Science laboratory automation enables accelerated discovery in life sciences and materials. However, it requires interdisciplinary collaboration to address challenges such as robust and flexible autonomy, reproducibility, throughput, standardization, the role of human scientists, and ethics. This article highlights these issues, reflecting perspectives from leading experts in laboratory automation across different disciplines of the natural sciences.

Modeling has become a widespread, useful tool in mathematics applied to diverse fields, from physics to economics to biomedicine. Practitioners of modeling may use algebraic or differential equations, to the elements of which they attribute an intuitive relationship with some relevant aspect of reality they wish to represent. More sophisticated expressions may include stochasticity, either as observation error or system noise. However, a clear, unambiguous mathematical definition of what a model is and of what is the relationship between the model and the real-life phenomena it purports to represent has so far not been formulated. The present work aims to fill this gap, motivating the definition of a mathematical model as an operator on a Hilbert space of random variables, identifying the experimental realization as the map between the theoretical space of model construction and the computational space of statistical model identification, and tracing the relationship of the geometry of the model manifold in the abstract setting with the corresponding geometry of the prediction surfaces in statistical estimation.

For a code $C$ in a space with maximal distance $n$, we say that $C$ has symmetric distances if its distance set $S(C)$ is symmetric with respect to $n / 2$. In this paper, we prove that if $C$ is a binary code with length $2n$, constant weight $n$ and symmetric distances, then \[ |C| \leq \binom{2 n - 1}{|S(C)|}. \] This result can be interpreted using the language of Johnson association schemes. More generally, we give a framework to study codes with symmetric distances in Q-bipartite Q-polynomial association schemes, and provide upper bounds for such codes. Moreover, we use number theoretic techniques to determine when the equality holds.

Symbiotic Autonomous Systems (SAS) are advanced intelligent and cognitive systems exhibiting autonomous collective intelligence enabled by coherent symbiosis of human-machine interactions in hybrid societies. Basic research in the emerging field of SAS has triggered advanced general AI technologies functioning without human intervention or hybrid symbiotic systems synergizing humans and intelligent machines into coherent cognitive systems. This work presents a theoretical framework of SAS underpinned by the latest advances in intelligence, cognition, computer, and system sciences. SAS are characterized by the composition of autonomous and symbiotic systems that adopt bio-brain-social-inspired and heterogeneously synergized structures and autonomous behaviors. This paper explores their cognitive and mathematical foundations. The challenge to seamless human-machine interactions in a hybrid environment is addressed. SAS-based collective intelligence is explored in order to augment human capability by autonomous machine intelligence towards the next generation of general AI, autonomous computers, and trustworthy mission-critical intelligent systems. Emerging paradigms and engineering applications of SAS are elaborated via an autonomous knowledge learning system that symbiotically works between humans and cognitive robots.

The Internet of Things (IoT) is regarded as an improved communication system that has revolutionized traditional lifestyles. To function successfully, IoT requires a combination of cloud, fog, and edge computing architectures. Few studies have addressed cloud, fog, and edge computing simultaneously, comparing them and their issues, although several studies have looked into ways of integrating IoT with either one or two computing systems. Thus, this review provides a thorough understanding of IoT integration with these three computing architectures, as well as their respective applications and limitations. It also highlights the advantages, unresolved issues, future opportunities and directions of IoT integration with the computing systems to advance the IoT. IoT can use the Cloud's almost limitless resources to overcome technology restrictions, such as data processing, storage, and transmission. While edge computing can outperform cloud computing in many circumstances, IoT and edge computing become increasingly integrated as IoT devices increase. Cloud computing also poses a few issues, including managing time-sensitive IoT applications like video gaming, simulation, and streaming, which can be addressed by fog computing integrated with IoT. Due to the proximity of fog computing resources to the edge, data transfers and communication delays to the cloud can be reduced as a result of combining the two. The integration of IoT with cloud, fog, and edge computing will create new business prototypes and opportunities. Since IoT has the potential to greatly enhance connectivity infrastructure as an inevitable component of the future internet, further study is needed before it can be fully integrated.

