We review recent interferometric schemes designed to probe physics beyond the Standard Model through the detection of geometric phases. We discuss how interactions with hidden-sector degrees of freedom, such as axion-like particles and mirror-matter candidates, can induce potentially observable phase shifts in ordinary fermion systems.

Habitat loss driven by climate and anthropogenic pressures alters patch morphology, with critical consequences for population persistence. Geometric and mechanistic metrics are commonly used to quantify degradation, yet their respective limitations remain poorly understood. Here, we address this gap using a reaction-diffusion framework for population growth and dispersal in a viable patch embedded in a hostile environment. We compare geometric descriptors of patch shape with a mechanistic metric derived from population growth near the extinction threshold. Along degradation trajectories, we find that geometric metrics systematically overestimate persistence, suggesting moderate and decelerating impacts, whereas mechanistic indicators reveal rapid, accelerating approaches to extinction. These results highlight fundamental limitations of geometric approaches and underscore the need for mechanistic assessments when evaluating biodiversity loss in complex landscapes.

HyperSpectral-MultiSpectral Image (HSI-MSI) fusion enables high-resolution hyperspectral imaging by combining the rich spectral information of low-spatial-resolution hyperspectral images with the detailed spatial structure of multispectral images. Classical methods such as Coupled Nonnegative Matrix Factorization (CNMF) benefit from a strong physical interpretability but suffer from inferior results compared to their deep-learning counterparts. To address this limitation, we propose SCALMU (Synthetically-trained Coupling of Adaptive Learned Multiplicative Updates), a novel unrolled neural network architecture that integrates adaptive learnable matrices within the classical framework of CNMF multiplicative updates, improving its results. Due to its architectural proximity with CNMF, the resulting algorithm preserves physical interpretability and nonnegativity constraints. To overcome data scarcity for training, we additionally generate a synthetic HSI-MSI dataset via the dead leaves model, enabling synthetic supervision. SCALMU is then trained end-to-end on this dataset. Experiments demonstrate SCALMU's superiority over state-of-the-art methods on several datasets. The code is available at https://github.com/xinxinxu99/SCALMU.git

We investigate the projected sensitivity of the FCC-ee in probing the LFV decay of the 125 GeV Higgs boson, $h\toμτ$, $h\to eτ$, and $h \to eμ$ at center-of-mass energy of 240 GeV with an integrated luminosity of 5 ab$^{-1}$. With the clean multi-lepton final states, we consider the Higgs production modes that contribute to $e^+e^- \to \ell\ell h$, in particular, the Higgs-strahlung and the vector boson fusion production channels. The 95\% CL upper limits on branching ratio are found to be $5.92 \times 10^{-4}$, $6.27 \times 10^{-4}$, and $7.48 \times 10^{-5}$ for the channels $h\toμτ$, $h\to eτ$, and $h \to eμ$, respectively. In addition, we also consider the LFV decay of a new CP-even Higgs boson with mass in the range of $110-200$ GeV. The projected FCC-ee sensitivities are then compared to those from low energy searches for $\ell\to\ell'γ$ decay. We find that the FCC-ee sensitivity for the LFV decays of the Higgs in the $e-τ$ and $μ-τ$ channels is superior to the low-energy constraints. However, in the $e-μ$ case, the low energy search offers stronger constraints.

Chord diagrams encode boundary correlators in the double-scaled holographic Sachdev-Ye-Kitaev model, but currently capture only a limited class of bulk interactions that yield pure power-law correlators. In this article, we investigate a general construction based on Fock-space flux models with arbitrary periodic lattice size, clarifies how lattice dimensions control probe configurations and bulk contact vertices. Developing a systematic matching scheme and using the chord path integral formalism, we compute three- to six-point contact correlators and reproduce a broad class of AdS$_2$ scalar contact Witten diagrams, including those with logarithmic singularities. The results demonstrate that chord diagrams, in full generality, provide a microscopic description of bulk contact interactions and thereby establish a principled framework for reconstructing bulk locality from boundary data.

