Related papers: Visible and hidden observables in super-linearizat…

The notions of $k$-separability and $k$-producibility are useful and expressive tools for the characterization of entanglement in multipartite quantum systems, when a more detailed analysis would be infeasible or simply needless. In this…

Numerous embedding models have been recently explored to incorporate semantic knowledge into visual recognition. Existing methods typically focus on minimizing the distance between the corresponding images and texts in the embedding space…

We consider the dimensions of finite type of representations of a partially ordered set, i.e. such that there is only finitely many isomorphism classes of representations of this dimension. We give a criterion for a dimension to be of…

A common problem to all applications of linear finite dynamical systems is analyzing the dynamics without enumerating every possible state transition. Of particular interest is the long term dynamical behaviour. In this paper, we study the…

While many approaches exist in the literature to learn low-dimensional representations for data collections in multiple modalities, the generalizability of multi-modal nonlinear embeddings to previously unseen data is a rather overlooked…

A majority of methods from dynamical systems analysis, especially those in applied settings, rely on Poincar\'e's geometric picture that focuses on "dynamics of states". While this picture has fueled our field for a century, it has shown…

Using geometric methods for linearizing systems of second order cubically semi-linear ordinary differential equations and third order quintically semi-linear ordinary differential equations, we extend to the fourth order by differentiating…

When a linear order has an order preserving surjection onto each of its suborders we say that it is strongly surjective. We prove that the set of countable strongly surjective linear orders is complete for the class of sets which are the…

One approach to monitoring a dynamic system relies on decomposition of the system into weakly interacting subsystems. An earlier paper introduced a notion of weak interaction called separability, and showed that it leads to exact…

Data-driven models for nonlinear dynamical systems based on approximating the underlying Koopman operator or generator have proven to be successful tools for forecasting, feature learning, state estimation, and control. It has become well…

For a general class of translationally invariant systems with a specific category of nonlinearity in the output, this paper presents necessary and sufficient conditions for global observability. Critically, this class of systems cannot be…

Neural representations are not unique objects. Even when two systems realize the same downstream computation, their hidden coordinates may differ by reparameterization. A probe family intended to reveal structure already present in a…

We demonstrate when and how an entire left-infinite orbit of an underlying dynamical system or observations from such left-infinite orbits can be uniquely represented by a pair of elements in a different space, a phenomenon which we call…

System identification is a key step for model-based control, estimator design, and output prediction. This work considers the offline identification of partially observed nonlinear systems. We empirically show that the certainty-equivalent…

In this paper, we presented a novel semi-supervised one-class classification algorithm which assumes that class is linearly separable from other elements. We proved theoretically that class is linearly separable if and only if it is maximal…

We study linear programming and general LP-type problems in several big data (streaming and distributed) models. We mainly focus on low dimensional problems in which the number of constraints is much larger than the number of variables. Low…

Koopman operators model nonlinear dynamics as a linear dynamic system acting on a nonlinear function as the state. This nonstandard state is often called a Koopman observable and is usually approximated numerically by a superposition of…

We introduce a machine-learning approach for identifying hidden structural features of open quantum dynamics under restricted experimental access. Unlike most existing data-driven methods which focus on detection or prediction of dynamical…

We study the problem of learning similarity by using nonlinear embedding models (e.g., neural networks) from all possible pairs. This problem is well-known for its difficulty of training with the extreme number of pairs. For the special…

Linear mixed models (LMMs) are used extensively to model dependecies of observations in linear regression and are used extensively in many application areas. Parameter estimation for LMMs can be computationally prohibitive on big data.…