Papers

A prediction presented at HADRON 2025 proposed two baryon-like states containing an additional hypothesized $f$ quark that could appear in the decay $\Bbar\to\Lb\Lc K^-$ in the form of narrow $\Lc K^-$ resonances at 3800 and 3950~MeV. Public LHCb data are used here to compare three hypotheses with an unbinned, background-aware two-dimensional Dalitz likelihood. The baseline contains nonresonant three-body phase space and an $N(1900)$ contribution in $\Lb K^-$. A second model tests the two a-priori prediction masses directly, fixing $\Lc K^-$ resonances at 3800 and 3950~MeV while fitting their widths. A third model keeps the 3800-MeV mass fixed, allows the second $\Lc K^-$ mass and width to float, and adds two exotic $\Lc\Lb$ contributions. The second model gives a nominal Wilks-equivalent improvement of $4.02\sigma$ over the baseline, while the third gives a nominal value of $6.17\sigma$. The quoted significances are model-comparison diagnostics only: the resonance fractions are constrained to be non-negative, some fitted widths reach parameter boundaries, the floating mass introduces a trials effect, and efficiency and systematic uncertainties are not yet incorporated.

Every neighborhood assignment on a charming space $X$ has a countable kernel whose closure in $X$ is Lindelöf $\Sigma$. Consequently, for any two neighborhood assignments $M$ and $N$ on $X$, there is a closed discrete set $D\subseteq X$ such that $M[N[D]]=X$. We give an exact one-step formulation of the remaining $D$-space problem and identify the universal pointwise square-refinement condition with the classical $z$-space condition. For continuous closed surjections, we prove a fixed-assignment lifting equivalence. We also show that every uncountable $\mathrm{HFC}_{\mathrm w}$ subspace of $[\omega_1]^{\leq\omega}$ is dually closed countable but not charming. For a fixed Lindelöf $\Sigma$ kernel $Y$, we iterate the Hu–Yin boundary reduction by a transfinite closed-core process. At every stage, the current iterate is a $D$-space if and only if $X$ is a $D$-space. The iteration stabilizes before $hL(Y)^+$ at the largest closed subspace in which the kernel trace and its complement are both dense. The bound is sharp: for every infinite cardinal $\kappa$ and every $\gamma<\kappa^+$, there is a compact example with a dense $\sigma$-compact Lindelöf $\Sigma$ kernel $Y$ satisfying $hL(Y)=|Y|=\kappa$ whose first stabilization stage is $\gamma$.

Emoji can easily lead to misunderstanding. On WeChat, [Smile] is often used by the elderly to express positive emotions such as joy and praise, but young people often regard [Smile] as sarcasm. In this case, misunderstandings can easily occur. In order to confirm the existence of this phenomenon and analyze people's understanding of emoji, this study selected 20 smiley emoji on WeChat platform and directly asked people's opinions on these emoji through questionnaires, including whether they recommend others to use, and rating of emotion joy, praise, sarcasm. Analyses were performed based on the total sample and by age group. The results showed that [Smile] and [Bye] were interpreted in opposite ways by older people and younger people. Older people thought they represented positive emotion (joy, praise), while younger people thought they represented sarcasm. Such emojis are easy to misunderstand. On the other hand, some emojis like [Yeah!], both the old and the young have a similar understanding that it represents a positive emotion.

Automatic Speech Recognition (ASR) models such as OpenAIs Whisper have substantially improved speech recognition quality but remain expensive to fine-tune, especially when large amounts of transcribed audio are available. This makes it challenging for many practitioners to adapt these models to new languages or domains. In this work, we introduce an embedding-based subset selection approach for selecting smaller training sets for ASR fine-tuning. Using Whispers pretrained encoder, we map each audio sample into a fixed-dimensional embedding space and apply a greedy k-center algorithm to select diverse and representative subsets of the training data. We evaluate this approach on both Hebrew and Danish, showing that k-center selection often improves upon random sampling, particularly at smaller subset sizes. An analysis of lexical diversity reveals that k-center subsets capture a broader range of linguistic content than random subsets of the same size, which may help explain their observed effectiveness. Overall, our results demonstrate that embedding-based subset selection provides a practical strategy for ASR subset selection in the two evaluated languages, with the clearest recognition benefits observed at smaller sample budgets.

