Sub-Neptune exoplanets frequently exhibit muted transmission spectra, with GJ 1214 b being the most prominent example. Following years of intense observing campaigns yielding featureless planetary spectra, recent observations with JWST revealed the first possible atmospheric signatures. We present high-resolution transmission spectroscopy of GJ 1214 b based on eight transits obtained with the CRIRES$^+$ spectrograph in the K band. We used SYSREM to remove telluric and stellar signals and searched for signatures of H2O, CO, CH4, H2S, NH3, and CO2 using the cross-correlation technique. We obtained non-detections for the first five molecules and used injection recovery tests to derive upper limits on the atmosphere. For CO$_2$ we measure a CCF signal at S/N ~ 3.6, with a detailed investigation showing no obvious indication that it is caused by correlated noise. A Welch t-test confirmed the in-trail and out-of-trail distributions to be different at $3.4 σ$ confidence. A Bayesian retrieval framework with free chemistry, resulted in volume mixing ratios corresponding to a metallicity of $[\mathrm{M/H}]=0.48^{+0.89}_{-1.70}$, an opacity deck pressure of $\log_{10}(P_\mathrm{c}) = -3.04^{+2.52}_{-1.53}$ and a planet temperature of $T_\mathrm{iso}=398^{+283}_{-197}$ K, consistent with a value intermediate between the day- and night-side T-p's derived from JWST data. While these values correspond to relatively large signal amplitudes predicted for CO2 features in the mid-infrared, they are compatible with JWST NIRSpec observations within the models' $1.5σ$ uncertainties. Further modelling and additional data are required to confirm the atmospheric signatures and obtain a comprehensive interpretation of low- and high-resolution data. Overall, our results support previous findings that CO2 is likely to be a significant component of the atmosphere of GJ 1214 b.

Pearl's front-door criterion provides a set of sufficient conditions for estimating the total causal effect from observational data in the presence of latent confounding, using the functional P(y | do(x := x*)) = \sum_z P(z | x*) \sum_x P(y | x, z) P(x). An open question is whether these conditions can be generalized to be both necessary and sufficient for the validity of this functional, similar to the generalization achieved for the back-door adjustment criterion by Shpitser. In this paper, we present a new, weakened set of graph-based conditions sufficient for the front-door formula to estimate the total causal effect, expanding the scope of problems amenable to front-door identification.

Neutrino self-interactions delay the onset of free-streaming in the early universe, leaving distinct, scale-dependent signatures on the matter power spectrum. We investigate these signatures in post-reionization 21-cm intensity mapping and the Lyman-$α$ (Ly$α$) forest at redshifts $z \sim 2$--$3.5$, and forecast the constraints achievable with upcoming surveys using Fisher matrix analysis. Modeling neutrino self-interactions through an effective four-fermion parameterization with coupling $G_{\rm eff}$, we compute modifications to the Ly$α$ and 21-cm auto- and cross-power spectra for both strongly interacting (SI$_ν$, $\log_{10}G_{\mathrm{eff}} = -1.77$) and moderately interacting (MI$_ν$, $\log_{10}G_{\mathrm{eff}} = -5$) scenarios. We then combine these with forecasts for a representative next-generation cosmic microwave background (CMB) mission to evaluate the capabilities of SKA1-Mid and PUMA. We find that the Ly$α$--21-cm cross-correlation provides a systematics-resilient probe of the interaction signal, and decisively breaks the degeneracy between the primordial scalar power spectrum amplitude ($A_s$) and $G_{\rm eff}$ that limits CMB only analysis, particularly for the SI$_ν$ mode. Furthermore, the CMB+PUMA combination emerges as the optimal survey configuration for both regimes, reaching 1$σ$ constraints of $\mathcal{O}(10^{-3})$ on $σ(\log_{10}G_{\rm eff})$ for the SI$_ν$ mode and $\mathcal{O}(10^{-2})$ for the MI$_ν$ mode. Compared to the CMB-only baseline, this represents an improvement of approximately one order of magnitude for the SI$_ν$ mode, and nearly two orders of magnitude for the MI$_ν$ mode. We show that this conclusion holds uniformly over the full range of coupling strengths from $\log_{10}G_{\rm eff} = -6$ to $-1.77$.

