Papers

In this conference proceeding we review an extension of the Chiral Mean Field (CMF) model that consistently incorporates interacting thermal mesons with self-consistent in-medium masses. In this approach, the in-medium masses of pseudoscalar and vector mesons are evaluated through the explicit chiral symmetry-breaking and vector-interaction terms in the Lagrangian respectively, before applying the mean-field approximation. These medium-modified meson properties introduce additional feedback into the CMF equations of motion, leading to a revised equation of state. The impact of this refinement is analyzed by comparing the hadronic model predictions with recent lattice QCD data and other hadronic descriptions, such as the hadron resonance gas model. The modified CMF framework, featuring an improved meson treatment (mCMF),demonstrates enhanced consistency with lattice-QCD results for thermodynamic observables across a broad range of temperatures and baryon chemical potentials.

We bound the difference between two stochastic Volterra processes with identical Lipschitz coefficients but different kernels. For non-convolution kernels, we establish estimates in $C^0([0,T];L^p(\Omega))$, $p\geq 2$, and for convolution kernels in $L^p(\Omega;L^q(0,T))$, $q \in [1,p]$, and $C^\beta([0,T];L^p(\Omega))$, $L^p(\Omega;C^\beta([0,T]))$, where the range of the Hölder exponent $\beta \in (0,1]$ is the maximal permitted by the regularity of the processes. For the fractional kernel, we then construct Markovian approximations whose error we show to decay as $e^{-a\sqrt{N}}$ in the aforementioned norms, using an $N$-node quadrature based on sinc methods. Numerical experiments for the fractional Brownian motion verify our findings.

We study quasinormal modes governed by the Teukolsky equation in Kerr-Newman-de Sitter spacetime, formally treating the spin weight and field charge as arbitrary parameters. We use exact Heun connection formulae expressed through classical conformal blocks. We analytically derive the quasinormal mode spectra in the small cosmological constant, near-extremal, and near-Nariai limits. In the small cosmological constant limit, we obtain the leading charged de Sitter spectrum together with its subleading corrections. In both the small cosmological constant and near-extremal limits, solving the full connection condition beyond the leading pole approximation gives rise to generically noninteger-power corrections to the quasinormal mode frequencies, whereas no analogous correction appears in the near-Nariai limit. We also analyze the angular eigenvalue problem as an illustration of the same connection-formula method.

The Chiral Mean-Field (CMF) model describes dense matter in terms of baryons and quarks interacting through scalar and vector meson mean fields. In the mean-field approximation, the meson fields are replaced by their expectation values. Their role in generating interactions and in-medium properties is retained, but explicit thermal mesonic excitations are absent. This becomes increasingly problematic at high temperature, where mesons contribute significantly to the thermodynamics of hadronic matter. Here, we keep the original CMF description of dense matter and add the thermal mesonic degrees of freedom using the mesonic sector of the Hadron Resonance Gas (HRG) module in the MUSES framework. Ground-state pseudoscalar and vector mesons account for the missing thermal excitations, while mesonic resonances provide, within the HRG picture, an effective description of mesonic interactions through resonance formation. We study how these contributions affect the pressure, entropy density, energy density, and baryon density, and compare the resulting equation of state with continuum-extrapolated lattice-QCD calculations.

Explicit computations of generic infinitesimal Newton–Okounkov bodies are difficult even for varieties with simple product structure. We give an explicit formula in arbitrary dimension for positive-degree external tensor products on products of smooth projective curves. Writing $d^\downarrow=(d_1^\downarrow,\ldots,d_n^\downarrow)$ for the decreasing rearrangement of the degree vector and setting $d_{n+1}^\downarrow=0$, the body admits the explicit Minkowski decomposition $\sum_{j=1}^n(d_j^\downarrow-d_{j+1}^\downarrow)S_j^{(n)}$, where the $S_j^{(n)}$ are the embedded simplices defined below. Using this description, we give a sharp criterion for equality in the Minkowski inclusion. A simultaneous relabeling argument also allows finitely many such bodies to be realized on a common very general locus of flags after independent decreasing rearrangements of their degree vectors.

