Abstract:
In South Africa (SA) universal access to treatment for HIV-infected individuals in need has yet to be achieved. Currently ~1 million receive treatment, but an additional 1.6 million are in need. It is being debated whether to use a universal ‘test and treat’ (T&T) strategy to try to eliminate HIV in SA; treatment reduces infectivity and hence transmission. Under a T&T strategy all HIV-infected individuals would receive treatment whether in need or not. This would require treating 5 million individuals almost immediately and providing treatment for several decades. We use a validated mathematical model to predict impact and costs of: (i) a universal T&T strategy and (ii) achieving universal access to treatment. Using modeling the WHO has predicted a universal T&T strategy in SA would eliminate HIV within a decade, and (after 40 years) cost ~$10 billion less than achieving universal access. In contrast, we predict a universal T&T strategy in SA could eliminate HIV, but take 40 years and cost ~$12 billion more than achieving universal access. We determine the difference in predictions is because the WHO has under-estimated survival time on treatment and ignored the risk of resistance. We predict, after 20 years, ~2 million individuals would need second-line regimens if a universal T&T strategy is implemented versus ~1.5 million if universal access is achieved. Costs need to be realistically estimated and multiple evaluation criteria used to compare ‘treatment as prevention’ with other prevention strategies. Before implementing a universal T&T strategy, which may not be sustainable, we recommend striving to achieve universal access to treatment as quickly as possible. We predict achieving universal access to treatment would be a very effective ‘treatment as prevention’ approach and bring the HIV epidemic in SA close to elimination, preventing ~4 million infections after 20 years and ~11 million after 40 years.

Abstract:
Integrable operators arise in random matrix theory, where they describe the asymptotic eigenvalue distribution of large self-adjoint random matrices from the generalized unitary ensembles. This paper considers discrete Tracy-Widom operators, and gives sufficient conditions for a discrete integrable operator to be the square of a Hankel matrix. Examples include the discrete Bessel kernel and kernels arising from the almost Mathieu equation and the Fourier transform of Mathieu's equation.

Abstract:
Mathematical models have been used to understand the spatial-temporal transmission dynamics of influenza. They have also been used as health policy tools to predict the effect of public health interventions on mitigating future epidemics or pandemics. The potential epidemiological impact of both behavioral and biomedical interventions has been investigated. Here we present a review of the literature of influenza modeling studies and discuss how results from these studies can provide insights into the future of the currently circulating strain of novel influenza A (H1N1). This strain was formerly known as swine flu [1].The first mathematical model that could be used to describe an influenza epidemic was developed early in the 20th century by Kermack and McKendrick [2]. This model is known as the Susceptible-Infectious-Recovered (SIR) model, and is shown as a flow diagram in Figure 1. To simulate an influenza epidemic the model is analyzed on a computer and one infected individual (I) is introduced into a closed population where everyone is susceptible (S). Each infected individual (I) transmits influenza, with probability β, to each susceptible individual (S) they encounter. The number of susceptible individuals decreases as the incidence (i.e., the number of individuals infected per unit time) increases. At a certain point the epidemic curve peaks, and subsequently declines, because infected individuals recover and cease to transmit the virus. Only a single influenza epidemic can occur in a closed population because there is no inflow of susceptible individuals. The severity of the epidemic and the initial rate of increase depend upon the value of the Basic Reproduction Number (R0). R0 is defined as the average number of new infections that one case generates, in an entirely susceptible population, during the time they are infectious. If R0 > 1 an epidemic will occur and if R0 < 1 the outbreak will die out. The value of R0 for any specific epidemic can be estimated

Abstract:
We model airborne transmission of infectious viral particles of H1N1 within a Boeing 747 using methodology from the field of quantitative microbial risk assessment.The risk of catching H1N1 will essentially be confined to passengers travelling in the same cabin as the source case. Not surprisingly, we find that the longer the flight the greater the number of infections that can be expected. We calculate that H1N1, even during long flights, poses a low to moderate within-flight transmission risk if the source case travels First Class. Specifically, 0-1 infections could occur during a 5 hour flight, 1-3 during an 11 hour flight and 2-5 during a 17 hour flight. However, within-flight transmission could be significant, particularly during long flights, if the source case travels in Economy Class. Specifically, two to five infections could occur during a 5 hour flight, 5-10 during an 11 hour flight and 7-17 during a 17 hour flight. If the aircraft is only partially loaded, under certain conditions more infections could occur in First Class than in Economy Class. During a 17 hour flight, a greater number of infections would occur in First Class than in Economy if the First Class Cabin is fully occupied, but Economy class is less than 30% full.Our results provide insights into the potential utility of air travel restrictions on controlling influenza pandemics in the winter of 2009/2010. They show travel by one infectious individual, rather than causing a single outbreak of H1N1, could cause several simultaneous outbreaks. These results imply that, during a pandemic, quarantining passengers who travel in Economy on long-haul flights could potentially be an important control strategy. Notably, our results show that quarantining passengers who travel First Class would be unlikely to be an effective control strategy.Clearly air travel, by transporting infectious individuals from the epicentre in Mexico to other geographic locations, significantly affected the rate of spread of

