Representation theorems for formal systems often take the form of an inductive translation that satisfies certain invariants, which are proved inductively. Theory morphisms and logical relations are common patterns of such inductive constructions. They allow representing the translation and the proofs of the invariants as a set of translation rules, corresponding to the cases of the inductions. Importantly, establishing the invariants is reduced to checking a finite set of, typically decidable, statements. Therefore, in a framework supporting theory morphisms and logical relations, translations that fit one of these patterns become much easier to formalize and to verify. The lambdaPi-calculus modulo rewriting is a logical framework designed for representing and translating between formal systems that has previously not systematically supported such patterns. In this paper, we extend it with theory morphisms and logical relations. We apply these to define and verify invariants for a number of translations between formal systems. In doing so, we identify some best practices that enable us to obtain elegant novel formalizations of some challenging translations, in particular sort-erasure translations from sorted to unsorted languages.

Extremely large-scale multiple-input multiple-output (XL-MIMO) is a key technology for next-generation wireless communication systems. By deploying significantly more antennas than conventional massive MIMO systems, XL-MIMO promises substantial improvements in spectral efficiency. However, due to the drastically increased array size, the conventional planar wave channel model is no longer accurate, necessitating a transition to a near-field spherical wave model. This shift challenges traditional beam training and channel estimation methods, which were designed for planar wave propagation. In this article, we present a comprehensive review of state-of-the-art beam training and channel estimation techniques for XL-MIMO systems. We analyze the fundamental principles, key methodologies, and recent advancements in this area, highlighting their respective strengths and limitations in addressing the challenges posed by the near-field propagation environment. Furthermore, we explore open research challenges that remain unresolved to provide valuable insights for researchers and engineers working toward the development of next-generation XL-MIMO communication systems.

A theorem of Wiegerinck asserts that the Bergman space of an open subset of the complex numbers is either infinite-dimensional or trivial. Recently, this has been generalized to holomorphic vector bundles over the projective line by the third author and later to vector bundles over any compact Riemann surface by Gallagher, Gupta and Vivas. In the present paper we extend the above results to the case of certain singular metrics associated to divisors on a Riemann surface. As corollaries we obtain versions of Wiegerinck's theorem for both projective and affine algebraic curves.

In the present work, we introduce, develop, and investigate a connection between multiphoton quantum interference, a core element of emerging photonic quantum technologies, and Hopfieldlike Hamiltonians of classical neural networks, the paradigmatic models for associative memory and machine learning in systems of artificial intelligence. Specifically, we show that combining a system composed of Nph indistinguishable photons in superposition over M field modes, a controlled array of M binary phase-shifters, and a linear-optical interferometer, yields output photon statistics described by means of a p-body Hopfield Hamiltonian of M Ising-like neurons +-1, with p = 2Nph. We investigate in detail the generalized 4-body Hopfield model obtained through this procedure and show that it realizes a transition from a memory retrieval to a memory black-out regime, i.e. a spin-glass phase, as the amount of stored memory increases. The mapping enables novel routes to the realization and investigation of disordered and complex classical systems via efficient photonic quantum simulators, as well as the description of aspects of structured photonic systems in terms of classical spin Hamiltonians.

Let $G$ be a finite group of even order, let $k$ be an algebraically closed field of characteristic $2$, and let $B$ be a block of the group algebra $kG$ which is of domestic representation type. Up to splendid Morita equivalence, precisely three cases can occur: $kV_4$, $k\mathfrak{A}_4$ and the principal block of $k\mathfrak{A}_5$. In each case, given the character values of the ordinary irreducible characters of $B$, we determine the ordinary characters of all trivial source $B$-modules.

We propose schemes to produce highly nuclear-spin polarized small molecules in an intense and cold molecular beam via microwave or infrared rotational excitation, followed by hyperfine-induced quantum beats. Repumping schemes can be used to achieve polarization above $90\%$ in cases where single-pumping schemes are insufficient. We discuss the possibility of high production rates which allow applications including nuclear-magnetic-resonance signal enhancement, and spin-polarized nuclear fusion, where polarized nuclei are known to enhance D-T and D-$^3$He fusion cross sections by $50\%$.

