Liquidity providers (LPs) are essential figures in the operation of automated market makers (AMMs); in exchange for transaction fees, LPs lend the liquidity that allows AMMs to operate. While many prior works have studied the incentive structures of LPs in general, we currently lack a principled understanding of a special class of LPs known as Just-In-Time (JIT) LPs. These are strategic agents who momentarily supply liquidity for a single swap, in an attempt to extract disproportionately high fees relative to the remaining passive LPs. This paper provides the first formal, transaction-level model of JIT liquidity provision for a widespread class of AMMs known as Concentrated Liquidity Market Makers (CLMMs), as seen in Uniswap V3, for instance. We characterize the landscape of price impact and fee allocation in these systems, formulate and analyze a non-linear optimization problem faced by JIT LPs, and prove the existence of an optimal strategy. By fitting our optimal solution for JIT LPs to real-world CLMMs, we observe that in liquidity pools (particularly those with risky assets), there is a significant gap between observed and optimal JIT behavior. Existing JIT LPs often fail to account for price impact; doing so, we estimate they could increase earnings by up to 69% on average over small time windows. We also show that JIT liquidity, when deployed strategically, can improve market efficiency by reducing slippage for traders, albeit at the cost of eroding average passive LP profits by up to 44% per trade.

We consider matrix quantum mechanics with multiple bosonic matrices, including those obtained from dimensional reduction of Yang-Mills theories. Using the matrix bootstrap, we study simple observables like $\langle \mathop{tr} X^2 \rangle$ in the confining phase of the theory in the infinite $N$ limit. Exploiting the symmetries of these models and applying nonlinear relaxation, we impose constraints that include traces of words of length up to 14. Our results yield rigorous bounds on the large-$N$ ground-state dynamics, along with estimates of selected low-order observables to eight significant digits.

Regular black holes and horizonless black hole mimickers offer mathematically consistent alternatives to address the challenges posed by standard black holes. However, the formation mechanism of these alternative objects is still largely unclear and constitutes a significant open problem since understanding their dynamical formation represents a first step to assess their existence. We here investigate, for the first time and without invoking higher-curvature corrections, the dynamical formation of a well-known horizonless black hole mimicker, namely, a gravastar. More specifically, starting from the collapse of a uniform dust sphere as in the case of the Oppenheimer-Snyder collapse, we demonstrate that, under fine-tuned conditions, a gravastar can form from the nucleation and expansion of a de Sitter region with initial zero size at the center of the collapsing sphere. Furthermore, the de Sitter expansion naturally slows down near the Schwarzschild radius, where it meets the collapsing dust surface and gives rise to a static equilibrium. Interestingly, we also find a maximum initial compactness of the collapsing star of $\mathcal{C}= 3/8$, above which the collapse to a black hole is inevitable.

We investigate the boundary separating regular and chaotic dynamics in the generalized Chirikov map, an extension of the standard map with a control parameter $K$ and a phase-shifted (phase $τ$) secondary sequence of kicks with a control parameter $K_α$. Lyapunov maps were computed across the parameter space $(K, K_α; τ)$ and used to train a convolutional neural network (ResNet18) for binary classification of dynamical regimes. The trained model reproduces the known critical control parameter $K_c$ for the onset of global chaos in the standard map and identifies two-dimensional boundaries $(K, K_α)$ in the generalized map for varying phase shifts $τ$. The results reveal systematic deformation of the boundary as $τ$ increases, highlighting the sensitivity of the system to phase modulation and demonstrating the ability of machine learning to extract interpretable features of complex Hamiltonian dynamics. This framework allows precise characterization of stability boundaries in nontrivial nonlinear systems.

In this paper, we compute the inflationary trispectrum of primordial gauge fields generated through the scalar and tensor exchanges in models with spectator $U(1)$ gauge fields which are kinetically coupled to the inflaton. Focusing on the connected four-point autocorrelation function of gauge fields, we derive exact analytical expressions for the full trispectrum of both electric and magnetic fields using the in-in formalism and cosmological diagrammatic rules, and explore their respective contributions in specific momentum configurations. For the scalar exchange, we find that the trispectrum signal in the equisided configuration grows with the exchange momentum and reaches its maximum in the flattened limit. However, in the counter collinear limit, we show that the non-linearity parameter associated with the trispectrum scales quadratically with the corresponding parameter of the cross-correlation bispectrum of magnetic fields and curvature perturbations, thereby establishing a hierarchical relation between the higher- and lower-order correlation functions. For the tensor exchange, the trispectrum displays a richer angular dependence, reflecting the sensitivity to the orientation of the momentum quadrilateral with respect to the tensor polarisation, producing characteristic angular modulations in the trispectrum. Detecting such angular signatures in future high-precision cosmological observations would provide a novel window into tensor-mediated interactions in the early universe.