We evaluate deterministic higher-order product formulae for molecular ground-state energy estimation. Motivated by recent fault-tolerant architectures in which non-Clifford operations may be generated more locally and cheaply than in conventional assumptions, we re-examine such formulae as practical candidates for quantum chemistry. Using one-dimensional hydrogen chains from $\mathrm{H}_2$ to $\mathrm{H}_{15}$ as benchmarks, we estimate both the total gate count and the depth of $R_Z$-rotation layers required to reach a target energy error. To make this comparison feasible at larger system sizes, we use a perturbative method to estimate the eigenvalue error induced by each product formula and thereby evaluate the cost of the corresponding phase-estimation procedure. Among the previously considered formulae, the eighth-order construction introduced by Morales et al. [M. E. S. Morales et al., "Greatly improved higher-order product formulae for quantum simulation," arXiv:2210.15817v2 (2024)] minimizes both cost metrics in the benchmark at a chemically relevant target error. We also find that increasing the formal order does not automatically reduce the total cost: near chemical accuracy, the tenth-order formula introduced in the same work can be less efficient than the eighth-order one. Motivated by this observation, we construct a new fourth-order formula; it achieves the lowest total gate count among the formulae considered for all H-chain instances near chemical accuracy and over much of the 0.1-10 mHa target-error window for most instances, while also reducing the $R_Z$-layer depth. These results clarify how deterministic higher-order product formulae should be selected for molecular ground-state energy estimation.

We adapt the notion of mixing of all orders to random dynamical systems and use it to establish quenched limit theorems. Assuming quenched exponential mixing of all orders, we prove both the central limit theorem and the Poisson limit theorem. Compared to existing approaches, this framework offers two main advantages. First, it allows for substantially weaker assumptions on the random constants appearing in mixing estimates: in the exponential mixing regime, logarithmic integrability suffices for the central limit theorem, while in the Poisson case, no integrability condition is required. Second, it applies naturally to invertible systems, where standard methods based on $L^{\infty}$-type estimates or spectral decay are less well suited.

Aging trajectories vary among individuals of similar age and disease burden. Comorbidity indices, e.g. the Elixhauser index, summarize conditions cross-sectionally, but discard the timing, sequence, and pace of morbidity accumulation. Here we ask whether longitudinal hospital diagnosis histories contain information beyond age, sex, and comorbidity burden, and where it is concentrated. Using 13 years of Austrian inpatient data covering 7.4 million patients, we trained a visit-level contrastive transformer to encode diagnosis sequences and inter-admission timing into patient-history embeddings. In a downstream cohort of 1.7 million individuals, embeddings improved prediction over the Elixhauser-based comorbidity model for 93 of 131 incident ICD-10 disease-block outcomes, with a modest median AUC gain of 0.006. Gains concentrated in mental, musculoskeletal, nervous system, and metabolic disorders. We then evaluated event-free survival, defined as remaining alive without accumulating a second unrecorded ICD-10 disease block. The embedding model achieved an AUC of 0.726 versus 0.722 for the comorbidity model. However, among patients with similar age, sex, and comorbidity-model risk, those assigned high residual risk had 132--183 fewer event-free days over five years and observed event rates comparable to low-residual-risk patients more than a decade older. Together, these findings link the embedding's signal to the breadth, recency, and pace of prior disease accumulation.

Let $(x_n)_{n\geq 1}$ be a sequence of distinct points on the unit circle. After the first $n$ points are inserted, the circle is divided into $n$ intervals. For a fixed integer $r\geq 1$, let $M_n^{(r)}$ and $m_n^{(r)}$ denote respectively the largest and smallest total lengths of $r$ consecutive intervals. A theorem of de Bruijn and Erdős gives \[ \limsup_{n\to\infty}\frac{M_n^{(r)}}{m_n^{(r)}}\geq 1+\frac1r . \] The case $r=1$ is sharp and gives the classical factor $2$. The cases $r\geq 2$ remain much less understood. We prove the improved lower bound \[ \limsup_{n\to\infty}\frac{M_n^{(r)}}{m_n^{(r)}} \geq 1+\frac{r}{r^2-1} \qquad (r\geq 2). \] In particular, for two consecutive intervals the lower bound becomes $5/3$, improving the de Bruijn--Erdős bound $3/2$.