We investigate the problem asking when any square matrix whose entries lie in a finite field of characteristic 2 is decomposable into the sum of a diagonalizable matrix and a nilpotent matrix with index of nilpotency at most 2 and, as a result, we completely resolve this question in the affirmative for any finite field of characteristic 2 having strictly more than three elements. Our main theorem of that type, combined with results from our recent publication in Linear Algebra & Appl. (2026) (see [7]), totally settle this problem for all finite fields different from $\mathbb{F}_2$ and $\mathbb{F}_3$. However, in this paper we also prove that each matrix over $\mathbb{F}_2$ is expressible as the sum of a potent matrix with index of potency not exceeding 4 and a nilpotent matrix with index of nilpotency not exceeding 2, thus substantiating recent examples due to Šter in Linear Algebra & Appl. (2018) and Shitov in Indag. Math. (2019) (see, respectively, [9] and [8]).

Cell-cell adhesion is widely hypothesised to maintain cohesion within the long streams of follower cells that trail leader subpopulations during collective migration, including in neural crest cell migration, angiogenesis, and cancer cell invasion. Mathematically, non-local advection-diffusion equations provide the canonical continuum framework within which to study such adhesive cell-cell interactions. Here, we study a minimal model of leader-follower migration within this framework, in which leaders migrate at constant velocity while followers are attracted to leaders and to one another over a finite spatial interaction range. Numerical simulations reveal that, although the model can maintain small cohorts of travelling follower cells, the size of these cohorts is limited by the adhesive interaction lengthscale, and is far below what is needed to reproduce the extended streams observed in vivo. This points to a structural limitation of the standard non-local adhesion formulation and highlights the need for the development of extended continuum models capable of sustaining long, coherent migratory streams through purely mass-conserving collective cell movement.

Recent studies have shown that distributed storage systems can achieve significant space savings by adapting redundancy levels to varying disk failure rates. This adaptation is performed via code conversion, wherein data encoded under an initial code are transformed to data encoded under a final code. While this process is typically resource-intensive, convertible codes are designed to enable these transformations efficiently while preserving desirable decodability constraints such as repair degree, or the number of nodes accessed during node repair. In this work, we focus on the bandwidth cost of conversion, or the total amount of data transferred during the conversion process. We study fundamental limits on the bandwidth cost of conversion between systematic optimal-distance Locally Repairable Codes (LRCs). We restrict our focus to the global merge regime, in which multiple initial codewords are combined to form a single final codeword while preserving information locality. We focus on stable convertible codes, wherein the number of unchanged nodes is maximized during conversion. We generalize an information-theoretic approach for modeling code conversion to the LRC setting, and derive the first non-trivial lower bounds on the bandwidth cost of conversion in this regime. Notably, our bounds do not rely on any linearity assumptions. Consequently, we show that the constructions of Maturana and Rashmi are bandwidth-optimal across a broad range of parameters in the global merge regime.

Hybrid High-performance Computing (HPC)-quantum workloads based on circuit cutting decompose large quantum circuits into independent fragments, but existing frameworks tightly couple cutting logic to execution orchestration, preventing HPC centers from applying mature resource management policies to Noisy Intermediate-Scale Quantum (NISQ) workloads. We present DQR (Dynamic Queue Router), a runtime framework that bridges this gap by treating circuit fragments as first-class schedulable units. The framework introduces a backend-agnostic fragment descriptor to expose structural properties without requiring execution layers to parse quantum code, a wave-based coordinator that achieves pipeline concurrency via non-blocking polling, and a production-ready implementation on the CESGA Qmio supercomputer integrating both QPUs local on-premises (Qmio) and remote cloud (IBM Torino) backends. Experiments on a 32-qubit Hardware-Efficient Ansatz (HEA) circuit demonstrate not only makespan improvements over a monolithic CPU baseline but also transparent per-fragment failover recovery-specifically rerouting tasks from the local QPU to classical simulators upon encountering hardware-level incompatibilities-without pipeline restart. For deeper circuits, the coordination residual accounts for only 5% of the total execution time, highlighting the framework's scalability. These results show that DQR enables HPC centers to integrate NISQ workloads into existing production infrastructure while preserving the flexibility to adopt improved cutting algorithms or heterogeneous backend technologies.

