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This paper addresses the task of counting human actions of interest using sensor data from wearable devices. We propose a novel exemplar-based framework, allowing users to provide exemplars of the actions they want to count by vocalizing predefined sounds ''one'', ''two'', and ''three''. Our method first localizes temporal positions of these utterances from the audio sequence. These positions serve as the basis for identifying exemplars representing the action class of interest. A similarity map is then computed between the exemplars and the entire sensor data sequence, which is further fed into a density estimation module to generate a sequence of estimated density values. Summing these density values provides the final count. To develop and evaluate our approach, we introduce a diverse and realistic dataset consisting of real-world data from 37 subjects and 50 action categories, encompassing both sensor and audio data. The experiments on this dataset demonstrate the viability of the proposed method in counting instances of actions from new classes and subjects that were not part of the training data. On average, the discrepancy between the predicted count and the ground truth value is 7.47, significantly lower than the errors of the frequency-based and transformer-based methods. Our project, code and dataset can be found at https://github.com/cvlab-stonybrook/ExRAC.

Protein-protein interactions (PPIs) are critical for various biological processes, and understanding their dynamics is essential for decoding molecular mechanisms and advancing fields such as cancer research and drug discovery. Mutations in PPIs can disrupt protein binding affinity and lead to functional changes and disease. Predicting the impact of mutations on binding affinity is valuable but experimentally challenging. Computational methods, including physics-based and machine learning-based approaches, have been developed to address this challenge. Machine learning-based methods, fueled by extensive PPI datasets such as Ab-Bind, PINT, SKEMPI, and others, have shown promise in predicting binding affinity changes. However, accurate predictions and generalization of these models across different datasets remain challenging. Geometric graph learning has emerged as a powerful approach, combining graph theory and machine learning, to capture structural features of biomolecules. We present GGL-PPI, a novel method that integrates geometric graph learning and machine learning to predict mutation-induced binding free energy changes. GGL-PPI leverages atom-level graph coloring and multi-scale weighted colored geometric subgraphs to extract informative features, demonstrating superior performance on three validation datasets, namely AB-Bind, SKEMPI 1.0, and SKEMPI 2.0 datasets. Evaluation on a blind test set highlights the unbiased predictions of GGL-PPI for both direct and reverse mutations. The findings underscore the potential of GGL-PPI in accurately predicting binding free energy changes, contributing to our understanding of PPIs and aiding drug design efforts.

End-to-end deep learning approaches has been proven to be efficient in autonomous driving and robotics. By using deep learning techniques for decision-making, those systems are often referred to as a black box, and the result is driven by data. In this paper, we propose PaaS (Planning as a Service), a vanilla module to generate local trajectory planning for autonomous driving in CARLA simulation. Our method is submitted in International CARLA Autonomous Driving Leaderboard (CADL), which is a platform to evaluate the driving proficiency of autonomous agents in realistic traffic scenarios. Our approach focuses on reactive planning in Frenet frame under complex urban street's constraints and driver's comfort. The planner generates a collection of feasible trajectories, leveraging heuristic cost functions with controllable driving style factor to choose the optimal-control path that satisfies safe travelling criteria. PaaS can provide sufficient solutions to handle well under challenging traffic situations in CADL. As the strict evaluation in CADL Map Track, our approach ranked 3rd out of 9 submissions regarding the measure of driving score. However, with the focus on minimizing the risk of maneuver and ensuring passenger safety, our figures corresponding to infraction penalty dominate the two leading submissions for 20 percent., Comment: accepted on 05.06.2023, revised on 15.06.2023, to be published on ICSSE 2023

Understanding and accurately predicting protein-ligand binding affinity are essential in the drug design and discovery process. At present, machine learning-based methodologies are gaining popularity as a means of predicting binding affinity due to their efficiency and accuracy, as well as the increasing availability of structural and binding affinity data for protein-ligand complexes. In biomolecular studies, graph theory has been widely applied since graphs can be used to model molecules or molecular complexes in a natural manner. In the present work, we upgrade the graph-based learners for the study of protein-ligand interactions by integrating extensive atom types such as SYBYL and extended connectivity interactive features (ECIF) into multiscale weighted colored graphs (MWCG). By pairing with the gradient boosting decision tree (GBDT) machine learning algorithm, our approach results in two different methods, namely $^\text{sybyl}\text{GGL}$-Score and $^\text{ecif}\text{GGL}$-Score. Both of our models are extensively validated in their scoring power using three commonly used benchmark datasets in the drug design area, namely CASF-2007, CASF-2013, and CASF-2016. The performance of our best model $^\text{sybyl}\text{GGL}$-Score is compared with other state-of-the-art models in the binding affinity prediction for each benchmark. While both of our models achieve state-of-the-art results, the SYBYL atom-type model $^\text{sybyl}\text{GGL}$-Score outperforms other methods by a wide margin in all benchmarks.

