Related papers: Module Theorem for The General Theory of Stable Mo…
We show that a persistence module (for a totally ordered indexing set) consisting of finite-dimensional vector spaces is a direct sum of interval modules. The result extends to persistence modules with the descending chain condition on…
We classify localising subcategories of the stable module category of a finite group that are closed under tensor product with simple (or, equivalently all) modules. One application is a proof of the telescope conjecture in this context.…
This paper introduces a fundamental result, which is relevant for Answer Set programming, and planning. For the first time since the definition of the stable model semantics, the class of logic programs for which a stable model exists is…
Over the last couple of decades, there has been a considerable effort devoted to the problem of updating logic programs under the stable model semantics (a.k.a. answer-set programs) or, in other words, the problem of characterising the…
Recently Ferraris, Lee and Lifschitz proposed a new definition of stable models that does not refer to grounding, which applies to the syntax of arbitrary first-order sentences. We show its relation to the idea of loop formulas with…
We prove that applying a projective functor to a holonomic simple module over a semi-simple finite dimensional complex Lie algebra produces a module that has an essential semi-simple submodule of finite length. This implies that holonomic…
This paper concerns a generalization of the Rees algebra of ideals due to Eisenbud, Huneke and Ulrich that works for any finitely generated module over a noetherian ring. Their definition is in terms of maps to free modules. We give an…
Linear Software Models is a systematic effort to formulate a theory of software systems neatly based upon standard mathematics, viz. linear algebra. It has appeared in a series of papers dealing with various aspects of the theory. But one…
In this work, we explore the application of modulus in matroid theory, specifically, the modulus of the family of bases of matroids. This study not only recovers various concepts in matroid theory, including the strength, fractional…
It has been hypothesized that some form of "modular" structure in artificial neural networks should be useful for learning, compositionality, and generalization. However, defining and quantifying modularity remains an open problem. We cast…
We introduce layers to modal type theories, which subsequently enables type theories for pattern matching on code in meta-programming and clean and straightforward semantics.
The fine-tuning of deep pre-trained models has revealed compositional properties, with multiple specialized modules that can be arbitrarily composed into a single, multi-task model. However, identifying the conditions that promote…
Structural modularity is a pervasive feature of biological neural networks, which have been linked to several functional and computational advantages. Yet, the use of modular architectures in artificial neural networks has been relatively…
Aggregation functions are widely used in answer set programming for representing and reasoning on knowledge involving sets of objects collectively. Current implementations simplify the structure of programs in order to optimize the overall…
In this paper, we first introduce and study the notion of random Chebyshev centers. Further, based on the recently developed theory of stable sets, we introduce the notion of random complete normal structure so that we can prove the two…
Methods for learning Bayesian network structure can discover dependency structure between observed variables, and have been shown to be useful in many applications. However, in domains that involve a large number of variables, the space of…
While decomposition of one-parameter persistence modules behaves nicely, as demonstrated by the algebraic stability theorem, decomposition of multiparameter modules is known to be unstable in a certain precise sense. Until now, it has not…
We prove an induction theorem for the higher algebraic K-groups of group algebras $kG$ of finite groups $G$ over characteristic $p$ finite fields $k$. For a certain class of finite groups, which we call $p$-isolated, this reduces…
In this paper, a decomposition theorem for (covariant) unitary group representations on Kaplansky-Hilbert modules over Stone algebras is established, which generalizes the well-known Hilbert space case (where it coincides with the…
Modular programming is a development paradigm that emphasizes self-contained, flexible, and independent pieces of functionality. This practice allows new features to be seamlessly added when desired, and unwanted features to be removed,…