The widening gap between processor speed and storage latency has made data movement a dominant bottleneck in modern systems. Two lines of storage-layer innovation attempted to close this gap: persistent memory shortened the latency hierarchy, while computational storage devices pushed processing toward the data. Neither has displaced conventional NVMe SSDs at scale, largely due to programming complexity, ecosystem fragmentation, and thermal/power cliffs under sustained load. We argue that storage-side compute should be \emph{reversible}: computation should migrate dynamically between host and device based on runtime conditions. We present \sys, which realizes this principle on CXL SSDs by decomposing I/O-path logic into migratable \emph{storage actors} compiled to WebAssembly. Actors share state through coherent CXL.mem regions; an agility-aware scheduler migrates them via a zero-copy drain-and-switch protocol when thermal or power constraints arise. Our evaluation on an FPGA-based CXL SSD prototype and two production CSDs shows that \sys turns hard thermal cliffs into elastic trade-offs, achieving up to 2$\times$ throughput improvement and 3.75$\times$ write latency reduction without application modification.

The flow around two circular cylinders arranged in a tandem exhibits complex wake interactions that lead to amplified unsteady loads, particularly in the co-shedding regime where a fully developed wake forms in the gap between the cylinders. Although various control strategies have been proposed to mitigate these effects, most prior studies have focused primarily on load alleviation. Complete suppression of vortex shedding, both in the gap region and in the wake of the second cylinder, has so far only been achieved using open-loop approaches. In this work, we propose a closed-loop control framework for suppressing vortex shedding in tandem cylinder flows in the co-shedding regime. Focusing on low Reynolds numbers and sufficiently large spacings, we derive a parametric reduced-order model using a global weakly nonlinear analysis of the incompressible Navier-Stokes equations. The model is generalized to account for time dependent forcing and facilitates the real time prediction of the flow evolution. Using this model, we design a model predictive controller and apply it to the full-order system via velocity measurements and volumetric forcing. The approach is demonstrated for a cylinder spacing of eight diameters. Vortex shedding is fully suppressed in both the gap region and the downstream wake for Reynolds numbers $Re=50$, $60$, and $70$, while a significant reduction in flow unsteadiness is achieved at $Re=80$. We further show that effective control is possible with limited sensing: suppression is achieved using a single measurement point for $Re=50$ and two-point measurements for $Re=60$ and $70$.

The dimensionality of entanglement, quantified by the Schmidt number, is a valuable resource for a wide range of quantum information processing tasks. In this work, we introduce the notion of the absolute Schmidt number, referring to states whose Schmidt number cannot be increased by any global unitary transformation. We provide a characterization of the set of arbitrary-dimensional states whose Schmidt number is invariant under all global unitaries. Our approach enables us to develop both witness-based and moment-based techniques to detect nonabsolute Schmidt number states which could provide significant operational advantages through Schmidt number enhancement by global unitaries. We next formulate two resource-theoretic measures of nonabsolute Schmidt number states, based respectively on Schmidt number witness and robustness, and demonstrate an operational utility of the latter in a channel discrimination task. Finally, we extend our analysis to quantum channels by introducing a new class of channels that possess the absolute Schmidt number property. We derive a necessary and sufficient condition for identifying when a channel has the absolute Schmidt number property, confining our analysis to the class of covariant channels.

A few weeks after launch, the PLATO spacecraft is expected to start its payload commissioning, which will be completed within the first three months of the mission. This phase includes the in-orbit verification, calibration, and configuration of the instrument prior to nominal science operations. During this mission-critical period, and again later during regular spacecraft rotations and re-pointings, a set of reference stars is required to complete various calibration steps. This set, referred to as the calibration PLATO Input Catalog (cPIC), is part of the PIC. The cPIC comprises various stellar samples, each serving a dedicated technical calibration purpose, and it contains 71671 unique stellar targets across PLATO's entire field of view (FoV). Once the spacecraft commences science observations, the on-board Fine Guidance System (FGS) will rely on a small set of guide stars. These stars must be particularly bright and will be observed with the two fast cameras, which cover only a smaller central region of PLATO's FoV. This target list, referred to as the fine-guidance PLATO Input Catalog (fgPIC), contains 2640 unique targets, of which about 30 are used by the FGS at any given time. In this paper, we present the selection criteria for both the cPIC and the fgPIC, and asses their impact on the construction of these calibration catalogs for PLATO.