Contemporary data-driven and technology-integrated era, various matrix-valued integer-valued time series, such as cross-regional crime statistics, multi-category sales records, and network traffic matrices, exhibit high dimensionality, complex structures, and strong row-column intertwined dependencies. Although the existing matrix integer-valued autoregressive (MINAR) model provides a framework that directly handles matrix data and captures bidirectional row-column dependencies, it suffers from limited interpretability and inflexible structural representation, as its parameters often lack clear empirical meaning and the model cannot separately distinguish the effects arising from rows, columns, and lagged dynamics. To overcome these drawbacks, this paper proposes the additive matrix integer-valued autoregressive (Add-MINAR) model. By introducing an additive structure that explicitly decomposes the matrix response into row effects, column effects, and lagged effects, the proposed model not only preserves the matrix-valued nature but also significantly enhances parameter interpretability and structural flexibility. Two estimation methods, namely projection estimation and iterative conditional least squares estimation, are developed for parameter identification and inference, and their asymptotic properties, including consistency and asymptotic normality, are rigorously established. Simulation results show that the iterative conditional least squares estimator generally outperforms the projection estimator in most scenarios. Empirical analysis of Chicago crime data further demonstrates that the Add-MINAR model achieves superior in-sample fitting and out-of-sample forecasting performance compared to benchmark models such as MINAR, making it particularly suitable for practical applications with explicit row-column interaction features.

In the previous papers in the series, we characterized partial cross-sections for general flows, in the spirit of Fried's work on global cross-sections. In this paper, we deduce several consequences for Anosov flows. We provide a homology criterion for the existence of a partial cross-section in a given cohomology class. Additionally, there are at most finitely many partial cross-sections in that cohomology class. We deduce that on a 3-dimensional hyperbolic manifold, any Anosov flow is homologically full.

We present a non-intrusive version of the index-aware learning framework introduced in arXiv:2309.00958. Index-aware learning itself is an approach for learning the time and parameter dependent solutions of differential-algebraic equations (DAEs), in particular those of electrical circuits. A key feature of the approach is that it ensures the learned solutions to remain physics-consistent, i.e.\ inherent constraints of the solution, such as e.g.\ Kirchhoff's laws, remain fulfilled. In general, this is achieved by leveraging a decoupling of the DAE into its differential and algebraic parts, while the non-intrusive version of the approach additionally relies on results from arXiv:2604.20475 and arXiv:2107.07755. We illustrate the overall workflow and compare the non-intrusive and intrusive versions using a buck converter as an example.

GP-GOMEA is a state-of-the-art evolutionary algorithm for symbolic regression, known for discovering small and interpretable models. However, its computational cost remains substantial, limiting its applicability to larger datasets and more complex target expressions. In contrast, the rise of modern subsymbolic approaches, particularly deep learning, has been driven largely by the massive parallelism offered by GPUs. In this work, we take the first major step toward a fully GPU-accelerated GP-GOMEA by introducing a GPU-based fitness evaluation scheme. We design a GPU-friendly representation of GP-GOMEA's template-based individuals and a corresponding evaluation strategy that exploits the inherent parallelism of population-based search. This substantially increases evaluation throughput, enabling orders of magnitude more evaluations within the same time budget. Across four standard symbolic regression benchmarks, this increased evaluation capacity yields performance improvements, particularly for larger datasets and larger population sizes. Moreover, the ability to efficiently evaluate much larger datasets and more complex templates enables analyses that were previously infeasible, allowing us to systematically analyze what makes expressions increasingly difficult for GP-GOMEA, providing new insights into how expression structure affects search difficulty. Finally, for the first time, this expanded capability allows a problem-agnostic evolutionary algorithm to reliably regress one of the largest Feynman equations within four hours.

The simplest models of slow-roll inflation predict a featureless, nearly scale-invariant power spectrum of primordial curvature perturbations, consistent with current observations. However, in many non-minimal realisations of inflation, one generically expects the primordial power spectrum (PPS) to be ''wiggly'' with features that strongly deviate from scale-invariance. Current and next generation large scale structure (LSS) surveys will probe the PPS with unprecedented accuracy and therefore also increase sensitivity to power spectrum wiggles. However, accessing the information contained in these data will require an understanding of the behaviour of wiggly power spectra beyond the linear regime of structure formation. In this work, we use high resolution $N$-body simulations to study the non-linear evolution of scenarios in which the PPS has superimposed oscillations, calibrate a one-parameter semi-analytic damping model to describe their signatures in the late-time matter power spectrum and test the relative improvement on constraints by implementing this modelling strategy in a likelihood analysis via Gaussian Process Regression (GPR) emulation. Paying special attention to identifying our approach's domain of validity and quantifying as well as propagating uncertainties, we demonstrate that as long as the frequency of the PPS modulation is large enough, we are able to predict the matter power spectrum with sub-percent accuracy -- thereby enabling us to search for inflationary wiggles in LSS data.