Balogh, Bollobás and Narayanan conjectured that among all finite simple $r$-uniform $d$-regular hypergraphs, the number of weak independent sets is maximized by a natural quasi-bipartite construction $H_{r,d}$. We give three types of evidence for this conjecture. For every fixed $r$, we prove the conjectured asymptotic exponential rate whenever the twin quotient has maximum pair codegree $o(d)$. The proof uses the hypergraph container method. For hypergraphs with no cross-edges, the occupancy method gives the sharper error bound $O_r(\log d/d)$. We show that a stronger version of the conjecture in terms of the so-called occupancy fraction is not true, by providing a counterexample for every $r\ge 3$. We also prove exact cases of the conjecture when the hypergraph is $2$-regular. Using an entropy decomposition in the dual edge-cover problem, we settle every odd $r$ and the case $(r,d)=(4,2)$.

We show that the universal rigid monoidal category on one object has an abelian envelope. Since it was proven by Coulembier-Etingof-Ostrik-Pauwels (2023) that this category cannot have an abelian envelope with the quotient property, this disproves the conjecture in [op.cit.] saying that every abelian envelope has the quotient property. Monoidal Ringel duality (Flake-Gruber arxiv:2512.19558) yields a candidate envelope as a lower finite highest weight category. Our proof that this is an abelian envelope relies on Coulembier-Etingof's (2024) continuants to show the required universal property. AI was used to find these results.

Let $n \geq 5$. We prove that the helical maximal operator is bounded on $L^p(\mathbb{R}^n)$ for some $p<2n-4$. This improves the previously known range $p>2n-4$ obtained by Gan-Maldague-Oh. As observed by Beltran-Hickman, the exponent $2n-4$ is the natural limit of the standard local smoothing method.

Scalable quantum computation is expected to rely on fault-tolerant quantum computation (FTQC), in which quantum error correction (QEC) suppresses physical errors sufficiently to support reliable logical operations. This requires quantum compilation to move beyond general-purpose circuit optimization toward encoding-aware and protocol-structured compilation across the full stack of fault-tolerant quantum computers. Beyond circuit synthesis and hardware mapping, an FTQC compiler must lower algorithm-level operations into the logical gate set supported by the chosen code, coordinate encoded data and ancilla resources, realize logical operations together with repeated syndrome extraction under hardware constraints, and provide the resulting measurement stream to real-time decoding. This survey presents a full-stack view of compiler design for QEC-protected quantum computation. We organize existing work into three interacting layers: logical-level QEC compilation, physical-level QEC realization, and decoder runtime integration. At the logical level, we review surface-code lattice-surgery compilers, beyond-surface-code code-surgery frameworks including emerging qLDPC approaches, and compilation support for non-Clifford operations such as magic-state distillation and code switching. At the physical level, we survey hardware-aware QEC realization on superconducting, trapped-ion, and neutral-atom platforms. We further examine decoder models, real-time decoding systems, and frame-management mechanisms that close the feedback loop during fault-tolerant execution. Finally, we identify open challenges in cross-layer optimization, qLDPC compilation, compiler-decoder co-design, runtime adaptivity, and the development of integrated and benchmarkable FTQC compilation stacks. An actively maintained paper list is available at: github.com/chenghongz/QEC-compiler-design.

