Cycles are one of the fundamental subgraph patterns and being able to enumerate them in graphs enables important applications in a wide variety of fields, including finance, biology, chemistry, and network science. However, to enable cycle enumeration in real-world applications, efficient parallel algorithms are required. In this work, we propose scalable parallelisation of state-of-the-art sequential algorithms for enumerating simple, temporal, and hop-constrained cycles. First, we focus on the simple cycle enumeration problem and parallelise the algorithms by Johnson and by Read and Tarjan in a fine-grained manner. We theoretically show that our resulting fine-grained parallel algorithms are scalable, with the fine-grained parallel Read-Tarjan algorithm being strongly scalable. In contrast, we show that straightforward coarse-grained parallel versions of these simple cycle enumeration algorithms that exploit edge- or vertex-level parallelism are not scalable. Next, we adapt our fine-grained approach to enable the enumeration of cycles under time-window, temporal, and hop constraints. Our evaluation on a cluster with 256 CPU cores that can execute up to 1024 simultaneous threads demonstrates a near-linear scalability of our fine-grained parallel algorithms when enumerating cycles under the aforementioned constraints. On the same cluster, our fine-grained parallel algorithms achieve, on average, one order of magnitude speedup compared to the respective coarse-grained parallel versions of the state-of-the-art algorithms for cycle enumeration. The performance gap between the fine-grained and the coarse-grained parallel algorithms increases as we use more CPU cores.
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The design process of centrifugal compressors requires applying an optimization process which is computationally expensive due to complex analytical equations underlying the compressor's dynamical equations. Although the regression surrogate models could drastically reduce the computational cost of such a process, the major challenge is the scarcity of data for training the surrogate model. Aiming to strategically exploit the labeled samples, we propose the Active-CompDesign framework in which we combine a thermodynamics-based compressor model (i.e., our internal software for compressor design) and Gaussian Process-based surrogate model within a deployable Active Learning (AL) setting. We first conduct experiments in an offline setting and further, extend it to an online AL framework where a real-time interaction with the thermodynamics-based compressor's model allows the deployment in production. ActiveCompDesign shows a significant performance improvement in surrogate modeling by leveraging on uncertainty-based query function of samples within the AL framework with respect to the random selection of data points. Moreover, our framework in production has reduced the total computational time of compressor's design optimization to around 46% faster than relying on the internal thermodynamics-based simulator, achieving the same performance.
Graph representations are the generalization of geometric graph drawings from the plane to higher dimensions. A method introduced by Tutte to optimize properties of graph drawings is to minimize their energy. We explore this minimization for spherical graph representations, where the vertices lie on a unit sphere such that the origin is their barycentre. We present a primal and dual semidefinite program which can be used to find such a spherical graph representation minimizing the energy. We denote the optimal value of this program by $\rho(G)$ for a given graph $G$. The value turns out to be related to the second largest eigenvalue of the adjacency matrix of $G$, which we denote by $\lambda_2$. We show that for $G$ regular, $\rho(G) \leq \frac{\lambda_{2}}{2} \cdot v(G)$, and that equality holds if and only if the $\lambda_{2}$ eigenspace contains a spherical 1-design. Moreover, if $G$ is a random $d$-regular graph, $\rho(G)=\left(\sqrt{(d-1)} +o(1)\right)\cdot v(G)$, asymptotically almost surely.
The aim of latent variable disentanglement is to infer the multiple informative latent representations that lie behind a data generation process and is a key factor in controllable data generation. In this paper, we propose a deep neural network-based self-supervised learning method to infer the disentangled rhythmic and harmonic representations behind music audio generation. We train a variational autoencoder that generates an audio mel-spectrogram from two latent features representing the rhythmic and harmonic content. In the training phase, the variational autoencoder is trained to reconstruct the input mel-spectrogram given its pitch-shifted version. At each forward computation in the training phase, a vector rotation operation is applied to one of the latent features, assuming that the dimensions of the feature vectors are related to pitch intervals. Therefore, in the trained variational autoencoder, the rotated latent feature represents the pitch-related information of the mel-spectrogram, and the unrotated latent feature represents the pitch-invariant information, i.e., the rhythmic content. The proposed method was evaluated using a predictor-based disentanglement metric on the learned features. Furthermore, we demonstrate its application to the automatic generation of music remixes.
In the realm of algorithmic economics, voting systems are evaluated and compared by examining the properties or axioms they satisfy. While this pursuit has yielded valuable insights, it has also led to seminal impossibility results such as Arrow's and Gibbard-Satterthwaite's Impossibility Theorems, which pose challenges in designing ideal voting systems. Enter the domain of quantum computing: recent advancements have introduced the concept of quantum voting systems, which have many potential applications including in security and blockchain. Building on recent works that bypass Arrow's Impossibility Theorem using quantum voting systems, our research extends Quantum Condorcet Voting (QCV) to counter the Gibbard-Satterthwaite Impossibility Theorem in a quantum setting. To show this, we introduce a quantum-specific notion of truthfulness, extend ideas like incentive compatibility and the purpose of onto to the quantum domain, and introduce new tools to map social welfare functions to social choice functions in this domain.