Modelling has become a third distinct line of scientific enquiry, alongside experiments and theory. Molecular dynamics (MD) simulations serve to interpret, predict and guide experiments and to test and develop theories. A major limiting factor of MD simulations is system size and in particular the difficulty in handling, storing and processing trajectories of very large systems. This limitation has become significant as the need to simulate large system sizes of the order of billions of atoms and beyond has been steadily growing. Examples include interface phenomena, composite materials, biomaterials, melting, nucleation, atomic transport, adhesion, radiation damage and fracture. More generally, accessing new length and energy scales often brings qualitatively new science, but this has currently reached a bottleneck in MD simulations due to the traditional methods of storing and post-processing trajectory files. To address this challenge, we propose a new paradigm of running MD simulations: instead of storing and post-processing trajectory files, we calculate key system properties on-the-fly. Here, we discuss the implementation of this idea and on-the-fly calculation of key system properties in the general-purpose MD code, DL_POLY. We discuss code development, new capabilities and the calculation of these properties, including correlation functions, viscosity, thermal conductivity and elastic constants. We give examples of these on-the-fly calculations in very large systems. Our developments offer a new way to run MD simulations of large systems efficiently in the future.

In this paper, we first introduce the notion of the Laplace transform for an abstract-valued function from $[0, \infty)$ to a $\mathcal{T}_{\varepsilon, λ}$-complete random normed module $S$. Then, combining respective advantages of the $(\varepsilon, λ)$-topology and the locally $L^0$-convex topology on $S$, we prove the differentiability, Post-Widder inversion formula and uniqueness of such a Laplace transform. Second, based on the above work, we establish the Hille-Yosida theorem for an exponentially bounded $C$-semigroup on $S$, considering both the dense and nondense cases of the range of $C$, respectively, which extends and improves several important results. Finally, we also apply such a Laplace transform to abstract Cauchy problems in the random setting.

We use valid inequalities (cuts) of the binary integer program for winner determination in a combinatorial auction (CA) as "artificial items" that can be interpreted intuitively and priced to generate Artificial Walrasian Equilibria. We thus provide a method for converting a CA problem that admits only non-anonymous, nonlinear bundle prices into one that admits anonymous linear prices over the augmented item space, forestalling ex-post bidder complaints about opaque and strongly discriminatory pricing. To this end, we introduce a refinement of the Walrasian equilibrium which we call a "price-match equilibrium" (PME) in which all prices are justified by providing an iso-revenue reallocation for the hypothetical removal of any single bidder. We prove the existence of PME for any CA and characterize their economic properties and computation. We implement minimally artificial PME rules and compare them with other prominent CA payment rules in the literature.

Time series play a fundamental role in many domains, capturing a plethora of information about the underlying data-generating processes. When a process generates multiple synchronized signals we are faced with multidimensional time series. In this context a fundamental problem is that of motif mining, where we seek patterns repeating twice with minor variations, spanning some of the dimensions. State of the art exact solutions for this problem run in time quadratic in the length of the input time series. We provide a scalable method to find the top-k motifs in multidimensional time series with probabilistic guarantees on the quality of the results. Our algorithm runs in time subquadratic in the length of the input, and returns the exact solution with probability at least $1-δ$, where $δ$ is a user-defined parameter. The algorithm is designed to be adaptive to the input distribution, self-tuning its parameters while respecting user-defined limits on the memory to use. Our theoretical analysis is complemented by an extensive experimental evaluation, showing that our algorithm is orders of magnitude faster than the state of the art.

Gallium oxide is a wide-bandgap semiconductor which has been steadily growing in popularity due to its ultra-wide bandgap, suitability for harsh environments and distinctive opto-electrical properties. Notable applications include deep-UV photodetectors, low loss waveguides or even transparent solar cells. RF sputtering stands out among possible techniques for the epitaxial deposition of Ga$_{2}$O$_{3}$ thin films with high quality and at a low cost. By using sapphire substrates, and through thermal annealing, we can form a $β$-(Al$_{x}$Ga$_{1-x}$)$_{2}$O$_{3}$ alloy by Al diffusion, which has tunable opto-electrical properties such as the bandgap and breakdown electric field. In this work, techniques such as X-ray diffraction, Rutherford backscattering spectrometry, Raman spectroscopy, atomic force microscopy and optical transmission are used to determine the optical properties, morphology and composition of Ga$_{2}$O$_{3}$ deposited and annealed thin films. To explore the formation of the $β$-(Al$_{x}$Ga$_{1-x}$)$_{2}$O$_{3}$ alloy, annealing was performed at variable temperature, in ambient air. It was determined that the bandgap can indeed be tuned between 4.85 and 5.30 eV by varying the annealing temperature, corresponding to an Al content between 0$-$68.5.

