arXiv subjects

Thomas Chen

Publications and source records attributed to Thomas Chen.

At least 37 records · Page 2Linked to original sources

arXiv2023

A Review of zk-SNARKs

A zk-SNARK is a protocol that lets one party, the prover, prove to another party, the verifier, that a statement about some privately-held information is true without revealing the information itself. This paper describes technical foundations, current applications, and some novel applications of zk-SNARKs. Regarding technical foundations, we go over the Quadratic Arithmetic Program reduction and the Pinocchio protocol. We then go over financial security applications like Zcash and Tornado Cash, and zk-Rollup applications like zkEVM and Darkforest. We propose novel zk-SNARK protocols for private auctions and decentralized card games on the blockchain, providing code for the proposed applications. We conclude by touching on promising zk-SNARK innovations, such as zk-STARKs.

cs.CR↗

arXiv2023

On the Well-posedness and Stability of Cubic and Quintic Nonlinear Schrödinger Systems on ${\mathbb T}^3$

In this paper, we study cubic and quintic nonlinear Schrödinger systems on 3-dimensional tori, with initial data in an adapted Hilbert space $H^s_{\underlineλ},$ and all of our results hold on rational and irrational rectangular, flat tori. In the cubic and quintic case, we prove local well-posedness for both focusing and defocusing systems. We show that local solutions of the defocusing cubic system with initial data in $H^1_{\underlineλ}$ can be extended for all time. Additionally, we prove that global well-posedness holds in the quintic system, focusing or defocusing, for initial data with sufficiently small $H^1_{\underlineλ}$ norm. Finally, we use the energy-Casimir method to prove the existence and uniqueness, and nonlinear stability of a class of stationary states of the defocusing cubic and quintic nonlinear Schrödinger systems.

math-ph↗

arXiv2023

The Focusing Optics X-ray Solar Imager (FOXSI)

FOXSI is a direct-imaging, hard X-ray (HXR) telescope optimized for solar flare observations. It detects hot plasma and energetic electrons in and near energy release sites in the solar corona via bremsstrahlung emission, measuring both spatial structure and particle energy distributions. It provides two orders of magnitude faster imaging spectroscopy than previously available, probing physically relevant timescales (<1s) never before accessible to address fundamental questions of energy release and efficient particle acceleration that have importance far beyond their solar application (e.g., planetary magnetospheres, flaring stars, accretion disks). FOXSI measures not only the bright chromospheric X-ray emission where electrons lose most of their energy, but also simultaneous emission from electrons as they are accelerated in the corona and propagate along magnetic field lines. FOXSI detects emission from high in the tenuous corona, where previous instruments have been blinded by nearby bright features and will fully characterizes the accelerated electrons and hottest plasmas as they evolve in energy, space, and time to solve the mystery of how impulsive energy release leads to solar eruptions, the primary drivers of space weather at Earth, and how those eruptions are energized and evolve.

astro-ph.IM↗

arXiv2023

Recommending Low-Cost Compact Space Environment and Space Weather Effects Sensor Suites for NASA Missions

As miniaturized spacecraft (e.g., cubesats and smallsats) and instrumentation become an increasingly indispensable part of space exploration and scientific investigations, it is important to understand their potential susceptibility to space weather impacts resulting from the sometimes volatile space environment. There are multitude of complexities involved in how space environment interacts with different space hardware/electronics. Measurements of such impacts, however, have been lacking. Therefore, we recommend developing and/or procuring low-cost, low-power consumption, and compact sensor suites (mainly for space weather and impact purposes) and flying them on all future NASA (and U.S in general) missions in order to measure and quantify space weather impacts, in addition to the main instrumentation.

astro-ph.IM↗

arXiv2023

On the emergence of quantum Boltzmann fluctuation dynamics near a Bose-Einstein Condensate