This paper develops, analyzes, and validates a fast algorithm for computing guided modes within bent interfaces and non-periodic defects in high-contrast resonator crystals, where the Floquet--Bloch theory is not applicable. We first establish the resolvent convergence of the governing continuous operator to the discrete capacitance operator. This result rigorously justifies the reduction of the continuous spectral problem to a discrete eigenvalue problem. Then, we develop a truncation scheme of the discrete operator, named the patch approximation, and derive a rigorous error estimate for the patch approximation. Finally, we validate the accuracy and efficiency of our scheme through various examples. Our framework provides a general, computationally efficient, and rigorously justified approach to simulate guided modes in non-periodic systems of high-contrast resonators.

We introduce a physically grounded framework for coordination in a population based on information constrained feedback in a partially observed stochastic dynamical system. Population size evolves as a continuous time birth death Markov process whose transition rates respond to a shared stochastic measurement signal correlated with the underlying population state. Individuals neither communicate directly nor optimise strategies; instead, coordination emerges from macro to micro feedback mediated by imperfect common information. We show that geometric Brownian motion arises as a limiting case of the conditional dynamics when measurement strength and population statistics satisfy suitable conditions. More generally, varying the signal to noise properties of the measurement channel produces a wider class of stochastic growth processes, including diffusive and jump like regimes, even though ensemble average growth remains exponential. In an appropriate limit the framework recovers the stochastic multiplicative growth model of Peters and Adamou, providing a physical interpretation of coordination as inference and feedback under partial observability.

The Ricci matrix $R_T$ of a finite tree encodes its discrete Einstein metrics via the Perron eigenvector, with Lin-Lu-Yau's Ollivier Ricci curvature: $κ= -λ_{\max}(R_T)$. We show that edge subdivision, the natural operation of lengthening a tree, can decrease, preserve, or increase $λ_{\max}$. Compressing each branch into a scalar feedback function via the Schur complement reduces the spectral problem to a one-dimensional Chebyshev equation. We obtain an exact one-step trichotomy, a scalar transmission equation for arbitrary length, and the long-chain limit. Examples on double stars, including an asymmetric case where subdivision strictly increases $λ_{\max}$, illustrate the theory.

Higher-order interactions admit richer structural heterogeneity than pairwise networks. To understand how heterogeneity impacts collective phenomena we develop a framework based on the cavity method and apply it to the simplicial Ising model on heterogeneous hypergraphs. Unlike in homogeneous structures, group size and node degree play fundamentally different roles: size heterogeneity sharpens the transition via large-group unanimity, while degree heterogeneity softens it as hubs cooperatively seed ordering with non-hubs. Under either type of heterogeneity, continuous--discontinuous double transitions can arise, where the symmetry-breaking continuous transition is driven by pairs or by hubs, respectively. When both heterogeneities coexist, cross-order degree correlations further modulate the phase diagram, with anticorrelation delaying the group-driven discontinuous jump and broadening the hysteretic region. Our results reveal the intricate interplay between size and degree heterogeneities in collective phenomena beyond pairwise interactions.

We study the global structure of bifurcation diagrams for semilinear elliptic Dirichlet problems with supercritical nonlinearities in the unit ball. In particular, we focus on the borderline dimension $N = 10$, where the qualitative behavior of the bifurcation diagram is not determined solely by the growth rate of the nonlinearity. We show that the bifurcation curve is monotone, yielding uniqueness of classical solutions, for a class of nonlinearities including $f(u) = \exp((u+1)^p)$ with $p > 1$ and iterated exponential functions. Our approach is based on the construction of suitable singular subsolutions that satisfy a Hardy-type stability condition, avoiding the need for explicit representations of singular solutions. As a consequence, we show that, in dimension $N = 10$, these nonlinearities exhibit the same qualitative bifurcation diagram as the classical Gel'fand problem. We also characterize the monotonicity of the bifurcation curve in terms of the existence of global-in-time unbounded solutions to the associated parabolic problem.

