Algebraic Geometry of Matrix Product States

We quantify the representational power of matrix product states (MPS) for entangled qubit systems by giving polynomial expressions in a pure quantum state's amplitudes which hold if and only if the state is a translation invariant matrix product state or a limit of such states. For systems with few qubits, we give these equations explicitly, considering both periodic and open boundary conditions. Using the classical theory of trace varieties and trace algebras, we explain the relationship between MPS and hidden Markov models and exploit this relationship to derive useful parameterizations of MPS. We make four conjectures on the identifiability of MPS parameters

Giving New Zealand: Philanthropic Funding 2006

This report provides measurement of New Zealanders' philanthropic funding for the 2005/2006 year and what these funds supported

Approximating the Sachdev-Ye-Kitaev model with Majorana wires

The Sachdev-Ye-Kitaev (SYK) model describes a collection of randomly interacting Majorana fermions that exhibits profound connections to quantum chaos and black holes. We propose a solid-state implementation based on a quantum dot coupled to an array of topological superconducting wires hosting Majorana zero modes. Interactions and disorder intrinsic to the dot mediate the desired random Majorana couplings, while an approximate symmetry suppresses additional unwanted terms. We use random matrix theory and numerics to show that our setup emulates the SYK model (up to corrections that we quantify) and discuss experimental signatures.Comment: 7 pages, 2 figure

From the microbiome to the central nervous system, an update on the epidemiology and pathogenesis of bacterial meningitis in childhood [version 1; referees: 3 approved]

In the past century, advances in antibiotics and vaccination have dramatically altered the incidence and clinical outcomes of bacterial meningitis. We review the shifting epidemiology of meningitis in children, including after the implementation of vaccines that target common meningitic pathogens and the introduction of intrapartum antibiotic prophylaxis offered to mothers colonized with Streptococcus agalactiae. We also discuss what is currently known about the pathogenesis of meningitis. Recent studies of the human microbiome have illustrated dynamic relationships of bacterial and viral populations with the host, which may potentiate the risk of bacterial meningitis

Denial of Service in Voice Over IP Networks

In this paper we investigate denial of service (DoS) vulnerabilities in Voice over IP (VoIP) systems, focusing on the ITU-T H.323 family of protocols. We provide a simple characterisation of DoS attacks that allows us to readily identify DoS issues in H.323 protocols. We also discuss network layer DoS vulnerabilities that affect VoIP systems. A number of improvements and further research directions are proposed