Conical microfluidic channels filled with electrolytes exhibit volatile memristive behavior, offering a promising platform for energy-efficient, neuromorphic computing. Here, we integrate these iontronic channels as additional nonlinear elements in nonlinear Shinriki-inspired oscillators and demonstrate that they exhibit alternating chaotic and non-chaotic dynamics across a broad frequency range. Exploiting this behavior, we construct XOR and NAND gates by coupling three Memriki oscillators, and we further realize the full set of standard logic gates through combinations of NAND gates. Our results establish a new paradigm for iontronic computing and open avenues for scalable, low-power logical operations in microfluidic and bio-inspired systems.

The polarisation set of a vector-valued distribution generalises the wavefront set and captures fibre-directional information about its singularities in addition to their phase space description. Motivated by problems in quantum field theory on curved spacetimes, we consider normally hyperbolic operators on vector bundles over globally hyperbolic spacetimes, and compute the polarisation sets of the kernel distributions for their advanced and retarded Green operators and the difference thereof. This permits the computation of related polarisation and wavefront sets for operators whose solution theory is related to the normally hyperbolic case. As a particular example, we consider the Proca equation that describes massive relativistic spin-1 particles, identifying and closing a gap in a recent paper on that subject.

In theoretical studies of two-dimensional (2D) systems, the Mermin-Wagner theorem prevents continuous symmetry breaking at any finite temperature, thus forbidding a Landau phase transition at a critical temperature $T_c$. The difficulty arises when many-body theoretical studies predict a Landau phase transition at finite temperatures, which contradicts the Mermin-Wagner theorem and is termed a pseudo phase transition. To tackle this problem, we systematically develop a symmetrization scheme, defined as averaging physical quantities over all symmetry-breaking states, thus ensuring that it preserves the Mermin-Wagner theorem. We apply the symmetrization scheme to the GW-covariance calculation for the 2D repulsive Hubbard model at half-filling in the intermediate-to-strong coupling regime and at low temperatures, obtaining the one-body Green's function and spin-spin correlation function, and benchmark them against Determinant Quantum Monte Carlo (DQMC) with good agreement.The spin-spin correlation functions are approached within the covariance theory, a general method for calculating two-body correlation functions from a one-particle starting point, such as the GW formalism used here, which ensures the preservation of the fundamental fluctuation-dissipation relation (FDR) and Ward-Takahashi identities (WTI). With the FDR and WTI satisfied, we conjecture that the $χ$-sum rule, a fundamental relation from the Pauli exclusion principle, can be used to probe the reliability of many-body methods, and demonstrate this by comparing the GW-covariance and mean-field-covariance approaches. This work provides a novel framework to investigate the strong-coupling and doped regime of the 2D Hubbard model, which is believed to be applicable to real high-$T_c$ cuprate superconductors.

Based on chiral soliton models, the quantum fluctuation energies of quarks over a spatially inhomogeneous meson field background have been thoroughly studied. We have used a systematic calculation scheme initiated by Schwinger, in which the loop quantum fluctuation energies are evaluated by a nontrivial level summation over the eigenvalue spectrum of the effective Hamiltonian of the system. The effective Hamiltonian can be constructed by one loop effective action of fluctuations of quarks over a static chiral soliton field background. The corresponding Dirac equation is obtained. In a static and spatially spherical case and by the hedgehog ansatz the radial part and the angular part of the grand spin of the wave function for the Dirac equation can be separated. Due to the soliton background the eigenvalue spectrum are distorted. The scattering phase shift can be determined by solve the radial equations at different momentum. The density of states in momentum space can be derived. The effective Hamiltonian has been diagonalized in a Hilbert space where the eigenfunctions are labeled by the parity, grand spin and energy. The renormalization scheme can be carried out by a Born subtraction of the phase shift and the compensating Feynman diagram renormalization. Finally the finite quantum fluctuation energies over chiral soliton background at different parities and grand spins have been numerically evaluated, compared and discussed.

