An official website of the United States government
Let p ∈ Z p\in {\mathbb {Z}} be an odd prime. We show that the fiber sequence for the cyclotomic trace of the sphere spectrum S {\mathbb {S}} admits an “eigensplitting” that generalizes known splittings on K K -theory and T C TC . We identify the summands in the fiber as the covers of Z p {\mathbb {Z}}_{p} -Anderson duals of summands in the K ( 1 ) K(1) -localized algebraic K K -theory of Z {\mathbb {Z}} . Analogous results hold for the ring Z {\mathbb {Z}} where we prove that the K ( 1 ) K(1) -localized fiber sequence is self-dual for Z p {\mathbb {Z}}_{p} -Anderson duality, with the duality permuting the summands by i ↦ p − i i\mapsto p-i (indexed mod p − 1 p-1 ). We explain an intrinsic characterization of the summand we call Z Z in the splitting T C ( Z ) p ∧ ≃ j ∨ Σ j ′ ∨ Z TC({\mathbb {Z}})^{\wedge }_{p}\simeq j \vee \Sigma j’\vee Z in terms of units in the p p -cyclotomic tower of Q p {\mathbb {Q}}_{p} .
more »
« less
This content will become publicly available on April 22, 2027
Using Flory–Huggins-informed human-in-the-loop Bayesian optimization to map the phase diagram of polymer blends
Integrating Flory–Huggins theory into a Bayesian optimization workflow enhances the objectivity of mapping phase behavior in polymer blends.
more »
« less
- PAR ID:
- 10686110
- Publisher / Repository:
- Royal Society of Chemistry
- Date Published:
- Journal Name:
- Digital Discovery
- Volume:
- 5
- Issue:
- 4
- ISSN:
- 2635-098X
- Page Range / eLocation ID:
- 1675 to 1688
- Subject(s) / Keyword(s):
- polymer blends, AI, human in the loop, phase separation
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract. We study the p-rank stratification of the moduli space of cyclic degree ! covers of the projective line in characteristic p for distinct primes p and !. The main result is about the intersection of the p-rank 0 stratum with the boundary of the moduli space of curves. When ! = 3 and p ≡ 2 mod 3 is an odd prime, we prove that there exists a smooth trielliptic curve in characteristic p, for every genus g, signature type (r,s), and p-rank f satisfying the clear necessary conditions.more » « less
-
Shamir and Spencer proved in the 1980s that the chromatic number of the binomial random graph $$G_{n,p}$$ is concentrated in an interval of length at most $$\omega\sqrt{n}$$, and in the 1990s Alon showed that an interval of length $$\omega\sqrt{n}/\log n$$ suffices for constant edge-probabilities $$p\in (0,1)$$. We prove a similar logarithmic improvement of the Shamir-Spencer concentration results for the sparse case $${p=p(n) \to 0}$$, and uncover a surprising concentration `jump' of the chromatic number in the very dense case $${p=p(n) \to 1}$$.more » « less
-
Abstract The costs of foraging can be high while also carrying significant risks, especially for consumers feeding at the top of the food chain.To mitigate these risks, many predators supplement active hunting with scavenging and kleptoparasitic behaviours, in some cases specializing in these alternative modes of predation.The factors that drive differential utilization of these tactics from species to species are not well understood.Here, we use an energetics approach to investigate the survival advantages of hunting, scavenging and kleptoparasitism as a function of predator, prey and potential competitor body sizes for terrestrial mammalian carnivores.The results of our framework reveal that predator tactics become more diverse closer to starvation, while the deployment of scavenging and kleptoparasitism is strongly constrained by the ratio of predator to prey body size.Our model accurately predicts a behavioural transition away from hunting towards alternative modes of predation with increasing prey size for predators spanning an order of magnitude in body size, closely matching observational data across a range of species.We then show that this behavioural boundary follows an allometric power‐law scaling relationship where the predator size scales with an exponent nearing 3/4 with prey size, meaning that this behavioural switch occurs at relatively larger threshold prey body size for larger carnivores.We suggest that our approach may provide a holistic framework for guiding future observational efforts exploring the diverse array of predator foraging behaviours.more » « less
