We present polynomial force reconstruction from experimental intermodulation atomic force microscopy (ImAFM) data. We study the tip-surface force during a slow surface approach and compare the results with amplitude-dependence force spectroscopy (ADFS). Based on polynomial force reconstruction we generate high-resolution surface-property maps of polymer blend samples. The polynomial method is d...

This paper presents computable lower bounds of the penalty parameters for stable and convergent symmetric interior penalty Galerkin methods. In particular, we derive the explicit dependence of the coercivity constants with respect to the polynomial degree and the angles of the mesh elements. Numerical examples in all dimensions and for different polynomial degrees are presented. We show the num...

We develop the first polynomial-time algorithm for co-training of homogeneous linear separators under weak dependence, a relaxation of the condition of independence given the label. Our algorithm learns from purely unlabeled data, except for a single labeled example to break symmetry of the two classes, and works for any data distribution having an inverse-polynomial margin and with center of m...

Retention behavior of molecules mostly depends on their chemical structure. Retention data of biologically active molecules could be an indirect relationship between their structure and biological or pharmacological activity, since the molecular structure affects their behavior in all pharmacokinetic stages. In the present paper, retention parameters (RM0) of biologically active 1,2-O-isopropyl...

We show that s-term DNF formulas can be learned under the uniform distribution in quasi-polynomial time with statistical queries of tolerance Ω(ε/s). The tolerance improves on the known tolerance Ω(ε/s) and is optimal with respect to its dependence on the error parameter ε. We further consider the related model of learning with proper distance queries and show that DNF formulas can be learned u...

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1 The local Whittle (or Gaussian semiparametric) estimator of long range dependence , proposed by Künsch (1987) and analyzed by Robinson (1995a), has a relatively slow rate of convergence and a finite sample bias that can be large. In this paper, we generalize the local Whittle estimator to circumvent these problems. Instead of approximating the short-run component of the spectrum, ϕ(λ) by a co...

In this paper we study algorithms for pricing of interest rate instruments using a lattice interest model. The price is defined as expected discounted cash flow. If the cash-flows generated by the instrument depend on the full or partial history of the interest rates (path dependent contracts), then the pricing algorithms are typically of exponential complexity. We show that for some models, in...

We introduce the class of strongly Rayleigh probability measures by means of geometric properties of their generating polynomials that amount to the stability of the latter. This class contains e.g. product measures, uniform random spanning tree measures, and large classes of determinantal probability measures and distributions for symmetric exclusion processes. We show that strongly Rayleigh m...

High-dimensional sparse data present computational and statistical challenges for supervised learning. We propose compact linear sketches for reducing the dimensionality of the input, followed by a single layer neural network. We show that any sparse polynomial function can be computed, on nearly all sparse binary vectors, by a single layer neural network that takes a compact sketch of the vect...