Papers

Bell sampling efficiently learns the stabilizer group, and hence the stabilizer nullity, of pure states with little magic, a primitive underlying tomography and certification of low-magic states. Real devices, however, only prepare noisy images of the target, which we model as a Pauli channel acting on the ideal state; the resulting noisy state generically has no exact Pauli stabilizers. Existing structure learners for mixed states rely on such exact stabilizers. Agnostic tomography does not, but its guarantees scale exponentially in the nullity $t$. We show that the ideal stabilizer group remains encoded in the noisy state as the set of Pauli operators under which it is invariant. We give Bell-sampling algorithms that learn the group to accuracy $\varepsilon$ for states of nullity at most $t$. The difficulty is that noisy samples break the group structure pure-state learners rely on, so more samples can erase structure rather than reveal it. We resolve this with a finder-verifier scheme that extracts stabilizer structure from partially corrupted sample batches while certifying proposed updates. For sufficiently weak global depolarizing noise, both samples and runtime are $\mathrm{poly}(n,t,1/\varepsilon)$ when the channel's total error probability is at most of order $\varepsilon n/t$. Up to a constant total error probability ($\approx 0.16$), samples remain polynomial while classical processing costs $2^t$, and for any error probability below one a $4^t$ overhead suffices. Arbitrary Pauli channels exhibit the same three regimes, with more restrictive thresholds. For weak Pauli noise, this closes much of the gap between agnostic learners such as stabilizer bootstrapping and polynomial pure-state algorithms.

Existing convergence analyses of Muon either assume exact orthogonalization or analyze classical Newton–Schulz polynomials, and guarantee only stationarity, so it is unresolved what Muon's five tuned Newton–Schulz steps preserve and whether that suffices to reach a prescribed neural-network training loss. We establish a finite-time training guarantee that accounts for both momentum accumulation before orthogonalization and the tuned finite-step update. For full-batch training of a sufficiently wide two-layer ReLU network with fixed random output weights and a positive-definite limiting neural tangent kernel, we prove that Muon reaches any target empirical squared loss $\varepsilon>0$ with high probability over initialization. For every momentum parameter $\mu\in[0,1)$, a target-dependent constant learning rate proportional to $(1-\mu)\sqrt{\varepsilon}$ yields a hitting-time bound of $O((1-\mu)^{-1}\varepsilon^{-1/2})$, with other problem parameters fixed. The sufficient width is independent of both target accuracy and momentum. The analysis shows that the tuned Newton–Schulz map preserves alignment with the momentum buffer while bounding the update's spectral norm. Control of gradient variation near initialization transfers this alignment to the current gradient, ensuring descent until the target is reached without requiring exact orthogonalization. Numerical experiments support these mechanisms at widths below the sufficient theoretical threshold: gradient-update alignment remains above the analytical reference, and all 30 runs across six widths and five student initializations on a fixed teacher-student dataset reach the target loss while maintaining kernel positivity.

We derive the sub-Riemannian geodesics of the affine-additive group using the Pontryagin Maximum Principle (PMP) and compute the associated cut times. We then proceed to construct the Carnot-Carathéodory sphere of the affine-additive group as well as the flask surface; the latter is the analogue of the Pansu sphere (bubble set) in the first Heisenberg group.

Understanding the speed with which various classes of quantum systems can scramble information is a key goal of quantum information theory, with relevance to both fundamental physics and the study of the efficiency of quantum algorithms. Famously, such understanding enabled Hayden and Preskill to show that, under the assumption that black hole dynamics may be modelled by a Haar-random unitary, old black holes act as ”mirrors”, reflecting infalling quantum information back out again effectively instantaneously. In this work, we investigate which aspects of this mirror behaviour survive beyond the Haar-random setting by considering a random free fermionic model of black hole dynamics. We find that the rate of information release is governed by the underlying representation-theoretic structure; such a black hole acts as a ”polarised mirror”, retaining information encoded in low fermionic-degree irreps while reflecting information encoded in high fermionic-degree irreps much more rapidly. As a result of the retention of low-degree information, we show that faithful recovery of the infalling quantum information is impossible until all but a vanishing fraction of the black hole has evaporated. However, augmenting the dynamics with a fixed Clifford unitary can restore their reflective behaviour, even though the ensemble's frame potential remains unchanged and far above its Haar value. Remarkably, we find that such black holes can outperform their fully Haar-random counterparts: in the high-fidelity limit, recovering a single-qubit message requires asymptotically approximately $37\%$ fewer emitted qubits.

