of local categories. In particular, the equivalence between inverse (restriction) categories and inverse local categories is a generalization of the celebrated Ehresmann-Schein-Nambooripad theorem for inverse semigroups.

The fuzzy-sphere regularization is an emerging numerical and theoretical technique for studying conformal field theories (CFTs). In this paper, we apply it to the $O(N)$ vector model, one of the most prominent theories for critical behavior in three space-time dimensions. We construct a model that realizes the $O(N)$ Wilson-Fisher and free-scalar CFTs for general $N$. For $N=2,3,4$, we present numerical evidence including the operator spectra and correlation functions in agreement with conformal symmetry and conformal bootstrap results.

The deployment of autonomous AI agents in Internet of Things (IoT) energy systems requires decision-making mechanisms that remain robust, efficient, and trustworthy under real-time constraints and imperfect monitoring. While reinforcement learning enables adaptive prosumer behaviors, ensuring economic consistency and preventing strategic manipulation remain open challenges, particularly when sensing noise or partial observability reduces the operator's ability to verify actions. This paper introduces a trust-enforcement framework for IoT energy trading that combines an approximate Vickrey-Clarke-Groves (VCG) double auction with an immediate one-shot penalty. Unlike reputation- or history-based approaches, the proposed mechanism restores truthful reporting within a single round, even when allocation accuracy is approximate and monitoring is noisy. We theoretically characterize the incentive gap induced by approximation and derive a penalty threshold that guarantees truthful bidding under bounded sensing errors. To evaluate learning-enabled prosumers, we embed the mechanism into a multi-agent reinforcement learning environment reflecting stochastic generation, dynamic loads, and heterogeneous trading opportunities. Experiments show that improved allocation accuracy reduces deviation incentives, the required penalty matches analytical predictions, and learned bidding behaviors remain stable and interpretable despite imperfect monitoring. These results demonstrate that lightweight penalty designs can reliably align strategic IoT agents with socially efficient energy-trading outcomes.

In a recent paper [8], we introduced a data-based approach to design event-triggered controllers for linear systems directly from data. Here, we extend the results in [8] to a class of nonlinear systems. We provide two data-based designs certified by a (classical) Lyapunov function. For these two designs, we devise event-triggered policies that rely on the previously found Lyapunov function, have parameters tuned from data, ensure a positive minimum inter-event time, and act based either on the state error or on the library error. These two different policies, and their respective advantages, are illustrated numerically.

The Electron--Ion Collider in China (EicC) provides an excellent opportunity to explore the internal structure of pions and kaons via the Sullivan process in deep-inelastic scattering (DIS). In this study, we present detailed projections for the pion and kaon structure functions, $F_2^π$ and $F_2^K$, at EicC, with a focus on both statistical and systematic uncertainties. Leveraging EicC's high luminosity and broad kinematic coverage, the accessible kinematic region is extended beyond previous measurements. The projected statistical uncertainties for $F_2^π$ and $F_2^K$ are below 5\% and 8\%, respectively, across most kinematic bins. Systematic uncertainties arising from detector effects have been carefully evaluated. These results significantly enhance the precision of meson structure function measurements and provide important constraints on theoretical models of meson parton distributions. Moreover, this study bridges the gap between fixed-target and collider-era measurements, highlighting the pivotal role of EicC in advancing our understanding of hadronic structure.

Modern precision measurements, such as interferometry for detecting gravitational waves, rely on the estimation of optical phases encoded in light fields. Here, we propose to exploit the collectively enhanced output field of a driven-dissipative many-body quantum system as a light source in order to improve the precision of estimating optical phases. Pronounced temporal correlations of such output fields benefit the sensitivity of measurement protocols, which we show theoretically by employing a boundary time crystal as a light source. The fundamental bound on the precision of such estimation shows scaling with the number of constituents $N$ of the many-body system as $N^4$ while scaling linearly with the measurement time $T$. We discuss this scaling both from a perspective of the resources employed to build the light source and of the resources produced by the light source, namely the number of emitted photons and their correlations. We show that a protocol, in which the phase shifted light field is guided into an auxiliary replica system, which serves as a detector that is sensitive to non-trivial temporal correlations of light, can saturate the fundamental bound on precision at an optimal operating point.

