Inexpensive numerical methods are key to enable simulations of systems of a large number of particles of different shapes in Stokes flow. Several approximate methods have been introduced for this purpose. We study the accuracy of the multiblob method for solving the Stokes mobility problem in free space, where the 3D geometry of a particle surface is discretised with spherical blobs and the pair-wise interaction between blobs is described by the RPY-tensor. The paper aims to investigate and improve on the magnitude of the error in the solution velocities of the Stokes mobility problem using a combination of two different techniques: an optimally chosen grid of blobs and a pair-correction inspired by Stokesian dynamics. Optimisation strategies to determine a grid with a certain number of blobs are presented with the aim of matching the hydrodynamic response of a single accurately described ideal particle, alone in the fluid. Small errors in this self-interaction are essential as they determine the basic error level in a system of well-separated particles. With a good match, reasonable accuracy can be obtained even with coarse blob-resolutions of the particle surfaces. The error in the self-interaction is however sensitive to the exact choice of grid parameters and simply hand-picking a suitable blob geometry can lead to errors several orders of magnitude larger in size. The pair-correction is local and cheap to apply, and reduces on the error for more closely interacting particles. Two different types of geometries are considered: spheres and axisymmetric rods with smooth caps. The error in solutions to mobility problems is quantified for particles of varying inter-particle distances for systems containing a few particles, comparing to an accurate solution based on a second kind BIE-formulation where the quadrature error is controlled by employing quadrature by expansion (QBX).

The hypergraph Moore bound is an elegant statement that characterizes the extremal trade-off between the girth - the number of hyperedges in the smallest cycle or even cover (a subhypergraph with all degrees even) and size - the number of hyperedges in a hypergraph. For graphs (i.e., $2$-uniform hypergraphs), a bound tight up to the leading constant was proven in a classical work of Alon, Hoory and Linial [AHL02]. For hypergraphs of uniformity $k>2$, an appropriate generalization was conjectured by Feige [Fei08]. The conjecture was settled up to an additional $\log^{4k+1} n$ factor in the size in a recent work of Guruswami, Kothari and Manohar [GKM21]. Their argument relies on a connection between the existence of short even covers and the spectrum of a certain randomly signed Kikuchi matrix. Their analysis, especially for the case of odd $k$, is significantly complicated. In this work, we present a substantially simpler and shorter proof of the hypergraph Moore bound. Our key idea is the use of a new reweighted Kikuchi matrix and an edge deletion step that allows us to drop several involved steps in [GKM21]'s analysis such as combinatorial bucketing of rows of the Kikuchi matrix and the use of the Schudy-Sviridenko polynomial concentration. Our simpler proof also obtains tighter parameters: in particular, the argument gives a new proof of the classical Moore bound of [AHL02] with no loss (the proof in [GKM21] loses a $\log^3 n$ factor), and loses only a single logarithmic factor for all $k>2$-uniform hypergraphs. As in [GKM21], our ideas naturally extend to yield a simpler proof of the full trade-off for strongly refuting smoothed instances of constraint satisfaction problems with similarly improved parameters.

Node elimination is a numerical approach to obtain cubature rules for the approximation of multivariate integrals. Beginning with a known cubature rule, nodes are selected for elimination, and a new, more efficient rule is constructed by iteratively solving the moment equations. This paper introduces a new criterion for selecting which nodes to eliminate that is based on a linearization of the moment equation. In addition, a penalized iterative solver is introduced, that ensures that weights are positive and nodes are inside the integration domain. A strategy for constructing an initial quadrature rule for various polytopes in several space dimensions is described. High efficiency rules are presented for two, three and four dimensional polytopes. The new rules are compared with rules that are obtained by combining tensor products of one dimensional quadrature rules and domain transformations, as well as with known analytically constructed cubature rules.

We present a correlated \textit{and} gate which may be used to propagate uncertainty and dependence through Boolean functions, since any Boolean function may be expressed as a combination of \textit{and} and \textit{not} operations. We argue that the \textit{and} gate is a bivariate copula family, which has the interpretation of constructing bivariate Bernoulli random variables following a given Pearson correlation coefficient and marginal probabilities. We show how this copula family may be used to propagate uncertainty in the form of probabilities of events, probability intervals, and probability boxes, with only partial or no knowledge of the dependency between events, expressed as an interval for the correlation coefficient. These results generalise previous results by Fr\'echet on the conjunction of two events with unknown dependencies. We show an application propagating uncertainty through a fault tree for a pressure tank. This paper comes with an open-source Julia library for performing uncertainty logic.