Uncertainty quantification (UQ) for random partial differential equations (PDEs) is ubiquitous in computational science and engineering. However, classical spectral solvers for this class of problems face the curse of dimensionality, and existing neural solvers often ignore the stochastic structure that makes moments and calibration tractable. We introduce a stochastic separable physics-informed neural network, dubbed S$^{2}$-PINN, that represents the solution $u(t,\mathbf{x},\mathbf{Z})$ of a random PDE with a learnable Gaussian spatial dictionary, Fourier temporal features, and a generalized polynomial chaos (gPC) stochastic basis, coupled by a low-rank Canonical Polyadic (CP) tensor decomposition core. The method is trained with a hybrid strong-form and gPC-projected residual loss. Our theoretical analysis establishes that the separable class is dense in $L^2$ under mild conditions, and the projected residual corresponds exactly to a stochastic Galerkin constraint. Furthermore, we show that mini-batch projection coefficients are logarithmically dependent on the number of gPC modes, and that the orthogonality penalty controls the conditioning of the learned spatial dictionary. Using four manufactured random PDE benchmarks, we show that S$^{2}$-PINN outperforms nine baselines in terms of mean and variance accuracy, as well as calibration, while using significantly fewer parameters. Further evaluations on non-manufactured Poisson and Darcy problems, a stochastic Navier–Stokes problem, a diffusion scaling study of higher random dimensions, and two stochastic inverse problems reveal the generalization capabilities of the proposed structure. Together, these results support stochastic separability as an effective design principle for physics-informed neural UQ. The code for the experiments can be found in https://github.com/DMax1314/s2pinn

We show that ample stability suffices to apply Teleman quantisation to the endomorphism bundle of the universal representation on a quiver moduli space, and thus in particular to deduce its infinitesimal rigidity. This answers a question left open in our earlier work with Brecan, Franzen, and Reineke on the sheaf cohomology of universal bundles. This sufficiency makes several recent results applicable in the widest possible range, subject only to ample stability, which for coprime dimension vectors guarantees that the Picard rank of the moduli space is maximal.

We construct a finite cyclic $L_3$ presentation (that is, a cyclic $L_\infty$ algebra with brackets vanishing above arity three) of the variational deformation theory defined by the heterotic $G_2$ superpotential near a torsion-free standard embedding, to first order in $\alpha'$. Auxiliary fields for the inverse coframe, spinor derivative, flux and induced tangent connection give a shifted-cotangent Hamiltonian of degree at most four. Eliminating the auxiliary fields recovers the physical functional. On the flat seven-torus, this functional has a nonzero quintic Taylor coefficient in local physical spinor coordinates. For $Y=S^1\times X$, with $X$ a Calabi–Yau threefold, we restrict to the product locus with horizontal gauge and gerbe data. The functional reduces to $ \frac L4\operatorname{Im}\int_X(H+i\,d\omega)\wedge\Omega, $ where $L$ is the circle length and $\Omega=e^{-2\Phi}\Psi$ is the weighted complex volume. The induced $SU(3)$ structure selects a Hermitian tangent Courant subalgebroid. Transverse isotropic lifts in its complexification encode the holomorphic connection and string equations, together with the induced tangent connection, weighted canonical line and gerbe hierarchy. Their Taylor brackets form an $L_3$ algebra whose string part agrees with the known holomorphic heterotic algebra. We then show that this holomorphic theory is obtained by characteristic Hamiltonian reduction of a finite contractible stabilization of the product variational theory, in every cochain degree. While the quotient captures the holomorphic equations, conformal balance, gauge primitivity and leading-flux admissibility are additional conditions on a real representative.