The correlation discrete variable representation (CDVR) enables efficient quantum dynamics calculation with the multi-layer multi-configurational time-dependent Hartree (MCTDH) approach on general potential energy surfaces. It employs a time-dependent quadrature to compute potential energy matrix elements, thereby eliminating the need to refit the potential to a sum of products form. The non-hierarchical CDVR conserves the inherent symmetry properties of tree-shaped wavefunction representations and drastically reduces the number of grid points compared to the original hierarchical CDVR. However, it requires projection on the space spanned by the single-hole functions (SHFs) at each node of the tree, which can introduce unphysical couplings for unconverged basis sets. In this work, the non-hierarchical CDVR is revisited and a revised approach that avoids explicit projection on the single-hole space is introduced. The computational costs of the revised approach scale favorably with the number of single-particle functions (SPFs): for a tree with three edges at each node and $n$ SPFs at each edge, a n^4 scaling is achieved. Furthermore, a revised scheme that uses artificial SPFs to systematically increase the accuracy of the CDVR quadrature is presented. Computations studying the photodissociation of NOCl, the vibrational states of methyl, and the non-adiabatic quantum dynamics of photoexcited pyrazine demonstrate the accuracy and efficiency of the revised non-hierarchical CDVR. Notably, for the 24-dimensional pyrazine system the use of the CDVR does not increase the required CPU time compared to calculations utilizing the sum of products form of the vibronic coupling model.

Magnetic Resonance Elastography (MRE) has become an essential tool in assessing the mechanical properties of soft tissues in-vivo, prompting significant progress in new inversion algorithms. This creates a need for a benchmarking framework to promote uniformity and accessibility. To address this, we introduce a comprehensive in-silico dataset acquired by solving the forward Finite Element calculations of shear wave propagation in a linear visco-elastic material. This dataset aims to serve as a platform for evaluating inversion schemes by providing data that can be used as input with known mechanical properties to these methods. It includes simulations on homogeneous cuboidal domains of varying spatial and temporal resolution, and an extension to more physiological variations, including material inhomogeneity and internal arterial pulsation. We present a comprehensive case study using simulated data as an input to a direct inversion (DI) scheme, which allows for an expedient local inversion into the underlying material parameters. When aiming to reconstruct the parameters describing the linear visco-elastic material behavior via DI, we find that due to compromised convergence properties of frequency-domain stencils, stemming from truncation and subtractive cancellation errors, the reconstruction accuracy depends non-monotonically on the spatial and temporal resolution of the measurement grid. For inhomogeneous domains, the reconstruction was successful with notable interface boundaries. In the presence of pressurized vascular inclusions, a general stiffening of the domain was noted, as the recovered shear modulus was higher than the one assumed in forward modeling. Our study highlights the potential of this dataset as a vital benchmarking tool for advancing the development and refinement of MRE techniques, contributing to more accurate and reliable assessment of soft tissue mechanics.

We carry out a test of the fundamental Etherington relation (cosmic distance duality relation) which relates the luminosity distance $D_{\rm L}$ and angular diameter distance $D_{\rm A}$ in metric theories of gravity. We use the latest measurements of the angular diameter distance as a function of redshift from the Dark Energy Spectroscopic Instrument Data Release 2 (DESI-DR2) and the luminosity distance from a variety of compilations of Supernovae of Type Ia (SNeIa). Our results indicate that these measurements are statistically consistent with the Etherington relation. In addition to providing a confirmation of the underlying assumptions of the Etherington relation, i.e., the metric nature of gravity, Lorentz invariance and photon number conservation, our results are also a stringent test of any residual systematic effects. We interpret the absence of evidence of any deviation from this relation to constrain the evolution of the absolute magnitude of SNeIa to $dM/dz = 0.07 \pm 0.07$ over and above the systematics that are already accounted for in the SNeIa analyses. We discuss how the Etherington relation can be used to constrain systematic parameters in the analyses of dynamical dark energy using geometric probes, to make it more robust against systematic effects.

