arXiv subjects
Publications and source records attributed to Andrew Ye.
We show that for any closed, orientable surface $K$ smoothly embedded in $\mathbb{R}^4$, the unit $4$-ball $B^4 \subset \mathbb{R}^4$ can be tiled using $n \geq 3$ tiles each congruent to a regular neighborhood (with corners) of a surface smoothly isotopic to $K$. This gives a 4-dimensional analog of tilings of the $3$-ball that were constructed in the 90's using congruent knotted tori.
We propose and study the integration of sentiment analysis and deep reinforcement learning ensemble algorithms for stock trading by evaluating strategies capable of dynamically altering their active agent given the concurrent market environment. In particular, we design a simple-yet-effective method for extracting financial sentiment and combine this with improvements on existing trading agents, resulting in a strategy that effectively considers both qualitative market factors and quantitative stock data. We show that our approach results in a strategy that is profitable, robust, and risk-minimal - outperforming the traditional ensemble strategy as well as single agent algorithms and market metrics. Our findings suggest that the conventional practice of switching and reevaluating agents in ensemble every fixed-number of months is sub-optimal, and that a dynamic sentiment-based framework greatly unlocks additional performance. Furthermore, as we have designed our algorithm with simplicity and efficiency in mind, we hypothesize that the transition of our method from historical evaluation towards real-time trading with live data to be relatively simple.
Nonlinear optics lies at the heart of classical and quantum light generation. The invention of periodic poling revolutionized nonlinear optics and its commercial applications by enabling robust quasi-phase-matching in crystals such as lithium niobate. However, reaching useful frequency conversion efficiencies requires macroscopic dimensions, limiting further technology development and integration. Here we realize a periodically poled van der Waals semiconductor (3R-MoS$_2$). Due to its exceptional nonlinearity, we achieve macroscopic frequency conversion efficiency of 0.03% at the relevant telecom wavelength over a microscopic thickness of 3.4${\mu}$m (that is, 3 poling periods), $10-100\times$ thinner than current systems with similar performances. Due to unique intrinsic cavity effects, the thickness-dependent quasi-phase-matched second harmonic signal surpasses the usual quadratic enhancement by $50\%$. Further, we report the broadband generation of photon pairs at telecom wavelengths via quasi-phase-matched spontaneous parametric down-conversion, showing a maximum coincidence-to-accidental-ratio of $638 \pm 75$. This work opens the new and unexplored field of phase-matched nonlinear optics with microscopic van der Waals crystals, unlocking applications that require simple, ultra-compact technologies such as on-chip entangled photon-pair sources for integrated quantum circuitry and sensing.
Twisted 2D materials form complex moir\'e structures that spontaneously reduce symmetry through picoscale deformation within a mesoscale lattice. We show twisted 2D materials contain a torsional displacement field comprised of three transverse periodic lattice distortions (PLD). The torsional PLD amplitude provides a single order parameter that concisely describes the structural complexity of twisted bilayer moir\'es. Moreover, the structure and amplitude of a torsional periodic lattice distortion is quantifiable using rudimentary electron diffraction methods sensitive to reciprocal space. In twisted bilayer graphene, the torsional PLD begins to form at angles below 3.89{\deg} and the amplitude reaches 8 pm around the magic angle of 1.1{\deg}. At extremely low twist angles (e.g. below 0.25{\deg}) the amplitude increases and additional PLD harmonics arise to expand Bernal stacked domains separated by well defined solitonic boundaries. The torsional distortion field in twisted bilayer graphene is analytically described and has an upper bound of 22.6 pm. Similar torsional distortions are observed in twisted WS$_2$, CrI$_3$, and WSe$_2$ / MoSe$_2$.