Abstract:
As was often the case with Vienna School art historians, Max Dvo ák (1874-1921) contributed a significant amount to the theory and practice of monument preservation. This paper considers his reactions to the precarious situation of artistic heritage during and after the first world war, which he conceived as a conflict between spiritual and material values. In writings that betray a less than objective patriotism, Italy emerges as Dvo ák’s principal antagonist, whilst critical voices in Austria – that of Karl Kraus in particular – undermined his position by calling for an end to the so-called monument cult.

Abstract:
Using Hankel operators and shift-invariant subspaces on Hilbert space, this paper develops the theory of the operators associated with soft and hard edges of eigenvalue distributions of random matrices. Tracy and Widom introduced a projection operator $W$ to describe the soft edge of the spectrum of the Gaussian unitary ensemble. The subspace $WL^2$ is simply invariant under the translation semigroup $e^{itD}$ $(t\geq 0)$ and invariant under the Schr\"odinger semigroup $e^{it(D^2+x)}$ $(t\geq 0)$; these properties characterize $WL^2$ via Beurling's theorem. The Jacobi ensemble of random matrices has positive eigenvalues which tend to accumulate near to the hard edge at zero. This paper identifies a pair of unitary groups that satisfy the von Neumann--Weyl anti-commutation relations and leave invariant certain subspaces of $L^2(0,\infty)$ which are invariant for operators with Jacobi kernels. Such Tracy--Widom operators are reproducing kernels for weighted Hardy spaces, known as Sonine spaces. Periodic solutions of Hill's equation give a new family of Tracy--Widom type operators.

Abstract:
Integrable operators arise in random matrix theory, where they describe the asymptotic eigenvalue distributions of large self-adjoint random matrices from the generalized unitary ensembles. This paper gives sufficient conditions for an integrable operator to be the square of a Hankel operator, and applies the condition to the Airy, associated Laguerre, modified Besses and Whittaker functions.

Abstract:
Suppose that $\Gamma$ is a continuous and self-adjoint Hankel operator on $L^2(0, \infty)$ and that $Lf=-(d/dx(a(x)df/dx))+b(x)f(x)$ with $a(0)=0$. If $a$ and $b$ are both quadratic, hyperbolic or trigonometric functions, and $\phi$ satisfies a suitable form of Gauss's hypergeometric equation, or the confluent hypergeometric equation, then $L\Gamma =\Gamma L$. The paper catalogues the commuting pairs $\Gamma$ and $L$, including important cases in random matrix theory. There are also results proving rapid decay of the singular numbers of Hankel integral operators with kernels that are analytic and of exponential decay in the right half plane.

Abstract:
The periodic KdV equation u_t=u_{xxx}+\beta uu_x arises from a Hamiltonian system with infinite-dimensional phase space L^2(T). Bourgain has shown that there exists a Gibbs measure \nu on balls \{\phi :\Vert\Phi\Vert^2_{L^2}\leq N\} in the phase space such that the Cauchy problem for KdV is well posed on the support of \nu, and \nu is invariant under the KdV flow. This paper shows that \nu satisfies a logarithmic Sobolev inequality. The stationary points of the Hamiltonian on spheres are found in terms of elliptic functions, and they are shown to be linearly stable. The paper also presents logarithmic Sobolev inequalities for the modified periodic KdV equation and the cubic nonlinear Schr\"odinger equation, for small values of N.

Abstract:
Tracy and Widom showed that fundamentally important kernels in random matrix theory arise from differential equations with rational coefficients. More generally, this paper considers symmetric Hamiltonian systems abd determines the properties of kernels that arise from them. The inverse spectral problem for self-adjoint Hankel operators gives a sufficient condition for a self-adjoint operator to be the Hankel operator on $L^2(0, \infty)$ from a linear system in continuous time; thus this paper expresses certain kernels as squares of Hankel operators. For a suitable linear system $(-A,B,C)$ with one dimensional input and output spaces, there exists a Hankel operator $\Gamma$ with kernel $\phi_{(x)}(s+t)=Ce^{-(2x+s+t)A}B$ such that $\det (I+(z-1)\Gamma\Gamma^\dagger)$ is the generating function of a determinantal random point field.