Papers

This work presents a comprehensive radiation hardness characterization of SiPM devices for space-based applications: FBK NUV-HD-MT and NUV-HD-LowCT (1$\times$1, 3$\times$3, and 6$\times$6~mm$^2$) and Hamamatsu S14160 MPPCs with equivalent active areas. Total Ionizing Dose (TID) tests were performed at the ESA/ESTEC Co-60 facility with a level of dose up to 20~krad in silicon, while displacement damage effects were evaluated using 100~MeV protons with a fluence up to $1.12\times10^{11}$~p/cm$^2$ at the Paul Scherrer Institute. Radiation damage in SiPMs manifests through two main mechanisms: ionizing energy loss and non-ionizing energy loss (NIEL), which increases dark current and dark count rate. In this work, breakdown voltage, dark current, and quenching resistance were systematically measured as functions of accumulated dose and fluence. Gain and dark count rates were indirectly measured from the characterized electrical parameters. Both technologies exhibit remarkable stability of most of the functional parameters across all dose levels, while dark current shows predictable increases significantly more pronounced under proton irradiation due to displacement damage. Based on these results, both FBK and Hamamatsu devices are confirmed suitable for Low Earth Orbit (LEO) mission environment.

We use stationary common-neighborhood properties to study highly connected Ramsey relations and partition hypotheses. For weakly compact $\kappa$, $\operatorname{Coll}(\omega_1,{<}\kappa)$ forces $\omega_2\to_{\mathrm{hc},<5}(\omega_2)^2_\omega$ and $\operatorname{PH}_1(\omega_2)$. If $\kappa$ is $T^{\kappa^+}_{\omega_1}$-Ramsey, the same collapse forces that every countable coloring of $[\omega_2]^2$ has a stationary set $X\subseteq\omega_2$ and a color $i$ such that every finite subset of $X$ has stationarily many color-$i$ common neighbors in $X$. From one weakly compact cardinal, we obtain a model of the ${<}5$-edge relation at $\omega_3$ and $\operatorname{PH}_1(\omega_3)$, in which $\check H^2(\omega_3,A_d)\ne0$ for every nontrivial abelian group $A$. This separates $\operatorname{PH}_1(\omega_3)$ from $\operatorname{PH}_2(\omega_3)$, with the exact consistency strength of one weakly compact cardinal. We also show that $\operatorname{PH}_1(\omega_2\times\omega_5)$ is equiconsistent with two weakly compact cardinals.

This paper introduces and investigates a non-classical positional numeral system constructed on the normalized Mersenne basis $M_k = (2^k-1)/3$, structurally linking the classical Mersenne sequence (OEIS A000225) with the integer sequence of alternating binary bitmasks (OEIS A002450). The main objective of this study is to provide a rigorous algebraic proof of the system's completeness—specifically, theorems on the existence and absolute uniqueness of a canonical representation for any natural number. We show that the internal dynamics of the basis are deterministically governed by the splitting identity $3M_k = M_{k+1} + 2M_{k-1}$, which strictly restricts the valid alphabet of coefficients to the set $\{0, 1, 2\}$. Based on the lemma concerning the supremum of lower-order digits and a constructive greedy algorithm, it is proven that the proposed basis forms a closed and unambiguous algebraic space, entirely precluding the overlap of positional masses.

We investigate late-time cosmic acceleration in mass-varying neutrino (MaVaN) dark energy scenarios, where the neutrino mass is coupled to a dynamical quintessence field through a conformal interaction. Starting from the coupled conservation equations, we derive the corresponding background evolution equations for three related scenarios: a constant dark-energy equation of state with a constant coupling (Case-I), an exponential neutrino mass linked to an exponential potential under an adiabatic minimum-tracking approximation (Case-II), and a CPL-type time-varying equation of state with constant coupling (Case-III). For each case we obtain the neutrino and dark energy density evolution and the corresponding Hubble parameter, and use an MCMC analysis (emcee) to test the models against DESI DR2 BAO data, the compressed Planck CMB likelihood, and three supernova compilations (Pantheon+, DES-SN5YR, Union3), taken one at a time. Across the three cases, $H_0$ and $\Omega_{m0}$ move together in a way set mainly by which supernova sample is used, following the pattern already seen in other DESI DR2 analyses. A nonzero coupling stays consistent with the data in most fits, though its size, and sometimes its sign, depend on how it enters the model and on the priors chosen for the underlying parameters. The resulting neutrino mass bounds range from about $0.06$ to $0.3\,\mathrm{eV}$, depending on the case and dataset combination. Comparing the Bayesian evidence of each case with flat $\Lambda$CDM gives a mixed picture, with no case preferred throughout, so we regard these results as suggestive rather than firm evidence for a coupling between neutrinos and dark energy.

