The Claremont Colleges (known colloquially as the 7Cs) are a consortium of seven high end private institutions of higher education located in Claremont, California, United States. They comprise five undergraduate colleges (the 5Cs)—Pomona College, Scripps College, Claremont McKenna College (CMC), Harvey Mudd College, and Pitzer College—and two graduate schools—Claremont Graduate University (CGU) and Keck Graduate Institute (KGI). All the members except KGI have adjoining campuses, together covering roughly 1 sq mi (2.6 km2).The consortium was founded in 1925 by Pomona College president James A. Blaisdell, who proposed a collegiate university design inspired by Oxford University. He sought to provide the specialization, flexibility, and personal attention commonly found in small colleges, but with the resources of a large university. The consortium has since grown to roughly 8,500 students and 3,270 faculty and staff, and offers more than 2,000 courses every semester. The colleges share a central library, campus safety services, health services, and other resources, managed by The Claremont Colleges Services (TCCS). Among the undergraduate schools, there is significant social interaction and academic cross-registration, but each college maintains a distinct identity.Admission to the Claremont Colleges is considered highly selective. For the Class of 2020 admissions cycle, four of the five most selective liberal art colleges in the U.S. by acceptance rate were among the 5Cs, and the remaining college, Scripps, had the second-lowest acceptance rate among women's colleges. The Fiske Guide to Colleges describes the consortium as "a collection of intellectual resources unmatched in America.S.S.
Let M_0 be a compact and orientable 3-manifold. After capping off spherical boundaries with balls and removing any torus boundaries, we prove that the resulting manifold M contains handlebodies of arbitrary genus such that the closure of their complement is hyperbolic. We then extend the octahedral decomposition to obtain bounds on volume for some of these handlebody complements.
We extend the Wirtinger number of links, an invariant originally defined by Blair, Kjuchukova, Velazquez, and Villanueva in terms of extending initial colorings of some strands of a diagram to the entire diagram, to spatial graphs. We prove that the Wirtinger number equals the bridge index of spatial graphs, and we implement an algorithm in Python which gives a more efficient way to estimate upper bounds of bridge indices. Combined with lower bounds from diagram colorings by elements from certain algebraic structures and clasping techniques, we obtain exact bridge indices for a large family of almost unknotted spatial graphs. We also show that for every possible negative Euler characteristic, there exist almost unknotted graphs of arbitrarily large bridge index.
Hunter proved that the complete homogeneous symmetric polynomials of even degree are positive definite. We prove a noncommutative generalization of this result, in which the scalar variables are replaced with hermitian operators. We provide a sharp lower bound and a sum of hermitian squares representation that are novel even in the scalar case.
At the center of narrow evolutionary psychology's theory lies the assumption that many human behavioral mechanisms evolved via natural selection. Although some components of this theory are falsifiable, its Lakatosian framework protects its core assumptions from falsifiability, even though most human behaviors probably do not require evolutionary explanations. Crucially, falsifiability is a necessary but insufficient quality of a good scientific theory, and the value of narrow evolutionary psychology can be questioned on other grounds. Narrow evolutionary psychology holds that only natural selection can create complex, functional adaptations, but natural selection is not a creative force; this process merely functions as a sieve that influences phenotype frequencies in descendant populations. Instead, only developmental processes can create the adaptations observed in individuals. Evolutionary explanations for behaviors will always be less useful than developmental explanations, given the context-dependent, emergent, and plastic nature of development. Evolutionary explanations will often be superfluous. (PsycInfo Database Record (c) 2026 APA, all rights reserved).
We characterize additive semigroups in {0,1,2,& mldr;} of matricial dimension 2 and produce a counterexample to the conjecture that a numerical semigroup whose small elements are lonely has matricial dimension at most 2.
