Papers

Multi-robot coordination methods often score a joint plan from singleton and pairwise terms, leaving out the terms that involve three or more robots. We measure the plan-selection regret of two pairwise approximations to delivered coverage using frozen multi-robot trajectories. For each four-robot plan on an indoor exploration benchmark, replaying all 16 robot subsets gives the exact delivered-coverage set function $F$. From the same subset values we compute two pairwise scores: the exact order-2 Möbius truncation $F_2$, which depends only on the singleton and pair values, and an equal-weight least-squares two-additive fit $G$. Ranking by $F_2$ instead of $F$ changes the selected plan on six of seven maps at the 15 m candidate-generation range in each of two candidate families, with regret up to 0.337 of map coverage. Switching to $G$ reduces the regret but still changes the selection on three of seven maps in each family. The additive score $F_1$, which keeps only the singleton terms, selects the exact winner on six of seven maps in one family and four of seven in the other, against one of seven for $F_2$. We also find that lower average reconstruction error does not guarantee lower selection regret.

Large language models (LLMs) are increasingly used as synthetic survey respondents to estimate population response distributions. In cross-cultural survey simulation, evaluations should assess not only distributional fidelity within countries but also whether differences across countries are preserved. However, existing distance-based metrics such as Jensen–Shannon divergence (JSD) do not directly capture such cross-country differences. To address this limitation, we introduce Cultural Divergence Preservation (CDP), a reference-light diagnostic based on a one-time human calibration. CDP identifies reduced cross-country divergence as cultural flattening and increased divergence as cultural caricature. To evaluate CDP, we conduct experiments across four LLM backbones, three persona-based prompting methods, and two survey domains, the World Values Survey (WVS) and the Big Five Personality Test. The results reveal a systematic discrepancy between conventional fidelity metrics and CDP. Controlled experiments show that CDP changes monotonically as cross-country divergence is attenuated or amplified, while the corresponding changes in JSD remain relatively small. In our audit of real LLM generations, DeepPersona-Inspired prompting is frequently favored by conventional fidelity metrics but exhibits the strongest flattening in every model–domain block. CDP thus complements fidelity metrics by directly quantifying the attenuation or amplification of cross-country divergence.

Billera, Jia, and Reiner (2009) introduced the quasisymmetric functions of matroids and showed that this defines a Hopf algebra homomorphism which is a valuative invariant, i.e., isomorphic matroids have the same quasisymmetric function and polytopal subdivisions of matroid base polytopes define relations among the corresponding quasisymmetric functions. In this project we study an analogue in non-commuting variables, the word-quasisymmetric functions. To every matroid $M$ we associate a word-quasisymmetric function $\psi(M)$ and call this the chromatic word-quasisymmetric functions of a matroid. Matroids and word-quasisymmetric functions form Hopf algebras, and our map $\psi$ between them is a homomorphism. We want to study the kernel, equivalently the image, of the map $\psi$ from matroids to word-quasisymmetric functions, that is, we would like to understand which matroids are indistinguishable by the chromatic word-quasisymmetric functions. The map $\psi$ is not an invariant, but we can show that it is valuative. Using Schubert matroids and nested matroids, special classes of matroids, we prove a lower bound of $2^d-d$ for the rank of the map $\psi$ from matroids to the chromatic word-quasisymmetric functions in degree $d$ and conjecture the upper bound of $d!$ is tight.

We investigate the dynamical and thermal behaviour of settling heavy inertial particles in bulk turbulent thermal convection. Direct numerical simulations are performed in a homogeneous Rayleigh-Benard convection setup, where a uniform mean temperature gradient drives statistically homogeneous convective turbulence seeded with passive inertial particles. We quantify the effects of dynamic and thermal inertia on particle statistics. In particular, we investigate how the fluctuations of particle velocity and temperature can be traced back to the correlations between particle and fluid variables, and how particle temperature statistics is affected by the interplay of settling and preferential concentration.

