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We study the complexity of the following related computational tasks concerning a fixed countable graph G: 1. Does a countable graph H provided as input have a(n induced) subgraph isomorphic to G? 2. Given a countable graph H that has a(n induced) subgraph isomorphic to G, find such a subgraph. The framework for our investigations is given by effective Wadge reducibility and by Weihrauch reducibility. Our work follows on "Reverse mathematics and Weihrauch analysis motivated by finite complexity theory" (Computability, 2021) by BeMent, Hirst and Wallace, and we answer several of their open questions.

With the fast development of modern microscopes and bioimaging techniques, an unprecedentedly large amount of imaging data are being generated, stored, analyzed, and even shared through networks. The size of the data poses great challenges for current data infrastructure. One common way to reduce the data size is by image compression. This present study analyzes classic and deep learning based image compression methods, and their impact on deep learning based image processing models. Deep learning based label-free prediction models (i.e., predicting fluorescent images from bright field images) are used as an example application for comparison and analysis. Effective image compression methods could help reduce the data size significantly without losing necessary information, and therefore reduce the burden on data management infrastructure and permit fast transmission through the network for data sharing or cloud computing. To compress images in such a wanted way, multiple classical lossy image compression techniques are compared to several AI-based compression models provided by and trained with the CompressAI toolbox using python. These different compression techniques are compared in compression ratio, multiple image similarity measures and, most importantly, the prediction accuracy from label-free models on compressed images. We found that AI-based compression techniques largely outperform the classic ones and will minimally affect the downstream label-free task in 2D cases. In the end, we hope the present study could shed light on the potential of deep learning based image compression and the impact of image compression on downstream deep learning based image analysis models.

We revisit existing linear computation coding (LCC) algorithms, and introduce a new framework that measures the computational cost of computing multidimensional linear functions, not only in terms of the number of additions, but also with respect to their suitability for parallel processing. Utilizing directed acyclic graphs, which correspond to signal flow graphs in hardware, we propose a novel LCC algorithm that controls the trade-off between the total number of operations and their parallel executability. Numerical evaluations show that the proposed algorithm, constrained to a fully parallel structure, outperforms existing schemes.

Sonification is a data visualization technique which expresses data attributes via psychoacoustic parameters, which are non-speech audio signals used to convey information. This paper investigates the binary estimation of cognitive load induced by psychoacoustic parameters conveying the focus level of an astronomical image via Electroencephalogram (EEG) embeddings. Employing machine learning and deep learning methodologies, we demonstrate that EEG signals are reliable for (a) binary estimation of cognitive load, (b) isolating easy vs difficult visual-to-auditory perceptual mappings, and (c) capturing perceptual similarities among psychoacoustic parameters. Our key findings reveal that (1) EEG embeddings can reliably measure cognitive load, achieving a peak F1-score of 0.98; (2) Extreme focus levels are easier to detect via auditory mappings than intermediate ones, and (3) psychoacoustic parameters inducing comparable cognitive load levels tend to generate similar EEG encodings.

Inverse problems, i.e., estimating parameters of physical models from experimental data, are ubiquitous in science and engineering. The Bayesian formulation is the gold standard because it alleviates ill-posedness issues and quantifies epistemic uncertainty. Since analytical posteriors are not typically available, one resorts to Markov chain Monte Carlo sampling or approximate variational inference. However, inference needs to be rerun from scratch for each new set of data. This drawback limits the applicability of the Bayesian formulation to real-time settings, e.g., health monitoring of engineered systems, and medical diagnosis. The objective of this paper is to develop a methodology that enables real-time inference by learning the Bayesian inverse map, i.e., the map from data to posteriors. Our approach is as follows. We parameterize the posterior distribution as a function of data. This work outlines two distinct approaches to do this. The first method involves parameterizing the posterior using an amortized full-rank Gaussian guide, implemented through neural networks. The second method utilizes a Conditional Normalizing Flow guide, employing conditional invertible neural networks for cases where the target posterior is arbitrarily complex. In both approaches, we learn the network parameters by amortized variational inference which involves maximizing the expectation of evidence lower bound over all possible datasets compatible with the model. We demonstrate our approach by solving a set of benchmark problems from science and engineering. Our results show that the posterior estimates of our approach are in agreement with the corresponding ground truth obtained by Markov chain Monte Carlo. Once trained, our approach provides the posterior distribution for a given observation just at the cost of a forward pass of the neural network.