We conducted eMERLIN and Gemini integral field unit (IFU) observations towards TXS 1033+026, a post-merger ultraluminous infrared galaxy, to study the radio continuum and $\rm H\alpha$ and HI 21 cm lines at sub-kiloparsec scales. We find a symmetric, two-sided core- jet structure in both L-($\approx 1.4$ GHz) and C-($\approx 4.8$ GHz) band continuum images. The active galactic nucleus likely has a double-double radio morphology, indicating possible multiple episodes of activity. The Gemini IFU observations provided sub-arcsecond resolution. Results from these observations suggest the presence of a kiloparsec-scale circumnuclear, warped $\rm H\alpha$ disc that rotates around the core. The HI 21 cm maps reveal a complex kinematic structure, with indications of two counter-rotating gas components orbiting the core-jet axis; one of these components counter-rotates relative to the kiloparsec-scale $\rm H\alpha$ disc. However, the true morphology of this structure may be more complex than our interpretation suggests. We estimate a HI 21 cm velocity-integrated optical depth of $\rm 90 \pm 3 \ km \ s^{-1}$. We note that these are the first results to probe $\rm H\alpha$ and cold neutral hydrogen gas in TXS 1033+026 at sub-kiloparsec scales.

We investigate the weakly nonlinear evolution of phototaxis-induced bioconvection in an absorbing and isotropically scattering algal suspension subjected to oblique and normal collimated irradiation. Two hydrodynamic configurations are considered, a rigid lower boundary with either a stress-free or a rigid upper surface. A multiple-scales expansion is carried to third order, and the Fredholm solvability condition yields a Stuart–Landau equation for the amplitude of the critical mode. Oblique irradiation affects the onset threshold in opposite ways in the two configurations. It progressively lowers the critical Rayleigh number beneath a stress-free surface and progressively raises it beneath a rigid surface. Beneath a stress-free surface the onset remains stationary, but the pitchfork bifurcation changes from supercritical to subcritical and becomes strongly subcritical at large incidence angles, where the preferred pattern wavelength also increases markedly. Beneath a rigid surface the critical mode changes from stationary to oscillatory at moderate obliquity, giving a supercritical Hopf bifurcation, and returns to stationary at large obliquity, where the pitchfork bifurcation becomes subcritical.

We determine which homotopy nine-spheres admit positive sectional curvature: they are precisely the four smooth types with vanishing real Dirac index. The other four admit no metric of nonnegative sectional curvature. In particular, we construct a strictly positively curved metric on the exotic Kervaire nine-sphere, answering the longstanding nonnegative-curvature existence question in this dimension. The proof keeps explicit attaching maps throughout. A quaternionic commutator realizes the Kervaire sphere, a mixed representation realizes the Hopf image of the exotic eight-sphere, and a four-periodic normal-framing formula identifies the remaining index-zero class. Following the compatible-disk method, we give the curvature and boundary estimates for the first two models, including an explicit lower bound for the Kervaire metric in terms of the curvature and first covariant-derivative norms of a fixed connection, with the base scale and fiber normalization fixed. For the third model, we construct a positive metric on a cylinder joining a quotient metric to its pullback by a marked right Hopf twist. A four-form modification controls the connection terms involving both left and right quaternionic multiplication. Two positive disk fillings close the cylinder with the prescribed attaching map. A local convolution lemma supplies the smooth gluing while preserving a strict sectional-curvature lower bound.

Purpose: This study extends our fluid-structure interaction (FSI) framework for surgical bioprosthetic heart valves in an experimental pulse duplicator to a transcatheter aortic valve replacement (TAVR) device. We assess hemodynamic and leaflet kinematic agreement across pulse rates and the transferability of calibrated boundary-model parameters. Methods: We compared simulated and experimental pressure, volumetric flow rate, projected dynamic valve area (PDVA), and leaflet kinematics at 60, 70, and 80 beats per minute (bpm). Reduced-order boundary-model parameters were calibrated using only data acquired at 70 bpm and were subsequently held fixed. At each pulse rate, a condition-specific pump-pressure waveform was constructed from the measured upstream pressure and flow rate. The 60 and 80 bpm cases therefore evaluate parameter transfer under measurement-informed upstream forcing. Results: Across the three conditions, normalized root-mean-square errors are 2.88-3.08% for aortic flow rate, 7.64-8.07% for upstream ventricular pressure, 3.50-6.21% for downstream aortic pressure, and 3.07-4.70% for PDVA. The simulations reproduce the principal pressure, flow, valve-opening, and valve-closure features. The downstream aortic pressure and PDVA measurements at 60 and 80 bpm were not used to construct the upstream forcing or recalibrate the model parameters and therefore provide the principal out-of-calibration validation evidence. Conclusion: The results provide conditional experimental bench validation evidence for downstream hemodynamics and valve dynamics under measurement-informed upstream forcing and support boundary-parameter transfer across pulse rates without recalibration. This work advances an experimentally supported, high-fidelity FSI framework for evaluating TAVR device performance.