Over the last decade, the development of Josephson devices based on van der Waals (vdW) materials has advanced rapidly, representing a paradigm shift driven by the advent of 2D materials. The diverse vdW materials library, combined with advanced fabrication techniques, enables the integration of materials with vastly disparate properties for scientific exploration. The vdW Josephson junctions (JJs) offer a unique route to explore novel functionalities and associated physics that remain inaccessible in conventional JJs, which have reached an industrial level in terms of fabrication. Beyond material diversity, vdW crystalline materials offer fundamental new control over device symmetries, enabling the realization of Hamiltonians unique to 2D systems. Furthermore, the long relaxation times of myriad excitations in 2D heterostructures open possibilities for creating exquisite quantum sensors, with the 2D material itself acting as an efficient bus for transmitting excitations to the active sensing element. This creative explosion in vdW-based superconducting electronics is rapidly growing, and our review highlights the resulting devices and physics. The confluence of vdW JJs with twistronics and topology has the potential to redefine superconducting quantum technology, enabling applications from quantum computation to ultra-sensitive hybrid sensors. While opportunities abound with vdW JJs, the challenge of scalability must be surmounted for translation into real-world devices. This review synthesizes current developments and offers a roadmap for researchers navigating this burgeoning field.

We theoretically investigate the generation of non-Gaussian quantum states, specifically Schrödinger cat-like states (SCLSs), via degenerate dual-pump spontaneous four-wave mixing in a $χ^{(3)}$-based microring resonator. By introducing a unitary transformation that exactly decouples the self-phase modulation (SPM) and cross-phase modulation (XPM) terms, we reduce the full nonlinear Hamiltonian to an effective three-mode interaction. The resulting dynamics (decoupled and full Hamiltonians) are studied using the Lindblad master equation, accounting for cavity losses. Unlike semiclassical or parametric approximations, our full quantum mechanical approach explicitly includes quantum pump depletion, which enables the emergence and observation of non-Gaussian features. We compute the Wigner function, photon number distributions, quadrature variances, Fano factor, Schmidt number, and fidelity to characterize the generated states. For the non-dissipative case, we find that the signal mode $\hat{b}_3$ or $\hat{a}_3$ exhibits clear non-Gaussian features with a structured Wigner function and even-dominated photon number distribution, characteristic of an even coherent state. In the presence of dissipation ($γ_j = 0.2$), the interference fringes become faint, odd photon numbers appear, and the fidelity with the ideal state remains high ($>0.9$), indicating robustness. The pump mode $\hat{b}_1$ or $\hat{a}_1$ remains Gaussian, while both modes display super-Poissonian statistics and entanglement ($>2$). Our results demonstrate that degenerate dual-pump spontaneous four-wave mixing in microring resonators is a promising platform for generating and controlling cat-like states under dissipative conditions.

In this paper, we focus on automating two of the widely used Verification and Validation (V&V) activities in the Software Development Lifecycle (SDLC): Software testing and software inspection (also known as review). Concerning the former, we concentrate on automated test case generation using Large Language Models (LLMs). For the latter, we enable inspection of the source code by LLMs. To address the known LLM hallucination problem, in which LLMs confidently produce incorrect outputs, we implement a Retrieval Augmented Generation (RAG) pipeline to integrate supplementary knowledge sources and provide additional context to the LLM. Our experimental results indicate that incorporating external context via the RAG pipeline has a generally positive impact on both test case generation and code inspection. This novel approach reduces the total project cost by saving human testers'/inspectors' time. It also improves the effectiveness and efficiency of these V&V activities, as evidenced by our experimental study.

We introduce a systematic framework to construct nonlocal observables with extensive quantum Fisher information (QFI) density in stabilizer codes. The construction maps stabilizer generators to dual Ising spins whose correlators equal string order parameters, converting hidden nonlocal order into a metrologically accessible observable. Applying this to monitored cluster codes and the toric code, we identify transitions in the QFI scaling from an extensive regime, where long-range string order prevails, to an intensive one driven by competing single-site measurements.