The purpose of this article is to address the issues of dimensional consistency that arise in the process of replacing the ordinary time derivative operator by a fractional derivative operator in order to write a fractional differential equation. We show that by performing a simple change of variables fulfilling certain conditions ensures the consistency in physical dimensions for fractional differential equations with non singular kernels. An example of the proposed method is given.

Retrieving relevant past interactions from long-term conversational memory typically relies on large dense retrieval models (110M-1.5B parameters) or LLM-augmented indexing. We introduce SelRoute, a framework that routes each query to a specialized retrieval pipeline -- lexical, semantic, hybrid, or vocabulary-enriched -- based on its query type. On LongMemEval_M (Wu et al., 2024), SelRoute achieves Recall@5 of 0.800 with bge-base-en-v1.5 (109M parameters) and 0.786 with bge-small-en-v1.5 (33M parameters), compared to 0.762 for Contriever with LLM-generated fact keys. A zero-ML baseline using SQLite FTS5 alone achieves NDCG@5 of 0.692, already exceeding all published baselines on ranking quality -- a gap we attribute partly to implementation differences in lexical retrieval. Five-fold stratified cross-validation confirms routing stability (CV gap of 1.3-2.4 Recall@5 points; routes stable for 4/6 query types across folds). A regex-based query-type classifier achieves 83% effective routing accuracy, and end-to-end retrieval with predicted types (Recall@5 = 0.689) still outperforms uniform baselines. Cross-benchmark evaluation on 8 additional benchmarks spanning 62,000+ instances -- including MSDialog, LoCoMo, QReCC, and PerLTQA -- confirms generalization without benchmark-specific tuning, while exposing a clear failure mode on reasoning-intensive retrieval (RECOR Recall@5 = 0.149) that bounds the claim. We also identify an enrichment-embedding asymmetry: vocabulary expansion at storage time improves lexical search but degrades embedding search, motivating per-pipeline enrichment decisions. The full system requires no GPU and no LLM inference at query time.

Entanglement purification protocols are fundamental primitives in quantum communication, enabling the distillation of high-quality entanglement using only local operations and classical communication. For large multipartite states, however, existing purification schemes typically require substantial resources and become progressively inefficient as system size increases. We introduce a new type of multipartite entanglement purification, Localized Entanglement Purification (LEP), a family of protocols that purify entanglement at the level of network regions rather than globally. By exploiting spatial noise asymmetries, LEP reduces resource consumption and enables scalable purification strategies for larger quantum systems.

We predict thermoelectric and current rectification effects in hybrid junctions formed by Ising superconductors and materials hosting valley-polarized states. Both effects originate from the interplay of intrinsic Ising spin-orbit coupling, spin-splitting from an exchange or Zeeman field, and valley polarization. The resulting transport signatures provide experimentally accessible probes of valley-polarized states in van der Waals heterostructures, such as junctions of few-layer transition metal dichalcogenides and twisted bilayer or rhombohedral graphene.

Understanding charge transport in strongly correlated systems remains a central challenge in condensed matter physics, particularly in light of the ubiquitous linear-in-$T$ resistivity observed in strange metals across many platforms from bulk cuprates to twisted bilayer graphene. Here, we investigate charge transport in the one-dimensional Hubbard model in the infinite-interaction limit. Focusing on the dilute limit with a fixed number of doped holes, we first construct the exact \emph{and explicit - i.e. beyond Bethe ansatz} energy spectrum and then derive a closed-form analytical expression for the charge Drude weight at arbitrary temperatures. We further analyze the low-temperature scaling and identify a linear-in-$T$ correction to the Drude weight. Upon regularizing the singular Drude contribution to the DC conductivity, we find that this behavior corresponds to an effective linear-in-$T$ resistivity, which may provide analytical insight into the emergence of strange-metal transport in two-dimensional strongly correlated systems.

