arXiv subjects
Publications and source records attributed to Bin Guo.
We design an Algorithm to fabricate universal holomorphic maps between any two complex Euclidean spaces, within preassigned transcendental growth rate. As by-products, universal holomorphic maps from $\mathbb{C}^n$ to $\mathbb{CP}^m$ ($n\leqslant m$) and to complex tori having slow growth are obtained. We take inspiration from Oka manifolds theory, Nevanlinna theory, and hypercyclic operators theory.
Learning accurate cross-domain preference mappings in the absence of overlapped users/items has presented a persistent challenge in Non-overlapping Cross-domain Recommendation (NOCDR). Despite the efforts made in previous studies to address NOCDR, several limitations still exist. Specifically, 1) while some approaches substitute overlapping users/items with overlapping behaviors, they cannot handle NOCDR scenarios where such auxiliary information is unavailable; 2) often, cross-domain preference mapping is modeled by learning deterministic explicit representation matchings between sampled users in two domains. However, this can be biased due to individual preferences and thus fails to incorporate preference continuity and universality of the general population. In light of this, we assume that despite the scattered nature of user behaviors, there exists a consistent latent preference distribution shared among common people. Modeling such distributions further allows us to capture the continuity in user behaviors within each domain and discover preference invariance across domains. To this end, we propose a Distributional domain-invariant Preference Matching method for non-overlapping Cross-Domain Recommendation (DPMCDR). For each domain, we hierarchically approximate a posterior of domain-level preference distribution with empirical evidence derived from user-item interactions. Next, we aim to build distributional implicit matchings between the domain-level preferences of two domains. This process involves mapping them to a shared latent space and seeking a consensus on domain-invariant preference by minimizing the distance between their distributional representations therein. In this way, we can identify the alignment of two non-overlapping domains if they exhibit similar patterns of domain-invariant preference.
Superconducting pairing symmetry are crucial in understanding the microscopic superconducting mechanism of a superconductor. Here we report the observation of a twofold superconducting gap symmetry in an interfacial superconductor Bi$_{2}$Te$_{3}$/FeTe, by employing quasiparticle interference (QPI) technique in scanning tunneling microscopy and macroscopic magnetoresistance measurements. The QPI patterns corresponding to energies inside and outside the gap reveal a clear anisotropic superconducting gap. Furthermore, both the in-plane angle-dependent magnetoresistance and in-plane upper critical field exhibit a clear twofold symmetry. This twofold symmetry align with the Te-Te direction in FeTe, which weakens the possible generation by bi-collinear antiferromagnetism order. Our finding provides key information in further understanding of the topological properties in Bi$_{2}$Te$_{3}$/FeTe superconducting system and propels further theoretical interests in the paring mechanism in the system.
Efficiently obtaining the up-to-date information in the disaster-stricken area is the key to successful disaster response. Unmanned aerial vehicles (UAVs), workers and cars can collaborate to accomplish sensing tasks, such as data collection, in disaster-stricken areas. In this paper, we explicitly address the route planning for a group of agents, including UAVs, workers, and cars, with the goal of maximizing the task completion rate. We propose MANF-RL-RP, a heterogeneous multi-agent route planning algorithm that incorporates several efficient designs, including global-local dual information processing and a tailored model structure for heterogeneous multi-agent systems. Global-local dual information processing encompasses the extraction and dissemination of spatial features from global information, as well as the partitioning and filtering of local information from individual agents. Regarding the construction of the model structure for heterogeneous multi-agent, we perform the following work. We design the same data structure to represent the states of different agents, prove the Markovian property of the decision-making process of agents to simplify the model structure, and also design a reasonable reward function to train the model. Finally, we conducted detailed experiments based on the rich simulation data. In comparison to the baseline algorithms, namely Greedy-SC-RP and MANF-DNN-RP, MANF-RL-RP has exhibited a significant improvement in terms of task completion rate.
In this paper, we study the higher integrability for the gradient of weak solutions of $p(x)$-Laplacians equation with drift terms. We prove a version of generalized Gehring's lemma under some weaker condition on the modulus of continuity of variable exponent $p(x)$ and present a modified version of Sobolev-Poincaré inequality with such an exponent. When $p(x)>2$ we derive the reverse Hölder inequality with a proper dependence on the drift and force terms and establish a specific high integrability result. Our condition on the exponent $p(x)$ is more specific and weaker than the known conditions and our results extend some results on the $p(x)$-Laplacian equations without drift terms.
We investigate the effects of the twist-2 operator in 2D symmetric orbifold CFTs. The twist operator can join together a twist-$M$ state and a twist-$N$ state, creating a twist-$(M+N)$ state. This process involves three effects: pair creation, propagation, and contraction. We study these effects by using a Bogoliubov ansatz and conformal symmetry. In this multi-wound scenario, pair creation no longer decouples from propagation, in contrast to the previous study where $M=N=1$. We derive equations for these effects, which organize themselves into recursion relations and constraints. Using the recursion relations, we can determine the infinite number of coefficients in the effects through a finite number of inputs. Moreover, the number of required inputs can be further reduced by applying constraints.
