Palantir, co-founded by the billionaire Donald Trump donor Peter Thiel (pictured), has been appointed for a three-month trial period. Palantir, co-founded by the billionaire Donald Trump donor Peter Thiel (pictured), has been appointed for a three-month trial period. Sun 22 Mar 2026 12.00 EDTLast modified on Sun 22 Mar 2026 22.30 EDT Palantir is to be granted access to a trove of highly sensitive UK financial regulation data, in a deal that has prompted fresh concerns about the US AI companyâ s deepening reach into the British state, the Guardian can reveal. The Financial Conduct Authority (FCA) has awarded Palantir a contract to investigate the watchdogâ s internal intelligence data in an effort to help it tackle financial crime, which includes investigating fraud, money laundering and insider trading. The Miami-based company, co-founded by the billionaire Donald Trump donor Peter Thiel, has been appointed for a three-month trial, paying more than £30,000 a week to analyse the FCAâ s vast â data lakeâ, which could lead to a full procurement of an AI system.

Formal Concept Analysis (FCA) is a mathematical framework for knowledge representation and discovery. It performs a hierarchical clustering over a set of objects described by attributes, resulting in conceptual structures in which objects are organized depending on the attributes they share. These conceptual structures naturally highlight commonalities and variabilities among similar objects by categorizing them into groups which are then arranged by similarity, making it particularly appropriate for variability extraction and analysis. Despite the potential of FCA, determining which of its properties can be leveraged for variability-related tasks (and how) is not always straightforward, partly due to the mathematical orientation of its foundational literature. This paper attempts to bridge part of this gap by gathering a selection of properties of the framework which are essential to variability analysis, and how they can be used to interpret diverse variability information within the resulting conceptual structures.

Algorithmic fairness in clustering aims to balance the proportions of instances assigned to each cluster with respect to a given sensitive attribute. While recently developed fair clustering algorithms optimize clustering objectives under specific fairness constraints, their inherent complexity or approximation often results in suboptimal clustering utility or numerical instability in practice. To resolve these limitations, we propose a new fair clustering algorithm based on a novel decomposition of the fair $K$-means clustering objective function. The proposed algorithm, called Fair Clustering via Alignment (FCA), operates by alternately (i) finding a joint probability distribution to align the data from different protected groups, and (ii) optimizing cluster centers in the aligned space. A key advantage of FCA is that it theoretically guarantees approximately optimal clustering utility for any given fairness level without complex constraints, thereby enabling high-utility fair clustering in practice. Experiments show that FCA outperforms existing methods by (i) attaining a superior trade-off between fairness level and clustering utility, and (ii) achieving near-perfect fairness without numerical instability.

Defeasible conditionals are a form of non-monotonic inference which enable the expression of statements like "if $ϕ$ then normally $ψ$". The KLM framework defines a semantics for the propositional case of defeasible conditionals by construction of a preference ordering over possible worlds. The pattern of reasoning induced by these semantics is characterised by consequence relations satisfying certain desirable properties of non-monotonic reasoning. In FCA, implications are used to describe dependencies between attributes. However, these implications are unsuitable to reason with erroneous data or data prone to exceptions. Until recently, the topic of non-monotonic inference in FCA has remained largely uninvestigated. In this paper, we provide a construction of the KLM framework for defeasible reasoning in FCA and show that this construction remains faithful to the principle of non-monotonic inference described in the original framework. We present an additional argument that, while remaining consistent with the original ideas around non-monotonic reasoning, the defeasible reasoning we propose in FCA offers a more contextual view on inference, providing the ability for more relevant conclusions to be drawn when compared to the propositional case.

Automating the extraction of concept hierarchies from free text is advantageous because manual generation is frequently labor- and resource-intensive. Free result, the whole procedure for concept hierarchy learning from free text entails several phases, including sentence-level text processing, sentence splitting, and tokenization. Lemmatization is after formal context analysis (FCA) to derive the pairings. Nevertheless, there could be a few uninteresting and incorrect pairings in the formal context. It may take a while to generate formal context; thus, size reduction formal context is necessary to weed out irrelevant and incorrect pairings to extract the concept lattice and hierarchies more quickly. This study aims to propose a framework for reducing formal context in extracting concept hierarchies from free text to reduce the ambiguity of the formal context. We achieve this by reducing the size of the formal context using a hybrid of a WordNet-based method and a frequency-based technique. Using 385 samples from the Wikipedia corpus and the suggested framework, tests are carried out to examine the reduced size of formal context, leading to concept lattice and concept hierarchy. With the help of concept lattice-invariants, the generated formal context lattice is compared to the normal one. In contrast to basic ones, the homomorphic between the resultant lattices retains up to 98% of the quality of the generating concept hierarchies, and the reduced concept lattice receives the structural connection of the standard one. Additionally, the new framework is compared to five baseline techniques to calculate the running time on random datasets with various densities. The findings demonstrate that, in various fill ratios, hybrid approaches of the proposed method outperform other indicated competing strategies in concept lattice performance.

