Shift-Symmetric Configurations in Two-Dimensional Cellular Automata: Irreversibility, Insolvability, and Enumeration

The search for symmetry as an unusual yet profoundly appealing phenomenon, and the origin of regular, repeating configuration patterns have long been a central focus of complexity science and physics. To better grasp and understand symmetry of configurations in decentralized toroidal architectures, we employ group-theoretic methods, which allow us to identify and enumerate these inputs, and argue about irreversible system behaviors with undesired effects on many computational problems. The concept of so-called configuration shift-symmetry is applied to two-dimensional cellular automata as an ideal model of computation. Regardless of the transition function, the results show the universal insolvability of crucial distributed tasks, such as leader election, pattern recognition, hashing, and encryption. By using compact enumeration formulas and bounding the number of shift-symmetric configurations for a given lattice size, we efficiently calculate the probability of a configuration being shift-symmetric for a uniform or density-uniform distribution. Further, we devise an algorithm detecting the presence of shift-symmetry in a configuration. Given the resource constraints, the enumeration and probability formulas can directly help to lower the minimal expected error and provide recommendations for system's size and initialization. Besides cellular automata, the shift-symmetry analysis can be used to study the non-linear behavior in various synchronous rule-based systems that include inference engines, Boolean networks, neural networks, and systolic arrays.Comment: 22 pages, 9 figures, 2 appendice

MRI-based Quantification of Optic Nerve Tortuosity and Subarachnoid Space 3D Geometry: Reliability Assessment

In some astronauts, long-duration space flight results in ophthalmic structure changes such as optic nerve (ON) kinking, ON distention, and globe flattening. Assessment of the ON and ON sheath (ONS) may provide insight into the mechanisms responsible for ophthalmic structure changes seen in a subset of astronauts. Automated and manual methods were developed to quantify 3D ON/ONS geometry and ON tortuosity

Stationary distributions for diffusions with inert drift

Consider reflecting Brownian motion in a bounded domain in $${\mathbb R^d}$$ that acquires drift in proportion to the amount of local time spent on the boundary of the domain. We show that the stationary distribution for the joint law of the position of the reflecting Brownian motion and the value of the drift vector has a product form. Moreover, the first component is uniformly distributed on the domain, and the second component has a Gaussian distribution. We also consider more general reflecting diffusions with inert drift as well as processes where the drift is given in terms of the gradient of a potential

FJMP: Factorized Joint Multi-Agent Motion Prediction over Learned Directed Acyclic Interaction Graphs

Predicting the future motion of road agents is a critical task in an autonomous driving pipeline. In this work, we address the problem of generating a set of scene-level, or joint, future trajectory predictions in multi-agent driving scenarios. To this end, we propose FJMP, a Factorized Joint Motion Prediction framework for multi-agent interactive driving scenarios. FJMP models the future scene interaction dynamics as a sparse directed interaction graph, where edges denote explicit interactions between agents. We then prune the graph into a directed acyclic graph (DAG) and decompose the joint prediction task into a sequence of marginal and conditional predictions according to the partial ordering of the DAG, where joint future trajectories are decoded using a directed acyclic graph neural network (DAGNN). We conduct experiments on the INTERACTION and Argoverse 2 datasets and demonstrate that FJMP produces more accurate and scene-consistent joint trajectory predictions than non-factorized approaches, especially on the most interactive and kinematically interesting agents. FJMP ranks 1st on the multi-agent test leaderboard of the INTERACTION dataset.Comment: CVPR 202

Polysemia as a concept to understand the encoding of sensory information

In this article, we explore the concept of polysemia in sensory information processing within the brain. We suggest that, just as words can have different meanings based on context, sensory inputs are interpreted differently depending on the animal’s current state and behavior. Focusing on the trigeminal sensory nuclei in rats, we highlight the role of inhibitory circuits in gating sensory information and propose that sensory signals are polysemic, with their meaning influenced by emotional, hormonal, and motivational factors

Phenotyping of field-grown wheat in the UK highlights contribution of light response of photosynthesis and flag leaf longevity to grain yield

Improving photosynthesis is a major target for increasing crop yields and ensuring food security. Phenotyping of photosynthesis in the field is critical to understand the limits to crop performance in agricultural settings. Yet, detailed phenotyping of photosynthetic traits is relatively scarce in field-grown wheat, with previous studies focusing on narrow germplasm selections. Flag leaf photosynthetic traits, crop development, and yield traits were compared in 64 field-grown wheat cultivars in the UK. Pre-anthesis and post-anthesis photosynthetic traits correlated significantly and positively with grain yield and harvest index (HI). These traits included net CO2 assimilation measured at ambient CO2 concentrations and a range of photosynthetic photon flux densities, and traits associated with the light response of photosynthesis. In most cultivars, photosynthesis decreased post-anthesis compared with pre-anthesis, and this was associated with decreased Rubisco activity and abundance. Heritability of photosynthetic traits suggests that phenotypic variation can be used to inform breeding programmes. Specific cultivars were identified with traits relevant to breeding for increased crop yields in the UK: pre-anthesis photosynthesis, post-anthesis photosynthesis, light response of photosynthesis, and Rubisco amounts. The results indicate that flag leaf longevity and operating photosynthetic activity in the canopy can be further exploited to maximize grain filling in UK bread wheat

Lost cities in the Steppe: investigating an enigmatic site type in early modern Mongolia

A Mongolian-German project is investigating abandoned early modern military and monastic sites in central Mongolia, including how the ruins of these urban nodes continue to shape cultural memory within nomadic society. Initial excavations have revealed a previously unknown site type, interpreted as garrisons from the period of Manchu rule (AD 1636–1911)

Fluctuations in an Evolutional Model of Two-Dimensional Young Diagrams

We discuss the non-equilibrium fluctuation problem, which corresponds to the hydrodynamic limit established in \cite{FS}, for the dynamics of two-dimensional Young diagrams associated with the uniform and restricted uniform statistics, and derive linear stochastic partial differential equations in the limit. We show that their invariant measures are identical to the Gaussian measures which appear in the fluctuation limits in the static situations.Comment: 43 pages, 2 figure