The importance of cybersecurity for Small and Medium Enterprises (SMEs) has never been greater, especially given the rise of AI-driven threats. Supporting SMEs requires a sustained effort to ensure they have access to resources and expertise covering awareness, protection, auditing, and incident response. Since 2019, our work with the Keep It Secure initiative has focused on helping Belgian (Walloon) SMEs strengthen their cybersecurity posture through access to a network of labelled cybersecurity experts. In this process, we interviewed over 120 professionals from around 90 companies and gathered rich insights about the nature, strengths and weaknesses of our regional ecosystem. While our initiative primarily targets the labelling of cybersecurity experts, we demonstrate increasing alignment with the broader Cyber Fundamentals framework deployed at the federal level in Belgium, which supports official certification. This paper reports on the progress and lessons learned from this long-term effort, highlighting how expert validation, based on a structured evaluation approach, can help improve SME cybersecurity.

Vacuum fluctuations of quantum fields provide an unavoidable environment for any quantum system coupled to it. We study the interplay between boundary conditions and acceleration in determining decoherence of a two-level Unruh-DeWitt detector coupled to a scalar field in a cylindrical cavity. We show that the decoherence rate closely follows the emission profile, and exhibits {\it Purcell-like} enhancement for both inertial and uniformly accelerated detectors. The acceleration induces an effective smearing of the resonant density of states, diluting the resonance enhancement for large accelerations while replacing the inertial off-resonant decay with an oscillatory behavior for small accelerations. For moderate accelerations, this interplay between cavity-induced and acceleration-assisted effects results in an extended region of cavity parameters where decoherence is strongly suppressed, particularly in regimes where the inertial detector otherwise experience strong decoherence. Thus, contrary to naive expectations, the Unruh thermality in a suitably engineered cavity can enhance rather than degrade quantum coherence, providing a very uncharacteristic feature of quantum fields in non-inertial frames.

Spontaneous breaking of discrete symmetries play non-trivial role in many well-motivated particle physics models. However, it leads to a network of cosmologically unwanted domain walls (DWs) which can be made unstable by introducing a bias term in the scalar potential. In this letter, we provide a novel origin of such bias terms at finite temperature due to radiative corrections from a Dirac fermion with large asymmetry $\sim \mathcal{O}(0.1)$ in its number density. In addition to getting a new viable region of parameter space for collapsing DWs not explored previously and resulting gravitational waves (GWs) accessible at future experiments, the viability of the scenario crucially depends on the temperature of asymmetry generation too. This provides a unique way of probing both the amount of asymmetry and the corresponding temperature via future observations of GWs from collapsing DWs. The large asymmetry in the Dirac fermion can also have interesting implications for the observed baryon asymmetry as well as dark matter and large neutrino asymmetry.

Recent efforts have focused on characterizing the set of separable states that cannot be made entangled by any global unitary transformation. Here we characterize the set of states whose entanglement content cannot be increased under any unitary. By employing linear maps (and their inverses), we derive constraints on the achievable degree of entanglement from the spectrum of the density matrix. In particular, we focus on the negativity and the Schmidt number. Our approach yields analytical and practical criteria for quantifying the entanglement content of full-rank states in arbitrary dimensions using only a subset of their eigenvalues. Moreover, some of the derived conditions can be used to bound the spectra of Schmidt number witnesses.

Stars are natural sources of feebly interacting particles, including putative particles with mass $m_χ$ and electric charge $qe$. The emission of such millicharged particles (MCPs) causes an energy loss which can alter stellar evolution. While MCP production rates have been computed for different plasma parameters, they have yet to be derived for the conditions relevant to late stages of stellar evolution, in which the temperature can reach values $T\simeq 10-100\,\rm keV$ while the plasma frequency is $ω_{\rm pl}\ll T$. In this paper, we compute the MCP energy-loss rates relevant for pre-supernova objects, finding three different regimes in which the dominant processes are respectively plasmon decay ($m_χ< ω_{\rm pl}/2$), Compton-like scattering ($m_χ> ω_{\rm pl}/2$, $T\lesssim 0.5\,\rm MeV$), and electron-positron annihilation. We obtain semi-analytical fits for the energy-loss rates suitable for implementation in stellar evolution codes.

