Global dynamics of the mixmaster model

The asymptotic behaviour of vacuum Bianchi models of class A near the initial singularity is studied, in an effort to confirm the standard picture arising from heuristic and numerical approaches by mathematical proofs. It is shown that for solutions of types other than VIII and IX the singularity is velocity dominated and that the Kretschmann scalar is unbounded there, except in the explicitly known cases where the spacetime can be smoothly extended through a Cauchy horizon. For types VIII and IX it is shown that there are at most two possibilities for the evolution. When the first possibility is realized, and if the spacetime is not one of the explicitly known solutions which can be smoothly extended through a Cauchy horizon, then there are infinitely many oscillations near the singularity and the Kretschmann scalar is unbounded there. The second possibility remains mysterious and it is left open whether it ever occurs. It is also shown that any finite sequence of distinct points generated by iterating the Belinskii-Khalatnikov-Lifschitz mapping can be realized approximately by a solution of the vacuum Einstein equations of Bianchi type IX.Comment: 16 page

Invariants of Artinian Gorenstein Algebras and Isolated Hypersurface Singularities

We survey our recently proposed method for constructing biholomorphic invariants of quasihomogeneous isolated hypersurface singularities and, more generally, invariants of graded Artinian Gorenstein algebras. The method utilizes certain polynomials associated to such algebras, called nil-polynomials, and we compare them with two other classes of polynomials that have also been used to produce invariants.Comment: 13 page

SOK: (State of) the Art of War: Offensive Techniques in Binary Analysis

Finding and exploiting vulnerabilities in binary code is a challenging task. The lack of high-level, semantically rich information about data structures and control constructs makes the analysis of program properties harder to scale. However, the importance of binary analysis is on the rise. In many situations binary analysis is the only possible way to prove (or disprove) properties about the code that is actually executed. In this paper, we present a binary analysis framework that implements a number of analysis techniques that have been proposed in the past. We present a systematized implementation of these techniques, which allows other researchers to compose them and develop new approaches. In addition, the implementation of these techniques in a unifying framework allows for the direct comparison of these apporaches and the identification of their advantages and disadvantages. The evaluation included in this paper is performed using a recent dataset created by DARPA for evaluating the effectiveness of binary vulnerability analysis techniques. Our framework has been open-sourced and is available to the security community

Stability and Chaotic Attractors of Memristor-Based Circuit with a Line of Equilibria

This report investigates the stability problem of memristive systems with a line of equilibria on the example of SBT memristor-based Wien-bridge circuit. For the considered system, conditions of local and global partial stability are obtained, and chaotic dynamics is studied.peerReviewe