Given two (closed) subgroups H, K of a profinite group G, we write Pr(H,K) for the probability that a random pair from HxK commutes. Here we are concerned with profinite groups containing Sylow subgroups P, Q such that Pr(P,Q) > 0. First, we show that if G is a profinite group containing a Sylow 2-subgroup L and a Sylow p-subgroup P , where p is odd, such that Pr(L,P) is positive, then G is virtually pro-p-soluble (Theorem 1.1). Then we handle similar issues for profinite groups admitting coprime automorphisms. In particular, we prove that if G is a profinite group admitting a group of coprime automorphisms A such that there is a Sylow 2-subgroup L of C_G(A) and an A-invariant Sylow p-subgroup P of G, where p is odd, for which Pr(L,P) > 0, then G is virtually pro-p-soluble (Theorem 1.3). On the other hand, if we only have Pr([L,A],[P,A]) > 0, then [G,A] need not be virtually pro-p-soluble. We show that in this case [G,A] has an open normal subgroup of non-p-soluble length at most 1 (Theorem 1.4). Furthermore, if P is an A-invariant Sylow p-subgroup of G such that Pr([P, A],[P, A]^x) > 0 for every x in G, then [G,A] has an open normal subgroup of non-p-soluble length at most 1 (Theorem 1.5).

We construct an explicit smooth projective Fano fourfold $X$ over an algebraically closed field $k$ of characteristic two with $H^1(X,\mathcal{O}_X)\simeq k$. Moreover, $X$ does not admit any free rational curve, and so it is not separably uniruled. The example has been constructed using ChatGPT.

Phoneticians often need to construct stimuli in which specific acoustic cues are precisely manipulated while preserving decent speech quality. Classical synthesis and modern neural methods sit along a trade-off between precise parametric control and high fidelity, and neural synthesis typically demands more data than phoneticians can easily obtain. We present ARIS (Analytic Resonant Interpretable Synthesis), a neural source-filter model that pairs neural parameter estimation with deterministic DSP synthesis. Every control is a coefficient of the synthesizer, so F0, formants and the glottal source can be edited directly. On five small single-speaker corpora in three languages, ARIS resynthesizes speech with quality comparable to WORLD and edits single parameters more accurately than Praat KlattGrid, with negligible crosstalk between cues. Compared with HiFi-Glot, pre-trained on a large corpus and fine-tuned on the same data, ARIS scores slightly lower on predicted naturalness but reproduces the recordings more faithfully and manipulates them more precisely. Audio samples: https://n1r.github.io/ARIS_nsf/.

We study the Petrov classification and Weyl double copy of the four-dimensional bulk metric dual to a $2+1$-dimensional relativistic Rindler fluid at first order in the relativistic gradient expansion. Upon imposing the fluid equations, the leading Weyl curvature is determined by the fluid vorticity and shear. At this order, the bulk geometry is generically of Petrov type II, with a type D branch for shear-free flows with nonzero vorticity and a type N branch for irrotational flows with nonzero shear. For the type D branch, we construct a purely magnetic Maxwell single copy on a fixed Rindler background and distinguish exact source-free solutions with a constant magnetic field from local perturbative solutions valid through first order in gradients. For the type N branch, we obtain a family of algebraic Weyl double copies parametrized by $\beta$. We derive explicit field strengths and gauge potentials for $\beta=0$ and $\beta=1$, together with the local Cauchy-Riemann conditions imposed by Maxwell's equations. These choices encode the fluid shear differently: for $\beta=0$, the shear dependence resides entirely in the zeroth-copy scalar, whereas for $\beta=1$, it enters the Maxwell field directly. Finally, using the non-relativistic hydrodynamic expansion with explicit $\epsilon$ counting, we derive the non-relativistic limits of the type D single copy and both type N choices, and compare the resulting structures with existing non-relativistic constructions.