I introduce heterogeneity into the analysis of peer effects arising from conformity by allowing peer-effect parameters to vary across agents' actions. Using a structural model based on a simultaneous network game with incomplete information, I derive conditions that guarantee the uniqueness of the equilibrium and the identification of heterogeneous peer-effect parameters. Applying the model to data on smoking and alcohol consumption among secondary school students, and conducting policy simulations, I show that assuming a homogeneous preference for conformity leads to biased estimates of peer effects and ex ante policy evaluations.

We propose an asympotically optimal choice of shared concentrated real poles of a family of rational approximants of time-dependent exponential functions $\exp(-tz)$ for $z \geq 0$ and $t$ in a positive time interval $T$. Our result extends a classical result by J.-E. Andersson [J. Approx. Theory, 32(2):85--95, 1981] on the asymptotic best rational approximation of $\exp(-z)$ with real poles. Numerical experiments demonstrate the near-optimality of our choice for various time ranges and for both small and large approximation degrees. An application of the uniform-in-time rational approximation using our proposed concentrated real poles to a linear constant-coefficient initial-value problem is also discussed.

We discuss the exact quantization of general one-dimensional potentials in view of the exact-WKB formalism. Building on our previous work, we perform analytic continuations across different sectors via the complexification to the spectral (energy) parameter $u$ and identify continuous and discontinuous transitions of the exact spectrum for generic potentials. When the transition is discontinuous, it is characterized by the Stokes phenomena, inducing different exact (median) quantization conditions, thereby distinct trans-series structures valid in different sectors. We analyze two illustrative examples, namely asymmetric triple-well (ATW) and tilted double-well (TDW), and verify the general qualitative analysis by deriving exact (median) quantization conditions in each sector. Moreover, by obtaining the trans-series solutions for each system, we identify bion/bounce configurations and show that the trans-series of ATW is organized in accordance with the cluster expansion of the bion gas and there should exist a previously neglected complex saddle in the TDW system. These identifications further strengthen the link between path integral and exact-WKB formalisms, while also demonstrating the predictive power of the latter. In parallel, for the P-NP relations of genus-1 systems, we derive transformation rules between any perturbative and non-perturbative pair of WKB-cycles. Our results show that the entire resurgence data of a genus-1 system transforms only by the change of classical parameters, i.e. frequencies and bion/bounce actions, and the perturbative energy series. This also reveals the underlying reasons of the previously found $S$-duality transformations.

Given an ordered structure, we study a natural way to extend the order to preorders on type spaces. For definably complete, linearly ordered structures, we give a characterisation of the preorder on the space of 1-types. We apply these results to the divisibility preorder on the space of ultrafilters on the set of natural numbers, giving an independence result about the suborder consisting of ultrafilters with only one fixed prime divisor, as well as a classification of ultrafilters with finitely many prime divisors.

We introduce multilevel Picard (MLP) approximations for McKean--Vlasov stochastic differential equations (SDEs) with nonconstant diffusion coefficient. Under standard Lipschitz assumptions on the coefficients, we show that the MLP algorithm approximates the solution of the SDE in the $L^2$-sense without the curse of dimensionality. The latter means that its computational cost grows at most polynomially in both the dimension and the reciprocal of the prescribed error tolerance. In two numerical experiments, we demonstrate its applicability by approximating McKean--Vlasov SDEs in dimensions up to 1000.

The supercritical state of matter is usually described as a continuous phase without sharp boundaries between liquid and gas regions. However, under non-equilibrium conditions, this view breaks down. Here we report an experimental investigation of non-equilibrium fluctuations in supercritical carbon dioxide (CO2) subjected to a stabilising temperature gradient. Using shadowgraphy, we reveal spontaneous stratification of the fluid into different layers, separated by transition regions, where thermodynamic properties vary dramatically. These signatures are particularly evident when the system crosses the Widom lines, loci of the extrema of the response function in the supercritical domain. The analysis of the intermediate scattering function of temperature fluctuations highlights the presence of Brunt-Vaisala oscillations within the fluid at multiple frequencies. These oscillations arise from the coupling of thermal and viscous modes under gravity and are a clear signature of the layered structure of the fluid. Our approach enables systematic exploration of a wide range of thermodynamic conditions in a single experiment. These findings suggest that the Widom region cannot be described as a homogeneous phase, but rather as a dynamic assembly of phase-like behaviours, challenging the applicability of classical thermodynamics in non-equilibrium supercritical regimes.

