Combinatorics and Optimizationhttp://hdl.handle.net/10012/99282023-09-24T14:58:32Z2023-09-24T14:58:32ZUniform Generation of Graphical Realizations of Joint Degree MatricesZhou, Qianyehttp://hdl.handle.net/10012/199012023-09-22T02:31:04Z2023-09-21T00:00:00ZUniform Generation of Graphical Realizations of Joint Degree Matrices
Zhou, Qianye
In this thesis, we introduce JDM_GEN, an algorithm designed to uniformly generate
graphical realizations of a given joint degree matrix. Amanatidis and Kleer previously
employed an MCMC-based method to address this problem. Their method fully resolved
the case of two degree classes, and showed that their switch Markov chain is rapidly mixing.
While our algorithm imposes certain restrictions on the maximum degrees, it is applicable
to any bounded number of degree classes and has a runtime complexity linear in the number
of edges.
2023-09-21T00:00:00ZRigidity of near-optimal superdense coding protocolsZhou, Xingyuhttp://hdl.handle.net/10012/198862023-09-20T02:31:08Z2023-09-19T00:00:00ZRigidity of near-optimal superdense coding protocols
Zhou, Xingyu
Rigidity in quantum information theory refers to the stringent constraints underlying optimal or near-optimal performance in certain quantum tasks. This property plays a crucial role in verifying untrusted quantum devices and holds significance for secure quantum protocols. Previous work by Nayak and Yuen demonstrated that all optimal superdense coding protocols are locally equivalent to the canonical Bennett-Wiesner protocol. For higher-dimensional superdense coding protocols, Nayak and Yuen showed they may exist only in a relaxed form, and Farkas, Kaniewski and Nayak showed there are infinitely many dimensions $d\geq 4$ such that the rigidity does not exist even in the relaxed form.
Our work is dedicated to establishing the rigidity properties of near-optimal superdense coding protocols. Specifically, we explore scenarios where Alice can employ finite but arbitrary ancilla qubits for encoding, Bob can perform positive operator-valued measure (POVM) for decoding and can answer with error. In such contexts, we prove that any near-optimal superdense coding must be locally equivalent to a superdense coding protocol close to the canonical Bennett-Wiesner protocol.
In the search for extending the result to higher dimensional superdense coding protocols, we find a method to orthogonalize any two unitary matrices in the same space. However, the question of whether it is feasible to orthogonalize more than two $d\times d$ unitary matrices when $d>2$ remains an intriguing yet unresolved matter.
2023-09-19T00:00:00ZDistance-Biregular Graphs and Orthogonal PolynomialsLato, Sabrinahttp://hdl.handle.net/10012/198662023-09-16T02:30:56Z2023-09-15T00:00:00ZDistance-Biregular Graphs and Orthogonal Polynomials
Lato, Sabrina
This thesis is about distance-biregular graphs– when they exist, what algebraic and structural properties they have, and how they arise in extremal problems.
We develop a set of necessary conditions for a distance-biregular graph to exist. Using these conditions and a computer, we develop tables of possible parameter sets for distancebiregular graphs. We extend results of Fiol, Garriga, and Yebra characterizing distance-regular graphs to characterizations of distance-biregular graphs, and highlight some new
results using these characterizations. We also extend the spectral Moore bounds of Cioaba et al. to semiregular bipartite graphs, and show that distance-biregular graphs arise as extremal examples of graphs meeting the spectral Moore bound.
2023-09-15T00:00:00ZTowards Private Biometric Authentication and IdentificationGold, Jonathanhttp://hdl.handle.net/10012/198332023-09-06T02:31:01Z2023-09-05T00:00:00ZTowards Private Biometric Authentication and Identification
Gold, Jonathan
Handwriting and speech are important parts of our everyday lives. Handwriting recognition is the task that allows the recognizing of written text, whether it be letters, words or equations, from given data. When analyzing handwriting, we can analyze static images or the recording of written text through sensors. Handwriting recognition algorithms can be used in many applications, including signature verification, electronic document processing, as well as e-security and e-health related tasks.
The OnHW datasets consists of a set of datasets which, through the use of various sensors, captures the writing of characters, words, symbols and equations, recorded in the form of multivariate time series. We begin by developing character recognition models, targeting letters (and later symbols), trained and tested using the OnHW-chars dataset (and later the split OnHW-equations dataset). Our models were able to improve upon the accuracy of the previous best results on both datasets explored. Using our machine learning (ML) models, we provide 11.3%-23.56% improvements over the previous best ML models. Using deep learning (DL), as well as ensemble techniques, we were able to improve on the best previous models by 3.08%-7.01%. In addition to the accuracy improvements, we aim to provide some level of explainability, using a specialized version of LIME for time series data. This explanation helps provide some rationale for why the models make sense for the data, as well as why ensemble methods may be useful to improve accuracy rates for this task. To verify the robustness of our models trained over the OnHW-chars dataset, we trained our DL models using the same model parameters over a more recently published OnHW-equations dataset. Our DL models with ensemble learning provide 0.05%-4.75% improvements over the previous best DL models.
While the character recognition task has many applications, when using it to provide a service, it is important to consider user privacy since handwriting is biometric data and contains private information. Next, we design a framework that uses multiparty computation (MPC) to provide users with privacy over their handwritten data, when providing a service for character recognition. We then implement the framework using the models trained on public data to provide private inference on hidden user data. This framework is implemented in the CrypTen MPC framework. We obtain results on the accuracy difference of the models when making inference using MPC, as well as the costs associated with performing this inference. We found a 0.55%-1.42% accuracy difference between plaintext inference and inference with MPC.
Next, we pivot to explore writer identification, which involves identifying the writer of some handwritten text. We use the OnHW-equations dataset for our analysis, which at the time of writing has not been used for this task before. We first analyze and reformat the data to fit the writer identification task, as well as remove bias. Using DL models, we obtain accuracy results of up to 91.57% in identifying the writer using their handwriting. As with private inference in the character recognition task, it is important to account for user privacy when training writer identification models and making inference. We design and implement a framework for private training and inference for the writer recognition task, using the CrypTen MPC framework. Since training these models is very costly, we use simpler CNN's for private writer recognition. The chosen CNN trained privately in MPC obtained an accuracy of 77.45%. Next, we analyze the costs associated with privately training the CNN and other CNN's with altered model architectures.
Finally, we switch to explore voice as a biometric in the speaker verification task. As with handwriting, a person's voice contains unique characteristics which can be used to determine the speaker. Not only can voice be analyzed similarly with handwriting, in that we can explore the speech recognition and speaker identification tasks, it comes with similar privacy risks for users. We design and implement a unique framework for private speaker verification using the MP-SPDZ MPC framework. We analyze the costs associated with training the model and making inferences, with our main goal being to determine the time it takes to make private inference. We then used these times as part of a survey conducted to determine how much people value the privacy of their biometrics and how long they were willing to wait for the increased privacy. We found that people were willing to tolerate significant time delays in order to privately authenticate themselves, when primed with the benefits of using MPC for privacy.
2023-09-05T00:00:00Z