Quarrying and Sustainability during Urbanazion: Gebze District Case

The requirement of construction materials increases along with the developing urbanization. Despite the most of quarries are established in rural or semi rural areas, their locations remain in or close to the urban areas in parallel with the expansion of residential areas in proportion to the rate of urbanization. Continuing population growth, social, industrial and economic developments require more construction materials. Gebze region uses approximately 8,000,000 tons of aggregate per year for construction sector. The present quarries are planned to be abandoned in the following years. Regardless of potential problems, it is important for planning to estimate future recources. Nowadays there are public housing, organized industrial zones and highway projects at planning and construction stages. Nevertheless, Ballıkayalar National Park is close to likely potential material quarries. By avoiding the national park area, the availability and the quality of materials should be established at an early stage, as material production and transportation costs can be an important consideration when selecting a design solution.

Order-unit-metric spaces

We study the concept of cone metric space in the context of ordered vector spaces by setting up a general and natural framework for it.Comment: 10 page

Randomized Sketches of Convex Programs with Sharp Guarantees

Random projection (RP) is a classical technique for reducing storage and computational costs. We analyze RP-based approximations of convex programs, in which the original optimization problem is approximated by the solution of a lower-dimensional problem. Such dimensionality reduction is essential in computation-limited settings, since the complexity of general convex programming can be quite high (e.g., cubic for quadratic programs, and substantially higher for semidefinite programs). In addition to computational savings, random projection is also useful for reducing memory usage, and has useful properties for privacy-sensitive optimization. We prove that the approximation ratio of this procedure can be bounded in terms of the geometry of constraint set. For a broad class of random projections, including those based on various sub-Gaussian distributions as well as randomized Hadamard and Fourier transforms, the data matrix defining the cost function can be projected down to the statistical dimension of the tangent cone of the constraints at the original solution, which is often substantially smaller than the original dimension. We illustrate consequences of our theory for various cases, including unconstrained and $\ell_1$-constrained least squares, support vector machines, low-rank matrix estimation, and discuss implications on privacy-sensitive optimization and some connections with de-noising and compressed sensing

An Efficient Formula Synthesis Method with Past Signal Temporal Logic

In this work, we propose a novel method to find temporal properties that lead to the unexpected behaviors from labeled dataset. We express these properties in past time Signal Temporal Logic (ptSTL). First, we present a novel approach for finding parameters of a template ptSTL formula, which extends the results on monotonicity based parameter synthesis. The proposed method optimizes a given monotone criteria while bounding an error. Then, we employ the parameter synthesis method in an iterative unguided formula synthesis framework. In particular, we combine optimized formulas iteratively to describe the causes of the labeled events while bounding the error. We illustrate the proposed framework on two examples.Comment: 8 pages, 5 figures, conference pape

Heuristic Analysis of Time Series Internal Structure

A method of analysis of Time Series Internal Structures based on Singular Spectrum Analysis is discussed. It has been shown that in the case when the Time Series contains deterministic additive components rank of the trajectory matrices equal to number of parameters of the components. Also it was proved that both eigen and factor vectors repeat shapes of the additive components and both eigen values and eigen vectors can be divided into additive groups. Some useful patterns of deterministic components were identified, which permit to provide graphical analysis of times series Internal Structures.Singular spectrum Analysis, Time series decomposition, Singular vectors, singular values, deterministic additive components, patterns