Molecular surface representations have been advertised as a great tool to study protein structure and functions, including protein-ligand binding affinity modeling. However, the conventional surface-area-based methods fail to deliver a competitive performance on the energy scoring tasks. The main reason is the lack of crucial physical and chemical interactions encoded in the molecular surface generations. We present novel molecular surface representations embedded in different scales of the element interactive manifolds featuring the dramatically dimensional reduction and accurately physical and biological properties encoders. Those low-dimensional surface-based descriptors are ready to be paired with any advanced machine learning algorithms to explore the essential structure-activity relationships that give rise to the element interactive surface area-based scoring functions (EISA-score). The newly developed EISA-score has outperformed many state-of-the-art models, including various well-established surface-related representations, in standard PDBbind benchmarks.

Machine learning methods have greatly changed science, engineering, finance, business, and other fields. Despite the tremendous accomplishments of machine learning and deep learning methods, many challenges still remain. In particular, the performance of machine learning methods is often severely affected in case of diverse data, usually associated with smaller data sets or data related to areas of study where the size of the data sets is constrained by the complexity and/or high cost of experiments. Moreover, data with limited labeled samples is a challenge to most learning approaches. In this paper, the aforementioned challenges are addressed by integrating graph-based frameworks, multiscale structure, modified and adapted optimization procedures and semi-supervised techniques. This results in two innovative multiscale Laplacian learning (MLL) approaches for machine learning tasks, such as data classification, and for tackling diverse data, data with limited samples and smaller data sets. The first approach, called multikernel manifold learning (MML), integrates manifold learning with multikernel information and solves a regularization problem consisting of a loss function and a warped kernel regularizer using multiscale graph Laplacians. The second approach, called the multiscale MBO (MMBO) method, introduces multiscale Laplacians to a modification of the famous classical Merriman-Bence-Osher (MBO) scheme, and makes use of fast solvers for finding the approximations to the extremal eigenvectors of the graph Laplacian. We demonstrate the performance of our methods experimentally on a variety of data sets, such as biological, text and image data, and compare them favorably to existing approaches.

Under the global health emergency caused by coronavirus disease 2019 (COVID-19), efficient and specific therapies are urgently needed. Compared with traditional small-molecular drugs, antibody therapies are relatively easy to develop and as specific as vaccines in targeting severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), and thus attract much attention in the past few months. This work reviews seven existing antibodies for SARS-CoV-2 spike (S) protein with three-dimensional (3D) structures deposited in the Protein Data Bank. Five antibody structures associated with SARS-CoV are evaluated for their potential in neutralizing SARS-CoV-2. The interactions of these antibodies with the S protein receptor-binding domain (RBD) are compared with those of angiotensin-converting enzyme 2 (ACE2) and RBD complexes. Due to the orders of magnitude in the discrepancies of experimental binding affinities, we introduce topological data analysis (TDA), a variety of network models, and deep learning to analyze the binding strength and therapeutic potential of the aforementioned fourteen antibody-antigen complexes. The current COVID-19 antibody clinical trials, which are not limited to the S protein target, are also reviewed., Comment: 30 pages, 10 figures, 5 tables

The coronavirus disease 2019 (COVID-19) pandemic caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has infected near 5 million people and led to over 0.3 million deaths. Currently, there is no specific anti-SARS-CoV-2 medication. New drug discovery typically takes more than ten years. Drug repositioning becomes one of the most feasible approaches for combating COVID-19. This work curates the largest available experimental dataset for SARS-CoV-2 or SARS-CoV main protease inhibitors. Based on this dataset, we develop validated machine learning models with relatively low root mean square error to screen 1553 FDA-approved drugs as well as other 7012 investigational or off-market drugs in DrugBank. We found that many existing drugs might be potentially potent to SARS-CoV-2. The druggability of many potent SARS-CoV-2 main protease inhibitors is analyzed. This work offers a foundation for further experimental studies of COVID-19 drug repositioning., Comment: 20 pages, 6 figures and 6 tables