Large language model agents increasingly combine generation, decision-making, execution, and self-evaluation within a single agentic loop. Although they operate under external specifications such as task instructions, guidelines, output schemas, and reusable skills, these specifications typically remain context for the same model that acts and declares completion, leaving no independent specification authority boundary. We identify two resulting gaps. The understanding–execution gap arises when a requirement is understood but not satisfied in execution; the state–authority gap arises when an agent's interpretation or completion claim does not establish the required state. On SkillsBench, using only agent-visible prompts, workspace information, and injected skill specifications, we extract 509 source-grounded task directions. Across seven models, only 79.6%–86.4% are satisfied, while completion-claim rates exceed official evaluator pass rates by 28.7–37.9 percentage points. We therefore separate agent proposals from authoritative state. Agents may plan, act, and request completion, but only admissible evidence from qualified providers may establish specification-governed state. SpecHarness operationalizes this principle by compiling visible specifications into source-linked obligations and governing execution and finalization through versioned obligation state. Verifiable requirements are mediated or validated at runtime, while ambiguous or subjective requirements remain advisory. Experiments on guideline-following and artifact-generation tasks show that specifications can serve not merely as behavioral guidance, but as authority over compliant execution and completion.

Mobile emergency networks can experience independently changing intermediate wireless links on timescales shorter than endpoint feedback can track. When an egress changes after packet emission, feedback affects only later source data, while the on-path node observes the current condition with the affected packet still mutable. This paper presents DINA, a packet-level in-network semantic adaptation method. An image is divided into self-describing spatial packets carrying coordinates, a current representation identifier, and payload. At each eligible node, an offline-trained frozen selector scores compatible operators, immediately transforms the packet, and forwards it without image reconstruction or cross-packet adaptation state. Later nodes can retain or further compact the packet through the same typed compatibility contract. The receiver places available packets by coordinate, fills missing regions with black, and runs a fixed machine task. We realize DINA in a 24-node UAV environment using XDP and AF_XDP. In the primary forest-fire trace, DINA raises deadline tile coverage from 40.4% to 72.6% and classification accuracy from 77.5% to 95.0% relative to forwarding. In an independently trained RescueNet segmentation case, it raises coverage from 65.6% to 91.7% and foreground mIoU from 0.486 to 0.541. Sufficient- and extreme-capacity profiles expose a no-gain boundary and a common task-failure boundary, respectively.

We establish uniqueness of the Veneziano four-point amplitude in a meromorphic class by combining six-point consistency with a known low-order supersymmetry relation. We consider planar tree-level scattering in four dimensions with a massless maximally supersymmetric vector multiplet and an additional scalar parity condition. A difference of supersymmetry Ward identities isolates massless factorization residues and eliminates every permitted contribution regular in a common kinematic limit. The resulting functional equation holds at every derivative order and fixes all angular dependence from the forward function after subtraction of the massless poles, at fixed Yang-Mills coupling. For a jointly meromorphic amplitude with simple planar poles, a nonempty spectrum of positive mass-squared poles separated from zero by a mass gap, nonnegative coefficients in the partial-wave expansions of scalar residues, and an exact unsubtracted forward dispersion relation, only the pole positions remain free. Positivity bounds their separation. The low-order relation saturates a sharp spectral inequality, requiring an infinite sequence of equally spaced mass-squared poles. The coupling and first massive pole position therefore determine the complete four-point function and all residues, without an initial finite-spin restriction.

We prove that the optimal Lojasiewicz–Simon exponent of a real-analytic functional on a Banach space is an intrinsic invariant of its finite-dimensional Lyapunov–Schmidt singularity under natural Fredholm and pairing-compatible hypotheses. More precisely, Lyapunov–Schmidt reduction preserves the entire set of admissible exponents, while the reduced germ on the kernel of the Hessian is intrinsic up to analytic right-equivalence tangent to the identity. We then identify this invariant with a real relative Lojasiewicz exponent of the pair consisting of the Jacobian ideal of the reduced energy and its principal energy ideal. Consequently, the optimal exponent admits equivalent descriptions by analytic arcs and by a finite maximum of divisorial ratios; in particular, it is rational. In Newton-nondegenerate cases, these formulas yield explicit monomial expressions. We apply the theory to several classes of singular energies. For the sum $Q_k$ of the squares of all $k\times k$ minors of a real matrix, we determine the associated ideal pair up to real integral closure and obtain the exact local exponent $$1-\frac1{2(k-s)}$$ at matrices of rank $s<k$. For Yang–Mills energy, we prove that the product flat connection on $\mathbb T^2$ has optimal exponent $3/4$ for every nonabelian compact structure group. For $\mathrm{SU}(2)$, the determinantal reduction extends this value to product flat connections on every $\mathbb T^d$, while sufficiently small nonzero constant flat connections have exponent $1/2$. Finally, for resonant semilinear Dirichlet energies, we identify higher-order resonant obstructions, establish an all-order obstruction ladder for simple resonance, and obtain a complete parity-dependent classification on $(0,\pi)$.

