Papers

We prove that the generalized Fermat equation $x^3+y^5=z^7$ has no solution in nonzero coprime integers, and we make explicit how the proof extends the prior work cited below. Dahmen-Siksek had established the signed local descent and eliminated the three cases in which the associated degree-seven algebra is reducible. Putz had then proved that the remaining irreducible case can involve only seven septic fields: six pure fields and one exceptional field. The missing step was to exclude those seven fields. For the six pure fields we construct an explicit Fano resolvent, descend to a smooth plane quartic of genus three over $\mathbb{Q}(\sqrt{-7})$, and prove that its rational-parameter locus consists only of five points above the branch values. For the exceptional field we combine the modularity and conductor results of Pacetti-Villagra Torcomian with level lowering over $\mathbb{Q}(\sqrt{5})$ and a finite Hecke comparison at $29$. We also reconstruct the three reducible-sector arguments of Dahmen-Siksek as independently replayable calculations, including their database-free identification of the quadratic field, and add an intrinsic formal-group treatment at the ramified prime. The paper labels every major step as a literature input, reconstructed input, or new argument. All project-specific finite calculations are supplied as exact certificates, programs, inputs, and authenticated logs.

In the chip testing problem, we are given $n$ chips, strictly more than half of which are good. Chips can test one another in pairs; a good chip always reports the status of the other chip correctly, whereas a bad chip may report arbitrarily and adversarially. The goal is to identify a single chip that is guaranteed to be good. The problem originates in system-level fault diagnosis and is closely related to the "knights and spies" puzzle. The standard textbook solution is a halving recursion that tests disjoint pairs in rounds and keeps one chip from each consistent pair. We present the Backtracking Candidate Elimination (BCE) algorithm, a sequential alternative that scans the chips once while maintaining a current candidate and a stack of retained chips. Every chip is tested at most once as the incoming chip; when a test is inconclusive the candidate and the incoming chip are discarded together, and the algorithm backtracks to the most recently retained chip. BCE uses at most $n-1$ tests and $O(n)$ time, needs no parity case analysis, and works online. Its correctness follows from two invariants: the retained chips all have the same type, and every discarded pair contains at least one bad chip. We explain how BCE can be viewed as the Boyer-Moore majority vote algorithm with its counter replaced by a stack of physical witnesses, and why that replacement is needed. We also give an early termination rule and a variant for the weaker model of one-directional tests.

The tails of macroeconomic outcomes can respond differently from the centre of their distribution to aggregate shocks. We demonstrate this via a threshold stochastic-volatility-in-mean VAR with regime-dependent leverage. The model allows interactions between the endogenous variables and their volatility, contemporaneous level-volatility dependence, and regime-specific propagation. We estimate the model using a long-run U.S. data set, finding evidence for three inflation-based regimes. We identify business-cycle, financial, macroeconomic-uncertainty, and financial-uncertainty shocks and decompose their contributions to growth- and inflation-at-risk. Business-cycle shocks dominate the median response of GNP growth but account for a substantially smaller share of growth-at-risk. In contrast, uncertainty makes a material contribution to both growth- and inflation-at-risk.

(Abridged) JWST has revealed extremely compact stellar clumps in galaxies at z>6, but their formation mechanism and subsequent evolution remain uncertain. We investigate whether such systems can form in-situ through the fragmentation of an early galactic disk and how stellar feedback regulates their properties. We perform a suite of radiation-hydrodynamical simulations of an isolated galaxy ("Ninfea_blu"), with $\rm M_{vir}=1.5\times10^{10} M_\odot$, evolved for 100 Myr from z=16 to 12.5 with a maximum spatial resolution of 3.6 pc. In all cases, the gas rapidly forms a rotationally supported disk, reaches a peak star formation rate of $10-15\rm M_\odot yr^{-1}$, and fragments into dense stellar clumps. Toomre-unstable regions ($Q_{\rm gas}<1$) appear before the onset of star formation, and the first stellar structures form preferentially within these regions, supporting a Toomre-like gravitational fragmentation pathway.The clumps have stellar masses of $10^6-2\times10^8\,M_\odot$, effective radii of 7-50 pc, and surface densities of $0.2-3\times10^4\rm M_\odot pc^{-2}$, overlapping much of the parameter space occupied by observed z>6 clumps. Feedback reduces the cumulative stellar mass by 30-40%, lowers the gas mass retained within clumps by ~1 dex, and suppresses their high-mass tail without preventing their initial formation. Clumps subsequently migrate, interact, undergo tidal stripping, and disperse. The clump mass function produces a power law slope of -1.88, which aligns closely with observations. Moreover, their contributions to the stellar mass and intrinsic UV luminosity decline from 0.41 and 0.40 at 20 Myr to 0.13 and 0.10 at 100 Myr, respectively. We conclude that fragmentation of compact, gas-rich disks provides a viable origin for many of the dense stellar systems observed in the early Universe, while feedback and internal dynamics primarily regulate their growth and fate.

