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Title: Bitcoin: A Natural Oligopoly
Although Bitcoin was intended to be a decentralized digital currency, in practice, mining power is quite concentrated. This fact is a persistent source of concern for the Bitcoin community. We provide an explanation using a simple model to capture miners' incentives to invest in equipment. In our model, n miners compete for a prize of fixed size. Each miner chooses an investment q_i, incurring cost c_iq_i, and then receives reward q^{\alpha}∑_j q_j^{\alpha}, for some \alpha≥1. When c_i = c+j for all i,j, and α=1, there is a unique equilibrium where all miners invest equally. However, we prove that under seemingly mild deviations from this model, equilibrium outcomes become drastically more centralized. In particular, (a) When costs are asymmetric, if miner i chooses to invest, then miner j has market share at least 1−c_j/c_i. That is, if miner j has costs that are (e.g.) 20% lower than those of miner i, then miner j must control at least 20% of the \emph{total} mining power. (b) In the presence of economies of scale (α>1), every market participant has a market share of at least 1−1/α, implying that the market features at most α/(α−1) miners in total. We discuss the implications of our results for the future design of cryptocurrencies. In particular, our work further motivates the study of protocols that minimize "orphaned" blocks, proof-of-stake protocols, and incentive compatible protocols.  more » « less
Award ID(s):
1717899
NSF-PAR ID:
10097713
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Innovations in Theoretical Computer Science
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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  5. Obeid, I. (Ed.)
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It is well known that state of the art algorithms in machine learning require vast amounts of data. Fields such as speech recognition [3], image recognition [4] and text processing [5] are able to deliver impressive performance with complex deep learning models because they have developed large corpora to support training of extremely high-dimensional models (e.g., billions of parameters). Other fields that do not have access to such data resources must rely on techniques in which existing models can be adapted to new datasets [6]. A preliminary version of this breast corpus release was tested in a pilot study using a baseline machine learning system, ResNet18 [7], that leverages several open-source Python tools. The pilot corpus was divided into three sets: train, development, and evaluation. Portions of these slides were manually annotated [1] using the nine labels in Table 1 [8] to identify five to ten examples of pathological features on each slide. Not every pathological feature is annotated, meaning excluded areas can include focuses particular to these labels that are not used for training. A summary of the number of patches within each label is given in Table 2. To maintain a balanced training set, 1,000 patches of each label were used to train the machine learning model. Throughout all sets, only annotated patches were involved in model development. The performance of this model in identifying all the patches in the evaluation set can be seen in the confusion matrix of classification accuracy in Table 3. The highest performing labels were background, 97% correct identification, and artifact, 76% correct identification. A correlation exists between labels with more than 6,000 development patches and accurate performance on the evaluation set. Additionally, these results indicated a need to further refine the annotation of invasive ductal carcinoma (“indc”), inflammation (“infl”), nonneoplastic features (“nneo”), normal (“norm”) and suspicious (“susp”). This pilot experiment motivated changes to the corpus that will be discussed in detail in this poster presentation. To increase the accuracy of the machine learning model, we modified how we addressed underperforming labels. One common source of error arose with how non-background labels were converted into patches. Large areas of background within other labels were isolated within a patch resulting in connective tissue misrepresenting a non-background label. In response, the annotation overlay margins were revised to exclude benign connective tissue in non-background labels. Corresponding patient reports and supporting immunohistochemical stains further guided annotation reviews. The microscopic diagnoses given by the primary pathologist in these reports detail the pathological findings within each tissue site, but not within each specific slide. The microscopic diagnoses informed revisions specifically targeting annotated regions classified as cancerous, ensuring that the labels “indc” and “dcis” were used only in situations where a micropathologist diagnosed it as such. Further differentiation of cancerous and precancerous labels, as well as the location of their focus on a slide, could be accomplished with supplemental immunohistochemically (IHC) stained slides. When distinguishing whether a focus is a nonneoplastic feature versus a cancerous growth, pathologists employ antigen targeting stains to the tissue in question to confirm the diagnosis. For example, a nonneoplastic feature of usual ductal hyperplasia will display diffuse staining for cytokeratin 5 (CK5) and no diffuse staining for estrogen receptor (ER), while a cancerous growth of ductal carcinoma in situ will have negative or focally positive staining for CK5 and diffuse staining for ER [9]. Many tissue samples contain cancerous and non-cancerous features with morphological overlaps that cause variability between annotators. The informative fields IHC slides provide could play an integral role in machine model pathology diagnostics. Following the revisions made on all the annotations, a second experiment was run using ResNet18. Compared to the pilot study, an increase of model prediction accuracy was seen for the labels indc, infl, nneo, norm, and null. This increase is correlated with an increase in annotated area and annotation accuracy. Model performance in identifying the suspicious label decreased by 25% due