Networked Control Systems (NCSs) have been instrumental in realizing fully connected and responsive intelligent environments within the context of real-time virtual control and management. However, traditional NCSs face considerable challenges in handling the vast amounts of data generated by large-scale control applications, particularly in terms of data acquisition, storage, and computational processing. To address these challenges, the emergence of cloud computing and advancements in control theory have empowered the new paradigm known as Cloud Control Systems (CCSs). Recently, CCSs have received substantial attention from industries for their potential properties, such as large-scale data management, complex computations, and data-centric optimized decisions. This study presents an extensive review of recent progress in CCSs spanning over multiple studies published between 2012 and 2025. Specifically, the focus is on providing a taxonomy of the current findings in CCS research, encompassing various perspectives, such as its efficient implementations in industrial automation, security and privacy considerations, and cloud-based control techniques. Each category is examined in depth through selected state-of-the-art analyses of different approaches and contrasting methodologies. Furthermore, we discuss future directions aimed at designing more efficient and practical CCSs. The insights gained from this study can help researchers, practitioners, and decision-makers in their domain for effective CCS design and deployment.

The spin Seebeck effect (SSE) enables thermoelectric conversion through thermally generated spin currents in magnetic materials, offering a promising transverse geometry for scalable devices. However, conventional SSE devices are confined to nanoscale thin-film architectures, with significantly restricted output power due to the intrinsic constraints of spin and magnon diffusion lengths. Here, we demonstrate a trans-scale SSE using nano-structured bulk composites composed of Pt-coated yttrium iron garnet powders fabricated via dynamic powder sputtering and low-temperature sintering. The resulting three-dimensional composites exhibit continuous Pt channels and robust mechanical integrity. Transverse thermoelectric measurements confirm isotropic SSE signals at the bulk scale. Power analysis indicates that the three-dimensional architecture enables scalable volumetric thermoelectric power generation beyond diffusion-limited thin-film SSE geometries. This work establishes a scalable platform for bulk SSE-based thermoelectrics, bridging nanoscale spin caloritronics with macroscopic device integration.

We investigate the mean value of the first moment of primitive quartic $L$-functions over $\mathbb{F}_q(T)$ in the non-Kummer setting. Specifically, we study the sum \begin{equation*} \sum_{\substack{χ primitive\ quartic\\ χ^2 primitive\\ genus(χ)=g}}L_q(\frac{1}{2}, χ), \end{equation*} where $L_q(s,χ)$ denotes the $L$-function associated with primitive quartic character $χ$. Using double Dirichlet series, we derive an error term of size $q^{(\frac{3}{5}+\varepsilon)g}$.

In this article, we study a degenerate version of Ramsey's theorem for pairs and two colors ($\mathsf{RT}^2_2$), in which the homogeneous sets for color 1 are of bounded size. By $\mathsf{RT}^2_2$, it follows that every such coloring admits an infinite homogeneous set for color 0. This statement, called $\mathsf{BRT}^2_2$, is known to be computably true, that is, every computable instance admits a computable solution, but the known proofs use $Σ^0_2$-induction ($\mathsf{I}Σ_2^0$). We prove that $\mathsf{BRT}^2_2$ follows from the Erdős-Moser theorem but not from the Ascending Descending sequence principle, and that its computably true version is equivalent to $\mathsf{I}Σ_2^0$ over $\mathsf{RCA}_0$.

