A CLT for Plancherel representations of the infinite-dimensional unitary group

We study asymptotics of traces of (noncommutative) monomials formed by images of certain elements of the universal enveloping algebra of the infinite-dimensional unitary group in its Plancherel representations. We prove that they converge to (commutative) moments of a Gaussian process that can be viewed as a collection of simply yet nontrivially correlated two-dimensional Gaussian Free Fields. The limiting process has previously arisen via the global scaling limit of spectra for submatrices of Wigner Hermitian random matrices. This note is an announcement, proofs will appear elsewhere.Comment: 12 page

Popular music, psychogeography, place identity and tourism: The case of Sheffield

Tourism and cultural agencies in some English provincial cities are promoting their popular music ‘heritage’ and, in some cases, contemporary musicians through the packaging of trails, sites, ‘iconic’ venues and festivals. This article focuses on Sheffield, a ‘post-industrial’ northern English city which is drawing on its associations with musicians past and present in seeking to attract tourists. This article is based on interviews with, among others, recording artists, promoters, producers and venue managers, along with reflective observational and documentary data. Theoretical remarks are made on the representations of popular musicians through cultural tourism strategies, programmes and products and also on the ways in which musicians convey a ‘psychogeographical’ sense of place in the ‘soundscape’ of the city

Statistical Mechanics of Logarithmic REM: Duality, Freezing and Extreme Value Statistics of 1/f1/f Noises generated by Gaussian Free Fields

We compute the distribution of the partition functions for a class of one-dimensional Random Energy Models (REM) with logarithmically correlated random potential, above and at the glass transition temperature. The random potential sequences represent various versions of the 1/f noise generated by sampling the two-dimensional Gaussian Free Field (2dGFF) along various planar curves. Our method extends the recent analysis of Fyodorov Bouchaud from the circular case to an interval and is based on an analytical continuation of the Selberg integral. In particular, we unveil a {\it duality relation} satisfied by the suitable generating function of free energy cumulants in the high-temperature phase. It reinforces the freezing scenario hypothesis for that generating function, from which we derive the distribution of extrema for the 2dGFF on the $[0,1]$ interval. We provide numerical checks of the circular and the interval case and discuss universality and various extensions. Relevance to the distribution of length of a segment in Liouville quantum gravity is noted.Comment: 25 pages, 12 figures Published version. Misprint corrected, references and note adde

Do cardiovascular responses to active and passive coping tasks predict future blood pressure 10 months later?

The study examined whether cardiovascular responses to active or passive coping tasks and single or multiple tasks predicted changes in resting blood pressure (BP) over a ten-month period. Heart rate (HR), BP, cardiac output (CO), and total peripheral resistance (TPR) were measured at rest, and during mental stress tests (mental arithmetic, speech, and cold pressor tasks). A total of 104 eligible participants participated in the initial study, and 77 (74.04%) normotensive adult participants’ resting BP were re-evaluated at ten-month follow-up. Regression analyses indicated that after adjustment for baseline BP, initial age, gender, body mass index, family history of cardiovascular disease, and current cigarette smoking, heightened systolic blood pressure (SBP) and HR responses to an active coping task (mental arithmetic) were associated with increased future SBP (R2 = .060, R2 =.045, respectively). Further, when aggregated, SBP responsivity (over the three tasks) resulted in a significant, but smaller increase in R2 accounting for .040 of the variance of follow-up SBP. These findings suggest that cardiovascular responses to active coping tasks predict future SBP. Furtherthe findings revealed that SBP responses to the tasks when aggregated were less predictive compared to an individual task (i.e., mental arithmetic). Of importance, hemodynamic reactivity (namely CO and TPR) did not predict future BP; suggesting that more general psychophysiological processes (e.g., inflammation, platelet aggregation) may be implicated, or that BP, but not hemodynamic reactivity may be a marker of hypertension

The identification and characterization of small molecules for the inhibition of NGF and proNGF8p75NTR interactions using surface plasmon resonance spectroscopy

! The!survival!of!neurons!in!both!the!central!and!peripheral!nervous!systems! depend!on!a!balance!between!pro8survival!and!pro8death!signaling!pathways.! Neurotrophins!and!their!precursors,!proneurotrophins,!are!a!unique!family!of! soluble!signaling!proteins,!which!act!to!preserve!this!balance.!Dysregulation!of!these! proteins,!however,!has!been!implicated!in!several!pathologies.!Specifically,!both! nerve!growth!factor!(NGF)!and!pro8nerve!growth!factor!(proNGF)!have!been! implicated!in!the!development!and!progression!of!neurodegenerative!diseases,!such! as!Parkinson’s!and!Alzheimer’s!diseases,!through!p75NTR8mediated!apoptotic! signaling.!!Therefore,!the!identification!of!small!molecule!inhibitors!capable!of! binding!to!and!modulating!NGF!and!proNGF!may!be!of!therapeutic!interest.!This! thesis!aims!to!characterize!the!inhibitory!action!of!previously!reported!small! molecule8based!NGF!inhibitors,!ALE80540,!PD90780,!Ro!0882750,!and!PQC!083,!as! well!as!novel!derivatives!of!these!compounds,!using!surface!plasmon!resonance! (SPR)!spectroscopy.!Of!the!established!inhibitors,!PD90780!offered!the!most! effective!inhibitory!action!for!both!NGF!and!proNGF!binding!to!p75NTR,!suggesting! that!this!compound!may!offer!multipotent!inhibition.!Further,!several!novel!ligand! specific!molecules!were!identified,!which!selectively!inhibited!either!NGF!or! proNGF8p75NTR!interactions.!Specifically,!BVNP!1,!BVNP!6,!and!BVNP!7!were!shown! to!be!effective!inhibitors!of!NGF8p75NTR!interactions,!while!BVNP!3!and!BVNP!4! were!found!to!be!selective!for!the!inhibition!of!proNGF!binding!to!p75NTR.!The! findings!of!this!thesis!offer!new!insight!into!the!use!of!small!molecule!inhibitors!to! ! iv! block!both!neurotrophin!and!proneurotrophin8mediated!signaling.!In!addition,!the! compounds!described!herein!may!be!used!for!future!lead!development.!Master of Science (MSc) in Biolog

