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We investigate the dynamics of chemical reaction networks (CRNs) with the goal of deriving an upper bound on their reaction rates. This task is challenging due to the nonlinear nature and discrete structure inherent in CRNs. To address this, we employ an information geometric approach, using the natural gradient, to develop a nonlinear system that yields an upper bound for CRN dynamics. We validate our approach through numerical simulations, demonstrating faster convergence in a specific class of CRNs. This class is characterized by the number of chemicals, the maximum value of stoichiometric coefficients of the chemical reactions, and the number of reactions. We also compare our method to a conventional approach, showing that the latter cannot provide an upper bound on reaction rates of CRNs. While our study focuses on CRNs, the ubiquity of hypergraphs in fields from natural sciences to engineering suggests that our method may find broader applications, including in information science.

In this article, we propose a new metaheuristic inspired by the morphogenetic cellular movements of endothelial cells (ECs) that occur during the tumor angiogenesis process. This algorithm starts with a random initial population. In each iteration, the best candidate selected as the tumor, while the other individuals in the population are treated as ECs migrating toward the tumor's direction following a coordinated dynamics through a spatial relationship between tip and follower ECs. This algorithm has an advantage compared to other similar optimization metaheuristics: the model parameters are already configured according to the tumor angiogenesis phenomenon modeling, preventing researchers from initializing them with arbitrary values. Subsequently, the algorithm is compared against well-known benchmark functions, and the results are validated through a comparative study with Particle Swarm Optimization (PSO). The results demonstrate that the algorithm is capable of providing highly competitive outcomes. Furthermore, the proposed algorithm is applied to real-world problems (cantilever beam design, pressure vessel design, tension/compression spring and sustainable explotation renewable resource). The results showed that the proposed algorithm worked effectively in solving constrained optimization problems. The results obtained were compared with several known algorithms.

Cryoablation is a minimally invasive and efficient therapy option for liver cancer. Liquid nitrogen was used to kill the unwanted cells via freezing. One of the challenges of cryosurgery is to destroy the complete tumor without damaging the surrounding healthy cells when the tumor is large. To overcome this challenge, multi-cryoprobes were arranged in a polygonal pattern to create a uniform cooling and optimum ablation zone in the tissue. Single, three, and four cryoprobes were placed in the center, triangle, and square patterns to analyze the temperature profile and ablation zone. The results showed that tissue will freeze quickly when cryoprobes are placed in a square pattern. After the treatment of 600 seconds, $99\%$, $96\%$, and $31\%$ of the tumor were killed using four, three, and single cryoprobes, respectively. One of the difficulties in the multi-probe technique is choosing the probe separation distance and cooling time. The volume of the ablation zone, the thermal damage to healthy cells, and the volume of tumor cells killed during the treatment for different probe separation distances of 10 mm, 15 mm, and 20 mm are analyzed. Compared to other settings, a multi-probe technique destroys the entire tumor with the least harm to healthy cells when probes are arranged in a square pattern with a 15 mm space between them.

The initial motivation for this work was the linguistic case of the spread of Germanic syntactic features into Romance dialects of North-Eastern Italy, which occurred after the immigration of German people to Tyrol during the High Middle Ages. To obtain a representation of the data over the territory suitable for a mathematical formulation, an interactive map is produced as a first step, using tools of what is called Geographic Data Science. A smooth two-dimensional surface G is introduced, expressing locally which fraction of territory uses a given German language feature: it is obtained by a piecewise cubic curvature minimizing interpolant of the discrete function that says if at any surveyed locality that feature is used or not. This surface G is thought of as the value at the present time of a function describing a diffusion-convection phenomenon in two dimensions (here said tidal mode), which is subjected in a very natural way to the same equation used in physics, introducing a contextual diffusivity concept: it is shown that with two different assumptions about diffusivity, solutions of this equation, evaluated at the present time, fit well with the data interpolated by G, thus providing two convincing different pictures of diffusion-convection in the case under study, albeit simplifications and approximations. Very importantly, it is shown that the linguistic diffusion model known to linguists as Schmidt waves can be counted among the solutions of the diffusion equation

Sumplete is a logic puzzle famous for being developed by ChatGPT. The puzzle consists of a rectangular grid, with each cell containing a number. The player has to cross out some numbers such that the sum of uncrossed numbers in each row and column is equal to a given integer assigned to that row or column. In this paper, we prove that deciding a solvability of a given Sumplete puzzle is NP-complete, even if the grid contains only two different numbers.