Personalized dialogue agents (DAs) powered by large pre-trained language models (PLMs) often rely on explicit persona descriptions to maintain personality consistency. However, such descriptions may not always be available or may pose privacy concerns. To tackle this bottleneck, we introduce PersonaPKT, a lightweight transfer learning approach that can build persona-consistent dialogue models without explicit persona descriptions. By representing each persona as a continuous vector, PersonaPKT learns implicit persona-specific features directly from a small number of dialogue samples produced by the same persona, adding less than 0.1% trainable parameters for each persona on top of the PLM backbone. Empirical results demonstrate that PersonaPKT effectively builds personalized DAs with high storage efficiency, outperforming various baselines in terms of persona consistency while maintaining good response generation quality. In addition, it enhances privacy protection by avoiding explicit persona descriptions. Overall, PersonaPKT is an effective solution for creating personalized DAs that respect user privacy.
Top-N recommendation aims to recommend each consumer a small set of N items from a large collection of items, and its accuracy is one of the most common indexes to evaluate the performance of a recommendation system. While a large number of algorithms are proposed to push the Top-N accuracy by learning the user preference from their history purchase data, a predictability question is naturally raised - whether there is an upper limit of such Top-N accuracy. This work investigates such predictability by studying the degree of regularity from a specific set of user behavior data. Quantifying the predictability of Top-N recommendations requires simultaneously quantifying the limits on the accuracy of the N behaviors with the highest probability. This greatly increases the difficulty of the problem. To achieve this, we firstly excavate the associations among N behaviors with the highest probability and describe the user behavior distribution based on the information theory. Then, we adopt the Fano inequality to scale and obtain the Top-N predictability. Extensive experiments are conducted on the real-world data where significant improvements are observed compared to the state-of-the-art methods. We have not only completed the predictability calculation for N targets but also obtained predictability that is much closer to the true value than existing methods. We expect our results to assist these research areas where the quantitative requirement of Top-N predictability is required.
Sharp $L^\infty$ estimates are obtained for general classes of fully non-linear PDE's on non-Kähler manifolds, complementing the theory developed earlier by the authors in joint work with F. Tong for the Kähler case. The key idea is still a comparison with an auxiliary Monge-Ampère equation, but this time on a ball with Dirichlet boundary conditions, so that it always admits a unique solution. The method applies not just to compact Hermitian manifolds, but also to the Dirichlet problem, to open manifolds with a positive lower bound on their injectivity radii, to $(n-1)$ form equations, and even to non-integrable almost-complex or symplectic manifolds. It is the first method applicable in any generality to large classes of non-linear equations, and it usually improves on other methods when they happen to be available for specific equations.
The ubiquity of camera-embedded devices and the advances in deep learning have stimulated various intelligent mobile video applications. These applications often demand on-device processing of video streams to deliver real-time, high-quality services for privacy and robustness concerns. However, the performance of these applications is constrained by the raw video streams, which tend to be taken with small-aperture cameras of ubiquitous mobile platforms in dim light. Despite extensive low-light video enhancement solutions, they are unfit for deployment to mobile devices due to their complex models and and ignorance of system dynamics like energy budgets. In this paper, we propose AdaEnlight, an energy-aware low-light video stream enhancement system on mobile devices. It achieves real-time video enhancement with competitive visual quality while allowing runtime behavior adaptation to the platform-imposed dynamic energy budgets. We report extensive experiments on diverse datasets, scenarios, and platforms and demonstrate the superiority of AdaEnlight compared with state-of-the-art low-light image and video enhancement solutions.
Graph neural networks (GNNs) have been successfully applied to early mild cognitive impairment (EMCI) detection, with the usage of elaborately designed features constructed from blood oxygen level-dependent (BOLD) time series. However, few works explored the feasibility of using BOLD signals directly as features. Meanwhile, existing GNN-based methods primarily rely on hand-crafted explicit brain topology as the adjacency matrix, which is not optimal and ignores the implicit topological organization of the brain. In this paper, we propose a spatial temporal graph convolutional network with a novel graph structure self-learning mechanism for EMCI detection. The proposed spatial temporal graph convolution block directly exploits BOLD time series as input features, which provides an interesting view for rsfMRI-based preclinical AD diagnosis. Moreover, our model can adaptively learn the optimal topological structure and refine edge weights with the graph structure self-learning mechanism. Results on the Alzheimer's Disease Neuroimaging Initiative (ADNI) database show that our method outperforms state-of-the-art approaches. Biomarkers consistent with previous studies can be extracted from the model, proving the reliable interpretability of our method.
