Computer Science and Mathematics

Abstract: Nowadays, the complexity of electronic health records (EHRs) requires tools capable of efficiently and accurately extracting and interpreting clinically relevant information to support clinicians. This study explores the use of the Cheshire Cat AI framework, configured with Ollama and using LLaMA3 as a language model, with the main purpose of performing automatic analysis of synthetic EHRs from Kaggle. Through specific structured queries, the model was able to successfully reconstruct patients’ clinical histories and extracted useful data such as diagnoses, treatments, visits, comorbidities and demographic data. A validation process through repeated queries was then performed, which confirmed a high level of accuracy. To preserve data privacy, only synthetic datasets were used in this work. Beyond the simple retrieval of information by means of queries, the study highlights the great potential of language models in clinical decision support. Their ability to interpret large and heterogeneous datasets certainly offers new opportunities to improve diagnostic accuracy, simplify workflows and personalise treatments. Specifically, natural language queries by tools such as Cheshire Cat AI can be used for intelligent support systems that can, for instance, integrate multimodal and real-time data to provide medical recommendations. These results represent a first step towards the exploitation of large language models not only for EHR analysis, but also to assist in clinical decision-making processes in different medical fields and, above all, for the study of specific complex diseases such as rare diseases.

Abstract: Large language models (LLMs) are being adopted quickly across biomedicine. Their value in clinical practice depends on more than accuracy: it also depends on whether they can run within the latency, hardware, privacy, cost, and staffing limits of real settings. In this scoping review of efficiency-oriented biomedical LLM research, we organize the literature along two axes: a taxonomy of efficiency techniques (prompting and retrieval, parameter-efficient and data-efficient adaptation, model compression, efficient architectures and inference, and agentic workflows) and a map of biomedical application domains. Across the corpus, prompting and parameter-efficient fine-tuning delivered efficiency most often, and studies reported it as savings in memory, trainable parameters, compute time, and human-workflow time, while energy and carbon were almost never measured. The reported gains are large and concrete: low-rank adaptation combined with low-precision quantization often shrinks the memory needed for adaptation enough to train and deploy a model on a single consumer or edge device, usually at a small and measured cost in task quality. Yet the evidence still leans toward retrospective benchmarking, with external validation, prospective evaluation, and clinical deployment all rare. We map which techniques serve which clinical domains, show how to read an efficiency claim against its comparator and clinical context, and identify what the field still needs to measure to turn demonstrated resource savings into validated clinical value.

Abstract: We prove that the total area of the power circles associated with an odd p-gon inscribed in and circumscribed about a pair of homothetic ellipses remains invariant throughout the Poncelet family. Our proof is based on a simple affine averaging principle, which also yields several related quadratic invariants, including explicit formulas for the sums of the squared distances from the center to the vertices, to the side midpoints, as well as for the sum of the squared side lengths. As an application, we show that a convex Poncelet pentagon and the corresponding star Poncelet pentagon, both circumscribed about the same inellipse, have equal total power-circle area. These results unify several metric invariants of odd Poncelet polygons within a common affine-geometric framework.

Abstract: We study the adjunction-defect calculus underlying MacPherson--Vilonen gluing. For an open--closed decomposition \(X=U\sqcup Z\), recollement gives adjoint triples \(j_!\dashv j^*\dashv j_*\) and \(i^*\dashv i_*\dashv i^!\). We package this data as a MacPherson--Vilonen adjunction package and compute the twist--cotwist defects of its four constituent adjunctions. The nontrivial open-adjunction defects are \(T_{D^b_c(X)}(j_!\dashv j^*)\simeq i_*i^*(-)[-1]\) and \(T_{D^b_c(X)}(j^*\dashv j_*)\simeq i_*i^!(-)[1]\). By contrast, full-faithfulness in genuine recollement forces several open and closed defects to vanish, so imposing sphericality on all four raw recollement adjunctions is degenerate. Thus compatible sphericalization is formulated only conditionally, requiring shared-object data and transportability of compatibility morphisms. The main unconditional result identifies the boundary residual \(\operatorname{BRes}_{Z}(M):=\operatorname{Cone}(j_!j^*M\to j_*j^*M)\) as an extension \(i_*i^*M\to \operatorname{BRes}_{Z}(M)\to i_*i^!M[1]\to\). Iterating over closed-stratum filtrations yields residual towers, with filtered--graded, duality, motivic, and schober-theoretic outlooks.

