In this short note, we present a self-contained exposition of the supersimplicity of certain expansions of the additive group of the integers, such as adding a generic predicate (due to Chatzidakis and Pillay), a predicate for the square-free integers (due to Bhardwaj and Tran) or a predicate for the prime integers (due to Kaplan and Shelah, assuming Dickson's conjecture).

We study the remote estimation of a linear Gaussian system over a channel that wears out over time and with every use. The sensor can either transmit a fresh measurement in the current time slot, restore the channel quality at the cost of downtime, or remain silent. Frequent transmissions yield accurate estimates but incur significant wear on the channel. Renewing the channel too often improves channel conditions but results in poor estimation quality. What is the optimal timing to transmit measurements and restore the channel? This problem is formulated as a semi-Markov decision process (SMDP). We establish monotonicity properties of the optimal policy and propose structure-aware solution methods.

In this paper, we extend a theorem of Toën and Vaquié to the non-Archimedean and formal settings. More precisely, we prove that a smooth and proper rigid analytic variety is algebraizable if and only if its category of perfect complexes is smooth and proper. As a corollary, we deduce an analogous statement for formal schemes and demonstrate that, in general, the bounded derived category of coherent sheaves on a formal scheme is not smooth.

We answer several fundamental geometric questions about reaction networks with power-law kinetics, on topics such as generic finiteness of the number of steady states, robustness, and nondegenerate multistationarity. In particular, we give an ideal-theoretic characterization of generic absolute concentration robustness, as well as conditions under which a network that admits multiple steady states also has the capacity for nondegenerate multistationarity. The key tools underlying our results come from the theory of vertically parametrized systems, and include a linear algebra condition that characterizes when the steady state system has positive nondegenerate zeros.

Hubness is a phenomenon in high-dimensional vector spaces where a point from the natural distribution is unusually close to many other points. This is a well-known problem in information retrieval that causes some items to accidentally (and incorrectly) appear relevant to many queries. In this paper, we investigate how attackers can exploit hubness to turn any image or audio input in a multi-modal retrieval system into an adversarial hub. Adversarial hubs can be used to inject universal adversarial content (e.g., spam) that will be retrieved in response to thousands of different queries, and also for targeted attacks on queries related to specific, attacker-chosen concepts. We present a method for creating adversarial hubs and evaluate the resulting hubs on benchmark multi-modal retrieval datasets and an image-to-image retrieval system implemented by Pinecone, a popular vector database. For example, in text-caption-to-image retrieval, a single adversarial hub, generated using 100 random queries, is retrieved as the top-1 most relevant image for more than 21,000 out of 25,000 test queries (by contrast, the most common natural hub is the top-1 response to only 102 queries), demonstrating the strong generalization capabilities of adversarial hubs. We also investigate whether techniques for mitigating natural hubness can also mitigate adversarial hubs, and show that they are not effective against hubs that target queries related to specific concepts.

We consider the problem of deciding whether the solution sets of a parametrized polynomial system are toric in the sense that they admit a monomial parametrization. We focus on vertically parametrized systems, which are sparse systems where we allow linear dependencies between coefficients in front of the same monomial. We give a matroid-theoretic characterization of the maximal-dimensional torus for which all solution sets are invariant under componentwise multiplication. Building on this, we provide necessary conditions and sufficient conditions for when the solution sets are unions of finitely many or a unique coset of this torus. The motivation of this work comes from the theory of reaction networks, where toric structure of the steady state system substantially simplifies the determination of multistationarity; here, we show that this is also the case for absolute concentration robustness and steady state invariants.

