Papers

We study the computational complexity of approximating the minimum distance of a stabilizer code. Classically, the minimum distance problem is NP-hard to approximate even to within an additive gap linear in the block length. For quantum codes, however, the reductions of Kapshikar and Kundu and of Grigorescu, Jha and Samperton reach only an additive $O(\sqrt{N})$ gap in the block length $N$. We close this gap and, in a separate direction, initiate the fine-grained study of the problem. We show that no randomized algorithm approximates the distance to within an additive $\alpha N$, for a constant $\alpha > 0$, unless $\mathsf{NP} \subseteq \mathsf{coRP}$. In the fine-grained setting, for every $\varepsilon > 0$, no randomized $2^{(1-\varepsilon)\kappa}\,\mathrm{poly}(N)$-time algorithm computes the distance of a code with $\kappa$ logical qubits unless SETH falls; and no randomized $2^{o(N)}$-time algorithm approximates the distance to within a linear additive gap, on instances where block length, number of logical qubits, and gap are simultaneously linear, unless non-uniform Gap-ETH falls.

Many LLM-as-a-judge evaluations score fixed outputs under a fixed task definition. Production multi-turn business agents instead require a maintained measurement system: correctness depends on business-specific facts and procedures, outcomes emerge across turns, and failures must be attributed to either agent capability or missing business knowledge before they are actionable. We present an integrated methodology spanning evaluation specification, modular LLM judges, intent-preserving user simulation, and human-in-the-loop governance. The specification defines conversation-level end states and actionable failure ownership. Atomic judges share versioned evidence and feed an explicit aggregation graph. The simulator is released only after task-preservation and stability checks. Independent human audits estimate measurement fidelity, renew tiered reference sets, and route disagreements to label correction, guideline revision, or judge improvement. Production studies show that system-level fidelity improved across repeated audits, that human reviewers and automated judges improved together under the shared feedback loop, and that their combined workflow had the strongest descriptive performance in both reported task-completion settings. Because the studies are observational and the human reference itself required revision, these findings demonstrate operational usefulness rather than causal or universal superiority. The contribution is a practical framework for making multi-turn agent measurement reliable, actionable, and maintainable as the evaluated system and its evidence evolve.

Differential-algebraic equations (DAEs) present a ubiquitous model class in the automated modeling, simulation, control and optimization of complex finite or infinite dimensional dynamical systems, in particular in the construction of digital twins. When combined with adequate space and time discretization methods they present the work-horse of developments in many engineering domains. However, this approach comes with certain challenges for the numerical methods and in particular in the coupling of systems from different physical domains with different scales or regularity requirements. We survey the modeling with DAEs and address how to overcome some of the challenges via the framework of port-Hamiltonian differential-algebraic systems (pHDAEs) and their simulation and optimization with space-time-model adaptive methods.

We study piecewise polynomial functions $\delta_k(c)$ that appear in the conjectured asymptotics for the variance of short-interval sums of von Mangoldt convolutions $\Lambda^{*k}$. By a theorem of Kuperberg and Lalín, a unitary matrix integral involving a sum of trace products governs the large-$q$ limit of the function-field analogue of this variance. We identify $\delta_k(c)$ as the leading-order coefficient of this integral when the total trace degree and matrix size grow with a fixed ratio $c$. Through an asymptotic analysis of two lattice-point representations for the matrix integral, we obtain explicit forms of $\delta_k(c)$. A finite spline expansion and a contour-integral representation expressing $\delta_k(c)$ as the inverse Laplace transform of a two-weight block Hankel determinant are also obtained.

Endothermic upscattering of heavy dark matter offers a compelling interpretation of the high-energy nuclear-recoil candidate recently reported by LUX-ZEPLIN (LZ), with a characteristic recoil energy $E_R \propto \delta$, where $\delta$ is the mass splitting between the dark matter states. Cosmological and experimental constraints motivate the depletion of the primordial heavier state, which can be regenerated in the Galactic halo. We show that, if the heavier state decays radiatively, the same mass splitting sets the energy of a gamma-ray line, $E_\gamma \simeq \delta$. For our benchmark, this leads to a sub-MeV line within the projected reach of the Compton Spectrometer and Imager (COSI), scheduled for launch in 2027. The confirmation of the LZ candidate event as a dark matter signal would therefore motivate dedicated searches for sub-MeV gamma-ray lines, with COSI providing a timely opportunity to test this interpretation.