The quintessential hallmark distinguishing metasurfaces from traditional optical components is the engineering of subwavelength meta-atoms to manipulate light at will. Enabling this freedom, in a reverse manner, to control objects constituted by metasurfaces could expand our capability of optical manipulation to go beyond the predominant microscopic and sub-microscopic scales. Here, we introduce a driving metaphotonic force fully controllable by meta-atoms to manipulate structured objects named metajets. Upon Newton's law of motion that can apply to classical and relativistic mechanics, we develop a first-principles theory to analyze optical forces generated by refraction and reflection at an interface. We find that three-dimensional motions of metajets would be possible if one could introduce an extra wavevector component. We achieve that by creating a spatially distributed phase gradient with deliberately arranged silicon nanopillars. Our experiments and simulations reveal an in-plane propulsion and, very importantly, out-of-plane levitation of the metajets, aligning well with the theory. We also find that the metaphotonic force augments with increased light power but is not limited by the size of metajets, which could unleash new opportunities for metaphotonic control in large settings, such as interstellar light sails.

Cloaking is a method of making obstacles undetectable. Here we cloak unit cells of a magnetic pattern squeezed into an otherwise periodic pattern from a magnetically driven colloidal flow. We apply a time-periodic external magnetic field loop to an ensemble of paramagnetic colloidal particles on the deformed periodic magnetic pattern. There exist topological loops where the particles avoid to trespass the cloaked regions by robustly traveling around the cloak. Afterwards the ensemble of particles continues with a motion identical to the motion as if the distorted region were nonexistent and the ensemble would have trespassed the undeformed region. We construct the cloak by continuously squeezing new conformally mapped unit cells between those of the originally undeformed and periodic pattern. We find a cloaking/decloaking transition as a function of the size and shape of the newly squeezed-in region. A cloak is scalable to arbitrary size if the biholomorphic map from the undistorted periodic lattice to the region outside the cloak locally rotates by less than an angle of forty five degrees. The work generalizes cloaking from waves toward particles.

We consider a sequence of Hawkes processes whose excitation measures may depend on the generation, and study its scaling limits in the near-unstable limiting regime. The limiting random measures, characterized via a nonlinear convolutional equation, form a family parameterized by a pair consisting of a locally finite measure and a geometrically infinitely divisible probability distribution on the positive real line. These measures can be interpreted as generalizations of the Feller diffusion and fractional Feller (CIR) processes, but also allow for a "driving noise" associated with general L\' evy-type operators of order at most $1$, including fractional derivatives of any order $α>0$ (formally corresponding to possibly negative Hurst parameters).

We give results on the asymptotic in Waring's problem over function fields that are stronger than the results obtained over the integers using the main conjecture in Vinogradov's mean value theorem. Similar estimates apply to Manin's conjecture for Fermat hypersurfaces over function fields. Following an idea of Pugin, rather than applying analytic methods to estimate the minor arcs, we treat them as complete exponential sums over finite fields and apply results of Katz, which bound the sum in terms of the dimension of a certain singular locus, which we estimate by tangent space calculations.

We measure the dynamical behavior of colloidal singlets and dumbbells on an inclined magnetic moiré pattern, subject to a precessing external homogeneous magnetic field. At low external field strength single colloidal particles and dumbbells move everywhere on the pattern: At stronger external field strengths colloidal singlets and dumbbells are localized in generic locations. There are however nongeneric locations of flat channels that cross the moiré Wigner Seitz cell. In the flat channels we find gravitational driven translational and non-translational dynamic phase behavior of the colloidal singlets and dumbbells depending on the external field strength and the precession angle of the external homogeneous magnetic field.