It has been rightfully emphasized that the use of AI for clinical decision making could amplify health disparities. An algorithm may encode protected characteristics, and then use this information for making predictions due to undesirable correlations in the (historical) training data. It remains unclear how we can establish whether such information is actually used. Besides the scarcity of data from underserved populations, very little is known about how dataset biases manifest in predictive models and how this may result in disparate performance. This article aims to shed some light on these issues by exploring new methodology for subgroup analysis in image-based disease detection models. We utilize two publicly available chest X-ray datasets, CheXpert and MIMIC-CXR, to study performance disparities across race and biological sex in deep learning models. We explore test set resampling, transfer learning, multitask learning, and model inspection to assess the relationship between the encoding of protected characteristics and disease detection performance across subgroups. We confirm subgroup disparities in terms of shifted true and false positive rates which are partially removed after correcting for population and prevalence shifts in the test sets. We further find a previously used transfer learning method to be insufficient for establishing whether specific patient information is used for making predictions. The proposed combination of test-set resampling, multitask learning, and model inspection reveals valuable new insights about the way protected characteristics are encoded in the feature representations of deep neural networks.

Since 2016, sharding has become an auspicious solution to tackle the scalability issue in legacy blockchain systems. Despite its potential to strongly boost the blockchain throughput, sharding comes with its own security issues. To ease the process of deciding which shard to place transactions, existing sharding protocols use a hash-based transaction sharding in which the hash value of a transaction determines its output shard. Unfortunately, we show that this mechanism opens up a loophole that could be exploited to conduct a single-shard flooding attack, a type of Denial-of-Service (DoS) attack, to overwhelm a single shard that ends up reducing the performance of the system as a whole. To counter the single-shard flooding attack, we propose a countermeasure that essentially eliminates the loophole by rejecting the use of hash-based transaction sharding. The countermeasure leverages the Trusted Execution Environment (TEE) to let blockchain's validators securely execute a transaction sharding algorithm with a negligible overhead. We provide a formal specification for the countermeasure and analyze its security properties in the Universal Composability (UC) framework. Finally, a proof-of-concept is developed to demonstrate the feasibility and practicality of our solution.

Cross-chain interaction is among different blockchains. When the number of blockchains increases, it is difficult for blockchains to form a single star topology or a fully connected topology. Meanwhile, different from legacy networks, the propagation method is required to keep the data validity. Thus, the blockchain topology and associated propagation methods are two key issues, which should be ensured during the propagation. In this paper, we first propose the confirmation-based propagation method to keep the validity of the cross-chain data. The confirmation method is to seal the cross-chain transaction synchronized from other blockchains. Second, we point out that a valid topology requires blockchains to be strongly connected. With this requirement, we propose several topologies, which match different connection scenarios. The simulation results show that the proposed methods can securely propagate the cross-chain data and the connection way is flexible.

Convolutional neural networks (CNN) are the dominant deep neural network (DNN) architecture for computer vision. Recently, Transformer and multi-layer perceptron (MLP)-based models, such as Vision Transformer and MLP-Mixer, started to lead new trends as they showed promising results in the ImageNet classification task. In this paper, we conduct empirical studies on these DNN structures and try to understand their respective pros and cons. To ensure a fair comparison, we first develop a unified framework called SPACH which adopts separate modules for spatial and channel processing. Our experiments under the SPACH framework reveal that all structures can achieve competitive performance at a moderate scale. However, they demonstrate distinctive behaviors when the network size scales up. Based on our findings, we propose two hybrid models using convolution and Transformer modules. The resulting Hybrid-MS-S+ model achieves 83.9% top-1 accuracy with 63M parameters and 12.3G FLOPS. It is already on par with the SOTA models with sophisticated designs. The code and models will be made publicly available.

The inductive biases of graph representation learning algorithms are often encoded in the background geometry of their embedding space. In this paper, we show that general directed graphs can be effectively represented by an embedding model that combines three components: a pseudo-Riemannian metric structure, a non-trivial global topology, and a unique likelihood function that explicitly incorporates a preferred direction in embedding space. We demonstrate the representational capabilities of this method by applying it to the task of link prediction on a series of synthetic and real directed graphs from natural language applications and biology. In particular, we show that low-dimensional cylindrical Minkowski and anti-de Sitter spacetimes can produce equal or better graph representations than curved Riemannian manifolds of higher dimensions.

