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Learning structured task representations from human demonstrations is essential for understanding long-horizon manipulation behaviors, particularly in bimanual settings where action ordering, object involvement, and interaction geometry can…
Let $X$ be a rearrangement-invariant space over a non-atomic $\sigma$-finite measure space $(\mathscr{R},\mu)$ and let $\alpha\in(0,\infty)$. We define the functional \begin{equation*} \|f\|_{X^{\langle \alpha \rangle}} =…
Understanding the neural mechanisms behind auditory and linguistic processing is key to advancing cognitive neuroscience. In this study, we use Magnetoencephalography (MEG) data to analyze brain responses to spoken language stimuli. We…
We test whether Speech Articulatory Coding (SPARC) features can linearly predict surface electromyography (sEMG) envelopes across aloud, mimed, and subvocal speech in twenty-four subjects. Using elastic-net multivariate temporal response…
The matrix-based Renyi's \alpha-order entropy functional was recently introduced using the normalized eigenspectrum of a Hermitian matrix of the projected data in a reproducing kernel Hilbert space (RKHS). However, the current theory in the…
We present an algebraic characterization of the complexity classes Logspace and Nlogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is rooted in proof theory…
It has long been known that two-point functions of conformal field theory (CFT) are nothing but the integral kernels of intertwining operators for two equivalent representations of conformal algebra. Such intertwining operators are known to…
Performing multiple computations within the same system, without spatial or temporal separation of tasks, requires encoding multiple data items into a well-defined physical state. The most widely explored mechanism for such encoding is the…
The symplectic group Sp(n) acts on phase space while the unitary representation of its double cover, Mp(n), the metaplectic group, acts on functions defined on configuration space. We will construct an extension Mp(n) of Mp(n) acting on…
Experimental evidence indicates that simple models outperform complex deep networks on many unsupervised similarity tasks. We provide a simple yet rigorous explanation for this behaviour by introducing the concept of an optimal…
In this paper, we introduce a method called graph fusion embedding, designed for multi-graph embedding with shared vertex sets. Under the framework of supervised learning, our method exhibits a remarkable and highly desirable synergistic…
Spherical representations and functions are the building blocks for harmonic analysis on riemannian symmetric spaces. In this paper we consider spherical functions and spherical representations related to certain infinite dimensional…
A novel language system has given rise to promising alternatives to standard formal and processor network models of computation. An interstring linked with a abstract machine environment, shares sub-expressions, transfers data, and…
Language sciences rely less and less on formal syntax as their base. The reason is probably its lack of psychological reality, knowingly avoided. Philosophers of science call for a paradigm shift in which explanations are by mechanisms, as…
Eigenvalues and eigenfunctions of the volume operator, associated with the symmetric coupling of three SU(2) angular momentum operators, can be analyzed on the basis of a discrete Schroedinger-like equation which provides a semiclassical…
This article addresses structure-preserving smooth approximation of semiconcave functions. semiconcave functions are of particular interest because they naturally arise in a variety of variational problems, including {optimal feedback…
We explore asynchronous programming with algebraic effects. We complement their conventional synchronous treatment by showing how to naturally also accommodate asynchrony within them, namely, by decoupling the execution of operation calls…
We propose a generative model for a sentence that uses two latent variables, with one intended to represent the syntax of the sentence and the other to represent its semantics. We show we can achieve better disentanglement between semantic…
Syntactic parsing is the task of assigning a syntactic structure to a sentence. There are two popular syntactic parsing methods: constituency and dependency parsing. Recent works have used syntactic embeddings based on constituency trees,…
Many numerical algorithms in scientific computing -- particularly in areas like numerical linear algebra, PDE simulation, and inverse problems -- produce outputs that can be represented by semialgebraic functions; that is, the graph of the…