Computer-Based Validation of 3n+1 Hypothesis for Numbers 3n−1

The formulation of the 3n−1 problem is simple but no one has found the solution yet. This paper transforms the original problem into its equivalent so that it becomes more suitable for computer validation. A new algorithm is proposed and implemented. The hypothesis is tested and proven to be valid for numbers 3n−1, conclusive with number 332768−1

A New Rymon Tree Based Procedure for Mining Statistically Significant Frequent Itemsets

In this paper we suggest a new method for frequent itemsets mining, which is more efficient than well known Apriori algorithm. The method is based on special structure called Rymon tree. For its implementation, we suggest modified sort-merge-join algorithm. Finally, we explain how support measure, which is used in Apriori algorithm, gives statistically significant frequent itemsets

On the Number of Candidates in Apriori Like Algorithms for Mining Frequent Itemsets

Frequent itemset mining has been a focused theme in data mining research for years. It was first proposed for market basket analysis in the form of association rule mining. Since the first proposal of this new data mining task and its associated efficient mining algorithms, there have been hundreds of follow-up research publications. In this paper we further develop the ideas from our previous work where we consider two problems from linear algebra, namely set intersection problem and scalar product problem, and make comparisons to the frequent itemset mining task. In this paper we formulate and prove new theorems that estimate the number of candidate itemsets that can be generated in the level-wise mining approach

ILC Reference Design Report Volume 1 - Executive Summary

The International Linear Collider (ILC) is a 200-500 GeV center-of-mass high-luminosity linear electron-positron collider, based on 1.3 GHz superconducting radio-frequency (SCRF) accelerating cavities. The ILC has a total footprint of about 31 km and is designed for a peak luminosity of 2x10^34 cm^-2s^-1. This report is the Executive Summary (Volume I) of the four volume Reference Design Report. It gives an overview of the physics at the ILC, the accelerator design and value estimate, the detector concepts, and the next steps towards project realization.The International Linear Collider (ILC) is a 200-500 GeV center-of-mass high-luminosity linear electron-positron collider, based on 1.3 GHz superconducting radio-frequency (SCRF) accelerating cavities. The ILC has a total footprint of about 31 km and is designed for a peak luminosity of 2x10^34 cm^-2s^-1. This report is the Executive Summary (Volume I) of the four volume Reference Design Report. It gives an overview of the physics at the ILC, the accelerator design and value estimate, the detector concepts, and the next steps towards project realization

International Linear Collider Reference Design Report Volume 2: PHYSICS AT THE ILC

This article reviews the physics case for the ILC. Baseline running at 500 GeV as well as possible upgrades and options are discussed. The opportunities on Standard Model physics, Higgs physics, Supersymmetry and alternative theories beyond the Standard Model are described.This article reviews the physics case for the ILC. Baseline running at 500 GeV as well as possible upgrades and options are discussed. The opportunities on Standard Model physics, Higgs physics, Supersymmetry and alternative theories beyond the Standard Model are described

ILC Reference Design Report Volume 4 - Detectors

This report, Volume IV of the International Linear Collider Reference Design Report, describes the detectors which will record and measure the charged and neutral particles produced in the ILC's high energy e+e- collisions. The physics of the ILC, and the environment of the machine-detector interface, pose new challenges for detector design. Several conceptual designs for the detector promise the needed performance, and ongoing detector R&D is addressing the outstanding technological issues. Two such detectors, operating in push-pull mode, perfectly instrument the ILC interaction region, and access the full potential of ILC physics.This report, Volume IV of the International Linear Collider Reference Design Report, describes the detectors which will record and measure the charged and neutral particles produced in the ILC's high energy e+e- collisions. The physics of the ILC, and the environment of the machine-detector interface, pose new challenges for detector design. Several conceptual designs for the detector promise the needed performance, and ongoing detector R&D is addressing the outstanding technological issues. Two such detectors, operating in push-pull mode, perfectly instrument the ILC interaction region, and access the full potential of ILC physics

ILC Reference Design Report Volume 3 - Accelerator

The International Linear Collider (ILC) is a 200-500 GeV center-of-mass high-luminosity linear electron-positron collider, based on 1.3 GHz superconducting radio-frequency (SCRF) accelerating cavities. The ILC has a total footprint of about 31 km and is designed for a peak luminosity of 2x10^34 cm^-2 s^-1. The complex includes a polarized electron source, an undulator-based positron source, two 6.7 km circumference damping rings, two-stage bunch compressors, two 11 km long main linacs and a 4.5 km long beam delivery system. This report is Volume III (Accelerator) of the four volume Reference Design Report, which describes the design and cost of the ILC.The International Linear Collider (ILC) is a 200-500 GeV center-of-mass high-luminosity linear electron-positron collider, based on 1.3 GHz superconducting radio-frequency (SCRF) accelerating cavities. The ILC has a total footprint of about 31 km and is designed for a peak luminosity of 2x10^34 cm^-2 s^-1. The complex includes a polarized electron source, an undulator-based positron source, two 6.7 km circumference damping rings, two-stage bunch compressors, two 11 km long main linacs and a 4.5 km long beam delivery system. This report is Volume III (Accelerator) of the four volume Reference Design Report, which describes the design and cost of the ILC