Complex reasoning queries can be decomposed into directed acyclic task graphs and distributed across heterogeneous LLMs, reducing latency through parallelism and enabling smaller models to solve complex tasks. In practice, however, the suitability of an LLM for a given subtask may be a priori unknown, and execution alone does not reveal output correctness. We propose JOVE, an online framework that jointly assigns executor LLMs and selects intermediate outputs for paid verification. Verification runs asynchronously and is used to improve future allocations, so the system must balance spending on execution now against learning for later. We study how to optimize this trade-off under a long-term budget and a per-query latency constraint, with stochastic, initially unknown LLM service quality, invocation costs, and execution times. JOVE makes execution and verification decisions by solving a sequence of per-query mixed-integer linear programs. Online learning updates task-dependent estimates of LLM quality based on verification feedback, while an information-gain bonus incorporates the value of learning into allocation decisions. Under a natural set of assumptions, we establish sublinear quality-learning regret for JOVE. Across four reasoning benchmarks, JOVE achieves competitive accuracy against standard inference baselines while reducing average cost and latency by at least 3.17 times.

An analog device implements a local Hamiltonian H, but a polynomial P (H) is in general not local, so the device cannot implement it. We carry P (H), to any prescribed accuracy, as the action of a single time-independent local Hamiltonian on an explicitly described invariant subspace. Short chains of ancilla qubits are attached to H. A chain of 2m sites has a unique isolated eigenvalue that is an analytic function of the input vanishing to order exactly 2m, because the input must cross the chain and come back before it can shift the energy at the far end. Chains of different lengths therefore form a triangular family, and a weighted sum of them reproduces a prescribed polynomial term by term. Even chains give the even part and odd chains the odd part, so any polynomial is reached. We prove uniqueness, analyticity and coefficient bounds uniform in the chain length for inputs H of norm below any r < 1. Where the circuit model pays degree 2l in 2l sequential oracle calls, the result here is one Hamiltonian of locality two more than that of H, which pays the degree in O(l^2 + log2^(1/eps)) ancillas and in energy scale. As an application we filter a marked eigenstate of a local Hamiltonian. Composing a synthesised square along the Chebyshev doubling identity works, but its energy scale grows quasi-polynomially with the degree. Iterating instead the exact eigenvalue branch of the two-site chain k times gives a filter on k + 1 ancilla qubits whose error decays geometrically in k, at an energy scale polynomial in the inverse passband width and independent of k, the locality growing by one per stage. In adiabatic optimisation with a rank-one driver, the construction replaces that non-local driver, by a Hamiltonian with O(log n) ancillas and O(log n)- body terms, at an energy scale polynomial in n. Simulations including every ancilla reproduce the spectrum of the ideal algorithm.

In this work, we investigate final-state interaction effects in $B^{\mp}\to K^+K^- \pi^{\mp}$ decays above 3 GeV with a twofold objective: (i) to study $CP$ asymmetry, and (ii) to search for possible signatures of the $X(3700)$ state (also denoted as $X(3720)$). We consider both tree-level and resonant contributions, with the latter arising from a triangle mechanism $B^{\mp} \to \bar{D}^0 D^{\ast \mp} (\to \pi^{\mp} D^0) \to K^+K^- \pi^{\mp}$, in which the $D \bar D \to K \bar K$ rescattering process carries the signature of the exotic $X(3700)$ state. We analyze the dependence of our results on the relative phase between the tree-level and resonant contributions, as well as on other relevant parameters. We estimate the differential mass distribution in the region where the $X(3700)$ may leave a trace, and the $CP$ asymmetry driven by final-state interactions. Our findings are compared with available data for the differential mass distributions and the $CP$ asymmetry. Taken together, these results may contribute to a better understanding of the properties of exotic states and the role of $CP$ asymmetry in $B$-meson phenomenology.