Many modern data analytics applications on graphs operate on domains where graph topology is not known a priori, and hence its determination becomes part of the problem definition, rather than serving as prior knowledge which aids the problem solution. Part III of this monograph starts by addressing ways to learn graph topology, from the case where the physics of the problem already suggest a possible topology, through to most general cases where the graph topology is learned from the data. A particular emphasis is on graph topology definition based on the correlation and precision matrices of the observed data, combined with additional prior knowledge and structural conditions, such as the smoothness or sparsity of graph connections. For learning sparse graphs (with small number of edges), the least absolute shrinkage and selection operator, known as LASSO is employed, along with its graph specific variant, graphical LASSO. For completeness, both variants of LASSO are derived in an intuitive way, and explained. An in-depth elaboration of the graph topology learning paradigm is provided through several examples on physically well defined graphs, such as electric circuits, linear heat transfer, social and computer networks, and spring-mass systems. As many graph neural networks (GNN) and convolutional graph networks (GCN) are emerging, we have also reviewed the main trends in GNNs and GCNs, from the perspective of graph signal filtering. Tensor representation of lattice-structured graphs is next considered, and it is shown that tensors (multidimensional data arrays) are a special class of graph signals, whereby the graph vertices reside on a high-dimensional regular lattice structure. This part of monograph concludes with two emerging applications in financial data processing and underground transportation networks modeling.

Inexpensive numerical methods are key to enable simulations of systems of a large number of particles of different shapes in Stokes flow. Several approximate methods have been introduced for this purpose. We study the accuracy of the multiblob method for solving the Stokes mobility problem in free space, where the 3D geometry of a particle surface is discretised with spherical blobs and the pair-wise interaction between blobs is described by the RPY-tensor. The paper aims to investigate and improve on the magnitude of the error in the solution velocities of the Stokes mobility problem using a combination of two different techniques: an optimally chosen grid of blobs and a pair-correction inspired by Stokesian dynamics. Optimisation strategies to determine a grid with a certain number of blobs are presented with the aim of matching the hydrodynamic response of a single accurately described ideal particle, alone in the fluid. Small errors in this self-interaction are essential as they determine the basic error level in a system of well-separated particles. With a good match, reasonable accuracy can be obtained even with coarse blob-resolutions of the particle surfaces. The error in the self-interaction is however sensitive to the exact choice of grid parameters and simply hand-picking a suitable blob geometry can lead to errors several orders of magnitude larger in size. The pair-correction is local and cheap to apply, and reduces on the error for more closely interacting particles. Two different types of geometries are considered: spheres and axisymmetric rods with smooth caps. The error in solutions to mobility problems is quantified for particles of varying inter-particle distances for systems containing a few particles, comparing to an accurate solution based on a second kind BIE-formulation where the quadrature error is controlled by employing quadrature by expansion (QBX).

The hypergraph Moore bound is an elegant statement that characterizes the extremal trade-off between the girth - the number of hyperedges in the smallest cycle or even cover (a subhypergraph with all degrees even) and size - the number of hyperedges in a hypergraph. For graphs (i.e., $2$-uniform hypergraphs), a bound tight up to the leading constant was proven in a classical work of Alon, Hoory and Linial [AHL02]. For hypergraphs of uniformity $k>2$, an appropriate generalization was conjectured by Feige [Fei08]. The conjecture was settled up to an additional $\log^{4k+1} n$ factor in the size in a recent work of Guruswami, Kothari and Manohar [GKM21]. Their argument relies on a connection between the existence of short even covers and the spectrum of a certain randomly signed Kikuchi matrix. Their analysis, especially for the case of odd $k$, is significantly complicated. In this work, we present a substantially simpler and shorter proof of the hypergraph Moore bound. Our key idea is the use of a new reweighted Kikuchi matrix and an edge deletion step that allows us to drop several involved steps in [GKM21]'s analysis such as combinatorial bucketing of rows of the Kikuchi matrix and the use of the Schudy-Sviridenko polynomial concentration. Our simpler proof also obtains tighter parameters: in particular, the argument gives a new proof of the classical Moore bound of [AHL02] with no loss (the proof in [GKM21] loses a $\log^3 n$ factor), and loses only a single logarithmic factor for all $k>2$-uniform hypergraphs. As in [GKM21], our ideas naturally extend to yield a simpler proof of the full trade-off for strongly refuting smoothed instances of constraint satisfaction problems with similarly improved parameters.