The advent of pseudoentanglement and computational entanglement theory bootstrapped a wave of research at the intersection of computer science and information theory. In parallel, computational cryptography has undergone substantial development, prompted by the introduction of pseudorandom states and followed by the establishment of a baseline for the computational hardness required for quantum cryptography, from which EFI pairs emerge as a central primitive. We study the connection between pseudoentanglement and computational cryptography through EFI pairs. Our goal is to enable the use of resources arising from computational entanglement theory in the field of cryptography. For this, we establish the relation between operational instances of pseudoentanglement and the hierarchy of minimal assumptions for computational cryptography. We show that the existence of pseudoentanglement under two different operational definitions, with efficient state generation, is a sufficient condition for the existence of EFI pairs. Combined with a previously established result that the converse also holds under the second definition, this allows us to also demonstrate their equivalence. This places pseudoentanglement alongside other minimal assumptions in cryptography, not only offering an alternative perspective on this fundamental problem, but also building a bridge that allows insights from either area to inform the other. While proving these theorems, we introduce and demonstrate technical lemmas in quantum information and computational entanglement theory, relating the computational entanglement measures to the distance between states, establishing distinguishing conditions for mixtures of two families given pairwise distances between their states, and demonstrating the first continuity relation for a computational entanglement measure.

We establish a stability threshold for the 3D Boussinesq equations around Couette flow $(y,0,0)$ with linearly stratified temperature profile $1+y$ on $\mathbb{T}\times\mathbb{R}^2$, with distinct viscosity $\kappa$ and thermal diffusivity $\mu$ and arbitrary Brunt-Väisälä frequency $\beta>0$. Assume that $\mu$ and $\kappa$ are comparable, and set $\nu=\min\{\kappa,\mu\}$. For sufficiently small \(a_0>0\) and \(s\geq4\), we prove that if the initial perturbation satisfies $\|(u_{in},\theta_{in})\|_{H^s}+\|(u_{0,in},\theta_{0,in})\|_{W^{s,1}}\lesssim\nu^{\frac{2}{3}} |\ln{\nu}|^{-2-2a_0}$, then the corresponding solution exists globally in time. We also establish Strichartz-type estimates for zero mode. Moreover, our estimates further allow for a nonlinear amplification of order $\nu^{-1/6}$ in the high-regularity norm of the zero mode of the first component $u^1_0$.

This letter investigates a non-uniform activation aided distributed generalized spatial modulation (DGSM) scheme in a downlink distributed multiple-input multiple-output (DMIMO) system formed by geographically separated transmission reception points (TRPs). Unlike conventional uniform-activation DGSM, the proposed scheme assigns adaptive activation probabilities to different TRP subsets, thereby jointly exploiting the data-domain transmission capability and the index-domain information carried by cooperative subset selection. We derive a mutual-information upper bound under non-uniform activation and formulate a joint activation-probability and power allocation problem subject to a long-term average power constraint. To solve this problem, we develop a semi-closed-form joint probability and power optimization (SC-JPPO) algorithm, where the optimal activation probabilities are shown to follow a Softmax function of the effective utilities. Simulation results demonstrate that the proposed scheme improves spectral efficiency under the same activation scale and power budget compared with existing benchmarks.