During zirconium carbide oxidation, liberated carbon can remain beneath the oxide or escape as gas, complicating the interpretation of mass measurements. We adapt the small-cell ensemble method using sixteen 140 ps ab initio molecular dynamics trajectories at 873-1273 K under a sustained high oxygen flux with gas removal. The average rates of net mass gain and total carbon transfer into gas or retained chains follow Arrhenius trends. Above 973 K, gas evolution levels off while total carbon transfer increases. The fraction of transferred carbon retained in chains rises from 40 % at 973 K to 66 % at 1273 K. Fits after 40 ps suggest declining carbon transfer rates over time, although not in every trajectory. These results show that carbon partitioning during early oxidation depends on temperature, with increasing temperature above 973 K favouring chain formation over gasification.

We study global bifurcation for Yamabe-type equations on closed Riemannian manifolds with symmetries. For isometric group actions with interval orbit space and a suitable range of exponents, we prove the existence of pairwise disjoint unbounded continua bifurcating from the positive eigenvalues of the Laplace–Beltrami operator that admit invariant eigenfunctions. All nontrivial solutions in these continua change sign. The results cover critical and some supercritical exponents. On spheres and complex and quaternionic projective spaces, we obtain lower bounds on the number of geometrically distinct continua bifurcating from the same eigenvalue.

Integer-valued leaky integrate-and-fire (I-LIF) neurons and spike firing approximation (SFA) reduce temporal training cost by representing spike trains as firing counts and normalized firing rates, respectively. However, applying spiking self-attention (SSA) directly to these compressed query, key, and value representations introduces cross-time interactions that are absent during spike-driven inference. We term this operator-level discrepancy Temporal Interaction Mismatch (TIM). We propose Parallel Time-Aligned Spiking Self-Attention (PT-SSA), which reconstructs consecutive virtual spike slices from either I-LIF counts or SFA firing rates, computes attention only between time-aligned slices in parallel, and sums the per-step outputs. To accommodate the reduced attention output scale under SFA, we further introduce Adaptive PT-SSA, which learns a positive per-block rescaling before the output SFA neuron to improve firing-level utilization. Experiments on CIFAR-10, CIFAR-100, and ImageNet-1K show that the proposed methods substantially reduce train–inference mismatch. On CIFAR-100 with I-LIF, PT-SSA reduces the mean Top-1 gap from 1.85 to 0.29 percentage points. On ImageNet-1K, Adaptive PT-SSA reduces the Top-1 gap from 27.78 to 0.06 percentage points and achieves 74.53% spike-driven Top-1 accuracy. A Triton-fused PT-SSA training kernel retains a $2.91\times$ throughput advantage over recurrent LIF SSA.

Lung ultrasound (LUS) is attractive for tuberculosis (TB) screening at primary-care level, but labelled cohorts are small. Echocardiography carries no such constraint, while sharing the same underlying ultrasound imaging physics, signal processing and B-mode appearance as LUS. We ask whether an encoder pretrained on that high-resource ultrasound domain carries representations that remain usable in the low-resource one. Only the encoder varies, across seventeen encoders spanning three architecture families. Among them, a latent-predictive video encoder pretrained on generic video (V-JEPA2-L) and its echocardiography counterpart (EchoJEPA-L) differ in pretraining corpus alone. The choice among these encoders does not resolve the classification, the whole family spanning 2.50 percentage points against a measurement resolution of 2.71. What moves the task instead is feature conditioning. Standardising the features between the encoder and the classifier improves all seventeen encoders by a mean of +1.23 percentage points at $p=1.5\times10^{-5}$. On the held-out test set every encoder selected on the development folds stands above the baseline system by up to +2.57 percentage points of area under the receiver operating characteristic curve (AUROC), and specificity at 90% sensitivity reaches 79.3% against 60.3%. The contrast specified in advance, EchoJEPA-L against V-JEPA2-L, measures -0.16 percentage points at $p=0.926$. We therefore find no evidence that shared ultrasonic physics alone makes echocardiography a more productive pretraining corpus than generic video, and any advantage, if present, is smaller than this cohort can resolve. The video encoders receive replicated still images, however, so whether this absence of an effect reflects the pretraining domain or a video encoder applied to static frames cannot be separated. The limiting factor is the labelled cohort rather than the encoder.