Multi-agent systems split a task across a tree of agents and justify the split with folklore: smaller contexts, cleaner separation, parallelism. We ask what the split does to how much of what the leaves discover reaches the root. Model a decomposition as a tree in which an agent handed $b$ items keeps any one with probability $r(b)$. If $r(b)=1/b$, every tree delivers exactly one finding, for every task size and every shape; we verify this to $2.4 \times 10^{-15}$ on 20,000 random irregular trees. If $r(b)=Cb^{-\delta}$, a depth-$k$ tree over $N$ findings yields $C^k N^{1-\delta}$: task size and architecture separate, and architecture contributes only $C \le 1$ per level, so flat is optimal for yield and no arrangement of agents escapes the exponent $\delta$. On 600 production deep-research traces $\delta = 0.34$ [0.30, 0.38], by three identifications that do not share a failure mode. At a hop where item boundaries come from the tool rather than a text heuristic, and where $b=1$ occurs 550 times, $C = 0.571$ [0.527, 0.615] is observed rather than extrapolated, over 16,082 hops. A tier also costs alignment: on 1,012 annotated multi-agent traces one brief in sixteen goes off-target, giving $\mu = 0.939$ and a per-tier penalty $C\mu = 0.536$. Depth is bought on two other axes. The root context is the only state that persists and the only one that cannot cheaply forget, and depth cuts its exposure from $N$ items to $N^{1/k}$. Depth is also cheaper: production flat agents bill as $N^{1.39}$, not the $N^2$ an append-only context predicts, and at equal spend two tiers overtake flat at 403 findings. Across every parameter we measured the model says 0.7% to 11.3% of production sessions are worth delegating, against 7.8% that do. A hazard model on 743,819 production tool calls finds that delegation does not respond to a filling context and is instead an opening move.

Robot swarms, by virtue of their decentralised architecture, are a natural tool for scalable, robust modelling of spatial fields, such as water temperature, wind velocity, or terrain elevation. However, existing methods rely on external positioning systems that allow each robot to determine its own position in space. Here, we introduce location-unaware Gaussian process regression (LU-GPR) as a solution to the modelling of spatial fields in the absence of such positioning systems. LU-GPR allows each robot to infer the posterior mean and variance of the field in space, while simultaneously agreeing on a common frame of reference with its peers, using only local sensing and communication. We propose an online algorithm that allows each robot to consistently infer local estimates as its local frame of reference converges to the common one. By means of a product of experts model, each robot also combines the estimates of its peers with its own to obtain a global model. Our results show that LU-GPR scales well with the number of robots and is robust to limited communication ranges. We also demonstrate how it can be used in real-world monitoring scenarios to estimate the flow of an evacuating crowd.

Scalar-Tensor theories extend General Relativity (GR) by including both a scalar field and a metric tensor in describing gravity. Although the matter sector is minimally coupled to the metric in GR, the scalar field coupling to matter may be adjusted by means of Disformal Transformations. One of the most general of these transformations, formulated by Takahashi, Motohashi, and Minamitsuji, include arbitrarily high-order derivatives of the scalar field and are designed to map between two ghost-free Higher-order Scalar-Tensor theories. We used these transformations to determine the most general conditions for the disformal form-invariance of the Klein-Gordon equation for the scalar field. In the second-order case, we identified a family of disformally-related metrics that result in the same propagation solutions. Additionally, higher-order cases could comply with theoretical and phenomenological constraints alongside KG-invariance. Finally, we investigated the notion of disformal transformations as “deformations” of the spacetime manifold.

The (massless) sinh-Gordon model is defined in terms of a continuum massless Gaussian free field perturbed by a cosh interaction. For the hierarchical version of the model, we prove existence of the infinite volume limit, a uniform log-Sobolev inequality, and a mass gap. Our results hold for all $b^2 \in (0,1)$ and simplify for $b^2 \in (0,1/2)$ for which the Gaussian multiplicative chaos has two moments. In an appendix, our renormalization group analysis is compared with the conjectures and controversies in physics which are mostly based on formal analytic continuation of conjectures for the sine-Gordon model and we raise some questions.