Abstract: Self-attention couples every pair of positions in a sequence, incurring a cost that grows quadratically with se-quence length and a key–value state that grows without bound during generation. Here we introduce the inductive algebraicresonance memory (IARM), an attention-free sequence-mixing mechanism that replaces pairwise attention with two ingre-dients: a softmax-gated mixture of learned low-rank operators that modulates a positive feature map of the query, and acoordinatewise causal memory that reads each feature channel as a normalized cumulative average of the value stream.The resulting layer runs in time linear in sequence length and maintains a constant-size recurrent state per channel, so au-toregressive decoding requires no growing cache. We instantiate IARM as a 118 003 200-parameter decoder-only languagemodel, pretrain it on a 10-billion-token educational web corpus, and fine-tune it for two epochs on 207 865 UltraChat con-versations, reducing the assistant-token perplexity from 20.4 to 6.90. Diagnostics over all 528 learned operators show thatthey converge to near rank-1 maps, that the four operators in each head are engaged in balance, and that the effectivememory window sharpens monotonically with network depth. A custom groupwise 4-bit export reproduces the weightsto within a mean relative error of 9.3 % while compressing the model 3.67-fold, and is loaded by an accompanying Apple-silicon (MLX) runtime that ports the mechanism one-to-one. IARM is offered as a transparent, fully reproducible testbedfor attention-free causal modelling rather than as a benchmarked production model.

Abstract: Domain shift remains a major obstacle to robust histopathology image segmentation, especially when models trained on several source organs are deployed to unseen anatomical sites. This study addresses cross-organ adenocarcinoma segmentation by introducing an evidence-guided vision-language segmentation framework that incorporates pathology-relevant morphological evidence into dense mask prediction. The proposed method uses a pathology vision-language encoder to extract image and text representations, a semantic query booster to form image-aware segmentation queries, and an evidence-guided decoding module that integrates positive tumour-supporting evidence and negative misleading evidence. A feature-level style regularization branch is further used during training to improve robustness to source-domain appearance variation. Experiments were conducted on cross-organ adenocarcinoma datasets under a source-only domain generalization setting, using colorectum, stomach, and pancreas as source domains and ampullary, gallbladder, and intestine as unseen target domains. The proposed framework achieved 79.48%/88.57% IoU/Dice on seen source organs and 79.89%/88.82% on unseen target organs, with a small seen-unseen gap of 0.41 IoU points and 0.25 Dice points. These results suggest that structured pathology evidence can provide useful semantic guidance for cross-organ tumour segmentation and may reduce reliance on organ-specific visual shortcuts.

Abstract: When using the few-shot recognition model, due to the influence of materials, light directions and background textures of the industrial inspection images, there will be domain drift, and the recognition accuracy of the model will be unstable when used in different equipment. We built a new dataset with 54, 000 images of 5 types of equipment and 5 types of defects to improve the generalization ability of defect recognition in new equipment scenarios. We present a cross domain few shot recognition model that combines ConvNeXt texture features extraction, domain adversarial feature alignment and prototype network discrimination. The experimental results demonstrate that the model gets the average accuracy of 88.3% and F1 score of 84.7% in defect classification with 50 labeled target samples per class. For the unseen equipment, the recall rates for superficial cracks and pitting corrosion were 81.6% and 85.2%, respectively. The results show that the method can further improve the cross-domain aggregation function for similar defects and improve the stability of the model transfer and deployment in complex industrial scenes.

Abstract: We define a class of Markov cell processes P_X on a finite set X as a product of conditional probabilities on cells (subsets of X forming a partially directed intersection graph). The class of Markov cell processes includes Bayesian networks and Markov edge processes. A nested conditional independence (NCI) condition is introduced that allows an explicit expression of a joint probability distribution through its marginals. The NCI condition is used in our construction of consistent Markov cell processes P_X whose marginals coincide with P_X′ on smaller sets X′ ⊂ X. We discuss three classes of consistent Markov cell processes on rectangular domains X ⊂ Z³ equipped with ‘cubic’ cells, which include Arak model and 3D Pickard model.