We apply the gradient-flow framework to determine the nonperturbative medium contribution to the jet transport coefficient $\hat q$ using quenched lattice QCD in the temperature range $0.76T_c \leq T \leq 2.25T_c$. The calculation focuses on the leading-twist contribution at leading order for an asymptotically energetic quark propagating through a thermal pure-gluon plasma. In the infinite-energy limit, the operator-product expansion expresses $\hat q/T^3$ in pure gauge theory as the product of a perturbative short-distance coefficient and the entropy density $s/T^3$. The latter is determined from the gradient-flow energy-momentum tensor at three lattice spacings for each temperature and the former is estimated perturbatively at one-loop order. We find that $\hat q/T^3$ is strongly suppressed below $T_c$, rises rapidly across the deconfinement transition, and remains approximately constant at $\hat q/T^3\simeq1.1$ throughout the deconfined temperature range studied. This is statistically consistent with the previous quenched lattice determination based on a different renormalization procedure, providing a nontrivial validation of the gradient-flow framework for the jet transport coefficient. The systematic treatment of operator renormalization and matching provided by gradient flow becomes particularly important in full QCD, because the need to renormalize quark operators and account for their mixing with the gluonic sector can likewise be addressed within the same framework.

Survival prediction for glioblastoma multiforme (GBM) demands models that are both accurate and interpretable, yet existing approaches treat these objectives as com- peting, where performant models sacrifice transparency, while interpretable models accept degraded predictive power. We argue that this trade-off is not inherent. Graph neural net- works offer a structural foundation for extracting interpretable, explainable representations without compromising discriminative ability. Furthermore, current methods typically rely on a single imaging modality, underutilizing the complementary information available across multi-modal MRI and clinical metadata. We propose a multi-modal framework that inte- grates three components to address both objectives simultaneously: (1) a sheaf hypergraph neural network that captures higher-order relationships among tissue patches through direc- tional, asymmetric message passing; (2) a concept bottleneck layer that compresses learned representations into clinically grounded concepts, enforcing ante-hoc interpretability; and (3) an extension sufficiency test (EST) regularizer that penalizes unfaithful explanations during training, ensuring that model explanations genuinely reflect the internal decision process. Clinical and genomic features are incorporated through gated fusion, preserving the dominant prognostic signal of molecular markers while retaining concept-level traceabil- ity. Evaluated on 593 patients from the UPenn-GBM dataset under 5-fold cross-validation, our framework achieves a concordance index of 0.643 with the lowest fold-level variance among all compared models (std = 0.015). To our knowledge, this is the first work to unify sheaf hypergraph convolution, concept bottleneck supervision, and EST regularization for interpretable survival prediction from brain MRI

High-order isogeometric discretizations produce a small number of non-physical outlier modes at the top of the discrete spectrum. These modes can pollute the numerical solution in wave propagation and structural dynamics. Most existing remedies modify the spatial discretization through outlier-free bases, mass lumping, subspace projection, and related constructions. We introduce MIISO (Modal Integrators for Isogeometric Stabilization of Outliers), a family of exponential Rosenbrock-Krylov methods of orders two through six that suppress the outliers in the time integrator and leave the spatial discretization unchanged. We construct a non-holomorphic amplification map by blending a Padé approximation that preserves physical oscillatory modes with a Pade approximation that damps high frequencies, with the blend placed at the known spectral location of the outliers. For orders three and higher the damping approximant is repaired so that the method is unconditionally A-stable. Physical modes receive no numerical dissipation and the outliers are driven to zero. The outlier handling and the method steps are fully matrix-free, and the method extends to nonlinear problems. Numerical experiments recover the predicted orders, match spatial outlier removal without changing the discretization, show lower cost than generalized-alpha at matched accuracy and in scaling, and demonstrate the method on nonlinear and three-dimensional problems.