We propose an incremental approach for safety proofs that decomposes a proof with a complex inductive invariant into a sequence of simpler proof steps. Our proof system combines rules for (i) forward reasoning using inductive invariants, (ii) backward reasoning using inductive invariants of a time-reversed system, and (iii) prophecy steps that add witnesses for existentially quantified properties. We prove each rule sound and give a construction that recovers a single safe inductive invariant from an incremental proof. The construction of the invariant demonstrates the increased complexity of a single inductive invariant compared to the invariant formulas used in an incremental proof, which may have simpler Boolean structures and fewer quantifiers and quantifier alternations. Under natural restrictions on the available invariant formulas, each proof rule strictly increases proof power. That is, each rule allows to prove more safety problems with the same set of formulas. Thus, the incremental approach is able to reduce the search space of invariant formulas needed to prove safety of a given system. A case study on Paxos, several of its variants, and Raft demonstrates that forward-backward steps can remove complex Boolean structure while prophecy eliminates quantifiers and quantifier alternations.

Determining whether two graphs are isomorphic is a fundamental problem with practical applications in areas such as molecular chemistry or social network analysis, yet it remains a challenging task, with exact solutions often being computationally expensive. We address this task using persistent homology built on motif-based filtrations of graphs, a method from topological data analysis that summarizes the shape of data by tracking the persistence of structural features along filtrations. Specifically, we use edge-weighting schemes based on the densities of triangles, chordless squares, and chordless pentagons, which have been shown to be effective for detecting network dimensionality. Our cycle-density filtrations distinguish non-isomorphic graphs perfectly or nearly perfectly across four demanding graph families, many of which exhibit symmetries. We outperform curvature-based, degree-based, and Vietoris--Rips filtrations, and match or exceed the accuracy of egonet-distance methods while incurring a lower computational cost. The expressive power of our filtrations goes beyond isomorphism testing: because they capture rich structural information from graphs, they consistently achieve top performance on property prediction tasks using real-world data, and exhibit high sensitivity to edge rewiring and removal. Together, these findings establish cycle-density filtrations as an effective and computationally tractable framework for graph comparison and characterization, bridging topological data analysis and network science.

We show that a rational agent with true and refinable knowledge of events cannot know if she knows everything or not. This epistemic limitation is not resolved by introspection about tautologies or by learning about new events.

We develop a quantum algorithm for estimating the free energy as well as the total Gibbs state of interacting quantum Coulomb gases and molecular systems in dimensions $d \in \{2,3\}$ at finite temperature. These systems lie beyond the reach of existing methods due to their singular interactions and infinite-dimensional Hilbert space structure. First, we show that the free energy of the full many-body Hamiltonian can be approximated by that of the same Hamiltonian with a finite-rank low-energy truncation of the interaction, with an explicit error bound polynomial in the particle number. This reduces the problem to a controlled finite-rank perturbation problem. Second, we introduce a quantum Gibbs sampling scheme tailored to this truncated system, based on a class of quantum Markov semigroups. Our main analytical result establishes that the associated generator has a strictly positive spectral gap for every truncation, implying exponential convergence to the target Gibbs state. This provides, to our knowledge, the first rigorous mixing-time guarantee for Gibbs sampling in a Coulomb interacting continuous-variable quantum system. Finally, we give an explicit quantum circuit implementation of the dynamics and derive an end-to-end complexity bound for approximating the free energy and the Gibbs state itself. Our results provide a mathematically rigorous route to quantum algorithms for free energy estimation in interacting quantum systems, without relying on classical approximations such as the Born-Oppenheimer reduction.