We present a feasibility study of the longitudinal double-spin asymmetry $A_{LL}$ in inclusive $J/ψ$ production in polarized proton-proton collisions at $\sqrt{s}\approx 27~\mathrm{GeV}$ at the Spin Physics Detector (SPD) of the Nuclotron-based Ion Collider fAcility (NICA). At these moderate energies, $J/ψ$ production is dominated by gluon-gluon fusion, probing gluon momentum fractions $x\approx 0.1$-$0.2$ at central rapidity and highly asymmetric configurations at forward rapidity, where one parton can reach $x\approx 0.5$-$0.9$. This provides direct sensitivity to the poorly constrained moderate- to large-$x$ region of the gluon helicity distribution $Δg(x)$. We estimate $A_{LL}$ as a function of transverse momentum and rapidity using polarized parton distribution functions, focusing on the underlying partonic spin asymmetry. Nonperturbative long-distance effects are treated in a simplified manner and largely cancel in the asymmetry, enabling a direct assessment of gluon polarization sensitivity. We find asymmetries reaching $|A_{LL}|\approx 0.09$ at $p_T=3~\mathrm{GeV}$, with enhanced sensitivity at forward rapidity. The dominant theoretical uncertainty arises from polarized parton distribution functions. These results demonstrate that inclusive $J/ψ$ measurements at SPD/NICA provide a sensitive and complementary probe of gluon polarization at moderate and large $x$, extending constraints from RHIC into a kinematic regime not directly accessible to the EIC.

We present the first variational Monte Carlo study of nuclear and hypernuclear excited states within the neural-network quantum states (NQS) framework. We implement both the overlap penalty (OP) and natural excited state (NES) methods to compute low-lying excitation spectra. To address the spin contamination in hypernuclear calculations, we propose a quantum number targeting (QNT) technique for the OP method. Both the OP-QNT and NES methods can reproduce diagonal observables, such as energies and spatial structures, in excellent agreement with rigorous benchmarks. We further provide, to our knowledge, the first \textit{ab initio} calculation of the $M1$ transition strength for $^{4}_Λ\mathrm{H}$. The calculated transition strength is consistent with the weak-coupling limit, exhibiting a $\sim$1.3\% suppression. This work demonstrates that NQS can be elevated from ground-state solvers to practical tools for nuclear and hypernuclear spectroscopy.

Modeling non-stationary stochastic systems requires balancing the representational capacity of deep learning with the structural transparency of classical probabilistic models. Markov transition matrices provide such a framework, but traditional frequency-based estimation collapses at high resolutions due to data sparsity. We propose a hybrid approach that parameterizes the manifold of stochastic matrices through a neural network, enabling estimation of time-inhomogeneous Markov chains in sparse-data regimes, and use financial markets as a testbed to investigate the Markov state variable as a critical inductive bias. We show that conditioning on realized volatility produces a more internally consistent Markovian structure than return-based states, achieving a $5.6\%$ reduction in Chapman-Kolmogorov discrepancy and superior held-out likelihood in 9 of 10 assets. Unlike black-box sequence models, our approach generates explicit matrices amenable to direct geometric analysis, surfacing structural findings such as the universal homogenization of transition probabilities under high-volatility regimes.

Supercontinuum generation is a key technology in nonlinear optics, supporting a wide range of applications in frequency metrology and spectroscopy. Integrated photonics offers a promising route toward compact and efficient supercontinuum sources, yet extending the bandwidth while maintaining high spectral flatness remains a central challenge. Here we demonstrate an integrated broadband supercontinuum source based on segment-chirped periodically poled lithium niobate (SC-PPLN) nanophotonic waveguides. By discretizing the chirped poling profile into independently optimized segments, this approach enables high-fidelity ferroelectric domain inversion with near-ideal duty cycles and establishes broadband quasi-phase matching, overcoming the domain inhomogeneity and efficiency limitations commonly encountered in conventional chirped poling. The engineered phase-matching landscape supports efficient wavelength conversion and simultaneous activation of multiple second- and third-order nonlinear processes. Experimentally, we achieve a spectrally flat supercontinuum spanning three optical octaves, from 320 nm in the ultraviolet to 2600 nm in the mid-infrared. These results establish segment-chirped poling as a practical strategy for broadband wavelength conversion and supercontinuum generation in integrated photonics.

The pursuit of a universal description for nonequilibrium critical dynamics in quantum many-body systems stands as a central frontier in modern statistical physics. For driven critical dynamics starting far from the critical point, the well-known Kibble-Zurek (KZ) scaling holds only when the driving rate lies below an upper bound. Here we study driven dynamics restricted to the critical region, and show that robust dynamic scaling behavior exists for arbitrary driving rates. We develop a generalized finite-time scaling (FTS) framework, which provides a unified understanding on the driven dynamics for the full range of quench rates, bridging the KZ scaling in the slow-driving regime and the De~Grandi-Gritsev-Polkovnikov (DGP) scaling in the sudden-quench limit. We verify this unified FTS form through numerical simulations in both quantum critical and tricritical points. The good agreement between theoretical predictions and numerical results confirms the generality of our theory. Our work establishes a universal theory for nonequilibrium critical dynamics spanning the full range of driving rates, with broad implications for quantum quench experiments and out-of-equilibrium statistical mechanics.