Node elimination is a numerical approach to obtain cubature rules for the approximation of multivariate integrals. Beginning with a known cubature rule, nodes are selected for elimination, and a new, more efficient rule is constructed by iteratively solving the moment equations. This paper introduces a new criterion for selecting which nodes to eliminate that is based on a linearization of the moment equation. In addition, a penalized iterative solver is introduced, that ensures that weights are positive and nodes are inside the integration domain. A strategy for constructing an initial quadrature rule for various polytopes in several space dimensions is described. High efficiency rules are presented for two, three and four dimensional polytopes. The new rules are compared with rules that are obtained by combining tensor products of one dimensional quadrature rules and domain transformations, as well as with known analytically constructed cubature rules.

We present a correlated \textit{and} gate which may be used to propagate uncertainty and dependence through Boolean functions, since any Boolean function may be expressed as a combination of \textit{and} and \textit{not} operations. We argue that the \textit{and} gate is a bivariate copula family, which has the interpretation of constructing bivariate Bernoulli random variables following a given Pearson correlation coefficient and marginal probabilities. We show how this copula family may be used to propagate uncertainty in the form of probabilities of events, probability intervals, and probability boxes, with only partial or no knowledge of the dependency between events, expressed as an interval for the correlation coefficient. These results generalise previous results by Fr\'echet on the conjunction of two events with unknown dependencies. We show an application propagating uncertainty through a fault tree for a pressure tank. This paper comes with an open-source Julia library for performing uncertainty logic.

It has been rightfully emphasized that the use of AI for clinical decision making could amplify health disparities. An algorithm may encode protected characteristics, and then use this information for making predictions due to undesirable correlations in the (historical) training data. It remains unclear how we can establish whether such information is actually used. Besides the scarcity of data from underserved populations, very little is known about how dataset biases manifest in predictive models and how this may result in disparate performance. This article aims to shed some light on these issues by exploring new methodology for subgroup analysis in image-based disease detection models. We utilize two publicly available chest X-ray datasets, CheXpert and MIMIC-CXR, to study performance disparities across race and biological sex in deep learning models. We explore test set resampling, transfer learning, multitask learning, and model inspection to assess the relationship between the encoding of protected characteristics and disease detection performance across subgroups. We confirm subgroup disparities in terms of shifted true and false positive rates which are partially removed after correcting for population and prevalence shifts in the test sets. We further find a previously used transfer learning method to be insufficient for establishing whether specific patient information is used for making predictions. The proposed combination of test-set resampling, multitask learning, and model inspection reveals valuable new insights about the way protected characteristics are encoded in the feature representations of deep neural networks.

Since 2016, sharding has become an auspicious solution to tackle the scalability issue in legacy blockchain systems. Despite its potential to strongly boost the blockchain throughput, sharding comes with its own security issues. To ease the process of deciding which shard to place transactions, existing sharding protocols use a hash-based transaction sharding in which the hash value of a transaction determines its output shard. Unfortunately, we show that this mechanism opens up a loophole that could be exploited to conduct a single-shard flooding attack, a type of Denial-of-Service (DoS) attack, to overwhelm a single shard that ends up reducing the performance of the system as a whole. To counter the single-shard flooding attack, we propose a countermeasure that essentially eliminates the loophole by rejecting the use of hash-based transaction sharding. The countermeasure leverages the Trusted Execution Environment (TEE) to let blockchain's validators securely execute a transaction sharding algorithm with a negligible overhead. We provide a formal specification for the countermeasure and analyze its security properties in the Universal Composability (UC) framework. Finally, a proof-of-concept is developed to demonstrate the feasibility and practicality of our solution.

Cross-chain interaction is among different blockchains. When the number of blockchains increases, it is difficult for blockchains to form a single star topology or a fully connected topology. Meanwhile, different from legacy networks, the propagation method is required to keep the data validity. Thus, the blockchain topology and associated propagation methods are two key issues, which should be ensured during the propagation. In this paper, we first propose the confirmation-based propagation method to keep the validity of the cross-chain data. The confirmation method is to seal the cross-chain transaction synchronized from other blockchains. Second, we point out that a valid topology requires blockchains to be strongly connected. With this requirement, we propose several topologies, which match different connection scenarios. The simulation results show that the proposed methods can securely propagate the cross-chain data and the connection way is flexible.