Many electrostatic actuators require multi-kilovolt drive voltages at sub-milliamp currents, a task poorly suited for conventional switching devices. As an alternative, we demonstrate a high-voltage amplifier using optocouplers as active elements. The amplifier produces a 20-kV peak-to-peak output with up to 500 Hz bandwidth while maintaining a minimal component count. By using optocouplers as linear devices in feedback, lower harmonic distortion and higher bandwidth are achieved than offered by equivalent PWM amplifiers. This design improves the viability of electrostatic actuators by providing a simpler method to achieve useful drive waveforms.

Many-shot in-context learning (ICL) enables large language models (LLMs) to adapt to complex tasks by conditioning on thousands of demonstration examples, but this paradigm shifts the inference efficiency bottleneck to the key-value (KV) cache memory. Due to the linear scaling behavior of the KV cache, storing these intermediate tensors has become a paramount challenge for both online serving and on-device deployment. To address this issue, we propose a novel compression framework, termed MILO, that exploits the low-rank redundancy inherent in many-shot contexts. Specifically, MILO features a block-wise low-rank compression strategy that compresses the KV cache at the block granularity, where each block contains multiple many-shot examples. Furthermore, to handle the heterogeneous context density across different blocks, MILO dynamically allocates rank budgets based on the information entropy, preserving the fidelity of critical blocks while aggressively compressing redundant ones. Experimental results on Qwen2.5 models demonstrate that our method achieves up to 50% reduction in KV cache memory and 1.8x throughput improvement, with negligible performance degradation on classification and reasoning benchmarks, significantly outperforming prior baselines.

With the growing demand for privacy-preserving and occlusion-resilient human pose recognition (HPR), 5G channel state information (CSI) offers a promising contactless sensing modality by integrating communication and sensing capabilities. However, collecting large-scale synchronized CSI-pose pairs remains costly in practical 5G systems. To address this limitation, we propose StructFlow-HPR, a structured pose-conditioned flow matching framework for generative CSI augmentation. StructFlow-HPR learns a continuous latent transport process from Gaussian noise to real CSI representations under pose guidance, while preserving the receiver-frequency topology of CSI through a reconstruction-preserving autoencoder. A pose-conditioned Transformer is further designed to model the latent velocity field and generate pose-aligned CSI samples via ordinary differential equation sampling. Experiments on real-world 5G sensing data show that StructFlow-HPR can produce realistic CSI-pose pairs and improve downstream HPR performance under limited-data conditions.

Dark matter that is weakly mixed with particles in a thermal plasma can be produced through both, oscillatory and collisional freeze-in. While plasma effects have long been known to suppress the former, their role in collisional freeze-in remains less clear quantitatively, leading to conflicting results in sterile neutrino dark matter production via collisional freeze-in. Using first-principles nonequilibrium Kadanoff-Baym equations in the flavour-covariant formulation, we establish the general result that plasma effects also suppress collisional freeze-in: the vacuum mixing angle in the collision rate is replaced by its plasma-corrected counterpart. Applying this result, we conclude that sterile neutrinos cannot be dark matter in the keV-MeV mass range when produced from the Standard Model plasma.

In this paper, we establish a general identity for three-term recurrence sequences and then give applications to orthogonal polynomials and Apéry-like numbers.

In this work, we extend our previous diabatic framework for the charmonium-like spectrum below $4.3$ GeV by introducing the complex scaling method. Unlike the previous framework, the present approach explicitly incorporates couplings to the meson-meson continuum, comprehensively accounting for its contributions to the physical states. Consequently, it allows bound and resonant states to be treated on an equal footing, enabling the direct extraction of decay widths from complex energy eigenvalues without introducing any additional free parameters. Using the obtained solutions, we calculate the channel weights and complex root-mean-square radii ($r_{\scriptscriptstyle{RMS}}$ ) to elucidate their internal structures. Specifically, we find that the $\chi_{c1}(3872)$, $\psi(4040)$, and $\psi(4230)$ states exhibit significant molecular characteristics. Furthermore, we propose the $X(3940)$ as a candidate for a $J^{PC}=1^{++}$ state and discuss the nature of the $\chi_{c0}(2P)$ resonance in detail.