Persistent homology is constrained to purely topological persistence while multiscale graphs account only for geometric information. This work introduces persistent spectral theory to create a unified low-dimensional multiscale paradigm for revealing topological persistence and extracting geometric shape from high-dimensional datasets. For a point-cloud dataset, a filtration procedure is used to generate a sequence of chain complexes and associated families of simplicial complexes and chains, from which we construct persistent combinatorial Laplacian matrices. We show that a full set of topological persistence can be completely recovered from the harmonic persistent spectra, i.e., the spectra that have zero eigenvalues, of the persistent combinatorial Laplacian matrices. However, non-harmonic spectra of the Laplacian matrices induced by the filtration offer another power tool for data analysis, modeling, and prediction. In this work, non-harmonic persistent spectra are successfully devised to analyze the structure and stability of fullerenes and predict the B-factors of a protein, which cannot be straightforwardly extracted from the current persistent homology. Extensive numerical experiments indicate the tremendous potential of the proposed persistent spectral analysis in data science., Comment: 53 pages, 16 figures

Recently, molecular fingerprints extracted from three-dimensional (3D) structures using advanced mathematics, such as algebraic topology, differential geometry, and graph theory have been paired with efficient machine learning, especially deep learning algorithms to outperform other methods in drug discovery applications and competitions. This raises the question of whether classical 2D fingerprints are still valuable in computer-aided drug discovery. This work considers 23 datasets associated with four typical problems, namely protein-ligand binding, toxicity, solubility and partition coefficient to assess the performance of eight 2D fingerprints. Advanced machine learning algorithms including random forest, gradient boosted decision tree, single-task deep neural network and multitask deep neural network are employed to construct efficient 2D-fingerprint based models. Additionally, appropriate consensus models are built to further enhance the performance of 2D-fingerprintbased methods. It is demonstrated that 2D-fingerprint-based models perform as well as the state-of-the-art 3D structure-based models for the predictions of toxicity, solubility, partition coefficient and protein-ligand binding affinity based on only ligand information. However, 3D structure-based models outperform 2D fingerprint-based methods in complex-based protein-ligand binding affinity predictions.

It remains a challenging task to generate a vast variety of novel compounds with desirable pharmacological properties. In this work, a generative network complex (GNC) is proposed as a new platform for designing novel compounds, predicting their physical and chemical properties, and selecting potential drug candidates that fulfill various druggable criteria such as binding affinity, solubility, partition coefficient, etc. We combine a SMILES string generator, which consists of an encoder, a drug-property controlled or regulated latent space, and a decoder, with verification deep neural networks, a target-specific three-dimensional (3D) pose generator, and mathematical deep learning networks to generate new compounds, predict their drug properties, construct 3D poses associated with target proteins, and reevaluate druggability, respectively. New compounds were generated in the latent space by either randomized output, controlled output, or optimized output. In our demonstration, 2.08 million and 2.8 million novel compounds are generated respectively for Cathepsin S and BACE targets. These new compounds are very different from the seeds and cover a larger chemical space. For potentially active compounds, their 3D poses are generated using a state-of-the-art method. The resulting 3D complexes are further evaluated for druggability by a championing deep learning algorithm based on algebraic topology, differential geometry, and algebraic graph theories. Performed on supercomputers, the whole process took less than one week. Therefore, our GNC is an efficient new paradigm for discovering new drug candidates., Comment: 22 pages, 12 figures

We present the performances of our mathematical deep learning (MathDL) models for D3R Grand Challenge 4 (GC4). This challenge involves pose prediction, affinity ranking, and free energy estimation for beta secretase 1 (BACE) as well as affinity ranking and free energy estimation for Cathepsin S (CatS). We have developed advanced mathematics, namely differential geometry, algebraic graph, and/or algebraic topology, to accurately and efficiently encode high dimensional physical/chemical interactions into scalable low-dimensional rotational and translational invariant representations. These representations are integrated with deep learning models, such as generative adversarial networks (GAN) and convolutional neural networks (CNN) for pose prediction and energy evaluation, respectively. Overall, our MathDL models achieved the top place in pose prediction for BACE ligands in Stage 1a. Moreover, our submissions obtained the highest Spearman correlation coefficient on the affinity ranking of 460 CatS compounds, and the smallest centered root mean square error on the free energy set of 39 CatS molecules. It is worthy to mention that our method for docking pose predictions has significantly improved from our previous ones., Comment: 24 pages, 9 figure, and one table