Abstract: This paper develops a theory of fractional Landau inequalities in mixed Sobolev norms, extending classical derivative estimates to anisotropic function spaces. We introduce mixed fractional Sobolev spaces \( W_{\alpha}^{\nu,p}(\mathbb{R}^{k}) \), where \( \alpha = (\alpha_1,\dots,\alpha_k) \) encodes directional scaling and characterizes functions with coordinate-dependent regularity. Within this framework, we establish fractional Landau inequalities with constants depending explicitly on the fractional order ν and the anisotropy vector α. The analysis relies on techniques from anisotropic harmonic analysis, including directional Littlewood–Paley decompositions and anisotropic maximal function estimates. The sharpness of the inequalities is discussed, and connections to approximation theory are outlined. These results provide a mathematical bridge between fractional calculus, harmonic analysis, and high-dimensional approximation.

Abstract: In 1970, Dana Scott proposed his highly influential ''mathematical theory of computation'' to define the relationship between the text of a program and what the program computes (or denotes) --- the ''semantics'' of the program. Scott used a complete lattice based on the ''information ordering'', with the bottom element representing undefined --- a program failing to terminate normally, thus producing no information. The top element, however, was unused. Hence most subsequent applications of denotational semantics have used mathematical structures that avoid top elements. We suggest that the information ordering is relevant not only to semanticists, but also to working programmers, as a basis for determining if a program component or a computation is correct according to their intentions. We also suggest that a return to the use of complete lattices is called for if we wish to broaden formal semantics to allow it to encompass programmer intentions. That is because often those intentions permit more than one runtime behaviour for a given input. For example, several declarative debugging tools allow a programmer to declare that a runtime call is ''inadmissible'', loosely meaning the called program component should never be used with such input. If the input is garbage, the programmer does not care what garbage is output --- all results are acceptable, which can be modeled by the top element of a complete lattice. In this paper we explore the connections between the information ordering, correctness of computations and programs, and debugging. We present a general theory and describe several instances where the intention for what our logic/functional code computes plus what it actually computes can be described by elements in a complete lattice. This extends both the theoretical basis and practical flexibility of declarative debugging and reasoning about partial correctness and gives an attractive mathematical framework that encompasses our intentions, our programs and what they compute.

Abstract: We develop a sharp local-to-global transition calculus for monotone profiles whose centered holomorphic extension maps a horizontal strip into the unit disk. Schwarz-Pick contraction gives the pointwise bounds |G′| ≤ [π/(4a)](1 − G²) and 0 ≤ F′ ≤ [π/(2a)]F(1 − F), where G = 2F − 1. Integration yields optimal two-point, anchored-envelope, and threshold-duration inequalities. Equality at one real point, equality for one distinct pair, or contact with an anchored envelope at one later point forces the complete logistic profile. A speed-defect identity measures accumulated transition delay, while quantile-spacing, variance, and area bounds show that every admissible transition is at least as dispersed as the logistic extremizer. We separate the disk-contractivity hypothesis from spectral growth: compact spectral support supplies an entire function of exponential type, while strip-to-disk contractivity is the geometric condition that produces the nonlinear speed limit. The resulting framework is a portable analytic theorem; a domain realization supplies its physical clock and dynamics.

Abstract: We introduce a new class of split inverse problems, termed the Split Pseudomonotone Equilibrium Problem with Multiple Output Sets, which generalizes classical equilibrium formulations to accommodate multiple decision outputs and pseudomonotonicity. To solve this problem, we propose a novel iterative method that employs an inertial technique and self adaptive step sizes to improve the convergence properties. Under suitable conditions, we establish the convergence of the method and provide a detailed theoretical analysis. The proposed framework is then applied to medical diagnosis classification tasks, considering diabetes, chronic kidney disease, heart disease, and breast cancer datasets where decision making involves heterogeneous data. Numerical tests reveal the algorithm’s strength and effectiveness, underscoring its potential for wider use in optimization-based classification and decision-making systems.

