Pinched manifolds becoming dull

In this thesis, we prove short-time existence for Ricci flow, for a class of metrics with unbounded curvature. Our primary motivation in investigating this class of metrics is that it includes many final-time limits of Ricci flow singularities. Well known examples include neckpinches and degenerate neckpinches. We provide an example of Ricci flow modifying a neighborhood of a manifold with the topological change [mathematical equation], although we only rigorously deal with the second part of the transformation. We also provide forward evolution from some manifolds with ends of infinite length and unbounded curvature, such as the submanifold given by [mathematical equation]. In this example, the two ends with unbounded curvature immediately become compact and with bounded curvature, so the topology of the forward evolution is S³.Mathematic

Synthetic steganography: Methods for generating and detecting covert channels in generated media

Issues of privacy in communication are becoming increasingly important. For many people and businesses, the use of strong cryptographic protocols is sufficient to protect their communications. However, the overt use of strong cryptography may be prohibited or individual entities may be prohibited from communicating directly. In these cases, a secure alternative to the overt use of strong cryptography is required. One promising alternative is to hide the use of cryptography by transforming ciphertext into innocuous-seeming messages to be transmitted in the clear. ^ In this dissertation, we consider the problem of synthetic steganography: generating and detecting covert channels in generated media. We start by demonstrating how to generate synthetic time series data that not only mimic an authentic source of the data, but also hide data at any of several different locations in the reversible generation process. We then design a steganographic context-sensitive tiling system capable of hiding secret data in a variety of procedurally-generated multimedia objects. Next, we show how to securely hide data in the structure of a Huffman tree without affecting the length of the codes. Next, we present a method for hiding data in Sudoku puzzles, both in the solved board and the clue configuration. Finally, we present a general framework for exploiting steganographic capacity in structured interactions like online multiplayer games, network protocols, auctions, and negotiations. Recognizing that structured interactions represent a vast field of novel media for steganography, we also design and implement an open-source extensible software testbed for analyzing steganographic interactions and use it to measure the steganographic capacity of several classic games. ^ We analyze the steganographic capacity and security of each method that we present and show that existing steganalysis techniques cannot accurately detect the usage of the covert channels. We develop targeted steganalysis techniques which improve detection accuracy and then use the insights gained from those methods to improve the security of the steganographic systems. We find that secure synthetic steganography, and accurate steganalysis thereof, depends on having access to an accurate model of the cover media

Objective Assessment and Design Improvement of a Staring, Sparse Transducer Array by the Spatial Crosstalk Matrix for 3D Photoacoustic Tomography.

Accurate reconstruction of 3D photoacoustic (PA) images requires detection of photoacoustic signals from many angles. Several groups have adopted staring ultrasound arrays, but assessment of array performance has been limited. We previously reported on a method to calibrate a 3D PA tomography (PAT) staring array system and analyze system performance using singular value decomposition (SVD). The developed SVD metric, however, was impractical for large system matrices, which are typical of 3D PAT problems. The present study consisted of two main objectives. The first objective aimed to introduce the crosstalk matrix concept to the field of PAT for system design. Figures-of-merit utilized in this study were root mean square error, peak signal-to-noise ratio, mean absolute error, and a three dimensional structural similarity index, which were derived between the normalized spatial crosstalk matrix and the identity matrix. The applicability of this approach for 3D PAT was validated by observing the response of the figures-of-merit in relation to well-understood PAT sampling characteristics (i.e. spatial and temporal sampling rate). The second objective aimed to utilize the figures-of-merit to characterize and improve the performance of a near-spherical staring array design. Transducer arrangement, array radius, and array angular coverage were the design parameters examined. We observed that the performance of a 129-element staring transducer array for 3D PAT could be improved by selection of optimal values of the design parameters. The results suggested that this formulation could be used to objectively characterize 3D PAT system performance and would enable the development of efficient strategies for system design optimization

Plasma microRNA levels following resection of metastatic melanoma

Melanoma remains the leading cause of skin cancer–related deaths. Surgical resection and adjuvant therapies can result in disease-free intervals for stage III and stage IV disease; however, recurrence is common. Understanding microRNA (miR) dynamics following surgical resection of melanomas is critical to accurately interpret miR changes suggestive of melanoma recurrence. Plasma of 6 patients with stage III (n = 2) and stage IV (n = 4) melanoma was evaluated using the NanoString platform to determine pre- and postsurgical miR expression profiles, enabling analysis of more than 800 miRs simultaneously in 12 samples. Principal component analysis detected underlying patterns of miR expression between pre- vs postsurgical patients. Group A contained 3 of 4 patients with stage IV disease (pre- and postsurgical samples) and 2 patients with stage III disease (postsurgical samples only). The corresponding preoperative samples to both individuals with stage III disease were contained in group B along with 1 individual with stage IV disease (pre- and postsurgical samples). Group A was distinguished from group B by statistically significant analysis of variance changes in miR expression ( P < .0001). This analysis revealed that group A vs group B had downregulation of let-7b-5p, miR-520f, miR-720, miR-4454, miR-21-5p, miR-22-3p, miR-151a-3p, miR-378e, and miR-1283 and upregulation of miR-126-3p, miR-223-3p, miR-451a, let-7a-5p, let-7g-5p, miR-15b-5p, miR-16-5p, miR-20a-5p, miR-20b-5p, miR-23a-3p, miR-26a-5p, miR-106a-5p, miR-17-5p, miR-130a-3p, miR-142-3p, miR-150-5p, miR-191-5p, miR-199a-3p, miR-199b-3p, and miR-1976. Changes in miR expression were not readily evident in individuals with distant metastatic disease (stage IV) as these individuals may have prolonged inflammatory responses. Thus, inflammatory-driven miRs coinciding with tumor-derived miRs can blunt anticipated changes in expression profiles following surgical resection

Arguments for a "U.S. Kamioka": SNOLab and its Implications for North American Underground Science Planning

We argue for a cost-effective, long-term North American underground science strategy based on partnership with Canada and initial construction of a modest U.S. Stage I laboratory designed to complement SNOLab. We show, by reviewing the requirements of detectors now in the R&D phase, that SNOLab and a properly designed U.S. Stage I facility would be capable of meeting the needs of North America's next wave of underground experiments. We discuss one opportunity for creating a Stage I laboratory, the Pioneer tunnel in Washington State, a site that could be developed to provide dedicated, clean, horizontal access. This unused tunnel, part of the deepest (1040 m) tunnel system in the U.S., would allow the U.S. to establish, at low risk and low cost, a laboratory at a depth (2.12 km.w.e., or kilometers of water equivalent) quite similar to that of the Japanese laboratory Kamioka (2.04 km.w.e.). We describe studies of cosmic ray attenuation important to properly locating such a laboratory, and the tunnel improvements that would be required to produce an optimal Stage I facility. We also discuss possibilities for far-future Stage II (3.62 km.w.e.) and Stage III (5.00 km.w.e.) developments at the Pioneer tunnel, should future North American needs for deep space exceed that available at SNOLab.Comment: 23 pages, 10 figures; revised version includes discusion about neutrino-factory magic baseline