Towards the Characterization of Terminal Cut Functions: a Condition for Laminar Families

We study the following characterization problem. Given a set $T$ of terminals and a $(2^{|T|}-2)$-dimensional vector $\pi$ whose coordinates are indexed by proper subsets of $T$, is there a graph $G$ that contains $T$, such that for all subsets $\emptyset\subsetneq S\subsetneq T$, $\pi_S$ equals the value of the min-cut in $G$ separating $S$ from $T\setminus S$? The only known necessary conditions are submodularity and a special class of linear inequalities given by Chaudhuri, Subrahmanyam, Wagner and Zaroliagis. Our main result is a new class of linear inequalities concerning laminar families, that generalize all previous ones. Using our new class of inequalities, we can generalize Karger's approximate min-cut counting result to graphs with terminals

Multi-level Fusion of Wav2vec 2.0 and BERT for Multimodal Emotion Recognition

The research and applications of multimodal emotion recognition have become increasingly popular recently. However, multimodal emotion recognition faces the challenge of lack of data. To solve this problem, we propose to use transfer learning which leverages state-of-the-art pre-trained models including wav2vec 2.0 and BERT for this task. Multi-level fusion approaches including coattention-based early fusion and late fusion with the models trained on both embeddings are explored. Also, a multi-granularity framework which extracts not only frame-level speech embeddings but also segment-level embeddings including phone, syllable and word-level speech embeddings is proposed to further boost the performance. By combining our coattention-based early fusion model and late fusion model with the multi-granularity feature extraction framework, we obtain result that outperforms best baseline approaches by 1.3% unweighted accuracy (UA) on the IEMOCAP dataset.Comment: Accepted to INTERSPEECH 202

Query Complexity of the Metric Steiner Tree Problem

We study the query complexity of the metric Steiner Tree problem, where we are given an $n \times n$ metric on a set $V$ of vertices along with a set $T \subseteq V$ of $k$ terminals, and the goal is to find a tree of minimum cost that contains all terminals in $T$. The query complexity for the related minimum spanning tree (MST) problem is well-understood: for any fixed $\varepsilon > 0$, one can estimate the MST cost to within a $(1+\varepsilon)$-factor using only $\tilde{O}(n)$ queries, and this is known to be tight. This implies that a $(2 + \varepsilon)$-approximate estimate of Steiner Tree cost can be obtained with $\tilde{O}(k)$ queries by simply applying the MST cost estimation algorithm on the metric induced by the terminals. Our first result shows that any (randomized) algorithm that estimates the Steiner Tree cost to within a $(5/3 - \varepsilon)$-factor requires $\Omega(n^2)$ queries, even if $k$ is a constant. This lower bound is in sharp contrast to an upper bound of $O(nk)$ queries for computing a $(5/3)$-approximate Steiner Tree, which follows from previous work by Du and Zelikovsky. Our second main result, and the main technical contribution of this work, is a sublinear query algorithm for estimating the Steiner Tree cost to within a strictly better-than-$2$ factor, with query complexity $\tilde{O}(n^{12/7} + n^{6/7}\cdot k)=\tilde{O}(n^{13/7})=o(n^2)$. We complement this result by showing an $\tilde{\Omega}(n + k^{6/5})$ query lower bound for any algorithm that estimates Steiner Tree cost to a strictly better than $2$ factor. Thus $\tilde{\Omega}(n^{6/5})$ queries are needed to just beat $2$-approximation when $k = \Omega(n)$; a sharp contrast to MST cost estimation where a $(1+o(1))$-approximate estimate of cost is achievable with only $\tilde{O}(n)$ queries

The Application of OCTA in Assessment of Anti-VEGF Therapy for Idiopathic Choroidal Neovascularization

Purpose. To assess the morphology of idiopathic choroidal neovascularization (ICNV) by optical coherence tomography angiography (OCTA) and determine the therapeutic effects of intravitreal antivascular endothelial growth factor (anti-VEGF). Method. Patients with naive ICNV were assessed by spectral domain optical coherence tomography (SD-OCT) and OCTA in this observational study. The timing of observation was before treatment, 1 day after treatment with intravitreal anti-VEGF injection, and 1 month after the treatment. The central retina thickness (CRT) on SD-OCT, selected CNV area, and flow area on OCTA were measured. Results. A total of 17 eyes from 17 patients with ICNV were included in this study. OCTA showed visible irregular choroidal neovascularization with “tree-in-bud” form on outer retinal layer. After treatment, as well as in the 1-day follow-up, CNV decreased in size from the periphery, and the vessel density was reduced. As shown on OCTA, the selected CNV area and flow area were significantly reduced compared to pretreatment. The rate of CNV vessel area changes was higher on OCTA than the changes in CRT on SD-OCT at 1-day and 1-month follow-up. Conclusion. Intravitreal injection of anti-VEGF is effective for idiopathic choroidal neovascularization, and the treatment outcomes are observable after 1 day. OCTA provides a useful approach for monitoring and evaluating the treatment of intravitreal anti-VEGF for CNV

NeRF-Enhanced Outpainting for Faithful Field-of-View Extrapolation

In various applications, such as robotic navigation and remote visual assistance, expanding the field of view (FOV) of the camera proves beneficial for enhancing environmental perception. Unlike image outpainting techniques aimed solely at generating aesthetically pleasing visuals, these applications demand an extended view that faithfully represents the scene. To achieve this, we formulate a new problem of faithful FOV extrapolation that utilizes a set of pre-captured images as prior knowledge of the scene. To address this problem, we present a simple yet effective solution called NeRF-Enhanced Outpainting (NEO) that uses extended-FOV images generated through NeRF to train a scene-specific image outpainting model. To assess the performance of NEO, we conduct comprehensive evaluations on three photorealistic datasets and one real-world dataset. Extensive experiments on the benchmark datasets showcase the robustness and potential of our method in addressing this challenge. We believe our work lays a strong foundation for future exploration within the research community

Molecular Conformation Generation via Shifting Scores

Molecular conformation generation, a critical aspect of computational chemistry, involves producing the three-dimensional conformer geometry for a given molecule. Generating molecular conformation via diffusion requires learning to reverse a noising process. Diffusion on inter-atomic distances instead of conformation preserves SE(3)-equivalence and shows superior performance compared to alternative techniques, whereas related generative modelings are predominantly based upon heuristical assumptions. In response to this, we propose a novel molecular conformation generation approach driven by the observation that the disintegration of a molecule can be viewed as casting increasing force fields to its composing atoms, such that the distribution of the change of inter-atomic distance shifts from Gaussian to Maxwell-Boltzmann distribution. The corresponding generative modeling ensures a feasible inter-atomic distance geometry and exhibits time reversibility. Experimental results on molecular datasets demonstrate the advantages of the proposed shifting distribution compared to the state-of-the-art.Comment: 18 pages, 7 figure