We study symplectic groups and indefinite orthogonal groups over involutive, possibly noncommutative, algebras $(A, σ)$. In the case when the algebra $(A, σ)$ is Hermitian, or the complexification $(A_{\mathbb C}, σ_{\mathbb C})$ of a Hermitian involutive algebra, one can identify maximal compact subgroups of such groups, and consider their associated Riemannian symmetric spaces. This new perspective allows for the realization of various geometric models for the symmetric space. We describe explicitly the complexified tangent space for each of the models, as well as the diffeomorphisms between them and their differentials. In the second part of the article, we give a number of applications of this theory. The geometric realizations of the Riemannian symmetric spaces described in the first part provide new geometric interpretations of Higgs bundle data that can be used for the study of fundamental group representations into symplectic or into indefinite orthogonal groups over Hermitian involutive algebras. We give an exact component count for the moduli spaces of $\rm{Sp}_2(A_{\mathbb C}, σ_{\mathbb C})$-Higgs bundles and of $\rm O(A_{\mathbb C}, σ_{\mathbb C})$-Higgs bundles, using the topology of the corresponding maximal compact subgroups rather than Morse-Bott theory techniques. Furthermore, we use the noncommutative symmetric-space models to construct a factorization of the Hitchin morphism for $\rm{Sp}_2(A_{\mathbb C},σ_{\mathbb C})$-Higgs bundles, together with analogous factorizations for the real groups $\rm{Sp}_2(A,σ)$ and $\rm O_{(1,1)}(A,σ)$. These factorizations are induced by quadratic norm maps from the corresponding tangent models to Jordan-algebraic targets and pass through intermediate affine GIT quotients. As a consequence, they reduce the algebraic complexity required in order to characterize the Hitchin base explicitly.

We introduce triple quadratic residue symbols $[\mathfrak{p}_1, \mathfrak{p}_2, \mathfrak{p}_3]$ for certain finite primes $\mathfrak{p}_i$'s of a real quadratic field $k$ with trivial narrow class group. For this, we determine a presentation of the Galois group of the maximal pro-2 Galois extension over $k$ unramified outside $\mathfrak{p}_1, \mathfrak{p}_2, \mathfrak{p}_3$ and infinite primes, from which we derive mod 2 arithmetic triple Milnor invariants $μ_2(123)$ yielding the triple symbol $[\mathfrak{p}_1, \mathfrak{p}_2, \mathfrak{p}_3] = (-1)^{μ_2(123)}$. Our symbols $[\mathfrak{p}_1, \mathfrak{p}_2, \mathfrak{p}_3]$ describes the decomposition law of $\mathfrak{p}_3$ in a certain dihedral extension $K$ over $k$ of degree 8, determined by $\mathfrak{p}_1, \mathfrak{p}_2$. The field $K$ and our symbols $[\mathfrak{p}_1, \mathfrak{p}_2, \mathfrak{p}_3]$ are generalizations over real quadratic fields of Rédei's dihedral extension of $\mathbb{Q}$ and Rédei's triple symbol of rational primes. We give examples of Rédei type extensions $K$ over real quadratic fields. We also give a cohomological interpretation of our symbols in terms of Massey products.

We prove a differential transcendence result of type "Ax-Lindemann-Weierstrass" for Euler's gamma function. Given meromorphic functions $ζ_1,\dots,ζ_n$ of a complex variable $ν$ that are pairwise distinct modulo $\mathbb Z$ and algebraic over the field $k$ of meromorphic $1$-periodic functions, the functions $ Γ(ν-ζ_1(ν)),\dots,Γ(ν-ζ_n(ν))$ are differentially independent over the field $k(ν)$. We determine the structure of certain difference field extensions related to the torsion of an avatar of the Carlitz module over meromorphic functions. These extensions are abelian and purely transcendental, the latter property being crucial in our main result, and obtained applying a criterion of differential algebraicity of Hardouin and Singer.

This paper investigates a low Earth orbit (LEO) satellite communication system enhanced by an active stacked intelligent metasurface (ASIM), mounted on the backplate of the satellite solar panels to efficiently utilize limited onboard space and reduce the main satellite power amplifier requirements. The system serves multiple ground users via rate-splitting multiple access (RSMA) and IoT devices through a symbiotic radio network. Multi-layer sequential processing in the ASIM improves effective channel gains and suppresses inter-user interference, outperforming active RIS and beyond-diagonal RIS designs. Three optimization approaches are evaluated: block coordinate descent with successive convex approximation (BCD-SCA), model-assisted multi-agent constraint soft actor-critic (MA-CSAC), and multi-constraint proximal policy optimization (MCPPO). Simulation results show that BCD-SCA converges fast and stably in convex scenarios without learning, MCPPO achieves rapid initial convergence with moderate stability, and MA-CSAC attains the highest long-term spectral and energy efficiency in large-scale networks. Energy-spectral efficiency trade-offs are analyzed for different ASIM elements, satellite antennas, and transmit power. Overall, the study demonstrates that integrating multi-layer ASIM with suitable optimization algorithms offers a scalable, energy-efficient, and high-performance solution for next-generation LEO satellite communications.