Neural models can learn to generate various solutions to the inverse kinematics problem from data, but are usually limited to a single robot. We present MorphIK, a flow-matching model that solves inverse kinematics for revolute-joint-based kinematic chains it has never seen during training. The model uses a transformer architecture to encode the robot's morphology along with the target pose. This encoding then conditions a flow-matching head that generates poses from noise. Trained on purely synthetic data from procedurally generated robots, the model reaches a precision of about 5 cm on unseen real-world robots with 6 to 9 Degrees of Freedom. For higher precision, the model serves as an excellent Prior for further optimization algorithms, reducing error to less than 1 cm after a single step of Damped Least Squares optimization and to sub-1 mm error after 3 steps in most cases. Building on flow matching's generative capabilities to produce highly diverse outputs, our model can efficiently sample the robot's null space, providing a wide variety of configurations for the same pose. Thus, overall, MorphIK allows learning and generalizing neural inverse kinematics for a multitude of known and unknown robots.

We apply the Poincaré-Lindstedt method to the perturbed Binet equation describing conservative dynamics of the perturbed Kepler problem. We show that a simple treatment of divergent terms directly determines the frequency shift of the radial motion and hence the periastron advance. We provide explicit expressions for polynomial, logarithmic and inverse power perturbations, extend the procedure to higher perturbative orders and to problems involving several perturbation parameters. Applying this method to different physical effects relevant to compact binaries, we recover known results. We also obtain new contributions to the periastron advance, including the leading-order effects of arbitrary mass- and current-type tidal multipoles and mass-type spin-induced multipoles, the NNLO current-type tidal quadrupole contribution, electromagnetic electric-dipole contributions to NNLO and the eccentric corrections to the electric charge. Finally, we illustrate how the method can be directly applied to the problem of particle motion in Reissner-Nordström, de Sitter-Schwarzschild metrics and in a Yukawa potential.

The estimation of Annual Average Daily Traffic (AADT) is vital for transportation planning and infrastructure maintenance, yet obtaining accurate values for an entire urban network across multiple years remains challenging due to the high cost and spatial sparsity of physical sensors. This research proposes a novel spatio-temporally complementary feature propagation framework that leverages the strengths of two distinct data sources: spatially sparse but temporally dense loop detector data, and a spatially complete but temporally sparse macroscopic transportation model. The methodology highlights a feature propagation algorithm on directed graphs, formulated as a Poisson energy minimization considering residues. The standard binary adjacency matrix is replaced with flow ratio matrices to capture real-world vehicle turn ratios at intersections. Validated in the city of Zurich, the algorithm demonstrates high computational efficiency, achieving convergence within minutes. Results indicate that the framework effectively reconciles theoretical models with empirical ground truths, yielding a normalized mean absolute error below $10\%$. This scalable approach provides a feasible solution for spatio-temporal network-wide AADT estimation through combining real-world limited sensor coverage and traffic models.

A production network can remain largely unidentified even when the economic decision it supports is identified. We characterize sufficient measurements for exposure-based decisions and compute sharp maximum regret over networks consistent with released totals. Using earlier and later vintages of Japan's interregional input-output accounts, we select measurements from the 1995 table and evaluate the frozen design against the 2005 benchmark. At roughly half the statistics required for full disclosure, the resulting monitoring set loses only 0.07 percentage points of average exposure relative to the benchmark optimum, yet its sharp maximum regret across compatible networks is 4.83 points. In U.S. coal deliveries surrounding a 2005 Wyoming rail disruption, additional shipment measurements identify the optimal set of plants to monitor for inventory risk, even though four monitored plants' exposures to the affected coal supply remain unidentified. The results distinguish good benchmark performance from a decision guarantee and show that decisions can be identified before individual exposures. They suggest evaluating network data by the economic decisions they support.

