Hellings-Nordtvedt theory is a vector-tensor theory in which a vector field $A_μ$ is nonminimally coupled to curvature through two independent interactions $A^2{\cal R}$ and $A^μA^ν{\cal R}_{μν}$. When supplemented by a potential whose zero-energy minimum occurs at nonzero $A^2$, the restricted $A^μA^ν{\cal R}_{μν}$ sector is known to admit black-hole and neutron-star solutions with a monopole-like asymptotic vacuum structure. We examine whether this structure is a generic consequence of the nonzero vector vacuum or instead relies on the special Ricci-tensor coupling. By analyzing the field equations near spatial infinity, we show that the asymptotic vacuum condition is incompatible with generic nonzero values of both couplings and instead selects two allowed single-coupling sectors. The $A^μA^ν{\cal R}_{μν}$ sector reproduces the known monopole-like asymptotics, whereas the $A^2{\cal R}$ sector admits an asymptotically flat Schwarzschild metric with a nontrivial radial vector field. We further compute the Noether mass in the $A^2{\cal R}$ sector, derive the corresponding Solar-System constraints, and construct neutron-star configurations. Although the weak-field deviation is constrained to be small, neutron stars can still show appreciable departures from both general relativity and the Ricci-tensor-coupling sector in their masses, radii, and moments of inertia. Our results identify that the $A^2{\cal R}$ sector of massive Hellings-Nordtvedt theory as a viable and useful framework for studying strong-field compact objects with a nonzero vector vacuum while remaining compatible with weak-field tests.

We prove equidistribution of two pairs of statistics on boxed plane partitions: (volume, trace) and (corner-hook volume, number of corners). The proof relies on different 3d visualizations of the corresponding non-intersecting path systems. In particular, we obtain a new visual proof for a volume generating function of plane partitions. We also introduce a new statistic called the cohook area on ordinary partitions, and prove that it is equidistributed with the area of partitions.

We study the weakly nonlinear saturation of the flutter instability of a planar Cosserat rod in a viscous fluid driven by a terminal follower force. This instability, established in our preceding work as a Hopf bifurcation of a non-self-adjoint linear operator, produces stable limit-cycle oscillations in the fully nonlinear overdamped dynamics. Here we derive an analytical description of the emergence of this limit cycle near threshold. Working close to the critical follower force, we perform a multiple-scale expansion about the compressed straight base state and systematically remove secular growth at higher orders. Solvability at cubic order, enforced using the adjoint eigenmode of the non-Hermitian operator, yields a Stuart-Landau amplitude equation for the critical oscillatory mode. The Landau coefficients are expressed as explicit inner products involving the critical eigenmode, its adjoint, and quadratic corrections. The resulting reduced theory predicts a supercritical Hopf bifurcation with a steady-state tip oscillation amplitude scaling as the square root of the distance from threshold. These predictions rationalize the near-threshold scaling observed in nonlinear simulations and provide an analytical normal form for the onset of self-sustained beating in pressure-driven soft robotic arms at low Reynolds number.

In the theory of combinatorial algebras, there is a sequence of embeddings between Kleene's second model, van Oosten's model, and Scott's graph model. We prove that none of these embeddings can be reversed. We also prove nonembedding results for the effective versions of these models, and in addition we discuss relativized embeddings. This answers several questions from the literature.

This article establishes a bilinear embedding for second-order divergence-form operators with complex coefficients, characterized by the simultaneous presence of first-order terms and negative potentials. This work provides a further development of the theory initiated by Carbonaro and Dragičević for the homogeneous case, and recently extended by the second author to cases where first-order terms or negative potentials were treated in isolation. We work in the general setting of arbitrary open subsets of $\mathbb{R}^d$ under Dirichlet, Neumann, or mixed boundary conditions. Our main contribution is the introduction of a unified notion of generalized $p$-ellipticity that extends all its predecessors and serves as the natural condition for the bilinear inequality. Methodologically, we overcome the rigidity of the Bellman-heat method on arbitrary open subsets by introducing a novel sequence-based approach that unifies and simplifies the previous techniques. As fundamental applications, we prove the boundedness of the $H^\infty$-calculus on $L^p$ and establish $L^p$-maximal regularity. Moreover, we show that this generalized $p$-ellipticity provides a sufficient condition for the $L^p$-contractivity and $L^p$-analyticity of the generated semigroup.