In this work, we study the quantum fluctuation dynamics in a Bose gas on a torus $Λ=(L\mathbb{T})^3$ that exhibits Bose-Einstein condensation, beyond the leading order Hartree-Fock-Bogoliubov (HFB) fluctuations. Given a Bose-Einstein condensate (BEC) with density $N$ surrounded by thermal fluctuations with density $1$, we assume that the system is described by a mean-field Hamiltonian. We extract a quantum Boltzmann type dynamics from a second-order Duhamel expansion upon subtracting both the BEC dynamics and the HFB dynamics. Using a Fock-space approach, we provide explicit error bounds. It is known that the BEC and the HFB fluctuations both evolve at microscopic time scales $t\sim1$. Given a quasifree initial state, we determine the time evolution of the centered correlation functions $\langle a\rangle$, $\langle aa\rangle-\langle a\rangle^2$, $\langle a^+a\rangle-|\langle a\rangle|^2$ at mesoscopic time scales $t\simλ^{-2}$, where $0<λ\ll1$ denotes the size of the HFB interaction. For large but finite $N$, we consider both the case of fixed system size $L\sim1$, and the case $L\sim λ^{-2-}$. In the case $L\sim1$, we show that the Boltzmann collision operator contains subleading terms that can become dominant, depending on time-dependent coefficients assuming particular values in $\mathbb{Q}$; this phenomenon is reminiscent of the Talbot effect. For the case $L\sim λ^{-2-}$, we prove that the collision operator is well approximated by the expression predicted in the literature. In either of those cases, we have $λ\sim \Big(\frac{\log \log N}{\log N}\Big)^α$, for different values of $α>0$.

math-ph↗

arXiv2022

On an $L^2$ critical Boltzmann equation

We prove the existence of a class of large global scattering solutions of Boltzmann's equation with constant collision kernel in two dimensions. These solutions are found for $L^2$ perturbations of an underlying initial data which is Gaussian jointly in space and velocity. Additionally, the perturbation is required to satisfy natural physical constraints for the total mass and second moments, corresponding to conserved or controlled quantities. The space $L^2$ is a scaling critical space for the equation under consideration. If the initial data is Schwartz then the solution is unique and again Schwartz on any bounded time interval.

math.AP↗

arXiv2021

Hierarchical Summarization for Longform Spoken Dialog

Every day we are surrounded by spoken dialog. This medium delivers rich diverse streams of information auditorily; however, systematically understanding dialog can often be non-trivial. Despite the pervasiveness of spoken dialog, automated speech understanding and quality information extraction remains markedly poor, especially when compared to written prose. Furthermore, compared to understanding text, auditory communication poses many additional challenges such as speaker disfluencies, informal prose styles, and lack of structure. These concerns all demonstrate the need for a distinctly speech tailored interactive system to help users understand and navigate the spoken language domain. While individual automatic speech recognition (ASR) and text summarization methods already exist, they are imperfect technologies; neither consider user purpose and intent nor address spoken language induced complications. Consequently, we design a two stage ASR and text summarization pipeline and propose a set of semantic segmentation and merging algorithms to resolve these speech modeling challenges. Our system enables users to easily browse and navigate content as well as recover from errors in these underlying technologies. Finally, we present an evaluation of the system which highlights user preference for hierarchical summarization as a tool to quickly skim audio and identify content of interest to the user.

cs.CL↗

arXiv2021

Computational Hardness of the Hylland-Zeckhauser Scheme

We study the complexity of the classic Hylland-Zeckhauser scheme [HZ'79] for one-sided matching markets. We show that the problem of finding an $ε$-approximate equilibrium in the HZ scheme is PPAD-hard, and this holds even when $ε$ is polynomially small and when each agent has no more than four distinct utility values. Our hardness result, when combined with the PPAD membership result of [VY'21], resolves the approximation complexity of the HZ scheme. We also show that the problem of approximating the optimal social welfare (the weight of the matching) achievable by HZ equilibria within a certain constant factor is NP-hard.

cs.GT↗

arXiv2019

Small data global well-posedness for a Boltzmann equation via bilinear spacetime estimates