This work reports surface acoustic wave (SAW) acoustic delay lines (ADLs) on an aluminum scandium nitride (AlScN) on diamond platform operating in the X band and approaching the Ku band. The large acoustic-velocity contrast between the AlScN film and the diamond substrate produces a strongly dispersive Sezawa branch that decouples the phase velocity from the group velocity. Delay lines with a 1 $\mu$m wavelength show a Sezawa passband at 9.55 GHz with a fractional bandwidth of 1.05%, a propagation loss of 0.094 dB per wavelength, a propagation-limited quality factor of 465, and a group velocity of 5979 m/s, while co-fabricated resonators give a phase velocity of 9560 m/s, a ratio of about 1.6. Scaling the wavelength to 0.5 $\mu$m moves the passband to 16.5 GHz with a fractional bandwidth of 0.7%. The platform therefore reaches an operating frequency about 1.5 times higher than AlScN on sapphire at the same lithographic pitch while preserving group delay per unit length.

We demonstrate a method for determining the magnitude of the angle of arrival (AoA) of a linearly polarized radio-frequency (RF) field using the angle-dependent spectral amplitudes of AC Stark-shifted electromagnetically induced transparency (EIT) resonances. An off-resonant RF field produces distinct Stark shifts of the $|m_J|$ sublevels, while their relative excitation strengths depend strongly on the relative orientation of the RF and optical polarizations. Under the controlled polarization geometry considered here, this dependence enables determination of the AoA magnitude without requiring RF phase measurements or spatially separated sensing locations. We experimentally demonstrate the method at RF frequencies of 1.27 GHz, 2 GHz, 3 GHz, and 4 GHz using a subwavelength cesium vapor cell. Within the $20^\circ-40^\circ$ region of highest angular sensitivity, the estimated repeatability-based $1\sigma$ AoA uncertainty ranges from approximately $0.6^\circ$ to $2^\circ$ across the investigated RF frequencies. A model combining Floquet-Shirley calculations of the RF-dressed Rydberg states with a coherent hyperfine-to-fine-structure optical excitation model qualitatively reproduces the experimental observations. These results establish a path toward compact, phase-independent AoA sensing using spatially localized Rydberg-atom spectroscopy.

Table understanding is a core task in document intelligence, encompassing two key subtasks: table reconstruction and table visual question answering (TabVQA). While recent approaches predominantly rely on vision- language models (VLMs) operating on table images, we propose a more scalable and effective alternative based on structured textual representations. These representations are easier to process, align more naturally with LLMs, and eliminate the need for language-specific visual encoders, making them particularly suitable for multilingual documents. We present DELTA, which separates physical structure recognition, logical structure recognition, and OCR to extract both layout and content accurately. DELTA outputs tables in Optimised Table Structure Language (OTSL), a compact and unified format that encodes cell arrangements and textual content. On table structure recognition (TSR), DELTA achieves TEDS- Structure scores comparable with state-of-the-art methods across FinTabNet, PubTabNet, and PubTables-1M. We further establish its robustness on non-English tables through our curated Hindi benchmark, TORQUE. Building on this, we introduce TARQA, an LLM fine-tuned on OTSL sequences. Our approach yields gains of 9.3 p.p. on WTQ (TabQA) and 9.2 p.p. on FinTabNetQA (TabVQA), respectively. On TORQUE, our method ranks second among all VLMs and DELTA + LLM variants. We release our code, models, and benchmark at: https://github.com/Tihiitborg/Tables-Decoded

A random unitary quantum circuit is expected to be incompressible for exponentially long times. We show that the constant-error circuit complexity of a random unitary circuit grows almost linearly with time as $\Omega(T/\log T)$. The bound holds for all $2\leq T\leq 4^n$ where $n$ is the system size, and involves no other $n$-dependence. This improves previous lower bounds derived from spectral gaps and unitary designs by a factor of $\mathrm{poly}(n)$. Drawing on insights from stochastic calculus, geometric functional analysis, and randomized linear algebra, our approach exploits the circuit's response to variations of individual gates and requires no control over convergence to high-order unitary designs.

