A geometric extension algebra is an extension algebra of a semi-simple perverse sheaf (allowing shifts), e.g. a push-forward of the constant sheaf under a projective map. Particular nice situations arise for collapsings of homogeneous vector bundle over homogeneous spaces. In this paper, we study the relationship between partial flag and complete flag cases. Our main result is that the locally ...

The field of cybersecurity is adversarial – the real challenge lies in outsmarting motivated and knowledgeable human attackers. Sadly, this aspect is missing from current cybersecurity classes, which are often taught through lectures and occasionally through “get your feet wet” practical exercises. We propose Class Capture-theFlag exercises (CCTFs) to revitalize cybersecurity education. These a...

In a seminal 1994 paper [20], Lusztig extended the theory of total positivity by introducing the totally non-negative part (G/P )≥0 of an arbitrary (generalized, partial) flag variety G/P . He referred to this space as a “remarkable polyhedral subspace,” and conjectured a decomposition into cells, which was subsequently proven by the first author [27]. In this article we use discrete Morse theo...

This is a paper about noncontractive logical systems: systems not closed under contraction. (Contraction is what allows us to conclude that Γ,A⊢B from the claim that Γ,A,A⊢B.)These systems form one family of substructural logical systems: systems that do not impose the full budget of what are called structural rules, or in which there are counterexamples to the structural metainferences associa...

We present some results on flag-transitive symmetric designs. First we see what conditions are necessary for a symmetric design to admit an imprimitive, flag-transitive automorphism group. Then we move on to study the possibilities for a primitive, flag-transitive automorphism group, and prove that for λ ≤ 3, the group must be affine or almost simple, and finally we analyse the case in which a ...

Eukaryotic endocytosis involves multivesicular bodies formation, which is driven by endosomal sorting complexes required for transport (ESCRT). Here, we showed the presence and expression of homologous ESCRT genes in Entamoeba histolytica. We cloned and expressed the Ehvps4 gene, an ESCRT member, to obtain the recombinant EhVps4 and generate specific antibodies, which immunodetected EhVps4 in c...

This paper develops a new method for studying the cohomology of orthogonal flag varieties. Restriction varieties are subvarieties of orthogonal flag varieties defined by rank conditions with respect to (not necessarily isotropic) flags. They interpolate between Schubert varieties in orthogonal flag varieties and the restrictions of general Schubert varieties in ordinary flag varieties. We give ...

The Capture the Flag domain is uncertain, adversarial, and continuous. It poses several hard planning problems. We have developed a planner that attempts to exploit Capture the Flag's inherent dynamics, instead of being stymied by them. In particular, it uses the notion of critical points to de ne states in this continuous domain. These states are then used to e ciently

Capture the Flag (CTF) is well-established as a computer security contest of skill in which teams compete in real time for prizes and bragging rights. At the time of this writing, CTFtime.org [4]—a tracking web site devoted to aggregating team standings across various CTF events— lists 76 such contests, and more spring up each year. But what is the point, exactly? In this paper we detail our ex...