Let $G_n$ be the partition graph whose vertices are the partitions of $n$, with adjacency given by elementary transfers of one cell between parts, followed by reordering. We study the support of a partition -- the set of distinct part sizes -- as a global vertex invariant of $G_n$. We show that support size $r$ occurs in $G_n$ if and only if $T_r=r(r+1)/2\le n$, so the maximal support size is $ρ(n)=\max\{r:T_r\le n\}$. We determine exactly how support changes along an edge: the support jump always lies in $\{-2,-1,0,1,2\}$, and we give an explicit birth-death formula in terms of the source and target part sizes. We also prove the degree bound $°(λ)\ge σ(λ)(σ(λ)-1)$ for every partition $λ$, with equality exactly for staircase partitions. In addition, support size is invariant under conjugation, the support-$1$ stratum consists exactly of rectangular partitions, and the coarse support-level graph always contains the chain $1-2-\cdots-ρ(n)$. We conclude with computational data for small $n$, including support-stratum counts, support-jump counts, and connectivity data for fixed-support subgraphs.
Robust decision-making requires compression. A system that forms a rich support state cannot usually preserve its full structure at the point of action. It must retain only those distinctions needed to act, verify, abstain, or defer under the current consequence geometry. This paper formalizes support sufficiency as action-sufficient compression. Let $H$ denote a full support state, $\mathcal{A}$ a finite action set, and $Z$ a consequence geometry specifying payoff structure. For fixed $Z$, the coarsest exactly action-sufficient compression is the quotient of support space by policy equivalence. Two support states may be merged exactly when they require the same optimal action. This clarifies why content-only and scalar-confidence-only arbitration fail whenever their induced partitions cross action boundaries. Approximate sufficiency is then defined by bounded expected policy regret. In the finite single-cycle setting, this yields a rate-regret problem with source $H$, reproduction alphabet $\mathcal{A}$, and distortion given by consequence-sensitive regret. The optimal stochastic action channel inherits the standard rate-distortion Gibbs form, applied here to support states with r
Empiric antibiotic prescribing in high-risk clinical contexts often requires decision making under conditions of incomplete information, where inappropriate coverage or unjustified escalation may compromise safety and antimicrobial stewardship. While clinical decision-support systems have been proposed to assist in this process, many approaches lack explicit governance and evaluation mechanisms defining scope, abstention conditions, recommendation permissibility, and expected system behavior. This work specifies a governance and evaluation framework for deterministic clinical decision-support systems operating under explicitly constrained scope. Deterministic behavior is adopted to ensure that identical inputs yield identical outputs, supporting transparency, auditability, and conservative decision support in high-risk prescribing contexts. The framework treats governance as a first-class design component, separating clinical decision logic from rule-based mechanisms that determine whether a recommendation may be issued. Explicit abstention, deterministic stewardship constraints, and exclusion rules are formalized as core constructs. The framework defines an evaluation methodology
Recently, multi-layer perceptrons (MLPs) widely used in modern AI applications suffer from limited real-time performance due to intensive memory access overhead. Kolmogorov--Arnold Networks (KANs) have attracted increasing attention as an alternative architecture with similar structures to MLPs but improved parameter efficiency. However, the lack of dedicated hardware support limits the practical performance benefits of KANs. Moreover, since many edge workloads still rely heavily on MLPs, accelerators designed exclusively for KANs become inefficient and impractical. In this work, we present VIKIN, a reconfigurable accelerator that efficiently supports both KAN and MLP inference using unified hardware. VIKIN introduces a pipeline execution mode and two-stage sparsity support for efficient KAN processing, while enabling parallel-mode acceleration to improve MLP throughput under the same sparsity framework. Experiments on real-world datasets demonstrate that replacing MLPs with KANs on VIKIN achieves $1.28\times$ acceleration with $19.58\%$ reduced accuracy loss. For a higher-accuracy KAN model requiring $3.29\times$ more operations, VIKIN incurs only $1.24\times$ latency overhead com
Generative AI tools often answer questions using source documents, e.g., through retrieval augmented generation. Current groundedness and hallucination evaluations largely frame the relationship between an answer and its sources as binary (the answer is either supported or unsupported). However, this obscures both the syntactic moves (e.g., direct quotation vs. paraphrase) and the interpretive moves (e.g., induction vs. deduction) performed when models reformulate evidence into an answer. This limits both benchmarking and user-facing provenance interfaces. We propose the development of a reader-centred taxonomy of grounding as a set of support relations between generated statements and source documents. We explain how this might be synthesised from prior research in linguistics and philosophy of language, and evaluated through a benchmark and human annotation protocol. Such a framework would enable interfaces that communicate not just whether a claim is grounded, but how.