Background: Measles resurged in the United States during 2025-2026, with more than 4,600 reported cases. Timely detection and transmission inference require integrated genomic, epidemiological, environmental, and clinical data. We developed a multimodal machine learning (ML) framework integrating genomic sequences, epidemiological indicators, wastewater surveillance, and clinical rash images. Methods: We evaluated a three-stage pipeline using public data. Stage 1 classified transmission linkage among 903 sequence pairs from the 2021 Ohio-Arizona-Washington outbreak using k-mer TF-IDF-SVD embeddings and pairwise single-nucleotide polymorphism (SNP) distances with leave-one-cluster-out cross-validation. Stage 2 predicted state-week outbreak risk using logistic regression and XGBoost with wastewater, mobility, and vaccination features under leave-one-year-out cross-validation. Stage 3 used BiomedCLIP ViT-B/16 embeddings and a fine-tuned multilayer perceptron for rash classification on MSLD v2.0 (755 images, 6 classes). InfoNCE contrastive learning aligned genomic and imaging embeddings. Results: Transmission-linkage classification achieved AUC 0.924 and F1 0.912 with logistic regression. Outbreak-risk prediction achieved AUC 0.707 with logistic regression across 2025-2026 leave-one-year-out folds. Contrastive alignment achieved Recall@1 = 0.985 on held-out paired data. Ablation showed genomic features dominated transmission-linkage prediction (genomic-only AUC 0.983), whereas wastewater positivity was the strongest outbreak-risk predictor (importance 0.402). Conclusions: Multimodal ML integrating genomic, epidemiological, wastewater, and clinical imaging data can support measles surveillance and transmission inference using public data. Prospective validation with paired clinical-genomic data, expanded wastewater coverage, and real-world workflows is needed before deployment.

Large language models are increasingly used to simulate and probe human behavior, e.g., for surveys. For these applications, a key property is that outputs satisfy distributional alignment: to match its output distribution with some reference (in this case, human) distribution. An obstacle in achieving distributional alignment is generalizing from small training data. In this work, we study (1) how to distributionally align LLMs; and (2) how aligned LLMs might generalize to unseen samples and unrelated topics and tasks. Using two large-scale benchmarks, we find that LLMs can indeed achieve distributional alignment and generalize to unseen questions of the same domain. Cross-topic generalization depends on the relationship between topics (e.g., questions about politics are related to trust in institutions). However, aligned LLMs can degrade in surprising ways (e.g., lose their creative ability), suggesting that its generalization properties are inherently unpredictable and unstable.

Activation interventions can make a language model produce a target answer, but can the model use the intended condition in other computations? We study this question in Qwen3.5-27B on tool-use tasks where time or permissions determine eligibility and selection. Across 32 fresh worlds, two case-specific residual-writing variants raise familiar target-selection correctness from 35/128 to 119/128 and from 33/128 to 114/128. Yet these gains disappear when familiar facts and identifiers are recombined within the same selection task, while selection of previously rewarded identifiers increases. The gains persist across output formats but yield little improvement in independent judgments about whether a candidate is eligible or should be selected. Internal edits can nevertheless change how a source fact affects a judgment: in a prespecified secondary comparison, an early-layer source patch changes 50/64 judgments when that source is used, with one adverse change among 64 cases where it is not. This selective effect does not ensure correct complete actions. Together, these results separate target-selection control, condition-sensitive judgments, and complete-action correctness. Evaluating how an edited state is used, rather than only its trained answer, exposes these differences.

Generative AI's growing role in academic writing has driven a rise in fabricated references across dissertations and student reports. We present the Fabrication Severity Stack (FSS), a three-tiered framework classifying citation fabrications by detection complexity - from non-existent references to subtle content misattribution. Building on the FSS, we propose a staged heuristic verification workflow, executable through mainstream LLM interfaces. We argue that this framework offers computer science educators/examiners a practical, zero-cost basis for embedding reference verification into the assessment of dissertation and students' reports. In a pilot study on 100 citations (20% seeded with Level 1 and Level 2 fabrications), the proposed heuristic workflow enabled mainstream LLM interfaces to correctly flag 9-10 of 10 non-existent references and partially detect metadata corruption. These preliminary results suggest that freely accessible, general-purpose LLMs can achieve high recall on citation verification without reliance on proprietary detection tools.