Abstract: The textile and clothing value chain faces increasing pressure to improve reuse and recycling rates, particularly in post-consumer scenarios where garments must be rapidly assessed, classified, and routed toward appropriate end-of-life pathways. Manual sorting remains labor-intensive and difficult to scale, especially when garments must be evaluated according to visual condition, type, color, fiber-related characteristics, and reuse potential. This article proposes and evaluates an AI-based framework for automated clothing sorting to support textile reuse and recycling. The proposed framework combines YOLO-based object detection with a Vision-Language Model for semantic interpretation in identifying garments, interpreting visual attributes, and supporting sorting decisions. The framework first distinguishes reusable garments from non-reusable items and then further classifies, using two ConvNeXt-based visual classifiers, non-reusable textiles according to characteristics relevant to recycling. By integrating computer vision and vision-language reasoning, the approach aims to improve the speed, consistency, and scalability of garment classification in circular textile systems. The results demonstrate the potential of AI-assisted sorting as a decision-support tool for increasing the recovery value of post-consumer clothing and reducing the amount of textile waste directed to landfill or incineration.

Abstract: Open Educational Resources (OER) are teaching, learning, and research materials that are freely accessible and openly licensed, allowing users to use, adapt, and redistribute them with few or no restrictions. This article presents a quality evaluation experience over a set of OERs, a prior step to a clusterization process based on specific criteria. The evaluators have been students, from a teacher training master's program, that were instructed in concepts related to Open Learning, digital educational repositories, design and production processes for digital educational materials, and OER quality standards. The experiment consisted of evaluating the OERs stored in an online repository called Procomun, resources associated with the discipline of Computer Science. The resources have been created by both professionals and the students themselves, with the aim of comparing production quality levels and various specific criteria between them. For this purpose, two types of evaluations were carried out. First, the quality of the repository’s semantic tagging, based on the Learning Object Metadata (LOM) standard, was assessed using the Metadata Quality Assessment Model. Second, the UNE 71362 standard was applied to a selected collection of OERs obtaining a set of spider diagrams. Finally, to evaluate the value of the quality assessment itself, two types of processes were carried out: students acted as evaluators of the resources they had produced themselves (as a self-assessment task), and peer assessment was also carried out by other students. The article describes the entire experience, the evaluation process, the quality framework and the results obtained in the experimentation.

Abstract: Quantum Machine Learning (QML) has been proposed as a framework that may offer theoretical advantages over classical machine learning, especially in computational complexity and parallel processing of high-dimensional data. However, due to the limitations imposed by the Noisy Intermediate-Scale Quantum (NISQ) era, implementing large-scale quantum algorithms remains infeasible, making hybrid quantum-classical approaches a more viable alternative. In this work, we formulate and implement custom quantum-hybrid versions of classical clustering algorithms and compare their performance on an Autism Spectrum Disorder (ASD) screening dataset, which represents a highly relevant clinical domain characterized by a complex mix of behavioral and demographic features. We evaluate classical k-means, DBSCAN, spectral clustering, and agglomerative clustering against these formulated quantum-hybrid implementations. For the evaluation, we use inner metrics (Silhouette, Davies-Bouldin, Calinski-Harabasz) and outer metrics (AMI, ARI) on the generated partitions. The results show that the formulated hybrid implementations achieve a partition quality comparable to that of classical counterparts, except in the case of Q-DBSCAN, where the classical algorithm outperformed our hybrid implementation due to the high-dimensional mapping. Thus, we present empirical information about strengths, weaknesses and potential viability of these formulated hybrid implementations in real-life applications in the NISQ era.

Abstract: Visual Internet-of-Things (IoT) sensors are increasingly used to collect artistic images in museums, galleries, cultural heritage sites, and public spaces. Centralizing these images for analysis, however, can expose sensitive information concerning artwork ownership, exhibition layouts, visitor activities, and institutional collections. Federated learning offers a decentralized alternative, but its application is challenged by non-independent and identically distributed image data, resource-constrained sensor nodes, communication overhead, and privacy leakage from model updates. This paper proposes FedArtSense, a privacy-preserving federated learning framework for artistic image analytics in visual IoT sensor networks. FedArtSense introduces prototype-guided representation alignment to reduce client drift caused by heterogeneous artistic styles and collection distributions. An adaptive privacy mechanism dynamically determines gradient-clipping thresholds and noise levels according to update sensitivity, while a Rényi differential privacy accountant provides quantifiable privacy guarantees. In addition, importance-aware sparse aggregation reduces communication costs by transmitting only informative model updates. Experiments on the WikiArt, ArtBench-10, and Behance Artistic Media datasets under realistic non-IID and resource-constrained IoT settings demonstrate that FedArtSense consistently improves classification performance and convergence stability compared with representative federated learning and privacy-preserving baselines. It also achieves a favorable balance among analytical accuracy, privacy protection, and communication efficiency. These results indicate that FedArtSense provides an effective solution for secure and scalable artistic image analysis across distributed visual IoT infrastructures.