We develop a framework for detecting regime transitions in dynamical systems using the Mixup Euler Characteristic Profile (Mixup ECP) -- the Euler characteristic of the geometric intersection of ball unions around adjacent delay-embedded trajectory segments, viewed as a function of filtration scale. The Mixup ECP provides a detection statistic with a built-in null and guaranteed stability. We formalize regime detection as a low-side-permutation test, establish its validity and consistency, and introduce a multi-delay extension that automatically selects the most informative dynamical timescale. Complementing the topological signal with Complexity Variance, Higuchi fractal dimension, and a rolling mean baseline, the four-signal combined method achieves $9.50$ days MAE on Indian monsoon onset (Nepal target) -- a $32\%$ improvement over the rolling mean baseline and $9\%$ over CUSUM. Validated on the Lorenz system, logistic map, and three monsoon systems spanning both hemispheres (Indian/Nepal, Indian/Kerala, Western North Pacific), plus ENSO and a synthetic EEG dataset, the framework adds value precisely when the transition is gradual or obscured by noise.

Stationary black hole geometries with non-degenerate Cauchy horizons are classically unstable due to mass inflation. At extremality, mass inflation is absent, but a different dynamical instability arises: the Aretakis instability. In this work, we investigate the properties of degenerate horizons and their associated Aretakis instabilities. By studying examples with increasingly higher-order horizon degeneracy, we show that the Aretakis instability weakens as the degree of degeneracy grows. Motivated by these results, we propose a new black hole geometry characterized by an infinitely degenerate horizon, which we argue is stable under Aretakis-type perturbations and may therefore provide a concrete realization of a "graveyard" end state for these objects.

Photonic architectures are one of the leading platforms for demonstrating quantum computational advantage, with Boson Sampling and Gaussian Boson Sampling as the primary schemes. Yet, we lack for these photonic primitives a systematic theoretical understanding of linear cross-entropy benchmarking (LXEB), which is a central tool for testing quantum advantage proposals. In this work, we develop a representation-theoretic framework for the classical computation of average LXEB scores and second moments of output probability distributions, covering a range of quantum advantage experiments based on scattering $n$-photon states through $m$-mode Haar-random interferometers. Our methods apply in any regime, including the saturated regime, where the (expected) number of photons is comparable to the number of optical modes. The same second-moment techniques also allow us to prove anticoncentration for traditional Fock-state Boson Sampling in the saturated regime. Interestingly, for Gaussian Boson Sampling second moments are not sufficient to establish a meaningful anticoncentration statement. The technical core of our approach rests on decomposing two copies of the $n$-particle bosonic space $\mathrm{Sym}^n(\mathbb{C}^m)$ into irreducible representations of $\mathrm{U}(m)$. This reduces two-copy Haar averages to computing purities of initial states after partial traces over particles, highlighting the role that particle entanglement plays for LXEB and anticoncentration.

We present a lattice QCD study of dilepton production in charmonium transitions, specifically focusing on the $1^{+-} \to 0^{-+}$ and $1^{++} \to 1^{--}$ processes: $h_c \to η_c \ell^+ \ell^-$ and $χ_{c1} \to J/ψ\ell^+ \ell^-$, where $\ell = e, μ$. The relevant hadronic matrix elements are computed using gauge field configurations generated by the Extended Twisted Mass Collaboration with $N_f = 2+1+1$ dynamical Wilson--Clover twisted-mass fermions at four lattice spacings. Simulations are performed at physical dynamical $u$, $d$, $s$, and $c$ quark masses, except for the coarsest lattice, where the lightest sea quark mass corresponds to a slightly heavier pion mass. A controlled continuum extrapolation is carried out. In the continuum limit for the $h_c$ decays, we obtain $Γ(h_c \to η_c e^+ e^-) = 5.45(19)~\mathrm{keV}$, and $Γ(h_c \to η_c μ^+ μ^-) = 0.635(22)~\mathrm{keV}$. For the $χ_{c1}$ decays, we find: $Γ(χ_{c1} \to J/ψe^+ e^-)= 2.869(90)~\mathrm{keV}$, and $Γ(χ_{c1} \to J/ψμ^+ μ^-) = 0.1993(72)~\mathrm{keV}$. Our results for the $χ_{c1}$ decays show good compatibility with experimental data. However, our prediction for the $h_c \to η_c e^+ e^- $ decay rate is approximately $3σ$ larger than the BESIII result. We also present predictions for the differential decay widths as functions of the dilepton invariant mass, $q^2$, and for angular observables sensitive to longitudinal transition form factors, which are inaccessible in radiative decays with real photon emission. These results constitute the first fully dynamical lattice QCD predictions for dilepton decay rates in $h_c$ and $χ_{c1}$ charmonium transitions, including their differential distributions and angular observables. They provide benchmark predictions for future experimental studies.