We construct many-body scar states in multi-flavour fermionic lattice models that possess strong magnetic or superconducting correlations of a given type specified by a unitary matrix $A$. One of the states maximizes the one-point correlations over the full Hilbert space and has the form of the BCS wavefunction. It may always be made the ground state by adding the correlations as a "pairing potential" to any Hamiltonian supporting group-invariant scars. In our single-flavour, spin-full fermions example we consider a superconducting $A$. The BCS scar ground state is a linear combination of the well-known $η$-pairing states. In the multi-orbital fermions example the BCS-like ground state maximizes unconventional magnetic correlations. The broad class of eligible Hamiltonians includes many conventional condensed matter interactions. The part of the Hamiltonian that governs the exact dynamics of the scar subspace coincides with the BCS mean-field Hamiltonian. We therefore show that its eigenstates are many-body scars that are decoupled from the rest of the Hilbert space and thereby protected from thermalization. Our results point out a connection between the fields of superconductivity and weak ergodicity breaking (many-body scars) and will hopefully encourage further investigations. They also provide the first feasible protocol to initialize a fermionic system to a scar state in (a quantum simulator) experiment.

The neutron star low-mass X-ray binary, EXO 0748--676, recently returned to outburst after a $\sim$ 16 year-long quiescence. Since its return, there has been a global effort to capture the previously unseen rise of the source and to understand its somewhat early return to outburst, as it is typical for a source to spend longer in quiescence than in outburst. Here, we report on the simultaneous optical and X-ray detection of a type I X-ray burst, captured by XMM-Newton during a DDT observation on 30th June 2024. The data show 3 X-ray eclipses consistent with the known ephemeris and one type I X-ray burst at 60492.309 MJD. The X-ray burst is reprocessed into the optical band and captured by XMM-Newton's Optical Monitor during a 4399 s exposure with the B filter in image + fast mode. We determine that the optical peak lags the X-ray peak by 4.46 $\pm$ 1.71s. The optical and X-ray rise times are similar, but the optical decay timescale is shorter than the X-ray decay timescale. The reprocessing site is likely within a few light seconds of the X-ray emitting region, so the companion star, accretion disc and ablated material are all plausible.

Nowadays, low-rank approximations of matrices are an important component of many methods in science and engineering. Traditionally, low-rank approximations are considered in unitary invariant norms, however, recently element-wise approximations have also received significant attention in the literature. In this paper, we propose an accelerated alternating minimization algorithm for solving the problem of low-rank approximation of matrices in the Chebyshev norm. Through the numerical evaluation we demonstrate the effectiveness of the proposed procedure for large-scale problems. We also theoretically investigate the alternating minimization method and introduce the notion of a $2$-way alternance of rank $r$. We show that the presence of a $2$-way alternance of rank $r$ is the necessary condition of the optimal low-rank approximation in the Chebyshev norm and that all limit points of the alternating minimization method satisfy this condition.

Quantum synchronizable codes are quantum error correcting codes that can correct not only Pauli errors but also errors in block synchronization. The code can be constructed from two classical cyclic codes $\mathcal{C}$, $\mathcal{D}$ satisfying $\mathcal{C}^{\perp} \subset \mathcal{C} \subset \mathcal{D}$ through the Calderbank-Shor-Steane (CSS) code construction. In this work, we establish connections between quantum synchronizable codes, subsystem codes, and hybrid codes constructed from the same pair of classical cyclic codes. We also propose a method to construct a synchronizable hybrid subsystem code which can correct both Pauli and synchronization errors, is resilient to gauge errors by virtue of the subsystem structure, and can transmit both classical and quantum information, all at the same time. The trade-offs between the number of synchronization errors that the code can correct, the number of gauge qubits, and the number of logical classical bits of the code are also established. In addition, we propose general methods to construct hybrid and hybrid subsystem codes of CSS type from classical codes, which cover relevant codes from our main construction.

