Local spatio-temporal features are popular in the human action recognition task. In practice, they are usually coupled with a feature encoding approach, which helps to obtain the video-level vector representations that can be used in learning and recognition. In this paper, we present an efficient local feature encoding approach, which is called Approximate Sparse Coding (ASC). ASC computes the...

The ε-approximate degree of a Boolean function f : {−1, 1} → {−1, 1} is the minimum degree of a real polynomial that approximates f to within ε in the `∞ norm. We prove several lower bounds on this important complexity measure by explicitly constructing solutions to the dual of an appropriate linear program. Our first result resolves the ε-approximate degree of the two-level AND-OR tree for any...

From very early in life, humans can approximate the number and surface area of objects in a scene. The ability to discriminate between 2 approximate quantities, whether number or area, critically depends on the ratio between the quantities, with the most difficult ratio that a participant can reliably discriminate known as the Weber fraction. While developmental improvements in the Weber fracti...

The classical condition number is a very rough measure of the effect of perturbations on the inverse of a square matrix. First, it assumes that the perturbation is infinitesimally small. Second, it does not take into account the perturbation structure (e.g., Vandermonde). Similarly, the classical notion of the inverse of a matrix neglects the possibility of large, structured perturbations. We d...

We introduce a method for making approximate Bayesian inference based on quantizing the hypothesis space and repartitioning it as observations become available. The method relies on approximating an optimal inference by using a probability distribution for quantized intervals of the unknown quantity, and by adjusting the intervals so as to obtain higher resolution in regions of higher probabili...

We argue that the optimization of a quantum process based on customarily used fidelity between actual and expected outputs may not be sufficient. introduce quantity namely “quantum randomness”, which is standard deviation distribution Born probabilities corresponding to orthonormal measurement projects output onto eigenstates output, obtain trade-off randomness for an arbitrary process. conside...

The main purpose of this paper is to study the approximate best proximity pair of cyclic maps and their diameter in fuzzy normed spaces defined by Bag and Samanta. First, approximate best point proximity points on fuzzy normed linear spaces are defined and four general lemmas are given regarding approximate fixed point and approximate best proximity pair of cyclic maps on fuzzy normed spaces. U...

Quantity plays an important role in the analysis of a wide variety of phonological and morphological phenomena in many languages including the analysis of word stress, tone, compensatory lengthening, shortening processes, minimal word requirements, templatic restrictions and allomorphy selection. These phenomena frequently distinguish between syllables that are short (or light) from those that ...