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In this paper an algebraic model for unbased rational homotopy theory from the perspective of curved Lie algebras is constructed. As part of this construction a model structure for the category of pseudo-compact curved Lie algebras with…

In [3] (Rend. Lincei Mat. Appl. 26 (2015), 1-10; see also arXiv:1503.08145 [math.DS]) the following result has been announced: Theorem. Consider a real-analytic nearly-integrable mechanical system with potential $f$, namely, a Hamiltonian…

Deep artificial neural networks show high predictive performance in many fields, but they do not afford statistical inferences and their black-box operations are too complicated for humans to comprehend. Because positing that a relationship…

We show two results on higher amalgamation in the theory $\mathrm{ACFA}^{+}$, the model companion of the theory of difference fields with an additive character (added as a continuous logic predicate) on the fixed field in characteristic 0.…

We give an explicit example of a fibration $f \colon X \to Y$ between smooth projective varieties whose "orbifold base" $\Delta_f$ in the sense of Campana has the property that the induced morphism $X \to (Y, \Delta_f)$ is not a morphism of…

We show that there is a special bijection between the indecomposable summands of the two modules which form a basic support $\tau$--tilting pair and the indecomposable summands of the two modules which form another basic support…

Homotopy type theory is an interpretation of Martin-L\"of's constructive type theory into abstract homotopy theory. There results a link between constructive mathematics and algebraic topology, providing topological semantics for…

Large language models (LLMs) enable increasingly capable tutoring-style conversational agents, yet effective tutoring requires sensitivity to learners' affective and cognitive states beyond text alone. Facial expressions provide immediate…

Deep learning models in computer vision have made remarkable progress, but their lack of transparency and interpretability remains a challenge. The development of explainable AI can enhance the understanding and performance of these models.…

The class of local languages is a well-known subclass of the regular languages that admits many equivalent characterizations. In this short note we establish the PSPACE-completeness of the problem of determining, given as input a…

Let $A$ be the one point extension of an algebra $B$ by a projective $B$-module. We prove that the extension of a given support $\tau$-tilting $B$-module is a support $\tau$-tilting $A$-module; and, conversely, the restriction of a given…

Many unconventional computing models, including some that appear to be quite different from traditional ones such as Turing machines, happen to characterise either the complexity class P or PSPACE when working in deterministic polynomial…

We propose a type-based analysis to infer the session protocols of channels in an ML-like concurrent functional language. Combining and extending well-known techniques, we develop a type-checking system that separates the underlying ML type…

We propose MToMnet - a Theory of Mind (ToM) neural network for predicting beliefs and their dynamics during human social interactions from multimodal input. ToM is key for effective nonverbal human communication and collaboration, yet,…

What structural inductive bias helps transformers reason over knowledge graphs? Through controlled ablations of a minimal transformer modification with four independently removable components (sparse adjacency masking, edge-type biases,…

We prove in ZF that there is an inner product space, in fact, nicely definable with no orthonormal basis.

We present a type system for an extension of lambda calculus with a conditional construction, named STAB, that characterizes the PSPACE class. This system is obtained by extending STA, a type assignment for lambda-calculus inspired by…

We prove the non-abelian Poincare lemma in higher gauge theory in two different ways. The first method uses a result by Jacobowitz which states solvability conditions for differential equations of a certain type. The second method extends a…

Gregory McColm conjectured that positive elementary inductions are bounded in a class K of finite structures if every (FO + LFP) formula is equivalent to a first-order formula in K. Here (FO + LFP) is the extension of first-order logic with…

Probabilistic programming provides the means to represent and reason about complex probabilistic models using programming language constructs. Even simple probabilistic programs can produce models with infinitely many variables. Factored…