We propose a minimal inverse seesaw model with $S_4$ symmetry for the Majorana neutrinos with only one real ($m_0$)-and two complex ($α, β$) parameters in neutrino sector which gives reasonable predictions for the neutrino oscillation parameters, the observed baryon asymmetry of the Universe and the charged lepton flavor violation. The resulting model reveals a favor for normal neutrino mass ordering, a higher octant of $θ_{23}$ and a lower half-plane of Dirac CP violation phase. The predictions of the model for sum of neutrino masses and the effective Majorana neutrino mass are centered around 58.98 meV and 6.2 meV, respectively. The model also provides the predictions of the baryon asymmetry and charged lepton flavour violation processes which are consistent with the experimental observations.

This paper introduces new empirical process tools for analyzing a broad class of statistical learning models under heavy-tailed noise and complex function classes. Our primary contribution is the derivation of two Dudley-type maximal inequalities for expected empirical processes that remove restrictive assumptions such as light tails and uniform boundedness of the function class. These inequalities enlarge the scope of empirical process theory available for statistical learning and nonparametric estimation. Exploiting the new bounds, we establish robustness guarantees for deep ReLU network estimators in Huber and quantile regression. In particular, we prove a unified non-asymptotic sub-Gaussian concentration bound that remains valid even under infinite-variance noise and provide a comprehensive analysis of non-asymptotic robustness for deep Huber estimators across all noise regimes. For deep quantile regression, we provide the first non-asymptotic sub-Gaussian bounds without requiring moment assumptions. As an additional application, our framework yields estimation error bounds for nonparametric least-squares estimators that simultaneously accommodate infinite-variance noise, non-Donsker function classes, and approximation error. Moreover, unlike prior approaches based on specialized multiplier processes, our framework extends to broader empirical risk minimization problems, including the nonparametric generalized linear models and the ``set-structured'' models.

We investigate the exceptional points (EPs) and their pseudospectra in black hole perturbation theory. By considering a Gaussian bump modification to the Regge-Wheeler potential with variable amplitude, position, and width parameters, $(\varepsilon,d,σ_0)$, a continuous line of EPs (exceptional line, EL) in this three-dimensional parameter space is revealed. Notably, the EL exhibits an anisotropic spectral response: parameters migrating along the EL direction leaves the coalesced QNM spectra nearly unchanged, while moving parameters away from the EL induces the characteristic $ε^{1/2}$ scaling, highlighting the directional nature of spectral instability in exceptional structures. We find that the vorticity $ν=\pm1/2$ and the Berry phase $γ=π$ for loops encircling the EL, while $ν=0$ and $γ=0$ for those do not encircle the EL. In the neighborhood of an eigenvalue, through matrix perturbation theory, we prove that the $ε$-pseudospectrum contour size scales as $ε^{1/q}$ at an EP , where $q$ is the order of the largest Jordan block of the Hamiltonian-like operator associated with that eigenvalue, contrasting with the linear $ε$ scaling at non-EPs. Numerical implements confirm this observation, demonstrating enhanced spectral instability at EPs for non-Hermitian systems including black holes.

We present a measurement of the free-streaming length of dark matter (DM) and subhalo abundance around 28 quadruple image strong lenses using observations from JWST MIRI presented in Paper III of this series. We improve on previous inferences on DM properties from lensed quasars by simultaneously reconstructing extended lensed arcs with image positions and relative magnifications (flux ratios). Our forward modeling framework generates full populations of subhalos, line-of-sight halos, and globular clusters, uses an accurate model for subhalo tidal evolution, and accounts for free-streaming effects on halo abundance and concentration. Modeling lensed arcs leads to more-precise model-predicted flux ratios, breaking covariance between subhalo abundance and the free-streaming scale parameterized by the half-mode mass $m_{\rm{hm}}$. Assuming subhalo abundance predicted by the semi-analytic model {\tt{galacticus}} ($N$-body simulations), we infer (Bayes factor of 10:1) $m_{\rm{hm}} < 10^{7.4} \mathrm{M}_{\odot}$ ($m_{\rm{hm}} < 10^{7.2} \mathrm{M}_{\odot}$), a 0.4 dex improvement relative to omitting lensed arcs. These bounds correspond to lower limits on thermal relic DM particle masses of $6.5$ and $7.4$ keV, respectively. Conversely, assuming DM is cold, we infer a projected mass in subhalos ($10^6 < m/M_{\odot}<10^{10.7}$) of $1.7_{-1.2}^{+2.6} \times 10^7 \ \mathrm{M}_{\odot} \ \rm{kpc^{-2}}$ at $95 \%$ confidence. This is consistent with {\tt{galacticus}} predictions ($0.9 \times 10^7 \mathrm{M}_{\odot} \ \rm{kpc^{-2}}$), but in mild tension with recent $N$-body simulations ($0.6 \times 10^7 \mathrm{M}_{\odot} \ \rm{kpc^{-2}}$). Our results are among the strongest bounds on WDM, and the most precise measurement of subhalo abundance around strong lenses. Further improvements will follow from the large sample of lenses to be discovered by Euclid, Rubin, and Roman.