The test-negative design has become popular for evaluating the effectiveness of post-licensure vaccines using observational data. In addition to its logistical convenience on data collection, the design is also believed to control for the differential health-care-seeking behavior between vaccinated and unvaccinated individuals, an important while often unmeasured confounder between the vaccination and infection. Hence, the design has been employed routinely to monitor seasonal flu vaccines and more recently to measure the COVID-19 vaccine effectiveness. Despite its popularity, the design has been questioned, in particular about its ability to fully control for the unmeasured confounding. In this paper, we explore deviations from a perfect test-negative design, and propose various sensitivity analysis methods for estimating the effect of vaccination measured by the causal odds ratio on the subpopulation of individuals with good health-care-seeking behavior. We start with point identification of the causal odds ratio under a test-negative design, comparing different forms of identification assumptions and their corresponding estimands. We then propose two approaches for conducting sensitivity analysis, addressing the influence of the unmeasured confounding in two different ways. Specifically, one approach investigates partial control for unmeasured confounding in the test-negative design, while the other examines the impact of unmeasured confounding on both vaccination and infection. Furthermore, we combine these approaches to provide narrower bounds on the true causal odds ratio, and further sharpen the bounds by restricting the treatment effect heterogeneity. Finally, we apply the proposed methods to evaluate the effectiveness of COVID-19 vaccines using observational data from test-negative designs.

The paper explores scaling properties of bubbles -- a complex analogue of Arnold tongues, associated to a one-dimensional family of analytic circle diffeomorphisms. Bubbles are smooth loops in the upper half-plane attached at all rational points of the real line. Results of a paper by X.~Buff and N.~Goncharuk (2015) show that the size of a $p/q$-bubble has order at most $q^{-2}$. In the current paper we improve this estimate by showing that the size of a $p/q$-bubble near a bounded-type irrational number $α$ has order $d^{ξ(α)} \cdot q^{-2}$, where $ξ(α)>0$, and $d$ is the distance between $α$ and $p/q$. Proofs are based on a renormalization technique. In particular, $ξ(α)$ is related to the unstable and the top stable eigenvalues of the renormalization operator at the rotation by $α$.

We study the coherent photoproduction of light vector mesons in Pb-Pb collisions in the framework of color dipole approach. We employ the Glauber--Gribov formalism supplemented by an effective suppression factor $R_G$ accounting for the gluon shadowing correction. We adjust the latter to reproduce the deep inelastic structure function $F_2$ (E665) and $ρ$ meson photoproduction (ALICE) data. We achieve a good description of the available data points with $R_G = 0.85$ at scale $M_ρ^2/4 = 0.15$ GeV$^2$. In addition, employing this suppression factor, we present predictions for coherent $ρ(2S)$, $ω(1S,2S)$ and $ϕ(1S,2S)$ photoproduction observables using the holographic vector meson wave functions.

In this paper, we propose a novel approach that employs kinetic equations to describe the collective dynamics emerging from graph-mediated pairwise interactions in multi-agent systems. We formally show that for large graphs and specific classes of interactions a statistical description of the graph topology, given in terms of the degree distribution embedded in a Boltzmann-type kinetic equation, is sufficient to capture the collective trends of networked interacting systems. This proves the validity of a commonly accepted heuristic assumption in statistically structured graph models, namely that the so-called connectivity of the agents is the only relevant parameter to be retained in a statistical description of the graph topology. Then we validate our results by testing them numerically against real social network data.

We show that the Ramsey theory of block sequences in infinite-dimensional discrete vector spaces can be parametrized by perfect sets. As special cases, we prove combinatorial dichotomies for definable families of partitions and linear transformations on those spaces. We also consider the extent to which analogues of selective ultrafilters in this setting are preserved by Sacks forcing.

We apply the Worldvolume Hybrid Monte Carlo (WV-HMC) method [arXiv:2012.08468] to the two-dimensional Hubbard model, which is known to suffer from a severe sign problem when the system is doped (away from half filling). We show that the method predicts physical observables with controlled statistical errors on an $8 \times 8$ lattice at temperature $T/t = 1/6.4 \approx 0.156$ and interaction strength $U/t = 8.0$ ($t$ is the hopping amplitude), for which the standard determinant quantum Monte Carlo fails.

In a Scanning Tunneling Microscope (STM), when a tunneling electron treated as a point charge enters the barrier region between the tip and the sample, it induces image charges on the conducting surfaces, which modifies the shape of the potential barrier it sees. In this paper, the effect of the modification in the barrier potential due to these induced charges on the tunneling current density and currents in an STM,is studied as a function of the tip-sample distance $d$ and the Bias Potential $eV_b$. The image potential is found to reduce the height and the effective width of the potential barrier, leading to a huge increase in the tunneling current densities. This huge increase (by several order of magnitudes) is however unreasonable, prompting a revisit of the assumption that the electron in the barrier region is a point particle.