Covariates missing not at random generally prevent point identification of regression coefficients without untestable restrictions. This paper studies linear regression when every missing covariate is restricted to a prespecified compact interval. The resulting population target is the set of best linear predictor coefficients compatible with the observed-data law. Under a non-atomic observed-data law and the stated regularity conditions, we can represent this identified set as the image, under the least-squares moment map, of the Aumann expectation of a random moment set. For the population set and its empirical analogue, we derive explicit bounds under bounded, sub-exponential and polynomial envelope conditions. The bounds show their dependence on sample size, dimension, confidence level and tail parameters. Under a Donsker condition and a uniform zero-set error bound, an oracle enlargement of the set-valued Z-estimator also converges at the root n rate. We separately study a Hadamard-design method for exploring the effect of admissible imputations without enumerating all vertices and build intuition to detect situations where the population target can be approximated by a zonotope. A numerical experiment illustrates how co-missingness and the width of the imputation intervals affect this diagnostic.

Visual data communication in digital media is increasingly characterized by short attention spans and snapshot-based viewing, often employing line charts to convey trends and patterns. Among all visual elements, titles are crucial elements that can shape how viewers interpret visual information and form chart takeaways. In this study, we examine how title characteristics, particularly title word count and intended message, influence people's pattern identification in single-class line charts. Participants viewed 50 line charts collected from online news media and identified the pattern they perceived. Our results demonstrate that both title word count and intended message significantly influence viewers' pattern identification. Our findings highlight the importance of title framing in shaping quick-view pattern takeaways and supporting effective visualization communication.

Using perturbation theory for the fine-structure constant $\alpha$ and the electron-to-muon mass ratio, we calculated new contributions to the hyperfine structure of the ground state of the muon-electron helium atom. Compared to our previous results, we calculated new corrections in second-order perturbation theory. This calculation reduces the discrepancy between the theoretical value and the new experimental hyperfine structure measurement.

There is an absolute constant $c>0$ such that, for every $0<\varepsilon\leq1$, arbitrarily large finite sets $A\subset\mathbb{C}$ satisfy \[ |A+A|\leq |A|^{1+\varepsilon},\qquad |AA|\leq |A|^{2-c\varepsilon},\qquad \nu_1(A)\geq |A|^{1+c\varepsilon}, \] where $\nu_1(A)$ counts unordered unit-distance pairs. We combine the arithmetic directions from the recent unit-distance construction with the multiplicative enlargement used in the recent sum-product construction. The arithmetic ingredients are stated as explicit inputs.

We demonstrate a fast readout method for tethered optomechanical pressure sensors. The fast readout method allows mechanical ring-down measurement rates that exceed the total mechanical damping rate $\Gamma_t$. We model the uncertainty of our ring-down measurements with the Cramér-Rao bound, including the effect of thermomechanical noise. Both our data and the Cramér-Rao bound indicate that measurement rates on the order of the mechanical damping rate produce the lowest uncertainty. At low pressures, using the optimal measurement rate allows 10$\times$ faster measurements or 3$\times$ lower uncertainty compared to allowing our sensor to ring down to the thermomechanical noise floor. Our results allow tethered optomechanical pressure sensors to operate at rates comparable to commercially available pressure gauges, removing an obstacle to adoption of optomechanical pressure sensors in industrial settings.

We study generalized amenability of locally compact quantum groups $\mathbb{G}=(\scr M, \Delta, \phi, \psi)$. Let $C_r^*(\mathbb{G})$ and $VN(\mathbb{G})$ denote, respectively, the C*-algebra and von Neumann algebra generated by the quantum left regular representation of $\mathbb{G}$. With natural covariance assumptions and a traceability condition on $VN(\mathbb{G})$, we show that if $C_r^*(\mathbb{G})$ is approximately amenable, then $\mathbb{G}$ admits an invariant quantum mean. We show further that the same conclusion holds if the predual algebra $\scr M_*$ has a bounded approximate identity and is approximately amenable.