to the decrease of 57% in the total annotated area described by this label. A summary of the model performance is given in Table 4, which shows the new prediction accuracy and the absolute change in error rate compared to Table 3. The breast tissue subset we are developing includes 3,505 annotated breast pathology slides from 296 patients. The average size of a scanned SVS file is 363 MB. The annotations are stored in an XML format. A CSV version of the annotation file is also available which provides a flat, or simple, annotation that is easy for machine learning researchers to access and interface to their systems. Each patient is identified by an anonymized medical reference number. Within each patient’s directory, one or more sessions are identified, also anonymized to the first of the month in which the sample was taken. These sessions are broken into groupings of tissue taken on that date (in this case, breast tissue). A deidentified patient report stored as a flat text file is also available. Within these slides there are a total of 16,971 total annotated regions with an average of 4.84 annotations per slide. Among those annotations, 8,035 are non-cancerous (normal, background, null, and artifact,) 6,222 are carcinogenic signs (inflammation, nonneoplastic and suspicious,) and 2,714 are cancerous labels (ductal carcinoma in situ and invasive ductal carcinoma in situ.) The individual patients are split up into three sets: train, development, and evaluation. Of the 74 cancerous patients, 20 were allotted for both the development and evaluation sets, while the remain 34 were allotted for train. The remaining 222 patients were split up to preserve the overall distribution of labels within the corpus. This was done in hope of creating control sets for comparable studies. Overall, the development and evaluation sets each have 80 patients, while the training set has 136 patients. In a related component of this project, slides from the Fox Chase Cancer Center (FCCC) Biosample Repository (https://www.foxchase.org/research/facilities/genetic-research-facilities/biosample-repository -facility) are being digitized in addition to slides provided by Temple University Hospital. This data includes 18 different types of tissue including approximately 38.5% urinary tissue and 16.5% gynecological tissue. These slides and the metadata provided with them are already anonymized and include diagnoses in a spreadsheet with sample and patient ID. We plan to release over 13,000 unannotated slides from the FCCC Corpus simultaneously with v1.0.0 of TUDP. Details of this release will also be discussed in this poster. Few digitally annotated databases of pathology samples like TUDP exist due to the extensive data collection and processing required. The breast corpus subset should be released by November 2021. By December 2021 we should also release the unannotated FCCC data. We are currently annotating urinary tract data as well. We expect to release about 5,600 processed TUH slides in this subset. We have an additional 53,000 unprocessed TUH slides digitized. Corpora of this size will stimulate the development of a new generation of deep learning technology. In clinical settings where resources are limited, an assistive diagnoses model could support pathologists’ workload and even help prioritize suspected cancerous cases. ACKNOWLEDGMENTS This material is supported by the National Science Foundation under grants nos. CNS-1726188 and 1925494. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. REFERENCES [1] N. Shawki et al., “The Temple University Digital Pathology Corpus,” in Signal Processing in Medicine and Biology: Emerging Trends in Research and Applications, 1st ed., I. Obeid, I. Selesnick, and J. Picone, Eds. New York City, New York, USA: Springer, 2020, pp. 67 104. https://www.springer.com/gp/book/9783030368432. [2] J. Picone, T. Farkas, I. Obeid, and Y. Persidsky, “MRI: High Performance Digital Pathology Using Big Data and Machine Learning.” Major Research Instrumentation (MRI), Division of Computer and Network Systems, Award No. 1726188, January 1, 2018 – December 31, 2021. https://www. isip.piconepress.com/projects/nsf_dpath/. [3] A. Gulati et al., “Conformer: Convolution-augmented Transformer for Speech Recognition,” in Proceedings of the Annual Conference of the International Speech Communication Association (INTERSPEECH), 2020, pp. 5036-5040. https://doi.org/10.21437/interspeech.2020-3015. [4] C.-J. Wu et al., “Machine Learning at Facebook: Understanding Inference at the Edge,” in Proceedings of the IEEE International Symposium on High Performance Computer Architecture (HPCA), 2019, pp. 331–344. https://ieeexplore.ieee.org/document/8675201. [5] I. Caswell and B. Liang, “Recent Advances in Google Translate,” Google AI Blog: The latest from Google Research, 2020. [Online]. Available: https://ai.googleblog.com/2020/06/recent-advances-in-google-translate.html. [Accessed: 01-Aug-2021]. [6] V. Khalkhali, N. Shawki, V. Shah, M. Golmohammadi, I. Obeid, and J. Picone, “Low Latency Real-Time Seizure Detection Using Transfer Deep Learning,” in Proceedings of the IEEE Signal Processing in Medicine and Biology Symposium (SPMB), 2021, pp. 1 7. https://www.isip. piconepress.com/publications/conference_proceedings/2021/ieee_spmb/eeg_transfer_learning/. [7] J. Picone, T. Farkas, I. Obeid, and Y. Persidsky, “MRI: High Performance Digital Pathology Using Big Data and Machine Learning,” Philadelphia, Pennsylvania, USA, 2020. https://www.isip.piconepress.com/publications/reports/2020/nsf/mri_dpath/. [8] I. Hunt, S. Husain, J. Simons, I. Obeid, and J. Picone, “Recent Advances in the Temple University Digital Pathology Corpus,” in Proceedings of the IEEE Signal Processing in Medicine and Biology Symposium (SPMB), 2019, pp. 1–4. https://ieeexplore.ieee.org/document/9037859. [9] A. P. Martinez, C. Cohen, K. Z. Hanley, and X. (Bill) Li, “Estrogen Receptor and Cytokeratin 5 Are Reliable Markers to Separate Usual Ductal Hyperplasia From Atypical Ductal Hyperplasia and Low-Grade Ductal Carcinoma In Situ,” Arch. Pathol. Lab. Med., vol. 140, no. 7, pp. 686–689, Apr. 2016. https://doi.org/10.5858/arpa.2015-0238-OA. 
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