The problem of differentiating Lipschitz curves in Banach spaces goes back to Tamarkin in the early 1930s and is one of the origins of the Radon–Nikodým property in classical Banach space theory. In this article we characterize those quasi-Banach spaces $X$ for which every Lipschitz curve $F\to\mathbb{R}\to X$ admits a point of differentiability and prove that this property holds if and only if $X$ is isomorphic to a Banach space with the Radon–Nikodým property, thus substantiating a conjecture of Kalton, communicated personally to the first-named author in 2008. Equivalently, every nonlocally convex quasi-Banach space admits a nowhere differentiable Lipschitz curve. Our result is obtained from a quantitative characterization of local convexity in terms of the infinitesimal oscillation of Lipschitz curves. Motivated by this obstruction, we then investigate positive differentiability phenomena in $\ell_p$, $0<p<1$, and identify natural decoupled-coordinate constructions for which Lipschitz regularity nevertheless implies almost-everywhere differentiability. We also contrast this behavior with metric differentiability for the natural metric and the quasi-metric on $\ell_p$.

We have examined the nature of elementary excitations in particular, their spin polarization, in recently discovered zero-field fractional Chern insulator in twisted bilayer MoTe$_2$. We have found that the finite-size bilayer system, in close proximity to a planar parabolic quantum dot containing a single electron (or a hole), forms an incompressible spin-unpolarized fractional Chern insulator at 1/3 filling factor. The corresponding energy gap is found to be large and weakly dependent on the separation between the quantum dot and the bilayer. We predict that in this fractional Chern insulator coupled to a quantum dot, spin-unpolarized quasiparticles and quasiholes are expected to appear as low-energy elementary excitations. The charge density results indicate that, for the spin-unpolarized quasiparticles, the positive charge is strongly localized near the negatively charged QD within the spin-flipped component, whereas for the spin-polarized quasiparticles, such localization is much less pronounced.

Natural Visibility Graph (NVG)-based representations provide a promising approach for capturing structural patterns in sequential network traffic. However, whether different cyber-attack classes exhibit distinctive topological signatures in such representations remains insufficiently understood. This study investigates the discriminative and structural characteristics of NVG-based network traffic representations using the CSE-CIC-IDS2018 dataset. Seventy-six numerical traffic features were independently transformed into NVGs within overlapping frames of 40 observations, and ten graph-theoretic metrics were extracted from each graph, resulting in 760 topological descriptors per frame. The discriminative capability of these representations was evaluated using a multi-branch convolutional neural network (CNN) with stratified five-fold cross-validation. The model achieved an average accuracy of 96.20% and a Matthews correlation coefficient (MCC) of 0.9566. To characterize class-specific topological differences, Kruskal-Wallis and Mann-Whitney U tests were combined with Benjamini-Hochberg false discovery rate correction and effect-size measures. Of the 10,640 attack-versus-benign comparisons, 7,777 (73.1%) remained statistically significant after FDR correction, with 4,844 exhibiting large Cliff's delta effects. The strongest global differences were predominantly associated with backward-traffic and packet-length-related features combined with connectivity, clustering, and centrality measures. These findings indicate that NVG-derived representations can provide strong discriminative capability while revealing class-dependent topological patterns associated with different cyber-attack classes.