Multiply imaged, gravitationally lensed supernovae are rare but powerful tools for providing independent measurements on cosmological parameters. Supernova (SN) 2025wny ("SN Winny") is the first gravitationally-lensed Type I superluminous supernova and the first lensed supernova in a galaxy-scale system that is suitable for time-delay cosmography studies. In this work, we present high-resolution $K_p$-band adaptive optics imaging of SN Winny obtained with the near-infrared camera (NIRC2) on the W. M. Keck II telescope. With exquisite image quality (FWHM$\approx0.^{\prime\prime}065$) we determine and make use of the precise astrometric positions of the five multiple images as constraints for our lens mass models. With lenstronomy and Glee, we parameterize the total mass of the system with a singular isothermal ellipsoid, a singular isothermal sphere, and external shear. The two independent models are in excellent agreement and reproduce the observed image positions with sub-milli-arcsecond residuals. The inferred projected total masses enclosed within the Einstein radii of the primary and secondary lens galaxies are M$_1$ = 4.44$^{+0.06}_{-0.05}\times10^{11} M_\odot$ and M$_2$ = 0.96$^{+0.02}_{-0.02}\times10^{11} M_\odot$, respectively. Likewise, the inferred effective velocity dispersion of the primary lens is $σ_{1} = $ 277.4$^{+0.9}_{-0.7}$ km/s, consistent with the independent spectroscopic measurement made by DESI of $σ_{\star,1} = $ 298$\,\pm\,37$ km/s. Our modeling results are also consistent with previous results for the same system with data from the Large Binocular Telescope (LBT), using the same lens modeling codes. We also corroborate their finding that the SN multiple image A has an anomalous excess of flux by a factor of ~2-3 beyond what our smooth mass models predict.

We develop a rigorous system-agnostic method to predict quantum thermalization in an overwhelming fraction of accessible pure states in a many-body system, entirely in terms of certain out-of-time-ordered correlators of few-body observables. In contrast to previous rigorous results on thermalization with semiclassical counterparts, our method is not limited to statistical averages of observables, such as time averages in ergodicity or state averages in mixing. Moreover, consistent with such approaches, we retain the advantage of not requiring a detailed knowledge of energy eigenstate structure or thermodynamically large times, which can become intractable for systems with more than a handful of particles. Our approach is centered on a geometric result that connects thermalization to the alignment of high dimensional subspaces in a Hilbert space, which is determined by the saturation of "controllably nonlocal" out-of-time-ordered correlators. This formalism reduces the problem of establishing pure state quantum thermalization at finite times in almost all complex many-body states to a theoretically or experimentally accessible study of few-body correlators, even in thermodynamically large systems.

Quadratic unconstrained binary optimization (QUBO) provides problem formulations for various computational problems that can be solved with dedicated QUBO solvers, which can be based on classical or quantum computation. A common approach to constrained combinatorial optimization problems is to enforce the constraints in the QUBO formulation by adding penalization terms. Penalization introduces an additional hyperparameter that significantly affects the solver's efficacy: the relative weight between the objective terms and the penalization terms. We develop a pre-computation strategy for determining penalization weights with provable guarantees for Gibbs solvers and polynomial complexity for broad problem classes. Experiments across diverse problems and solver architectures, including large-scale instances on Fujitsu's Digital Annealer, show robust performance and order-of-magnitude speedups over existing heuristics.

Dijkgraaf-Witten theories have a wide range of applications in topological phases of matter and the study of generalized global symmetries. We develop a method to construct BF-type Lagrangians for Dijkgraaf-Witten theories with non-abelian gauge group by gauging $H^{(0)}$ symmetries from a BF-Lagrangian of an abelian Dijkgraaf-Witten theory. When $H$ nontrivially permutes the operators of the original theory, the Lagrangian of the $H$-gauged theory is constructed with cohomologies with local coefficients. We analyze the structure of the Lagrangians and their gauge transformations with homotopy theory. We also construct the operator spectrum and verify the Lagrangians by matching elementary linking invariants.

We investigate the impact of millicharged particles (MCPs) on massive stars undergoing pulsational pair-instability supernovae and on the location of the lower edge of the black hole mass gap. We find that energy losses due to MCP emission weaken the pulsations, allowing the star to retain more mass and thereby shifting the lower edge of the mass gap to higher black hole masses. The mass gap is sensitive to a region of MCP parameter space with masses $35\,{\rm keV}\lesssim m_χ\lesssim 200\,{\rm keV}$ and charges $10^{-10}\lesssim q \lesssim 10^{-9}$, which remains unconstrained by existing astrophysical probes. If confirmed, recent gravitational wave observations placing the lower edge of the mass gap near $45\,{\rm M}_\odot$ would translate directly into bounds on this parameter space.