Ordinal outcomes are common in clinical settings where they often represent increasing levels of disease progression or different levels of functional impairment. In this article, we focus on representing the average treatment effect for ordinal outcomes via intrinsic pairwise outcome comparisons captured through win estimands, such as the win ratio and win difference. Recognizing the value of baseline covariate adjustment toward enhanced precision, we first develop propensity score weighting estimators, including both inverse probability weighting (IPW) and overlap weighting (OW), tailored to estimating win estimands. Furthermore, we develop augmented weighting estimators that leverage an additional ordinal outcome regression to potentially improve efficiency over weighting alone. Leveraging the theory of U-statistics, we establish the asymptotic theory for all estimators, and derive closed-form variance estimators to support statistical inference. We also prove that all of the covariate-adjusted estimators do not compromise consistency for the target estimand even when the associated working models are incorrectly specified; hence these covariate-adjusted estimators are model-robust. Through simulations we demonstrate the enhanced efficiency of the weighted estimators over the unadjusted estimator, with the augmented weighting estimators showing a further improvement in efficiency except for extreme cases. Finally, we illustrate our proposed methods with the ORCHID trial, and implement our covariate adjustment methods in an R package winPSW.

We study the quantum critical point between the fermionic $ν=8$ quantum Hall state and the bosonic $ν=2$ quantum Hall state of Cooper pairs. Our study is motivated by the composite fermion construction for the daughter states of even-denominator fractional quantum Hall states and the experimentally observed transition between the daughter and the Jain states at the same filling. We show that this transition is equivalent to the transition between a neutral invertible $E_8$ state and a topologically trivial state. These transitions can be described in a partonic framework as a cascade of mass changes of four neutral Dirac fermions coupled to multiple Abelian Chern--Simons $U(1)$ gauge fields. In the absence of fine-tuning, the transition is split into a series of at least eight distinct transitions, with at least seven distinct intermediate topologically ordered phases that host neutral anyons.

High-resolution estimates of population health indicators are critical for precision public health. We propose a method for high-resolution estimation that fuses distinct data sources: an unbiased, low-resolution data source (e.g. aggregated administrative data) and a potentially biased, high-resolution data source (e.g. individual-level online survey responses). We assume that the potentially biased, high-resolution data source is generated from the population under a model of sampling bias where observables can have arbitrary impact on the probability of response but the difference in the log probabilities of response between units with the same observables is linear in the difference between sufficient statistics of their observables and outcomes. Our data fusion method learns a distribution that is closest (in the sense of KL divergence) to the online survey distribution and consistent with the aggregated administrative data and our model of sampling bias. This approach significantly reduces bias in high-resolution estimates compared to baselines that rely on a single data source alone on a testbed that includes repeated measurements of three indicators measured by both the (online) Household Pulse Survey and ground-truth data sources at two geographic resolutions over the same time period.

Through the study of the Rep($D_8$) non-invertible symmetry, we show how non-invertible symmetries manifest in dynamics. Results are presented for dynamics generated by Hamiltonians as well as Floquet unitaries. For both examples, the role of the non-invertible symmetry is studied through the appearance of non-invertible symmetry protected edge modes. In addition, the role of the non-invertible symmetry for the Hamiltonian is studied through eigenstate order. In particular, by considering the effect of symmetry preserving disorder, the non-invertible symmetry is shown to give rise to degeneracies in the spectra of the Hamiltonian that can only be completely lifted at orders of perturbation that scale with system size. The eigenstates of disordered Hamiltonians, whose ground state correspond to non-trivial symmetry protected topological (SPT) states, are shown to have either trivial or non-trivial SPT order that are detected as non-zero expectation value of string order-parameters. In contrast, non-trivial SPT order is absent in the eigenstates of trivial SPT Hamiltonians with disorder. The interface between two different SPT phases host edge modes whose dynamics is studied numerically and analytically. The edge mode is shown to oscillate at frequencies related to different effective chain lengths that are weighted by the temperature, becoming an exact zero mode in the limit of zero temperature. A Floquet model with the non-invertible symmetry is constructed whose edge mode is shown to exhibit period-doubled dynamics at low effective-temperatures. The zero and period-doubled edge modes differ from those in conventional SPTs by being symmetric under the invertible symmetry, while being charged under the non-invertible symmetry.

