Invariant Jordan curves of Sierpiski carpet rational maps

In this paper, we prove that if $R\colon\widehat{\mathbb{C}}\to\widehat{\mathbb{C}}$ is a postcritically finite rational map with Julia set homeomorphic to the Sierpi\'nski carpet, then there is an integer $n_0$, such that, for any $n\ge n_0$, there exists an $R^n$-invariant Jordan curve $\Gamma$ containing the postcritical set of $R$.Comment: 16 pages, 1 figu

End-to-End Tracking and Semantic Segmentation Using Recurrent Neural Networks

In this work we present a novel end-to-end framework for tracking and classifying a robot's surroundings in complex, dynamic and only partially observable real-world environments. The approach deploys a recurrent neural network to filter an input stream of raw laser measurements in order to directly infer object locations, along with their identity in both visible and occluded areas. To achieve this we first train the network using unsupervised Deep Tracking, a recently proposed theoretical framework for end-to-end space occupancy prediction. We show that by learning to track on a large amount of unsupervised data, the network creates a rich internal representation of its environment which we in turn exploit through the principle of inductive transfer of knowledge to perform the task of it's semantic classification. As a result, we show that only a small amount of labelled data suffices to steer the network towards mastering this additional task. Furthermore we propose a novel recurrent neural network architecture specifically tailored to tracking and semantic classification in real-world robotics applications. We demonstrate the tracking and classification performance of the method on real-world data collected at a busy road junction. Our evaluation shows that the proposed end-to-end framework compares favourably to a state-of-the-art, model-free tracking solution and that it outperforms a conventional one-shot training scheme for semantic classification

Intelligent Extensive Markup Language Parser

The purpose of this project was to simplify the process of modifying the Extensible Markup Language (XML) file elements. Having to modify multiple XML files that are used in huge database servers or websites is a huge time-consuming work. I intended to simplify the process with a program. This program was coded with C#. The focus of this project was on making it user friendly, and have the user do less job to complete the XML modification process. The XML base file was extracted from the famous Korean online computer game, Maple Story. There are multiple versions of the XML file, so I intended to make a program that transforms new XML files that are not supported by many programs to old XML, compatible with many other programs and old client versions. The project provides the algorithm and the mechanism of the program. The completion of the project indicates that many processes that cannot be done easily with just a mouse and keyboard can be done easily with just a single button in a program

Is Capital Expenditure Contagious? An Analysis of UCC Data from Ohio and Its Neighbors

ECONOMIC CONDITIONS ARE OFTEN OBSERVED TO BE CORRELATED ACROSS SPACE AND TIME. ONE INTERPRETATION OF THIS PHENOMENON IS THAT ECONOMIC ACTIVITY IS “CONTAGIOUS.” THAT IS, GOOD OR BAD CONDITIONS IN ONE ECONOMIC AREA MAY LATER CAUSE SIMILAR CONDITIONS TO OCCUR IN NEARBY AREAS. THE PREVALENCE AND EXTENT OF THESE RELATIONSHIPS IS IMPORTANT TO UNDERSTAND FOR THOSE SEEKING TO FOSTER REGIONAL ECONOMIC DEVELOPMENT. WE FOCUS ON CAPITAL EQUIPMENT SPENDING AT THE STATE LEVEL AT A MONTHLY FREQUENCY. THIS IS POSSIBLE GIVEN OUR ACCESS TO A UNIQUE DATA SET, THE RANDALL-REILLEY CAPITAL INVESTMENT INDEX (RRCII). THIS INDEX MEASURES CAPITAL EXPENDITURE USING UNIFORM COMMERCIAL CODE (UCC) FORMS FILED EACH MONTH WITH EACH STATE’S SECRETARY OF STATE. THE DATA IS CLASSIFIED INTO THREE INDUSTRIES: AGRICULTURE, CONSTRUCTION, AND MACHINE TOOLS, AS WELL AS A COMPOSITE MEASURE. IN THIS STUDY, WE UTILIZE THE INDEX’S STATE-LEVEL DATA FOR OHIO AND ITS NEIGHBORS: MICHIGAN, INDIANA, KENTUCKY, WEST VIRGINIA, AND PENNSYLVANIA. OUR METHODOLOGY CONSISTS OF TYPICAL TIME SERIES TECHNIQUES: GRANGER CAUSALITY TESTS, VECTOR AUTOREGRESSIONS, AND THEIR ASSOCIATED IMPULSE RESPONSE FUNCTIONS. OUR INITIAL RESULTS SUGGEST THAT MICHIGAN IS THE ONLY STATE WITH A SIGNIFICANT RELATIONSHIP WITH OHIO AT THE COMPOSITE LEVEL, BUT THAT PENNSYLVANIA AND WEST VIRGINIA SHOW SOME RELATIONSHIP WITH OHIO IN CONSTRUCTION, AS DOES INDIANA WITH MACHINE TOOLS

Graph Concatenation for Quantum Codes

Graphs are closely related to quantum error-correcting codes: every stabilizer code is locally equivalent to a graph code, and every codeword stabilized code can be described by a graph and a classical code. For the construction of good quantum codes of relatively large block length, concatenated quantum codes and their generalizations play an important role. We develop a systematic method for constructing concatenated quantum codes based on "graph concatenation", where graphs representing the inner and outer codes are concatenated via a simple graph operation called "generalized local complementation." Our method applies to both binary and non-binary concatenated quantum codes as well as their generalizations.Comment: 26 pages, 12 figures. Figures of concatenated [[5,1,3]] and [[7,1,3]] are added. Submitted to JM