Novel-view synthesis from a single image is a fundamentally ambiguous problem. As the camera moves away from the input viewpoint, previously hidden regions become visible, exposing missing geometry and holes in the reconstructed scene. Existing methods often rely on generative models to complete such regions. However, many of these artifacts are small gaps near depth boundaries and do not require generating new scene content. In order to eliminate expensive process of generating image we introduce ORCA, an occlusion-aware method for reconstructing and completing explorable 3D scenes from a single image. ORCA first introduces 3D structure into a Gaussian-anchor representation using monocular depth while preserving the original camera-ray correspondence. During scene exploration, missing regions are handled based on their size and structure. Small disocclusions are repaired using RGB-D information already available in the reconstruction, while generative inpainting is reserved for larger regions that cannot be reliably recovered from the scene. New Gaussian anchors are added and optimized locally without modifying the existing representation. By reducing unnecessary reliance on generative inpainting, ORCA limits generation-induced hallucinations and better preserves the content and structure of the original scene. On DIV2K, ORCA improves novel-view quality over VistaDream across all reported metrics, increasing MUSIQ from 61.60 to 68.71 and CLIP-IQA from 0.474 to 0.574. These results show that many novel-view artifacts can be repaired effectively by reusing information already present in the reconstructed scene.

We study the Arnold-Beltrami-Childress (ABC) flow in perturbative regimes near its three elementary integrable coordinate axes. Starting from a degenerate family of periodic streamlines of the limiting integrable system, we use first-order averaging to prove the existence of two isolated periodic solutions of the perturbed flow. The three perturbative regimes are related by the cyclic symmetry of the ABC vector field. In each case, the corresponding two-dimensional averaged system possesses two simple equilibria, one elliptic and the other hyperbolic, depending on the sign of the relevant parameter ratio. Poincaré sections illustrate how the degenerate periodic structure of the integrable limit breaks under perturbation and how the isolated periodic orbits predicted by averaging emerge within the surrounding dynamics. These periodic orbits provide the natural link between the perturbative analysis and the integrability problem. The eigenvalues of the linearized averaged system determine the leading-order behavior of the nontrivial characteristic multipliers of the bifurcating periodic solutions. Combining this relation with the Poincaré-Llibre-Valls criterion, we prove that, in a neighborhood of each of these periodic orbits, there exists no nonconstant first integral $H\in C^1$ that is regular along the orbit. The analytical results are further illustrated and confirmed by direct shooting, monodromy-matrix computations, and continuation of the elliptic and hyperbolic branches, demonstrating that the first-order averaging approximation remains quantitatively accurate over a substantially wider parameter range than the strict asymptotic regime.

We describe transversal singularity types of the singular locus of the $A$-discriminant for $A\subset\mathbb Z$, and deduce a Whitney type theorem for a coordinate projection of a surface defined by a general polynomial equation with a given Newton polytope $N$: under mild combinaorial conditions on $N$, all multisingularities are stable (folds, cusps, and double folds). We then enumerate the multisingularities in terms of $N$. The results rely on the analysis of degeneracy of relevant Vandermonde/Schur type matrices, which may be of independent interest.

We investigate the relaxation of an approximately conserved charge in interacting quantum systems close to local equilibrium. To this end, we provide a pedagogical review of Zubarev's non-equilibrium statistical operator approach in the minimal setting of a single non-conserved charge and apply it to the problem at hand. We explicitly highlight the physical assumptions that lead to a local relaxation law: weak charge violation, a separation between the short timescale of microscopic correlations and the much longer timescale of charge relaxation, and the resulting loss of microscopic memory. Under these conditions, the leading relaxation rate is determined by an equilibrium correlation function of the charge-violating operator. We show that the same result follows from a simpler local-equilibrium construction based on the system's evolution over an intermediate timescale, providing a direct alternative for practical calculations and making the common physical ingredients of the two approaches explicit. Beyond the decay law itself, we relate the relaxation rate to the equilibrium diffusion of the same charge. We then allow the charge density to vary in space, which leads to a diffusion-relaxation equation. Finally, we illustrate the formalism through electroweak $\mathrm{B+L}$ washout and a perturbative scalar model, where agreement with the linearized Boltzmann equation establishes a direct connection between equilibrium-correlator and kinetic descriptions.