Strikingly, when hydrogel particles are embedded in ice in a temperature gradient, they move through the solid ice towards warmer temperatures, while swelling as they warm up. This motion comes from a flow of unfrozen water through the hydrogel mesh, driven by a process known as `cryosuction'. Here, we show how one can use this behavior to measure – with extremely high resolution – a range of different hydrogel transport properties, and how these change as a hydrogel deswells. These properties include permeability, compressibility, and poroelastic diffusivity: all of which are challenging to measure, but widely important for phenomena involving swelling, dehydration, transpiration and filtration. We demonstrate the measurement technique using poly(ethylene glycol) diacrylate (PEGDA) hydrogels. The technique uses picoliter-scale hydrogel volumes, and yields measurements of hydrogel properties that are consistent with existing literature data. The high resolution of our measurements also allows us to test commonly-used, classical predictions for hydrogel properties (derived assuming an idealized, homogeneous polymer network in the hydrogel). We show that these classical predictions do not work well, highlighting the need for new models that can accurately describe real hydrogels.

For a $3$-graph $F$, the Turán number of $F$, denoted by $\ex(n,F)$, is the maximum number of edges in a $3$-graph on $n$ vertices containing no subgraph isomorphic to $F$. Let $F^-_{4,3}$ be the $3$-graph formed by a complete four-vertex core and three outer vertices, with all but one of the twelve triples containing one core vertex and two outer vertices. We prove that, for every $n\ge8$, \[ \ex(n,F^-_{4,3})=\binom n3-\binom{\lfloor n/2\rfloor}{3}-\binom{\lceil n/2\rceil}{3}, \] and the balanced complete bipartite $3$-graph is the unique extremal configuration. This determines the exact value and all equality cases in the asymptotic theorem of Mubayi and Rödl. It also extends the exact Turán Number of $F_{3,3}$ and resolves a conjecture of Frankl, Huang and Rödl.

A new proposal called DM-SMC (Diffusion Model - Sequential Monte Carlo) is investigated, which samples ensembles defined in terms of an action, using diffusion models trained on samples from the ensemble. The SMC setup allows for accurate sampling in spite of an approximate diffusion model and the finite stepsize used in the numerical solution of the stochastic process. Improved update strategies are also investigated. Results are presented for a $Z_2$ symmetric scalar field theory in 2 dimensions near its 2nd order phase transition.

Enterprise AI is transitioning from single-user, reactive tools toward proactive, multi-user 'teammates,' but our empirical understanding of this transition is limited. In this paper, we present an in-situ qualitative study of a persistent, proactive AI agent 'teammate' deployed across multiple teams in a large technology company. Our findings reveal the boundaries of the human-agent workplace are actively in flux, triggering breakdowns and negotiations across: 1) tacit rules of collaborative human workflows, 2) the relational boundaries of this new non-human actor, and 3) the redistribution of trust and human agency. We use these early micro-negotiations as signals to chart a new research, design, and organizational agenda that intentionally preserves human agency in a workplace shared with non-human organizational actors.

Precise conditions are provided for the existence and criticality of Turing bifurcations in a general class of activator-inhibitor reaction-diffusion equations on a one-dimensional infinite domain. The class includes generalised Schnakenberg and Brusselator models, as well as other models with cubic autocatalytic nonlinear terms. Previous numerical work suggests the existence of a bifurcation structure containing localised patterns due to the so-called homoclinic snaking mechanism. This paper provides explicit calculations to justify those results. Two distinct scalings of parameters that lead to tractable normal-form coefficients are considered in the limit that the diffusion ratio $\delta \to 0$. First, under a small-parameter scaling, the Turing bifurcation is shown to be always subcritical. Second, a large-parameter scaling reveals the Turing bifurcation to be supercritical, leading, by continuity, to the existence of a codimension-two degenerate bifurcation. The sign of a 5th-order normal form coefficient is also computed, which is shown to have the correct sign for the local birth of homoclinic snaking. For the case of the Brusselator, two such codimension-two points can be found explicitly, as can the leading-order expression for the Maxwell point, in a parameter wedge about which localised patterns emerge. Numerical results are found to be consistent with the theory.