The Fréchet mean is a fundamental notion of central tendency defined as a minimizer of a sum of squared distances in a general metric space. In this paper, we study Fréchet means in tropical geometry -- a piecewise linear, combinatorial, and polyhedral variant of algebraic geometry -- by formulating and solving the associated tropical quadratic optimization problem. We give a geometric characterization of the collection of all tropical Fréchet means as a bounded set that is simultaneously tropically and classically convex, hence a polytrope. We establish the existence of positivity certificates for maxima of finitely many quadratic polynomials in $\mathbb{R}[x_1,\ldots,x_n]$ whose homogeneous quadratic components are sums of squares, which provides a symbolic framework for exact optimization. Using this structure, we develop algorithms for computing tropical Fréchet means and the associated Fréchet mean polytrope. We further describe a combinatorial type decomposition of the objective function induced by braid arrangements, yielding a piecewise quadratic representation and a fully symbolic method for exact computation.

We address the problem of solving a system of linear equations via the Quantum Singular Value Transformation (QSVT). One drawback of the QSVT algorithm is that it requires huge quantum resources if we want to achieve an acceptable accuracy. To reduce the quantum cost, we propose a hybrid quantum-classical algorithm that improves the accuracy and reduces the cost of the QSVT by adding iterative refinement in mixed-precision A first quantum solution is computed using the QSVT, in low precision, and then refined in higher precision until we get a satisfactory accuracy. For this solver, we present an error and complexity analysis, and first experiments using the quantum software stack myQLM.

A chain of dipole-coupled elongated magnetic islands whose long axes are oriented perpendicular to the chain is studied for its magnetization properties. With a magnetic field applied perpendicular to the chain, the competition between dipolar energy, shape anisotropy, and field energy leads to three types of uniform states with distinct magnetizations: (1) oblique to the chain, (2) perpendicular to the chain, and (3) zero due to having alternating dipoles. The response of these states to a slowly varying field is analyzed, focusing on their stability limits and related oscillation modes, and the dependencies on the dipolar and anisotropy constants. Based on identifiable transitions among the three states and their instability points, the theoretically predicted zero-temperature magnetization curves show significant dependence on the anisotropy. The model suggests a path for designing advanced materials with desired magnetic properties. Different geometries and magnetic media for the islands are considered.

Every finite graph $G$ can be decomposed in a canonical way that displays its local connectivity-structure [DJKK26]. These decompositions are defined via a suitable more tree-like covering of $G$, whose tangle-tree structure is projected down to $G$. The covering graphs needed here are almost always infinite, and their tangle-tree structure is defined in terms of their (global) low-order separations. The canonical decompositions they induce on $G$ are therefore not computable following their definition. We reconstruct these decompositions of $G$ from finite information in $G$ itself that is sufficiently local to be reflected in the cover. This involves the reconstruction of canonical tangle structure in terms of a new theory of local separations in finite graphs, which we develop for this purpose. As an application, we find that the canonical graph-decompositions from [DJKK26] are computable.

Twisted transition metal dichalcogenides (TMDs) host bands with opposite Chern number for the two spin species and could thus be host for fractional topological insulator states. In multicomponent quantum Hall systems, where the spins have equal Chern number, the resulting topological liquid states can be well modeled by trial wavefunctions such as the Halperin $(lmn)$ wavefunctions. These wavefunctions are exact zero energy states of certain short-range (pseudopotential) Hamiltonians. However, we show that such a construction fails in the case where the Chern numbers of the two spins are opposite, since the electrons with opposite Chern number cannot avoid one another. This underlines the importance of suppressing the short-range interspin Coulomb repulsion in order to realize fractional topological insulators in twisted TMDs. We introduce a trial wavefunction for the opposite Chern number Landau levels for filling factor $ν=\frac{1}{3}+\frac{1}{3}$ in terms of pairing of composite fermions and show that it has good overlaps with the exact diagonalization ground state when the short-range Coulomb repulsion is sufficiently softened.