The increasing adoption of robotic systems in surgery, together with the expanding range of procedures they can support and the growing level of autonomy they provide, has substantially increased the complexity of surgical robots. As these systems integrate more sensors, controllers, communication interfaces, and model-driven control components, their attack surface continues to expand. A compromise of the integrity of a surgical robot can therefore cause unintended robot behavior and potentially threaten patient safety. In this paper, we characterize the detection boundary of malicious injections on RAVEN II using a public dataset that pairs the platform's telemetry with external high-resolution encoder ground truth. We identify three injection points spanning the command and observation paths and evaluate three injection patterns with increasing temporal dispersion. To capture different detection behaviors, we perform detection at two timescales: the window scale and the session scale. Rather than reporting detection rates at an arbitrarily chosen threshold, we quantify, for each injection point and injection pattern, the smallest end-effector deviation that can be resolved while maintaining an alarm rate acceptable for surgical operation. Our results show that detectability is strongly influenced by how the injected deviation is distributed over time. An abrupt step can be detected at deviations well below the 1 mm clinical tolerance, whereas the same overall deviation spread across a window or a session can remain hidden from single-window statistics. The open source code can be found at http://github.com/RAVENIIROS/RAVENIIIntegrity.

As AI becomes part of how books are authored, reader response to suspected AI authorship grows more consequential, yet remains unexamined. We analyze 863 low-star reviews of 78 Amazon bestsellers across 8 categories at three levels of proximity to AI. Suspicion concentrates in Generative AI books (35.1%) but appears in every category, including Gardening (5.7%). Reviews citing AI authorship complain more about shallow content and poor presentation than other critical reviews. Suspicion takes two forms: ambient, where "AI-generated" is a generic complaint about formulaic writing, and corroborated, where reviewers of the same book independently cite concrete evidence. We propose two mechanisms by which suspicion arises: topical concentration, where a book's AI subject matter supplies vocabulary for quality complaints, and artifact detection, where readers notice ChatGPT-style formatting regardless of topic. Star ratings can hide this suspicion: the most-flagged book holds 4.1 stars while 50% of its critical reviews cite AI authorship.

We demonstrate a modification of the high-low method of Guth-Maldague-Wang that yields a decoupling theorem which gives the sharp estimate for the discrete restriction constant for the parabola and also a diameter-free bound for the three-fold additive energy of rational points on the parabola and circle. These results were recently obtained by Deng-Fan-Guo-Guo-Luo and Cushman-Demeter-Wu, respectively. The novel features in this argument are an orthogonal expansion of $F^3$ and a new square function that also keeps the wavepackets discarded after pruning, resulting in new and more efficient high and low lemmas.

We consider latency attacks on object detectors, where the attacker's goal is not to corrupt a prediction but to make the system fail to respond in time, targeting real-time applications such as autonomous driving. Modern object detectors eliminate Non-Maximum Suppression (NMS) through one-to-one assignment or set prediction, removing the classical detector-side latency bottleneck exploited by prior latency (“sponge”) attacks. We show that NMS-free does not mean latency-robust: this architectural change does not eliminate the attack surface but relocates it downstream to multi-object tracking, whose data-association cost remains content dependent. We present TrackFlood, a unified white-box overload attack against NMS-free detect-then-track pipelines spanning both one-to-one detectors (YOLOv10 and YOLO26) and query-based detectors (RT-DETR). TrackFlood recovers differentiable confidence tensors and optimizes perturbations that flood the tracker with spatially distributed phantom detections while leaving detector inference unchanged. Evaluated entirely on an NVIDIA Jetson AGX Orin (TensorRT FP16), detector latency remains essentially constant, whereas tracker latency increases substantially. At a standard imperceptible budget ($L_\infty{=}8/255$), a universal perturbation produces clearly measurable tracker overload but only modest end-to-end slowdown, without deadline misses for the association-dominated trackers; a separate higher-budget stress test drives severe end-to-end slowdowns and sustained deadline misses. We further evaluate a lightweight, architecture-agnostic bounded-admission layer that caps the tracker workload and largely restores end-to-end latency, at a non-trivial cost in admitted clean detections. Our results demonstrate that evaluating NMS-free perception systems requires considering downstream tracking and end-to-end timing, not detector inference alone.

