In the first part of the talk I will review Bob Fernholz' theory of functionally generated portfolios. In the second part I will discuss questions related to the existence of short-term arbitrage opportunities.
This is joint work with Bob Fernholz and Ioannis Karatzas
Modelling catalytic kinetics is indispensable for the design of reactors and chemical processes. However, developing accurate and computationally efficient kinetic models remains challenging. Empirical kinetic models incorporate assumptions about rate-limiting steps and may thus not be applicable to operating regimes far from those where they were derived. Detailed microkinetic modelling approaches overcome this issue by accounting for all elementary steps of a reaction mechanism. However, the majority of such kinetic models employ mean-field approximations and are formulated as ordinary differential equations, which neglect spatial correlations. On the other hand, kinetic Monte Carlo (KMC) approaches provide a discrete-space continuous-time stochastic formulation that enables a detailed treatment of spatial correlations in the adlayer (resulting for instance from adsorbate-adsorbate lateral interactions), but at a significant computation expense.1,2
Motivated by these challenges, we discuss the necessity of KMC descriptions that incorporate detailed models of lateral interactions. Focusing on a titration experiment involving the oxidation of pre-adsorbed O by CO gas on Pd(111), we discuss experimental findings that show first order kinetics at low temperature (190 K) and half order kinetics at high temperature (320 K), the latter previously attributed to island formation.3 We perform KMC simulations whereby coverage effects on reaction barriers are captured by cluster expansion Hamiltonians and Brønsted-Evans-Polanyi (BEP) relations.4 By quantifying the effect of adlayer structure versus coverage effects on the observed kinetics, we rationalise the experimentally observed kinetics. We show that coverage effects lead to the half order kinetics at 320 K, rather than O-island formation as previously thought.5,6
Subsequently, we discuss our ongoing work in the development of approximations that capture such coverage effects but are much more computationally efficient than KMC, making it possible to use such models in reactor design. We focus on a model for NO oxidation incorporating first nearest neighbour lateral interactions and construct a sequence of approximations of progressively higher accuracy, starting from the mean-field treatment and continuing with a sequence of Bethe-Peierls models with increasing cluster sizes. By comparing the turnover frequencies of these models with those obtained from KMC simulation, we show that the mean-field predictions deviate by several orders of magnitude from the KMC results, whereas the Bethe-Peierls models exhibit progressively higher accuracy as the size of the explicitly treated cluster increases. While more computationally intensive than mean-field, these models still enable significant computational savings compared to a KMC simulation, thereby paving the road for employing them in multiscale modelling frameworks.
References
1 M. Stamatakis and D. G. Vlachos, ACS Catal. 2 (12), 2648 (2012).
2 M. Stamatakis, J Phys-Condens Mat 27 (1), 013001 (2015).
3 I. Nakai, H. Kondoh, T. Shimada, A. Resta, J. N. Andersen, and T. Ohta, J. Chem. Phys. 124 (22), 224712 (2006).
4 J. Nielsen, M. d’Avezac, J. Hetherington, and M. Stamatakis, J. Chem. Phys. 139 (22), 224706 (2013).
5 M. Stamatakis and S. Piccinin, ACS Catal. 6 (3), 2105 (2016).
6 S. Piccinin and M. Stamatakis, ACS Catal. 4, 2143 (2014).
Feedforward layers are integral step in processing and transmitting sensory information across different regions the brain. Yet experiments reveal the difficulty of stable propagation through layers without causing neurons to synchronize their activity. We study the limits of stable propagation in a discrete feedforward model of binary neurons. By analyzing the spectral properties of a mean-field Markov chain model, we show when such information transmission persists. Addition of inhibitory neurons and synaptic noise increases the robustness of asynchronous rate transmission. We close with an example of feedforward processing in the input layer to cerebellum.
In numerical analysis the design and analysis of computational methods is often based on, and closely linked to, a well-posedness result for the underlying continuous problem. In particular the continuous dependence of the continuous model is inherited by the computational method when such an approach is used. In this talk our aim is to design a stabilised finite element method that can exploit continuous dependence of the underlying physical problem without making use of a standard well-posedness result such as Lax-Milgram's Lemma or The Babuska-Brezzi theorem. This is of particular interest for inverse problems or data assimilation problems which may not enter the framework of the above mentioned well-posedness results, but can nevertheless satisfy some weak continuous dependence properties. First we will discuss non-coercive elliptic and hyperbolic equations where the discrete problem can be ill-posed even for well posed continuous problems and then we will discuss the linear elliptic Cauchy problem as an example of an ill-posed problem where there are continuous dependence results available that are suitable for the framework that we propose.
Subgroup separability is a group-theoretic property that has important implications for geometry and topology, because it allows us to lift immersions to embeddings in a finite sheeted covering space. I will describe how this works in the case of graphs, and go on to motivate the construction of special cube complexes as an attempt to generalise the technique to higher dimensions.
Erdos, Faudree, Gould, Gyarfas, Rousseau and Schelp, conjectured that
whenever the edges of a complete graph are coloured using three colours
there always exists a set of at most three vertices which have at least
two-thirds of their neighbours in one of the colours. We will describe a
proof of this conjecture. This is joint work with Rahil Baber
For Logic Seminar: Note change of time and place.
We propose a model where an algorithmic trader takes a view on the distribution of prices at a future date and then decides how to trade in the direction of her predictions using the optimal mix of market and limit orders. As time goes by, the trader learns from changes in prices and updates her predictions to tweak her strategy. Compared to a trader that cannot learn from market dynamics or form a view of the market, the algorithmic trader's profits are higher and more certain. Even though the trader executes a strategy based on a directional view, the sources of profits are both from making the spread as well as capital appreciation of inventories. Higher volatility of prices considerably impairs the trader's ability to learn from price innovations, but this adverse effect can be circumvented by learning from a collection of assets that co-move.
The talk is on impacts, penetrations and lift-offs involving bodies and fluids, with applications that range from aircraft and ship safety and our tiny everyday scales of splashing and washing, up to surface movements on Mars. Several studies over recent years have addressed different aspects of air-water effects and fluid-body interplay theoretically. Nonlinear interactions and evolutions are key here and these are to be considered in the presentation. Connections with experiments will also be described.