Multimodal Large Language Models (MLLMs) achieve strong performance across vision-language tasks, yet the internal mechanisms by which visual and textual information are fused across layers remain insufficiently understood. We investigate representative MLLMs from two architectural paradigms: concatenation architectures and native multimodal architectures. We conduct three progressively connected analyses: alignment decoupling identifies which modality changes, attention routing and entropy characterize how cross-modal information is distributed, and intrinsic dimensionality examines how fusion reshapes feature spaces. Separately, we perform causal intervention experiments as a validation of the resulting interpretation. As a supplementary analysis, we use visual CKA to examine the Platonic Representation Hypothesis. Together, these analyses reveal two distinct fusion pathways: concatenation models follow a text-first, vision-later pathway, whereas native models exhibit earlier visual-textual co-adaptation and feature-space reorganization. This work provides a mechanistic perspective for understanding multimodal fusion and supports architecture-aware diagnostics of multimodal representations.

In this paper, we study a generalised family of fractional BBM equations on the $d$ dimensional torus $\mathbb{T}^d$ for $d\geq 1$. We establish low regularity local and global well-posedness results on the $H^s(\mathbb{T}^d)$ scale that improve upon the works of Bona and Chen (2003) and Kim and Kwak (2026). We also prove endpoint global well-posedness for the cubic regularised Benjamin-Ono equation in $H^{1/2}(\mathbb{T})$. Furthermore, we obtain a well-posedness result for the generalised fractional BBM in the spaces $L^{k+1}(\mathbb{T}^d)$ where $k$ is order of the polynomial nonlinearity. As an application of this result, we show that for a certain range of values and for a suitable randomisation of the initial data, the model is almost surely globally well-posed in $H^s(\mathbb{T}^d)$ for $s\geq 0$. Lastly, we show that the family exhibits a strong form of ill-posedness in $H^s(\mathbb{T}^d)$ for $s<0$ in the form of an infinite loss of regularity at all initial datum.

We prove that all excited states $-\sin(nx)$, $n\geq2$, of the De Gregorio equation on the torus are nonlinearly unstable in the sense of Hadamard. More precisely, perturbations arbitrarily small in $H^2$ leave a fixed $H^1$ neighborhood of the state. For every $n\geq2$, the linearized operator has a real eigenvalue $\lambda_n\in(0.56,0.6)$. To prove this, we transform the eigenvalue problem into a Fuchsian equation on the complex disk and obtain a matching condition for the eigenvalue. This condition is verified rigorously using interval arithmetic. The nonlinear instability follows from a bootstrap argument in the spirit of Guo, Hallstrom, and Spirn.

Agentic Reinforcement Learning (RL) trains LLM agents through multi-turn interactions with external tool environments. Its multi-turn nature exposes two system-level bottlenecks unaddressed by existing agentic RL frameworks. First, end-to-end training throughput is constrained by the slowest trajectories to complete, yet optimizing per-GPU utilization alone scatters rollout progress across many groups, delaying the completion of enough groups to unblock the next training step. Second, tool sandboxes are statically over-provisioned by their declared memory ceilings, leaving most physical memory stranded while replicating near-identical state across sandboxes launched from the same prompt. We present VenusRL, a fully disaggregated agentic RL system that addresses both bottlenecks. VenusRL's priority-aware action scheduler uses length-prediction heuristics to identify sample groups whose completion is most likely to unblock the next training step, and pushes them ahead of others across batch admission, KV Cache residency, and cross-worker request orchestration. VenusRL's environment resource manager combines a memory-aware admission threshold with a template-keyed page-sharing pool, packing more sandboxes per node while preserving strict memory isolation via write-protected page table entry aliasing and copy-on-write. Across representative agentic RL workloads, VenusRL achieves up to 4.24x end-to-end training speedup over state-of-the-art baselines and reduces environment cost by up to 89%.