Our understanding of high-lying states within the charmonium family remains incomplete, particularly in light of recent observations of charmonium states at energies around 4 GeV. In this study, we investigate the spectroscopic properties of several high-lying charmonia, focusing on the $2D$ and $1F$ states. A mass spectrum analysis is conducted, incorporating the unquenched effects. We then present a detailed study of the strong decay properties, including partial decay widths for two-body strong decays permitted by the Okubo-Zweig-Iizuka (OZI) rule. Additionally, we explore the primary radiative decay channels associated with these states. Finally, we discuss the radiative transitions of the $2D$ and $1F$ states via $e^+e^-$ annihilation. Theoretical predictions provided here aim to guide future experimental searches for high-lying charmonium states at facilities such as BESIII, Belle II, LHCb, and the future STCF.

This paper presents an underwater acoustic reconfigurable intelligent surface (UA-RIS) designed for long-range, high-speed, and environmentally friendly communication in oceanic environments. The proposed UA-RIS comprises multiple pairs of acoustic reflectors that utilize a synthetic reflection scheme to flexibly control the amplitude and phase of reflected waves. This capability enables precise beam steering to enhance or attenuate sound levels in specific directions. A prototype UA-RIS with 4*6 acoustic reflection units is constructed and tested in both tank and lake environments to evaluate performance. Experimental results using a continuous wave (CW) as the source signal demonstrate that the prototype is capable of effectively pointing reflected waves to targeted directions while minimizing side lobes through synthetic reflection. Field tests reveal that deploying the UA-RIS on the sender side considerably extends communication ranges by 28% in deep water and 46% in shallow waters. Furthermore, with a fixed communication distance, positioning the UA-RIS at the transmitter side substantially boosts the receiving signal-to-noise ratio (SNR), with an average increase of 2.13 dB and peaks up to 2.92 dB. When positioned on the receiver side, the UA-RIS can expand the communication range in shallow and deep water environments by 40.6% and 66%, respectively. Moreover, placing the UA-RIS close to the receiver enhances SNR by an average of 2.56 dB, reaching up to 4.2 dB under certain circumstances.

We establish a characterization (under some natural conditions) of those orders in Dedekind domains which allow a transfer homomorphism to a monoid of zero-sum sequences. As a consequence, the inclusion map to the Dedekind domain is a transfer homomorphism, with the exception of a particular case. The arithmetic of Krull and Dedekind domains is well understood, and the existence of a transfer homomorphism implies that the order and the associated Dedekind domain share the same arithmetic properties. This is not the case for arbitrary orders in Dedekind domains.

This paper employs the Riemann-Hilbert problem to provide a comprehensive analysis of the asymptotic behavior of the high-genus Korteweg-de Vries soliton gases. It is demonstrated that the two-genus soliton gas is related to the two-phase Riemann-Theta function as \(x \to +\infty\), and approaches to zero as \(x \to -\infty\). Additionally, the long-time asymptotic behavior of this two-genus soliton gas can be categorized into five distinct regions in the \(x\)-\(t\) plane, which from left to right are rapidly decay, modulated one-phase wave, unmodulated one-phase wave, modulated two-phase wave, and unmodulated two-phase wave. Moreover, an innovative method is introduced to solve the model problem associated with the high-genus Riemann surface, leading to the determination of the leading terms, which is also related with the multi-phase Riemann-Theta function. A general discussion on the case of arbitrary \(N\)-genus soliton gas is also presented.

Given a smooth variety $X$ over the field $\mathbb{R}$ of real numbers and a line bundle $\mathcal{L}$ on $X$ with associated topological line bundle $L=\mathcal{L}(\mathbb{R})$, we study the quadratic real cycle class map $\widetildeγ_{\mathbb{R}}^c:\widetilde{\mathrm{CH}}^c(X,\mathcal{L})\rightarrow\mathrm{H}^c(X(\mathbb{R}),\mathbb{Z}(L))$ from the $c$-th Chow-Witt group of $X$ to the $c$-th cohomology group of its real locus $X(\mathbb{R})$ with coefficients in the local system $\mathbb{Z}(L)$ associated with $L$. We focus on the cases $c\in\{0,d-2,d-1,d\}$ where $d$ is the dimension of $X$ and we formulate a precise conjecture on the image of $\widetildeγ_{\mathbb{R}}$ in terms of the exponents of its cokernel that is corroborated by the results obtained in those codimensions.