Disk Heating, Galactoseismology, and the Formation of Stellar Halos

Deep photometric surveys of the Milky Way have revealed diffuse structures encircling our Galaxy far beyond the "classical" limits of the stellar disk. This paper reviews results from our own and other observational programs, which together suggest that, despite their extreme positions, the stars in these structures were formed in our Galactic disk. Mounting evidence from recent observations and simulations implies kinematic connections between several of these distinct structures. This suggests the existence of collective disk oscillations that can plausibly be traced all the way to asymmetries seen in the stellar velocity distribution around the Sun. There are multiple interesting implications of these findings: they promise new perspectives on the process of disk heating, they provide direct evidence for a stellar halo formation mechanism in addition to the accretion and disruption of satellite galaxies, and, they motivate searches of current and near-future surveys to trace these oscillations across the Galaxy. Such maps could be used as dynamical diagnostics in the emerging field of "Galactoseismology", which promises to model the history of interactions between the Milky Way and its entourage of satellites, as well examine the density of our dark matter halo. As sensitivity to very low surface brightness features around external galaxies increases, many more examples of such disk oscillations will likely be identified. Statistical samples of such features not only encode detailed information about interaction rates and mergers, but also about long sought-after dark matter halo densities and shapes. Models for the Milky Way's own Galactoseismic history will therefore serve as a critical foundation for studying the weak dynamical interactions of galaxies across the universe.Comment: 20 pages, 5 figures, accepted in for publication in a special edition of the journal "Galaxies", reporting the proceedings of the conference "On the Origin (and Evolution) of Baryonic Galaxy Halos", Puerto Ayora, Ecuador, March 13-17 2017, Eds. Duncan A. Forbes and Ericson D. Lope

Fluctuations for the Ginzburg-Landau ∇ϕ\nabla \phi Interface Model on a Bounded Domain

We study the massless field on $D_n = D \cap \tfrac{1}{n} \Z^2$, where $D \subseteq \R^2$ is a bounded domain with smooth boundary, with Hamiltonian \CH(h) = \sum_{x \sim y} \CV(h(x) - h(y)). The interaction \CV is assumed to be symmetric and uniformly convex. This is a general model for a $(2+1)$-dimensional effective interface where $h$ represents the height. We take our boundary conditions to be a continuous perturbation of a macroscopic tilt: $h(x) = n x \cdot u + f(x)$ for $x \in \partial D_n$, $u \in \R^2$, and $f \colon \R^2 \to \R$ continuous. We prove that the fluctuations of linear functionals of $h(x)$ about the tilt converge in the limit to a Gaussian free field on $D$, the standard Gaussian with respect to the weighted Dirichlet inner product $(f,g)_\nabla^\beta = \int_D \sum_i \beta_i \partial_i f_i \partial_i g_i$ for some explicit $\beta = \beta(u)$. In a subsequent article, we will employ the tools developed here to resolve a conjecture of Sheffield that the zero contour lines of $h$ are asymptotically described by $SLE(4)$, a conformally invariant random curve.Comment: 58 page

Conformal Curves in Potts Model: Numerical Calculation

We calculated numerically the fractal dimension of the boundaries of the Fortuin-Kasteleyn clusters of the $q$-state Potts model for integer and non-integer values of $q$ on the square lattice. In addition we calculated with high accuracy the fractal dimension of the boundary points of the same clusters on the square domain. Our calculation confirms that this curves can be described by SLE$_{\kappa}$.Comment: 11 Pages, 4 figure

Pre-freezing of multifractal exponents in Random Energy Models with logarithmically correlated potential

Boltzmann-Gibbs measures generated by logarithmically correlated random potentials are multifractal. We investigate the abrupt change ("pre-freezing") of multifractality exponents extracted from the averaged moments of the measure - the so-called inverse participation ratios. The pre-freezing can be identified with termination of the disorder-averaged multifractality spectrum. Naive replica limit employed to study a one-dimensional variant of the model is shown to break down at the pre-freezing point. Further insights are possible when employing zero-dimensional and infinite-dimensional versions of the problem. In particular, the latter version allows one to identify the pattern of the replica symmetry breaking responsible for the pre-freezing phenomenon.Comment: This is published version, 11 pages, 1 figur

Hidden clusters: the articulation of agglomeration in City Regions

For many years, local economic development has been driven by the desire to maintain, attract and nurture clusters of economic activity in targeted industrial sectors. However, where clusters are not conventionally sector-based, public policy needs to develop alternative approaches to leverage the economic benefits and realise competitive advantage. Drawing on a study of the Sheffield City Region (SCR), the paper explores the challenge of leveraging ‘hidden’ cross-sectoral clusters, which do not fit dominant discourses of agglomeration-led growth. We posit that it is the cross-sectoral connections and networks in the SCR which represent its key strength, yet these are only partially reflected by current place marketing and policy considerations, and, in many ways, are overlooked and thus remain ‘hidden’. The paper argues that the competitive advantage of the SCR is undermined when it characterises clusters in terms of industrial sectors, and instead needs to articulate its strengths as a strategically important industrial centre. The paper concludes by drawing out a number of implications for academic theory and policy development