We reconstruct the generalized hexagon of order $(2,8)$ from an abstract even rank-$26$ lattice of determinant $3$ and minimum $4$, and conversely reconstruct the lattice from the hexagon. Harmonic theta identities determine the $819$ shortest vectors in a non-zero discriminant class and their association scheme, and show that every non-empty positive-norm shell of the lattice and its dual is a spherical $5$-design. In the converse direction, the rank-$26$ idempotent gives the lattice, with saturation proved by a short dual-coset argument. A positive-definite Niemeier construction proves existence and uniqueness of the lattice and hence of the hexagon. The third moment of a projective $3$-design in the Cayley plane reconstructs the traceless Albert product. This upgrades angle-preserving bijections to elements of $F_4(\mathbb R)$ and proves geometric uniqueness of the tight $819$-point projective $5$-design. Finally, line deletion gives a rootless index-four sublattice of $N(A_1^{24})$ with a Golay trio and an oriented gluing. The gluing data form eight root-sign orbits, on which $L_3(2)\cong L_2(7)$ acts as on $\mathbf P^1(\mathbf{F}_7)$; two explicit Golay permutations prove transitivity. This proves uniqueness and gives the automorphism-group order. The group is identified afterward as ${}^3D_4(2):3$, with a central factor $C_2$ for the full lattice group. The reconstruction and deletion arguments parallel the length-$26$ binary code construction.

Data assimilation aims to infer the state of complex dynamical systems based on observational data. However, accurate inference of the multimodal posteriors induced by nonlinear or non-injective observation operators remains a key challenge under high-dimensional and sparse observation conditions. Ensemble filters scale to high dimensions but are confined by restrictive distributional assumptions, while training-free generative filters (e.g., EnSF, EnFF) alleviate this limitation but may introduce structural errors and hinder information propagation under sparse observations. To address these issues, we propose a training-free, asymptotically exact posterior transport method. Firstly, a covariance-aware posterior transport scheme is designed, which embeds the forecast cross-covariance into flow-based transport and accurately recovers unobserved states while preserving the non-Gaussian posterior structure. Furthermore, the method combines a tractable observation-adaptive proposal with posterior correction, ensuring accurate approximation of the nonlinear posterior distribution. Finally, we establish the corresponding posterior flow theory, from which the asymptotic exactness of the proposed method relative to finite-ensemble surrogates and the Wasserstein error bound are derived. Experiments on Double-Well, Lorenz-96, and Kolmogorov flow show that the proposed method captures complex posterior structure and remains accurate under sparse, nonlinear, and non-injective observations. In the sparse non-injective setting, it reduces RMSE by 56% relative to the best baseline.

We construct finite-state Markov arrival-rate processes for which faster modulation increases the mean stationary workload of a stable single-server queue, disproving the universal ordering in Leskelä's formulation of Ross's second conjecture. A 64-state example has positive transition rates between every pair of states, independent service times uniform on $[0.99,1.01]$, and an explicit positive workload gap. A 128-state example additionally has strictly positive arrival-rate autocovariance at every lag. More generally, finite-state examples can exhibit any prescribed finite number of separated workload rises and falls. The proofs use a second-order expansion with a nonnegative, speed-uniform remainder under only a finite second service moment. We characterize the service distributions for which the second-order workload coefficient is nonincreasing for every bounded stationary environment: the function $s\mapsto\mathbb{E}(1-\cos(sB))/s^2$ must be nonincreasing. Mixtures of exponential service distributions satisfy this criterion. An exact Palm identity transfers the workload reversals to customer waiting times.

Detector outcome probabilities can be independent of a later measurement setting even when earlier timestamps, detector seeds, or environmental records depend on that setting. We characterize complete-record preservation for a positive wrapped-Cauchy retrocausal spin source. An antipodal identity yields necessary and sufficient conditions for passive and environmental readouts, and source compensation permits a common normalized analyzer for source spins and prepared continuations. Gaussian controller and reset calculations distinguish inverse raw history weights from normalized thermal operations. A quantum instrument provides an operational benchmark, whereas a setting-dependent separable source produces setting-dependent statistics at an earlier joint probe. For two equal-width contexts, a calibrated weak probe requires a minimum source change of $\operatorname{sech}(2g)/8$ in trace distance for exact protection at every nonzero strength. The signal–source-change tradeoff is sharp for this pair of contexts. A contextual positive-history construction recovers the isolated hidden law and preserves records for a specified class of finite adaptive quantum apparatuses, subject to quantum calibration and restricted field access. Direct readout of an added likelihood field distinguishes two future axes with unit probability. The analytical results are supported by continuous-angle and quantum-trajectory simulations, deterministic quadrature, and exhaustive enumeration of a finite policy class. The analysis concerns the specified statistical models; their microscopic physical realization remains an open question.