In the late 1990's, Bremner conjectured that long arithmetic progressions among the $x$-coordinates of rational points of an elliptic curve $E$ over $\mathbb{Q}$ should force the rank of $E$ to be large. This conjecture (and a broad generalization of it) was proved by the authors two decades later, by combining Nevanlinna theory and the Uniform Mordell--Lang theorem of Gao--Ge--Kühne. The proof inspired subsequent work by the authors where a generalization of the Bogomolov--Fu--Tschinkel conjecture was proved by similar means. In this note we isolate a flexible pattern principle implicit in the latter work, obtaining rank-dependent (but otherwise uniform) bounds for more general patterns in the image of finite rank subgroups of elliptic curves under maps to the projective line. These patterns include, for instance, arithmetic progressions, geometric progressions, additive shifts, multiplicative shifts, and Möbius orbits.

Physical Unclonable Functions (PUFs) are hardware security primitives whose inherent physical complexity can be exploited for secure authentication and cryptographic key generation. Silicon photonic devices, owing to their suitability for quantum and artificial intelligence applications alongside standard CMOS fabrication processes, constitute a highly promising substrate for integrated multifunctional PUFs. Despite the advanced security guarantees offered by quantum cryptographic protocols and the central role of silicon photonics in quantum technologies, quantum readout strategies based on single-photon states for photonic PUFs remain largely unexplored. In this work, we experimentally demonstrate a silicon nitride (SiN) programmable photonic Mach Zehnder interferometer mesh that implements a unitary transformation and operates as a PUF, whose secret physical signature arises from uncontrollable waveguide variations during fabrication. Using experimentally derived parameters from the SiN integrated mesh, we further introduce and numerically evaluate a quantum readout protocol that combines single-photon states with PUFs. Maximally mixed quantum states are employed to conceal the underlying unitary transformation from passive eavesdropping. Security against adversaries possessing devices fabricated under similar conditions is assessed, with authentication performance quantified through Monte Carlo analysis of the false acceptance and false rejection rates as a function of the number of detected events and corrected errors. The results indicate exceptional performance with equal error rates as low as 10 to the minus 14, highlighting the potential of quantum secure PUFs for high security authentication applications.

When considering how self-interaction affects an object's motion, it can be convenient to decompose the self-force into conservative and dissipative pieces. As a toy model for understanding such decompositions of the gravitational self-force, we consider objects that do not affect the spacetime, but are instead coupled to a nonlinear scalar field. There is then a standard splitting of the first-order scalar self-force into conservative and dissipative components. Multiple criteria can be used to obtain this splitting, all of which imply the same result. However, the implications of these criteria generically differ at higher orders. Demanding that any reasonable conservative sector be Hamiltonian, we identify multiple possible definitions of the conservative second-order self-force. Motivations for these possibilities and their properties are discussed and relevant Hamiltonians are obtained. We assume the existence of a three-point function with certain properties that is a generalization of the Detweiler-Whiting two-point function. These results apply to the two-body problem but are restricted to unbound scattering trajectories, due to infrared divergences that arise for bound orbits.