Academic theses are a valuable source of scientific knowledge, yet their semantic exploitation remains limited. While Scholarly Knowledge Graphs have significantly advanced the representation of scientific publications, knowledge graph construction for academic theses has received comparatively limited attention. This paper provides a systematic review of existing approaches and analyzes their potential application for the thesis domain. We analyzed 46 peer-reviewed studies published between 2021 and 2025, and organised existing approaches into a structured classification of techniques, models, and tools. The review reveals a methodological evolution from natural language processing techniques for entity and relation extraction to ontology engineering, Semantic Web technologies, and AI-driven enrichment through knowledge graph embeddings, Linked Open Data, and Large Language Models. The findings provide a consolidated view of the current state of the art and identify methodological foundations and future research directions for building knowledge graphs for the thesis domain.

There is growing interest in automating business activities with Agentic Artificial Intelligence (AI) due to latter's seeming ease of use. Never has it been easier, or costlier, to do less with more. However, little is known about when agents are preferable to established alternatives such as local computation, Representational State Transfer (REST), the Simple Object Access Protocol (SOAP), and the Model Context Protocol (MCP), particularly when development speed, performance, and operational cost are considered. We investigate this question using a controlled mathematical task that compares seven methods on a benchmark of 1,000 arithmetic expressions where semantics of operator precedence has to be preserved. We ran this setup across a native Function Calling baseline (Python library), REST, SOAP and MCP microservice architectures, direct responses from large language models (LLMs) using a Groq cloud API and five locally deployed Ollama models, and agentic systems in which five local LLMs invoke MCP tools. The deterministic methods achieve 100% accuracy with negligible latency. Direct LLM evaluation achieves at most 92.9% accuracy at over 22,000x the latency of a native function call. With MCP tools, the best agent reaches 99.9% accuracy, but incurs nearly 1,000,000x the baseline latency. These results demonstrate that LLMs approaches are poorly suited for exact arithmetic evaluation and motivate an informed architectural decision framework (ADF) for choosing an architecture based on accuracy and throughput requirements. We recognize that an actual interaction with an agent may span both reasoning and linguistic tasks. Hence our recommendation is to explore multiple architectural choices (based on task type) rather than one-size-fits-all solution (LLMs). Code is available at - https://github.com/Ritvik-G/adf/

For integers $r \ge 3$, $c \ge 2$, and $s \ge 0$, let $\mathsf{M}_r^{\star}(c,s)$ denote the smallest integer such that any set of at least $\mathsf{M}_r^{\star}(c,s)$ points in the plane in general position (no three on a line), colored with $c$ colors, contains a monochromatic $r$-gon (not necessarily convex) with at most $s$ interior points. Define $\lambda_r^{\star}(c)$ to be the smallest integer such that $\mathsf{M}_r^{\star}(c,\lambda_r^{\star}(c)) < \infty$. The case of triangles, that is, $r=3$, has been studied in recent years. In this paper, we establish bounds on $\lambda_r^{\star}(c)$, for $r \ge 4$. Specifically, in the bichromatic case, we prove that $\lambda_r^{\star}(2)\leq \lfloor\frac{r-2}{2}\rfloor$, for every $r\geq3$. For hexagons, we sharpen this bound to $\lambda_6^{\star}(2)\leq1$, that is, every sufficiently large bichromatic planar point set in general position contains a monochromatic hexagon with at most one interior point. Next, for any number of colors $c\geq3$ and $r\geq3$, we show that $$(r - 2) \left \lfloor \frac{c-1}{2} \right \rfloor \leq \lambda_r^\star(c) \leq (r-2)(c-2)+\left\lfloor(r-2)\delta_c\right\rfloor, $$ for some constant $\delta_c \in (0, \frac{1}{2}]$, depending on $c$. The upper bounds combine spiral polygonizations with nested convex-hull arguments and, in the hexagon case, incidence counting in $4$-connected triangulations. The lower bounds follow from colored Horton-set constructions.