Self-calibrating monitors adapt their threshold online to guarantee a prescribed long-run false-alarm rate under arbitrary drift. We compute the price of that guarantee, stating every law with its exact domain of validity. First, the guarantee is an accounting identity, insensitive to what the monitor is meant to detect. Two evidence identities make the cost exact for the online quantile tracker: a persistent step of height $\delta$ yields excess alarm mass within one alarm of $\delta/\eta$, and exactly $\delta/\eta$ pathwise when $\delta$ is a lattice multiple of the gain $\eta$; a ramp of slope $c$ yields a stationary excess rate of exactly $c/\eta$, independent of accumulated size, up to a boundary $c=\eta(1-\alpha)$ coinciding with the alarm-rate cap. Second, the certificate's own fluctuation obeys an exact law: the windowed alarm rate has standard deviation of order $1/L$, not the binomial $1/\sqrt{L}$, since the windowed mass telescopes to a difference of a tight internal state; the closed-form constant is validated with no fitted parameter. Detectors calibrated on the binomial scale are miscalibrated by $\sqrt{\eta\varphi(q_0)L}$, and correct calibration turns detection windows from quadratic to linear in the inverse fault speed. Third, any monitor required to tolerate a drift class $\mathcal{D}$ is blind, at any horizon and for any rule, to every fault in $\mathcal{D}-\mathcal{D}$; the proof is a deliberately elementary two-point argument and the contribution is the object it identifies: for speed-bounded classes the blind set is exactly the doubled-speed class, and the tracker absorbs a speed class fixed by its own gain, so that under a certification regime declaring absorbed drift normal, the monitor manufactures $\mathcal{D}$. An exact Gaussian projection bound, sharper than Pinsker and never vacuous, quantifies power outside it.

In work of the first author, the geometric Satake equivalence was (non-rigorously) reinterpreted as an equivalence between two algebraically-defined $2$-categories, one built from representations of a Lie algebra, and one built using singular Soergel bimodules. It was then explained how to $q$-deform this equivalence in type $A$, replacing the special linear Lie algebra with its quantum group, and using singular Soergel bimodules for a deformed reflection representation. Both the algebraic reformulation and its $q$-deformation were only proven in types $A_1$ and $A_2$. In this paper, we prove the result in type $A_{n-1}$ for $n \ge 4$, while working generically: more precisely, we work over a field of characteristic zero, where $q$ is not a root of unity, and having adjoined an $n$-th root of $q$. Along the way we generalize certain results in the literature (e.g. the Soergel-Williamson categorification theorem, the Soergel conjecture for spherical elements, various symmetries) to the deformed reflection representation.

A robot policy is trained with one of two action parameterizations: absolute joint targets, or deltas relative to the current state. The choice is a live engineering decision in robot learning, and a world model conditioned on actions inherits it silently. We show the inheritance is catastrophic. A latent dynamics model trained on one parameterization and handed the identical commanded trajectory written in the other collapses: retrieval degrades by 2.6-13.4x across three robot datasets and two morphologies, goal-conditioned action selection falls from 53% to 15%, and on PushT the two beliefs about the same future are near-orthogonal (cos = 0.067, worst case -0.377), so the predictor does not degrade gracefully, it answers a different question. This is not a distribution-shift artifact in the usual sense: the two encodings are mutually reconstructible at R^2 = 0.996 given the joint input, so no information is lost, and we give the test that separates a valid re-parameterization from a lossy summary or a sensor swap. The test rejected three of the four axes we proposed. The defect lives in the action channel, which the invariance literature for visual models does not examine: work there concerns crops, jitter and camera pose, while the parameterization of the commands goes unaudited. The repair is averaging over the two encodings, and where it goes matters. Averaging the objective restores task performance by itself; averaging the outputs, safe for probabilities by concavity, is not available for direction-valued prediction, where the normalized mean can score below every member of the orbit. What objective-averaging leaves behind is the tail: worst-case agreement stays at 0.78, a disagreement penalty closes it to 0.995, and over a latent rollout it is the difference between a worst case that erodes and one that holds. On PushT, averaging alone does not repair the axis.

