We discuss a number of techniques for determining the Minkowski dimension of bounded subsets of some Euclidean space of any dimension, including: the box-counting dimension and equivalent definitions based on various box-counting functions; the similarity dimension via the Moran equation (at least in the case of self-similar sets); the order of the (box-)counting function; the classic result on...

Constrained counting is important in domains ranging from artificial intelligence to software analysis. There are already a few approaches for counting models over various types of constraints. Recently, hashing-based approaches achieve both theoretical guarantees and scalability, but still rely on solution enumeration. In this paper, a new probabilistic polynomial time approximate model counte...

Let α, β,m, n be positive integers. Fix a line L : y = αx + β, and a lattice point Q = (m,n) on L. It is well known that the number of lattice paths from the origin to Q which touches L only at Q is given by β m+ n “m+ n m ” . We extend the above formula in various ways, in particular, we consider the case when α and β are arbitrary positive reals. The key ingredient of our proof is a new varia...

Understanding the number of people and the flow of the persons is useful for efficient promotion of the institution managements and company’s sales improvements. This paper introduces an automated method for counting passerby using virtualvertical measurement lines. The process of recognizing a passerby is carried out using an image sequence obtained from the USB camera. Space-time image is rep...

We propose a new interpretation of objective deterministic chances in statistical physics based on physical computational complexity. This notion applies to a single physical system (be it an experimental set– up in the lab, or a subsystem of the universe), and quantifies (1) the difficulty to realize a physical state given another, (2) the ‘distance’ (in terms of physical resources) of a physi...

We present three streaming algorithms that (2, δ)− approximate 1 the number of triangles in graphs. Similar to the previous algorithms [3], the space usage of presented algorithms are inversely proportional to the number of triangles while, for some families of graphs, the space usage is improved. We also prove a lower bound, based on the number of triangles, which indicates that our first algo...

2 Preface In distributed and parallel computing environments, there are many computational problems that require efficient communication and coordination between the processes. For such problems there have been proposed several distributed structures, each designed to solve a particular problem or a class of problems. The distributed structures take into account the particularities of the speci...

Objective: A randomized, controlled trial was performed to evaluate a computer-assisted method for counting sponges using a barcode system. Background: Retained sponges are a rare and preventable problem but persist in surgery despite standardized protocols for counting. Technology that improves detection of counting errors could reduce risk to surgical patients. Methods: We performed a randomi...