Papers

Several public-key schemes base their security on the belief that inverting a unit of a group ring is hard. A recent result showed that this belief is false on a quantum computer when the group is abelian. To restore security, designers moved to non-abelian groups, especially dihedral groups, believing that the hardness of the dihedral hidden subgroup problem (HSP) would protect the scheme. This paper shows that unit inversion is a different problem and does not require an HSP solver. Instead, it can be solved by a change of basis that splits the group ring into small matrix blocks. We prove that unit inversion is polynomial-time, classically and quantumly, when an efficient generalized Fourier transform exists, the group ring is semisimple, and the largest matrix block has polynomial size. Dihedral group rings satisfy these conditions because their irreducible representations have dimension at most 2 and an efficient Fourier transform exists. We give an explicit reversible quantum circuit for the block-inversion step and validate it in a register-level simulator. We also identify the exact structural boundary where the method stops and propose a candidate construction in the surviving regime under a new, clearly stated security assumption. The constructive results are supported by reproducible software artifacts and experiments.

The 2026 LUX-ZEPLIN (LZ) high energy nuclear recoil search reports one event at $248\pm23_{\rm stat}\pm23_{\rm sys}~\mathrm{keV}$ and finds the elastic isovector interaction $\mathcal L_6^v$ locally favored at about $3.3\sigma$ in the heavy dark matter regime. We examine whether this recoil scale can arise from resolved nuclear response within the elastic interaction and compare its spectral, target, and annual modulation behavior with endothermic dark sector excitation. Covariant matching correlates four Galilean operators, removes the longitudinal spin response algebraically, and fixes interference between density and orbital spin orbit amplitudes. The GCN and JJ55 xenon shell model calculations give a second natural xenon cancellation at $211$ and $214~\mathrm{keV}$. In the heavy mass regime, its position changes by less than $0.01~\mathrm{keV}$ from a dark matter mass of $200~\mathrm{GeV}$ to the asymptotic limit. A curvature weighted isotope centroid reproduces the position and residual depth of the natural xenon minimum. Direct $^{40}$Ar calculations shift the nuclear feature to about $350$ and $425~\mathrm{keV}$, whereas endothermic excitation follows reduced mass scaling set by the dark state splitting. At a dark matter mass of $1~\mathrm{TeV}$, the endothermic Ar to Xe scale ratio is $1.082$, compared with $1.63$ to $2.01$ for the nuclear calculations. Elastic scattering gives a few percent annual modulation in the adopted halo model, while endothermic solutions near the maximum laboratory halo speed show much larger seasonal variation. These scaling and timing behaviors provide tests of a target-dependent nuclear cancellation against an excitation energy set by dark sector kinematics.

The quantum model of the two-sentence liar paradox proposed by Aerts, Broekaert, and Smets is an early example of the use of quantum formalism to describe cognitive dynamics. Our reconstruction is primarily pedagogical in intent, but it also leads to a number of clarifications, and to some new observations, concerning the structure of the model. Rewriting the model in Dirac notation, we make explicit the distinction between truth values originating from a decision and from semantic inference, and show that the associated enlargement of the one-sentence state space corresponds to a factorization with respect to which the non-paradoxical configurations are separable while the genuine liar state is entangled. We also derive the Hamiltonian generating the four-state cyclic evolution, express it in compact operator form, and give the resulting transition probabilities in closed form. We emphasize that the liar cycle admits a unitarily equivalent representation in the four-dimensional truth-only space, where the unmeasured liar state is separable, so the dimensional enlargement is not required by the unitary part of the dynamics; it is required, however, by the measurement structure. The enlargement is also required by the dynamics as soon as revision processes are admitted, in which states with identical truth content but different origins have different successors, the origin degree of freedom then acting as a minimal form of cognitive memory. We conclude by discussing the possible relationship between the model and more general deliberative processes.