In certain real-world scenarios, obtaining labeled data is excessively expensive, motivating increasing interest in adapting models without annotations. Vision-language models (VLMs) provide pseudo-labels for unlabeled images through image-text similarity, enabling adaptation without manual labeling. The previous unsupervised vision-language model adaption methods assume access to an adaptation vocabulary containing all class names. However, a complete vocabulary is difficult to construct in real-world scenarios, as unlabeled data may contain classes that are overlooked or fall outside the current task scope. Thus, we propose Vocabulary-Incomplete Unsupervised Vision-language model Adaptation (VI-UVA), where only a subset of class names are available during adaptation. The vocabulary incompleteness induces an adaptation bias toward provided classes, which degrades omitted-class recognition. To address this issue, we propose Label Space Reconstruction (LSR), which reconstructs a latent label space from the unlabeled data and incorporates it into prompt tuning, thereby extending adaptation beyond the incomplete vocabulary and mitigating the adaptation bias. Furthermore, we derive an omitted-class semantic discrepancy bound for LSR and identify the key factors affecting the bound. Extensive experiments across eight benchmarks demonstrate that LSR outperforms existing state-of-the-art methods.

Unified multimodal models answer questions about images and also generate images with one shared set of weights. This creates a post-training risk that single-purpose models do not have: fine-tuning one capability can damage another that works in a different modality. We measure this cross-modal forgetting for LoRA post-training of Janus-Pro-7B. Every target is chosen by how poorly the base model already handles it, from a poetic register to a language it barely speaks, so that retention is tested against a real intervention; we then evaluate the capabilities we never trained, first after a single run and then after chaining three. A single run looks entirely safe: nothing we did not train degrades on four public benchmarks or in free-form English, even when the adapter cuts held-out Welsh perplexity by 76% with a relative weight change under 2%. That safety belongs to the run, not to the recipe. Chaining three runs destroys the capability learned one run earlier and raises general-text perplexity by one to two orders of magnitude above the never-adapted model, on the very measures that stayed flat before. The cause is in the objective, which constrains only the modality being trained and leaves the other head unconstrained: cutting the learning rate to one fifth does not prevent the collapse, while anchoring the other head removes the damage to the capabilities we never trained, at no cost to what is learned. What is learned also stays inside its own modality, with Welsh acquired from text closing only 3% of the English-Welsh gap in image generation.

LLMs can generate Lean specifications from task descriptions, but those descriptions are often underspecified or ambiguous and may omit verifier-relevant edge cases, yielding imperfect formal specifications. We study whether an elicitation agent (EA) can improve verifier-checked Lean specifications by seeking clarification from a reference-grounded simulated developer before formalization. The agent decomposes the task, identifies unresolved decisions, asks bounded clarification questions, and uses the answers to write a refined natural-language specification that an LLM formalizer then translates into Lean. On 189 Verina Lean 4 specification-generation tasks, we compare single-shot generation with elicitation under question budgets of k=3 and k=10, allowing at most three or ten EA questions per task, across same-model and cross-model configurations. The same-model Claude Sonnet 4.6 pipeline has negative strict pass@1 estimates at both budgets, showing elicitation is not a uniform accuracy booster. In contrast, the Sonnet 4.6-to-GPT-5.6 and Sonnet 4.6-to-Gemini 3.8 Flash pipelines have positive strict estimates. The largest strict result reaches 65.6%, a +6.3-point change (+12 tasks), in the Sonnet 4.6-to-GPT-5.6 pipeline. Six of eight conditions have positive compile-conditional estimates, with a maximum cross-model difference of +4.9 points among compiling outputs. Treatment estimates also differ across the basic and advanced splits; the largest advanced-task change occurs in the Sonnet 4.6-to-GPT-5.6 configuration at k=10, from 42.0% to 50.6%. Failure analysis identifies postconditions as the largest source of degradation. These findings suggest future autoformalization systems should treat elicited natural-language specifications as intermediate artifacts and optimize jointly for semantic correctness among compiling outputs and reliable translation of clarified information into Lean.

The origin of segregated axial bands for size-bidisperse particles in long rotating tumblers is a long-standing question in granular flows and a problem of both fundamental and practical interest. Using DEM simulations, we consider the streamwise and time-dependent development of the underlying instability as well as performing a broad parametric study over a wide range of particle size ratios, tumbler lengths and diameters, species fractions, and fill levels to determine the conditions under which axially segregated bands appear. We show that initial radial segregation of the small and large particles in the surface flowing layer results in a layer of mixed particles with a higher bulk density due to more efficient packing over a layer of nearly monodisperse small particles with a lower bulk density. This leads to a granular Rayleigh-Taylor-like instability that produces recirculation cells driving axial band formation. The appearance of a layer of high-density mixed particles over a layer of lower-density monodisperse particles can be directly connected to the operating conditions, explaining why axially segregated bands appear only under certain conditions. Typically, increasing the particle size ratio improves packing and increases the density of the mixed layer, enhancing the Rayleigh-Taylor instability and accelerating axial segregation.