Cyber-physical systems (CPS) offer immense optimization potential for manufacturing processes through the availability of multivariate time series data of actors and sensors. Based on automated analysis software, the deployment of adaptive and responsive measures is possible for time series data. Due to the complex and dynamic nature of modern manufacturing, analysis and modeling often cannot be entirely automated. Even machine- or deep learning approaches often depend on a priori expert knowledge and labelling. In this paper, an information-based data preprocessing approach is proposed. By applying statistical methods including variance and correlation analysis, an approximation of the sampling rate in event-based systems and the utilization of spectral analysis, knowledge about the underlying manufacturing processes can be gained prior to modeling. The paper presents, how statistical analysis enables the pruning of a dataset's least important features and how the sampling rate approximation approach sets the base for further data analysis and modeling. The data's underlying periodicity, originating from the cyclic nature of an automated manufacturing process, will be detected by utilizing the fast Fourier transform. This information-based preprocessing method will then be validated for process time series data of cyber-physical systems' programmable logic controllers (PLC).

We introduce a novel neuromorphic network architecture based on a lattice of exciton-polariton condensates, intricately interconnected and energized through non-resonant optical pumping. The network employs a binary framework, where each neuron, facilitated by the spatial coherence of pairwise coupled condensates, performs binary operations. This coherence, emerging from the ballistic propagation of polaritons, ensures efficient, network-wide communication. The binary neuron switching mechanism, driven by the nonlinear repulsion through the excitonic component of polaritons, offers computational efficiency and scalability advantages over continuous weight neural networks. Our network enables parallel processing, enhancing computational speed compared to sequential or pulse-coded binary systems. The system's performance was evaluated using the MNIST dataset for handwritten digit recognition, showcasing the potential to outperform existing polaritonic neuromorphic systems, as demonstrated by its impressive predicted classification accuracy of up to 97.5%.

We study the convergence of stochastic gradient descent (SGD) for non-convex objective functions. We establish the local convergence with positive probability under the local \L{}ojasiewicz condition introduced by Chatterjee in \cite{chatterjee2022convergence} and an additional local structural assumption of the loss function landscape. A key component of our proof is to ensure that the whole trajectories of SGD stay inside the local region with a positive probability. We also provide examples of neural networks with finite widths such that our assumptions hold.

Deep neural network based recommendation systems have achieved great success as information filtering techniques in recent years. However, since model training from scratch requires sufficient data, deep learning-based recommendation methods still face the bottlenecks of insufficient data and computational inefficiency. Meta-learning, as an emerging paradigm that learns to improve the learning efficiency and generalization ability of algorithms, has shown its strength in tackling the data sparsity issue. Recently, a growing number of studies on deep meta-learning based recommenddation systems have emerged for improving the performance under recommendation scenarios where available data is limited, e.g. user cold-start and item cold-start. Therefore, this survey provides a timely and comprehensive overview of current deep meta-learning based recommendation methods. Specifically, we propose a taxonomy to discuss existing methods according to recommendation scenarios, meta-learning techniques, and meta-knowledge representations, which could provide the design space for meta-learning based recommendation methods. For each recommendation scenario, we further discuss technical details about how existing methods apply meta-learning to improve the generalization ability of recommendation models. Finally, we also point out several limitations in current research and highlight some promising directions for future research in this area.

Deep learning constitutes a recent, modern technique for image processing and data analysis, with promising results and large potential. As deep learning has been successfully applied in various domains, it has recently entered also the domain of agriculture. In this paper, we perform a survey of 40 research efforts that employ deep learning techniques, applied to various agricultural and food production challenges. We examine the particular agricultural problems under study, the specific models and frameworks employed, the sources, nature and pre-processing of data used, and the overall performance achieved according to the metrics used at each work under study. Moreover, we study comparisons of deep learning with other existing popular techniques, in respect to differences in classification or regression performance. Our findings indicate that deep learning provides high accuracy, outperforming existing commonly used image processing techniques.