The gray matter structural connectome and its relationship to alcohol relapse: Reconnecting for recovery.

Gray matter (GM) atrophy associated with alcohol use disorders (AUD) affects predominantly the frontal lobes. Less is known how frontal lobe GM loss affects GM loss in other regions and how it influences drinking behavior or relapse after treatment. The profile similarity index (PSI) combined with graph analysis allows to assess how GM loss in one region affects GM loss in regions connected to it, ie, GM connectivity. The PSI was used to describe the pattern of GM connectivity in 21 light drinkers (LDs) and in 54 individuals with AUD (ALC) early in abstinence. Effects of abstinence and relapse were determined in a subgroup of 36 participants after 3 months. Compared with LD, GM losses within the extended brain reward system (eBRS) at 1-month abstinence were similar between abstainers (ABST) and relapsers (REL), but REL had also GM losses outside the eBRS. Lower GM connectivities in ventro-striatal/hypothalamic and dorsolateral prefrontal regions and thalami were present in both ABST and REL. Between-networks connectivity loss of the eBRS in ABST was confined to prefrontal regions. About 3 months later, the GM volume and connectivity losses had resolved in ABST, and insula connectivity was increased compared with LD. GM losses and GM connectivity losses in REL were unchanged. Overall, prolonged abstinence was associated with a normalization of within-eBRS connectivity and a reconnection of eBRS structures with other networks. The re-formation of structural connectivities within and across networks appears critical for cognitive-behavioral functioning related to the capacity to maintain abstinence after outpatient treatment

Quantum Information Geometry in the Space of Measurements

We introduce a new approach to evaluating entangled quantum networks using information geometry. Quantum computing is powerful because of the enhanced correlations from quantum entanglement. For example, larger entangled networks can enhance quantum key distribution (QKD). Each network we examine is an n-photon quantum state with a degree of entanglement. We analyze such a state within the space of measured data from repeated experiments made by n observers over a set of identically-prepared quantum states -- a quantum state interrogation in the space of measurements. Each observer records a 1 if their detector triggers, otherwise they record a 0. This generates a string of 1's and 0's at each detector, and each observer can define a binary random variable from this sequence. We use a well-known information geometry-based measure of distance that applies to these binary strings of measurement outcomes, and we introduce a generalization of this length to area, volume and higher-dimensional volumes. These geometric equations are defined using the familiar Shannon expression for joint and mutual entropy. We apply our approach to three distinct tripartite quantum states: the GHZ state, the W state, and a separable state P. We generalize a well-known information geometry analysis of a bipartite state to a tripartite state. This approach provides a novel way to characterize quantum states, and it may have favorable scaling with increased number of photons.Comment: 21 pages, 7 figure

Angle and Volume Studies in Quantized Space

The search for a quantum theory of gravity is one of the major challenges facing theoretical physics today. While no complete theory exists, a promising avenue of research is the loop quantum gravity approach. In this approach, quantum states are represented by spin networks, essentially graphs with weighted edges. Since general relativity predicts the structure of space, any quantum theory of gravity must do so as well; thus, "spatial observables" such as area, volume, and angle are given by the eigenvalues of Hermitian operators on the spin network states. We present results obtained in our investigations of the angle and volume operators, two operators which act on the vertices of spin networks. We find that the minimum observable angle is inversely proportional to the square root of the total spin of the vertex, a fairly slow decrease to zero. We also present numerical results indicating that the angle operator can reproduce the classical angle distribution. The volume operator is significantly harder to investigate analytically; however, we present analytical and numerical results indicating that the volume of a region scales as the 3/2 power of its bounding surface, which corresponds to the classical model of space.Comment: Undergraduate thesis. 85 pp. (incl. TOC & appendices), 21 figures (not incl. diagrams in eqns.