Given a support variety theory defined on the compact part of a monoidal triangulated category, we define an extension to the non-compact part following the blueprint of Benson--Carlson--Rickard, Benson--Iyengar--Krause, Balmer--Favi, and Stevenson. We generalize important aspects of the theory of extended support varieties to the noncommutative case, and give characterizations of when an extended support theory detects the zero object, under certain assumptions. In particular, we show that when the original support variety theory is based on a Noetherian topological space, detects the zero object, satisfies a generalized tensor product property, and comes equipped with a comparison map, then the extended support variety also detects the zero object. In the case of stable categories of finite tensor categories, this gives conditions under which the central cohomological support admits an extension that detects the zero object, confirming part of a recent conjecture made by the second author together with Nakano and Yakimov.
Cross-disciplinary communication is often hindered by specialized language (i.e., jargon) and uneven background knowledge. Recent advances in speech-to-text and large language models make it possible to provide jargon support during online meetings, but generic support (i.e., defining the same terms for everyone) can overwhelm listeners with definitions they do not need. We present ParseJargon, a system for personalized jargon support in real-time online meetings. We begin with an initial prototype to probe the use of single-sentence user profiles for personalization. We conducted a controlled study and showed that even this minimal personalization enhanced listeners' comprehension and engagement over generic support because of more precise jargon identification. Guided by insights from participants' feedback, we refined the system with more advanced personalization techniques, including in-session user feedback and portable glossary-based profiles. We evaluated how these techniques can further improve jargon identification precision using data collected in the controlled study to simulate personalization over time. We also conducted a latency test, complemented by a lightweight de
We prove a multilevel non-shadow refinement of the Alon--Babai--Suzuki (ABS) nonuniform restricted-intersection theorem. Let $K=\{k_1,\dots,k_r\}$ and let $L$ be a set with $|L|=s$. If $\mathcal{F}\subseteq \bigcup_{k\in K}\binom{[n]}{k}$ is $L$-intersecting and $k_i>s-r$ for every $i$, then $|\mathcal{F}| + \sum_{j=s-r+1}^{s} |\mathcal{N}_j(\mathcal{F})| \le N(n,s,r),$ equivalently $|\mathcal{F}| \le \sum_{j=s-r+1}^{s} |\partial_j\mathcal{F}|.$ Thus the ABS bound is sharpened by the total non-shadow deficit on the top $r$ levels. In the modular setting, we take a coefficient-sensitive viewpoint: the polynomial method depends not just on the degree of the annihilator polynomial $P_L(t)=\prod_{\ell\in L}(t-\ell)\in\mathbb{F}_p[t]$, but on which binomial terms actually appear in it. This yields a gap-free modular bound depending only on the active support levels of $P_L$. For almost-initial residue patterns $L=\{0,1,\dots,s-m-1\}\cup R \pmod p$ we obtain the collapse $|\mathcal{F}|\le \sum_{i=0}^{m}\binom{n}{s-i}.$ In particular, for consecutive residues $L=\{0,1,\dots,s-1\}\pmod p$ we get the sharp bound $|\mathcal{F}|\le \binom{n}{s}$, giving a partial negative answer to a quest
Unlike non-volatile memory that resides on the processor memory bus, memory-semantic solid-state drives (SSDs) support both byte and block access granularity via PCIe or CXL interconnects. They provide scalable memory capacity using NAND flash at a much lower cost. In addition, they have different performance characteristics for their dual byte/block interface respectively, while offering essential memory semantics for upper-level software. Such a byte-accessible storage device provides new implications on the software system design. In this paper, we develop a new file system, named ByteFS, by rethinking the design primitives of file systems and SSD firmware to exploit the advantages of both byte and block-granular data accesses. ByteFS supports byte-granular data persistence to retain the persistence nature of SSDs. It extends the core data structure of file systems by enabling dual byte/block-granular data accesses. To facilitate the support for byte-granular writes, \pname{} manages the internal DRAM of SSD firmware in a log-structured manner and enables data coalescing to reduce the unnecessary I/O traffic to flash chips. ByteFS also enables coordinated data caching between th
We prove a theorem on iterated forcing that can be used for preservation of $\aleph_2$ and $\aleph_1$ in iterations with supports of size $\aleph_1$ of forcings that have amalgamation properties similar to those present in the perfect set forcing. The work is modelled after Baumgartner's Axiom A and his proof that iterations with countable support of the same preserve $\aleph_1$. In honour of James E. Baumgartner, the property introduced here is called Property B$(κ)$. The known additional difficulties when forcing at cardinals higher than $\aleph_1$ make for a less general theorem and a more complex theorem on the iteration, which is not an iteration theorem in the classical sense. The results extend to other cardinals $κ$ such that $κ^{<κ}=κ$, in place of $\aleph_1$. We give examples of individual forcings that have Property B$(κ)$ and their products. In particular, we introduce a correct version of the generalised perfect set forcing, which we call Perfect Set Forcing with Respect to a Filter. We give its basic properties and show that for the right kind of filter $\mathcal F$ this kind of forcing is iterable with supports of size $\leκ$.