Convolutional neural networks (CNN) are the dominant deep neural network (DNN) architecture for computer vision. Recently, Transformer and multi-layer perceptron (MLP)-based models, such as Vision Transformer and MLP-Mixer, started to lead new trends as they showed promising results in the ImageNet classification task. In this paper, we conduct empirical studies on these DNN structures and try to understand their respective pros and cons. To ensure a fair comparison, we first develop a unified framework called SPACH which adopts separate modules for spatial and channel processing. Our experiments under the SPACH framework reveal that all structures can achieve competitive performance at a moderate scale. However, they demonstrate distinctive behaviors when the network size scales up. Based on our findings, we propose two hybrid models using convolution and Transformer modules. The resulting Hybrid-MS-S+ model achieves 83.9% top-1 accuracy with 63M parameters and 12.3G FLOPS. It is already on par with the SOTA models with sophisticated designs. The code and models will be made publicly available.

The inductive biases of graph representation learning algorithms are often encoded in the background geometry of their embedding space. In this paper, we show that general directed graphs can be effectively represented by an embedding model that combines three components: a pseudo-Riemannian metric structure, a non-trivial global topology, and a unique likelihood function that explicitly incorporates a preferred direction in embedding space. We demonstrate the representational capabilities of this method by applying it to the task of link prediction on a series of synthetic and real directed graphs from natural language applications and biology. In particular, we show that low-dimensional cylindrical Minkowski and anti-de Sitter spacetimes can produce equal or better graph representations than curved Riemannian manifolds of higher dimensions.

Many modern data analytics applications on graphs operate on domains where graph topology is not known a priori, and hence its determination becomes part of the problem definition, rather than serving as prior knowledge which aids the problem solution. Part III of this monograph starts by addressing ways to learn graph topology, from the case where the physics of the problem already suggest a possible topology, through to most general cases where the graph topology is learned from the data. A particular emphasis is on graph topology definition based on the correlation and precision matrices of the observed data, combined with additional prior knowledge and structural conditions, such as the smoothness or sparsity of graph connections. For learning sparse graphs (with small number of edges), the least absolute shrinkage and selection operator, known as LASSO is employed, along with its graph specific variant, graphical LASSO. For completeness, both variants of LASSO are derived in an intuitive way, and explained. An in-depth elaboration of the graph topology learning paradigm is provided through several examples on physically well defined graphs, such as electric circuits, linear heat transfer, social and computer networks, and spring-mass systems. As many graph neural networks (GNN) and convolutional graph networks (GCN) are emerging, we have also reviewed the main trends in GNNs and GCNs, from the perspective of graph signal filtering. Tensor representation of lattice-structured graphs is next considered, and it is shown that tensors (multidimensional data arrays) are a special class of graph signals, whereby the graph vertices reside on a high-dimensional regular lattice structure. This part of monograph concludes with two emerging applications in financial data processing and underground transportation networks modeling.

Inexpensive numerical methods are key to enable simulations of systems of a large number of particles of different shapes in Stokes flow. Several approximate methods have been introduced for this purpose. We study the accuracy of the multiblob method for solving the Stokes mobility problem in free space, where the 3D geometry of a particle surface is discretised with spherical blobs and the pair-wise interaction between blobs is described by the RPY-tensor. The paper aims to investigate and improve on the magnitude of the error in the solution velocities of the Stokes mobility problem using a combination of two different techniques: an optimally chosen grid of blobs and a pair-correction inspired by Stokesian dynamics. Optimisation strategies to determine a grid with a certain number of blobs are presented with the aim of matching the hydrodynamic response of a single accurately described ideal particle, alone in the fluid. Small errors in this self-interaction are essential as they determine the basic error level in a system of well-separated particles. With a good match, reasonable accuracy can be obtained even with coarse blob-resolutions of the particle surfaces. The error in the self-interaction is however sensitive to the exact choice of grid parameters and simply hand-picking a suitable blob geometry can lead to errors several orders of magnitude larger in size. The pair-correction is local and cheap to apply, and reduces on the error for more closely interacting particles. Two different types of geometries are considered: spheres and axisymmetric rods with smooth caps. The error in solutions to mobility problems is quantified for particles of varying inter-particle distances for systems containing a few particles, comparing to an accurate solution based on a second kind BIE-formulation where the quadrature error is controlled by employing quadrature by expansion (QBX).