Hexapod robots can achieve static stability with fewer actuated joints than bipeds or quadrupeds, yet many platforms still use 3-DOF legs, increasing weight and continuous torque requirement with limited gain in locomotion capability on flat, inclined and moderately rough terrains. We release Spiderbot, an open-source hexapod that uses a 4-bar linkage with a passive spring to mechanically support body weight, with a 2-DOF per-leg design that substantially reduces energy consumption. This mechanism substantially offloads gravitational torque during standing stance consuming only 1.5W (reduction of over 90% over the unsprung version and up to 96% over other similar hexapods). The passive spring compensation extends to payloads of up to 3.25kg with no additional torque requirements. The platform enables long-duration deployments on a modest battery budget and costs under \$400, making it suitable for large-scale multi-agent experiments. We validate the locomotion capabilities of the platform with an RL policy trained in mjlab, including successful sim-to-real transfer, despite the complexity of the mechanism. The platform is evaluated on flat and rough terrains, slope up to $15^\circ$ and step obstacles. We release all the CAD files, assembling instructions, and full training and deployment code along with the model checkpoints at https://erc-bpgc.github.io/SpiderBot/.

The interplay between non-trivial background geometries and quantum dynamics has emerged as a powerful tool to tailor the electronic properties of 2D materials. In this work, we investigate the effective quantum dynamics of massless Dirac fermions confined to a twisted graphene structure called a catenoid bridge, which connects two single-layer sheets. By adopting a continuum approach, where the electron dynamics is governed by a purely covariant curved Dirac equation, we obtain the effective Hamiltonian containing both curvature and twist interactions. We found that the torsion modifies the electronic states by producing a geometric phase on the wave function. In addition, the twist also deforms the surface geometry, which leads to a new geometric term in the effective Hamiltonian. This twist potential enhances the barrier around the catenoid throat, which increases the suppression of the inter-layer transmission coefficient. Like the spin-curvature interaction, the spin-twist term has a chiral dependence which is invariant under a combined parity and spin flip transformation. As a result, the electronic states can be restricted to the upper or lower layer. These findings provide valuable insights into how mechanical deformations can be harnessed to control quantum transport in graphene-based wormhole architectures.

We introduce a magnetic coherent–state frame over the Landau levels of the two–dimensional Landau Hamiltonian, indexed by a discrete metric space combining spatial and energy degrees of freedom. Although overcomplete, the frame is almost–orthogonal, and we use it to endow the CAR $C^*$–algebra over the one–particle Hilbert space with an asymptotic quasi–local (AQL) structure, in which graded commutators of observables localized on disjoint index sets decay exponentially rather than vanish exactly. By means of a family of conditional expectations onto the resulting local subalgebras, we construct a Fréchet $*$–subalgebra of almost–local observables, invariant under the discrete group of lattice translations, which act on it by continuous automorphisms. For the full continuous group of magnetic translations we establish a quantitative control on how local observables spread through this almost–local algebra, and we show that this control suffices to extend graded asymptotic abelianness from the lattice to the entire continuous translation group. The results provide a discrete–continuum dictionary intended as the starting point for extending Lieb–Robinson–type techniques from lattice systems to interacting continuum electrons in a magnetic field.

For multimodal large language models, when images or speech conflict with accompanying text, measured text reliance can entangle modality preference with evidence position. Earlier studies of text bias often used a fixed evidence order or moved task instructions with the evidence, leaving the contribution of order unclear. In this paper, we use a paired comparison that keeps the instructions and evidence content fixed and swaps only the positions of the two sources to quantify this potential influence. Across vision and speech models, placing an image or recording after conflicting text consistently shifts answers toward its content. We also revisit previous studies and analyze why their experimental settings can lead to misleading conclusions. These findings reveal cross-modal evidence noncommutativity: the same evidence can lead to different judgments when its order changes, and placing perceptual evidence later can increase the model's reliance on its content.

Knowledge Graphs (KGs) play an increasingly important role in numerous applications ranging from traditional knowledge representation to serving as memory for LLMs to support downstream tasks. However, their construction is labor-intensive; thus, in recent years, numerous approaches for automizing this process have been proposed. Compared to the popularity of construction approaches that focus on textual input data, methods for semi-structured inputs remain underrepresented and as a result, no comprehensive benchmark and evaluation suite exists to judge the quality of mapping predictions and generated KGs. This is problematic, as a KG's quality has direct influence on the downstream applications it supports and thus, strong evaluation mechanisms for their construction are urgently needed. In this work, we thus focus on the evaluation of KG construction from semi-structured data and present a benchmark and evaluation pipeline for KG construction that combines the quality dimensions (1) syntactic validity, (2) semantic accuracy, (3) consistency, (4) conciseness, (5) completeness, and (6) pragmatic quality measured on a KG's ability to provide answers to competency questions. This work contributes a realistic task definition, extends current state of the art evaluation frameworks, allows evaluation of systems that predict mappings and RDF data alike, and combines evaluation of both KG construction and downstream usage. We provide a comprehensive metrics suite, provide ten expert-curated datasets from seven domains, and showcase evaluation using two reference systems.