We consider inclusions $\mathcal{S}\leq \mathcal{R}$ of discrete, probability measure-preserving orbit equivalence relations. In previous work with Abért-Fraçzyk, we established the pointwise almost sure existence of the cospectral radius of a random walk on the $\mathcal{R}$-classes. In this paper, we investigate the connections of this cospectral radius to the coamenability of the inclusion $\mathcal{S}\leq \mathcal{R}$. We also undertake a systematic study of coamenability for inclusions of relations, establishing several equivalence formulations of this notion.

Power-law probability distributions are widely used to model extreme statistical events in complex systems, with applications to a vast array of natural phenomena ranging from earthquakes to stock market crashes to pandemics. We show that analogous heavy tails arise naturally in open quantum systems with nonlinear dissipation. Introducing a prototypical family of quantum dynamical models, we analytically prove the emergence of power-law tails in the steady state energy distribution, originating from an amplification of quantum noise whose microscopic fluctuations grow with energy. Moreover, our analysis suggests a general mechanism for heavy-tail statistics in the nonequilibrium steady states of open quantum systems: Nonlinear dissipation generically induces multiplicative quantum noise, enforced by the constraints of quantum mechanics, which is responsible for the heavy-tail behavior. This is supported by numerical simulations of a general class of nonlinear dynamics known as quantum Liénard systems. Remarkably, even when the corresponding classical system is stable, we find power-law tails in both steady-state populations and coherences, which occur for typical parameters without fine-tuning. This phenomenon can potentially be harnessed to develop extreme photon sources for novel applications in light-matter interaction and sensing.

Synthetic antiferromagnets offer rich magnon energy spectra in which optical and acoustic magnon branches can hybridize. Here, we demonstrate a broken intrinsic symmetry induced coupling of acoustic and optical magnons in a synthetic ferrimagnet consisting of two dissimilar antiferromagnetically interacting ferromagnetic metals. Two distinct magnon modes hybridize at degeneracy points, as indicated by an avoided level-crossing. The avoided level-crossing gap depends on the interlayer exchange interaction between the magnetic layers, which can be controlled by adjusting the non-magnetic interlayer thickness. A large avoided level crossing gap of 3.9 GHz is revealed, exceeding the coupling strength that is typically found in other magnonic hybrid systems based on a coupling of magnons with photons or magnons with phonons.

Let $G$ be a countable group acting properly on a metric space with contracting elements and $\{H_i:1\le i\le n\}$ be a finite collection of Morse subgroups in $G$. We prove that each $H_i$ has infinite index in $G$ if and only if the relative second bounded cohomology $H^{2}_b(G, \{H_i\}_{i=1}^n; \mathbb{R})$ is infinite-dimensional. In addition, we also prove that for any contracting element $g$, there exists $k>0$ such that $H^{2}_b(G, \langle \langle g^k\rangle \rangle; \mathbb{R})$ is infinite-dimensional. Our results generalize a theorem of Pagliantini-Rolli for finite-rank free groups and yield new results on the (relative) second bounded cohomology of groups.

We study the cohomology rings of tiling spaces $Ω$ given by cubical substitutions. While there have been many calculations before of cohomology groups of such tiling spaces, the innovation here is that we use computer-assisted methods to compute the cup-product structure. This leads to examples of substitution tilings with isomorphic cohomology groups but different cohomology rings. Part of the interest in studying the cup product comes from Bellissard's gap-labeling conjecture, which is known to hold in dimensions $\le 3$, but where a proof is known in dimensions $\ge 4$ only when the Chern character from $K^0(Ω)$ to $H^*(Ω,\mathbb{Q})$ lands in $H^*(Ω,\mathbb{Z})$. Computation of the cup product on cohomology often makes it possible to compute the Chern character. We introduce a natural generalization of the gap-labeling conjecture, called the equivariant gap-labeling conjecture, which applies to tilings with a finite symmetry group. Again this holds in dimensions $\le 3$, but we are able to show that it fails in general in dimensions $\ge 4$. This, plus some of our cup product calculations, makes it plausible that the gap-labeling conjecture might fail in high dimensions.

