Recent advances in interactive large language models like ChatGPT have revolutionized various domains; however, their behavior in natural and role-play conversation settings remains underexplored. In our study, we address this gap by deeply investigating how ChatGPT behaves during conversations in different settings by analyzing its interactions in both a normal way and a role-play setting. We introduce a novel dataset of broad range of human-AI conversations annotated with user motives and model naturalness to examine (i) how humans engage with the conversational AI model, and (ii) how natural are AI model responses. Our study highlights the diversity of user motives when interacting with ChatGPT and variable AI naturalness, showing not only the nuanced dynamics of natural conversations between humans and AI, but also providing new avenues for improving the effectiveness of human-AI communication.

Existing methods to characterise the evolving condition of traumatic brain injury (TBI) patients in the intensive care unit (ICU) do not capture the context necessary for individualising treatment. Here, we integrate all heterogenous data stored in medical records (1,166 pre-ICU and ICU variables) to model the individualised contribution of clinical course to six-month functional outcome on the Glasgow Outcome Scale - Extended (GOSE). On a prospective cohort (n=1,550, 65 centres) of TBI patients, we train recurrent neural network models to map a token-embedded time series representation of all variables (including missing values) to an ordinal GOSE prognosis every two hours. The full range of variables explains up to 52% (95% CI: 50%-54%) of the ordinal variance in functional outcome. Up to 91% (95% CI: 90%-91%) of this explanation is derived from pre-ICU and admission information (i.e., static variables). Information collected in the ICU (i.e., dynamic variables) increases explanation (by up to 5% [95% CI: 4%-6%]), though not enough to counter poorer overall performance in longer-stay (>5.75 days) patients. Highest-contributing variables include physician-based prognoses, CT features, and markers of neurological function. Whilst static information currently accounts for the majority of functional outcome explanation after TBI, data-driven analysis highlights investigative avenues to improve dynamic characterisation of longer-stay patients. Moreover, our modelling strategy proves useful for converting large patient records into interpretable time series with missing data integration and minimal processing.

The largest ICT employer in Hungary, Deutsche Telekom IT Solutions (formerly IT-Services Hungary, ITSH) is a subsidiary of the Deutsche Telekom Group. Established in 2006, the company provides a wide portfolio of IT and telecommunications services with more than 5000 employees. ITSH was awarded with the Best in Educational Cooperation prize by HIPA in 2019, acknowledged as one of the most attractive workplaces by PwC Hungary's independent survey in 2021 and rewarded with the title of the Most Ethical Multinational Company in 2019. The company continuously develops its four sites in Budapest, Debrecen, Pécs and Szeged and is looking for skilled IT professionals to join its team. We seek our new passionate Tech Lead for our existing MLOps platform.

Given a nonnegative matrix factorization, $R$, and a factorization rank, $r$, Exact nonnegative matrix factorization (Exact NMF) decomposes $R$ as the product of two nonnegative matrices, $C$ and $S$ with $r$ columns, such as $R = CS^\top$. A central research topic in the literature is the conditions under which such a decomposition is unique/identifiable, up to trivial ambiguities. In this paper, we focus on partial identifiability, that is, the uniqueness of a subset of columns of $C$ and $S$. We start our investigations with the data-based uniqueness (DBU) theorem from the chemometrics literature. The DBU theorem analyzes all feasible solutions of Exact NMF, and relies on sparsity conditions on $C$ and $S$. We provide a mathematically rigorous theorem of a recently published restricted version of the DBU theorem, relying only on simple sparsity and algebraic conditions: it applies to a particular solution of Exact NMF (as opposed to all feasible solutions) and allows us to guarantee the partial uniqueness of a single column of $C$ or $S$. Second, based on a geometric interpretation of the restricted DBU theorem, we obtain a new partial identifiability result. This geometric interpretation also leads us to another partial identifiability result in the case $r=3$. Third, we show how partial identifiability results can be used sequentially to guarantee the identifiability of more columns of $C$ and $S$. We illustrate these results on several examples, including one from the chemometrics literature.

When a patient is admitted to the intensive care unit (ICU) after a traumatic brain injury (TBI), an early prognosis is essential for baseline risk adjustment and shared decision making. TBI outcomes are commonly categorised by the Glasgow Outcome Scale-Extended (GOSE) into 8, ordered levels of functional recovery at 6 months after injury. Existing ICU prognostic models predict binary outcomes at a certain threshold of GOSE (e.g., prediction of survival [GOSE>1] or functional independence [GOSE>4]). We aimed to develop ordinal prediction models that concurrently predict probabilities of each GOSE score. From a prospective cohort (n=1,550, 65 centres) in the ICU stratum of the Collaborative European NeuroTrauma Effectiveness Research in TBI (CENTER-TBI) patient dataset, we extracted all clinical information within 24 hours of ICU admission (1,151 predictors) and 6-month GOSE scores. We analysed the effect of 2 design elements on ordinal model performance: (1) the baseline predictor set, ranging from a concise set of 10 validated predictors to a token-embedded representation of all possible predictors, and (2) the modelling strategy, from ordinal logistic regression to multinomial deep learning. With repeated k-fold cross-validation, we found that expanding the baseline predictor set significantly improved ordinal prediction performance while increasing analytical complexity did not. Half of these gains could be achieved with the addition of 8 high-impact predictors (2 demographic variables, 4 protein biomarkers, and 2 severity assessments) to the concise set. At best, ordinal models achieved 0.76 (95% CI: 0.74-0.77) ordinal discrimination ability (ordinal c-index) and 57% (95% CI: 54%-60%) explanation of ordinal variation in 6-month GOSE (Somers' D). Our results motivate the search for informative predictors for higher GOSE and the development of ordinal dynamic prediction models.