Plant sap-feeding insects must dispose of excess fluid, yet at millimeter scales droplet release is constrained by capillary adhesion and contact-line pinning. How phloem-feeding insects solve this puzzle, particularly as the excretory apparatus changes in size and form from nymph to adult, has remained unclear. Combining micro-CT, high-speed imaging, measurements of honeydew properties, and reduced-order modeling, we show that the spotted lanternfly (Lycorma delicatula) uses distinct release mechanics across ontogeny. Nymphs release honeydew with an anal stylus that acts as a capillary rectifier, imposing a curvature asymmetry that biases the attached droplet toward detachment through a Laplace-pressure difference. Adults use a longer stylus associated with an elastic basal region, maintain stylus-droplet contact through a finite compression phase, and release droplets with greater translational and rotational momentum. In both stages, stylus rotation is ultrafast, with peak angular accelerations of order $10^7$ rad/s$^{-2}$ and release unfolding on millisecond timescales, yet droplet ejection speed remains below stylus tip speed. Weber-Bond scaling based on measured honeydew properties places both stages at $We_d<1$ and $Bo_d<1$ at the outlet, but distinguishes their post-release states: nymphal droplets remain surface-tension dominated, whereas adult droplets enter deformation- and spin-influenced regimes. Development therefore maintains waste clearance across ontogeny under the same outlet-scale capillary constraint by changing how stylus motion is coupled to the droplet at release, linking life-stage biomechanics to honeydew placement in this invasive phloem feeder and suggesting bioinspired strategies for droplet ejection, antifouling, and self-cleaning surfaces.

It has been known that gravitational waves (GWs) transfer energy to viscous matter through which they propagate, but the effect is too weak to be astrophysically significant. Using linearized perturbations about a Minkowski background, we previously showed that the interaction can become important when the distance between matter and source is smaller than the GW wavelength. Here, we review extensions to more realistic backgrounds, namely Schwarzschild spacetime and a static spherically symmetric setting. We find that GW damping and the associated heating of the viscous fluid are enhanced, and can lead to substantial attenuation or even gamma-ray bursts. We investigate astrophysical scenarios where these effects may be relevant, including core-collapse supernovae, binary neutron star mergers, and accretion onto binary black hole mergers.

Let $w$ be a finite word of length $n$. In this paper, we study the maximum possible number of distinct rational power factors in a finite word. A rational power is a word of the form $u=p^kp'$, where $p$ is a nonempty finite word, $k$ is an integer larger than $1$, $p^k$ is a concatenation of $k$ copies of $p$ and $p'$ is a prefix of $p$. The rational powers can be recognized as a generalization of $k$-powers, and it is proved in [Li,Pachocki,Radoszewski 24] that, the number $C_k(w)$ of distinct $k$-powers in $w$ satisfies $C_k(w) \leq \frac{n-1}{k-1}$. However, the number of rational powers has not been studied in the literature. In this article, we prove that the number $\mathrm{RP}(w)$ of distinct rational power factors of $w$ satisfies $\mathrm{RP}(w)\le\frac18n^2+O(n)$. We also illustrate a novel approach to study pattern-counting problems: using a graph-theoretic representation of words and a few word equations, we transform the traditional pattern-counting problems into a constrained extremal problem.

Randomized controlled trials often enroll participants whose characteristics differ from those of a target population, which can limit the generalizability of the estimated treatment effects when effect modifiers differ across populations. While existing generalizability methods primarily focus on estimating the average treatment effect (ATE) in the target population, such summaries may obscure important heterogeneity that is relevant for clinical and policy decision-making. In this work, we illustrate an approach for estimating the conditional average treatment effect (CATE) in a target population of trial-eligible individuals as a function of prespecified effect modifiers within a nested trial setting. Our approach combines semiparametric theory with flexible estimation: we first estimate nuisance functions using data-adaptive methods and construct pseudo-outcomes from conditional influence functions, then estimate the CATE function via local linear (kernel) regression. Sample splitting and cross-fitting are used to reduce overfitting bias and ensure asymptotic valid inference. Finite-sample performance is assessed via simulations and illustrated in the Coronary Artery Surgery Study (CASS).

Proton Exchange Membrane Fuel Cell (PEMFC) is widely recognized for its cleanliness and high efficiency, but is still facing challenges in cold environments. At low temperatures, the formation of ice and repeated freezing/thawing cycles may cause cell performance reduction and irreversible degradation. The cathode flow field of PEMFCs has a significant effect on the performance. In contrast to the conventional ``channel-ridge'' flow field, the metal foam has the advantages of excellent pre-distribution of gases and water drainage, which make it a promising candidate for the cold start. This paper examines the cold start of PEMFCs with metal foam flow field (MFFF) and serpentine flow field (SFF), and the influence of constant current mode, constant voltage mode, and ramping current mode is investigated experimentally through performance test and electrochemical characterization. The results show that lowering the voltage and increasing the current can enhance the cold-start performance of fuel cells. The MFFF fuel cell has superior cold start performance compared to the SFF fuel cell under the constant voltage mode of 0.3 V. Furthermore, the variable current mode is developed by considering the distinct properties of heat and water production during various phases, and the results indicate that increasing the current density at the unsaturated stage leads to an elevated rate of heat production and a reduced rate of water production, which can improve the cold start of PEMFCs.