Let $R$ be the closed linear span of the Rademacher functions in $L^1(0,1)$. We prove that $L^1(0,1)/R$ embeds isomorphically into $L^1(0,1)$, answering affirmatively a question of González and Martínez-Abejón \cite[p.~140]{GM97}. We then use this embedding to show that the weak Calkin algebra of the quotient is uniformly incompressible. \end{abstract

Understanding how liquid-liquid phase separation impacts the mechanics of filament networks is a fundamental physical problem at the heart of biological cellular processes and soft material design. While a few theoretical mechanisms have been proposed, a clear demonstration of the direct coupling of phase separation to the overall network stiffness is missing. We report experiments that reveal a universal mechanism by which the condensation of macromolecular crowders induces a rigidity transition in a model filament network. We reconstituted stiff sterically interacting helical filaments and polymeric crowders. Initially, the macromolecules were uniformly dissolved and the filaments formed bundles that assembled a rigid entangled network. Once the crowders condensed into droplets, the network structure lost its rigidity and its mechanical response weakened by an order-of-magnitude. The subsequent dissolution of the condensates was accompanied by the re-establishment of rigidity. Our results show that crowder phase separation modulates the mechanics of filament networks by tuning the osmotic pressure holding the network together. This principle may serve as a paradigm for devising dynamically tunable filamentous materials.

In complex systems theory, there are different ways to describe a system in terms of information, such as emergence (Shannon entropy), self-organization, and com- plexity. These measures provide information about the dynamic behavior of a complex system. We study the differences in entropy and complexity for many-body systems undergoing a transition from a regular to a chaotic regime. To do this, we analyze the eigenvectors of the 48 Ca nucleus for different quadrupole-type two-body interactions. We obtain the eigenvectors by diagonalizing the two-body Hamiltonian for 48 Ca us- ing the Antoine code. We then calculate the entropy and complexity for the different quadrupole-type interactions. The differences found in information entropy and com- plexity are clear when comparing a regular system with a chaotic one. We find that the complexity of the regular and chaotic states of 48 Ca shows differences associated with its internal interactions.

We describe deploying imaging AI at six hospitals through PACS-AI, an open self-hosted platform. The binding constraint is not model accuracy but infrastructure to route studies, display results, capture feedback, and audit what runs. At one center, angiography models completed 515 of 607 jobs (84.8%); failures reflected absent diagnostic views, and 78.1% of 638 clinician ratings were positive. Publishing honest readiness levels for every model is itself a governance practice.

We prove that the irrationality exponent of $\zeta(3)$ satisfies $\mu(\zeta(3)) < 5.5138800$, improving the bound $5.513891$ obtained by Rhin and Viola in 2001, which has been the best known for twenty-five years. The proof is an application of their Theorem 5.1 at a new integral direction. That direction is not reached by enlarging the search range: its eight parameters are 52000 times theirs, shifted by at most 23. The mechanism is the one recently used by Bai for $\pi$. In particular the Rhin-Viola point, optimal in every region covered by enumeration, is not optimal.

Gaussian processes (GPs) provide a flexible framework for learning unknown functions from noisy measurements while quantifying predictive uncertainty, making them well suited for estimation in multi-agent systems. However, when measurements are collected by multiple agents, maintaining a unified GP model without centralized processing requires efficient distributed algorithms that can operate using local measurements and communication with neighboring agents. In this work, we develop two distributed recursive GP (RGP) algorithms for multi-output GP regression: ADMM-RGP and PDMM-RGP. We analyze the stability and convergence of both algorithms and develop parameter selection strategies to accelerate convergence, thus reducing the communication burden. The proposed methods are validated on a real-world multi-output wind dataset, and their convergence behavior is examined across communication graphs with varying connectivity. Numerical experiments demonstrate that ADMM-RGP and PDMM-RGP can significantly reduce communication relative to the state of the art, while maintaining comparable estimation accuracy and network-wide consensus.