We establish a concentration–compactness theory for a one-dimensional singular Moser-type functional with logarithmic weight function $$\sup\limits_{v\in E }\int_0^1 e^{\left(\log\frac{e}{s}+\gamma\log\log\frac{e}{s}\right)\frac{v^2(s)}{s}}ds<\infty,~\gamma\in[0,1],$$ where $$E:= \left\{u \in H^{1}(0, 1): u(0) = 0, \int_0^1 |u'|^2dx=1\right\}.$$ In particular, we prove compactness for all normalized sequences in the subcritical range $\gamma<1$, thereby resolving an open problem proposed in [J. M. do Ó, B. Ruf and P. Ubilla, CVPDE 2023]. We also study the critical Bliss-Moser inequality: \begin{equation}\nonumber \sup\limits_{v\in E }I^c(v)< +\infty,\quad I^c(v)=\int_0^1 e^{\left(\log\frac{e}{s}+\log\log\frac{e}{s}+cs\right)\frac{v^2(s)}{s}}ds. \end{equation} For any $c\in(-\infty,+\infty)$, we determine the sharp concentration level $$\sup_{v_j\in E,v_j~\text{is~NCS}}\limsup\limits_{j\to\infty} I^c(v_j)=1+e^2,$$ and obtain explicit sufficient conditions for attainability under $c>c^*$ and non-attainability under $c<-c_*$. This results describe how linear perturbations govern the transition between compactness, concentration, and attainability at the critical level.

Cryptocurrency markets exhibit extreme price swings and sentiment-driven regime shifts, which traditional volatility models often fail to capture. To address this, we develop a partially observed Markov processes (POMP) model augmented with sentiment and heavy-tailed distributions. Specifically, we extend Breto's framework by including the Fear and Greed Index (FGI) as an exogenous regressor in the latent volatility dynamics and replacing Gaussian measurement noise with a Student's t distribution. We fit the model via simulation-based inference using daily Bitcoin returns and FGI data from January 2020 to April 2025. Our approach significantly outperforms three benchmark models in log-likelihood and filter stability. Moreover, our model yields interpretable parameters consistent with known features of financial volatility. These results demonstrate that incorporating sentiment signals and heavy-tailed noise improves the modeling of volatility and regime shifts in cryptocurrency markets.

The Fresnel wave surface governs the propagation of light in a transparent biaxial crystal. It is a special Kummer quartic, and we identify it exactly. Over the complex numbers the wave surface of a crystal is the Kummer surface of the Jacobian of an explicit genus-two curve branched at the signed square roots of the three principal permittivities. This Jacobian is isogenous, by an isogeny with kernel of order four, to a product of two elliptic curves. One elliptic curve carries the three permittivities, and the other carries the optic-axis angle. The physical family is Zariski dense in the locus of genus-two curves with an extra involution, and its automorphism strata are explicit. The identification instantiates a task-aware quotient, which identifies parameters that differ by a nuisance transformation and carries invariant coordinates and explicit strata. For biaxial crystals, two ratios of the permittivities form a complete invariant of the wave surface up to rotation and rescaling, and the four real nodes are given in closed form. At an interface the candidate transmitted waves are the roots of a quartic of exact degree four. Its real-root count, root order, and repeated-root events are decided by exact algebraic predicates, and along the generic single-node encounters of the paper its discriminant vanishes to second order. Floating-point solvers drop forward transmitted modes near the optic axes, and the certified solver does not. On exact equivalence classes, learned models on quotient coordinates are invariant and more accurate than models on raw tensors, while learned root-count predicates fail near the optic axes.