We extend the support theory of Benson--Iyengar--Krause to the non-Noetherian setting by introducing a new notion of small support for modules. This enables us to prove that the stable module category of a finite group is canonically stratified by the action of the Tate cohomology ring, despite the fact that this ring is rarely Noetherian. In the tensor triangular context, we compare the support theory proposed by W. Sanders (which extends the Balmer--Favi support theory beyond the weakly Noetherian setting) with our generalized BIK support theory. When the Balmer spectrum is homeomorphic to the Zariski spectrum of the endomorphism ring of the unit, the two support theories coincide as do their associated theories of stratification. We also prove a negative result which states that the Balmer--Favi--Sanders support theory can only stratify categories whose spectra are weakly Noetherian. This provides additional justification for the weakly Noetherian hypothesis in the work of Barthel, Heard and B. Sanders. On the other hand, the detection property and the local-to-global principle remain interesting in the general setting.
The integration of Large Language Models (LLMs) into healthcare holds significant potential to enhance diagnostic accuracy and support medical treatment planning. These AI-driven systems can analyze vast datasets, assisting clinicians in identifying diseases, recommending treatments, and predicting patient outcomes. This study evaluates the performance of a range of contemporary LLMs, including both open-source and closed-source models, on the 2024 Portuguese National Exam for medical specialty access (PNA), a standardized medical knowledge assessment. Our results highlight considerable variation in accuracy and cost-effectiveness, with several models demonstrating performance exceeding human benchmarks for medical students on this specific task. We identify leading models based on a combined score of accuracy and cost, discuss the implications of reasoning methodologies like Chain-of-Thought, and underscore the potential for LLMs to function as valuable complementary tools aiding medical professionals in complex clinical decision-making.
Background: AI-driven prediction algorithms have the potential to enhance emergency medicine by enabling rapid and accurate decision-making regarding patient status and potential deterioration. However, the integration of multimodal data, including raw waveform signals, remains underexplored in clinical decision support. Methods: We present a dataset and benchmarking protocol designed to advance multimodal decision support in emergency care. Our models utilize demographics, biometrics, vital signs, laboratory values, and electrocardiogram (ECG) waveforms as inputs to predict both discharge diagnoses and patient deterioration. Results: The diagnostic model achieves area under the receiver operating curve (AUROC) scores above 0.8 for 609 out of 1,428 conditions, covering both cardiac (e.g., myocardial infarction) and non-cardiac (e.g., renal disease, diabetes) diagnoses. The deterioration model attains AUROC scores above 0.8 for 14 out of 15 targets, accurately predicting critical events such as cardiac arrest, mechanical ventilation, ICU admission, and mortality. Conclusions: Our study highlights the positive impact of incorporating raw waveform data into decision support models, im
This paper presents a novel, structured decision support framework that systematically aligns diverse artificial intelligence (AI) agent architectures, reactive, cognitive, hybrid, and learning, with the comprehensive National Institute of Standards and Technology (NIST) Cybersecurity Framework (CSF) 2.0. By integrating agent theory with industry guidelines, this framework provides a transparent and stepwise methodology for selecting and deploying AI solutions to address contemporary cyber threats. Employing a granular decomposition of NIST CSF 2.0 functions into specific tasks, the study links essential AI agent properties such as autonomy, adaptive learning, and real-time responsiveness to each subcategory's security requirements. In addition, it outlines graduated levels of autonomy (assisted, augmented, and fully autonomous) to accommodate organisations at varying stages of cybersecurity maturity. This holistic approach transcends isolated AI applications, providing a unified detection, incident response, and governance strategy. Through conceptual validation, the framework demonstrates how tailored AI agent deployments can align with real-world constraints and risk profiles, e
Software plays an ever increasing role in complex system development and prototyping, and in recent years, MIT Lincoln Laboratory has sought to improve both the effectiveness and culture surrounding software engineering in execution of its mission. The Homeland Protection and Air Traffic Control Division conducted an internal study to examine challenges to effective and efficient research software development, and to identify ways to strengthen both the culture and execution for greater impact on our mission. Key findings of this study fell into three main categories: project attributes that influence how software development activities must be conducted and managed, potential efficiencies from centralization, opportunities to improve staffing and culture with respect to software practitioners. The study delivered actionable recommendations, including centralizing and standardizing software support tooling, developing a common database to help match the right software talent and needs to projects, and creating a software stakeholder panel to assist with continued improvement.