Although algebraic graph theory based models have been widely applied in physical modeling and molecular studies, they are typically incompetent in the analysis and prediction of biomolecular properties when compared with other quantitative approaches. There is a need to explore the capability and limitation of algebraic graph theory for molecular and biomolecular modeling, analysis, and prediction. In this work, we propose novel algebraic graph learning (AGL) models that encode high-dimensional physical and biological information into intrinsically low-dimensional representations. The proposed AGL model introduces multiscale weighted colored subgraphs to describe crucial molecular and biomolecular interactions via graph invariants associated with the graph Laplacian, its pseudo-inverse, and adjacent matrix. Additionally, the AGL models are incorporated with an advanced machine learning algorithm to connect the low-dimensional graph representation of biomolecular structures with their macroscopic properties. Three popular protein-ligand binding affinity benchmarks, namely CASF-2007, CASF-2013, and CASF-2016, are employed to validate the accuracy, robustness, and reliability of the present AGL model. Numerical results indicate that the proposed AGL method outperforms the other state-of-the-art methods in the binding affinity predictions of the protein-ligand complexes., Comment: 13 pages, 6 figures

Motivation: Despite its great success in various physical modeling, differential geometry (DG) has rarely been devised as a versatile tool for analyzing large, diverse and complex molecular and biomolecular datasets due to the limited understanding of its potential power in dimensionality reduction and its ability to encode essential chemical and biological information in differentiable manifolds. Results: We put forward a differential geometry based geometric learning (DG-GL) hypothesis that the intrinsic physics of three-dimensional (3D) molecular structures lies on a family of low-dimensional manifolds embedded in a high-dimensional data space. We encode crucial chemical, physical and biological information into 2D element interactive manifolds, extracted from a high-dimensional structural data space via a multiscale discrete-to-continuum mapping using differentiable density estimators. Differential geometry apparatuses are utilized to construct element interactive curvatures %Gaussian curvature, mean curvature, minimum curvature and maximum curvature in analytical forms for certain analytically differentiable density estimators. These low-dimensional differential geometry representations are paired with a robust machine learning algorithm to showcase their descriptive and predictive powers for large, diverse and complex molecular and biomolecular datasets. Extensive numerical experiments are carried out to demonstrated that the proposed DG-GL strategy outperforms other advanced methods in the predictions of drug discovery related protein-ligand binding affinity, drug toxicity, and molecular solvation free energy., Comment: 28 pages, 14 figures

Advanced mathematics, such as multiscale weighted colored graph and element specific persistent homology, and machine learning including deep neural networks were integrated to construct mathematical deep learning models for pose and binding affinity prediction and ranking in the last two D3R grand challenges in computer-aided drug design and discovery. D3R Grand Challenge 2 (GC2) focused on the pose prediction and binding affinity ranking and free energy prediction for Farnesoid X receptor ligands. Our models obtained the top place in absolute free energy prediction for free energy Set 1 in Stage 2. The latest competition, D3R Grand Challenge 3 (GC3), is considered as the most difficult challenge so far. It has 5 subchallenges involving Cathepsin S and five other kinase targets, namely VEGFR2, JAK2, p38-$\alpha$, TIE2, and ABL1. There is a total of 26 official competitive tasks for GC3. Our predictions were ranked 1st in 10 out of 26 official competitive tasks., Comment: 15 pages, 4 figures

Protein-ligand binding is essential to almost all life processes. The understanding of protein-ligand interactions is fundamentally important to rational drug design and protein design. Based on large scale data sets, we show that protein rigidity strengthening or flexibility reduction is a pivoting mechanism in protein-ligand binding. Our approach based solely on rigidity is able to unveil a surprisingly long range contribution of four residue layers to protein-ligand binding, which has a ramification for drug and protein design. Additionally, the present work reveals that among various pairwise interactions, the short range ones within the distance of the van der Waals diameter are most important. It is found that the present approach outperforms all the other state-of-the-art scoring functions for protein-ligand binding affinity predictions of two benchmark data sets, Comment: 9 pages, 6 figures

