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Molecular representation learning (MRL) is a fundamental task for drug discovery. However, previous deep-learning (DL) methods focus excessively on learning robust inner-molecular representations by mask-dominated pretraining framework, neglecting abundant chemical reactivity molecular relationships that have been demonstrated as the determining factor for various molecular property prediction tasks. Here, we present MolCAP to promote MRL, a graph pretraining Transformer based on chemical reactivity (IMR) knowledge with prompted finetuning. Results show that MolCAP outperforms comparative methods based on traditional molecular pretraining framework, in 13 publicly available molecular datasets across a diversity of biomedical tasks. Prompted by MolCAP, even basic graph neural networks are capable of achieving surprising performance that outperforms previous models, indicating the promising prospect of applying reactivity information for MRL. In addition, manual designed molecular templets are potential to uncover the dataset bias. All in all, we expect our MolCAP to gain more chemical meaningful insights for the entire process of drug discovery.

Rapid developments in satellite remote-sensing technology have enabled the collection of geospatial data on a global scale, hence increasing the need for covariance functions that can capture spatial dependence on spherical domains. We propose a general method of constructing nonstationary, locally anisotropic covariance functions on the sphere based on covariance functions in R^3. We also provide theorems that specify the conditions under which the resulting correlation function is isotropic or axially symmetric. For large datasets on the sphere commonly seen in modern applications, the Vecchia approximation is used to achieve higher scalability on statistical inference. The importance of flexible covariance structures is demonstrated numerically using simulated data and a precipitation dataset.

Inspired by allocation strategies in multi-armed bandit model, we propose a pathwise construction of Walsh diffusions. For any infinitesimal generator on a star shaped graph, there exists a unique time change associated with a multi-parameter process such that the time change of this multi-parameter process is the desired diffusion. The time change has an interpretation of time allocation of the process on each edge, and it can be derived explicitly from a family of equations., Comment: Typos corrected and some lemmata whose are added for additional clarification

Model compression aims to reduce the redundancy of deep networks to obtain compact models. Recently, channel pruning has become one of the predominant compression methods to deploy deep models on resource-constrained devices. Most channel pruning methods often use a fixed compression rate for all the layers of the model, which, however, may not be optimal. To address this issue, given a target compression rate for the whole model, one can search for the optimal compression rate for each layer. Nevertheless, these methods perform channel pruning for a specific target compression rate. When we consider multiple compression rates, they have to repeat the channel pruning process multiple times, which is very inefficient yet unnecessary. To address this issue, we propose a Conditional Automated Channel Pruning(CACP) method to obtain the compressed models with different compression rates through single channel pruning process. To this end, we develop a conditional model that takes an arbitrary compression rate as input and outputs the corresponding compressed model. In the experiments, the resultant models with different compression rates consistently outperform the models compressed by existing methods with a channel pruning process for each target compression rate.

We study the role of anharmonicity at interfaces with an added intermediate layer designed to facilitate interfacial phonon transport. Our results demonstrate that while in the harmonic limit the bridge may lower the conductance due to fewer available channels, anharmonicity can strongly enhance the thermal conductance of the bridged structure due to added inelastic channels. Moreover, we show that the effect of anharmonicity on the conductance can be tuned by varying temperature or the bridge layer thickness, as both parameters change the total rate of occurrence of phonon-phonon scattering processes. Additionally, we show that the additive rule of thermal resistances(Ohms law) is valid for bridge layer thickness quite shorter than the average bulk MFP, beyond the regime it would be expected to fail.

A \emph{new} notion of equilibrium, which we call \emph{strong equilibrium}, is introduced for time-inconsistent stopping problems in continuous time. Compared to the existing notions introduced in ArXiv: 1502.03998 and ArXiv: 1709.05181, which in this paper are called \emph{mild equilibrium} and \emph{weak equilibrium} respectively, a strong equilibrium captures the idea of subgame perfect Nash equilibrium more accurately. When the state process is a continuous-time Markov chain and the discount function is log sub-additive, we show that an optimal mild equilibrium is always a strong equilibrium. Moreover, we provide a new iteration method that can directly construct an optimal mild equilibrium and thus also prove its existence., Comment: Final version. To appear in Mathematical Finance. Keywords:Time-inconsistency, optimal stopping, strong equilibria, weak equilibria, mild equilibria, non-exponential discounting, subgame perfect Nash equilibrium

We numerically investigate thermal transport at solid-solid interfaces with graded intermediate layers whose masses vary exponentially from one side to the other. Using Non-Equilibrium Green's Function and Non-Equilibrium Molecular Dynamics simulations, we show that an exponentially mass-graded junction with a finite thickness can result in 68\% of enhancement in thermal conductance larger compared to a single bridging layer (29\%) and a linear mass-graded junction (64\%) of similar thickness. We examine how the thermal conductance at such interfaces is influenced by geometric qualities and strength of anharmonicity. For geometric properties, we tested the effects from number of layers and the junction thickness. In the absence of anharmonicity, increasing the number of layers results in better elastic phonon transmission at each individual boundary, countered by the decrease of available conducting channels. Consequently, in the harmonic regime, conductance initially increases with number of layers due to better bridging, but quickly saturates. The presence of slight anharmonic effects (at ultra-low temperature T = 2 K) turns the saturation into a monotonically increasing trend. Anharmonic effects can facilitate interfacial thermal transport through the thermalization of phonons. At high temperature, however, the role of anharmonicity as a facilitator of interfacial thermal transport reverses. Strong anharmonicity introduces significant intrinsic resistance, overruling the enhancement in thermal conduction at the boundaries. Our analysis shows that in our model Lennard-Jones system, the influence of a mass-graded junction on thermal conductance is dominated by the phonon thermalization through anharmonic effects, while elastic phonon transmission plays a secondary role.

Inspired by Strotz's consistent planning strategy, we formulate the infinite horizon mean-variance stopping problem as a subgame perfect Nash equilibrium in order to determine time consistent strategies with no regret. Equilibria among stopping times or randomized stopping times may not exist. This motivates us to consider the notion of liquidation strategies, which lets the stopping right to be divisible. We then argue that the mean-standard deviation variant of this problem makes more sense for this type of strategies in terms of time consistency. It turns out that an equilibrium liquidation strategy always exists. We then analyze whether optimal equilibrium liquidation strategies exist and whether they are unique and observe that neither may hold., Comment: Final version. To appear in the SIAM Journal on Financial Mathematics. Keywords: Time-inconsistency, optimal stopping, liquidation strategy, mean-variance problem, subgame perfect Nash equilibrium