We present the case of a Gottesman-Kitaev-Preskill (GKP) state-enhanced optical interferometry with detailed analysis of the phase sensitivity for both the SU(2) and SU(1,1) interferometers. The conventional quantum-enhanced SU(2) interferometer, employing coherent light at one input port and squeezed light at the other, is compared with a modified configuration using coherent light and a GKP state. While it is known that the squeezed vacuum state is the optimal Gaussian resource input mode when paired with the coherent state, we show that the finite-energy GKP state with sufficiently broad envelope outperforms the squeezed vacuum injection, irrespective of the presence of optical losses. This can be attributed to the enhanced robustness coming from the availability of multiple squeezed peaks in the GKP case. However, because lowering the mean photon number reduces the GKP envelope width, the squeezed vacuum input performs better when compared with a GKP state of equal or lower mean photon number. We also observe that optical losses tend to diminish the relative advantage of either input state, since both states approach the (unsqueezed) vacuum state asymptotically. Our work demonstrates the direct application of finite-energy GKP states in optical interferometry along with a methodology for estimating the quantum Fisher information (QFI) and presents a phase estimation procedure using non-Gaussian resources in comparison with conventional Gaussian states.

Understanding the brain's mechanisms is crucial in neuroscience, particularly for simulating natural intelligence and advancing artificial general intelligence (AGI). Liu et al. (2024) and Deco et al. (2025) propose that quantum entanglement may underlie the synchronization of millions of neurons, introducing the Liu-Chen-Ao (LCA) hypothesis of entangled nerve fibers. However, directly testing this idea remains challenging. Here we employ a nonlocal many-body wave equation, introducing a generalized probability-wave framework to model collective behaviors among adaptive, interacting agents, particles, or neurons. This approach enables testable eigenmodes, offering an indirect means of examining the LCA hypothesis by observing patterns in collective trading behaviors. These patterns, rooted in behavioral psychology, are thought to mirror the internal brain's decision-making and underlying mechanisms. Our analysis of Chinese intraday stock market data shows that adaptive entangled game modes explain 82%-94% of decision patterns, sharply contrasting neoclassical finance predictions assuming independent rational agents. Additionally, 2-12% of actions adapt to news, events, and environmental changes, marked by rapid equilibrium shifts, while truly independent behaviors make up less than 5%. These results empirically support the LCA hypothesis and underscore the need to simulate the brain's mechanisms and generate adaptive, entangled modules for AGI. They also expose the shortcomings of conventional artificial neural networks (ANNs) that depend on vast, opaque parameters. By combining ANN-based AI with probability-wave-based entangled brain simulations, machine learning enables the creation of human-like processing units (HPUs). Such HPUs promise more efficient and robust AGI, particularly for embodied intelligence and robotics.

Collective excitations can survive profound changes in the microscopic degrees of freedom that generate them. We track a layer-odd collective response from an exact weak-coupling hybridisation anchor into the paired regime of an attractive Hubbard bilayer and find that its Hamiltonian sensitivities evolve in a manner consistent with a crossover from single-particle interlayer hybridisation towards collective pair superexchange. At weak coupling, an exact identity for identical tunnel-coupled layers fixes a relative-phase Gaussian kernel zero at $2t_h$, independent of the intralayer hopping. Sign-free determinant quantum Monte Carlo reveals an interaction-driven softening of the many-body spectral scale without analytic continuation, while Gaussian response theory supplies the continuous pole interpretation and shows a shift from layer-density to relative-pair-phase character. In the paired regime, the characteristic response scale acquires a growing fractional sensitivity to the intralayer hopping and an interaction dependence partway towards the $1/U$ law. These results show how a collective excitation can be tracked across a fermion-to-composite-boson crossover while constraining changes in its microscopic drive.

Encoding classical data into quantum systems is a foundational step in the execution of nearly all quantum algorithms, and a critical bottleneck in realizing practical quantum advantage. This review provides a comprehensive account of the concepts, algorithms, and practical considerations associated with quantum data encoding. We trace the development from its early conceptual foundations to recent advances, considering commonly used access models, such as quantum state preparation, unitary synthesis, QRAM and block encoding. We survey the circuit size, depth, space-time tradeoffs, as well as non-Clifford resources required for fault-tolerant implementation. We also discuss the roles of different access models in quantum algorithms. Special attention is given to structured data, such as sparse data, Boolean functions and data represented by tensor networks. This review bridges theory and applications, serving both as a pedagogical guide for newcomers and as a reference for active researchers. We also highlight the pivotal role of quantum data encoding in quantum computing and provide insights into future directions that will enable quantum advantage.