Likewise, the current trend is to produce new resources in a digital format (e.g., in the context of social networks), which entails an in-depth paradigm shift in almost all the humanistic, social, scientific and technological fields. In particular, the field of the humanities is one which is going through a significant transformation as a result of these digitalization efforts and the paradigm shift associated with the digital age. Indeed, we are witnessing the emergence of a whole host of disciplines, those of Digital Humanities (Berry 2012), which are closely dependent on the production and proper organization of digital collections. As a result of the undoubted importance of digital collections in modern society, the search for effective and efficient methods to carry out the production, preservation and enhancement of such digital collections has become a key challenge in modern society (Calhoun, 2013). In particular, the annotation of resources with metadata that enables their proper cataloging, search, retrieval and use in different application scenarios is one of the key elements to ensuring the profitability of these collections of digital objects.

Formal Concept Analysis (FCA) is an approach to creating a conceptual hierarchy in which a \textit{concept lattice} is generated from a \textit{formal context}. That is, a triple consisting of a set of objects, $G$, a set of attributes, $M$, and an incidence relation $I$ on $G \times M$. A \textit{concept} is then modelled as a pair consisting of a set of objects (the \textit{extent}), and a set of shared attributes (the \textit{intent}). Implications in FCA describe how one set of attributes follows from another. The semantics of these implications closely resemble that of logical consequence in classical logic. In that sense, it describes a monotonic conditional. The contributions of this paper are two-fold. First, we introduce a non-monotonic conditional between sets of attributes, which assumes a preference over the set of objects. We show that this conditional gives rise to a consequence relation that is consistent with the postulates for non-monotonicty proposed by Kraus, Lehmann, and Magidor (commonly referred to as the KLM postulates). We argue that our contribution establishes a strong characterisation of non-monotonicity in FCA. Typical concepts represent concepts where the intent aligns with expectations from the extent, allowing for an exception-tolerant view of concepts. To this end, we show that the set of all typical concepts is a meet semi-lattice of the original concept lattice. This notion of typical concepts is a further introduction of KLM-style typicality into FCA, and is foundational towards developing an algebraic structure representing a concept lattice of prototypical concepts.

Relational concept analysis (RCA) is an extension of formal concept analysis allowing to deal with several related contexts simultaneously. It has been designed for learning description logic theories from data and used within various applications. A puzzling observation about RCA is that it returns a single family of concept lattices although, when the data feature circular dependencies, other solutions may be considered acceptable. The semantics of RCA, provided in an operational way, does not shed light on this issue. In this report, we define these acceptable solutions as those families of concept lattices which belong to the space determined by the initial contexts (well-formed), cannot scale new attributes (saturated), and refer only to concepts of the family (self-supported). We adopt a functional view on the RCA process by defining the space of well-formed solutions and two functions on that space: one expansive and the other contractive. We show that the acceptable solutions are the common fixed points of both functions. This is achieved step-by-step by starting from a minimal version of RCA that considers only one single context defined on a space of contexts and a space of lattices. These spaces are then joined into a single space of context-lattice pairs, which is further extended to a space of indexed families of context-lattice pairs representing the objects manippulated by RCA. We show that RCA returns the least element of the set of acceptable solutions. In addition, it is possible to build dually an operation that generates its greatest element. The set of acceptable solutions is a complete sublattice of the interval between these two elements. Its structure and how the defined functions traverse it are studied in detail.

We quantify the impact of thermo-optic and free-carrier effects on time-delay reservoir computing using a silicon microring resonator. We identify pump power and frequency detuning ranges with NMSE less than 0.05 for the NARMA-10 task depending on the time constants of the two considered effects.

This article is the second in a series on areas impacted by AI. It focuses on the upcoming implementation of a new Consumer Duty, a higher standard of behaviour for financial services firms directly or indirectly interacting with retail customers in the UK. The article explores the potential benefits and associated risks of financial services firms' increasing reliance on AI. This article is the second in a series on the range of regulations and legal areas impacted by artificial intelligence (AI) and machine learning. We previously published an article analyzing the recent discussion paper (DP5/22) published by the Bank of England, PRA and FCA on AI and machine learning.