Nitrogen-vacancy (NV) centers in diamond are a leading platform for solid-state quantum sensing and quantum information processing. While most optical studies rely on the visible fluorescence associated with the triplet transitions, the infrared singlet transition near $1042$ nm, which is typically considered dark within the singlet manifold of the NV optical cycle, provides an alternative optical channel. Here, we report wavelength-resolved optically detected magnetic resonance (ODMR) measurements of this infrared emission. We directly observe ODMR contrast in the $1042$ nm emission and analyze its dependence on the magnetic field. The field-dependent spectral dispersion of the ODMR signal demonstrates that the spin-state information encoded in the NV center is transcribed to the infrared singlet emission through the spin-selective intersystem crossing, in close analogy to the visible fluorescence readout. These results establish infrared ODMR as a high-fidelity optical readout pathway. Crucially, by extending spin-state transcription directly into the $1300-1600$ nm range, this work demonstrates a direct, conversion-free interface between diamond spin-qubits and standard telecommunication infrastructure, bypassing the efficiency bottlenecks of active frequency conversion and benefiting from the already well-developed technologies in this range of the electromagnetic spectrum.

A three-dimensional $\mathcal{N}=4$ gauge theory is constructed whose Higgs branch realizes the affine closure of the cotangent bundle of the minimal nilpotent orbit of $\mathfrak{sl}_n$. This space is a symplectic singularity recently identified by Fu and Liu as a $\mathrm{U}(1)$ hyperkähler quotient of the closure of the minimal nilpotent orbit of $\mathfrak{so}_{2n+2}$. The theory arises by gauging an $\mathrm{SO}(2)\cong\mathrm{U}(1)$ subgroup of the flavour symmetry of $\mathrm{SU}(2)$ SQCD with $n+1$ flavours. The Hilbert series is computed and the stratification is determined. A non-simply laced magnetic quiver is proposed whose Coulomb branch reproduces the same singularity. Evidence is thereby provided for a mirror pair involving a non-simply laced quiver, further tested through quiver subtraction and Hasse diagram inversion. A related $\mathbb{Z}_2$ quotient of the magnetic lattice is also analysed, and the exceptional behaviour in the case $n=2$, where $A_1 \cong C_1$, is explained. This construction provides a concrete example in which the Higgs-branch structure associated with a non-simply laced magnetic quiver can be inferred and validated through its mirror dual.

We present a multi-wavelength study of the massive protocluster G286.21+0.17 (G286) using \emph{JWST} near-infrared imaging and ALMA H$^{13}$CO$^{+}$(1--0) observations. The \emph{JWST} images uncover a compact ($\sim$0.5 pc) hub-filament system (HFS), comprising a dense central hub connected by at least four converging filaments seen in absorption, along with multiple H$_2$ protostellar jets/outflows. The hub hosts dense core G286c1. The H$^{13}$CO$^{+}$ emission confirms this HFS over [$-$19.2, $-$16.4]~km~s$^{-1}$. The \emph{JWST} images further trace prominent photodissociation regions around the H\,{\sc ii}~region~A, powered by a B-type star. The radial distribution of ALMAGAL 1.38 mm core properties reveals steep power-law slopes toward the hub center. Within the inner hub (r < 8'', $\sim0.1$~pc), the core number density follows $ρ~[\rm pc^{-2}] \propto r^{-2.4\pm0.5}$, the surface density scales as $Σ~[\rm g~cm^{-2}] \propto r^{-1.0\pm0.2}$, and the enclosed core mass varies as $M_{\rm core}~[M_{\odot}] \propto r^{-1.2\pm0.2}$, while core diameters remain approximately constant ($D_{\rm core}~[\rm AU] \propto r^{-0.1\pm0.1}$). These trends, along with filament mass accretion rates of $7\times10^{-6}$--$1.8\times10^{-4}$~$M_\odot$~yr$^{-1}$, support a competitive accretion scenario in which gravitational focusing enhances core growth toward the hub center. Filament linewidths increase from tail/outer-region to head/hub-region, consistent with gravity-driven turbulence. However, the absence of a preferred alignment between velocity gradients and gravitational force directions may indicate a dynamically evolved system. The HFS likely formed through large-scale gas layer interactions and compression by the adjacent H\,{\sc ii} region. Overall, star formation in G286 appears regulated by filamentary accretion, competitive core growth in the hub, and stellar feedback.

