Generalised Riemann Hypothesis
Resumo: In August 1859 the young and still little known Bernhard Riemann presented a paper to the Berlin Academic titled
On the number of primes less than a given quantity
In the middle of that paper, Riemann made a guess — remark or conjecture — on the zeros of analytic function which controls the growth of the primes. Mathematics has never been the same since.
The seminar presents the captive story behind this problem and discusses how the original conjecture can be extended to all Dirichlet functions, giving rise to the Generalised Riemann Hypothesis for the non-trivial zeros of all these functions. We show that the solution of the Generalised Riemann Hypothesis can be obtained employing ideas and methods which come from statistical physics, i.e. from the stochastic world of random walks and alike.
A review on classification methods for functional data
Resumo: In this presentation, most of the classification methods for functional data are reviewed. The revision includes methods that are designed for binary classification (like those based on generalized regression methods) jointly with more flexible methods and even methods adapted from machine learning literature. The revision will pay special attention to the specific issues to multiclass problems and examples with imbalanced data.
Resumo: This talk is the sixth lecture of the VISGRAF Seminar Series "Next Media for Storytelling: Fundamentals and State-of-the-Art".
We will describe how to create digital models of virtual humans. The process starts with the definition of a complete representation of a humanoid character, including body shape, pose, and tissue dynamics. This leads to a mathematical and computational model that is simple, low-dimensional, easy to animate and fit to real data.
Dynamic quantile models of rational behaviour
Resumo: I will describe a dynamic model of rational behavior under uncertainty, in which the agent maximizes the stream of the future τ-quantile utilities, for τ ∈ (0, 1). That is, the agent has a quantile utility preference instead of the standard expected utility. Quantile preferences have useful advantages, such as dynamic consistency, monotonicity, and allows the separation between risk aversion and elasticity of intertemporal substitution. Although quantiles do not share some of the helpful properties of expectations, such as linearity and the law of iterated expectations, we are able to establish all the standard results in dynamic models. Namely, we show that the quantile preferences are dynamically consistent, the corresponding dynamic problem yields a value function, via a fixed point argument, establish its concavity and differentiability and show that the principle of optimality holds. Additionally, we derive the corresponding Euler equation, which is well suited for using well- known quantile regression methods for estimating and testing the economic model.
Statistical Indicators of Asset Price Bubbles and the ‘Everything Bubble’
Resumo: Everyone knows that asset price bubbles exist. The history of financial markets is full of them, from the 17th Century Tulip Bubble to the 21st Century ‘Credit Bubble’
The critical issue for traders, long term investors and central banks is the extent to which bubbles can be recognised before they burst.
Our approach to this, initiated at the request of a G7 Central Bank, has identified statistical markers that have had high predictive power historically both in identifying bubbles and in quantifying the level to which they will subsequently correct.
It also identifies ‘anti-bubbles’ of panic selling and corresponding correction levels.
Ten years of unprecedented monetary intervention by the world’s Central Banks has produced bubbles in assets of all sorts. The extent of the coming corrections and the timing of the bubble deflation vary greatly across regions, countries and asset class sectors.
Some have already burst producing anti-bubbles of panic selling while others are still inflating. This produces a range of opportunities and challenges for market participants and policy makers.