These are notes that I used myself to lecture from. A modified version was handed to the students, which is reflected in various changes of fonts and marginal hacks in this version. These things were not in their version. In particular, certain things were omitted and they were given space to write things that either were in my notes or on which I expanded in class. The first part of the course...

Variational principle for probabilistic learning Yet another justification More simplification of updates for mean-field family Examples Dirichlet Process Mixture On minimization of divergence measures Energy minimization justifications Variational learning with exponential family Mean parametrization and marginal polytopes Convex dualities The log-partition function and conjugate duality Belie...

These are reading notes of She eld's Conformal welding of random surfaces: SLE and the quantum gravity zipper [11]. In that paper, She eld constructs a stationary process (ht, ηt)t∈R whose marginal law is given by a Gaussian free eld and an independent SLE curve. This process evolves with a deterministic cutting and unzipping dynamics: the curve is progressively unzipped, and the eld varies acc...

Mounting of databases have become web accessible through Hyper Text Mark up Language based explore interfaces. When people browse for particular purpose the search results are obtained relevant to data or irrelevant to data. To get the desired data people need to search again from the obtained search results. To overcome this problem, we introduce an automatic marginal note method that initiall...

These notes provide an introduction to modeling with copulas. Copulas are the mechanism which allows us to isolate the dependency structure in a multivariate distribution. In particular, we can construct any multivariate distribution by separately specifying the marginal distributions and the copula. Copula modeling has played an important role in finance in recent years and has been a source o...

LTEX’s output routine is designed with fixed layout and functionality in mind. This is even true for the current state of the new output routine work by the LTEX3 team. When typesetting things like critical editions, one may have to cater for multiple levels of marginal notes (like verse/line numbers and additional cross references), multiple and nested levels of footnotes, footnotes also carry...

to evaluate the influence of core thickness and fabrication stages on the marginal accuracy of ips e.max press crowns.twenty ips e.max press crowns, 1.5mm thick, were fabricated on metal dies. the crowns had two different core thicknesses, 0.8mm for group a and 1mm for group b, ten for each group. marginal gap was measured after each stage of core fabrication, veneering and glaze firing. the sp...