In this study, we explore the behavior of photon added coherent states in a deformed harmonic oscillator subjected to dissipative decoherence. We use $q-$deformation as our nonlinear function to model our system. By adjusting the deformation parameter, we show that $q-$deformed photon added coherent state (DPACS) exhibit greater nonclassicality and resilience to decoherence compared to those of a standard harmonic oscillator. Additionally, we investigate the nonclassical properties and entanglement of DPACS under decoherence induced by interaction with a dissipative photon-loss environment.

This paper addresses the dynamic event-triggered control for a class of discrete-time nonlinear systems described by a difference-algebraic representation (DAR), using a gain-scheduled controller. An outstanding aspect of the proposed method is the incorporation of information about the system's nonlinearities into the control law and the trigger function. The proposed event-triggered mechanism also incorporates information on the asynchronous terms induced by the event-based sampling. All these ingredients enable the derivation of a less conservative co-design condition for the simultaneous design of the gain-scheduled control law and the dynamic triggering mechanism to ensure the asymptotic stability of the closed-loop system. An estimate of the region of attraction of the origin of the closed-loop system is obtained to guarantee the closed-loop system's operation within the domain of validity of the DAR. Then, an optimization problem is formulated to reduce the number of events and enlarge the estimated region of attraction. Finally, the effectiveness of the proposed condition is illustrated by a numerical example.

Modern implementations of path integral molecular dynamics (PIMD) simulations of distinguishable particles frequently make use of high order factorization schemes for the Boltzmann operator to expedite convergence of equilibrium averages. Among these methods is the generalized Suzuki-Chin factorization (GSF), which is accurate up to fourth order in the imaginary-time step. In this work, we show that the GSF decomposition of the Boltzmann operator is applicable to bosonic PIMD, and results in an improved convergence of estimators. In particular, we show that the recently developed quadratic scaling bosonic PIMD need not change when using the GSF. The GSF scheme is implemented as a re-weighting factor for observables, without affecting the sampling generated by the standard, second-order, primitive factorization. We study the effect of this factorization for bosons in a harmonic trap and a sinusoidal potential. We also assess the effectiveness of GSF in calculating fermionic expectation values for harmonically-trapped atoms. In all these cases, we find that the GSF speeds up convergence with the Trotter number by a factor of $\sim 2-4$ across a wide temperature range, at only a modest computational cost.

A consistent non-compact axion cosmology requires a non-periodic field, an effective field theory valid sufficiently above the inflationary scale, and a small non-QCD contribution to the potential that tilts the axionic vacuum landscape in order to trigger a timely domain-wall collapse. All conditions can be met by the dilaton -- the pseudo-Nambu-Goldstone boson of spontaneously broken approximate scale invariance.

We announce a series of results on the combinatorial study of the q-Catalan triangle (C_{n,k}(q)), defined by C_{n,0}(q)=q^{n(n-1)/2} and C_{n,k}(q)=C_{n,k-1}(q)+q^{n-k-1}C_{n-1,k}(q). We establish combinatorial interpretations via a universal combinatorial family of seven components: four families of pattern-avoiding permutations weighted by inversion or co-inversion statistics, Dyck paths, binary words and triangulations. We introduce the mirror polynomial C-tilde_{n,k}(q)=q^{n(n-1)/2}C_{n,k}(q^{-1}), prove its dual recurrence and co-inversion interpretation. The q,p-Catalan triangle and a multivariate generalization opening the way to cyclotomic q-analogues are introduced. Theorems on the q-Catalan triangle via 312-avoiding permutations and the mirror recurrence are proved completely here. This is the first paper of series W0-W5 on classical and q-deformed interpretations of the Catalan triangle.

We show that Glauber dynamics for $ p$-spin glass mixes exponentially slowly at inverse temperatures larger than a constant times $ \ln (p)/p $ for large enough $ p $. This is done by analyzing the energy landscape using Gaussian decompositions and establishing a bottleneck bound.

A sufficiently large information flux in recurrent neural networks, quantified by the mutual information between successive network states, is considered a prerequisite for rich information processing capabilities. This raises the question of whether biological neural networks, such as cortical microcolumns, may be structurally organized to enhance information flux. To investigate this possibility, we study a simplified model of the cortical layer 5 architecture, in which a densely and strongly interconnected core population is embedded within a larger supporting network. Surprisingly, we find that the embedding network exerts a pronounced flux-enhancing effect on the core dynamics. Systematic reverse-engineering analyses reveal that the embedding network provides two key contributions: first, it generates effective biases that shift core neurons into a higher-entropy operating regime; second, it supplies stochastic fluctuations that prevent the network from becoming trapped in simple fixed-point or oscillatory attractors through the mechanism of Recurrence Resonance. We further show that the information flux can be increased even beyond the biologically embedded case by applying individually optimized biases to the core neurons, and that these biases can emerge from a simple self-organization principle. Our findings are relevant both for the functional interpretation of biological neural circuits and for the design of artificial recurrent systems such as reservoir computers.