Quantum entanglement lies at the heart of quantum information science, yet its reliable detection in high-dimensional or noisy systems remains a fundamental computational challenge. Semidefinite programming (SDP) hierarchies, such as the Doherty-Parrilo-Spedalieri (DPS) and Extension (EXT) hierarchies, offer complete methods for entanglement detection, but it is well known that their practical use is limited by exponential growth in problem size if implemented naively. We make three contributions. First, we introduce a new SDP hierarchy, PST, that is sandwiched between EXT and DP -- offering a tighter approximation to the set of separable states than EXT, while incurring significantly lower computational overhead than DPS. Second, we explicitly construct compact, polynomially-scalable descriptions of EXT and PST using partition mappings and operators. These descriptions in turn yield formulations that satisfy desirable properties such as the Slater condition and are well-suited to both first-order methods (FOMs) and interior-point methods (IPMs). Third, we design a suite of entanglement detection algorithms: three FOMs (Frank-Wolfe, projected gradient, and fast projected gradient) based on a least-squares formulation, and a custom primal-dual IPM based on a conic programming formulation. These methods are numerically stable and capable of producing entanglement witnesses or proximity measures, even in cases where states lie near the boundary of separability. Numerical experiments on benchmark quantum states demonstrate that our algorithms improve the ability to solve deeper levels of the SDP hierarchy.

We establish a connection between the stochastic self-propagating star-formation model and spatio-temporal point processes by showing that, under suitable discretisation, the SSPSF update law can be represented by a separable spatio-temporal Hawkes process. Building on this connection, we propose a spatio-temporal log-Gaussian Cox-Hawkes process as a continuous point-process model for stochastic star formation. The model represents star-formation events as point patterns driven jointly by deterministic galactic structure, latent spatio-temporal background variation, and dependence on past events. Its key feature is that the deterministic mean field, latent Gaussian random field, and history-dependent interaction field enter through a single log-intensity. This log-scale construction differs from additive Cox-Hawkes formulations and allows the history effect to be signed: past events may either increase or decrease future local intensity while the conditional intensity remains positive. The resulting framework provides an interpretable point-process model for representing latent clustering, self-excitation, local inhibition, and event-driven propagation in stochastic star formation. Beyond linking SSPSF to spatio-temporal point-process theory, it offers a continuous stochastic formulation for analysing the propagation of star formation in galaxies and for interpreting observational surveys of star-forming regions within a unified statistical model.

Complete intersections may be unexpectedly simple over fields of positive characteristic: for instance, they may be unirational despite being of general type. One explanation is given by profiles, structure that tracks the special shape of polynomials, refining the degree. The aim of this work is to show that complete intersections with small profile should be considered simple by generalizing two classical results on low degree complete intersections: First, the basic geometry of Fano schemes associated with complete intersections depends only on the profile, so that complete intersections with small profile contain many linear spaces. Second, a general complete intersection is unirational once its dimension is sufficiently large compared to its profile.