Feature Selection is a crucial procedure in Data Science tasks such as Classification, since it identifies the relevant variables, making thus the classification procedures more interpretable, cheaper in terms of measurement and more effective by reducing noise and data overfit. The relevance of features in a classification procedure is linked to the fact that misclassifications costs are frequently asymmetric, since false positive and false negative cases may have very different consequences. However, off-the-shelf Feature Selection procedures seldom take into account such cost-sensitivity of errors. In this paper we propose a mathematical-optimization-based Feature Selection procedure embedded in one of the most popular classification procedures, namely, Support Vector Machines, accommodating asymmetric misclassification costs. The key idea is to replace the traditional margin maximization by minimizing the number of features selected, but imposing upper bounds on the false positive and negative rates. The problem is written as an integer linear problem plus a quadratic convex problem for Support Vector Machines with both linear and radial kernels. The reported numerical experien
This paper introduces GTX, a standalone main-memory write-optimized graph data system that specializes in structural and graph property updates while enabling concurrent reads and graph analytics through ACID transactions. Recent graph systems target concurrent read and write support while guaranteeing transaction semantics. However, their performance suffers from updates with real-world temporal locality over the same vertices and edges due to vertex-centric lock contentions. GTX has an adaptive delta-chain locking protocol on top of a carefully designed latch-free graph storage. It eliminates vertex-level locking contention, and adapts to real-life workloads while maintaining sequential access to the graph's adjacency lists storage. GTX's transactions further support cache-friendly block level concurrency control, and cooperative group commit and garbage collection. This combination of features ensures high update throughput and provides low-latency graph analytics. Based on experimental evaluation, in addition to not sacrificing the performance of read-heavy analytical workloads, and having competitive performance similar to state-of-the-art systems, GTX has high read-write tran
COOL is an Object-Oriented programming language used to teach compiler design in many undergraduate and graduate courses. Because most students are unfamiliar with the language and code editors and IDEs often lack the support for COOL, writing code and test programs in COOL are a burden to students, causing them to not fully understand many important and advanced features of the language and compiler. In this tool paper, we describe COOLIO,an extension to support COOL in the popular VSCode IDE. COOLIOprovides (i) syntax highlighting supports for the COOL language through lexing and parsing, (ii) semantics-aware autocompletion features that help students write less code and reduce the burden of having to remember unfamiliar COOL grammar and syntax, and (iii) relevant feedback from the underlying COOL interpreter/compiler (e.g., error messages, typing information) to the students through VSCode editor to aid debugging. We believe that COOLIO will help students enjoy writing COOL programs and consequently learn and appreciate more advanced compiler concepts.
Despite the high prevalence and burden of mental health conditions, there is a global shortage of mental health providers. Artificial Intelligence (AI) methods have been proposed as a way to address this shortage, by supporting providers with less extensive training as they deliver care. To this end, we developed the AI-Assisted Provider Platform (A2P2), a text-based virtual therapy interface that includes a response suggestion feature, which supports providers in delivering protocolized therapies empathetically. We studied providers with and without expertise in mental health treatment delivering a therapy session using the platform with (intervention) and without (control) AI-assistance features. Upon evaluation, the AI-assisted system significantly decreased response times by 29.34% (p=0.002), tripled empathic response accuracy (p=0.0001), and increased goal recommendation accuracy by 66.67% (p=0.001) across both user groups compared to the control. Both groups rated the system as having excellent usability.
This research explores the integration of chatbot technology powered by GPT-3.5 and GPT-4 Turbo into higher education to enhance internationalization and leverage digital transformation. It delves into the design, implementation, and application of Large Language Models (LLMs) for improving student engagement, information access, and support. Utilizing technologies like Python 3, GPT API, LangChain, and Chroma Vector Store, the research emphasizes creating a high-quality, timely, and relevant transcript dataset for chatbot testing. Findings indicate the chatbot's efficacy in providing comprehensive responses, its preference over traditional methods by users, and a low error rate. Highlighting the chatbot's real-time engagement, memory capabilities, and critical data access, the study demonstrates its potential to elevate accessibility, efficiency, and satisfaction. Concluding, the research suggests the chatbot significantly aids higher education internationalization, proposing further investigation into digital technology's role in educational enhancement and strategy development.