Underwater images suffer from severe wavelength-dependent light absorption and scattering, and turbidity due to suspended particles, degrading visual quality for applications in autonomous underwater vehicles (AUVs), marine biology, archaeology, and offshore infrastructure inspection. Classical IFM inadequately capture nonlinear underwater light behavior, while purely data-driven methods lack physical interpretability. This paper proposes a three-stage network named ADR, that extends the underwater image formation model with additional terms to perform underwater dehazing, followed by Retinex-based enhancement and attention-enabled U-Net++ refinement. Experiments on UIEB and UFO-120 benchmark datasets demonstrate competitive performance with state-of-the-art methods.

Dielectric metasurfaces have introduced a new paradigm for substance detection by exploiting their resonant properties to enhance light-matter interaction. This enhancement can be used for sensing either through refractive index changes or through absorption-based mechanisms. Most works focus on high-quality factor resonators, aiming to increase field confinement in the vicinity of the resonant structure to improve sensitivity. In this work, we explore an alternative approach based on low-quality factor, fully dielectric metasurfaces, with engineered modes to enhance near-field concentration. We investigate different topologies that, despite their low-quality factors, achieve sensitivity and detection performance beyond what is typically reported for low-Q structures in the literature. This improvement is enabled by near-field engineering of the evanescent modes, allowing us to control the spatial distribution of the electromagnetic field and maximize its overlap with the analyte. Our results show that careful mode engineering provides a powerful strategy to boost sensing performance without relying on ultra-high-Q resonances.

Agentic AI systems are entering software engineering workflows, yet empirical evidence on how industrial organizations actually adopt them remains sparse. We present a qualitative interview study with sixteen practitioners across twelve companies of varying size and domain. This study characterizes the current agentic AI adoption state of these companies, employing a six-level maturity framework adapted from established AI-driven organizations. The findings reveal that seven companies operate at Level~1 (AI Assistants), four companies at Level~2 (AI Compensators), and only one in Level~3 (Multi-Agent Orchestration), with large and safety-regulated organizations among the most advanced adopters. The primary finding is a capability-deployment verification gap, four companies demonstrated higher-level experimental AI capabilities but cannot integrate them into production workflows because adequate output verification mechanisms are absent, leaving human-in-the-loop as the only trusted verification mechanism. This gap is shaped by four recurring barriers: context window of LLMs constraints especially when diverse knowledge aggregation is needed, under-performance on proprietary programming languages and protocols, non-determinism incompatible with qualification standards, and data confidentiality concerns. Two interdependent dimensions of this gap emerge from these findings (information asymmetry and qualification absence) framing a core open problem for industrial agentic integration.

This work focuses on the fourth order correlations $χ^{BQ}_{31}$, $χ^{QB}_{31}$, $χ^{BQ}_{22}$, $χ^{BS}_{31}$, $χ^{SB}_{31}$, $χ^{BS}_{22}$, $χ^{QS}_{31}$, $χ^{SQ}_{31}$, $χ^{QS}_{22}$, $χ^{BQS}_{211}$, $χ^{QBS}_{211}$, $χ^{SBQ}_{211}$ of baryon number $B$, electric charge $Q$ and strangeness $S$ at finite temperature, magnetic field and vanishing quark chemical potential. The study is carried out in the framework of a three-flavor PNJL model, considering both cases with and without inverse magnetic catalysis effect. We find that, fourth order correlations $χ^{BQ}_{31}$ at chiral restoration phase transition is more sensitive to the magnetic field than other second order and fourth order correlations and fluctuations, and can be served as a more effective magnetometer of QCD.

