Related papers: n-dependent continuous theories and hyperdefinable…
These lecture notes provide an overview of existing methodologies and recent developments for estimation and inference with high dimensional time series regression models. First, we present main limit theory results for high dimensional…
We study the problem of learning probabilistic first-order logical rules for knowledge base reasoning. This learning problem is difficult because it requires learning the parameters in a continuous space as well as the structure in a…
We introduce the first cut-free nested sequent systems for first-order modal logics that admit increasing, decreasing, constant, and empty domains along with so-called general path conditions and seriality. We obtain such systems by means…
We characterize structures such as monotonicity, convexity, and modality in smooth regression curves using persistent homology. Persistent homology is a key tool in topological data analysis that detects higher-dimensional topological…
We investigate infinite sets that witness the failure of certain Ramsey-theoretic statements, such as Ramsey's or (appropriately phrased) Hindman's theorem; such sets may exist if one does not assume the Axiom of Choice. We obtain very…
We study two notions of being well-structured for classes of graphs that are inspired by classic model theory. A class of graphs $C$ is monadically stable if it is impossible to define arbitrarily long linear orders in vertex-colored graphs…
We address the problem of characterizing $H$-coloring problems that are first-order definable on a fixed class of relational structures. In this context, we give several characterizations of a homomorphism dualities arising in a class of…
We study the first-order consequences of Ramsey's Theorem for $k$-colourings of $n$-tuples, for fixed $n, k \ge 2$, over the relatively weak second-order arithmetic theory $\mathrm{RCA}^*_0$. Using the Chong-Mourad coding lemma, we show…
We study the model theory of expansions of Hilbert spaces by generic predicates. We first prove the existence of model companions for generic expansions of Hilbert spaces in the form first of a distance function to a random substructure,…
We consider the general problem of modeling temporal data with long-range dependencies, wherein new observations are fully or partially predictable based on temporally-distant, past observations. A sufficiently powerful temporal model…
An infinite structure has the finite length property (over a given field) if, for each of its finite powers, chains of equivariant subspaces in the corresponding free vector space are bounded in length. Prior work showed that the countable…
Multidimensional persistence has been proposed to study the persistence of topological features in data indexed by multiple parameters. In this work, we further explore its algebraic complications from the point of view of higher…
The evolution of sequence modeling architectures, from recurrent neural networks and convolutional models to Transformers and structured state-space models, reflects ongoing efforts to address the diverse temporal dependencies inherent in…
We introduce some properties describing dependence in indiscernible sequences: $F_{ind}$ and its dual $F_{Mb}$, the definable Morley property, and $n$-resolvability. Applying these properties, we establish the following results: We show…
A theoretical development is carried to establish fundamental results about rank-initial embeddings and automorphisms of countable non-standard models of set theory, with a keen eye for their sets of fixed points. These results are then…
In causal models, a given mechanism is assumed to be invariant to changes of other mechanisms. While this principle has been utilized for inference in settings where the causal variables are observed, theoretical insights when the variables…
We use fast-growing finite and infinite sequences of natural numbers and more complicated constructs to define models of hypercomputation and interpret non-arithmetic predicates, with the strongest extensions reaching full second order…
We study the problem of learning properties of nodes in tree structures. Those properties are specified by logical formulas, such as formulas from first-order or monadic second-order logic. We think of the tree as a database encoding a…
It is known that for subgraph-closed graph classes the first-order model checking problem is fixed-parameter tractable if and only if the class is nowhere dense [Grohe, Kreutzer, Siebertz, STOC 2014]. However, the dependency on the formula…
We study the expressive power of the two-variable fragment of order-invariant first-order logic. This logic departs from first-order logic in two ways: first, formulas are only allowed to quantify over two variables. Second, formulas can…