The determinant of a tournament $T$, denoted by $\det(T)$, is defined as the determinant of the skew-adjacency matrix of $T$. It is well-known that $\det(T)$ is equal to $0$ if $n$ is odd, and $\det(T)$ is the square of an odd integer if $n$ is even. For a positive odd integer $k$, let $\mathcal{D}_k$ be the set of tournaments whose all subtournaments have determinant at most $k^2$. Former studies showed that for $k \in \{1,3,5\}$, a tournament $T \in \mathcal{D}_k \backslash \mathcal{D}_{k-2}$ ($T \in \mathcal{D}_1$ when $k=1$) if and only if $T$ is switching equivalent to a transitive blowup of $L_{k+1}$, where $L_{k+1}$ is a tournament of order $k+1$ with a specific structure. For $k \geq 7$, no characterization results are known. A natural problem is to characterize tournaments in $\mathcal{D}_{k} \backslash \mathcal{D}_{k-2}$ that can be switching equivalent to a transitive blowup of $L_{k+1}$ for $k \geq 7$. To address this problem and to further explore the structural properties of tournaments in $\mathcal{D}_{k}$, we introduce CR tournaments, strong CR tournaments, basic tournaments and $Z$-matrices, and investigate their properties. We use these properties to characterize those tournaments $T \in \mathcal{D}_{k} \backslash \mathcal{D}_{k-2}$ where $T$ contains a subtournament switching isomorphic to a basic strong CR tournament in $\mathcal{D}_{k} \backslash \mathcal{D}_{k-2}$. This result implies former characterizations of $\mathcal{D}_3\backslash \mathcal{D}_1$ and $\mathcal{D}_5 \backslash \mathcal{D}_3$. Using $Z$-matrices, we also show that for even $n$, $L_{n}$ is a basic strong CR tournament, and thus solve the open problem posed in [Discrete Math. 349 (2) (2026) 114766].

With over two dozen detections in the Milky Way, double neutron stars (DNSs) provide a unique window into massive binary evolution. We use the POSYDON binary population synthesis code to model DNS populations and compare them to the observed Galactic sample. By tracing their origins to underlying single and binary star physics, we place constraints on the detailed evolutionary stages leading to DNS formation. Our study reveals a bifurcation within the well-known common envelope (CE) formation channel for DNSs, which naturally explains an observed split in the orbital periods of the Galactic systems. The two subchannels are defined by whether the donor star has a helium core (Case B mass transfer) or a carbon-oxygen core (Case C) at the onset of the CE, with only the helium core systems eventually merging due to gravitational wave-modulated orbital decay. We find that across different treatments of the CE phase, the formation of DNSs through both subchannels requires either a generous core definition of $\simeq$ 30% H-fraction or a high CE ejection efficiency of $α_{\rm CE}\gtrsim1.2$. By testing different supernova kick velocity models, we find that galactic DNSs are best reproduced using a prescription that favors low velocity kicks ($\lesssim 50 \, \rm km/s$), in agreement with previous studies. Furthermore, our models indicate that merging DNSs are born from a stripped progenitor with a median pre-supernova envelope mass $\sim$ 0.2$M_{\odot}$. Our results highlight the value of detailed evolutionary models for improving our understanding of exotic binary star formation.

The combined symmetry of charge conjugation and parity ($C\!P$) is tested in the hadronic transition $ψ(3686)\toπ^+π^{-}J/ψ$, using a dataset of $(2712.4\pm14.3)\times10^6$ $ψ(3686)$ events collected by the BESIII detector at the BEPCII collider. The resulting asymmetry observable is $A_{cp} = (0.6\pm1.8\pm0.1)\times10^{-4}$, which is determined by combining the two channels $J/ψ\to e^+e^-$ and $J/ψ\toμ^+μ^-$. Additionally, by considering the relationship between the chromoelectric dipole moment (CEDM) and the $A_{cp}$ observable derived from the quantum chromodynamics multipole expansion theory based on the Chen-Kuang model and the Cornell potential model, we obtain the results of charm quark's CEDM with $d^{\prime}_{c} = (2.6\pm7.8\pm0.4\pm0.6)\times10^{-16}$ $e$cm, and $d^{\prime}_{c} = (3.5\pm10.5\pm0.6\pm0.5)\times10^{-16}$ $e$cm, respectively. The uncertainties are statistical, systematic, and theoretical, respectively. These results correspond to an upper limit of $|d^{\prime}_{c}|<2.1\times10^{-15}$ $e$ cm at 90\% confidence level, representing an order of magnitude improvement in sensitivity compared to the previous direct bound using the same decay process.

We first obtain a simpler proof of the main results in [IEOT, {\bf 93}(2021), 17], which characterized the bounded and compact differences $C_{u,φ}-C_{v,ψ}$ of two weighted composition operators acting between different Bergman spaces. More importantly, we get some characterizations for the difference of two weighted composition operators belonging to Schatten class. Futhermore, the compact difference of two weighted composition operators acting on Hardy-Hilbert spaces is also studied.