Diffusion language models (DLMs) promise fast parallel generation, yet high-quality samples often require large number of refinement steps, which diminishes their advantage in practice. This has led to massive interest in and rapid development of new methods for effective few-step generation. We show that much of the supposed quality gap at few steps can instead arise from a suboptimally configured sampler. Modest sampler sharpening, without any model retraining, enables a couple years old masked DLM to rival supposedly far improved successors. This differently sampled DLM in fact achieves lower generative perplexity in just 16 steps than what its standard sampler obtains with 1024, while improving both judged quality and semantic diversity. We further show that conventional per-output metrics can fundamentally obscure these gains, since any optimal trade-off between two such metrics can be attained by a generator supported on at most two outputs. We subsequently introduce GroupEval, which separately evaluates quality and across-output semantic diversity, and offers fresh insights including uncovering how 1.5-4.7x perplexity gains of a distilled model yield no corresponding quality gain. Finally, we explain why sharpening helps: parallel unmasking destroys dependencies among simultaneously generated tokens, creating a gap between prediction and generation. We prove that pervasive temperature choice of one is generically suboptimal under parallel sampling even for an exact denoiser, and that worse predictions can yield better samples. Through these results, we argue for a broader evaluation principle of treating the deployed generator as the object of comparison, benchmarking it against tuned baselines, and assessing quality and diversity jointly and with more human-aligned measures.

Standard Big-M mixed-integer programming reformulations of chance-constrained programs (CCPs) with finite support often yield weak linear relaxations and scale poorly as the number of scenarios increases. To address this limitation, we derive two families of intersection cuts from problem-specific S-free sets and develop decomposition-based branch-and-cut frameworks. The first one exploits the submodular structure of the scenario requirement function, while the second one uses probability covers. We propose hybrid separation strategies that combine classical mixing inequalities and quantile cuts with the proposed intersection cuts. Computational experiments on integrated production-distribution planning instances show that the proposed hybrid methods reduce computational time compared to pure methods.

Let $G$ be a graph. Under a strong edge coloring of $G$, every color class is an induced matching. The strong chromatic index of $G$, denoted by $\chi'_s(G)$, is the smallest integer $k$ such that $G$ admits a strong edge coloring with $k$ colors. Denote by $\Delta(G)$ the maximum degree of $G$. In this paper, we prove that every graph $G$ with $\Delta(G)\le 6$ satisfies $\chi'_s(G)\le 57$, improving the best known upper bound $60$.

Jointly generating future video and actions has become a standard recipe for world-action models, and the strongest systems denoise the two streams on separate schedules: actions are decoded in few steps so control stays fast, while the video stream runs longer to keep the predicted future sharp. The design is deliberate, but it leaves the two streams on different clocks, and an action can become executable while the future that should justify it is still largely unresolved. We formalize this as a two-clock view of asynchronous inference and introduce the commitment-evidence gap, a quantity read directly from a model's own sampling schedule rather than measured by search. The gap is predictive: as it widens, candidate utility becomes harder to identify and extra candidate sampling buys less, while advancing the world stream buys more, and the two cross. Spending more world computation is therefore not simply better. The useful interval is closed at both ends, and both ends can be read off the schedule before any rollout. ReSync places the computation inside it: hold the action state, advance only the world within the supported window, then resume native denoising. No parameters change and no candidates are compared. On a frozen paired RoboCasa panel this improves success by 4.48 points, while an equal-compute control that waits without advancing the world does not move, and the same rule transfers to a second benchmark and a second backbone without retuning.