We present an acceleration method for sequences of large-scale linear systems, such as the ones arising from the numerical solution of time-dependent partial differential equations coupled with algebraic constraints. We discuss different approaches to leverage the subspace containing the history of solutions computed at previous time steps in order to generate a good initial guess for the iterative solver. In particular, we propose a novel combination of reduced-order projection with randomized linear algebra techniques, which drastically reduces the number of iterations needed for convergence. We analyze the accuracy of the initial guess produced by the reduced-order projection when the coefficients of the linear system depend analytically on time. Extending extrapolation results by Demanet and Townsend to a vector-valued setting, we show that the accuracy improves rapidly as the size of the history increases, a theoretical result confirmed by our numerical observations. In particular, we apply the developed method to the simulation of plasma turbulence in the boundary of a fusion device, showing that the time needed for solving the linear systems is significantly reduced.
Interactive Design and Optics-Based Visualization of Arbitrary Non-Euclidean Kaleidoscopic Orbifolds
Orbifolds are a modern mathematical concept that arises in the research of hyperbolic geometry with applications in computer graphics and visualization. In this paper, we make use of rooms with mirrors as the visual metaphor for orbifolds. Given any arbitrary two-dimensional kaleidoscopic orbifold, we provide an algorithm to construct a Euclidean, spherical, or hyperbolic polygon to match the orbifold. This polygon is then used to create a room for which the polygon serves as the floor and the ceiling. With our system that implements M\"obius transformations, the user can interactively edit the scene and see the reflections of the edited objects. To correctly visualize non-Euclidean orbifolds, we adapt the rendering algorithms to account for the geodesics in these spaces, which light rays follow. Our interactive orbifold design system allows the user to create arbitrary two-dimensional kaleidoscopic orbifolds. In addition, our mirror-based orbifold visualization approach has the potential of helping our users gain insight on the orbifold, including its orbifold notation as well as its universal cover, which can also be the spherical space and the hyperbolic space.
Microservices are increasingly used in modern applications, leading to a growing need for effective service integration solutions. However, we argue that traditional API-centric integration mechanisms (e.g., RPC, REST, and Pub/Sub) hamper the modularity of microservices. These mechanisms introduce rigid code-level coupling, scatter integration logic, and hinder visibility into cross-service state exchanges. Ultimately, these limitations complicate the maintenance and evolution of microservice-based applications. In response, we propose a rethinking of service integration and present Knactor, a new state-centric integration framework to restore the modularity that microservices were intended to offer. Knactor decouples service integration from service development, allowing integration to be implemented as explicit state exchanges among multiple services. Our initial case study suggests that Knactor simplifies service integration and creates new opportunities for optimizations.
Mesh degeneration is a bottleneck for fluid-structure interaction (FSI) simulations and for shape optimization via the method of mappings. In both cases, an appropriate mesh motion technique is required. The choice is typically based on heuristics, e.g., the solution operators of partial differential equations (PDE), such as the Laplace or biharmonic equation. Especially the latter, which shows good numerical performance for large displacements, is expensive. Moreover, from a continuous perspective, choosing the mesh motion technique is to a certain extent arbitrary and has no influence on the physically relevant quantities. Therefore, we consider approaches inspired by machine learning. We present a hybrid PDE-NN approach, where the neural network (NN) serves as parameterization of a coefficient in a second order nonlinear PDE. We ensure existence of solutions for the nonlinear PDE by the choice of the neural network architecture. Moreover, we present an approach where a neural network corrects the harmonic extension such that the boundary displacement is not changed. In order to avoid technical difficulties in coupling finite element and machine learning software, we work with a splitting of the monolithic FSI system into three smaller subsystems. This allows to solve the mesh motion equation in a separate step. We assess the quality of the learned mesh motion technique by applying it to a FSI benchmark problem.
In pace with developments in the research field of artificial intelligence, knowledge graphs (KGs) have attracted a surge of interest from both academia and industry. As a representation of semantic relations between entities, KGs have proven to be particularly relevant for natural language processing (NLP), experiencing a rapid spread and wide adoption within recent years. Given the increasing amount of research work in this area, several KG-related approaches have been surveyed in the NLP research community. However, a comprehensive study that categorizes established topics and reviews the maturity of individual research streams remains absent to this day. Contributing to closing this gap, we systematically analyzed 507 papers from the literature on KGs in NLP. Our survey encompasses a multifaceted review of tasks, research types, and contributions. As a result, we present a structured overview of the research landscape, provide a taxonomy of tasks, summarize our findings, and highlight directions for future work.
We introduce a multi-task setup of identifying and classifying entities, relations, and coreference clusters in scientific articles. We create SciERC, a dataset that includes annotations for all three tasks and develop a unified framework called Scientific Information Extractor (SciIE) for with shared span representations. The multi-task setup reduces cascading errors between tasks and leverages cross-sentence relations through coreference links. Experiments show that our multi-task model outperforms previous models in scientific information extraction without using any domain-specific features. We further show that the framework supports construction of a scientific knowledge graph, which we use to analyze information in scientific literature.
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