An expository essay containing some new results. A learner holds a prior belief over Boolean maps that answer a finite set of $Q$ questions, and receives answers one by one. Each answer carries surprisal and can clear predictive uncertainty about both the question asked and questions still unasked. We quantify this effect by the leverage: table entropy cleared per bit of surprisal received. Taking expectations over the truth prior and the question order, define the aggregate leverage as the ratio of expected uncertainty cleared to expected surprisal received. It equals one for independent answers and can exceed one for correlated answers. At finite size, this ratio is determined exactly by a single sequence: the mean entropy $G_\ell$ of the answers to $\ell$ questions. As the number of input bits grows at fixed asked fraction $t=\ell/Q$, a limiting increment profile $\gamma(t)$ determines the macroscopic learning curve. With $\eta_0$ the limiting initial entropy per question, the leverage becomes $L(t)= \frac{\eta_0-(1-t)\gamma(t)} {\int_0^t\gamma(x),dx}$. For exchangeable priors, de Finetti's representation gives a constant bulk profile $\gamma(t)$: deduction is confined to a boundary layer at $t=0$, and the leverage is forced to a hyperbolic form, as surprisal grows linearly. By contrast, we construct a simplicity prior with nontrivial bulk learning by grading Boolean maps by their polynomial degree over $\mathbb{F}_2$ and allocating weight across degree classes through a CDF $F$. Reed-Muller capacity then yields $\gamma(t)=1-F(t)$. This realizes any nonincreasing profile taking values in $[0,1]$, together with the corresponding macroscopic leverage curve.

The study of two-body charmed anti-charmed baryonic $\overline B\to {\bf B}_c \overline {\bf B}_c$ decays using the topological amplitude approach is revisited. We include the $b\to u\bar u q$ contributions, in addition to the $b\to c\bar c q$ contributions, to these decays. The topological decomposition of $\overline B\to {\bf B}_c(\bf {\bar 3_f}) \overline {\bf B}_c(\bf { 3_f})$, ${\bf B}_c(\bf 6_f) \overline {\bf B}_c(\bf { 3_f})$, ${\bf B}_c(\bf {\bar 3_f}) \overline {\bf B}_c(\bf {\bar 6_f})$ and ${\bf B}_c(\bf 6_f) \overline {\bf B}_c(\bf {\bar 6_f})$ decay amplitudes are updated accordingly. Although the $b\to u\bar u q$ contributions are Cabibbo-Kobayashi-Maskawa (CKM) suppressed in $\Delta S=-1$ transitions, their effects are significantly amplified in $\Delta S=0$ transitions, as the relative size of the CKM factors in $b\to u\bar u q$ and $b\to c\bar c q$ contributions in $\Delta S=0$ transitions is enlarged by $\lambda^{-2}$, roughly a factor of 20, from the one in $\Delta S=-1$ transitions. Present data in $\overline B\to {\bf B}_c(\bf {\bar 3_f}) \overline {\bf B}_c(\bf { 3_f})$ decay rates allow or even slightly prefer non-negligible $b\to u\bar u q$ contributions. These $b\to u\bar u q$ contributions can allow much larger rates for $B^-\to \Xi_c^0 \bar \Xi_c^{-}$, $\overline B{}_s^0\to \Lambda_c^+ \bar \Xi_c^{-}$ and $\overline B{}^0\to \Xi_c^+ \bar \Xi_c^{-}$ decays than those only have $b\to c\bar c d$ contributions. Several modes containing only $b\to u\bar u q$ contributions in $\overline B\to {\bf B}_c(\bf 6_f) \overline {\bf B}_c(\bf { 3_f})$, ${\bf B}_c(\bf {\bar 3_f}) \overline {\bf B}_c(\bf {\bar 6_f})$ decays are also identified. Measuring these decays will be interesting and useful in clarifying the role of $b\to u\bar u q$ contributions in two-body charmed anti-charmed baryonic $\overline B$ decays.

Given a superconformal gauge theory at a fixed loop order, BPS states can be studied in two ways — by enumerating cohomology classes of a nilpotent supercharge or by diagonalizing the anomalous dimension matrix. The second one allows for a deeper look at how holographic theories distinguish between operators based on whether they are dual to horizonless geometries or black holes. To this end, we carry out the diagonalization in $\mathrm{U}(N)_k \times \mathrm{U}(N)_{-k}$ ABJM theory with $N$ as a formal parameter. This makes it possible to define trajectories of operators and focus on the fortuitous ones which are characterized by being BPS at only finitely many values of $N$. In contrast to $\mathcal{N} = 4$ Super Yang-Mills, where it has been numerically prohibitive to study more than one of these, ABJM gives us access to 16 such trajectories along with their descendants. We show that they take an especially simple form at large $N$ where they agree with the predictions of integrability. We also show that many of them, as with black holes, can only be dressed by certain types of gravitons and comment on how this exercise in cohomology also has implications for properties of the full operators. Finally, we show that the gap to the first non-BPS state in ABJM theory qualitatively differs from that of $\mathcal{N} = 4$ Super Yang-Mills in the expected way.