We study the Born-Oppenheimer approximation of a mass-imbalanced three-body system made of two heavy particles of mass M and one light particle of mass m for arbitrary angular momentum. In this system, heavy-light pairs interact via a zero-range force. We construct the light-particle Hamiltonian using self-adjoint extensions of the two-center point interaction and show that the corresponding effective potential is regular at the coincidence point of the heavy particles. Consequently, this model presents an alternative method to finite-range, cutoff, or short-distance heavy-heavy regularizations: the necessary three-body input is encoded in the self-adjoint realization of the light-particle Hamiltonian, while the heavy-light interactions remain point-like. In the unitary limit, after fixing the characteristic length scale, we derive an explicit Efimov spectrum. Our results recover the zero-angular-momentum case of R. Figari, H. Saberbaghi, and A. Teta, J. Phys. A: Math. Theor. 57(5), 2024, and provide a sufficient condition ensuring the absence of non-Efimov bound states. Away from unitarity, we show that the spatial size of the shallowest trimer near the threshold is approximately 2.8 times the heavy-light scattering length, in contrast to the common assumption that these two length scales coincide. We also derive a Bargmann-type bound on the number of three-body bound states and obtain an estimate sharper than previous results. Finally, we illustrate the method with numerical results for selected alkali mixtures.

The investigation of the volume, surface area, and other geometric properties of sections of convex bodies, and in particular cubes, has a long history and a rich literature. However, much less is known when the cube has a volume distribution that is different from the Lebesgue measure; for example, a Gaussian density. We study the probability densities in the standard cube $B^n_\infty=[-1,1]^n$ of $\mathbb R^n$ generated by $e^{-b\|x\|^2}$, $b> 0$. We prove that the limit of the induced Gaussian-type volume of hyperplane sections of $B^n_\infty$ through the origin and orthogonal to a main diagonal is \[ \sqrt{\frac bπ}\left (1-4\frac{e^{-b}\sqrt{b}}{2\sqrtπ\mathrm{erf}(\sqrt{b})}\right)^{-\frac12}, \] as $n\to\infty$. This extends the well-known result of Hensley (1979) for the Lebesgue measure and continues the investigations initiated by Barthe, Guédon, Mendelson, Naor (2005), Zvavitch (2008), and König, Koldobski (2013).

This paper studies a boundary between local self-application and global self-certification. Irrational quantities are treated operationally, as procedures whose approximations are refined by effective update rules. The golden ratio $Φ$ is used as a model of stable local recurrence: the reciprocal update $R(x)=1+1/x$ has a unique positive fixed point and admits finite witnessed approximations. By contrast, global reflection asks a system to certify its own correctness uniformly. The proof-theoretic claim is therefore contrastive: primitive-recursive proof checking and local soundness preserve correctness through bounded checks and bounded witnesses, but they do not yield internal global reflection. No complexity advantage, decision procedure, or new reflection principle is claimed.

We settle the complexity of satisfiability, finite-state satisfiability, and model-checking for generalized HyperLTL with stuttering and contexts, an expressive logic for the specification of asynchronous hyperproperties. Such properties cannot be specified in HyperLTL, as it is restricted to synchronous hyperproperties. Nevertheless, we prove that satisfiability is $Σ_1^1$-complete and thus not harder than for HyperLTL. On the other hand, we prove that model-checking and finite-state satisfiability are equivalent to truth in second-order arithmetic, and thus much harder than the decidable HyperLTL model-checking problem and the $Σ_0^1$-complete HyperLTL finite-state satisfiability problem. The lower bounds for the model-checking and finite-state satisfiability problems hold even when only allowing stuttering or only allowing contexts.