A fundamental challenge in deploying vision models is domain shift, which arises when training and test data follow different distributions, leading to degraded performance. This challenge is amplified when the same semantic concept appears under distinct visual forms, such as photographs and sketches, where visual similarity is weak despite semantic correspondence. Existing unsupervised domain-adaptation methods aim to align distributions across domains but often ignore semantic relationships among samples of the same class. To address this issue, this paper introduces SPACE, a method that exploits the semantic structure of CLIP's vision-language space for domain adaptation. The key idea is to use text descriptions as semantic anchors by applying Singular Value Decomposition to CLIP embeddings of class descriptions, yielding an orthogonal basis that captures semantic relationships among categories. Visual features from both domains are projected into this semantic subspace, aligning images based on meaning rather than appearance.

I present new results for the massive cusp anomalous dimension at four loops in QCD. I combine partial exact and conjectured analytical expressions with an approximation that is based on the asymptotic behavior of the cusp anomalous dimension to produce the newest estimates. Detailed comparisons are made with previous approximate results that highlight the robustness of the calculational approach.

We investigate the physical origin of the bimodality in bulge-dominated galaxies, originally identified by Sampaio et al. (2025), by combining non-parametric morphological metrics, structural scaling relations, stellar kinematics, and environmental trends across a wide redshift range ($0.2 < z < 2.4$). Using the MEGG-based hybrid classification pipeline applied to CANDELS imaging, we examine the distributions of morphological metrics for two families of bulge-dominated galaxies: G1, with high specific star formation rate (sSFR) distributions, similar to discs, and G2 with lower sSFR. We find that G1 galaxies occupy an intermediate position between discs and G2 spheroids in morphological metrics, and this behaviour persists up to $z = 1.4$. Fitting the Kormendy relation separately for each family, we find a persistent offset in the zero-point across all redshifts: G2 galaxies are systematically brighter in mean effective surface brightness at fixed effective radius, likely indicating higher central stellar densities. This offset is present in both observed and rest-frame magnitudes, and we argue that it reflects a genuine difference in assembly history. A cross-match with MUSE observations reveals that G1 galaxies have higher projected angular momentum than G2 galaxies, with G1 galaxies overlapping with the disc population, while G2 galaxies are more dispersion-dominated. The redshift evolution of morphological fractions shows that, at high stellar masses, the G2 fraction grows, while discs follow the opposite trend. In parallel, G1 remains a stable, lower-mass population consistent with secular bulge growth. Finally, within galaxy clusters, G1 galaxies are preferentially found at larger cluster-centric radii, suggesting that high-density environments amplify the bimodality by accelerating quenching.

AlGaAs/GaAs asymmetric coupled quantum wells (ACQWs) are promising platforms for enhanced second-order optical nonlinearities, with their performance strongly influenced by the structural quality of heterostructures. Flat interfaces, together with high compositional homogeneity, are generally desirable for optimizing device functionality. Here we show that sharp and flat AlGaAs/GaAs interface morphology dominates the second harmonic generation (SHG) response in AlGaAs/GaAs ACQWs, even when significant compositional fluctuations in Al/Ga occupancy are present within the AlGaAs layers. Using multislice electron ptychography, we resolve the three-dimensional (3D) interface morphology and compositional distribution in AlGaAs/GaAs ACQWs under distinct growth interruptions. Longer growth interruptions sharpen and flatten the AlGaAs/GaAs interfaces, but at the same time cause stronger compositional fluctuations in the AlGaAs layers. These findings clarify how growth interruption tunes quantum wells structures and provide direct guidance for quantum wells design in next-generation optoelectronic devices.

We study numerical observables relevant to delocalization in the three-dimensional Manhattan mirror model, also known as the K-lattice. Our principal experiment separates the locations of transmitting boundary channels from the routing between them. We derive an exact conditional comparison that preserves all transmission and reflection aperture sets, and find a statistically resolved deficit of physical transmission relative to this comparison. Nearby transmitting channels are themselves suppressed relative to a uniform subset with the same cardinality. A second experiment resolves the contribution of repeated vertices by their return age. The squared norm of the signed old-memory remainder is consistent with an inverse-square-root decay over the measured range. Annular experiments quantify decreasing continuation losses, while an initially apparent history dependence fails independent replication. Finally, a periodic configuration has a connected auxiliary contact graph but only finite routing cycles. These results identify estimates on reflection routing and adaptively selected revisit charges that may assist a rigorous proof. They do not establish an infinite-volume delocalized phase.