Research suggests that acoustic technology may be able to detect ultra-high-energy neutrinos if a large amount of non-linear fluid is analyzed. When a neutrino interacts in water, it creates a quasi-instantaneous cascade of particles, heating that region of the fluid and emitting a tiny acoustic signal. This rapid heating produces a thermoacoustic Bipolar Pulse (BP) with unique characteristics such as a wide bandwidth and a narrow directivity for these frequencies. While dedicated devices for acoustic neutrino detection are currently non-existent, there are a few underwater neutrino telescopes that utilize optical technology, but often with an acoustic positioning system that deploys hydrophones in the infrastructure. The possibility of using them to study a BP caused by a neutrino interaction is currently being discussed. This study aims to evaluate the implementation of a trigger system to detect a possible BP in deep-sea hydrophones. For this, up to 24 hours of the raw acoustic signal recorded by the O$ν$DE-2 station, which was located 25 km off-shore from Catania in the Western Ionian Sea, at 2100 m depth, is analyzed. The station used calibrated hydrophones from a few Hz to 70 kHz. In this work, a synthetic BP is created and added to the experimental data, allowing the study of its detection and the calculation of precision and recall.

Quantum Communications promise advances in cryptography, quantum computing and clock synchronisation, among other emerging applications. However, communication based on quantum phenomena requires an extreme level of isolation from external disturbances, complicating the co-propagation of quantum and classical signals. The challenge is greater when deploying networks that are both heterogeneous (e.g., multiple vendors) and installed in production facilities, given that this type of infrastructure already supports networks loaded with their own requirements. Moreover, to achieve a broad acceptance among network operators, the joint management and operation of quantum and classical resources, compliance with standards, and legal and quality assurance need to be addressed. This article presents solutions to the aforementioned challenges validated in the Madrid quantum network during the implementation of the projects CiViC and OpenQKD. This network was designed to integrate quantum communications in the telecommunications ecosystem by installing quantum-key-distribution modules from multiple providers in production nodes of two different operators. The modules were connected through an optically-switched network with more than 130~km of deployed optical fibre. The tests were done in compliance with strict service level agreements that protected the legacy traffic of the pre-existing classical network. The goal was to ensure full quantum-classical interoperability at all levels, while limiting the modifications to optical transport and encryption and complying with relevant standards. This effort is intended to lay the foundation for large-scale quantum network deployments.

Automatically extracting personal information -- such as name, phone number, and email address -- from publicly available profiles at a large scale is a stepstone to many other security attacks including spear phishing. Traditional methods -- such as regular expression, keyword search, and entity detection -- achieve limited success at such personal information extraction. In this work, we perform a systematic measurement study to benchmark large language model (LLM) based personal information extraction and countermeasures. Towards this goal, we present a framework for LLM-based extraction attacks; collect four datasets including a synthetic dataset generated by GPT-4 and three real-world datasets with manually labeled eight categories of personal information; introduce a novel mitigation strategy based on prompt injection; and systematically benchmark LLM-based attacks and countermeasures using ten LLMs and five datasets. Our key findings include: LLM can be misused by attackers to accurately extract various personal information from personal profiles; LLM outperforms traditional methods; and prompt injection can defend against strong LLM-based attacks, reducing the attack to less effective traditional ones.