The paper is devoted to provide Michael-Simon-type $L^p$-logarithmic-Sobolev inequalities on complete, not necessarily compact $n$-dimensional submanifolds $\Sigma$ of the Euclidean space $\mathbb R^{n+m}$. Our first result, stated for $p=2$, is sharp, it is valid on general submanifolds, and it involves the mean curvature of $\Sigma$. It implies in particular the main result of S. Brendle [Comm. Pure Appl. Math.}, 2022]. In addition, it turns out that equality can only occur if and only if $\Sigma$ is isometric to the Euclidean space $\mathbb R^{n}$ and the extremizer is a Gaussian. The second result is a general $L^p$-logarithmic-Sobolev inequality for $p\geq 2$ on Euclidean submanifolds with constants that are codimension-free in case of minimal submanifolds. In order to prove the above results - especially, to deal with the equality cases - we elaborate the theory of optimal mass transport on submanifolds between measures that are not necessarily compactly supported. Applications are provided to sharp hypercontractivity estimates of Hopf-Lax semigroups on submanifolds. The first hypercontractivity estimate is for general submanifolds with bounded mean curvature vector, the second one is for self-similar shrinkers endowed with the natural Gaussian measure. The equality cases are characterized here as well.

The main goal of the present paper is to provide sharp hypercontractivity bounds of the heat flow $({\sf H}_t)_{t\geq 0}$ on ${\sf RCD}(0,N)$ metric measure spaces. The best constant in this estimate involves the asymptotic volume ratio, and its optimality is obtained by means of the sharp $L^2$-logarithmic Sobolev inequality on ${\sf RCD}(0,N)$ spaces and a blow-down rescaling argument. Equality holds in this sharp estimate for a prescribed time $t_0>0$ and a non-zero extremizer $f$ if and only if the ${\sf RCD}(0,N)$ space has an $N$-Euclidean cone structure and $f$ is a Gaussian whose dilation factor is reciprocal to $t_0$, up to a multiplicative constant. Applications include an extension of Li's rigidity result, almost rigidities, as well as topological rigidities of non-collapsed ${\sf RCD}(0, N)$ spaces. Our results are new even on complete Riemannian manifolds with non-negative Ricci curvature.

Anxiety is a common mental health condition characterised by excessive worry, fear and apprehension about everyday situations. Even with significant progress over the past few years, predicting anxiety from electroencephalographic (EEG) signals, specifically using error-related negativity (ERN), still remains challenging. Following the PRISMA protocol, this paper systematically reviews 54 research papers on using EEG and ERN markers for anxiety detection published in the last 10 years (2013 -- 2023). Our analysis highlights the wide usage of traditional machine learning, such as support vector machines and random forests, as well as deep learning models, such as convolutional neural networks and recurrent neural networks across different data types. Our analysis reveals that the development of a robust and generic anxiety prediction method still needs to address real-world challenges, such as task-specific setup, feature selection and computational modelling. We conclude this review by offering potential future direction for non-invasive, objective anxiety diagnostics, deployed across diverse populations and anxiety sub-types.

This study presents an uncertainty-aware stacked neural networks model for the reliable classification of COVID-19 from radiological images. The model addresses the critical gap in uncertainty-aware modeling by focusing on accurately identifying confidently correct predictions while alerting users to confidently incorrect and uncertain predictions, which can promote trust in automated systems. The architecture integrates uncertainty quantification methods, including Monte Carlo dropout and ensemble techniques, to enhance predictive reliability by assessing the certainty of diagnostic predictions. Within a two-tier model framework, the tier one model generates initial predictions and associated uncertainties, which the second tier model uses to produce a trust indicator alongside the diagnostic outcome. This dual-output model not only predicts COVID-19 cases but also provides a trust flag, indicating the reliability of each diagnosis and aiming to minimize the need for retesting and expert verification. The effectiveness of this approach is demonstrated through extensive experiments on the COVIDx CXR-4 dataset, showing a novel approach in identifying and handling confidently incorrect cases and uncertain cases, thus enhancing the trustworthiness of automated diagnostics in clinical settings.