A novel, stochastic approach to amputation, the process of introducing missing values to a complete dataset, is presented. It allows one to construct a wide variety of missingness patterns by only having to specify distributions of missingness indicators as opposed to specifying each missingness pattern manually. Missingness indicators are modeled in a principled way via copulas and Bernoulli margins, thus allowing one to incorporate dependence in missingness patterns. Besides more classical missingness mechanisms such as missing completely at random, missing at random, and missing not at random, the approach is able to model structured missingness such as block missingness and, via mixtures, monotone missingness, which are patterns of missing data frequently found in real-life datasets. Properties such as joint missingness probabilities or missingness correlation are derived mathematically. The flexibility of the approach in capturing different missingness patterns while only requiring to specify distributional assumptions on missingness indicators is demonstrated with mathematical examples and empirical illustrations in terms of a well-known example dataset of sufficiently small sample size that allows to identify each missing data point visually. Finally, an example application to multivariate financial time series is provided.

In both classical and quantum thermodynamics, physical quantities are typically assigned objective values defined independently of our observations. We then refer to the 'work performed by a gas', or the 'entropy of the gas', regardless of how they are evaluated. Here, we question this conception in the context of quantum thermodynamics, estimating how the definition of pivotal thermodynamic quantities is affected by experimental instruments of limited precision. We find that the coarse-grained thermodynamic quantities frequently lead to different conclusions from those drawn in fine-grained scenarios. For instance, the irreversibility of a process, or its work payoff, can significantly vary with the instrument precision. We show nonetheless that coarse-grained thermodynamic quantities satisfy the same relations (i.e., the second law inequality, the relation between dissipation and distinguishability of a process from its time-reverse, and the quantum work fluctuation theorems) as their fine-grained counterparts. These results highlight the observation-independence of relations linking thermodynamic quantities which are themselves observation-dependent.

The hexablock is a domain arising from a special case of the $μ$-synthesis problem. We study the commuting operator tuples having the hexablock as a spectral set. Such a tuple is called a hexablock-contraction or simply $\mathbb H$-contraction. We characterize the unitaries and isometries associated with $\mathbb H$-contractions. Two different types of dilation results for $\mathbb H$-contractions are obtained. We find connection of this theory with the operators associated with the symmetrized bidisc and tetrablock, two other domains related to the $μ$-synthesis problem.

We establish a connection between barcode entropy and metric entropy. Namely, we show that the barcode entropy bounds the metric entropy from below for a measure from a specific class of invariant measures associated with a pair of Lagrangian or Legendrian submanifolds, which we call pseudo-chord measures. This inequality refines, via the variational principle, the previously known upper bound of barcode entropy by topological entropy.

This paper considers coresets for the robust $k$-medians problem with $m$ outliers, and new constructions in various metric spaces are obtained. Specifically, for metric spaces with a bounded VC or doubling dimension $d$, the coreset size is $O(m) + \tilde{O}(kd\varepsilon^{-2})$, which is optimal up to logarithmic factors. For Euclidean spaces, the coreset size is $O(m\varepsilon^{-1}) + \tilde{O}(\min\{k^{4/3}\varepsilon^{-2}, k\varepsilon^{-3}\})$, improving upon a recent result by Jiang and Lou (ICALP 2025). These results also extend to robust $(k,z)$-clustering, yielding, for VC and doubling dimension, a coreset size of $O(m) + \tilde{O}(kd\varepsilon^{-2z})$ with the optimal linear dependence on $m$. This extended result improves upon the earlier work of Huang et al. (SODA 2025). The techniques introduce novel dataset decompositions, enabling chaining arguments to be applied jointly across multiple components.

We introduce a new multi-objective optimization approach to determine uncertainty-quantified nuclear reaction parameters in the Hauser-Feshbach framework. By simultaneously accounting for all available data across multiple reaction channels we capture parameter correlations and estimate data-driven uncertainties. We implement in the Ni-Ge region yielding uncertainty-quantified model parameters for both stable and unstable isotopes. We estimate resonance spacings for nuclei beyond experimental reach and validate our method by calculating a known cross-section outside our optimization region.