Brion's Formula realizes the Laurent polynomial of lattice points in a lattice polytope P as the sum of rational functions associated to the vertices of P. In this paper, we consider the special case where P is a generalized permutohedron. We introduce a modification of the rational functions associated to the vertices of P depending on a given matroid M. Upon summing these rational functions, we show that the resulting Laurent polynomial Q_M(P) behaves in certain ways like the lattice points of P, exhibiting natural recursive and reciprocity behaviors. Furthermore, upon evaluating Q_M(P) at 1, we recover the matroid Euler characteristic of Larson, Li, Payne, and Proudfoot, thereby providing a refined approach to studying these quantities.

This paper presents a tractable tube-based robust data-driven predictive control scheme that uses only a single finite noisy input-state trajectory of an unknown discrete-time linear time-invariant (LTI) system. A simplex constraint is imposed on the Hankel coefficient vector, yielding explicit polyhedral bounds on the prediction mismatch induced by bounded measurement noise. Using certified initial and terminal robust positively invariant (RPI) sets, we derive a tube-tightened formulation whose online optimization problem is a strictly convex quadratic program (QP). The resulting controller guarantees recursive feasibility, robust satisfaction of input and state constraints, and practical input-to-state stability of the closed loop with respect to measurement noise. Numerical examples illustrate the effectiveness, robustness, and closed-loop performance of the proposed method.

In this work, we build a novel frequency-momentum space for $(d+1)$-dimensional de Sitter (dS) correlators from first principles. This construction follows directly from the decomposition into unitary irreducible representations (UIRs) of the spacetime isometry group $\mathrm{SO}(1,d+1)$. While the spatial momentum space is given by the standard $d$-dimensional Fourier transform, the frequency space arises from diagonalising the quadratic Casimir operator, leading to the $(d+1)$-dimensional Kontorovich-Lebedev-Fourier (KLF) transform. We show that square-integrable functions decompose only along the principal series, whereas more general functions can receive discrete contributions from other UIRs. Applying this framework to the bulk CFT two-point function reproduces its Källén-Lehmann representation. Using the path integral formulation, we derive the Feynman rules for in-in perturbation theory in KLF space, leading to the introduction of KLF-space correlators, which are simply related to late-time correlation functions through a reduction formula. Furthermore, the KLF-space formulation sheds light on the simple mathematical structure of perturbative computations. In particular, the propagators take the form of simple rational functions, and tree-level diagrams can be written as spectral integrals over known meromorphic functions, as demonstrated in the example of the single-exchange four-point function. At the loop level, we show, through the example of the self-energy correction to the scalar propagator, that the group-theoretical nature of the construction allows the momentum integral to be recast as an orthogonality relation among $\mathrm{SO}(1,d+1)$ Clebsch-Gordan coefficients.

The MCORD detector is a modular scintillator-based system employing silicon photomultipliers (SiPMs) and FPGA-based digital signal processing, designed for applications such as cosmic muon detection, veto systems, and detector calibration support. In this work, we investigate the influence of ambient temperature variations on detector performance, with particular emphasis on SiPM gain stability. Several automatic temperature compensation loops were implemented to stabilize the operating voltage of the sensors. Based on controlled laboratory measurements, we evaluate the effectiveness of different control strategies, including variations in temperature averaging time and threshold response criteria. The performance of each approach is compared in terms of gain stability and response dynamics. We identify the optimal temperature control configuration for planned MCORD measurements and present recent modifications to the detector electronics, including updated software for AFE control. Additionally, we describe modifications made to the detectors electronics since the previous publication, including new software developed to control the AFE electronics.