We realize every closed flat 3-manifold as a cusp section of a complete, finite-volume hyperbolic 4-manifold whose symmetry group acts transitively on the set of cusps. Moreover, for every such 3-manifold, a dense subset of its flat metrics can be realized as cusp sections of a cusp-transitive 4-manifold. Finally, we prove that there are a lot of 4-manifolds with pairwise isometric cusps, for any given cusp type.

We offer a streamlined and computationally powerful characterization of higher representations (higher charges) for defect operators under generalized symmetries, employing the powerful framework of Symmetry TFT $\mathcal{Z}(\mathcal{C})$. For a defect $\mathscr{D}$ of codimension p, these representations (charges) are in one-to-one correspondence with gapped boundary conditions for the SymTFT $\mathcal{Z}(\mathcal{C})$ on a manifold $Y = Σ_{d-p+1} \times S^{p-1}$, and can be efficiently described through dimensional reduction. We explore numerous applications of our construction, including scenarios where an anomalous bulk theory can host a symmetric defect. This generalizes the connection between 't Hooft anomalies and the absence of symmetric boundary conditions to defects of any codimension. Finally we describe some properties of surface charges for (3 + 1)d duality symmetries, which should be relevant to the study of Gukov-Witten operators in gauge theories.

The hydrothermal synthesis of novel materials typically relies on both knowledge of the redox activities of all cations present in the reaction solution and a small toolset of so-called mineralizers to tune the solution's overall chemical potential. Upon the use of a less conventional mineralizer species, SiO$_2$, we show the stabilization of spiroffite-type Co$_2$Te$_3$O$_8$ under less forceful hydrothermal conditions than in previous reports. When synthesized in the presence of both SiO$_2$ and each respective alkali carbonate as a secondary mineralizer, silicon substitution in place of tellurium in the host structure becomes apparent, and the corresponding introduced disorder gives rise to enhanced low-temperature ferromagnetism. Our results highlight the complexities of underutilized and combined mineralizer species in the stabilization and tuning of complex magnetic ground states via hydrothermal synthesis techniques.

Let $T$ be the theory of an o-minimal field and $T_0$ a common reduct of $T$ and $T_{an}$. I adapt Mourgues' and Ressayre's constructions to deduce structure results for $T_0$-reducts of $T$-$λ$-spherical completion of models of $T_{\mathrm{convex}}$. These in particular entail that whenever $T$ is the theory of a reduct of $\mathbb{R}_{an,\exp}$ defining the exponentiation (e.g.\ $T=T_{\exp}$, the theory of the field of reals expanded by the exponential function), every model of $T$ has an initial elementary embedding in the field $\mathbf{No}$ of surreal numbers. This answers positively an open question in (arXiv:2002.07739). The main technical result is that expanding an integral domain of generalized series in the sense of Hahn-Higman-Ribenboim (such as a Hahn field) by a family of generalized power series interpreted as functions defined on certain infinitesimal elements, has the property that truncation closed subsets generate truncation closed substructures, provided that the family of generalized power series is itself closed under truncations and partial derivatives. It is also shown that the further closure of the generated set under solutions to certain equations is as well closed under truncations. The formal results on power series leave room for possible generalizations to the case in which $T_0$ is power bounded but not necessarily a reduct of $T_{an}$.