Quantum state discrimination, alongside its other applications, has recently found use as a tool for witnessing generalised contextuality. In this article, we derive noncontextuality inequalities for both conclusive and inconclusive outcomes across various guessing strategies. For minimum-error discrimination, the advantage is in terms of the confidences of individual outcomes, while for unambiguous state discrimination, it is in terms of the average guessing probability. For maximum-confidence discrimination, we show that contextual advantages occur not only for the confidence but also their average, the guessing probability, as well as the inconclusive outcome rate. Our results show that contextual advantages are observed across all two-state discrimination schemes and figures of merit. We envisage that various quantum information applications based on state discrimination may offer advantages over noncontextual theories.

In this paper, we study the problem of finding a collection of planted cycles in an \ER random graph $G \sim \mathcal{G}(n, λ/n)$, in analogy to the famous Planted Clique Problem. When the cycles are planted on a uniformly random subset of $δn$ vertices, we show that almost-exact recovery (that is, recovering all but a vanishing fraction of planted-cycle edges as $n \to \infty$) is information-theoretically possible if $λ< \frac{1}{(\sqrt{2 δ} + \sqrt{1-δ})^2}$ and impossible if $λ> \frac{1}{(\sqrt{2 δ} + \sqrt{1-δ})^2}$. Moreover, despite the worst-case computational hardness of finding long cycles, we design a polynomial-time algorithm that attains almost exact recovery when $λ< \frac{1}{(\sqrt{2 δ} + \sqrt{1-δ})^2}$. This stands in stark contrast to the Planted Clique Problem, where a significant computational-statistical gap is widely conjectured.

Although coupled ion-electron transfer (CIET) has emerged as a powerful framework to rationalize the kinetics of Faradaic reactions, its mechanism has lacked a fully microscopic, first-principles description. Here we show that the coupling of electron-transfer to ion-transfer can be understood as an extension of Marcus theory in which the ensemble of diabatic nuclear configurations is conditioned on a classical collective variable describing the interfacial anisotropy. This formalism enables direct construction of the CIET free-energy surface from constrained ab initio trajectories, providing a first-principles route to electrochemical current-overpotential relations. We demonstrate this method for CO2 redox on a gold electrode and find that the resulting two-dimensional saddle-point barriers differ substantially from one-dimensional treatments that consider only electron- or ion-transfer coordinates individually.

The dispersion measures (${\rm DMs}$) from fast radio bursts (FRBs) and the thermal Sunyaev--Zeldovich (tSZ) effect probe the free-electron density and thermal pressure, respectively, in the intergalactic medium (IGM) and the intervening galaxies and clusters. Their combination enables disentangling the gas density and temperature. In this work, we present the first detection of an angular cross-correlation between the ${\rm DMs}$ and the Compton $y$ parameter of the tSZ effect. The theoretical expectation is calculated using the halo model $\texttt{HMx}$, calibrated with hydrodynamic simulations. The observational cross-correlation is measured over angular separations of $1^\prime$--$1000^\prime$ using the ${\rm DMs}$ from $133$ localized FRBs and the $y$-maps from the Planck satellite and the Atacama Cosmology Telescope (ACT). We detect a positive correlation with amplitudes of $\mathcal{A}=2.01 \pm 0.50$ ($4.0 σ$) for Planck and $\mathcal{A}=1.23 \pm 0.82$ ($1.5 σ$) for ACT, where $\mathcal{A}=1$ corresponds to the theoretical prediction of the Planck 2018 $Λ$CDM cosmology. Assuming an isothermal gas, the measured amplitude implies an average electron temperature of $\approx 2 \times 10^7 \, {\rm K}$. The correlation is highly sensitive to the matter clustering parameter $σ_8$ and to baryon feedback, and its dependence on other cosmological and astrophysical parameters -- such as the ionized fraction and the Hubble constant -- differs from that of the ${\rm DM}$ alone. This suggests that future joint analyses of the ${\rm DMs}$ and the tSZ effect could help break degeneracies among these parameters.