We study online inverse linear optimization with a fixed unknown linear utility: in each round, an environment presents a compact action set, the learner recommends an action from it, and the environment returns an action that maximizes the utility over the same set. When the utility vector and the actions lie in the $d$-dimensional Euclidean unit ball, we give a randomized algorithm whose regret—the cumulative utility shortfall relative to optimal actions—is $O(\sqrt d)$ in expectation for every time horizon, without knowledge of the horizon. The dependence on $d$ is optimal up to a constant factor by the known $\Omega(\sqrt d)$ lower bound for horizons $T\ge d$. Our algorithm maintains matrix multiplicative weights on polynomial feature spaces at geometrically spaced scales. It selects a recommendation distribution by solving a linear program and updates its score matrices by comparing the available actions with the feedback action. With rational oracle outputs and feedback actions, an implementation computable relative to a linear-optimization oracle preserves the $O(\sqrt d)$ regret bound. Whether the same rate is attainable with running time polynomial in the dimension, horizon, and input length remains open.

Offline top-k evaluation often ranks one held-out relevant item together with sampled negatives. When several candidates receive exactly the same score, the tie-breaking rule becomes part of the ranking. A common implementation stores the relevant item first and then applies a stable sort, which preserves input order among equal scores; the relevant item therefore wins every tie. We call an evaluator row-order invariant when permuting the input candidates without changing their identities, labels, or scores leaves the final ranking unchanged. We audit this property by holding candidates and scores fixed and changing only the tie-breaking rule. On 30,000 Amazon Beauty & Personal Care rows, NDCG@10 for a rating-weighted attribute-overlap score is 0.85 under input-order tie-breaking. A deterministic hash tie-break based on user and item IDs lowers it to 0.17. The exact expectation under uniform random tie-breaking closely matches the mean over 100 independent hash seeds, while a residualized attribute score with few exact ties is nearly unchanged. MovieLens Tag Genome shows the same pattern for an attribute-overlap score, whereas item popularity is nearly unchanged. We derive expected Hit Rate and NDCG at cutoff k when the relevant item is randomly ordered among candidates with the same score, and we provide a practical reporting checklist. The same issue can occur in sampled or full-catalog evaluation whenever exact ties affect top-k membership or rank.

Learned context planning selects evidence atoms before an answer model reasons over them. We test whether this learned selection improves long-context multiple-choice QA after strong retrieval, routing, budgeted-selector, and reranking controls. Our primary diagnostic uses all 503 LongBench-v2 MCQ questions with Qwen2.5-7B-Instruct. The planner is SFT-trained on outcome-selected traces from 140 training and 28 development questions; because the 503-question analysis includes those questions, it is partly transductive. At an 18k-character budget, anchored hybrid retrieval reaches 36.18% accuracy and BM25 reaches 35.98%, while the best direct planner-guided method reaches 34.19%. On the untouched 152-question test split, anchored hybrid remains higher (42.11% versus 36.84%). Leakage-safe routers cannot convert a large oracle gap. Under tight budgets, the best planner is ahead by only 0.40 points at 6k and loses at 9k; planner-guided reranking has a +1.79-point estimate at 6k with a paired interval crossing zero and ties the control at 9k. Packing-order and score-flatness analyses did not identify a stable mechanism. Under this setup, learned planning is a weak relevance signal rather than a replacement for strong retrieval.

Reproduction studies can produce mixed outcomes. Reported values may differ while the ordering of the compared methods remains the same, a result may hold only under some experimental conditions, or a released implementation may fail to reproduce a result that the model can still reach. The terms repeatability, reproducibility, and replicability describe how a follow-up study relates to the original experiment, but not which parts of the original claim are supported by the new results. We introduce claim calibration as a way of stating the strongest claim supported by a follow-up study, together with the conditions under which it holds and the parts that remain untested. We apply this perspective to five original–follow-up paper pairs from recommender-systems research. The cases show that agreement in numerical values, method rankings, statistical results, and overall conclusions does not always coincide, and that follow-up studies often support only part of the original claim. Based on these observations, we propose a Claim Evidence Profile for reporting the original claim, its scope, the reproduction target, the reported results, the calibrated claim, and the parts of the original claim that remain unresolved.

