Curvatures of the Melnikov type, Hausdorff dimension, rectifiability, and singular integrals on R-n

One of the most fundamental steps leading to the solution of the analytic capacity problem ( for 1-sets) was the discovery by Melnikov of an identity relating the sum of permutations of products of the Cauchy kernel to the three-point Menger curvature. We here undertake the study of analogues of this so-called Menger-Melnikov curvature, as a nonnegative function defined on certain copies of R-n, in relation to some natural singular integral operators on subsets of R-n of various Hausdorff dimensions. In recent work we proved that the Riesz kernels x\x\(-m-1) (m is an element of N\ {1}) do not admit identities like that of Melnikov in any L-k norm (k is an element of N). In this paper we extend these investigations in various ways. Mainly, we replace the Euclidean norm \.\ by equivalent metrics delta(., .) and we consider all possible k, m, n, delta(., .). We do this in hopes of finding better algebraic properties which may allow extending the ideas to higher dimensional sets. On the one hand, we show that for m > 1 no such identities are admissible at least when is a norm that is invariant under reflections and permutations of the coordinates. On the other hand, for m = 1, we show that for each choice of metric, one gets an identity and a curvature like those of Melnikov. This allows us to generalize those parts of the recent singular integral and recti ability theories for the Cauchy kernel that depend on curvature to these much more general kernels, and provides a more general framework for the curvature approach

Three-dimensional surface grid generation for calculation of thermal radiation shape factors

A technique is described to generate three dimensional surface grids suitable for calculating shape factors for thermal radiative heat transfer. The surface under consideration is approximated by finite triangular elements generated in a special manner. The grid is generated by dividing the surface into a two dimensional array of nodes. Each node is defined by its coordinates. Each set of four adjacent nodes is used to construct two triangular elements. Each triangular element is characterized by the vector representation of its vertices. Vector algebra is used to calculate all desired geometric properties of grid elements. The properties are used to determine the shape factor between the element and an area element in space. The grid generation can be graphically displayed using any software with three dimensional features. DISSPLA was used to view the grids

Predicting protein-protein interactions as a one-class classification problem

Protein-protein interactions represent a key step in understanding proteins functions. This is due to the fact that proteins usually work in context of other proteins and rarely function alone. Machine learning techniques have been used to predict protein-protein interactions. However, most of these techniques address this problem as a binary classification problem. While it is easy to get a dataset of interacting protein as positive example, there is no experimentally confirmed non-interacting protein to be considered as a negative set. Therefore, in this paper we solve this problem as a one-class classification problem using One-Class SVM (OCSVM). Using only positive examples (interacting protein pairs) for training, the OCSVM achieves accuracy of 80%. These results imply that protein-protein interaction can be predicted using one-class classifier with reliable accuracy

Green Fluorescent Protein (GFP) in Vector Systems Played Sense Role of Epigenetic in Plants

The green fluorescent protein (GFP) of jellyfish (_Aequorea victoria_) has significant advantages over other reporter genes, because expression can be detected in living cells without any substrates. Recently, epigenetic phenomena are important to consider in plant biotechnology experiments for elucidate unknown mechanism. Therefore, soybean immature cotyledons were generated embryogenesis cells and engineered with two different gene constructs (pHV and pHVS) using gene gun method. Both constructs contain a gene conferring resistance to hygromycin (_hpt_) as a selective marker and a modified glycinin (11S globulin) gene (_V3-1_) as a target. However, sGFP(_S65T_) as a reporter gene was used only in pHVS as a reporter gene for study the relation between using sGFP(_S65T_) and gene silencing phenomena. Fluorescence microscopic was used for screening after the selection of hygromycin, identified clearly the expression of sGFP(_S65T_) in the transformed soybean embryos bombarded with the pHVS construct. Protein analysis was used to detect gene expression overall seeds using SDS-PAGE. Percentage of gene down regulation was highly in pHV construct compared with pHVS. Thus, sGFP(_S65T_) as a reporter gene in vector system may be play useful role for transgenic evaluation and avoid gene silencing in plants for the benefit of plant transformation system

The Riesz kernels do not give rise to higher dimensional analogues of the Menger-Melnikov curvature

Ever since the discovery of the connection between the Menger-Melnikov curvature and the Cauchy kernel in the L2 norm, and its impressive utility in the analytic capacity problem, higher dimensional analogues have been coveted. The lesson from 1-sets was that any such (nontrivial, nonnegative) expression, using the Riesz kernels for m-sets in Rn , even in any Lk norm (k [member] N), would probably carry nontrivial information on whether the boundedness of these kernels in the appropriate norm implies rectifiability properties of the underlying sets or measures. Answering such questions would also have an impact on another important problem, namely whether totally unrectifiable m-sets are removable for Lipschitz harmonic functions in Rm+1. It has generally been believed that some such expressions should exist at least for some choices of m, k, or n, but the apparent complexity involved made the search rather difficult, even with the aid of computers. However, our rather surprising result is that, in fact, not a single higher dimensional analogue of this useful curvature can be derived from the Riesz kernels in the same fashion, and that, even for 1-sets, the Menger-Melnikov curvature is unique in a certain sense

