Moment-angle complexes, monomial ideals, and Massey products

Associated to every finite simplicial complex K there is a "moment-angle" finite CW-complex, Z_K; if K is a triangulation of a sphere, Z_K is a smooth, compact manifold. Building on work of Buchstaber, Panov, and Baskakov, we study the cohomology ring, the homotopy groups, and the triple Massey products of a moment-angle complex, relating these topological invariants to the algebraic combinatorics of the underlying simplicial complex. Applications to the study of non-formal manifolds and subspace arrangements are given.Comment: 30 pages. Published versio

Local systems on complements of arrangements of smooth, complex algebraic hypersurfaces

We consider smooth, complex quasi-projective varieties $U$ which admit a compactification with a boundary which is an arrangement of smooth algebraic hypersurfaces. If the hypersurfaces intersect locally like hyperplanes, and the relative interiors of the hypersurfaces are Stein manifolds, we prove that the cohomology of certain local systems on $U$ vanishes. As an application, we show that complements of linear, toric, and elliptic arrangements are both duality and abelian duality spaces.Comment: 14 pages. Some corrections, more details, and updates to reference

Abelian duality and propagation of resonance

We explore the relationship between a certain "abelian duality" property of spaces and the propagation properties of their cohomology jump loci. To that end, we develop the analogy between abelian duality spaces and those spaces which possess what we call the "EPY property." The same underlying homological algebra allows us to deduce the propagation of jump loci: in the former case, characteristic varieties propagate, and in the latter, the resonance varieties. We apply the general theory to arrangements of linear and elliptic hyperplanes, as well as toric complexes, right-angled Artin groups, and Bestvina-Brady groups. Our approach brings to the fore the relevance of the Cohen-Macaulay condition in this combinatorial context.Comment: 30 page

Purification of Tannery Effluent by electrolytic corrosion of aluminium

Tannery Effluent is noxious because tanning process chemicals are preservatives, including chromium, and the pH is high. Electrolytic processing is feasible because the high salt content gives a high electrical conductivity. While research on the subject dates back to early in the 20th Century, commercialization has not occurred, perhaps due to excessive power consumption. Other researchers have produced promising results with rendering plant effluent (Tetrault 2003). During 2005 a specialised proprietary prototype with a novel anode design was trialed extensively at a Tannery site in New Zealand and produced good results during continuous inline operation despite wide variation in the inflow. Greater than 90% removal of chromium from solution with similar reductions in turbidity were achieved at lower operating cost, residual aluminum and total aluminum addition than by dosing with usual commercial aluminum based flocculants. Results from the field trials are shown and discussed

Opening the Black Box of Financial AI with CLEAR-Trade: A CLass-Enhanced Attentive Response Approach for Explaining and Visualizing Deep Learning-Driven Stock Market Prediction

Deep learning has been shown to outperform traditional machine learning algorithms across a wide range of problem domains. However, current deep learning algorithms have been criticized as uninterpretable "black-boxes" which cannot explain their decision making processes. This is a major shortcoming that prevents the widespread application of deep learning to domains with regulatory processes such as finance. As such, industries such as finance have to rely on traditional models like decision trees that are much more interpretable but less effective than deep learning for complex problems. In this paper, we propose CLEAR-Trade, a novel financial AI visualization framework for deep learning-driven stock market prediction that mitigates the interpretability issue of deep learning methods. In particular, CLEAR-Trade provides a effective way to visualize and explain decisions made by deep stock market prediction models. We show the efficacy of CLEAR-Trade in enhancing the interpretability of stock market prediction by conducting experiments based on S&P 500 stock index prediction. The results demonstrate that CLEAR-Trade can provide significant insight into the decision-making process of deep learning-driven financial models, particularly for regulatory processes, thus improving their potential uptake in the financial industry