Recently, a hybrid qudit-qubit algorithm [1] was presented for solving the integer programming problem with a polynomial quantum advantage. In this work, we investigate the algorithm [1] to understand the role of qudits ($d$-dimensional quantum system) by conducting a comparative resource analysis with its qubit-only implementation and the classical simulability of the algorithm by exploring the entanglement structure. The resource analysis part is performed in terms of logical gate counts, and fault-tolerant physical resources, including non-Clifford gates. The hybrid qudit-qubit implementation has a more compact structure of the unitary operators as opposed to its qubit-only simulation which reduces the logical and fault-tolerant resource requirements. Two example problems, one with qutrits ($d=3$) and the other with ququint ($d=5$), when contrasted with their qubit-only implementation, within a simplified fault-tolerant resource model, showed $\sim 180 \times $ and $\sim 2220\times$ fewer total resource count, respectively. For the entanglement study, volume-law-like entropy growth and signatures of multi-partite entanglement is observed leading to increasing difficulty in the classical simulation of the algorithm. The algorithm generates synergistic tri-partite entanglement even for a quadratic problem, revealing that the algorithmic structure itself can generate higher-order entanglement in the system independent of the problem.

We study two-timescale decision systems in which a planning layer periodically supplies a continuation-value function to a real-time optimizer that allocates arriving resources, with inventory placement as our motivating application. We propose an end-to-end reinforcement learning (RL) method for learning this function using proximal residual value functions, which combine a strictly convex potential of post-decision inventory with a learned convex residual. This general form yields a well-posed optimization layer that supports end-to-end differentiation while preserving an explicit convex objective for real-time execution. We characterize the necessary and sufficient conditions under which a smooth value function yields decisions that are consistent across the planning and execution timescales. In an offline simulation using historical inventory arrival and demand patterns from a large e-commerce retailer, learned proximal residual value functions reduce total routing and transfer cost relative to a historical-production-system proxy by 5.0%.

Uncertainty quantification (UQ) is increasingly recognized as an important component of reliable machine learning in medical imaging, yet practical resources connecting UQ theory, implementation, and evaluation remain limited. We developed Uncertainty Quantification in Medical Imaging Analysis (UQMIA), an open-access, hands-on tutorial comprising 19 sessions covering major UQ approaches, including variational inference, Monte Carlo dropout, deep ensembles, evidential deep learning, and conformal prediction, together with methods for evaluating uncertainty reliability. The tutorial is designed for researchers and practitioners with experience in medical imaging, progressing from foundational concepts to implementation and evaluation, with notebooks executable through Kaggle. Beyond presenting the tutorial, we introduce a framework using large language models (LLMs) to evaluate whether technical educational resources contain retrievable and usable knowledge. Using 100 four-option multiple-choice questions derived from primary methodological literature, we evaluated 20 instruction-tuned LLMs from six model families with and without retrieved tutorial context. Retrieval of UQMIA improved accuracy in 18 of 20 models, increasing mean accuracy from 0.680 to 0.742 (+0.062; Holm-adjusted P=0.00032), and improved area under the receiver operating characteristic curve (AUROC) in 18 of 20 models, increasing from 0.725 to 0.788 (+0.063; Holm-adjusted P=0.00032). UQMIA provides an accessible resource for learning UQ in medical imaging and demonstrates an LLM-based approach for evaluating technical educational material. The tutorial is available at https://benyamin-gheiji.github.io/Uncertainty-Quantification-Medical-Imaging-Analysis/ and its source code and notebooks at https://github.com/benyamin-gheiji/Uncertainty-Quantification-Medical-Imaging-Analysis/.