Runaway-electron avalanches in tokamak plasmas can be limited by kinetic instabilities driven by the non-Maxwellian runaway distribution. We formulate a reduced model for the quasi-steady state in which the total plasma current and bulk electron temperature are prescribed, while the inductive electric field is determined self-consistently from the partition between Ohmic bulk current and runaway-electron current. Because the wave growth time is short compared with the current-decay time, we consider a marginal-stability regime, in which whistler-wave drive by the runaway electrons balances collisional damping. The resulting states separate into three regimes: a subcritical Ohmic regime without an avalanche, an avalanche regime in which runaway growth relaxes the inductive field to the avalanche threshold, and an instability-regulated regime in which self-excited whistler waves enhance momentum-space diffusion and limit the runaway current. In the instability-regulated regime, the whistler wave spectrum forms a narrow ridge, and low-energy runaway electrons carry most of the runaway current.

Cavity magnonics is moving beyond the conventional paradigm of coherent spin–photon hybridization toward the controlled engineering of dissipative and coherent interactions, Floquet dynamics, and quantum fluctuations. This Perspective examines how these ingredients reshape collective dynamics and open new avenues for quantum state engineering, transport, and sensing. We discuss the role of dissipative coupling and anti-$\mathcal{PT}$ symmetry in enabling long-lived collective modes and enhanced spectral response, and highlight Floquet engineering as a means of engineering nonreciprocal transport and phase-controlled interactions. We then review recent progress in quantum magnonics, ranging from squeezed and entangled magnon states, including the squeezing of thermal magnons, to prospective schemes for preparing magnonic Schrödinger-cat states. We also discuss how parametric driving and active gain strongly modify hybrid susceptibilities and amplify magnon–photon response. These advances expand the scope of cavity magnonics beyond conventional polariton physics, establishing it as a versatile platform for sensing, transduction, spin transport, and hybrid quantum technologies.

The capacitance of thin-film diodes based on undoped semiconductors are dominated by injected charge carriers rather than doping-induced carriers. However, an analytical framework of the capacitance in these devices has remained elusive. Here, we derive an analytical description of the capacitance, fully accounting for injected charge carrier and electrode charge effects. Based on these findings, a method to extract the built-in voltage in these devices is presented. The theoretical framework is substantiated numerically by drift-diffusion simulations and experimentally on organic solar cells.

We perform a pulsation analysis of OO Dra using Light Curve data from TESS and present the first identification of six dipole modes as doublets from the primary star in OO Dra. The phases and amplitudes of these pulsation modes were analytically reconstructed. Among the six identified doublets, four are pulsating in $Y_{10x}$ mode with pulsation axis along the tidal axis, and two in $Y_{10y}$ with a pulsation axis orthogonal to tidal axis and the angular momentum axis. Our findings suggest that the primary star in a non-synchronized, post mass-transfer OO Dra could be a tidally tilted $\delta$ Scuti pulsator.

We present GridapGeosciences$.$jl, a new parallel distributed-memory Julia package for the numerical approximation of partial differential equations on general manifolds. Our abstract approach to generating discrete manifold domains relies on mesh refinement in general, and is implemented within the Gridap finite element library, whose high-level interface enables seamless definition of both intrinsic and extrinsic variational formulations. GridapGeosciences$.$jl features the cubed sphere manifold, which is used in this study to showcase the functionality of GridapGeosciences$.$jl in different applications. The first application involves scalar transport where we develop intrinsic formulations of common stabilisation terms, which are shown to be equivalent to well-known extrinsic stabilisation formalisations. Such stabilisation terms are used to develop an intrinsic formulation of the two-dimensional thermal shallow water equations that includes upwinded numerical fluxes. The final application is a linearisation of the Boussinesq equations where we demonstrate the capacity of GridapGeosciences$.$jl to capture both surface and vertical dynamics on a three-dimensional manifold.