We present a space-time finite element formulation for the transient analysis of geometrically exact shear-deformable beams. The formulation treats space and time within a unified finite element framework and employs a mixed approach in which translational and angular velocities are introduced as independent fields. The rotation field is parametrized using nodal rotation (pseudo-)vectors and a suitable objective interpolation of the triad field is employed. The resulting formulation supports generally curved beam structures, including geometric kinks and rigid joints. Furthermore, time-dependent material domains can be represented directly through the geometry of the space-time surface, enabling the treatment of non-material boundaries without modifying the underlying beam formulation. Numerical examples demonstrate convergence to solutions obtained with classical time-stepping schemes, objectivity of the formulation, and the influence of the space-time stabilization. Finally, the sliding spaghetti problem illustrates the applicability of the proposed approach to axially moving continua.

The $^{45}$Sc($p,\gamma$)$^{46}$Ti reaction plays an important role in both hydrostatic and explosive nucleosynthesis. During hydrostatic oxygen and silicon burning in massive stars, including dynamic processes such as convective carbon-oxygen (C-O) shell mergers, it acts as a bottleneck that regulates the reaction flow in the Sc-Ti mass region. In oxygen-neon (ONe) novae, the ejecta indicate the production of elements up to the Fe group, as observed in V1974 Cygni, and the $^{45}$Sc($p,\gamma$)$^{46}$Ti reaction links nuclei above Ca to the Fe region. In core-collapse supernovae (CCSNe), it influences the production of the radioactive isotope $^{47}$Sc. At present, the thermonuclear reaction rate is based on statistical model calculations. In this work, we report on measurements of the $^{45}$Sc($p,\gamma$)$^{46}$Ti reaction performed using the 5~MV accelerator at the Nuclear Science Laboratory, University of Notre Dame, over a laboratory proton energy range of 526–1275~keV. We present the first direct measurements of the resonance strengths for six resonances at $E^{\rm lab}_{\rm R} = 917.4$, 1026.0, 1031.1, 1049.7, 1059.4 and 1257.5~keV, together with integrated resonance strengths at $E^{\rm lab} = 555$, 630, 700, 761 and 871~keV. For resonance energies below the lowest directly measured energy, available transfer-reaction data were used to estimate the resonance strengths. An updated thermonuclear reaction rate is derived, and its astrophysical implications are discussed.

The ability of a device to localize itself within its surroundings is a fundamental prerequisite for spatial computing. Visual-inertial odometry (VIO) has proven to be a cost-effective and accurate solution for this task. Robots, wearables, XR devices, and drones can benefit significantly from efficient implementations of VIO since they allow for cooler, lighter, and cheaper devices with longer battery life and a better user experience. In this work, we propose to enhance the efficiency of a VIO system by leveraging the Hexagon DSP, a commodity co-processor present in many modern smartphones and XR devices. Our approach offloads the visual frontend of a stereo-inertial odometry system to the DSP while keeping the backend on the main CPU. By optimizing the implementation for the DSP architecture, we achieve significant reductions in power consumption and latency compared to CPU-only execution. Our system, HexVIO, demonstrates a 67% reduction in power consumption or an 86% increase in throughput on a commodity smartphone, with the ability to sustain long-term real-time 30 fps tracking for 0.83 W, corresponding to ~18 hours of tracking on the testing device. These results highlight the potential of commodity DSPs for enabling all-day visual-inertial tracking in robotics and mobile devices.

The investment acceleration principle is a heuristic for modelling investment time series out of consumption time series. The model presented herein develops a disaggregated accelerator equation whose coefficients are the weights of a Kohonen neural net that represents firms' decision-making. According to this model, investments take place when managers recognise emerging technological patterns. Furthermore, a technique borrowed from the theory of self-organising systems is used in order to disentangle innovation-driven investments from plant-replication investments.