The 2-Forrelation problem provides an optimal separation between classical and quantum query complexity and is also the problem used for separating $\mathsf{BQP}$ and $\mathsf{PH}$ relative to an oracle. A natural question is therefore to ask what are the minimal quantum resources needed to solve this problem. We show that 2-Forrelation can be solved using Instantaneous Quantum Polynomial-time ($\mathsf{IQP}$) circuits, a restricted model of quantum computation in which all gates commute. Concretely, two $\mathsf{IQP}$ circuits with two quantum queries and efficient classical processing suffice. For the signed variant of 2-Forrelation, even a single $\mathsf{IQP}$ circuit and query suffices. This answers a recent open question of Girish (arXiv:2510.06385) on the power of commuting quantum computations. We use this to show that $(\mathsf{BPP}^{\mathsf{IQP}})^O \not\subseteq \mathsf{PH}^O$ relative to an oracle $O$, strengthening the result of Raz and Tal (STOC 2019). Our results show that $\mathsf{IQP}$ circuits can be used for classically hard decision problems, thus providing a new route for showing quantum advantage with $\mathsf{IQP}$ circuits, avoiding the verification difficulties associated with sampling tasks. We also prove Fourier growth bounds for $\mathsf{IQP}$ circuits in terms of the size of their accepting set. The key ingredient is an algebraic identity of the quadratic function $Q(x) = \sum_{i < j} x_ix_j$ that allows extracting inner-product phases within an $\mathsf{IQP}$ circuit.

We study a variant of a polygon partition problem, introduced by Chung, Iwama, Liao, and Ahn [ISAAC'25]. Given orthogonal unit vectors $\mathbf{u},\mathbf{v}\in \mathbb{R}^2$ and a polygon $P$ with $n$ vertices, we partition $P$ into connected pieces by cuts parallel to $\mathbf{v}$ such that each resulting subpolygon has width at most one in direction $\mathbf{u}$. We consider the value version, which asks for the minimum number of strips, and the reporting version, which outputs a compact encoding of the cuts in an optimal strip partition. We give efficient algorithms and lower bounds for both versions on three classes of polygons of increasing generality: convex, simple, and self-overlapping. For convex polygons, we solve the value version in $O(\log n)$ time and the reporting version in $O\!\left(h \log\left(1 + \frac{n}{h}\right)\right)$ time, where $h$ is the width of $P$ in direction $\mathbf{u}$. We prove matching lower bounds in the decision-tree model, showing that the reporting algorithm is input-sensitive optimal with respect to $h$. For simple polygons, we present $O(n \log n)$-time, $O(n)$-space algorithms for both versions and prove an $Ω(n)$ lower bound. For self-overlapping polygons, we extend the approach for simple polygons to obtain $O(n \log n)$-time, $O(n)$-space algorithms for both versions, and we prove a matching $Ω(n \log n)$ lower bound in the algebraic computation-tree model via a reduction from the $δ$-closeness problem. Our approach relies on a lattice-theoretic formulation of the problem. We represent strip partitions as antichains of intervals in the Clarke--Cormack--Burkowski lattice, originally developed for minimal-interval semantics in information retrieval. Within this lattice framework, we design a dynamic programming algorithm that uses the lattice operations of meet and join.

We introduce `Goxpyriment', a new open-source software framework for programming behavioral and cognitive experiments using the Go programming language. The library is designed to address some limitations of existing Python-based experiment tools, particularly the runtime environment complexity that frequently complicates deployment across laboratories. Because Go is a compiled language that can natively embed assets (e.g., graphics, audio files, and stimulus lists), Goxpyriment compiles entire experiments into single, self-contained executable binaries with zero runtime dependencies. This drastically simplifies distribution to collaborators and testing computers. The programming interface, inspired by Expyriment (Krause & Lindemann, 2014), was designed to be human friendly. The library includes an array of visual stimuli (text, shapes, images, Gabor patches, motion clouds, ...) and audio capabilities (WAV playback and tone generation). While developing Goxpyriment, we focused on timing reliability. Input events are timestamped by the operating system at hardware-interrupt time, so reaction times are computed by subtracting two OS-level timestamps rather than relying on continuous polling. Go's garbage collector can be disabled, greatly reducing the probability of unpredictable pauses that could corrupt stimulus timing. Finally, a set of over forty psychology experiments implemented in Goxpyriment are provided that promote not only learning by humans but also improve the ability of modern AI-assisted coding tools to help program experiments. The framework is released under the GNU General Public License v3 and is freely available at https://github.com/chrplr/goxpyriment.