Sklar's theorem separates the marginals of a joint distribution from its dependence structure. We apply this viewpoint to Born statistics generated by local quantum measurements. For non-product two-qubit states, the dependence nuclei over all local binary projective measurement contexts determine the state up to at most a discrete double-spin-flip ambiguity. The corresponding scalar optimization, combined with the quantum total correlation, reproduces global quantum discord.

Proximal shunt obstruction is the leading cause of ventriculoperitoneal (VP) shunt failure in pediatric hydrocephalus and is closely tied to the near-wall shear environment at drainage holes. We used computational fluid dynamics (COMSOL) to decouple local wall-shear-stress (WSS) control via catheter-tip geometry from global drainage control via a valve opening. A cylindrical ventricle domain with Newtonian CSF ($\rho$ = 1000 kg/m$^3$, $\mu$ = 1 mPa$\cdot$s) and $\Delta P \approx$ 10 mmHg was solved under laminar Navier-Stokes flow while sweeping distal hole spacing, hole count/diameter, and a simplified valve constriction. Mesh-independence was achieved (minimum element size $\approx$ 0.021 mm; distal-hole velocity converged to $\approx$ 1.18$\times10^{-3}$ m/s). Perpendicular separation of the two most distal holes increased total outflow by $\approx$ 22% (2 mm vs 0.5 mm) and raised distal lateral-wall WSS by $\approx$ 19%, whereas longitudinal shifts of upstream holes produced only small changes. A valve opening near 0.166-0.17 mm set system drainage to $\approx$ 20 mL/h across geometries, indicating capacity is valve-limited while local WSS is geometry-controlled. The selected tip uses two conical holes (0.5 mm ID) in four rows with 1.4 mm spacing, concentrating WSS at the distal lateral walls, the surfaces where obstruction occurs, without exceeding clinical drainage targets. These findings yield design rules: prioritize distal-pair spacing, reduce hole count with smaller conical openings to elevate protective WSS, and regulate outflow with the valve. The framework provides a clear path to benchtop validation, long-term adhesion assays under mapped WSS, and anatomically realistic CFD.

The thesis develops symbolic representations of dynamical systems in finite-dimensional commutative real algebras. The algebraic framework (orthogonal idempotents, zero divisors, and the structure of finite-order algebras) supports algebra-valued Fourier and Laplace transforms and Walsh-function-based system identification. The methods yield exact, coordinate-free vectorial solutions for motion in non-inertial reference frames, including a generalized Larmor theorem, the Foucault pendulum, motion in central positional-force fields, and the two-body problem in arbitrarily rotating reference frames. This English edition is an audited LaTeX reconstruction of the 1995 original, with an editorial note documenting provenance.

Antiferromagnetic skyrmions evade the skyrmion Hall effect, but compensation suppresses their conventional topological charge Hall signal. We predict a semiclassical nonlinear topological orbital response of an isolated skyrmion in a $\mathcal{PT}$-symmetric hexagonal antiferromagnet without spin-orbit coupling. In the diffusive, weak-emergent-field regime, the spin-dependent emergent Lorentz force reshapes the carrier distribution, generating a local orbital Hall-current correction and a local orbital accumulation, both quadratic in the applied electric field. The current correction requires spin-asymmetric longitudinal scattering, whereas the accumulation survives spin-symmetric scattering. When the spin-diffusion length greatly exceeds the strip width, the current correction persists while the accumulation approaches zero. Both signals are even under electric-field reversal, odd under reversal of the skyrmion topological charge $Q$, and helicity independent within this model. These symmetries enable rectified detection and distinguish this mechanism from the $Q$-even quantum-regime topological orbital Hall effect.

Quantum mechanics sets the ultimate bounds on photon-limited sensing, yet practical measurements attaining these bounds are known only in special cases. This is particularly the case for visual sensing problems, where the goal is to infer features of a distant object based on the spatial structure of the light field it emits or reflects. Because of the potentially complex structure of such objects and fields, constructing optimal measurements on them is a challenging task. Here, we apply learned diffractive optics to state discrimination and parameter estimation of coherent and diffraction-limited incoherent light fields under a restricted photon budget. Optimized directly on each task's figure of merit, without prior knowledge of the optimal measurement, the physically realizable diffractive optical neural networks substantially outperform standard measurements and approach the quantum limits for a given number of photons as well as in the asymptotic limit.