The paper deals with fine volume growth estimates on metric measures spaces supporting various Sobolev-type inequalities. Given a generic metric measure space, we first prove a quantitative volume growth of metric balls under the validity of a Sobolev-type inequality (including Gagliardo-Nirenberg, Sobolev and Nash inequalities, as well as their borderlines, i.e., the logarithmic-Sobolev, Faber-Krahn, Morrey and Moser-Trudinger inequalities, respectively), answering partially a question of Ledoux [Ann. Fac. Sci. Toulouse Math., 2000] in a broader setting. We then prove sharp Gagliardo-Nirenberg-Sobolev interpolation inequalities -- with their borderlines -- in the setting of metric measure spaces verifying the curvature-dimension condition ${\sf CD}(0,N)$ in the sense of Lott-Sturm-Villani. In addition, the equality cases are also characterized in terms of the $N$-volume cone structure of the ${\sf CD}(0,N)$ space together with the precise profile of extremizers.

In recent years, large language models (LLMs) have achieved remarkable success in natural language processing (NLP). LLMs require an extreme amount of parameters to attain high performance. As models grow into the trillion-parameter range, computational and memory costs increase significantly. This makes it difficult for many researchers to access the resources needed to train or apply these models. Optimizing LLM performance involves two main approaches: fine-tuning pre-trained models for specific tasks to achieve state-of-the-art performance, and reducing costs or improving training time while maintaining similar performance. This paper presents a systematic literature review (SLR) following the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) statement. We reviewed 65 publications out of 983 from 2017 to December 2023, retrieved from 5 databases. The study presents methods to optimize and accelerate LLMs while achieving cutting-edge results without sacrificing accuracy. We begin with an overview of the development of language modeling, followed by a detailed explanation of commonly used frameworks and libraries, and a taxonomy for improving and speeding up LLMs based on three classes: LLM training, LLM inference, and system serving. We then delve into recent optimization and acceleration strategies such as training optimization, hardware optimization, scalability and reliability, accompanied by the taxonomy and categorization of these strategies. Finally, we provide an in-depth comparison of each class and strategy, with two case studies on optimizing model training and enhancing inference efficiency. These case studies showcase practical approaches to address LLM resource limitations while maintaining performance.

Unconditional security for smart grids is defined. Cryptanalyses of the watermarked security of smart grids indicate that watermarking cannot guarantee unconditional security unless the communication within the grid system is unconditionally secure. The successful attack against the dynamically watermarked smart grid remains valid even with the presence of internal noise from the grid. An open question arises: if unconditionally authenticated secure communications within the grid, together with tamper resistance of the critical elements, are satisfactory conditions to provide unconditional security for the grid operation.

We prove that the distribution of the product of two correlated normal random variables with arbitrary means and arbitrary variances is infinitely divisible. We also obtain exact formulas for the probability density function of the sum of independent copies of such random variables.

The Lambert $W$ function, giving the solutions of a simple transcendental equation, has become a famous function and arises in many applications in combinatorics, physics, or population dyamics just to mention a few. In the last decade it turned out that some specific relativistic equations and molecular physics problems need solutions of more general transcendental equations. Thus a generalization of the Lambert function is necessary. In this paper we construct this generalization which involves some special polynomials.

Previous research employing a conceptual approach with a digital twin has demonstrated that (noise-based) dynamic watermarking is incapable of providing unconditional security in smart electrical grid systems. However, the implementation of digital twins can be prohibitively costly or infeasible due to limited available data on critical infrastructure. In this study, we first analyze the spectral properties of dynamic watermarking and its associated protocol. Subsequently, we present a straightforward attack inspired by the digital twin method, which extracts and utilizes the grid noises and completely breaches the security of dynamic watermarking without requiring knowledge of the private watermarking signal. The attacker can fully expose the grid while evading detection by the controller. Our findings indicate that in the absence of secure and authenticated communications, dynamic watermarking offers neither conditional nor unconditional security. Conversely, when communication lines, sensors, and communicators are equipped with tamper-resistant and secure/authenticated links, dynamic watermarking becomes redundant for grid security.

We present a model to reconstruct partially visible objects. The model takes a mask as an input, which we call weighted mask. The mask is utilized by gated convolutions to assign more weight to the visible pixels of the occluded instance compared to the background, while ignoring the features of the invisible pixels. By drawing more attention from the visible region, our model can predict the invisible patch more effectively than the baseline models, especially in instances with uniform texture. The model is trained on COCOA dataset and two subsets of it in a self-supervised manner. The results demonstrate that our model generates higher quality and more texture-rich outputs compared to baseline models. Code is available at: this https URL.

In this short note we give a new upper bound for the size of a set family with a single Hamming distance. Our proof is an application of the linear algebra bound method.