We provide a new analysis of the Boltzmann equation with constant collision kernel in two space dimensions. The scaling-critical Lebesgue space is $L^2_{x,v}$; we prove global well-posedness and a version of scattering, assuming that the data $f_0$ is sufficiently smooth and localized, and the $L^2_{x,v}$ norm of $f_0$ is sufficiently small. The proof relies upon a new scaling-critical bilinear spacetime estimate for the collision "gain" term in Boltzmann's equation, combined with a novel application of the Kaniel-Shinbrot iteration.

math.AP↗

arXiv2019

OAuthGuard: Protecting User Security and Privacy with OAuth 2.0 and OpenID Connect

Millions of users routinely use Google to log in to websites supporting OAuth 2.0 or OpenID Connect; the security of OAuth 2.0 and OpenID Connect is therefore of critical importance. As revealed in previous studies, in practice RPs often implement OAuth 2.0 incorrectly, and so many real-world OAuth 2.0 and OpenID Connect systems are vulnerable to attack. However, users of such flawed systems are typically unaware of these issues, and so are at risk of attacks which could result in unauthorised access to the victim user's account at an RP. In order to address this threat, we have developed OAuthGuard, an OAuth 2.0 and OpenID Connect vulnerability scanner and protector, that works with RPs using Google OAuth 2.0 and OpenID Connect services. It protects user security and privacy even when RPs do not implement OAuth 2.0 or OpenID Connect correctly. We used OAuthGuard to survey the 1000 top-ranked websites supporting Google sign-in for the possible presence of five OAuth 2.0 or OpenID Connect security and privacy vulnerabilities, of which one has not previously been described in the literature. Of the 137 sites in our study that employ Google Sign-in, 69 were found to suffer from at least one serious vulnerability. OAuthGuard was able to protect user security and privacy for 56 of these 69 RPs, and for the other 13 was able to warn users that they were using an insecure implementation.

cs.CR↗

arXiv2018

Mean field dynamics of a quantum tracer particle interacting with a boson gas

We consider the dynamics of a heavy quantum tracer particle coupled to a non-relativistic boson field in ${\mathbb R}^3$. The pair interactions of the bosons are of mean-field type, with coupling strength proportional to $\frac1N$ where $N$ is the expected particle number. Assuming that the mass of the tracer particle is proportional to $N$, we derive generalized Hartree equations in the limit $N\rightarrow\infty$. Moreover, we prove the global well-posedness of the associated Cauchy problem for sufficiently weak interaction potentials.

math-ph↗

arXiv2018

The time-dependent Hartree-Fock-Bogoliubov equations for Bosons

In this article, we use quasifree reduction to derive the time-dependent Hartree-Fock-Bogoliubov (HFB) equations describing the dynamics of quantum fluctuations around a Bose-Einstein condensate in $\mathbb R^d$. We prove global well-posedness for the HFB equations for sufficiently regular pair interaction potentials, and establish key conservation laws. Moreover, we show that the solutions to the HFB equations exhibit a symplectic structure, and have a form reminiscent of a Hamiltonian system. In particular, this is used to relate the HFB equations to the HFB eigenvalue equations encountered in the physics literature. Furthermore, we construct the Gibbs states at positive temperature associated with the HFB equations, and establish criteria for the emergence of Bose-Einstein condensation.

math-ph↗

arXiv2018

On the Hartree-Fock-Bogoliubov equations

We review some results of our paper arXiv:1602.05171v2 on the "nonlinear quasifree approximation" to the many-body Schrödinger dynamics of Bose gases. In that paper, we derive, with the help of this approximation, the time-dependent Hartree-Fock-Bogoliubov (HFB) equations, providing an approximate description of the dynamics of quantum fluctuations around a Bose-Einstein condensate and study properties of these equations.