We explored potential associations between ongoing mass transfer and the pulsation properties of $\delta$ Scuti primaries in a sample of 17 oscillating eclipsing Algol systems. For this purpose, we combined binary modelling, updated O-C analyses, and frequency characterization based on TESS photometry. To ensure homogeneity, the $T_{\rm eff}$ of the components were derived using a consistent SED fitting approach. From the binary solutions and O-C diagrams, we determined the mass transfer indicators (Q, dP/dt, and dM/dt) and examined their relations with the dominant pulsation period and amplitude. For the full sample, the results indicate weak to moderate positive trends, with the strongest relation found between logdP/dt and logPpuls, while the relations involving dM/dt and pulsation amplitudes are weaker and statistically insignificant. After excluding the two prominent outliers, R CMa and BW Del, the correlations between logPpuls and the mass transfer indicators become statistically more significant, including relations with dP/dt, Q, and dM/dt under both conservative and non-conservative assumptions. These relationships may reflect the indirect effects of mass transfer on the structure of the accreting primary and on the orbital configuration, potentially reducing tidal constraints and allowing shifts toward longer pulsation periods. However, the large dispersion and limited sample size indicate that these relationships remain poorly constrained. Our results suggest that pulsation properties are primarily governed by intrinsic stellar parameters and the well established Porb-Ppuls relation, while ongoing mass transfer may contribute as a secondary factor. Although the present sample does not allow firm conclusions regarding the role of mass transfer, this study provides a homogeneous observational framework for future investigations based on larger samples and improved constraints.

We classify the metric radio emission associated with eruptive (CME-associated) and confined flares using the sample of events between 2010 and 2016 identified by Kazachenko (2023). We find striking differences in the occurrence of radio bursts between the two classes of flare: for soft X-ray flare sizes above M1.4, confined flares largely lack Type II (1% association rate) and Type IV (6%) emission. Approximately 15% of the sample of $\geq$M1.4 confined flares are associated with impulsive-phase Type III bursts. On the other hand, eruptive flares are associated with Type II, Type III (both impulsive and late phase), and Type IV bursts 45-60% of the time. The different types of radio burst are associated with different drivers (IIIs with electron beams, IIs with shocks, IVs with post-flare loops), so it is striking that the connection of all three burst types to eruptive flares is so pronounced. These results can be interpreted in terms of the reconnection topology of the principle candidate flare types, viz., reconnection between closed field lines for confined flares and X-point reconnection in a CSHKP model for eruptive flares, with interchange reconnection for jet-type flares and Type III bursts.

Stochastic models of gene expression typically begin with a microscopic model of transcription and propagate its statistics to the RNA distribution. Here we develop a doubly stochastic framework in which RNA production is Poisson conditional on a time-varying transcription rate $\lambda(t)$. For RNA lifetimes drawn independently from an arbitrary finite-mean distribution, we derive the RNA Fano factor in terms of the lifetime survival function and the autocovariance of $\lambda(t)$. For a Poisson degradation process with rate $\mu$, the survival kernel provides an exponential temporal filter, and the result depends only on the mean, variance, and normalized autocorrelation of $\lambda(t)$. These quantities may be calculated from an explicit rate model or, under ergodicity and adequate sampling, estimated from a sufficiently long rate trajectory. We validate the data-driven estimator using simulated transcription-rate trajectories, without supplying the known autocorrelation to the estimator. We also obtain exact analytical results for transcription-rate dynamics modeled by a discrete M/M/1 process and by drift-diffusion with reflecting, periodic, or first-passage-reset boundaries, and verify each result by direct simulation of the coupled transcription-rate and RNA copy-number processes.

Finite-range alignment can end either in a single flock or in several noninteracting clusters, yet convergence results rarely determine which outcome follows from a given finite-particle state. We study a one-dimensional normalized alignment model with a hard interaction cut-off and obtain exact predictions in an expansive regime. Velocity order is invariant, so pair separations are nondecreasing and the communication graph evolves through finitely many irreversible edge deletions. On each fixed graph, the group inverse of the random-walk Laplacian gives the total relative displacement remaining before relaxation. Comparing this displacement with the available interaction slack selects the next deletion and yields a finite recursion for the complete switching sequence, terminal partition, limiting cluster velocities, and internal geometry. For path configurations, an explicit Green kernel gives a necessary-and-sufficient fragmentation criterion and a sharp critical alignment rate, including asymptotic boundary contact at criticality. A spectral-geometric condition extends the theory to an open set of initially nonordered velocities, while a common self-weight extension covers both self-excluding and self-including local averages. Numerical computations reproduce the thresholds and multi-event cascades. The results provide an exact finite-size theory of fragmentation and terminal state selection for a class of finite-range interacting particle systems.