Globular clusters (GCs) display much lower binary fractions than found among main-sequence stars in the solar neighborhood. The physical cause of this difference is debatable: does it reflect different star formation outcomes at low metallicity and/or high density, the dynamical processing of primordial binaries over cluster lifetimes, or a combination of the two? Starting from the assumption that the initial binary distribution in GCs is the same as the binary distribution observed in the solar neighborhood, we show with straightforward analytical calculations that the dynamical dissolution of "soft" primordial binaries can fully explain the main-sequence binary fractions in present-day GCs. We validate our estimates against a detailed N-body simulation with the Cluster Monte Carlo code. Adopting the view that the observed binary fraction in a given cluster constrains the location of the hard/soft boundary at birth, we infer that surviving Milky Way GCs had a similar distribution of birth radii to young massive clusters in the local universe. Our findings underscore the crucial role of stellar black holes (through "black hole burning") in sculpting GC binary populations and reinforce the need for realistic initial conditions in theoretical modeling of GC dynamics.

We present a holographic construction of the QCD axion based on a warped 5D model. A key ingredient of our setup is the introduction of a bulk scalar field $θ$, which is holographically dual to the topological operator of QCD. This makes the relation among the axion, the $η'$, and the anomalies transparent. We identify the bulk modes corresponding to the $η'$ and axion states, and show that an adjustment analogous to that of the usual 4D axion takes place. We identify the origin of the axion quality problem in this framework and show that a large degree of axion compositeness is needed to solve it. We also find that, in the limit of a high quality axion, the physical axion state is predominantly contained in the bulk gauge field.

The paper extends the Scaled Relative Graph (SRG) framework of Ryu, Hannah, and Yin from Hilbert spaces to normed spaces. Our extension replaces the inner product with a regular pairing, whose asymmetry gives rise to directional angles and, in turn, directional SRGs. Directional SRGs are shown to provide geometric containment tests certifying key operator properties, including contraction and monotonicity. Calculus rules for SRGs under scaling, inversion, addition, and composition are also derived. The theory is illustrated by numerical examples, including a graphical contraction certificate for Bellman operators.

Golomb's sequence is the unique nondecreasing sequence of positive integers in which each $n$ appears exactly $a(n)$ times. It satisfies the global self-referential rule \[ a\bigl(a(n)+a(n-1)+\cdots+a(1)\bigr)=n, \] grows smoothly like a power of $n$ governed by the golden ratio, and is not $k$-regular for any $k\ge 2$. We introduce almost Golomb sequences, obtained by truncating the cumulative sum to a sliding window of fixed size $r$, \[ a\bigl(a(n)+a(n-1)+\cdots+a(n-r+1)\bigr)=n. \] This finite-memory truncation changes the nature of the sequence completely. The smooth power law gives way to oscillatory linear growth, and the sequence becomes $r$-regular for every $r\ge 2$. For small values of $r$ we establish explicit denesting formulas, prove that $a(n)/n$ does not converge, and uncover combinatorial structure including a cellular automaton and a palindromic substitution. A numerical surprise emerges when one varies $r$. The maximum multiplicity across the family of sequences is governed by Golomb's sequence itself. The sequence that was truncated reappears as the law controlling the family it generated.

Investigating black holes in modified theories of gravity offers fertile ground for exploring phenomena beyond the scope of general relativity. We investigate a novel class of charged anti-de Sitter (AdS) black holes within the ghost-free de Rham-Gabadadze-Tolley (dRGT) massive gravity, minimally coupled to an exponential form of nonlinear electrodynamics (NED). The NED sector is modelled by an exponential electrodynamics Lagrangian, which leads to singular black hole geometries in contrast to many regular configurations known in other NED models. In turn, we systematically investigate the thermodynamic properties and phase structure of the obtained black holes. The results show that the system has a rich thermodynamic structure. For different values of the magnetic charge $q$, the black hole can exhibit several types of phase transitions. These include van der Waals-like first-order phase transitions, second-order critical behavior, and a reentrant phase transition between small and large black holes without extending the phase space ($Λ=$constant). Our study enhances the understanding of AdS black holes in ghost-free massive gravity, providing further insights into the interplay between graviton mass and NED. The results highlight how the combined effects of graviton mass and electromagnetic nonlinearity can yield a rich and complex thermodynamic phase space, offering further insights relevant to the gauge/gravity duality and the ongoing search for observational signatures of modified gravity.

