In this paper we consider a form of cellular automata (CA) that allows for external input at each stage of it s evolut ion. The invest igat ion is carr ied out from an algebra ic viewp oint whereby the state st ructure of the CA, together with it s action, can be int erpret ed rin g-theoretically. Specifically, we conside r the st ruct ure of a t tract ors for different cont rols and the associ...

Motivated in part by the study of the stable homology of automorphism groups of free groups, we consider cohomological calculations in the category F(gr) of functors from finitely generated free groups to abelian groups. In particular, we compute the groups Ext F(gr) (T ◦a, T◦a) where a is the abelianization functor and T is the n-th tensor power functor for abelian groups. These groups are sho...

The concept of Koszul differential graded algebra (Koszul DG algebra) is introduced. Koszul DG algebras exist extensively, and have nice properties similar to the classic Koszul algebras. A DG version of the Koszul duality is proved. When the Koszul DG algebra A is AS-regular, the Ext-algebra E of A is Frobenius. In this case, similar to the classical BGG correspondence, there is an equivalence...

The Tor network is probably one of the most popular online anonymity systems in the world. It has been built based on the volunteer relays from all around the world. It has a strong scientific basis which is structured very well to work in low latency mode that makes it suitable for tasks such as web browsing. Despite the advantages, the low latency also makes Tor insecure against timing and tr...

In 1981, G. D. James proved two theorems about the decomposition matrices of Schur algebras involving the removal of the first row or column from a Young diagram. He established corresponding results for the symmetric group using the Schur functor. We apply James’ techniques to prove that row removal induces an injection on the corresponding Ext between simple modules for the Schur algebra. We ...

vibrio cholerae o1 are classified into two biotypes, classical and el tor based on susceptibility to bacteriophages and some biochemical properties, each encoding a biotype-specific genetic determinants. before 1961, most epidemics had been caused by the classical biotype. however, with the passage of time, the classical biotype missed from the scenario and the el tor emerged as the major bioty...

Let R be a ring and M a right R-module. M is called n-FP-projective if Ext M N = 0 for any right R-module N of FP-injective dimension ≤n, where n is a nonnegative integer or n = . R M is defined as sup n M is n-FP-projective and R M = −1 if Ext M N = 0 for some FP-injective right R-module N. The right -dimension r -dim R of R is defined to be the least nonnegative integer n such that R M ≥ n im...

Let U denote the category of unstable modules over the mod 2 Steenrod algebra A, and let Ext(−) = ExtsU(−,ΣZ2). Let M∞ = H̃∗(ΣCP∞ + ) denote the unstable A-module with nonzero classes xi such that i is odd and positive, and Sqx2k+1 = ( k j ) x2(j+k)+1. Then H∗(U) ≈ U(M∞), where the left side is the mod 2 cohomology of the infinite unitary group, and the right side the free unstable A-algebra gen...