The Distorted Wave Born Approximation (DWBA) is established for X-ray interface scattering, yet its domain of applicability has never been stated explicitly. The DWBA implicitly rests on the small refractive index deviation (SRID) condition - satisfied by X-rays ($|n-1| \sim 10^{-6}$) but violated by visible light ($|n-1| \sim 0.5$). The DWBA mixes microscopic and macroscopic Maxwell equations, whereas a rigorous optical theory must be built on the macroscopic Maxwell equations and constitutive relations. Rigorous alternatives for two specific inconsistencies in the standard DWBA are discussed. The Extended Transfer Matrix Approach (ETMA) for visible-light interface scattering is outlined.

Noncommutative polynomials, elements of the free algebra generated by several noncommuting variables $x_1,...,x_g,x_1^*,...,x_g^*$, are of importance in noncommutative algebra, free analysis and real algebraic geometry. We allow matrix coefficients and view these noncommutative polynomials as functions in several size-free matrix variables. The free locus of a noncommutative polynomial $f$ is the sequence of hypersurfaces $\mathscr{Z}_n(f)=\{X\in M_n(\mathbb{C})^g:\det f(X) = 0\}$. When $f$ is Hermitian, the positivity domain of $f$ is the sequence of semialgebraic sets $\mathcal{D}_n(f)=\{X\in M_n(\mathbb{C})^g:f(X)\text{ is positive semidefinite}\}$. We show for well-behaved cases that the Euclidean boundary of the positivity domain is Zariski dense in the free locus. This leads to a certificate for equality of positivity domains of coefficient-irreducible unsignatured atomic quadratics. Finally, we describe the geometric structure of positivity domains of hereditary quadratic polynomials through $\Gamma$-convexity.

Extending the Fokker–Planck equation to a coupled system of equations through non-Abelian symmetry groups offers a powerful theoretical framework for coupled multi-state stochastic systems. However, translating this abstract gauge field formulation into viable numerical predictions remains an unaddressed challenge. Motivated by our previous work on ice crystal habit evolution, in this work we bridge this gap by presenting the first numerical solver for an SU(2) gauge-coupled Fokker–Planck system in (1+1) dimensions. Using an operator-splitting scheme combined with a non-oscillatory advection solver, our algorithm strictly ensures probability conservation, non-negativity, and numerical stability. We demonstrate that non-Abelian gauge coupling acts as a cross-reactive feedback loop that fundamentally alters system dynamics, driving continuous probability exchange between states, suppressing localised density peaks, and forcing long-time spatial delocalisation. Validated across linear and quadratic coupling regimes up to strong interactions (g <= 1.0), this work establishes the foundational computational infrastructure needed to integrate complex multi-state physics. Overall, while our approach provides a key step toward improving ice cloud representation in atmospheric and climate models, the underlying physical framework and computational engine remain fundamentally general and multidisciplinary, offering a versatile paradigm for any domain requiring coupled multi-state stochastic equations.

Consider the "snaky" corridor $K_4 \subset \mathbb{R}^3$ from Problem 6.64 of arXiv:2511.02864: a tube of unit-square cross-section whose two right-angle turns lie in perpendicular planes, with a straight middle section of clear length $4$. We exhibit explicit rigid motions of connected bodies through $K_4$ and certify their volumes with the problem's own evaluation pipeline, unmodified, at the tight motion tolerances of its final scoring stage (translation $0.005$, rotation $0.05$ degrees). The certificates give $V^*(K_4) \ge 1.8355162$ at grid fineness $0.002$ and $V^*(K_4) \ge 1.8558404$ at grid fineness $0.001$, against the previously reported $1.81$; rerunning the pipeline's published best path under the identical configuration yields $1.8179428$, so every comparison is path against path under one fixed certifier. Three stages produce the record motion: a simple "staggered twist" backbone in which the whole 90-degree twist about the tube axis happens inside the second turn; evolutionary (CMA-ES) refinement, including a mixed-fidelity scheme that re-scores each generation's leading candidates on a grid twice as fine and lets those ranks steer recombination; and a gradient polish carried out directly at the finer carve resolution, guarded by periodic rebuilding of the frozen interpolation structure and by a penalty on control-pose spacing. These guards close three documented failure modes in which an optimizer inflates its own objective: frozen-structure inflation, spacing stretch, and exploitation of a coarse grid by optimizing and selecting on it. A staircase-based predictor with two grid bases, anchored by matching grid sensitivity, forecast the certificates to about $0.001$ before the runs. With the companion note's upper bound $V^*(K_4) \le 3.4083$, the problem now sits in the bracket $1.8558404 \le V^*(K_4) \le 3.4083$. All paths, notebooks and certified results are public.

