Research works

Deformations of Curves with Constant Curvature

We prove that curves of constant curvature satisfy the parametric [Formula: see text]-dense relative [Formula: see text]-principle in the space of immersed curves with nonvanishing curvature in Euclidean space [Formula: see text]. It follows that two knots of constant curvature i...

Polynomial-Augmented Neural Networks (PANNs) with Weak Orthogonality Constraints for Enhanced Function and PDE Approximation

Abstract. We present polynomial-augmented neural networks (PANNs), a novel machine learning architecture that combines deep neural networks (DNNs) with polynomial expansions. PANNs combine the strengths of DNNs (flexibility and efficiency in higher-dimensional approximation) with...

Optimal combination of composite likelihoods using approximate Bayesian computation with application to state-space models

Composite likelihood provides approximate inference when the full likelihood is intractable and sub-likelihood functions of marginal events can be evaluated relatively easily. It has been successfully applied for many complex models. However, its wider application is limited by t...

Categorical absorption of a non-isolated singularity

We study an example of a projective threefold with a non-isolated singularity and its derived category. The singular locus can be locally described as a line of surface nodes compounded with a threefold node at the origin. We construct a semiorthogonal decomposition where one com...

Filtered complexes and cohomologically equivalent subcomplexes

Inspired by Rumin’s work on a subcomplex in sub-Riemannian manifolds that is cohomologically equivalent to the de Rham complex, we present a more general construction that produces subcomplexes from any filtered cochain complex of finite depth and still computes the cohomology of...

Beyond Prediction Error: A Decision-Theoretic Model of Resistance to Belief Updating

Agents often decline to adopt revisions their own inference supports. We propose that posterior computation and belief implementation are distinct operations: Bayesian inference produces candidate revisions, and a cost-sensitive decision — an endorsement gate — determines whether...

EEG-Neurofeedback Targeting Gamma Oscillations at the Parieto-Occipital Region Reduces Pain Perception

Pain is closely associated with both spontaneous and stimulus-evoked gamma oscillations, which differ in their phenomenology and their relationship to pain perception. These associations make gamma oscillations a promising target for pain interventions, such as closed-loop real-t...

A Somatic Ontology for Computational Therapeutics: Formalizing Body-Based Experience for Digital Mental Health

The Cathexis Somatic Ontology (CSO) is a formal vocabulary and relational schema for encoding body-based therapeutic data. Its canonical name and namespace are CSO; it is registered as CXSO on NCBO BioPortal, where the acronym CSO was already taken. The two names refer to the sam...

Critical-Face Transfer and Prime Separation for Integer Circulant Determinants of Order 21

Let S(C21) denote the set of determinants of integral 21-by-21 circulantmatrices. This preprint analyzes the first nonautomatic local faces, 9m and49m, for cofactors m coprime to 21. A normalization-conductor calculationgives Pic(Z[C21]) isomorphic to C4 and determines the comple...

A Uniform Rational Critical-Face Theorem for Integer Circulant Determinants of Order 3p and the Pointwise Equivalence at Order 33

For a prime p greater than 3, this preprint compares the first locallyadmissible but globally nonautomatic critical faces 9m and p^2m for integercirculant determinants of order 3p, with m coprime to 3p. An exactnormalization-conductor calculation proves the uniform pointwise tran...

Multi types and reasonable space

Accattoli, Dal Lago, and Vanoni have recently proved that the space used by the Space KAM, a variant of the Krivine abstract machine, is a reasonable space cost model for the lambda-calculus accounting for logarithmic space, solving a longstanding open problem. In this paper, we...

Generalized Bell inequalities and frustrated spin systems

Abstract We find a close correspondence between generalized Bell inequalities (GBI’s) of a special kind and certain frustrated spin systems. For example, the Clauser–Horn–Shimony–Holt inequality corresponds to the frustrated square with the signs ++ + − for the nearest neighbor i...

Spatial qubit entanglement witness for quantum natured gravity

Abstract Witnessing the quantum nature of gravity through the entanglement of two masses has recently been proposed. Both non-Gaussian and Gaussian protocols have been shown to be useful for this purpose. In non-Gaussian protocols the complete 1/r gravitational interaction can in...

Modeling the combined effects of the 2023 Türkiye–Syria earthquake and an Atmospheric River event on landslide hazard

Abstract. The 6 February 2023 Türkiye–Syria earthquake doublet triggered thousands of coseismic landslides. On 14–15 March, an Atmospheric River (AR) delivered up to 183 mm of rainfall across the seismically weakened region, triggering hundreds of additional landslides and debris...

Questioning the Evidence for Host-Symbiont Codiversification in Mycorrhizal Symbioses

Abstract The vast majority of plants form mycorrhizal symbioses. The ecological importance of these mutualistic interactions has sparked interest in their long evolutionary history. By examining interaction networks and phylogenetic trees, several studies have suggested that plan...

Distinct cortical spatial representations learned along disparate visual pathways

Recent experimental studies have discovered diverse spatial properties, such as head direction tuning and egocentric tuning, of neurons in the postrhinal cortex (POR) and revealed how the POR spatial representation is distinct from the retrosplenial cortex (RSC). However, how the...

Loss of Quasiconvexity in the Periodic Homogenization of Viscous Hamilton–Jacobi Equations

Abstract. We show that in the periodic homogenization of uniformly elliptic Hamilton–Jacobi equations with quasiconvex Hamiltonians in arbitrary dimensions, the effective Hamiltonian is not necessarily quasiconvex. This observation is in sharp contrast with the first-order case,...

On the Lawson-Osserman conjecture

Abstract We prove that if $u : B_{1} \subset \mathbb{R}^{2} \rightarrow \mathbb{R}^{n}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>u</mml:mi> <mml:mo>:</mml:mo> <mml:msub> <mml:mi>B</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>⊂</mml:mo> <mml:msup> <mml:...

Unified framework for efficiently computable quantum circuits

Quantum circuits consisting of Clifford and matchgates are two classes of circuits that are known to be efficiently simulatable on a classical computer. We introduce a unified framework that shows in a transparent way the special structure that allows these circuits to be efficie...

Optimizing Inventory Placement for a Downstream Online Matching Problem

Problem definition: We study the inventory placement problem of splitting [Formula: see text] units of a single item across warehouses in advance of a downstream online matching problem that represents the dynamic fulfillment decisions of an e-commerce retailer. This is a challen...