Given a group $G$ and an integer $n \geq 0$, let $\mathcal{F}_n$ denote the family of all virtually abelian subgroups of $G$ of rank at most $n$. In this article, we show that for each $n \geq 1$, the minimal dimension of a model for the classifying space $E_{\mathcal{F}_n}G$ for the pure braid group of a surface of non-negative Euler characteristic with at least one boundary component or one puncture is equal to the virtual cohomological dimension of $G$ plus $n$. We prove an analogous result for the full braid group of the sphere. As an application, we compute the minimal dimension of a model for the classifying space associated to the family of amenable subgroups of pure surface braid groups.

If the Universe underwent a cosmic phase transition, it may have left behind a network of cosmic strings. When these strings arise from the breaking of a gauge symmetry, their decay produces a significant stochastic background of gravitational waves. In contrast, if they originate from the breaking of a global symmetry, their decay predominantly yields Nambu-Goldstone bosons, which can persist as dark matter or dark radiation. In this work, we assess the detectability of this particle spectrum using a range of cosmological probes. We employ semi-numerical methods to estimate the resulting energy density and compute the associated matter power spectrum. We then compare these predictions with observations of the cosmic microwave background, Lyman-$α$ forest, large-scale structure surveys, and the UV luminosity function, thereby deriving constraints on the Nambu-Goldstone boson mass and the symmetry-breaking scale. Finally, we present projections for the sensitivity of upcoming cosmic microwave background missions.

We develop a primal bootstrap framework for effective field theories in the presence of a graviton pole, based on finite-resolution sampling rather than smearing, while also allowing direct control over the number of subtractions. We show that this approach reproduces the known projective bounds obtained from smearing in $D{\ge}6$, while yielding slightly stronger bounds in $D{=}5$. This method also makes it straightforward to impose linearized unitarity directly and provides an access to the extremal spectra. Applying the method to crossing-symmetric dispersion relations, we derive new non-projective bounds that fix the overall scale of the EFT couplings. In $D{=}5$, for example, we find that $\frac{M}{M_{\rm P}}{\lesssim}7.8$, showing that the EFT cutoff cannot be taken parametrically larger than the Planck scale. At the extremal values of the couplings, the spectra exhibit a surprising structure: for projective bounds, they exhibit peaks around quadratic Regge-like trajectories, while for the non-projective bounds they form sharp quadratic bands. In the latter case, the leading coefficients further display an inverse-quadratic dependence on the band number.

Magnetic correlations of doped Mott insulators hold the key to the unusual characteristics of many quantum materials. Recent experiments with ultracold atoms in optical lattices have provided new information about the magnetic properties of the Fermi-Hubbard model on a square lattice. We demonstrate that recent measurements indicate that a single doping-dependent energy scale determines both static correlations and dynamical response of these systems. To understand these experimental findings, we employ a self-consistent formalism to describe the coupling between antiferromagnetic magnons and doped holes, and we uncover the emergence of a universal magnetic energy scale at finite doping, which we denote by $J^*$. We present the single- and two-magnon spectral properties at finite doping and discuss the appearance of a bimagnon peak in lattice-modulation spectroscopy, at frequencies set by $J^*$. Furthermore, we argue that this same energy scale sets the onset of pseudogap phenomena, leading to the hypothesis $k_BT^* = c J^*$, with $c$ an order one number. We identify another low-energy scale emerging from our analysis of magnetic excitations, and argue that it controls the stability of Néel order at the lowest temperatures, ultimately driving a transition to an incommensurate spin-density-wave at finite doping. We discuss the relation between this low-energy scale and the nature of fermionic quasiparticles. Our analysis suggests that stability of the commensurate antiferromagentic phase at finite doping can be controlled experimentally by introducing additional quasiparticle broadening via disorder or low-frequency noise.