Electronic structure calculations of molecular systems are among the most promising applications for fault-tolerant quantum computing (FTQC) in quantum chemistry and drug design. However, while recent algorithmic advancements such as qubitization and Tensor Hypercontraction (THC) have significantly reduced the complexity of such calculations, they do not yet achieve computational runtimes short enough to be practical for industrially relevant use cases. In this work, we introduce several advances to electronic structure calculation for molecular systems, resulting in a two-orders-of-magnitude speedup of estimated runtimes over prior-art algorithms run on comparable quantum devices. One of these advances is a novel framework for block-invariant symmetry-shifted Tensor Hypercontraction (BLISS-THC), with which we achieve the tightest Hamiltonian factorizations reported to date. We compile our algorithm for an Active Volume (AV) architecture, a technical layout that has recently been proposed for fusion-based photonic quantum hardware. AV compilation contributes towards a lower runtime of our computation by eliminating overheads stemming from connectivity issues in the underlying surface code. We present a detailed benchmark of our approach, focusing primarily on the computationally challenging benchmark molecule P450. Leveraging a number of hardware tradeoffs in interleaving-based photonic FTQC, we estimate runtimes for the electronic structure calculation of P450 as a function of the device footprint.

We propose a method to bound the expectation of the supremum of the price process in stochastic volatility models. It can be applied, for example, to the rough Bergomi model, avoiding the need to discuss finiteness of higher moments. Our motivation stems from the theory of American option pricing, as an integrable supremum implies the existence of an optimal stopping time for any linearly bounded payoff. Moreover, we survey the literature on martingales with non-integrable supremum, and give a new construction that yields uniformly integrable martingales with this property.

Quantum error correction is essential for bridging the gap between the error rates of physical devices and the extremely low logical error rates required for quantum algorithms. Recent error-correction demonstrations on superconducting processors have focused primarily on the surface code, which offers a high error threshold but poses limitations for logical operations. In contrast, the color code enables much more efficient logic, although it requires more complex stabilizer measurements and decoding techniques. Measuring these stabilizers in planar architectures such as superconducting qubits is challenging, and so far, realizations of color codes have not addressed performance scaling with code size on any platform. Here, we present a comprehensive demonstration of the color code on a superconducting processor, achieving logical error suppression and performing logical operations. Scaling the code distance from three to five suppresses logical errors by a factor of $Λ_{3/5}$ = 1.56(4). Simulations indicate this performance is below the threshold of the color code, and furthermore that the color code may be more efficient than the surface code with modest device improvements. Using logical randomized benchmarking, we find that transversal Clifford gates add an error of only 0.0027(3), which is substantially less than the error of an idling error correction cycle. We inject magic states, a key resource for universal computation, achieving fidelities exceeding 99% with post-selection (retaining about 75% of the data). Finally, we successfully teleport logical states between distance-three color codes using lattice surgery, with teleported state fidelities between 86.5(1)% and 90.7(1)%. This work establishes the color code as a compelling research direction to realize fault-tolerant quantum computation on superconducting processors in the near future.

Given an unknown $\mathbb{R}^n$-valued function $f$ on a metric space $X$, can we approximate the persistent homology of $f$ from a finite sampling of $X$ with known pairwise distances and function values? This question has been answered in the case $n=1$, assuming $f$ is Lipschitz continuous and $X$ is a sufficiently regular geodesic metric space, and using filtered geometric complexes with fixed scale parameter for the approximation. In this paper we answer the question for arbitrary $n$, under similar assumptions and using function-geometric multifiltrations. Our analysis offers a different view on these multifiltrations by focusing on their approximation properties rather than on their stability properties. We also leverage the multiparameter setting to provide insight into the influence of the scale parameter, whose choice is central to this type of approach. From a practical standpoint, we show that our approximation results are robust to input noise, and that function-geometric multifiltrations have good statistical convergence properties. We also provide an algorithm to compute our estimators, and we use its implementation to conduct extensive experiments, on both synthetic and real biological data, in order to validate our theoretical results and to assess the practicality of our approach.

