Related papers: Spatial Interpolants
Interpolation based software model checkers have been successfully employed to automatically prove programs correct. Their power comes from interpolating SMT solvers that check the feasibility of potential counterexamples and compute…
Nonlinear interpolants have been shown useful for the verification of programs and hybrid systems in contexts of theorem proving, model checking, abstract interpretation, etc. The underlying synthesis problem, however, is challenging and…
In areas such as kernel smoothing and non-parametric regression there is emphasis on smooth interpolation and smooth statistical models. Splines are known to have optimal smoothness properties in one and higher dimensions. It is shown, with…
Interpolation of jointly infeasible predicates plays important roles in various program verification techniques such as invariant synthesis and CEGAR. Intrigued by the recent result by Dai et al.\ that combines real algebraic geometry and…
Data sites selected from modeling high-dimensional problems often appear scattered in non-paternalistic ways. Except for sporadic clustering at some spots, they become relatively far apart as the dimension of the ambient space grows. These…
Editing materials of objects in images based on exemplar images is an active area of research in computer vision and graphics. We propose MARBLE, a method for performing material blending and recomposing fine-grained material properties by…
We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…
Analyzing and verifying heap-manipulating programs automatically is challenging. A key for fighting the complexity is to develop compositional methods. For instance, many existing verifiers for heap-manipulating programs require…
A spatially varying blur kernel $h(\mathbf{x},\mathbf{u})$ is specified by an input coordinate $\mathbf{u} \in \mathbb{R}^2$ and an output coordinate $\mathbf{x} \in \mathbb{R}^2$. For computational efficiency, we sometimes write…
Sparse shrunk additive models and sparse random feature models have been developed separately as methods to learn low-order functions, where there are few interactions between variables, but neither offers computational efficiency. On the…
Abstraction is a successful technique in software verification, and interpolation on infeasible error paths is a successful approach to automatically detect the right level of abstraction in counterexample-guided abstraction refinement.…
The use of unitary invariant subspaces of a Hilbert space $\mathcal{H}$ is nowadays a recognized fact in the treatment of sampling problems. Indeed, shift-invariant subspaces of $L^2(\mathbb{R})$ and also periodic extensions of finite…
Observations made in continuous time are often irregular and contain the missing values across different channels. One approach to handle the missing data is imputing it using splines, by fitting the piecewise polynomials to the observed…
We investigate the question of studying spectral clustering in a Hilbert space where the set of points to cluster are drawn i.i.d. according to an unknown probability distribution whose support is a union of compact connected components. We…
Despite the recent progress of automated program verification techniques, fully automated verification of programs manipulating recursive data structures remains a challenge. We introduce solvable tuple patterns (STPs) and conjunctive STPs…
Symmetries in mixed-integer (nonlinear) programs (MINLP), if not handled appropriately, are known to negatively impact the performance of (spatial) branch-and-bound algorithms. Usually one thus tries to remove symmetries from the problem…
Preserving data confidentiality in clouds is a key issue. Secret Sharing, a cryptographic primitive for the distribution of a secret among a group of $n$ participants designed so that only subsets of shareholders of cardinality $0 < t \leq…
In the field of chemistry, there have been many attempts to predict the properties of unknown compounds from statistical models constructed using machine learning. In an area where many known compounds are present (the interpolation area),…
Spline interpolation is a widely used class of methods for solving interpolation problems by constructing smooth interpolants that minimize a regularized energy functional involving the Laplacian operator. While many existing approaches…
Kernel interpolation is a fundamental technique for approximating functions from scattered data, with a well-understood convergence theory when interpolating elements of a reproducing kernel Hilbert space. Beyond this classical setting,…