We develop new approximate compilation schemes that significantly reduce the expense of compiling the Quantum Approximate Optimization Algorithm (QAOA) for solving the Max-Cut problem. Our main focus is on compilation with trapped-ion simulators using Pauli-$X$ operations and all-to-all Ising Hamiltonian $H_\text{Ising}$ evolution generated by Molmer-Sorensen or optical dipole force interactions, though some of our results also apply to standard gate-based compilations. Our results are based on principles of graph sparsification and decomposition; the former reduces the number of edges in a graph while maintaining its cut structure, while the latter breaks a weighted graph into a small number of unweighted graphs. Though these techniques have been used as heuristics in various hybrid quantum algorithms, there have been no guarantees on their performance, to the best of our knowledge. This work provides the first provable guarantees using sparsification and decomposition to improve quantum noise resilience and reduce quantum circuit complexity. For quantum hardware that uses edge-by-edge QAOA compilations, sparsification leads to a direct reduction in circuit complexity. For trapped-ion quantum simulators implementing all-to-all $H_\text{Ising}$ pulses, we show that for a $(1-ε)$ factor loss in the Max-Cut approximation ($ε>0)$, our compilations improve the (worst-case) number of $H_\text{Ising}$ pulses from $O(n^2)$ to $O(n\log(n/ε))$ and the (worst-case) number of Pauli-$X$ bit flips from $O(n^2)$ to $O\left(\frac{n\log(n/ε)}{ε^2}\right)$ for $n$-node graphs. We demonstrate significant reductions in noise are obtained in our new compilation approaches using theory and numerical calculations for trapped-ion hardware. We anticipate these approximate compilation techniques will be useful tools in a variety of future quantum computing experiments.

We introduce a permutationally invariant multipartite Bell inequality for many-body three-level systems and use it to investigate a connection between Bell nonlocality and (lack of) quantum chaos. An associated Bell operator is then defined via Born's rule, mapping the conditional probabilities of the Bell inequality to quantum measurement operators. This allows us to interpret the Bell operator as an effective Hamiltonian, which we use to analyze its spectral statistics across different SU(3) irreducible representations and measurement choices. Surprisingly, we find that, in every irreducible representation exhibiting nonlocality, the measurement settings yielding maximal violation result in a Bell operator with Poissonian level statistics, thus signaling integrable behavior. This integrability is both unique and fragile, since generic or slightly perturbed measurements lead to the Wigner-Dyson statistics associated with chaotic behavior. Through further analysis, we are able to identify an emergent parity symmetry in the Bell operator near the point of maximal violation, providing an explanation for the observed regularity in the spectrum. These results suggest a deep interplay between optimal quantum measurements, non-local correlations, and integrability, opening new perspectives at the intersection of Bell nonlocality and quantum chaos.

Given a closed surface $S$ with finitely generated Veech group $G$ and its $π_1(S)$-extension $Γ$, there exists a hyperbolic space $\hat{E}$ on which $Γ$ acts isometrically and cocompactly. The space $\hat{E}$ is obtained by collapsing some regions of the surface bundle over the convex hull of the limit set of $G$. Using the nice action of $Γ$ on the hyperbolic space $\hat{E}$, it is shown that $Γ$ is hierarchically hyperbolic. These are generalizations of results from Dowdall-Durham-Leininger-Sisto, which assume in addition that $G$ is a lattice. Because finitely generated Veech groups are among the most basic examples of subgroups of mapping class groups which are expected to qualify as geometrically finite, this result is evidence for the development of a broader theory of geometric finiteness.

Goussarov-Habiro's theory of clasper surgeries defines a filtration of the monoid of string links $L(m)$ on $m$ strands, in a way that geometrically realizes the Feynman diagrams appearing in low-dimensional and quantum topology. Concretely, $L(m)$ is filtered by $C_n$-equivalence, for $n\geq 1$, which is defined via local moves that can be seen as higher crossing changes. The graded object associated to the Goussarov-Habiro filtration is the Goussarov-Habiro Lie algebra of string links $\mathcal{L} L(m)$. We give a concrete presentation, in terms of primitive Feynman (tree) diagrams and relations ($\text{1T}$, $\text{AS}$, $\text{IHX}$, $\text{STU}^2$), of the rational Goussarov-Habiro Lie algebra $\mathcal{L} L(m)_{\mathbb{Q}}$. To that end, we investigate cycles in graphs of forests: flip graphs associated to forest diagrams and their $\text{STU}$ relations. As an application, we give an alternative diagrammatic proof of Massuyeau's rational version of the Goussarov-Habiro conjecture for string links, which relates indistinguishability under finite type invariants of degree $<n$ and $C_n$-equivalence.