Abstract: We study a delayed time-fractional semilinear evolution equation driven by the spectral fractional Laplacian. The model combines a Caputo time derivative, a source evaluated at the past state u(t−τ), and an absorption term evaluated at the present state u(t). The fractional structure is used throughout the analysis through the Caputo Volterra kernel, the spectral fractional energy form, and Mittag–Leffler resolvent estimates. We prove local existence, positivity and an L∞(Ω) continuation criterion for bounded mild solutions, and show that these solutions satisfy the weak formulation before the maximal time. In the pure delayed-source case μ=0, we prove global continuation and boundedness on every finite time interval, together with a stepwise propagation of positive lower bounds for the first Dirichlet mode. When μ>0 and the initial history is sufficiently small, the present absorption and the spectral damping dominate the delayed feedback. In this regime, the solution is globally bounded and satisfies u(t)L2(Ω)→0 as t→+∞, with a Mittag–Leffler type decay estimate for the L2-energy. The numerical section is restricted to reduced first-mode comparison computations and illustrates the scalar comparison estimates derived from the first-mode analysis.

Abstract: Self-improving autonomous agents are moving from research prototypes to deployed systems. The primary goal is controllable evolution, or adaptation, from experience with minimal or even no human input. This survey frames modern self-improving agents as adaptive systems that convert experience into accumulated capability gains. We offer a system-level framework that represents a modern agent as a configuration coupling a foundation model with an operational scaffold of prompts, memory, tools, and control logic. Within this framework, self-improvement is formalized as a self-induced update operator that obtains and commits updates to model parameters or scaffold components. We organize prior work by update target and by the signals that drive change, then review applications and discuss evaluation, before closing with open problems and future directions. For convenience, we track technical updates on this GitHub page.

Abstract: We give a certified finite verification of the literal vertex formulation currently displayed as Erd\H{o}s Problem \#580. Namely, for every $1\le n\le 19$, an $n$-vertex graph having at least $\lceil n/2\rceil$ vertices of degree at least $\lceil n/2\rceil$ contains every tree on at most $\lfloor n/2\rfloor$ vertices. The only order requiring new computer-assisted analysis is $n=18$. An edge-minimal counterexample is reduced to a host partition $V(G)=L\sqcup S$ with $|L|=|S|=9$, degree exactly $9$ on $L$, and $S$ independent. Exact embedding theorems cover $42$ of the $47$ non-isomorphic trees on nine vertices. The five remaining trees reduce, by deleting their leaves, to four rooted cores. For each core we construct a Boolean formula whose models are precisely the reduced hosts avoiding that rooted core. All four formulas are unsatisfiable. The deposited data include complete CNF instances and DRUP refutations. The archived traces were validated by reverse unit propagation, all four formulas are independently solved as unsatisfiable by a second SAT solver, a standalone semantic audit reconstructs the complete formulas---including all $3735$ base clauses and every avoidance clause---without importing the production generator, the complete $47$-tree witness table is generated from the classifier, and regeneration from the published encoder reproduces all four CNFs byte for byte. This is a finite partial result concerning trees on at most $n/2$ vertices; it does not settle the stronger classical formulation asking for trees with at most $n/2$ edges.

Abstract: Over a finite prime shell Fp, p=4κ+1, the roles of π and e are exact residues: the half-period π=2κ, and the exponential marker e=gλ(i). We determine the exact relation between these carriers and the classical values. Each classical value is the horizon readout of a chain of framed rationals n!/!n for e; the Wallis, arcsin and Machin chains for π; at IEEE-754 double precision the constants are the readouts of 18!/!18 and the Machin partial M10. Inside the shell the same chains carry exact residue lines that the readout deletes: the line of e is antiperiodic and terminates on Kurepa's left factorial, universal existence being equivalent to Kurepa's hypothesis; the line of $\pi$ is legible exactly up to the angular address of -1 and terminates on the calibration face π−1≡−2. Angularly the constants are dual: χ(−1)=eiπ holds exactly in every shell, while radian calibration of e is impossible in every shell and abundant across shells. π is structural, e statistical; transcendence belongs to the external completion, never to the shell element. All exact claims are machine-verified in integer and rational arithmetic.