Cutting Medusa's Path -- Tackling Kill-Chains with Quantum Computing

This paper embarks upon exploration of quantum vulnerability analysis. By introducing vulnerability graphs, related to attack graphs, this paper provides background theory and a subsequent method for solving significant cybersecurity problems with quantum computing. The example given is to prioritize patches by expressing the connectivity of various vulnerabilities on a network with a QUBO and then solving this with quantum annealing. Such a solution is then proved to remove all kill-chains (paths to security compromise) on a network. The results demonstrate that the quantum computer's solve time is almost constant compared to the exponential increase in classical solve time for vulnerability graphs of expected real world density. As such, this paper presents a novel example of advantageous quantum vulnerability analysis.Comment: 9 pages, 1 figure, 2 table

Quid Manumit -- Freeing the Qubit for Art

This paper describes how to `Free the Qubit' for art, by creating standalone quantum musical effects and instruments. Previously released quantum simulator code for an ARM-based Raspberry Pi Pico embedded microcontroller is utilised here, and several examples are built demonstrating different methods of utilising embedded resources: The first is a Quantum MIDI processor that generates additional notes for accompaniment and unique quantum generated instruments based on the input notes, decoded and passed through a quantum circuit in an embedded simulator. The second is a Quantum Distortion module that changes an instrument's raw sound according to a quantum circuit, which is presented in two forms; a self-contained Quantum Stylophone, and an effect module plugin called 'QubitCrusher' for the Korg Nu:Tekt NTS-1. This paper also discusses future work and directions for quantum instruments, and provides all examples as open source. This is, to the author's knowledge, the first example of embedded Quantum Simulators for Instruments of Music (another QSIM).Comment: 8 pages, 6 figures, to appear at ISQCMC in Berlin, Oct 5-6th 202

Computability and Tiling Problems

In this thesis we will present and discuss various results pertaining to tiling problems and mathematical logic, specifically computability theory. We focus on Wang prototiles, as defined in [32]. We begin by studying Domino Problems, and do not restrict ourselves to the usual problems concerning finite sets of prototiles. We first consider two domino problems: whether a given set of prototiles $S$ has total planar tilings, which we denote $TILE$, or whether it has infinite connected but not necessarily total tilings, $WTILE$ (short for `weakly tile'). We show that both $TILE \equiv_m ILL \equiv_m WTILE$, and thereby both $TILE$ and $WTILE$ are $\Sigma^1_1$-complete. We also show that the opposite problems, $\neg TILE$ and $SNT$ (short for `Strongly Not Tile') are such that $\neg TILE \equiv_m WELL \equiv_m SNT$ and so both $\neg TILE$ and $SNT$ are both $\Pi^1_1$-complete. Next we give some consideration to the problem of whether a given (infinite) set of prototiles is periodic or aperiodic. We study the sets $PTile$ of periodic tilings, and $ATile$ of aperiodic tilings. We then show that both of these sets are complete for the class of problems of the form $(\Sigma^1_1 \wedge \Pi^1_1)$. We also present results for finite versions of these tiling problems. We then move on to consider the Weihrauch reducibility for a general total tiling principle $CT$ as well as weaker principles of tiling, and show that there exist Weihrauch equivalences to closed choice on Baire space, $C_{\omega^\omega}$. We also show that all Domino Problems that tile some infinite connected region are Weihrauch reducible to $C_{\omega^\omega}$. Finally, we give a prototile set of 15 prototiles that can encode any Elementary Cellular Automaton (ECA). We make use of an unusual tile set, based on hexagons and lozenges that we have not see in the literature before, in order to achieve this.Comment: PhD thesis. 179 pages, 13 figure

Computability and Tiling Problems

In this thesis we will present and discuss various results pertaining to tiling problems and mathematical logic, specifically computability theory. We focus on Wang prototiles, as defined in [32]. We begin by studying Domino Problems, and do not restrict ourselves to the usual problems concerning finite sets of prototiles. We first consider two domino problems: whether a given set of prototiles S has total planar tilings, which we denote TILE, or whether it has infinite connected but not necessarily total tilings, WTILE (short for ‘weakly tile’). We show that both TILE ≡m ILL ≡m WTILE, and thereby both TILE and WTILE are Σ11-complete. We also show that the opposite problems, ¬TILE and SNT (short for ‘Strongly Not Tile’) are such that ¬TILE ≡m WELL ≡m SNT and so both ¬TILE and SNT are both Π11-complete. Next we give some consideration to the problem of whether a given (infinite) set of prototiles is periodic or aperiodic. We study the sets PTile of periodic tilings, and ATile of aperiodic tilings. We then show that both of these sets are complete for the class of problems of the form (Σ1 1 ∧Π1 1). We also present results for finite versions of these tiling problems. We then move on to consider the Weihrauch reducibility for a general total tiling principle CT as well as weaker principles of tiling, and show that there exist Weihrauch equivalences to closed choice on Baire space, Cωω. We also show that all Domino Problems that tile some infinite connected region are Weihrauch reducible to Cωω. Finally, we give a prototile set of 15 prototiles that can encode any Elementary CellularAutomaton(ECA). We make use of an unusual tileset, based on hexagons and lozenges that we have not seen in the literature before, in order to achieve this

Chronobiology of Epilepsy

A fine balance between neuronal excitation and inhibition governs the physiological state of the brain. It has been hypothesized that when this balance is lost as a result of excessive excitation or reduced inhibition, pathological states such as epilepsy emerge. Decades of investigation have shown this to be true in vitro. However, in vivo evidence of the emerging imbalance during the "latent period" between the initiation of injury and the expression of the first spontaneous behavioral seizure has not been demonstrated. Here, we provide the first demonstration of this emerging imbalance between excitation and inhibition in vivo by employing long term, high temporal resolution, and continuous local field recordings from microelectrode arrays implanted in an animal model of limbic epilepsy. We were able to track both the inhibitory and excitatory postsynaptic field activity during the entire latent period, from the time of injury to the occurrence of the first spontaneous epileptic seizure. During this latent period we observe a sustained increase in the firing rate of the excitatory postsynaptic field activity, paired with a subsequent decrease in the firing rate of the inhibitory postsynaptic field activity within the CA1 region of the hippocampus. Firing rates of both excitatory and inhibitory CA1 field activities followed a circadian- like rhythm, which is locked near in-phase in controls and near anti-phase during the latent period. We think that these observed changes are implicated in the occurrence of spontaneous seizure onset following injury