Focused electron beam induced deposition (FEBID) is an additive manufacturing technique uniquely suited for fabricating nanoscale 3D prototypes for a range of applications, including spintronic devices. However, the variation of growth dynamics associated with electron beam translation and sample interaction volumes results in structures with non-uniform composition when fabricating intricate 3D geometries. Herein, we measure changes in atomic composition and corresponding changes in magnetic induction in 3D ferromagnetic nanostructures with overhanging elements, e.g. bridges or arches. To investigate the effects of electron beam translation, we fabricated 41 Co and Fe nanowire (NW) structures with growth angle relative to the optic axis varying from 0° to 90°. The (scanning) transmission electron microscopy techniques of electron energy loss spectroscopy and off-axis electron holography were performed to map the NW elemental composition and magnetic induction as a function of NW growth angle. Comparison of the results reveals a reduction in metal content with increased oblique growth angle in FEBID NWs. The magnitude of metal content reduction can be tuned by controlling electron beam parameters, and ferromagnetic NWs with approximately equal metal content at growth angles from 0° to 60° were fabricated by using the lowest viable electron beam voltage and the highest viable beam current to reduce the interaction volume and increase the metal content, respectively.

In the shallow water approximation, the cross-sectional profiles of laboratory rivers satisfy a differential equation here shown to be formally the Friedmann equation of cosmology ruling the evolution of Anti-de Sitter universe. The ensuing cosmic analogy provides a counterintuitive Lagrangian for the transverse river profile. Extremizing the corresponding action corresponds to extremizing the friction force on the river bottom and the energy dissipation rate. Analysis of the second variation establishes that this extremum is a maximum.

In this paper, we study the asymptotic behavior of Jacobi biorthogonal polynomials. A Darboux-type formula is established using the method of steepest descent. In the proof, we construct an appropriate contour to apply the Rodrigues formula. Our result reduces to the classical Darboux formula in the orthogonal case.

We study the $α'$ corrections to self-dual gravitational instantons in the context of the four-dimensional Cano--Ruipérez action, which can be obtained by the compactification of the Bergshoeff--de Roo heterotic string effective action on $\mathbb{T}^{6}$ followed by a truncation and a field redefinition. We show that the metric of spaces of self-dual curvature does not receive any corrections, but their (initially trivial) dilaton and axion fields do, owing to their couplings to Gauss--Bonnet and Pontrjagin densities. We find the generic form of the corrections of the dilaton and axion fields for the Gibbons--Hawking multi-instanton solutions and their explicit form for the particular cases of the Euclidean Taub--NUT and Eguchi--Hanson spaces. We construct the boundary terms required to define a well-posed Dirichlet variational principle in the Euclidean Cano--Ruipérez theory, including the contributions associated with the Gauss--Bonnet and Pontrjagin terms. The boundary terms are normalized for asymptotically-locally-Euclidean solutions, and we evaluate with them the Euclidean action of the $α'$-corrected Eguchi--Hanson instanton showing that the total action receives no corrections to first order in $α'$. We also show that, at zeroth order in $α'$, one can construct Euclidean solutions similar to the string theory D-instanton with non-trivial dilaton and axion on the background of a self-dual purely gravitational instanton which remains unmodified. We also compute the $α'$ corrections to these solutions.

Stochastic gradient descent (SGD) has been studied extensively over the past decades due to its simplicity and broad applicability in machine learning. In this work, we analyze the local behavior of gradient descent and stochastic gradient descent for minimizing $C^2$-functions that satisfy the Polyak-Lojasiewicz (PL) inequality and under a multiplicative gradient noise model motivated by overparameterized neural networks. Using a geometric interpretation of the PL-condition, we prove a simple yet surprising fact: in this possibly non-convex setting, the asymptotic convergence rate of (S)GD matches the rate obtained for strongly convex quadratics.

We study static spherically symmetric Kundt solutions to the vacuum field equations of quadratic gravity with a cosmological constant, as well as specific models of six-derivative gravity. In quadratic gravity, we identify all solutions for coupling constants satisfying ${α\neq3β}$, while the case ${α=3β}$ is studied using the Frobenius method, where we derive the recurrence relations for the power series. In contrast, in six-derivative gravity, we focus on selected models to illustrate the variety of closed-form solutions; we also analyze possible indicial families of Frobenius solutions. For all solutions, we analyze curvature singularities and their accessibility to geodesic observers. We then construct exact gravitational-wave solutions propagating on some of these backgrounds in quadratic and six-derivative gravity. It is known that in Einstein gravity, gravitational waves on the Nariai background unavoidably contain singularities, which are interpreted as physical sources generating these gravitational waves. In contrast, in addition to singular solutions, for appropriate values of the coupling constants, higher-order gravities allow for globally smooth solutions representing gravitational waves.