The African School of Fundamental Physics and Applications, also known as the African School of Physics (ASP), was initiated in 2010, as a three-week biennial event, to offer additional training in fundamental and applied physics to African students with a minimum of three-year university education. Since its inception, ASP has grown to be much more than a school. ASP has become a series of activities and events to support academic development of African students, teachers, high school pupils (learners) and faculties. We report on the ninth African School of Physics, ASP2026, organized in Kenya, on July 5–19, 2026. ASP2026 included programs for university students, high school teachers and learners.

In this paper we revisited the analyse the vacuum polarizations effect associated wit charged matter fields in a higher-dimensional anti de-Sitter (AdS) spacetime in the presence of an idealized cosmic string carrying magnetic flux running along its core. Specifically we will consider, separately, charged bosonic and fermionic fields propagating in this manifold. Our main objective is to calculate the vacuum expectation values (VEV) of the energy-momentum tensor, $\langle T^\mu_\nu\rangle$, associated with both matters fields. As will see, these VEVs are even function of the magnetic flux running along the string's core, with period equal to the quantum flux $\Phi_0=\frac{2\pi}{e}$. Because the results obtained are expressed in terms of special functions, and a clear behavior for them are not very enlightening, we provide some graphs exhibiting their behavior as function of the distance to the string considering different values for the parameters presented in the model considered.

In the Kourovka Notebook, V.\,D.~Mazurov asked whether an automorphism $\alpha$ of prime order $m$ of the infinite free Burnside group $G=B(m,q)$ of prime period $q$ that cyclically permutes the free generators of $G$ must have a nontrivial fixed point. In this paper, we show that for $m\ge3$ the answer is negative for all sufficiently large prime periods $q$. Precisely, we prove that for any odd $m\ge3$, there exists $q_m>0$ such that for every prime period $q>q_m$, the automorphism of $B(m,q)$ of order $m$ that cyclically permutes its free generators is fixed-point-free.

Detecting failures in World Model (WM)-based planning requires monitoring whether the model is behaviorally aligned with the current task, which in turn requires studying its internal representations. Here, we show that centroids—sub-component Jacobian row-sums—effectively identify the behavioral properties of WMs, complementing traditional activation-based knowledge signals. The centroids of a model are easily computed through Jacobian vector products and characterize how the model organizes the geometry of its input space, yielding an efficient perspective on internal representations, including the generation of task-relevant saliency maps. Evaluated on continuous control tasks using JEPA WMs, this behavioral view reveals a structural dissociation, where the encoder correctly represents the goal while the predictor remains behaviorally unresponsive. This failure mode directly predicts planning failure before any action is taken, allowing for goal resampling to recapture out-of-distribution success. Moreover, centroid-based methods outperform baseline methods as distribution-shift detectors. Together, these tools yield a behavioral monitoring stack that is operational and consequential under distribution shifts.

Reliable 3D spatial understanding is essential for autonomous navigation, obstacle avoidance, and scene reconstruction. While state-of-the-art learned depth estimation techniques achieve high accuracy in-distribution, they often generalize poorly to novel viewpoints and altitudes. This paper presents a geometrically derived, training-free depth estimation method using epipolar transfer with only two monocular images and camera pose estimates. By leveraging camera motion to synthesize a virtual stereo pair with a freely chosen baseline, our approach transforms temporal correspondence into a stereo triangulation task while mitigating geometric degeneracies inherent to direct two-view triangulation. Validated across outdoor drone flights (to a maximum range of approximately 90\,m) and indoor OptiTrack environments against LiDAR ground truth, the method achieves an indoor AbsRel of 0.092 and $\delta < 1.25$ of 0.940, comparable to direct triangulation (AbsRel 0.073) while retaining valid depth over a larger fraction of challenging scenes, and substantially outperforms off-the-shelf learning-based baselines such as ZoeDepth (AbsRel 0.225) and Depth Anything V2 (AbsRel 0.570), which are not trained or fine-tuned for this domain, with no training data required.