Complex organic molecules (COMs) are typically observed in the warm inner envelopes of Class 0 protostars. In more evolved Class I sources, COM emission is confined to the compact inner disk and obscured by high dust opacity, but the FU Orionis-type binary L1551 IRS 5 offers a valuable opportunity to probe disk chemistry, as its outburst luminosity thermally sublimates ices out to large radii. We sought to spatially resolve the origins of COMs in this system to distinguish between central radiative heating and shock-induced chemistry driven by heterogeneous accretion pathways. We analyzed high-angular-resolution ALMA archival data, focusing on COMs (e.g., CH3OH, CH3OCHO) and the shock tracer SO, and compared their spatial morphologies and kinematics to diagnose the excitation conditions associated with different accretion flows. We find that the COM emission in L1551 IRS 5 arises from both radiative heating and localized accretion shocks. In the northern source, the widespread low-excitation COM emission is primarily consistent with thermal heating by the recent outburst. This source also exhibits dual-mode accretion with distinct chemical signatures, with COMs along the spiral arm tracing steady equatorial circumbinary disk-to-circumstellar disk accretion and high-excitation COMs with bright SO along the eastern disk surface tracing a vertical envelope-to-disk streamer impact. In the southern source, methanol is confined to the southeastern streamer impact site, whereas SO forms a ring-like structure at the tidal truncation radius. We attribute this difference to differential chemical survival timescales. L1551 IRS 5 thus serves as an ideal laboratory to investigate how shock chemistry and binary-regulated accretion shape the chemical structure of protostellar disks.

Maintaining precise beam coalignment is essential in laser interferometry, particularly for interspacecraft missions where angular misalignments introduce tilt-to-length coupling noise and risk complete link failure. This work presents a comprehensive theoretical and experimental framework for the beam angle-locked loop, which maintains coalignment between two interfering beams. Minute angular misalignments are detected via differential wavefront-sensing signals, which are used as the error signal for feedback control. A detailed linear control model incorporating an angle detector, a digital filter, a proportional-integral-double-integral servo, a digital-to-analog converter, and a beam-steering mechanism is developed. Using loop transfer functions, we establish a noise-propagation model that quantifies the contributions of individual components to both out-of-loop and in-loop angle errors. The analytical results are experimentally validated using a transponder-based interferometric link spanning two optical benches, with a hexapod simulating spacecraft attitude jitter. The measured transfer functions and coalignment performance agree well with theoretical predictions, yielding a pointing stability better than 10 urad$/\sqrt{\text{Hz}}$ between 0.2 mHz and 1 Hz. Furthermore, a loop-optimization strategy is demonstrated to minimize angle misalignment within a target frequency band by tuning the servo gain, without requiring hardware modifications. This validated framework provides a reliable architecture for designing and optimizing active beam alignment in laser interferometry.

Metric-affine gravity provides a natural geometric framework in which spacetime curvature, torsion, and non-metricity are treated as independent degrees of freedom, leading to novel cosmological dynamics beyond General Relativity. A generic consequence of such theories is the emergence of effective interactions among the cosmological fluids, even in the absence of explicit phenomenological couplings. Interestingly, the above happens while the Standard Model of Particle physics remains unmodified. In this work, we investigate interacting cosmological models that arise from metric-affine gravity and analyze their implications for the background evolution of the Universe. We derive the modified continuity equations governing the matter, radiation, and dark-energy components, highlighting the geometric origin of energy exchange in the dark sector. We discuss how these interactions modify the expansion history and can effectively mimic evolving dark-energy behavior. The resulting cosmological scenarios are confronted with the most recent observational data from Type Ia Supernovae (Pantheon+), Cosmic Chronometers, and Baryon Acoustic Oscillations (DESI DR2). Moreover, using model selection criteria, e.g., Akaike Information Criterion, Bayesian Information Criterion and the Bayesian Evidence, we compare the aforementioned models against the standard $\Lambda$CDM model. We find that the proposed framework performs slightly better than $\Lambda CDM$, in the light of the data sets considered here. Our analysis demonstrates that metric-affine-induced interactions constitute a viable and theoretically motivated alternative for the description of the Universe.

