S. Patwardhan, Ş. Erkol, F. Radicchi, & M. Barthelemy

Proc. Natl. Acad. Sci. U.S.A. 123 (29) e2535998123,

Public transit agencies face the challenge of allocating limited resources across routes with varying demand. Analyzing bus systems across 19 metropolitan areas, we show that, despite differences in cities, agencies, and planning practices, realized operations exhibit a specific scaling pattern in service allocation. This regularity is not imposed by a universal planning formula, but emerges across institutional and urban contexts. We show that it can be understood through a constrained-optimization principle balancing passenger waiting time, crowding, and limited resources. The result connects urban transit to complex flow systems in physics and biology by highlighting a regime where demand fixes flows, and cities allocate service capacity. This framework explains unequal returns to investment across systems and guides efficient, equitable planning.

Read the full article at: www.pnas.org

Tim Gebbie

Complex systems are often organised into hierarchies whose internal interactions are stronger or faster than interactions across levels. When markets are treated as genuinely multilevel systems it becomes natural to represent them as systems with hierarchical causality. Here we show that reflexivity can be formulated within such a discrete hierarchical causal system; but one in which a higher-level actor state restricts the lower-level transition kernels that remain admissible. Then event dynamics can be separated from calendar embeddings: a set-valued actor-conditioned correspondence can be used to define the admissible family of event kernels, while joint state and waiting-time laws can be used to determine compatible timing to then natural demonstrate reflexivity. A selected event-state law need not determine a unique calendar embedding. Locally, uniqueness of the joint event or timing specification requires uniqueness of both the admissible event kernel and its compatible timing law. Reflexivity is thus the endogenous closure of a hierarchical constraint loop, while timing and projection can generate calendar-time memory or causal ambiguity even for Markov event dynamics.

Read the full article at: arxiv.org

Marta Zava

Training a frontier artificial intelligence model costs hundreds of millions of dollars before a product exists, and few investors can write that cheque. This paper shows that the number who can falls as the fixed cost of a first training run rises, at a rate set by the concentration of the fund size distribution, so that doubling the cost removes about two thirds of the possible backers. The firms that compete are therefore selected by a small group of allocators before any customer has expressed a view. Three results follow. The price paid by the winner separates into a rational bid, a premium created by the fund’s deployment clock, and an error from failing to adjust for adverse selection, and the sign of the price response to competition identifies which one dominates. Concentration trades breadth for depth, improving the funded set only when the skill advantage of the few outweighs the information lost through having fewer independent views, a loss that is small when investors think alike. And large upfront cheques reduce the value of stopping, so ventures funded under deployment pressure should fail later and larger rather than more often. The effective policy margin is access to compute rather than regulation of the capital market.Training a frontier artificial intelligence model costs hundreds of millions of dollars before a product exists, and few investors can write that cheque. This paper shows that the number who can falls as the fixed cost of a first training run rises, at a rate set by the concentration of the fund size distribution, so that doubling the cost removes about two thirds of the possible backers. The firms that compete are therefore selected by a small group of allocators before any customer has expressed a view. Three results follow. The price paid by the winner separates into a rational bid, a premium created by the fund’s deployment clock, and an error from failing to adjust for adverse selection, and the sign of the price response to competition identifies which one dominates. Concentration trades breadth for depth, improving the funded set only when the skill advantage of the few outweighs the information lost through having fewer independent views, a loss that is small when investors think alike. And large upfront cheques reduce the value of stopping, so ventures funded under deployment pressure should fail later and larger rather than more often. The effective policy margin is access to compute rather than regulation of the capital market.

Read the full article at: papers.ssrn.com