Every group has a canonical coloring of its unordered pairs by inverse pairs of differences. We prove that this coloring can be coarsened to four colors without changing its color-preserving permutation group, for groups of arbitrary cardinality. Four is the least uniform bound. A related construction applies to finite homogeneous coherent configurations: if every basic relation has valency at most $d$, where $d\geq 2$, a coarsening with at most $2d+1$ off-diagonal colors in the symmetric case, or $2d+3$ off-diagonal arc colors in general, has the original configuration as its coherent closure. Two-dimensional Weisfeiler-Leman refinement recovers that partition within $2\lceil\log_2 n\rceil$ rounds on $n$ points, with the specified atomic initialization. Affine-plane schemes show that linear dependence on valency is necessary. We apply the group realization to classify groups admitting naturalizing invariant metrics and show that, for a suitable such metric, naming the identity determines the compatible multiplication uniquely. Finally, using additional Cayley-realization and finite-classification inputs and explicit certificates, we determine the least number of metric values for every group. The direct universal construction and the finite coherent-reconstruction theorem do not depend on those computations.

Test-Time Adaptation (TTA) and Generalized Category Discovery (GCD) are traditionally treated as disjoint problems: the former adapts models to domain shift assuming all test classes are known, while the latter discovers novel categories assuming labeled training data for known classes. However, real-world deployment rarely fits either setting. Motivated by this gap, we introduce Test-Time Generalized Category Discovery (TT-GCD), a unified and more realistic scenario where a vision-language model must adapt to distribution shifts, classify known categories using only textual supervision, and discover novel categories, all during test time and without access to labeled data. To address this challenging scenario, we propose PACT (Prototype Assignment for Category discovery at Test time), a fully unsupervised framework that casts known-class recognition and novel-class discovery via prototype assignment. PACT first re-aligns shifted visual features with the text-derived class representations of the VLM using confident zero-shot predictions. Known and novel categories are then both represented by prototypes in the visual embedding space, estimated from the unlabeled test stream, and each test image is assigned to the category whose prototype is most similar to its visual feature. Extensive experiments across corruption and domain-shift benchmarks demonstrate that PACT outperforms adapted state-of-the-art TTA and GCD methods, effectively bridging the gap between adaptation and discovery.

Recent research argues that language models exhibit pronounced homogeneity in open-ended generation, framing such behavior as an Artificial Hivemind that poses a long-term threat to human creativity. We examine three of its central results. First, the flagship example is that model responses to "Write a metaphor involving time" collapse into two clusters. Visualization, spectral analysis, clustering, and language model labels all contradict this description. The labels record each response's vehicle, what it compares time to. Our responses and the original authors' own show one dominant vehicle plus a heavy tail of distinct minority vehicles. "Time" is one of our least diverse topics, so the example is a favorable case, not a representative one. Second, the paper measures homogeneity against an undemanding null: responses to unrelated prompts. Under a more demanding null (same-prompt responses expressing genuinely different ideas), 20%-32% of such pairs already exceed the paper's 0.8 convergence threshold. A residual effect survives this null. The paper's same-prompt pairs exceed 0.8 roughly two to three times as often as our different-idea pairs. Much of what the paper calls homogeneity is the shared geometry of answering the same prompt. The remaining measurements lack any null: no human baseline is collected, and the model-indistinguishability statistic has no null. Third, the paper concludes that inference-time interventions are inadequate for combating the Artificial Hivemind, writing that "more generalizable solutions are needed at the model training level." We show that this conclusion is unsupported in three ways, and that an inference-time intervention (prompting) reliably raises measured response diversity. We do not resolve whether the Artificial Hivemind is real. We show that the published evidence does not establish it.

Adapting video models to new tasks typically requires dedicated data curation and fine-tuning. While visual analogy provides a training-free alternative by specifying tasks in-context, it remains restricted to the image domain. To explore whether analogy-based methods can unify diverse video tasks and generalize to out-of-distribution scenarios, we introduce ViGeo, a framework that extends visual in-context learning to the video domain via spatiotemporal canvas completion. Evaluated on a diverse task taxonomy with a strict train-test split, ViGeo generalizes to unseen video manipulations and zero-shot modalities (e.g., event cameras). Finally, we identify task internalization, where a query format associated with a pretrained task overrides the demonstration, and show that this shortcut can be removed with a small amount of task-unrelated data, highlighting the need to decorrelate prompt format from task identity.