Purpose: Free-breathing multi-echo MRI enables hepatic PDFF/R2* quantification without breath-holds, but respiratory motion can affect R2* estimation through motion-induced field variations. We investigated whether respiratory motion sensitivity is reduced at 0.55T versus 3T and developed a time-resolved free-breathing 4D MRI approach without respiratory binning. Methods: A navigator-embedded multi-echo stack-of-stars sequence was implemented. Ten subjects were scanned during free breathing and deliberate bulk motion at both 3T and 0.55T. Data were reconstructed using motion-averaged, motion-resolved, and time-resolved approaches. Quantitative performance was also evaluated in a PDFF/R2* phantom using Cartesian and radial acquisitions. Results: Phantom experiments showed close radial-Cartesian agreement for R2* and PDFF at 3T. At 0.55T, R2* showed good agreement over the low-to-moderate range but higher uncertainty at high R2*, where larger radial-Cartesian PDFF differences were also observed. R2* was substantially less sensitive to respiratory motion at 0.55T than at 3T, whereas PDFF was relatively insensitive at both field strengths. Under bulk motion, time-resolved reconstruction provided robust R2* and PDFF measurements, with particularly high consistency between free-breathing and bulk-motion acquisitions at 0.55T. Conclusion: R2* quantification was less sensitive to respiratory motion at 0.55T than at 3T, while PDFF remained relatively insensitive. Time-resolved reconstruction provided additional robustness to bulk motion. Reduced susceptibility effects at 0.55T and time-resolved reconstruction may provide complementary advantages for motion-robust free-breathing hepatic R2* and PDFF quantification.

An automated fact-checking system returns a label: the claim is true, or it is false. In many such systems the verdict remains the primary output. What is generally missing is a record of which document settled the question, of what would have had to be different for the verdict to change, or of whether the same claim, reworded, would have been judged the same way. We call the missing piece a warrant: a separate statement of what was guaranteed and on what grounds. Formal methods produce evidence of this kind, and regulation is beginning to ask for it, since the Digital Services Act and the AI Act both call for auditable evidence about how systems behave. Surveys of automated fact-checking are usually organised by pipeline stage, and treat logic as one technique among many. We organise the field by what is being formalised instead, which gives five levels: the claim, the reasoning, the system doing the checking, the ecosystem the claim spreads through, and the regulatory obligation. Sorting 121 works into those levels, two patterns stand out. Most of the relevant formal machinery already exists, but it was built for other domains and has rarely been applied here, and the gap is widest for verifying the checking system itself. Several stages of the routine professional fact-checkers follow also have no stated correctness criterion, and two of them, writing a claim in checkable form and correcting a verdict already published, are not formally specified in any work we coded. We close with open problems, each with a suggested first step.

We relate the monodromy group of a branched cover to the monodromy groups of its restrictions. We show that the presence of a transposition in a restricted monodromy group significantly constrains the monodromy group of the original branched cover. Using this result, we complete the sparse trace test algorithm, which numerically verifies whether a set of solutions to a sparse polynomial system is complete. Along the way, we develop a generalization of the notion of a trace test in the setting of branched covers.

Fofana spaces, introduced on the basis of Wiener amalgam spaces, have attracted some interest recently and have found applications in the field of partial differential equations. In this paper, we study the normed Köthe structure of the predual spaces $\mathcal{H}(p^{\prime}(\cdot),q^{\prime},\alpha^{\prime})$ of Fofana spaces with variable exponent $(L^{p(\cdot)}, \ell^{q})^{\alpha}$, where $1\leq p(\cdot) \leq \alpha \leq q\leq \infty$. As an application of this investigation, we identify the Köthe duals and Köthe biduals of these two spaces, and we obtain a predual of $\mathcal{H}(p^{\prime}(\cdot),q^{\prime},\alpha^{\prime})$. Finally, we prove that neither $(L^{p(\cdot)}, \ell^{q})^{\alpha}$ nor $\mathcal{H}(p^{\prime}(\cdot),q^{\prime},\alpha^{\prime})$ is reflexive.

We prove the lower bounds \[ B_\infty>0.51,\qquad L>0.51, \] where $B_\infty$ is the locally univalent Bloch constant and $L$ is Landau's constant, improving the bound $\frac{1}{2}+2\cdot10^{-8}$ of Chen and Shiba. The argument passes to the logarithm $g=\log f'$ of a normalized locally univalent Bloch function, where the Bloch condition becomes a one-sided linear constraint on $\operatorname{Re} g$; positive Toeplitz moment matrices then provide a finite-dimensional outer relaxation for the low logarithmic coefficients, and any non-negative dual vector for a linear program over that relaxation certifies a bound. Floating-point linear programming is used only to discover such dual vectors; the same duality also certifies the second-derivative bounds that control the Taylor allowances and the coefficient caps that contract the cover. An independent arbitrary-precision interval-arithmetic program reconstructs every witness and checks a finite cover of the normalized coefficient body by $1179$ boxes, the smallest certified radius being $0.51003$. All numerical premises were verified with Arb at $80$ decimal digits.