What distinguishes the solution of a difficult mathematical problem from a conceptual revolution? Some mathematical innovations do more than establish new results: they reorganize the relations among problems. We propose to describe such events through changes in the transfer structure of mathematics, namely the pattern determining which problems can naturally inform one another, which methods can move between them, and which new questions become accessible. The eighteenth-century controversy over the vibrating string provides our central historical case. D'Alembert found a famous model for wave propagation, Bernoulli proposed a modal interpretation, Euler broadened the class of admissible profiles, and Lagrange constructed a finite-dimensional strategy based on modal decomposition. Later, Fourier analysis gave the trigonometric language in which all the previous descriptions can interact. This motivates our Rewiring Thesis: a conceptual revolution is a persistent, large-scale reorganization of transfer relations among mathematical problems. The productive representation is one mechanism capable of producing such rewiring, but some stress tests (involving Galois, Riemann, Lebesgue-Schwartz and Wiles) show that it is not the only one. The musical notation provides an independent case in which the representation becomes operationally generative without being informationally complete. The resulting framework suggests a stronger criterion for artificial mathematical creativity than problem solving alone. The relevant question is not merely "whether AI can solve a famous conjecture", but "whether it can recognize that an inherited conceptual organization is itself an obstruction and produce a new one that reorganizes several problems at once". In this sense, the decisive achievement may be the invention of "the next Fourier transform".

A central problem for surgery with quantum Low-Density Parity Check (LDPC) codes is the design of auxiliary systems which measure large sets of logical operators in parallel, while preserving sparsity and fault distance. We introduce a very general method for designing surgery gadgets which are 'high rate', meaning that the number of operators measured in parallel is large in comparison to the size of the auxiliary system. Given an arbitrary initial $[[ n, k, d ]]$ quantum LDPC Calderbank-Shor-Steane (CSS) code, and an arbitrary subcode of size $\mu \leq n$ that contains $t \leq k$ logical qubits, the method produces a sparse high-rate surgery gadget with size $\mu (\log\mu)^{O(\log\log \mu)}=\mu^{1+o(1)}$ which measures all $t$ logicals in the subcode. The space overhead is asymptotically optimal up to subpolynomial factors, as the lower bound is $\Omega(\mu)$. This gadget is produced in time polynomial in $\mu$. When logical measurement is performed using these surgery gadgets, the phenomenological fault distance is at least $d$ when performed for $d$ rounds. Our main result comes from relating surgery gadgets with relative cosystolic expansion to linear Probabilistically Checkable Proofs of Proximity (PCPPs), which allow a randomised verifier to probabilistically verify the input to a linear circuit, using only oracle access to the input and a claimed proof.

Training Universal Differential Equations (UDEs) traditionally relies on backpropagating through numerical ODE solvers, creating memory footprints far exceeding the capabilities of edge microcontrollers. We present Lie-Taylor jet matching, a solver-free training framework that fits a hybrid vector field directly to the first and second time-derivatives of observed system states. These derivatives, the truncated Lie-Taylor jet, are estimated online via Savitzky-Golay filtering, yielding fully analytic gradients without automatic differentiation software. We evaluate whether eliminating the solver compromises accuracy against a conventional baseline (fixed-step RK4 integration, multiple shooting, exact discrete adjoints, Adam) sharing identical dynamics, noise models, network architectures, and metrics. While naive derivative matching degrades under sensor noise, our noise-adaptive mechanisms close and reverse this gap: full-rate phase-shifted sampling, a reservoir buffer, cosine-annealed optimization with weight averaging, on-device noise estimation, and polynomial-misfit quality gating. On a damped pendulum and chaotic double pendulum, our method matches or exceeds baseline accuracy at matched data windows and recovers unmodeled damping coefficients. Across noise levels from 0% to 5%, it attains a geometric-mean relative field error of 0.65x that of the baseline within 108 kB of static memory, compared with megabytes of solver tape. On an ESP32 microcontroller, the on-device run reaches a field error of 0.0020 and recovers the damping coefficient to c = 0.400 (true 0.400) within 61.3 kB of static memory and 7.24 ms per update (18.1% duty cycle at 25 Hz), confirming real-time on-device training is feasible without a numerical solver.