This is an introduction to a particular class of auxiliary complex Monge-Ampère equations which had been instrumental in $L^\infty$ estimates for fully non-linear equations and various questions in complex geometry. The essential comparison inequalities are reviewed and shown to apply in many contexts. Adapted to symplectic geometry, with the auxiliary equation given now by a real Monge-Ampère equation, the method gives an improvement of an earlier theorem of Tosatti-Weinkove-Yau, reducing Donaldson's conjecture on the Calabi-Yau equation with a taming symplectic form from an exponential bound to an $L^1$ bound.
In the D1D5 CFT the twist operator of order 2 can twist together two copies in the untwisted sector into a single joined copy in the twisted sector. Traditionally, this effect is computed by using the covering map method. Recently, a new method was developed using the Bogoliubov ansatz and conformal symmetry to compute this effect in a toy model of one free boson. In this paper, we use this method with superconformal symmetry to compute the effect of the twist operator in the D1D5 CFT. This may provide more effective tools for computing correlation functions of twist operators in this system.
We prove a local volume noncollapsing estimate for Kähler metrics induced from a family of complex Monge-Ampère equations, assuming a local Ricci curvature lower bound. This local volume estimate can be applied to establish various diameter and gradient estimate.
Diameter estimates for Kähler metrics are established which require only an entropy bound and no lower bound on the Ricci curvature. The proof builds on recent PDE techniques for $L^\infty$ estimates for the Monge-Ampère equation, with a key improvement allowing degeneracies of the volume form of codimension strictly greater than one. As a consequence, diameter bounds are obtained for long-time solutions of the Kähler-Ricci flow and finite-time solutions when the limiting class is big, as well as for special fibrations of Calabi-Yau manifolds.
We consider D1-D5-P states in the untwisted sector of the D1-D5 orbifold CFT where one copy of the seed CFT has been excited with a left-moving superconformal primary. Despite being BPS at the orbifold point, such states can `lift' as the theory is deformed away from this point in moduli space. We compute this lifting at second order in the deformation parameter for arbitrary left-moving dimension $h$ of this class of states. This result displays an interesting universality since the lifting does not depend on the details of the superconformal primary; it depends only on the dimension. In the large-dimension limit the lift scales as $\sqrt{h}\,$; it is observed that such scaling appears to be a universal property of the lift of D1-D5-P states.
It is interesting to ask: how does the radial space direction emerge from the CFT in gauge-gravity duality? In this context we resolve a long-standing puzzle with the gravity duals of two classes of states in the D1D5 CFT. For each class the CFT states are in the untwisted sector, suggesting that the energy gap should be $1/R_y$ where $R_y$ is the radius of the circle on which the D1D5 CFT is compactified. For one class of states, the gravity dual indeed has exactly this gap, while for the other class, the gravity dual has a very deep throat, leading to an energy gap much smaller than $1/R_y$. We resolve this puzzle by showing that for the latter class of states, perturbing the CFT off its free point leads to the formation of a band structure in the CFT. We also explain why such a band structure does not arise for the first class of states. Thus for the case where a deep throat emerges in the gravity description, the dynamics of falling down this throat is described in the CFT as a sequential `hopping' between states all of which have the same energy at the free point; this hopping amplitude converts an integer spaced spectrum into a closely spaced band of energy levels.
Recent sequential recommendation models rely increasingly on consecutive short-term user-item interaction sequences to model user interests. These approaches have, however, raised concerns about both short- and long-term interests. (1) {\it short-term}: interaction sequences may not result from a monolithic interest, but rather from several intertwined interests, even within a short period of time, resulting in their failures to model skip behaviors; (2) {\it long-term}: interaction sequences are primarily observed sparsely at discrete intervals, other than consecutively over the long run. This renders difficulty in inferring long-term interests, since only discrete interest representations can be derived, without taking into account interest dynamics across sequences. In this study, we address these concerns by learning (1) multi-scale representations of short-term interests; and (2) dynamics-aware representations of long-term interests. To this end, we present an \textbf{I}nterest \textbf{D}ynamics modeling framework using generative \textbf{N}eural \textbf{P}rocesses, coined IDNP, to model user interests from a functional perspective. IDNP learns a global interest function family to define each user's long-term interest as a function instantiation, manifesting interest dynamics through function continuity. Specifically, IDNP first encodes each user's short-term interactions into multi-scale representations, which are then summarized as user context. By combining latent global interest with user context, IDNP then reconstructs long-term user interest functions and predicts interactions at upcoming query timestep. Moreover, IDNP can model such interest functions even when interaction sequences are limited and non-consecutive. Extensive experiments on four real-world datasets demonstrate that our model outperforms state-of-the-arts on various evaluation metrics.