This paper studies cache-aided wireless networks in the presence of active intelligent reflecting surfaces (IRSs) from an information-theoretic perspective. Specifically, we investigate interference management in a cache-aided wireless network assisted by an active IRS to enhance the achievable degrees of freedom (DoF). To this end, we jointly design the content placement, delivery phase, and IRS coefficients, and propose a one-shot achievability scheme. Our scheme exploits transmitters' cooperation, cache contents, interference alignment, and IRS capabilities, based on the network parameters. We derive the achievable one-shot sum-DoF for different cache sizes, network configurations, and numbers of IRS elements, followed by an upper bound. Our results highlight the potential of deploying an IRS in cache-aided wireless communication systems. In particular, they underscore the enhancement of achievable DoF for various parameter regimes, especially when cache sizes are inadequate. Notably, we show that access to an IRS with a sufficient number of elements enables the achievement of the maximum possible DoF for various parameter regimes of interest.

Analogously to de Bruijn sequences, Orientable sequences have application in automatic position-location applications and, until recently, studies of these sequences focused on the binary case. In recent work by Alhakim et al., recursive methods of construction were described for orientable sequences over arbitrary finite alphabets, requiring 'starter sequences' with special properties. Some of these methods required as input special orientable sequences, i.e. orientable sequences which were simultaneously negative orientable. We exhibit methods for constructing special orientable sequences with properties appropriate for use in two of the recursive methods of Alhakim et al. As a result we are able to show how to construct special orientable sequences for arbitrary sizes of alphabet (larger than a small lower bound) and for all window sizes. These sequences have periods asymptotic to the optimal as the alphabet size increases.

Hierarchical graph rewriting is a highly expressive computational formalism that manipulates graphs enhanced with box structures for representing hierarchies. It has provided the foundations of various graph-based modeling tools, but the design of high-level declarative languages based on hierarchical graph rewriting is still a challenge. For a solid design choice, well-established formalisms with backgrounds other than graph rewriting would provide useful guidelines. Proof nets of Multiplicative Exponential Linear Logic (MELL) is such a framework because its original formulation of cut elimination is essentially graph rewriting involving box structures, where so-called Promotion Boxes with an indefinite number of non-local edges may be cloned, migrated and deleted. This work builds on LMNtal as a declarative language based on hierarchical (port) graph rewriting, and discusses how it can be extended to support the above operations on Promotion Boxes of MELL proof nets. LMNtal thus extended turns out to be a practical graph rewriting language that has strong affinity with MELL proof nets. The language features provided are general enough to encode other well-established models of concurrency. Using the toolchain of LMNtal that provides state-space search and model checking, we implemented cut elimination rules of MELL proof nets in extended LMNtal and demonstrated that the platform could serve as a useful workbench for proof nets.

The colored Jones polynomial associated to a knot admits an expansion of knot invariants known as the large-color expansion or Melvin-Morton-Rozansky expansion. We will show how this expansion can be derived from the universal invariant arising from a Hopf algebra $\mathbb{D}$, as introduced by Bar-Natan and Van der Veen. We utilize a Mathematica implementation to compute the universal invariant $\mathbf{Z}_{\mathbb{D}}(\mathcal{K})$ up to a certain order for a given knot $\mathcal{K}$, allowing for experimental verification of our theoretical results.

Measures of inflation uncertainty and directional risk derived from higher moments of forecast distributions are contaminated by the first moment, but in distinct ways. Using individual density forecasts from the ECB Survey of Professional Forecasters, this paper shows that 42% of the variation in raw forecast variance reflects the distance of expected inflation from target, a mechanical level effect, while raw asymmetry is too noisy to identify directional risk without reference to the central forecast. We propose two complementary corrections. Normalized Uncertainty (NU) purges dispersion of its predictable component linked to the policy anchor, recovering genuine belief imprecision. Asymmetry Coherence (AC) extracts directional risk only when asymmetry aligns with the central forecast, formalizing the balance of risks. These corrections alter inference. In a replication of Barro (1995), the volatility effect on growth disappears once level contamination is removed, while the inflation-level coefficient regains significance. In a VAR, the sign of the policy response reverses: raw asymmetry suggests easing, whereas coherent upside risk predicts tightening. In the credit channel, higher uncertainty slows and weakens pass-through from policy easing to loan pricing, especially at longer maturities. A division of roles emerges: NU governs transmission, AC informs policy response. Higher moments are informative only when measurement separates macroeconomic signals from first-moment contamination.

