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The upper tail problem in a sparse Erd\H{o}s-R\'enyi graph asks for the probability that the number of copies of some fixed subgraph exceeds its expected value by a constant factor. We study the analogous problem for oriented subgraphs in directed random graphs. By adapting the proof of Cook, Dembo, and Pham, we reduce this upper tail problem to the asymptotic of a certain variational problem over edge weighted directed graphs. We give upper and lower bounds for the solution to the corresponding variational problem, which differ by a constant factor of at most $2$. We provide a host of subgraphs where the upper and lower bounds coincide, giving the solution to the upper tail problem. Examples of such digraphs include triangles, stars, directed $k$-cycles, and balanced digraphs., Comment: 18 pages

While piano music transcription models have shown high performance for solo piano recordings, their performance degrades when applied to ensemble recordings. This study aims to analyze the impact of different data augmentation methods on piano transcription performance, specifically focusing on mixing techniques applied to violin-piano ensembles. We apply mixing methods that consider both harmonic and temporal characteristics of the audio. To create datasets for this study, we generated the PFVN-synth dataset, which contains 7 hours of violin-piano ensemble audio by rendering MIDI files and corresponding labels, and also collected unaccompanied violin recordings and mixed them with the MAESTRO dataset. We evaluated the transcription results on both synthesized and real audio recordings datasets., Comment: To Appear IEEE ICASSP 2023

An almost complex torus manifold is a $2n$-dimensional compact connected almost complex manifold equipped with an effective action of a real $n$-dimensional torus $T^n \simeq (S^1)^n$ that has fixed points. For an almost complex torus manifold, there is a labeled directed graph which contains information on weights at the fixed points and isotropy spheres. Let $M$ be a 6-dimensional almost complex torus manifold with Euler number 6. We show that two types of graphs occur for $M$, and for each type of graph we construct such a manifold $M$, proving the existence. Using the graphs, we determine the Chern numbers and the Hirzebruch $\chi_y$-genus of $M$.

For any weakly mixing system $(X, \mathscr{B}, \mu, T)$ and $A, B \in \mathscr{B}$, there is a density zero set $J_{A,B}$ such that $\mu(A\cap T^{-n}B)$ converges to $\mu(A)\mu(B)$ for $n \notin J$. In this paper, we study bounds on the size of this exceptional set $J$. First, we show that, given the rate of weak mixing, we can find an upper bound on the size of $J$. We use this property to show the existence of an exceptional set $J$ of an interval exchange system with either $\left|J \cap [0, n]\right| \le Cn\log^{-a}n$ or $\left|J \cap [0, n]\right| \le Cn^{1 - \alpha}$, depending on whether or not the transformation is of rotation class. We also explicitly construct an exceptional set $J$ for the Chacon transformation and give upper and lower bounds for its size. More precisely, we show that there is a constant $C>0$ such that for any increasing function $h: \mathbb{R}_+ \to \mathbb{R}_+$ diverging to infinity, there is an exceptional set $J \subseteq \mathbb{N}$ such that $\left|J \cap [0, n]\right|\le Cf(n)$ for every Lebesgue measurable sets $A, B \subseteq [0,1]$, where $f(n) = (\log n)^{(\log \log n)^2h(n)}$. For the lower bound, we prove that for any $t>0$, there exists Lebesgue measurable sets $A, B\subseteq [0,1]$ and $C, N>0$ such that $\left|J_{A,B}\cap [0,n]\right|\geq C(\log n)^t$ for every $n>N$., Comment: 23 pages, 3 figures

Solar thermochemical hydrogen generation (STCH) is a promising approach for eco-friendly H2 production, but conventional STCH redox compounds often suffer from thermodynamic and kinetic limitations with limited tunability. Expanding from the nascent high-entropy ceramics field, this study explores a new class of compositionally complex perovskite oxides (La0.8Sr0.2)(Mn(1-x)/3Fe(1-x)/3CoxAl(1-x)/3)O3 for STCH. In situ X-ray diffraction demonstrates the phase stability during redox cycling and in situ X-ray photoelectron spectroscopy shows preferential redox of Co. The extent of reduction increases, but the intrinsic kinetics decreases, with increased Co content. Consequently, (La0.8Sr0.2)(Mn0.2Fe0.2Co0.4Al0.2)O3-{\delta} achieves an optimal balance between the thermodynamics and kinetics properties. The combination of a moderate enthalpy of reduction, high entropy of reduction, and preferable surface oxygen exchange kinetics enables a maximum H2 yield of 395 +- 11 {\mu}mol g-1 in a short 1-hour redox duration. Entropy stabilization expectedly contributes to the structure stability during redox without phase transformation, which enables an exceptional STCH stability for >50 cycles under harsh interrupted conditions. The underlying redox mechanism is further elucidated by the density functional theory based parallel Monte Carlo computation, which represents a new computation paradigm first established here. This study suggests a new class of non-equimolar compositionally complex ceramics for STCH and chemical looping.