The hypergraph Moore bound is an elegant statement that characterizes the extremal trade-off between the girth - the number of hyperedges in the smallest cycle or even cover (a subhypergraph with all degrees even) and size - the number of hyperedges in a hypergraph. For graphs (i.e., $2$-uniform hypergraphs), a bound tight up to the leading constant was proven in a classical work of Alon, Hoory and Linial [AHL02]. For hypergraphs of uniformity $k>2$, an appropriate generalization was conjectured by Feige [Fei08]. The conjecture was settled up to an additional $\log^{4k+1} n$ factor in the size in a recent work of Guruswami, Kothari and Manohar [GKM21]. Their argument relies on a connection between the existence of short even covers and the spectrum of a certain randomly signed Kikuchi matrix. Their analysis, especially for the case of odd $k$, is significantly complicated. In this work, we present a substantially simpler and shorter proof of the hypergraph Moore bound. Our key idea is the use of a new reweighted Kikuchi matrix and an edge deletion step that allows us to drop several involved steps in [GKM21]'s analysis such as combinatorial bucketing of rows of the Kikuchi matrix and the use of the Schudy-Sviridenko polynomial concentration. Our simpler proof also obtains tighter parameters: in particular, the argument gives a new proof of the classical Moore bound of [AHL02] with no loss (the proof in [GKM21] loses a $\log^3 n$ factor), and loses only a single logarithmic factor for all $k>2$-uniform hypergraphs. As in [GKM21], our ideas naturally extend to yield a simpler proof of the full trade-off for strongly refuting smoothed instances of constraint satisfaction problems with similarly improved parameters.

Node elimination is a numerical approach to obtain cubature rules for the approximation of multivariate integrals. Beginning with a known cubature rule, nodes are selected for elimination, and a new, more efficient rule is constructed by iteratively solving the moment equations. This paper introduces a new criterion for selecting which nodes to eliminate that is based on a linearization of the moment equation. In addition, a penalized iterative solver is introduced, that ensures that weights are positive and nodes are inside the integration domain. A strategy for constructing an initial quadrature rule for various polytopes in several space dimensions is described. High efficiency rules are presented for two, three and four dimensional polytopes. The new rules are compared with rules that are obtained by combining tensor products of one dimensional quadrature rules and domain transformations, as well as with known analytically constructed cubature rules.

We present a correlated \textit{and} gate which may be used to propagate uncertainty and dependence through Boolean functions, since any Boolean function may be expressed as a combination of \textit{and} and \textit{not} operations. We argue that the \textit{and} gate is a bivariate copula family, which has the interpretation of constructing bivariate Bernoulli random variables following a given Pearson correlation coefficient and marginal probabilities. We show how this copula family may be used to propagate uncertainty in the form of probabilities of events, probability intervals, and probability boxes, with only partial or no knowledge of the dependency between events, expressed as an interval for the correlation coefficient. These results generalise previous results by Fr\'echet on the conjunction of two events with unknown dependencies. We show an application propagating uncertainty through a fault tree for a pressure tank. This paper comes with an open-source Julia library for performing uncertainty logic.

It has been rightfully emphasized that the use of AI for clinical decision making could amplify health disparities. An algorithm may encode protected characteristics, and then use this information for making predictions due to undesirable correlations in the (historical) training data. It remains unclear how we can establish whether such information is actually used. Besides the scarcity of data from underserved populations, very little is known about how dataset biases manifest in predictive models and how this may result in disparate performance. This article aims to shed some light on these issues by exploring new methodology for subgroup analysis in image-based disease detection models. We utilize two publicly available chest X-ray datasets, CheXpert and MIMIC-CXR, to study performance disparities across race and biological sex in deep learning models. We explore test set resampling, transfer learning, multitask learning, and model inspection to assess the relationship between the encoding of protected characteristics and disease detection performance across subgroups. We confirm subgroup disparities in terms of shifted true and false positive rates which are partially removed after correcting for population and prevalence shifts in the test sets. We further find a previously used transfer learning method to be insufficient for establishing whether specific patient information is used for making predictions. The proposed combination of test-set resampling, multitask learning, and model inspection reveals valuable new insights about the way protected characteristics are encoded in the feature representations of deep neural networks.