We present a first-quantization, all-electron, full-potential Kohn-Sham density functional theory method for quantum computers, based on a classically optimized quantum-circuit eigensolver for the self-consistent field (SCF) eigenproblems in any orthonormal basis. The plane-wave-orthonormalized-orbital (PWOO) basis combines plane waves with atomic orbitals (AOs) orthonormalized against them and one another. The eigensolver has a dual-basis form: after full-basis bootstrap steps, it solves each SCF step in a contracted basis of $K$ functions ($\lceil\log_2 K\rceil$ qubits), updated in the full basis when the residual outside it exceeds a threshold. For an H$_8$ chain (SVWN, $K=8$), the state-vector-emulated SCF agrees with classical calculations within 0.02 mHa for 32768 plane waves and PWOO bases up to cc-pVTZ; contraction changes these PWOO energies by at most 5.7 $\mu$Ha. With emulated shot noise, the STO-3G PWOO SCF converges near the noise-free fixed point. On IonQ Forte-1, three-qubit-register readout reproduces the noise-free PWOO-AO energy difference within one standard deviation.

Richard Christopher Carrington carried out extensive sunspot observations from 1853 to 1861 and left numerous scientific legacies. However, despite his fame, consulting his original manuscripts, we have found Carrington's last sunspot drawing, which he never published. We date this drawing 23 Dec 1870, when Carrington was based at his Churt Observatory. The drawing allows us to count 3 sunspot groups and 10 individual sunspots and measure the group positions at N14{\deg} W37{\deg}, N11{\deg} W46{\deg}, and S08{\deg} W08{\deg}, where our longitude values represent longitudinal distance from the central meridian. In comparison with the existing datasets, his raw group counts look slightly lower than the contemporaneous observers. His position data look consistent. These additions contribute to the ongoing efforts for the sunspot number recalibration and butterfly diagram constructions, as long as we follow the standard assumption for the homogeneity of the "Schmidt backbone". Otherwise, this case instead questions the validity of the common assumption of "Schmidt backbone" keeping the data homogeneity. This sunspot drawing is unlikely to represent the tip of a huge, lost iceberg, but rather an isolated drawing that he left from his Churt era. Carrington may have temporarily revived his interest upon the solar eclipse of 22 Dec 1870. Otherwise, Carrington's references to his sunspot research in his Churt era are confined to priority claims in response to Chevalier's RAS obituary and a local newspaper report. The former confirms that Carrington was probably the first person, who counted and published sunspot data from Thomas Harriot's original sunspot drawings.

A dominating set $D$ of a nontrivial connected graph $G$ is called a semitotal dominating set of $G$ if every vertex in $D$ is at distance at most two from another vertex in $D$. If, in addition, $D$ is an independent set, then $D$ is called an independent semitotal dominating set of $G$. The (independent) semitotal domination number of $G$ is the minimum cardinality among all (independent) semitotal dominating sets of $G$. In this paper, we obtain closed formulas for these parameters in the following three well-known graph operators defined from a connected graph: the subdivision, middle, and central graphs.

Modern methods reconstruct or generate simulation-ready articulated objects, predicting not only their geometry but also how their parts are connected and allowed to move. Evaluating the geometry is straightforward, but evaluating the predicted articulation is not, because articulation specifies a motion rather than a shape, and there is no agreed distance between two motions. More specifically, existing protocols score joint type, axis direction, origin, and motion limits separately, although these parameters jointly describe a single physical motion, and the same motion can be written as different parameter values. As a result, a joint can score maximally wrong against an equivalent encoding of itself, and several component errors are ill-conditioned or undefined exactly where predictions become accurate. We propose ArticulateArena, a representation-invariant counterpart of Chamfer distance for articulation that compares the motions one-DOF joints induce rather than the parameters that encode them. It represents each joint by the unordered pair of its Lie-algebra endpoint twists, and we prove that the resulting quotient distance is a metric. It unifies fixed, revolute, prismatic, and helical joints, brings continuous joints into the same score through a compactification, and reads as the RMS motion of the moving part in meters when weighted by its mass distribution. A motion-aware tree edit distance lifts the metric to full kinematic trees, pricing structural errors such as spurious or missing joints in the same motion units as joint errors, and for a fixed inner product it remains a metric on trees up to relabeling. Alongside the metric we release ArticulateArena-20K, a new suite of 19,977 articulated objects with verified kinematics, and we re-evaluate published reconstruction methods on it under the new metric. Project page: https://heyumeng.com/ArticulateArena-web/