Due to long-distance correlation and powerful pretrained models, transformer-based methods have initiated a breakthrough in visual object tracking performance. Previous works focus on designing effective architectures suited for tracking, but ignore that data augmentation is equally crucial for training a well-performing model. In this paper, we first explore the impact of general data augmentations on transformer-based trackers via systematic experiments, and reveal the limited effectiveness of these common strategies. Motivated by experimental observations, we then propose two data augmentation methods customized for tracking. First, we optimize existing random cropping via a dynamic search radius mechanism and simulation for boundary samples. Second, we propose a token-level feature mixing augmentation strategy, which enables the model against challenges like background interference. Extensive experiments on two transformer-based trackers and six benchmarks demonstrate the effectiveness and data efficiency of our methods, especially under challenging settings, like one-shot tracking and small image resolutions.

Recently, graph neural networks have been gaining a lot of attention to simulate dynamical systems due to their inductive nature leading to zero-shot generalizability. Similarly, physics-informed inductive biases in deep-learning frameworks have been shown to give superior performance in learning the dynamics of physical systems. There is a growing volume of literature that attempts to combine these two approaches. Here, we evaluate the performance of thirteen different graph neural networks, namely, Hamiltonian and Lagrangian graph neural networks, graph neural ODE, and their variants with explicit constraints and different architectures. We briefly explain the theoretical formulation highlighting the similarities and differences in the inductive biases and graph architecture of these systems. We evaluate these models on spring, pendulum, gravitational, and 3D deformable solid systems to compare the performance in terms of rollout error, conserved quantities such as energy and momentum, and generalizability to unseen system sizes. Our study demonstrates that GNNs with additional inductive biases, such as explicit constraints and decoupling of kinetic and potential energies, exhibit significantly enhanced performance. Further, all the physics-informed GNNs exhibit zero-shot generalizability to system sizes an order of magnitude larger than the training system, thus providing a promising route to simulate large-scale realistic systems.

We consider the problem of discovering $K$ related Gaussian directed acyclic graphs (DAGs), where the involved graph structures share a consistent causal order and sparse unions of supports. Under the multi-task learning setting, we propose a $l_1/l_2$-regularized maximum likelihood estimator (MLE) for learning $K$ linear structural equation models. We theoretically show that the joint estimator, by leveraging data across related tasks, can achieve a better sample complexity for recovering the causal order (or topological order) than separate estimations. Moreover, the joint estimator is able to recover non-identifiable DAGs, by estimating them together with some identifiable DAGs. Lastly, our analysis also shows the consistency of union support recovery of the structures. To allow practical implementation, we design a continuous optimization problem whose optimizer is the same as the joint estimator and can be approximated efficiently by an iterative algorithm. We validate the theoretical analysis and the effectiveness of the joint estimator in experiments.

AI is undergoing a paradigm shift with the rise of models (e.g., BERT, DALL-E, GPT-3) that are trained on broad data at scale and are adaptable to a wide range of downstream tasks. We call these models foundation models to underscore their critically central yet incomplete character. This report provides a thorough account of the opportunities and risks of foundation models, ranging from their capabilities (e.g., language, vision, robotics, reasoning, human interaction) and technical principles(e.g., model architectures, training procedures, data, systems, security, evaluation, theory) to their applications (e.g., law, healthcare, education) and societal impact (e.g., inequity, misuse, economic and environmental impact, legal and ethical considerations). Though foundation models are based on standard deep learning and transfer learning, their scale results in new emergent capabilities,and their effectiveness across so many tasks incentivizes homogenization. Homogenization provides powerful leverage but demands caution, as the defects of the foundation model are inherited by all the adapted models downstream. Despite the impending widespread deployment of foundation models, we currently lack a clear understanding of how they work, when they fail, and what they are even capable of due to their emergent properties. To tackle these questions, we believe much of the critical research on foundation models will require deep interdisciplinary collaboration commensurate with their fundamentally sociotechnical nature.