Peculiar velocities trace gravitational dynamics directly, complementing density-based clustering as wide-field spectroscopic surveys (DESI, Euclid, PFS) and kinetic Sunyaev-Zel'dovich (kSZ) measurements enter the precision era. Observational analyses of pairwise velocities and the pairwise kSZ signal remain largely restricted to linear and quasi-linear scales ($\gtrsim20-30$ $h^{-1}Mpc$), despite substantial cosmological information available at smaller separations. We present a simulation-calibrated likelihood for $v_{12}(r,a)$, built on the exact pair conservation equation and PyCAMB HMcode-2020 non-linear clustering, and validate it against the QUIJOTE and TNG300-3 suites across resolution, particle sampling, box size, and redshift. Using QUIJOTE, we show that extending the fit to non-linear scales tightens the $1\sigma$ uncertainty on $\Omega_\mathrm{m}$ and $\sigma_8$ by $74\%$ and $81\%$ at $z=0.5$ ($r_{\rm min}=4$ $h^{-1}Mpc$), and by $70\%$ and $74\%$ at $z=0$ ($r_{\rm min}=8$ $h^{-1}Mpc$), relative to the linear-regime baseline ($r_{\rm min}=50$ $h^{-1}Mpc$) (all at fixed $r_{max}=140$ $h^{-1}Mpc$); $\sigma(f\sigma_8)$ tightens by up to $86\%$, and the joint $\Omega_\mathrm{m}$-$f\sigma_8$ Figure-of-Merit improves by up to $9.1\times$ relative to the same baseline. These constraints are conditional on $h$ fixed at its QUIJOTE fiducial value, due to a near-degenerate response with $\sigma_8$; jointly sampling $h$ shifts and widens them substantially. This framework provides a validated route to exploiting that information in upcoming direct peculiar-velocity, redshift-space, and kSZ analyses.

Crystallisation of liquids often occurs at solid surfaces, via heterogeneous nucleation or prefreezing. Understanding this process is crucial for controlling crystal morphology in thin films and developing efficient nucleating agents - especially for polymers, typically processed in a molten state. However, the efficiency of nucleation and prefreezing with respect to crystallisation kinetics and semicrystalline polymer morphology has not been well studied and remains unclear. Here, we address this challenge by conducting a systematic study of substrate-induced crystallisation in dewetted droplets of the model polymer poly($\varepsilon$-caprolactone) (PCL) on various crystalline and amorphous substrates. Using polarized light optical microscopy, droplet crystallisation temperature was monitored and varied across the substrates, revealing three scenarios: close-to-homogeneous nucleation on glass and silicon; heterogeneous nucleation on ordered and disordered carbon-rich substrates; and prefreezing on graphene. The temperature-dependent nucleation rate was analysed and found to obey classical nucleation theory for all systems except PCL on graphene, where it diverges as all the droplets crystallise simultaneously. The highest in- and out-of-plane PCL crystal orientation is found on graphene, where the epitaxially grown lamellae extend vertically over several hundred nanometres. These results demonstrate that prefreezing has a superior influence on crystallisation kinetics and crystal morphology, making prefreezing substrates perfect nucleating agents.

Sample-based quantum diagonalization (SQD) has emerged as a promising route for quantum-centric supercomputing, relying on classical diagonalization of the molecular Hamiltonian within a hardware-sampled determinant subspace. However, its accuracy degrades in strongly correlated regimes where the relevant determinant space exceeds what finite-shot sampling can capture. In this work, we introduce Quantum Wavefunction Augmentation via Variational Autoencoders (Q-WAVE), a hybrid method that combines determinants sampled via SqDRIFT Krylov circuits and configuration interaction singles and doubles (CISD) determinants with generative machine learning. Using a custom $\beta$-annealed variational autoencoder (VAE) model, Q-WAVE iteratively expands this basis toward the variational ground state. The VAE learns the wavefunction's primary support structure from the combined hardware and CISD seed in a continuous latent space, generating new dominant determinants beyond any fixed excitation hierarchy. The resulting compact wavefunction exceeds what can be extracted from raw hardware samples alone. We demonstrate sub-millihartree accuracy compared to full configuration interaction for $\text{H}_2\text{O}$ and $\text{N}_2$ dissociation. Finally, we establish Q-WAVE's scalability on a 52-qubit ethylene system (achieving sub-millihartree accuracy versus CCSD(T)) and a highly correlated 60-qubit $\text{Cr}_2$ stress test that attains chemical accuracy upon a final perturbative correction.