Inspired by the latest BESIII measurement of the $Λ(1520)\toγΣ^0$ radiative decay, we systematically study the decays $Λ(1520)\toγΛ(Σ^0)$ within the chiral unitary approach, where the $Λ(1520)$ is treated as a dynamically generated resonance from meson-baryon interactions. Compared with previous chiral unitary studies, we adopt dimensional regularization for $S$-wave loop integrals to preserve gauge invariance and, for the first time, include Feynman diagrams with photon coupling to intermediate baryons. Our calculated partial decay width $Γ(Λ(1520)\toγΣ^0)$ agrees well with the new BESIII data, whereas the predicted $Γ(Λ(1520)\toγΛ)$ is considerably smaller than the CLAS experimental result. By comparing our results with predictions from various quark models, we discuss the internal nature of the $Λ(1520)$ resonance, highlight its complex component structure, and stress the need for more refined theoretical frameworks and further experimental measurements.

The study addresses the problem of quadcopter motion control using output feedback. By applying a geometric approach, the quadcopter model is transformed into a normal form with a time-varying gain coefficient, which is subsequently made stationary through double integration of the control input. A robust output feedback control law is synthesised based on the extended observer method.

The use of mobile robotics in radioactive source seeking has become an important part of modern radiation-safety practices, supporting timely mitigation of contamination risks and helping protect public health. However, measuring radiation is often time-consuming, rendering traditional gradient-based source-seeking methods less effective due to lower sample efficiency. This paper proposes a sample-efficient Bayesian-Optimisation source-seeking strategy that utilises a heteroscedastic Gaussian process surrogate to balance exploration and exploitation. Excessive inter-sample travel is discouraged through a movement switching cost. The strategy is shown to generate sublinear regret in the source-seeking task, while simulations demonstrate its effectiveness in localising radioactive sources.

Projected priors were originally introduced to accommodate parameter constraints, but have recently regained popularity due to their ability to assign probability mass to low-dimensional parameter sets, such as the spaces of sparse vectors, directed acyclic graphs, or transport plans. When employed as a transformation of random variables, projection is especially useful, since its contraction property not only preserves probability concentration, but also often preserves differentiability for gradient-based posterior computation. On the other hand, unless the projection can be obtained by some non-iterative algorithm, posterior computation can be expensive because it requires nesting an iterative optimization routine within each Markov chain Monte Carlo iteration. In this article, inspired by the success of continuous shrinkage models as replacements for discrete spike-and-slab priors, we propose a continuous relaxation of projected priors. The key idea is to quantify the duality gap between the primal projection loss and the dual objective, and impose a probabilistic prior that shrinks this gap toward zero. The resulting gap-shrinkage prior has a tractable form, does not require running an optimization subroutine inside each posterior update, and puts probability mass near the exact projection. We demonstrate useful properties of gap-shrinkage priors, including connections to global-local shrinkage priors, broad applicability to generalized projection functions, and competitive performance in posterior contraction. We apply the gap-shrinkage model to a marketing data analysis aimed at identifying important predictor effects on multivariate grocery-shopping decisions.

Resonant cooling of the nuclear spin system of a semiconductor by spin-polarized charge carriers under pumping with helicity-modulated polarized light is considered theoretically. It is shown that in the case of strong Knight field of charge carriers, exceeding local fields of the dipole-dipole interaction of nuclear spins, the Overhauser field arising as a result of resonant cooling can considerably modify the overall shape of magnetic-field dependences of charge carrier spin polarization, experimentally observed as the Hanle effect.