math-ph↗

arXiv2018

Moments and Regularity for a Boltzmann Equation via Wigner Transform

In this paper, we continue our study of the Boltzmann equation by use of tools originating from the analysis of dispersive equations in quantum dynamics. Specifically, we focus on properties of solutions to the Boltzmann equation with collision kernel equal to a constant in the spatial domain $\mathbb{R}^d$, $d\geq 2$, which we use as a model in this paper. Local well-posedness for this equation has been proven using the Wigner transform when $\left< v \right>^βf_0 \in L^2_v H^α_x$ for $\min (α,β) > \frac{d-1}{2}$. We prove that if $α,β$ are large enough, then it is possible to propagate moments in $x$ and derivatives in $v$ (for instance, $\left< x \right>^k \left< \nabla_v \right>^\ell f \in L^\infty_T L^2_{x,v}$ if $f_0$ is nice enough). The mechanism is an exchange of regularity in return for moments of the (inverse) Wigner transform of $f$. We also prove a persistence of regularity result for the scale of Sobolev spaces $H^{α,β}$; and, continuity of the solution map in $H^{α,β}$. Altogether, these results allow us to conclude non-negativity of solutions, conservation of energy, and the $H$-theorem for sufficiently regular solutions constructed via the Wigner transform. Non-negativity in particular is proven to hold in $H^{α,β}$ for any $α,β> \frac{d-1}{2}$, without any additional regularity or decay assumptions.

math.AP↗

arXiv2018

Mitigating CSRF attacks on OAuth 2.0 and OpenID Connect

Many millions of users routinely use their Google, Facebook and Microsoft accounts to log in to websites supporting OAuth 2.0 and/or OpenID Connect-based single sign on. The security of OAuth 2.0 and OpenID Connect is therefore of critical importance, and it has been widely examined both in theory and in practice. Unfortunately, as these studies have shown, real-world implementations of both schemes are often vulnerable to attack, and in particular to cross-site request forgery (CSRF) attacks. In this paper we propose a new technique which can be used to mitigate CSRF attacks against both OAuth 2.0 and OpenID Connect.

cs.CR↗

arXiv2017

On the scattering problem for infinitely many fermions in dimensions $d\geq3$ at positive temperature

In this paper, we study the dynamics of a system of infinitely many fermions in dimensions $d\geq3$ near thermal equilibrium and prove scattering in the case of small perturbation around equilibrium in a certain generalized Sobolev space of density operators. This work is a continuation of our previous paper, and extends the important recent result of M. Lewin and J. Sabin of a similar type for dimension d=2. In the work at hand, we establish new, improved Strichartz estimates that allow us to control the case $d\geq3$.

math.AP↗

arXiv2017

Local well-posedness for Boltzmann's equation and the Boltzmann hierarchy via Wigner transform

We use the dispersive properties of the linear Schrödinger equation to prove local well-posedness results for the Boltzmann equation and the related Boltzmann hierarchy, set in the spatial domain $\mathbb{R}^d$ for $d\geq 2$. The proofs are based on the use of the (inverse) Wigner transform along with the spacetime Fourier transform. The norms for the initial data $f_0$ are weighted versions of the Sobolev spaces $L^2_v H^α_x$ with $α\in \left( \frac{d-1}{2},\infty\right)$. Our main results are local well-posedness for the Boltzmann equation for cutoff Maxwell molecules and hard spheres, as well as local well-posedness for the Boltzmann hierarchy for cutoff Maxwell molecules (but not hard spheres); the latter result holds without any factorization assumption for the initial data.

math.AP↗

arXiv2016

The weak coupling limit for the random Schrödinger equation: The average wave function

We consider the Schrödinger equation with a time-independent weakly random potential of a strength $ε\ll 1$, with Gaussian statistics. We prove that when the initial condition varies on a scale much larger than the correlation length of the potential, the compensated wave function converges to a deterministic limit on the time scale $t\simε^{-2}$. This is shown under the sharp assumption that the correlation function $R(x)$ of the random potential decays slower than $1/|x|^2$, which ensures that the effective potential is finite. When $R(x)$ decays slower than $1/|x|^2$ we establish an anomalous diffusive behavior for the averaged wave function on a time scale shorter than $ε^{-2}$, as long as the initial condition is "sufficiently macroscopic". We also consider the kinetic regime when the initial condition varies on the same scale as the random potential and obtain the limit of the averaged wave function for potentials with the correlation functions decaying faster than $1/|x|^2$. We use random potentials of the Schonberg class which allows us to bypass the oscillatory phase estimates.

math-ph↗