Analysis of the NIST database towards the composition of vulnerabilities in attack scenarios

The composition of vulnerabilities in attack scenarios has been traditionally performed based on detailed pre- and post-conditions. Although very precise, this approach is dependent on human analysis, is time consuming, and not at all scalable. We investigate the NIST National Vulnerability Database (NVD) with three goals: (i) understand the associations among vulnerability attributes related to impact, exploitability, privilege, type of vulnerability and clues derived from plaintext descriptions, (ii) validate our initial composition model which is based on required access and resulting effect, and (iii) investigate the maturity of XML database technology for performing statistical analyses like this directly on the XML data. In this report, we analyse 27,273 vulnerability entries (CVE 1) from the NVD. Using only nominal information, we are able to e.g. identify clusters in the class of vulnerabilities with no privilege which represent 52% of the entries

Conceptual Aspects of PT-Symmetry and Pseudo-Hermiticity: A status report

We survey some of the main conceptual developments in the study of PT-symmetric and pseudo-Hermitian Hamiltonian operators that have taken place during the past ten years or so. We offer a precise mathematical description of a quantum system and its representations that allows us to describe the idea of unitarization of a quantum system by modifying the inner product of the Hilbert space. We discuss the role and importance of the quantum-to-classical correspondence principle that provides the physical interpretation of the observables in quantum mechanics. Finally, we address the problem of constructing an underlying classical Hamiltonian for a unitary quantum system defined by an a priori non-Hermitian Hamiltonian.Comment: 11 page

CPT-symmetric discrete square well

A new version of an elementary PT-symmetric square well quantum model is proposed in which a certain Hermiticity-violating end-point interaction leaves the spectrum real in a large domain of couplings $\lambda\in (-1,1)$. Within this interval we employ the usual coupling-independent operator P of parity and construct, in a systematic Runge-Kutta discrete approximation, a coupling-dependent operator of charge C which enables us to classify our P-asymmetric model as CPT-symmetric or, equivalently, hiddenly Hermitian alias cryptohermitian.Comment: 12 pp., presented to conference PHHQP IX (http://www.math.zju.edu.cn/wjd/

Weak Measurements in Non-Hermitian Systems

"Weak measurements" -- involving a weak unitary interaction between a quantum system and a meter followed by a projective measurement -- are investigated when the system has a non-Hermitian Hamiltonian. We show in particular how the standard definition of the "weak value" of an observable must be modified. These studies are undertaken in the context of bound state scattering theory, a non-Hermitian formalism for which the Hilbert spaces involved are unambiguously defined and the metric operators can be explicitly computed. Numerical examples are given for a model system

Krein-Space Formulation of PT-Symmetry, CPT-Inner Products, and Pseudo-Hermiticity

Emphasizing the physical constraints on the formulation of a quantum theory based on the standard measurement axiom and the Schroedinger equation, we comment on some conceptual issues arising in the formulation of PT-symmetric quantum mechanics. In particular, we elaborate on the requirements of the boundedness of the metric operator and the diagonalizability of the Hamiltonian. We also provide an accessible account of a Krein-space derivation of the CPT-inner product that was widely known to mathematicians since 1950's. We show how this derivation is linked with the pseudo-Hermitian formulation of PT-symmetric quantum mechanics.Comment: published version, 17 page