Let $K_M \subset \mathbb{R}^3$ be the "snaky" corridor with unit-square cross-section: an infinite entry arm parallel to the $x$-axis, a middle arm parallel to the $y$-axis whose clear straight section has length $M$, and an infinite exit arm parallel to the $z$-axis, with the two turns lying in the $x$-$y$ and $y$-$z$ planes. Let $V^*(K_M)$ be the supremum of the volumes of connected bodies that can be moved continuously (by rigid motions) from the entry arm to the exit arm while remaining inside $K_M$. We prove $V^*(K_M) \le 7.8691$ for every $M \ge 3.53$ (Theorem A); by a sharper analysis of the same mechanism, $V^*(K_M) \le 4.2862$ for every $M \ge 2.61$ (Theorem B); and, by replacing the final analytic caps with a certified branch-and-bound computation over the compact family of entry tubes compatible with the forced events, $V^*(K_M) \le 3.4083$ for every $M > 2.2$ (Theorem C; computer-assisted, in double precision with conservative slack). In particular all three bounds apply to the corridor with $M = 4$ used in Problem 6.64 of Georgiev, Gómez-Serrano, Tao and Wagner (arXiv:2511.02864), and uniformly to every "turns far apart" reading of that problem. To the best of our knowledge, this is the first upper bound for the snaky-corridor 3D moving sofa problem; previously not even finiteness of $V^*$ had been recorded. This note proves upper bounds only; combined with the certified lower bound 1.8558404 from the author's separate certification work via the problem's own evaluation pipeline, the state of the problem becomes $1.8558404 \le V^*(K_4) \le 3.4083$. Theorems A and B are elementary and self-contained: a first-crossing (elbow) event forces a definite tilt of the body's own entry tube, and Fubini-type chord estimates for tilted tubes cap the volume. Theorem C certifies, by the same forced-event skeleton, the largest corridor volume that any admissible entry tube can carry.

We solve the near-tip coupled hydromechanical problem of a hydraulic fracture propagating in a permeable poroelastic medium, represented locally as a semi-infinite crack moving at constant velocity. In the moving tip frame, all fracture fields are steady. The porous solid obeys linear poroelasticity, fracture propagation follows LEFM, fluid flow within the tensile fracture is governed by lubrication theory, and the fracturing and pore fluids are treated as identical Newtonian liquids. The primary unknowns are the fracture opening and the fluid displacement function along the fracture, determined from the resulting non-linear system of equations. In a viscosity–toughness scaling, the problem depends on four dimensionless parameters: a dimensionless permeability $\varrho$ (associated with the intensity of fluid leak-in), a dimensionless effective confining stress $\Sigma_0'$ (measuring the relative importance of fluid leak-off and leak-in), the drained–undrained Poisson's ratio contrast $\beta$, and the poroelastic stress coefficient $\eta$. The solution evolves from a drained, toughness-dominated near-tip asymptote with uniform net pressure to an undrained, storage-viscosity-dominated far-field asymptote. Numerical solutions are obtained over parameter ranges representative of various rock types. The fully coupled model is compared with simplified models, namely uncoupled and one-way coupled formulations, over distances from the fracture front spanning laboratory-to-field scales. The resulting relative difference maps in the $(\varrho,\Sigma_0')$ parameter space identify four characteristic regimes: negligible poroelastic effects, dominance of the direct mechanical poroelastic response, importance of the poroelastic backstress, and a fully coupled regime. The latter occurs mainly at large $\varrho$ and small $\Sigma_0'$, corresponding to strong leak-in relative to leak-off.