The Parallel Meaning Bank is a corpus of translations annotated with shared, formal meaning representations comprising over 11 million words divided over four languages (English, German, Italian, and Dutch). Our approach is based on cross-lingual projection: automatically produced (and manually corrected) semantic annotations for English sentences are mapped onto their word-aligned translations, assuming that the translations are meaning-preserving. The semantic annotation consists of five main steps: (i) segmentation of the text in sentences and lexical items; (ii) syntactic parsing with Combinatory Categorial Grammar; (iii) universal semantic tagging; (iv) symbolization; and (v) compositional semantic analysis based on Discourse Representation Theory. These steps are performed using statistical models trained in a semi-supervised manner. The employed annotation models are all language-neutral. Our first results are promising., Comment: To appear at EACL 2017

Flexibility-rigidity index (FRI) has been developed as a robust, accurate and efficient method for macromolecular thermal fluctuation analysis and B-factor prediction. The performance of FRI depends on its formulations of rigidity index and flexibility index. In this work, we introduce alternative rigidity and flexibility formulations. The structure of the classic Gaussian surface is utilized to construct a new type of rigidity index, which leads to a new class of rigidity densities with the classic Gaussian surface as a special case. Additionally, we introduce a new type of flexibility index based on the domain indicator property of normalized rigidity density. These generalized FRI (gFRI) methods have been extensively validated by the B-factor predictions of 364 proteins. Significantly outperforming the classic Gaussian network model (GNM), gFRI is a new generation of methodologies for accurate, robust and efficient analysis of protein flexibility and fluctuation. Finally, gFRI based molecular surface generation and flexibility visualization are demonstrated., Comment: 12 pages, 4 figures

This paper explores the impact of surface area, volume, curvature and Lennard-Jones potential on solvation free energy predictions. Rigidity surfaces are utilized to generate robust analytical expressions for maximum, minimum, mean and Gaussian curvatures of solvent-solute interfaces, and define a generalized Poisson-Boltzmann (GPB) equation with a smooth dielectric profile. Extensive correlation analysis is performed to examine the linear dependence of surface area, surface enclosed volume, maximum curvature, minimum curvature, mean curvature and Gaussian curvature for solvation modeling. It is found that surface area and surfaces enclosed volumes are highly correlated to each others, and poorly correlated to various curvatures for six test sets of molecules. Different curvatures are weakly correlated to each other for six test sets of molecules, but are strongly correlated to each other within each test set of molecules. Based on correlation analysis, we construct twenty six nontrivial nonpolar solvation models. Our numerical results reveal that the Lennard-Jones (LJ) potential plays a vital role in nonpolar solvation modeling, especially for molecules involving strong van der Waals interactions. It is found that curvatures are at least as important as surface area or surface enclosed volume in nonpolar solvation modeling. In conjugation with the GPB model, various curvature based nonpolar solvation models are shown to offer some of the best solvation free energy predictions for a wide range of test sets. For example, root mean square errors from a model constituting surface area, volume, mean curvature and LJ potential are less than 0.42 kcal/mol for all test sets., Comment: 37 pages, 6 figures

Let $k$ be an algebraically closed field of characteristic $p > 0$, and let $G$ be a simple, simply connected algebraic group defined over $\mathbb{F}_p$. Given $r \geq 1$, set $q=p^r$, and let $G(\mathbb{F}_q)$ be the corresponding finite Chevalley group. In this paper we investigate the structure of the first cohomology group $H^1(G(\mathbb{F}_q),L(\lambda))$ where $L(\lambda)$ is the simple $G$-module of highest weight $\lambda$. Under certain very mild conditions on $p$ and $q$, we are able to completely describe the first cohomology group when $\lambda$ is less than or equal to a fundamental dominant weight. In particular, in the cases we consider, we show that the first cohomology group has dimension at most one. Our calculations significantly extend, and provide new proofs for, earlier results of Cline, Parshall, Scott, and Jones, who considered the special case when $\lambda$ is a minimal nonzero dominant weight., Comment: 24 pages, 5 figures, 6 tables. Typos corrected and some proofs streamlined over previous version