This paper considers the consequences of endowing an intelligent agent with the ability to modify its own code. The intelligent agent is patterned closely after AIXI [1], but the environment has read-only access to the agent’s description. On the basis of some simple modifications to the utility and horizon functions, we are able to discuss and compare some very different kinds of agents, speci...

We show that every infinite-dimensional commutative unital C∗-algebra has a Hilbert C∗-module admitting no frames. In particular, this shows that Kasparov’s stabilization theorem for countably generated Hilbert C∗-modules can not be extended to arbitrary Hilbert C∗-modules.

Let G be a finite group and A be a normal subgroup of G. We denote by ncc(A) the number of G-conjugacy classes of A and A is called n-decomposable, if ncc(A) = n. Set KG = {ncc(A)|A⊳ G}. Let X be a non-empty subset of positive integers. A group G is called X-decomposable, if KG = X . Ashrafi and his co-authors [1,2,3,4,5] have characterized the X-decomposable nonperfect finite groups for X = {1...

The concept of burden of proof is used in a wide range of discourses, from philosophy to law, science, skepticism, and even in everyday reasoning. This paper provides an analysis of the proper deployment of burden of proof, focusing in particular on skeptical discussions of pseudoscience and the paranormal, where burden of proof assignments are most poignant and relatively clear-cut. We argue t...

It is shown that for every k ∈ N there exists a Borel probability measure μ on {−1, 1}Rk × {−1, 1}Rk such that for every m,n ∈ N and x1, . . . , xm, y1, . . . , yn ∈ Sm+n−1 there exist x1, . . . , x ′ m, y ′ 1, . . . , y ′ n ∈ Sm+n−1 such that if G : R → R is a random k× (m+ n) matrix whose entries are i.i.d. standard Gaussian random variables then for all (i, j) ∈ {1, . . . ,m} × {1, . . . , n...

Let K be field of characteristic 2 and let G be a finite nonabelian 2-group with the cyclic derived subgroup G′, and there exists a central element z of order 2 in Z(G)\G′. We prove that the unit group of the group algebra KG possesses a section isomorphic to the wreath product of a group of order 2 with the derived subgroup of the group G, giving for such groups a positive answer to the questi...

"The Queen's Gambit," a thought-provoking drama series directed by A. Scott Frank, explores women's empowerment through the lens of protagonist Beth Harmon's personal journey and her struggle to make mark in male-dominated world chess. Employing textual analysis considering broader context social history evolution feminism during time period, this paper delves into inherent contradictions confl...