Real-space interference of wave packets is governed by their central momentum separation and momentum width, which set the oscillation wavelength and spatial envelope, respectively. Here, we show that in crystalline systems, quantum metric distribution in an isolated band can similarly give rise to real-space interference through the evanescent tails of a localized bound state. The location and width of a quantum metric hot spot in the momentum space set a complex wavevector as one evanescent plane wave component of a bound state. Consequently, with multiple quantum metric hot spots, the density distribution of a bound state or the total density of two spatially overlapped bound states exhibits an interference pattern, where the oscillation period and long-range decay length are determined by the momentum-space separation of the hot spots and the width of the narrowest hot spots, respectively. This quantum-geometric interference is particularly pronounced in (nearly) flat bands, where competing scales from band dispersion are suppressed. Furthermore, we demonstrate that using a Josephson STM the real-space interference can be experimentally observed through the tip-position dependence of the Josephson critical current. Our results reveal a direct correspondence between momentum-space quantum geometry and real-space interference, showing how bound-state profiles encode the momentum-resolved quantum metric.

The miniKanren and Relational Programming Workshop brings together researchers, implementors, and users of the miniKanren family of relational programming languages, including miniKanren, microKanren, core.logic, OCanren, Guanxi, and related systems. The workshop focuses on the design, implementation, and application of miniKanren-like languages, as well as new techniques and tools for relational programming. These proceedings collect the eleven accepted papers presented at the Seventh miniKanren and Relational Programming Workshop.

The latency, power, and area costs of LLC replacement remain poorly explored not because simulators cannot be instrumented–event counters feeding a power model are routine–but because no cost model takes a replacement policy as input. CACTI and McPAT price regular structures, a cache or a core, not the small, oddly shaped arrays and dependent logic a policy is made of, and no event count reveals a victim-selection path's logic depth. Without a model, cost has never been an objective a policy search could optimize. In practice, a policy is first selected in simulation for its IPC, and its cost is reduced later in RTL, after the algorithm is fixed. Cost thus enters the design too late to shape it. This paper asks what happens when cost is present from the start. We build CacheFit, the first policy-design loop for LLC replacement with circuit-level cost inside the search objective. CacheFit connects ChampSim to HARCOM, a circuit-level cost model, and to a large language model that proposes policy variants. Every candidate is scored on latency, area, power, and speedup while its algorithm is still being written. The designer sets the area, power, and latency budgets, and every proposal and every lesson the search learns is stored as readable text that the designer can check and edit. We apply CacheFit to two published policies. From MPPPB, the most expensive baseline in power and transistors, it produces Fit-MPPPB: 60.3% less storage, 56.3% less static power, and 58.9% fewer transistors, with 1.1% higher IPC and a hit rate 7.5 percentage points higher on SPEC CPU2017. From SHiP++, the highest-IPC baseline, it produces Fit-SHiP++: 56% less storage, 61% less static power, and 56% fewer transistors, for 1.54% lower IPC and a hit rate 2.1 points lower. A policy designed with its cost in view can therefore be far cheaper to build at similar or better performance.

We study how the two cusp expansions of the Rogers-Ramanujan continued fraction control its ordinary and logarithmic Mellin moments. Ramanujan's factorizations express the logarithmic transform as a combination of products of zeta and quadratic Dirichlet $L$-functions. Its adjacent integer and half-integer values give an invertible change of coordinates for the corresponding odd special values. We prove that every reciprocal-cusp coefficient is a quadratic irrational algebraic integer, with an explicit minimal polynomial, and that every logarithmic coefficient is quadratic irrational. These facts determine the exact poles of three normalized-moment generating functions. The logarithmic one has an absolutely convergent partial fraction expansion with a pole at every positive square. For the ordinary moments, a two-cusp incomplete-gamma expansion gives meromorphic continuation at every positive splitting point. A general Mellin lemma yields the corresponding nonholonomicity statements. We also establish reflection identities, vertical strip decay and an explicit truncation estimate.

We prove that $\mathrm{Mod}(S_g)$ acts faithfully by orientation-preserving homeomorphisms on a $(2g-1)$-sphere when $g \geq 3$ using equivariant blow-up and bi-orderability of the Torelli group.