This paper proposes a new family of Tweedie-based ratemaking models that explicitly account for mid-term policy cancellations. Using an automobile insurance dataset from a Canadian insurer, we document a marked difference in claims experience between policyholders who maintain their coverage until maturity and those who cancel their policies mid-term. Building on the classical Tweedie framework, we introduce flexible weighting functions and a premium penalty structure that depend on the level of exposure, allowing for a more realistic representation of the earned premium when coverage is interrupted before the end of the policy period. We compare several weighting structures within the Tweedie framework and examine their theoretical properties, as well as their empirical performance using deviance-based model comparison criteria, an area-between-curves criterion derived from concentration and Lorenz curves, and Murphy diagrams grounded in Bregman dominance. To operationalize the proposed models, monotonicity and non-negativity constraints are imposed on the penalty function, ensuring consistency with actuarial principles. Finally, using real-world data, we show that this approach provides both a strategic and competitive advantage: it allows the insurer to indirectly compensate for large losses through a cancellation surcharge, while preserving actuarial coherence and statistical consistency.

We study illusion elimination problems on directed social networks where each vertex is colored either red or blue. A vertex is under \textit{majority illusion} if it has more red out-neighbors than blue out-neighbors when there are more blue vertices than red ones in the network. In a more general phenomenon of $p$-illusion, at least $p$ fraction of the out-neighbors (as opposed to $1/2$ for majority) of a vertex is red. In the directed illusion elimination problem, we recolor minimum number of vertices so that no vertex is under $p$-illusion, for $p\in (0,1)$. Unfortunately, the problem is NP-hard for $p =1/2$ even when the network is a grid. Moreover, the problem is NP-hard and W[2]-hard when parameterized by the number of recolorings for each $p \in (0,1)$ even on bipartite DAGs. Thus, we can neither get a polynomial time algorithm on DAGs, unless P=NP, nor we can get a FPT algorithm even by combining solution size and directed graph parameters that measure distance from acyclicity, unless FPT=W[2]. We show that the problem can be solved in polynomial time in structured, sparse networks such as outerplanar networks, outward grids, trees, and cycles. Finally, we show tractable algorithms parameterized by treewidth of the underlying undirected graph, and by the number of vertices under illusion.

Objective: SNP heritability estimates vary substantially across estimation strategies, yet the downstream consequences for polygenic risk score (PRS) construction remain poorly characterised. We systematically benchmarked heritability estimation configurations and assessed their propagation into downstream PRS performance. Methods: We benchmarked 86 heritability-estimation configurations spanning six tool families (GEMMA, GCTA, LDAK, DPR, LDSC, and SumHer) and ten method groups across 10 UK Biobank phenotypes, yielding 844 configuration-level estimates. Each estimate was propagated into GCTA-SBLUP and LDpred2-lassosum2 PRS frameworks and evaluated across five cross-validation folds using null, PRS-only, and full models. Eleven binary analytical contrasts were tested using Mann-Whitney U tests to identify drivers of heritability variability. Results: Heritability ranged from -0.862 to 2.735 (mean = 0.134, SD = 0.284), with 133 of 844 estimates (15.8%) being negative and concentrated in unconstrained estimation regimes. Ten of eleven analytical contrasts significantly affected heritability magnitude, with algorithm choice and GRM standardisation showing the largest effects. Despite this upstream variability, downstream PRS test performance was only weakly coupled to heritability magnitude: pooled Pearson correlations between h^2 and test AUC were r = -0.023 for GCTA-SBLUP and r = +0.014 for LDpred2-lassosum2, with both being non-significant. Conclusion: SNP heritability is best interpreted as a configuration-sensitive modelling parameter rather than a universally stable scalar input. Heritability estimates should always be reported alongside their full estimation specification, and downstream PRS performance is comparatively robust to moderate variation in the heritability input.