Information Processing Capacity (IPC) is a powerful system-agnostic metric for quantifying a dynamical system's computational capability and is widely used in quantum reservoir computing. However, standard IPC suffers from severe computational limitations. Computing IPC involves estimating how well the system can reconstruct, via linear regression, an (in principle) infinite family of orthogonal polynomial functions of delayed inputs. In practice, this evaluation must be made finite, so we need only to consider polynomials up to a chosen maximum degree. Moreover, the computational complexity for computing IPC grows combinatorially with the considered maximum degree and delay. Here, we introduce Kernel-IPC (KIPC), a scalable framework that uses kernel methods to compute the total IPC without explicitly enumerating basis functions. This allows us to account for the full (infinite) basis (without degree truncation). We also provide a null-hypothesis test for statistically comparing the KIPC of two dynamical systems. We validate KIPC on an echo state network and demonstrate its utility for quantum reservoir computing on a disordered spin chain.

The exact limiting distribution of a volatility target index has recently been established under a log-normal assumption on the risky asset. In this paper, we show that the structural limit remains valid under a broad class of stochastic volatility processes. In addition, we show that, when the limit of the joint distribution of the volatility target index and the driving Brownian motions is considered, an extra independent Brownian motion must be involved. Besides the structural limit theorem, we derive a correction formula for the expected quadratic variation of the discrete rebalancing volatility target index, under the assumption that the volatility of the underlying risky asset is a deterministic function of time. As a consequence of the discrete correction formula, it is shown that, as the rebalancing time step $\Delta t\to 0$ and the observation window parameter $\lambda \to 1$ simultaneously along a path, the expected quadratic variation converges to the target variance if and only if $(1-\lambda)^{-1}\Delta t \to 0$ along the same path. Numerical results are provided to support the structural limit, using the local volatility model and the Heston stochastic volatility model as examples, as well as the effectiveness of the discrete correction formula.

A central topic in economics and finance is the valuation of strategic games and bets, of investments providing uncertain future cashflows, and of other asset-like structures and contracts. Often, such valuation involves a probabilistic model, random variables, and computing expectation values of complex payoffs. Extending beyond this classical framework, a scenario emerges where assets are non-commuting operators and the inherent uncertainty is described by quantum states. In this work, we combine such notions of quantum finance with a graph-theoretic framework and ideas from contextuality. We discuss exclusive quantum assets and introduce scenarios when holding such assets can provide advantages over holding classical assets. In particular, we consider a "quantum market" based on nonlocal games such as the CHSH game and demonstrate that this setting can function as a market with well-defined financial structures. We provide upper bounds on the fair prices of the quantum assets based on graph-theoretic quantities like the independence number and the Lovász theta number. Our insights into markets of non-commuting assets help to elucidate what a financial system in a world filled with quantum technology could look like.

As dexterous hands proliferate, collecting data and training policies separately for every morphology becomes increasingly impractical. Scalable cross-embodiment learning therefore requires a unified representation that captures shared manipulation structure while preserving morphology-specific control. Differences in hands, tasks, datasets, and control interfaces prevent existing studies from isolating the effects of representation, pretraining, and architecture. We introduce DexJoCo-X, a benchmark and toolkit for controlled comparison across seven representative dexterous hands, six single-arm and bimanual tasks, and 2,100 balanced demonstrations. DexJoCo-X provides a matched multi-hand, multi-task protocol with common scenes, success criteria, and execution interfaces, redesigned glove-to-hand mappings, and an automated pipeline that expands reviewed demonstrations across randomized scenes. Using $\pi_{0.5}$, Ego-Pi, and Being-H0.5, we examine whether a shared action interface is sufficient for multi-hand learning. Expanding $\pi_{0.5}$ to an 80-dimensional bimanual output yields near-zero success. Ego-Pi preserves the pretrained action head through interleaved prediction and supports per-hand multi-task learning, but remains ineffective for seven-hand joint training. By contrast, Being-H0.5 combines cross-embodiment pretraining, a unified action space, and embodiment-aware experts, enabling one policy to control all seven hands. Within this architecture, function-aligned action slots achieve 47.7% mean success, compared with 47.0% for native coordinates and 33.1% for DexLatent. These results show that cross-embodiment representation depends on the entire learning system: action coordinates, pretraining, and architecture must jointly separate shared manipulation structure from embodiment-specific control.