Using determinant quantum Monte Carlo simulations, we compare charge transport in the two-dimensional attractive and repulsive Hubbard models at strong coupling, $|U|/t=6$. Although the interaction with opposite signs generates qualitatively different low-energy spin, charge, and pairing correlations, both exhibit approximately linear-in-temperature resistivity over a broad intermediate- and high-temperature regime. At asymptotically high temperature this common behavior follows from the moment expansion of the conductivity, whose leading contribution is even in $U$. More strikingly, the similarity persists to temperatures well below $|U|$, where strong interaction-dependent correlations have already developed, and also irrespective of whether resistivity crosses the MIR limit. Using the Nernst–Einstein relation, we find that the common linear-in-temperature resistivity is primarily associated with an approximately Curie-like charge compressibility and weakly temperature-dependent diffusivity. The two models separate only at lower temperatures, where the attractive model develops a pronounced feature in the charge diffusivity correlated with signatures of pair formation. These results show that linear-in-temperature incoherent transport in the Hubbard model can be remarkably insensitive to the microscopic nature of the low-energy correlations. Our results suggest that transport in the incoherent regime appears insensitive to what the system will ultimately become at low temperature; the distinction between competing low-energy states becomes visible only when their characteristic correlations acquire sufficiently long spatial or temporal coherence.

Providing students with experience from chip specification to fabricated silicon can strengthen chip-design education, but integrating tapeout into regular teaching is difficult to scale, especially across universities with different curricula, schedules, regulations, and technical infrastructures. This article discusses the implementation experience and lessons learned from a cross-university approach developed within the Edu4Chip European project. The approach combines aligned learning outcomes, local Master's implementations, and a shared design-to-silicon framework across five European universities.

Optical space-time wave packets (STWPs) can be engineered to sustain tight transverse confinement over long distances. However, whether the requisite precise spatiotemporal correlations underlying this behavior survive volumetric scattering remains unclear. Here, we experimentally demonstrate that STWP light sheets with transverse thicknesses of 11 and 22 microns largely retain their prescribed spatiotemporal structure after transmission through 10 mm thick scattering phantoms (scattering coefficient = 0.84 per mm). Moreover, compared with size-matched Gaussian beams, STWPs exhibit greater preservation of their initial spectral intensity distribution across the prescribed space-time domain following scattering. Additionally, the transmitted STWPs remain tightly confined and preserve on-axis intensity decay rates similar to those of their unscattered counterparts. As the scattering conditions span biologically relevant regimes, the structural and propagation resilience of STWPs to scattering highlights their potential for extended-depth 3D biomedical microscopy.

Planning is a common yet complex activity shaped by constraints to satisfy and preferences to balance. Travel planning, as both an everyday activity and a frequent benchmark for evaluating intelligent systems, offers a rich context for examining how constraints and preferences emerge and evolve. While recent AI systems have achieved impressive results in generating personalized itineraries, they often assume that users can articulate stable goals upfront. To understand how real-world planning unfolds, we conducted a two-part interview study: one with eight travelers reflecting on their planning experiences, and one with nine travel agents sharing professional practices. We trace the dynamics of constraints and preferences as they are surfaced, refined, and coordinated throughout the planning process, and identified 11 actions revolving around constraints and preferences, which shaped the planning process. We offer design heuristics for planning tools that better support human-AI collaborative actions to support the fluid, contingent nature of planning.

We present a study of gas uplift by cavities and its role in promoting the formation of molecular gas in cool-core galaxy clusters. Using a sample of 24 clusters, we quantify the parameter space of gas uplift, including lifting masses, velocities, radii, and cooling times, and compare the displaced hot gas to observed molecular gas masses. Almost all clusters contain sufficient low-entropy gas within the central $\sim$10 kpc to account for the observed molecular gas. The molecular gas mass scales approximately linearly with the maximum gas mass displaced by cavities. Gas with cooling times of a few $10^8$ yr can be transported to typical H$\alpha$ filament radii of 10–30 kpc at characteristic velocities of 150–400 km s$^{-1}$, whereas gas with $t_{\rm cool}\sim10^9$ yr generally requires uplift to $\gtrsim60$ kpc. The mass expected to cool over the lifetimes of the currently observed cavities is comparable to the molecular reservoir in several systems, assuming that 50% of the displaced gas mass is lifted and cools, whereas other systems contain excess molecular gas. This suggests that the molecular gas reservoirs may have accumulated over multiple AGN feedback cycles involving repeated gas uplift and cooling, or through additional processes. H$\alpha$ and infrared luminosities increase linearly with X-ray cooling luminosity, linking the multiphase emission to the cooling atmosphere. Overall, our results support a picture in which repeated AGN outbursts with gas uplift promote the condensation of low-entropy gas and help build molecular reservoirs in cool-core BCGs.