### Lecture Notes on Spin Geometry. (arXiv:1911.09766v1 [math.DG])

We review the Atiyah-Singer Index theorem and some applications. Only basic knowledge of differential geometry and Lie groups is required.

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# Category Archives: Science

### Lecture Notes on Spin Geometry. (arXiv:1911.09766v1 [math.DG])

### The artefact of the Natural Resources Curse. (arXiv:1911.09681v1 [econ.GN])

### Investigating bankruptcy prediction models in the presence of extreme class imbalance and multiple stages of economy. (arXiv:1911.09858v1 [cs.LG])

### Estimation of the Parameters of Symmetric Stable ARMA and ARMA-GARCH Models. (arXiv:1911.09985v1 [stat.CO])

### Collectivised Pension Investment with Homogeneous Epstein-Zin Preferences. (arXiv:1911.10047v1 [q-fin.PM])

### Towards Quantification of Explainability in Explainable Artificial Intelligence Methods. (arXiv:1911.10104v1 [cs.AI])

### Phase mapping for cardiac unipolar electrograms with neural network instead of phase transformation. (arXiv:1911.09731v1 [eess.SP])

### Continuous and discrete abstractions for planning, applied to ship docking. (arXiv:1911.09773v1 [eess.SY])

### Speculative Trading, Prospect Theory and Transaction Costs. (arXiv:1911.10106v1 [q-fin.MF])

### Estimating Time-Varying Applied Current in the Hodgkin-Huxley Model. (arXiv:1911.09756v1 [q-bio.QM])

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We review the Atiyah-Singer Index theorem and some applications. Only basic knowledge of differential geometry and Lie groups is required.

This paper reexamines the validity of the natural resource curse hypothesis, using the database of mineral exporting countries. Our findings are as follows: (i) Resource-rich countries (RRCs) do not necessarily exhibit poor political, economic and social performance; (ii) RRCs that perform poorly have a low diversified exports portfolio; (iii) In contrast, RRCs with a low…

In the area of credit risk analytics, current Bankruptcy Prediction Models (BPMs) struggle with (a) the availability of comprehensive and real-world data sets and (b) the presence of extreme class imbalance in the data (i.e., very few samples for the minority class) that degrades the performance of the prediction model. Moreover, little research has compared…

In this article, we first propose the modified Hannan-Rissanen Method for estimating the parameters of the autoregressive moving average (ARMA) process with symmetric stable noise and symmetric stable generalized autoregressive conditional heteroskedastic (GARCH) noise. Next, we propose the modified empirical characteristic function method for the estimation of GARCH parameters with symmetric stable noise. Further, we…

In a collectivised pension fund, investors agree that any money remaining in the fund when they die can be shared among the survivors. We compute analytically the optimal investment-consumption strategy for a fund of $n$ identical investors with homogeneous Epstein–Zin preferences, investing in the Black–Scholes market in continuous time but consuming in discrete time. Our…

Artificial Intelligence (AI) has become an integral part of domains such as security, finance, healthcare, medicine, and criminal justice. Explaining the decisions of AI systems in human terms is a key challenge–due to the high complexity of the model, as well as the potential implications on human interests, rights, and lives . While Explainable AI…

Digital signal processing can be performed in two major ways. The first is a pipeline of signal transformations, and the second is machine learning approaches that require tagged data for training. This paper studies the third way. We generate a training dataset for a neural network in a series of numerical experiments and uses the…

We propose a hierarchical control framework for the synthesis of correct-by-construction controllers for nonlinear control-affine systems with respect to reach-avoid-stay specifications. We first create a low-dimensional continuous abstraction of the system and use Sum-of-Squares (SOS) programming to obtain a low-level controller ensuring a bounded error between the two models. We then create a discrete abstraction…

A speculative agent with Prospect Theory preference chooses the optimal time to purchase and then to sell an indivisible risky asset as to maximize the expected utility of the round-trip profit net of transaction costs. The optimization problem is formulated as a sequential optimal stopping problem and we provide a complete characterization of the solution.…

The classic Hodgkin-Huxley model is widely used for understanding the electrophysiological dynamics of a single neuron. While applying a constant current to the system results in a single voltage spike, it is possible to produce more interesting dynamics by applying time-varying currents, which may not be experimentally measurable. The aim of this work is to…

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