We compare notions of admissible surfaces for Cauchy fluxes, formulated as understanding when the normal trace of the underlying stress field can be represented by a measure. If this field is unbounded, the problem of admissibility is necessitated by the fact that the normal trace need not admit a measure representation on every regular surface, but only on ``almost all'' such surfaces. We compare an approach based on a precise majorant introduced by Šilhavý (Arch. Ration. Mech. Anal. 116.3 (1991)) with a Minkowski-type condition introduced by Chen, Torres and the first author (Arch. Ration. Mech. Anal. 249.6 (2025)) by showing that, under mild geometric conditions, the former condition implies the latter. We also show, by means of an explicit construction, that the latter admissibility condition can allow for arbitrary measure concentrations as a normal trace.

This paper presents generation of Fourier-limited pulses from a periodically phase-modulated CW laser field by phase manipulation of its spectral components. Phase modulation in the form of modulus function of sine (MFS) is considered. It allows to produce pedestal-free pulses with controllable repetition rate and duty cycle. Sidelobes of these pulses can be excluded by choosing a proper modulation index. The proposed method allows to produce pulses with 50\% duty ratio. It is shown that three-tone modulation of phase allows to simulate MFS phase modulation.

Full-space electromagnetic invisibility mainly includes light-bending and scattering-cancellation cloaking. Light-bending cloaking causes double-blind phenomenon and is incompatible with sensing, while scattering-cancellation cloaking allows signal interaction and is more suitable for sensors and communication systems. However, traditional scattering-cancellation cloaking depends highly on target shape and size, making it difficult to realize cloaking for irregular, inhomogeneous and electrically large objects. To solve these problems, this work proposes an electromagnetic invisibility gene injection strategy inspired by biological camouflage. Objects are decomposed into subwavelength units, and customized invisibility genes are injected into each unit according to electromagnetic parameters to achieve overall scattering cancellation. Simulations and microwave experiments verify that this method can realize efficient cloaking for objects with arbitrary shapes, dielectric constants from 2 to 10, and different unit morphologies. This strategy breaks the limits of traditional cloaking and provides a universal, flexible scheme for practical applications such as antenna supports and electromagnetic transparent covers.

We introduce the space of continuous and translation invariant area measures, which are measure-valued functionals on the space of convex bodies satisfying a certain locality condition. Our main result shows that the space of $\mathrm{GL}(n,\mathbb{R})$-smooth area measures coincides with the space of area measures obtained by integration with respect to the normal cycle. We show how this result yields Hadwiger-type classification results for continuous area measures that are equivariant with respect to compact groups acting transitively on the unit sphere. In addition, we establish a general density criterion for invariant submodules and show that mixed area measures generate dense submodules with respect to suitable topologies on the space of continuous area measures. As a byproduct, we discuss how McMullen's Conjecture can be obtained directly from the representation of $\mathrm{GL}(n,\mathbb{R})$-smooth translation invariant valuations on convex bodies in terms of integration with respect to the normal cycle.

Local structures in the Universe can influence the dynamics of light scalar fields when coupled to matter. We focus on light test fields evolving in matter modelled as a stochastic source. We describe the effective field theory for light scalars on large scales after integrating out the short distance dynamics. This is most conveniently performed in the Schwinger-Keldysh formalism where we find that the large distance theory involves a stochastic noise corresponding to the exchanges between short and large scales, and new interactions which can affect the time evolution of light scalars. We exemplify this back-reaction when the coupling between matter and scalars is small leading to corrections to the Klein-Gordon equation of the light scalars on large scales. In particular, the resulting corrections to the scalar potential could lead to effects akin to dynamical dark energy. We also consider the situation where all the substructures of the Universe are screened leading to the suppression of large scale dynamics and a cosmic Meissner effect. This highlights the potentially relevant effects of small scale structures on the cosmological dynamics of light scalar fields.

We prove that the Hutchinson operators of a wide class of Iterated Function Systems are equicontinuous. In particular, every Iterated Function System with an attractor has equicontinuous Hutchinson operator.