We show that an ir{\-}reducible cuspidal eta quotient of level~$N$ is uniquely identified by its orders of vanishing at $O((\log_2 N)^{r-1})$ cusps, where $r$ denotes the number of distinct prime divisors of $N$. In particular, all such eta quotients which are Fricke eigenforms of a prime power level, are uniquely identified only by their orders of vanishing at~$\infty$. We also prove that for all $k\in\N$, there exists a primitive and irreducible cuspidal eta quotient of weight $k/2$. It follows from the exhaustiveness of Zagier's list of the primitive holomorphic eta quotients of weight~$1/2$ that the 1st Mersmann level, $\cl{M}_1=12$. Here we show that for all $k\in\N$, the $k$-th Mersmann level is divisible by $2^{2k}$.

In this paper, we study Ricci flows with uniformly bounded scalar curvature. On such Ricci flows we establish uniform $L^2$ Riemannian curvature bounds and $L^4$ Ricci curvature bounds up to dimension 7. These estimates improves $L^{2-\varepsilon}$ curvature bounds established by Bamler and $L^2$ curvature bounds in dimension 4 established by Bamler and Zhang. More generally, we establish uniform $L^2$ curvature bounds on $n$-manifolds satisfying an integral $L^p$ Ricci curvature bound for $p> n/2$, a uniform volume lower bound, and a strong $\varepsilon$-regularity assumption. This result extends the celebrated $L^2$ curvature estimates of Jiang and Naber, which were established under pointwise two-sided Ricci curvature bounds. To overcome the lack of pointwise control, we develop an $L^p$ adaptation of the neck decomposition theorem and establish a superconvexity estimate for the curvature on neck regions. Furthermore, we demonstrate that our structural assumptions are dynamically natural on Ricci flows with bounded scalar curvature. As an application, by combining our estimate with the a priori $L^{4-\varepsilon}$ curvature radius bound of Ricci flow established by Bamler, we obtain uniform $L^2$ curvature bounds on Ricci flows with bounded scalar curvature of dimension $n \le 7$.

Fractional integral operators involving special functions as kernels have long been one of the main subjects of fractional calculus. As a discrete version of classical fractional calculus, $q$-fractional calculus not only brings often new phenomena and new perspectives but also provides new useful areas for describing and studying new problems of applied nature. Recently, Luo and Zhou (see below) developed a methodology for formulating well-behaved $q$-fractional integral operators steming from a basic general theory. Our aim in this paper is to define and introduce a new class of $q$-fractional integral operators whose kernel involves a new multivariate $q$-Mittag-Leffler function. We shall also define the corresponding $q$-fractional derivatives (as the inverses of $q$-fractional integral operators) and define also the $q$-Caputo fractional derivative operators. We discuss in detail the similarities and variations between the $q$-operators and their counterparts in classical theory, particularly in Prabakar fractional calculus. Further, applications of the defined operators in solving certain $q$-fractional differential equations are also considered. We also mention throughout this paper some useful relevances of our established results with certain known important cases. In the concluding remarks, we point out briefly few possible proposals (or directions) for further work on the present subject matter of $q$-calculus.

Sparse-view computed tomography (CT) reduces radiation dose and acquisition time and may mitigate motion artifacts. However, angular undersampling provides insufficient information to determine the image uniquely and stably. Limited-angle CT, arising from restricted angular coverage, produces strongly directional information loss associated with the missing angular range. In both settings, image directions may be strongly observed, weakly constrained, or unobservable, leading to severe ill-posedness and reconstruction ambiguity. Existing diffusion-based approaches incorporate measurement information through likelihood guidance, data-consistency operations, or range-null-space corrections. However, they do not generally use the continuously varying measurement sensitivity of the acquisition to jointly shape both reconstruction updates and stochastic exploration. We propose a geometry-aware diffusion-guided stochastic reconstruction framework for sparse-view and limited-angle CT. Its central component is a regularized noise-weighted pullback metric constructed from the CT forward operator and measurement-noise covariance. This metric continuously adapts both the measurement-aware update and stochastic exploration according to directional measurement sensitivity, suppressing changes along strongly constrained directions while permitting greater exploration along weakly constrained and unobservable directions. We complement this geometry-aware update with a regularized data-consistency correction and approximately null-space-restricted stochastic perturbations, implemented matrix-free using forward and backprojection operations together with conjugate-gradient solves. Experiments on sparse-view, noisy, and limited-angle CT demonstrate competitive reconstruction quality, strong measurement consistency, and spatially resolved empirical uncertainty estimates.