Unrectifiable 1-Sets with Moderate Essential Flatness Satisfy Besicovitch's 12-Conjecture

AbstractIn this paper we show that for a wide class of totally unrectifiable 1-sets in the plane (or even a Hilbert space) satisfying a mild measure-theoretic flatness condition almost everywhere, at sufficiently small scales, the lower spherical density is bounded above by 12 at almost every point, thereby affirming Besicovitch's conjecture, which states that for all totally unrectifiable 1-sets in the plane (or possibly even in Rn, or a Hilbert space), the lower spherical density is bounded above by 12 at almost every point

THE ANALYSIS OF URBAN CONCENTRATION AND DECENTRALIZATION IN EGYPT: CASE STUDY OF PORT SAID GOVERNORATE.

The structural spatial imbalances in Egypt have received considerable attention in recent years. Discussions have been characterized by both a focus towards the importance of the exploitation of the competitive advantages of regions and the reduction of socio-economic disparities by directing development towards backward regions. Those two opinions are drawing attention towards the need for an in-depth analysis of concentration and decentralization policies and their impacts on the land use distribution. This paper analyzes the urban growth scenarios in Port Said governorate within a framework of a decentralized concentration approach for the allocation of economic activities. The purpose of this approach is to support the preparation of a spatial and socio-economic plan that could assist in closing the gap between the rural/urban inequalities and socioeconomic disparities. The analysis of urban growth in Port Said area reveals that there is a strong need to create new employment centers along new transportation corridors to create polycentric regions, each functioning as an integrated socio-economic system that is formally independent from the others, yet connected and concentrated. Meanwhile, rural development has to be promoted as independent functional units that form an agropolitan system. It is concluded that the combination of urban polycentrism and rural concentrated decentralization could present a solution to the unmanaged urban growth on arable land, rural to urban migration and the low quality of life at the urban fringes of the main urban centers

Detecting, Modeling, and Predicting User Temporal Intention

The content of social media has grown exponentially in the recent years and its role has evolved from narrating life events to actually shaping them. Unfortunately, content posted and shared in social networks is vulnerable and prone to loss or change, rendering the context associated with it (a tweet, post, status, or others) meaningless. There is an inherent value in maintaining the consistency of such social records as in some cases they take over the task of being the first draft of history as collections of these social posts narrate the pulse of the street during historic events, protest, riots, elections, war, disasters, and others as shown in this work. The user sharing the resource has an implicit temporal intent: either the state of the resource at the time of sharing, or the current state of the resource at the time of the reader \clicking . In this research, we propose a model to detect and predict the user\u27s temporal intention of the author upon sharing content in the social network and of the reader upon resolving this content. To build this model, we first examine the three aspects of the problem: the resource, time, and the user. For the resource we start by analyzing the content on the live web and its persistence. We noticed that a portion of the resources shared in social media disappear, and with further analysis we unraveled a relationship between this disappearance and time. We lose around 11% of the resources after one year of sharing and a steady 7% every following year. With this, we turn to the public archives and our analysis reveals that not all posted resources are archived and even they were an average 8% per year disappears from the archives and in some cases the archived content is heavily damaged. These observations prove that in regards to archives resources are not well-enough populated to consistently and reliably reconstruct the missing resource as it existed at the time of sharing. To analyze the concept of time we devised several experiments to estimate the creation date of the shared resources. We developed Carbon Date, a tool which successfully estimated the correct creation dates for 76% of the test sets. Since the resources\u27 creation we wanted to measure if and how they change with time. We conducted a longitudinal study on a data set of very recently-published tweet-resource pairs and recording observations hourly. We found that after just one hour, ~4% of the resources have changed by ≥30% while after a day the change rate slowed to be ~12% of the resources changed by ≥40%. In regards to the third and final component of the problem we conducted user behavioral analysis experiments and built a data set of 1,124 instances manually assigned by test subjects. Temporal intention proved to be a difficult concept for average users to understand. We developed our Temporal Intention Relevancy Model (TIRM) to transform the highly subjective temporal intention problem into the more easily understood idea of relevancy between a tweet and the resource it links to, and change of the resource through time. On our collected data set TIRM produced a significant 90.27% success rate. Furthermore, we extended TIRM and used it to build a time-based model to predict temporal intention change or steadiness at the time of posting with 77% accuracy. We built a service API around this model to provide predictions and a few prototypes. Future tools could implement TIRM to assist users in pushing copies of shared resources into public web archives to ensure the integrity of the historical record. Additional tools could be used to assist the mining of the existing social media corpus by derefrencing the intended version of the shared resource based on the intention strength and the time between the tweeting and mining