We investigate the imprints on the angular power spectra of cosmological perturbations of a pre-inflationary bounce phase, as described by the hybrid and dressed metric approaches to loop quantum cosmology. For this purpose, we derive a new parametrization of the primordial power spectrum at the end of the inflationary regime. Apart from slow-roll coefficients and cosmological parameters that are present in the standard cosmological scenario without quantum modifications, this parametrization additionally depends only on pre-inflationary physics. More specifically, we find a dependence on the number of e-folds during the bounce epoch and on a characteristic suppression scale which, given the e-folds accumulated during cosmic evolution, is determined by the energy density at the bounce. Recall that this density depends on the Immirzi parameter and the area gap known from LQG. This leads to a robust and accurate parametrization of the primordial power spectrum. Since in pre-inflationary scenarios there is no preferred vacuum state, we adopt the NO-AHD proposal, which selects a vacuum that is optimally adapted to the background dynamics and yields a non-oscillatory primordial power spectrum. With this choice, we show that the tensor-to-scalar ratio in both quantization approaches coincides with its expression in the standard $Λ$CDM model when the observed scales are not much smaller than the power-suppressed region. Computing also the angular power spectrum, we find that, for a total cosmic expansion of about 140 e-folds, both the hybrid and the dressed metric approaches exhibit excellent agreement with Planck data at high multipoles, while apparently improving the fit with respect to $Λ$CDM for low multipole numbers.

Current cloud-based quantum processors offer access to advanced hardware hosted on a remote server, but do not guarantee data or algorithm privacy. Blind quantum computation provides information-theoretic privacy by enabling a client to execute an algorithm without disclosing information about either the task or the final result. Here, we execute a measurement-based blind quantum computation protocol on a superconducting processor comprising two flip-chip-bonded modules, one acting as a server and the other as a client. The server generates a two-dimensional cluster state and forwards it to the client. Using this resource, the client implements a universal gate set with only adaptive single-qubit rotations and measurements. To illustrate this approach, we execute a three-qubit instance of the Deutsch-Jozsa algorithm. We analyze the server's quantum state after each rotation of a measurement-based single-qubit gate to verify that negligible information about the computation is revealed to the server, consistent with the one-way flow of information that guarantees blindness. This proof-of-principle demonstration establishes key elements of blind quantum computation in superconducting-circuit architectures, indicating that intermediate-scale implementations of blind protocols may become feasible with realistic near-term improvements in gate fidelities.

Static resource allocations in high-performance computing (HPC) lead to inefficiencies for time-varying workloads, causing idle resources, queue delays, and higher node-hour costs. The Dynamic Management of Resources (DMR) middleware enables MPI process malleability in Slurm via a simple API decoupled from scheduler internals. In this work, we integrate DMR into the GROMACS molecular dynamics engine to obtain a malleable variant that can dynamically adapt its MPI process count by combining communication-efficiency-aware reconfiguration with GROMACS' native checkpoint/restart mechanism. We evaluate this design on the MareNostrum~5 supercomputer, comparing dynamic runs against static executions and quantifying reconfiguration overheads, time-to-solution, and node-hour savings for bursty GROMACS workloads.

Synchronization is a pervasive collective phenomenon underlying the firing of neurons, the beating of the heart, and the coherent emission of lasers. Across these systems, dissipation plays an organizing role, suppressing microscopic differences and steering coupled units toward a common macroscopic order. Here we harness engineered non-Hermitian dissipation to synchronize light directly in the optical domain. Implementing non Hermitian transition matrices on a silicon photonic processor, we drive arbitrary multimode optical fields toward a unique collective state with equal modal intensities and a globally locked phase, a process we call dissipation-induced phase synchronization. The synchronization rate and total optical power throughput are independently programmable, enabling control over the dissipative dynamics without compromising reconfigurability. These results recast dissipation as a functional resource and open a route to reconfigurable on-chip synchronization for classical and quantum photonic technologies.

We expand the treatment of the problem of the extraction of smeared spectral densities from Euclidean correlators introduced in [Phys. Rev. D 99, 094508], providing an alternative which does not rely on the Backus-Gilbert regularization. This is possible due to the observation that the solution can be decomposed into a sum of terms, in the spirit of the singular value decomposition, where those with the largest contribution to the statistical noise happen to contribute the least to the central value of the smeared spectral density. The analysis of the systematics of the inverse problem is then shifted to finding the optimal truncation of such summation, so that the signal is saturated before the noise explodes. We scrutinise the performance and systematics of this approach either as a standalone procedure, or to complement the stability analysis required to extrapolate the unbiased result in the Backus-Gilbert regulated version of the solution.