Since 2016, sharding has become an auspicious solution to tackle the scalability issue in legacy blockchain systems. Despite its potential to strongly boost the blockchain throughput, sharding comes with its own security issues. To ease the process of deciding which shard to place transactions, existing sharding protocols use a hash-based transaction sharding in which the hash value of a transaction determines its output shard. Unfortunately, we show that this mechanism opens up a loophole that could be exploited to conduct a single-shard flooding attack, a type of Denial-of-Service (DoS) attack, to overwhelm a single shard that ends up reducing the performance of the system as a whole. To counter the single-shard flooding attack, we propose a countermeasure that essentially eliminates the loophole by rejecting the use of hash-based transaction sharding. The countermeasure leverages the Trusted Execution Environment (TEE) to let blockchain's validators securely execute a transaction sharding algorithm with a negligible overhead. We provide a formal specification for the countermeasure and analyze its security properties in the Universal Composability (UC) framework. Finally, a proof-of-concept is developed to demonstrate the feasibility and practicality of our solution.

Cross-chain interaction is among different blockchains. When the number of blockchains increases, it is difficult for blockchains to form a single star topology or a fully connected topology. Meanwhile, different from legacy networks, the propagation method is required to keep the data validity. Thus, the blockchain topology and associated propagation methods are two key issues, which should be ensured during the propagation. In this paper, we first propose the confirmation-based propagation method to keep the validity of the cross-chain data. The confirmation method is to seal the cross-chain transaction synchronized from other blockchains. Second, we point out that a valid topology requires blockchains to be strongly connected. With this requirement, we propose several topologies, which match different connection scenarios. The simulation results show that the proposed methods can securely propagate the cross-chain data and the connection way is flexible.

Convolutional neural networks (CNN) are the dominant deep neural network (DNN) architecture for computer vision. Recently, Transformer and multi-layer perceptron (MLP)-based models, such as Vision Transformer and MLP-Mixer, started to lead new trends as they showed promising results in the ImageNet classification task. In this paper, we conduct empirical studies on these DNN structures and try to understand their respective pros and cons. To ensure a fair comparison, we first develop a unified framework called SPACH which adopts separate modules for spatial and channel processing. Our experiments under the SPACH framework reveal that all structures can achieve competitive performance at a moderate scale. However, they demonstrate distinctive behaviors when the network size scales up. Based on our findings, we propose two hybrid models using convolution and Transformer modules. The resulting Hybrid-MS-S+ model achieves 83.9% top-1 accuracy with 63M parameters and 12.3G FLOPS. It is already on par with the SOTA models with sophisticated designs. The code and models will be made publicly available.

The inductive biases of graph representation learning algorithms are often encoded in the background geometry of their embedding space. In this paper, we show that general directed graphs can be effectively represented by an embedding model that combines three components: a pseudo-Riemannian metric structure, a non-trivial global topology, and a unique likelihood function that explicitly incorporates a preferred direction in embedding space. We demonstrate the representational capabilities of this method by applying it to the task of link prediction on a series of synthetic and real directed graphs from natural language applications and biology. In particular, we show that low-dimensional cylindrical Minkowski and anti-de Sitter spacetimes can produce equal or better graph representations than curved Riemannian manifolds of higher dimensions.

Many modern data analytics applications on graphs operate on domains where graph topology is not known a priori, and hence its determination becomes part of the problem definition, rather than serving as prior knowledge which aids the problem solution. Part III of this monograph starts by addressing ways to learn graph topology, from the case where the physics of the problem already suggest a possible topology, through to most general cases where the graph topology is learned from the data. A particular emphasis is on graph topology definition based on the correlation and precision matrices of the observed data, combined with additional prior knowledge and structural conditions, such as the smoothness or sparsity of graph connections. For learning sparse graphs (with small number of edges), the least absolute shrinkage and selection operator, known as LASSO is employed, along with its graph specific variant, graphical LASSO. For completeness, both variants of LASSO are derived in an intuitive way, and explained. An in-depth elaboration of the graph topology learning paradigm is provided through several examples on physically well defined graphs, such as electric circuits, linear heat transfer, social and computer networks, and spring-mass systems. As many graph neural networks (GNN) and convolutional graph networks (GCN) are emerging, we have also reviewed the main trends in GNNs and GCNs, from the perspective of graph signal filtering. Tensor representation of lattice-structured graphs is next considered, and it is shown that tensors (multidimensional data arrays) are a special class of graph signals, whereby the graph vertices reside on a high-dimensional regular lattice structure. This part of monograph concludes with two emerging applications in financial data processing and underground transportation networks modeling.