Stanley's conjecture asserts that the $h$-vector of a matroid is a pure $O$-sequence. Corry, Dochtermann, McClain, Perkinson and Yi introduced cycle systems, which give a bijective proof for the matroids that admit one, through coparking functions, and proposed generalized cycle systems. Every matroid admitting a cycle system is regular, and the Wagner and Petersen graphs admit no generalized cycle system consisting of circuits. We propose a relaxation. Where the coparking recursion breaks down, at the strata whose unique union is independent, the coparking functions are replaced by a fibre: a pure multicomplex with the $h$-vector of the dead node, the minor of the matroid attached to the stratum. We prove, for any matroid with a fixed basis, that whenever the required fibres exist the relaxed coparking functions form a pure multicomplex whose degree sequence is the $h$-vector of the matroid, so Stanley's conjecture follows. The proof rests on a version of Dhar's burning algorithm for a matroid with a fixed basis, which gives the purity, and on a deletion-contraction identity that computes the gap between the $h$-vector and the coparking functions as a sum of local $h$-vectors, one per dead node. Coned, biconed and triconed graphs carry a fibre system with their canonical spanning trees, as do the Wagner and Petersen graphs. Beyond graphs, every basis of a matroid of corank two, of a matroid of rank at most four or of a uniform matroid carries a fibre system, so Stanley's conjecture follows for those classes. We also give a graph of radius two on twelve vertices which, with its breadth-first spanning tree, carries no fibre system.

Complex networks are often compared using selected graph-theoretical measures that capture a selected set of properties with effects ranging from local to global, such as degree, clustering or betweenness centrality. Here we introduce a structural fingerprinting framework based on graphlets: small rooted subgraphs whose distributions provide a systematic description of local-to-mesoscale topology. Across synthetic networks generated from several random graph models, graphlet fingerprints capture parameter-dependent structural differences, outperform standard graph-theoretical measures, and identify even subtle local patterns driving discrimination. We then apply the framework to empirical resting-state functional connectomes, documenting that while graphlets show superior sensitivity also to controlled topological perturbations of brain connectivity, specifically in schizophrenia-control classification they perform only comparably to classical graph-theoretical features. This is in line with the notion that schizophrenia-related alterations are dominated by spatially localized connectivity changes rather than general topological reorganization. Altogether, the generative modeling, targeted perturbations and real-world neuroimaging classification challenge position graphlets as flexible structural fingerprints of complex networks, while carefully outlining their strength and weaknesses compared to more classical graph theoretical features.

Integrated Kerr microresonators provide on-chip optical nonlinearity for wavelength conversion, optical frequency combs, and quantum light sources. Traditionally, their dispersion engineering has tied nonlinear functionality to resonator geometry, forcing trade-offs with other device objectives. In particular, Kerr microresonators usually feature narrow resonator waveguides, but wide waveguides support higher Q through reduced sidewall scattering. We propose that modal phase matching - invoking multiple spatial mode families to satisfy dispersion requirements - facilitates Kerr nonlinear optics beyond traditional geometries. Working with a commercial foundry, we design and fabricate high-$ (>10^7) microresonators on a 160-nm-thick silicon nitride platform and demonstrate Kerr optical parametric oscillation. We achieve 20% conversion efficiency and gap-free wavelength tuning over >1 nm for parametric oscillation at the cesium D1 transition. Modal phase matching further supports pumping in both 1060-nm and 795-nm bands, without custom device layers, for wavelength generation between 600 nm to 1400 nm. Our work expands the Kerr design space, effectively decoupling Q and dispersion to create new opportunities with high-Q nonlinear devices.