We prove that every $L$-bilipschitz mapping $\mathbb{Z}^2\to\mathbb{R}^2$ can be extended to a $C(L)$-bilipschitz mapping $\mathbb{R}^2\to\mathbb{R}^2$ and provide a polynomial upper bound for $C(L)$. Moreover, we extend the result to every separated net in $\mathbb{R}^2$ instead of $\mathbb{Z}^2$, with the upper bound gaining a polynomial dependence on the separation and net constants associated to the given separated net. This answers an Oberwolfach question of Navas from 2015 and is also a positive solution of the two-dimensional form of a decades old open (in all dimensions at least two) problem due to Alestalo, Trotsenko and Väisälä.

Chiral symmetry is a fundamental property with profound implications for the properties of elementary particles, that implies a spectral symmetry (i.e. E => -E ) in their dispersion relation. In condensed matter physics, chiral symmetry is frequently associated with superconductors or materials hosting Dirac fermions such as graphene or topological insulators. There, chiral symmetry is an emergent low-energy property, accompanied by an emergent spectral symmetry. While the chiral symmetry can be broken by crystal distortion or external perturbations, the spectral symmetry frequently survives. As the presence of spectral symmetry does not necessarily imply chiral symmetry, the question arises how these two properties can be experimentally differentiated. Here, we demonstrate how a system with preserved spectral symmetry can reveal underlying broken chiral symmetry using topological defects. Our study shows that these defects induce a spectral imbalance in the Landau level spectrum, providing direct evidence of symmetry alteration at topological domain walls. Using high-resolution STM/STS we demonstrate the intricate interplay between chiral and translational symmetry which is broken at step edges in topological crystalline insulator Pb$_{1-x}$Sn$_x$Se. The chiral symmetry breaking leads to a shift in the guiding center coordinates of the Landau orbitals near the step edge, thus resulting in a distinct chiral flow of the spectral density of Landau levels. This study underscores the pivotal role of topological defects as sensitive probes for detecting hidden symmetries, offering profound insights into emergent phenomena with implications for fundamental physics.

Assuming the abundance conjecture and the existence of a Zariski dense set of rational curves on terminal Calabi--Yau varieties, we show that a complex projective weakly special manifold $X$ with no rational curves is an étale quotient of an Abelian variety. The same conclusion holds true if $X$ contains a Zariski dense entire curve, assuming Lang's conjecture. This implies that any non-hyperbolic complex projective manifold contains the image of an Abelian variety, according to another conjecture of Lang. We illustrate this last conjecture by producing examples of canonically polarised submanifolds of abelian varieties containing no subvariety of general type, except for a finite number of disjoint copies of some simple abelian variety, which can be chosen arbitrarily. We also show, more generally, that any projective manifold containing a Zariski dense entire curve appears as the `exceptional set' in Lang's sense of some general type manifold.

We investigate the well-posedness in the Hadamard sense and the absence of price manipulation in the optimal execution problem within the Almgren-Chriss framework, where the temporary and permanent impact parameters vary deterministically over time. We present sufficient conditions for the existence of a unique solution and provide second-order conditions for the problem, with a particular focus on scenarios where impact parameters change monotonically over time. Additionally, we establish conditions to prevent transaction-triggered price manipulation in the optimal solution, i.e. the occurence of buying and selling in the same trading program. Our findings are supported by numerical analyses that explore various regimes in simple parametric settings for the dynamics of impact parameters.

The way in which the large-scale cosmic environment affects galactic properties is not yet understood. Dark matter halos, which embed galaxies, initially evolve following linear theory. Their subsequent evolution is driven by non-linear structure formation in the halo region and in its outer environment. In this work, we present the first study where we explicitly control the linear part of the evolution of the halo, thus revealing the role of non-linear effects on halo formation. We focus specifically on the effect of proximity to a large cosmological filament. We employ the splicing method to keep fixed the initial density, velocity, and potential fields where a halo will form while changing its outer environment, from an isolated state to one where the halo is near a large filament. In the regime of Milky Way-mass halos, we find that mass and virial radius of such halos are not affected by even drastic changes of environment, whereas halo spin and shape orientation with respect to a massive filament is largely impacted, with fluctuations of up to 80 % around the mean value. Our results suggest that halo orientation and shape cannot be predicted accurately from a local analysis in the initial conditions alone. This has direct consequences on the modeling of intrinsic alignment for cosmic shear surveys, like Euclid. Our results highlight that non-linear couplings to the large-scale environment may have an amplitude comparable to linear effects, and should thus be treated explicitly in analytical models of dark matter halo formation.