Extending forecast lead times while maintaining predictive skill remains a major challenge in environmental forecasting. We investigate diffusion-based rollouts as a stabilization mechanism for recursive forecasting using low-dimensional water-level time series and high-dimensional precipitation fields. Across both modalities, diffusion suppresses recursive error growth, with the largest stabilization occurring where deterministic rollouts are most unstable. However, stabilization does not guarantee forecast fidelity. In the water-level experiments, forecasts progressively lose event-level fidelity as the rollout loses access to external predictive information, and trajectory-level comparisons show that diffusion can remain numerically stable while contracting toward central values and exhibiting reduced variability. In the precipitation experiments, which retain conditioning from numerical weather prediction throughout the rollout, diffusion better preserves spatial organization and event-detection skill. Together, these contrasting experiments indicate that diffusion can control recursive error amplification, while its practical benefit also depends on the predictive information available to constrain future evolution.

The one-dimensional swarmalator model is usually understood through three macroscopic states: synchrony, the phase wave, and asynchrony. We show that the identical model also contains a much larger set of hidden stable equilibria - families of q-twisted and m-clustered states - which random initial conditions almost never reach, because many are embedded in a degenerate neutral manifold of vanishing global basin. They are nonetheless locally robust: under Gaussian perturbations of per-coordinate amplitude {\epsilon} their survival radii shrink only algebraically, as 1/q and 1/m, in sharp contrast to the Gaussian basins and winding ceiling of twisted states on a nearest-neighbour Kuramoto ring, both removed by mean-field coupling. A block-circulant Jacobian fixes the stability in closed form, and far-kick experiments indicate the basins are compact cores rather than tentacled sets. Several patterns reported in extended swarmalator models thus already exist, stable or neutrally stable, in the minimal one.

Predicting spatial gene expression from histology images could scale spatial transcriptomics (ST) to image-only cohorts, but conventional histology-based ST prediction is trained and evaluated mainly by per-gene spatial-profile reconstruction. This objective is misaligned with a key downstream use of ST: differentially expressed gene (DEG) discovery, where genes are ranked for a biological or morphology-defined contrast by evidence of between-group expression differences. We formulate image-based differential expression ranking (IDER), which asks whether predicted expression profiles preserve the contrast-specific ranked gene list obtained from measured profiles. IDER compares gene rankings induced by differential-expression statistics, rather than raw expression magnitudes or per-gene spatial correlations. We further introduce a differentiable IDER objective that aligns these statistics across genes and can be trained with morphology-derived proxy contrasts without predefined biological group labels. Experiments on public ST datasets show improved DEG-ranking agreement and pathway-enrichment overlap over conventional reconstruction objectives, including morphology-derived and pathologist-annotated tissue-region evaluations.

This study explores the optimization of the Phi-2 Small Language Models (SLMs) for real-time chatbot applications through Parameter-Efficient Fine-Tuning (PEFT) and Quantized Low-Rank Adaptation (QLoRA). QLoRA specifically refers to the integration of PEFT with LoRA alongside a 4-bit quantization process, aimed at enhancing computational efficiency. These models, initially designed for high performance with minimal computational overhead, are further refined to address the constraints of mobile and edge computing environments. By integrating PEFT with QLoRA, the research aims to reduce memory usage significantly while maintaining, or potentially improving, the accuracy of model responses in real-time interactions. The effectiveness of these techniques was evaluated using the ROUGE metric system, which showed notable improvements in the summarization tasks performed by the models. This approach not only confirms the feasibility of using SLMs in resource-restricted environments but also opens up new avenues for deploying advanced AI-driven applications in real-time settings. The study's findings have significant implications for the development of efficient, scalable, and accessible AI technologies, paving the way for broader adoption in various industries.