Abstract: A method is provided that comprises collecting financial data points and normalizing the data points into a time series. The time series is merged into aggregates according to sliding windows that comprise different time periods and a sliding step increment. A periodic change in an increasing and convex transformation is computed for each aggregate, and multi-dimensional time-delayed coordinate embedding is applied to each aggregate. The sliding windows are applied to the time-delayed aggregates, and time series of variances and point clouds are derived within each sliding window. Persistence homologies and time series norms are computed for the point clouds, and the time series norms are correlated with the time series of variances. A warning of an impending financial crisis is output if the correlation of the time series norms with the time series of variances exceeds a predefined threshold.

Abstract: A method, apparatus, system, and computer program code for determining a financial risk to a financial security. A computer system obtains historical time series of the annual counts of tropical cyclones globally and of the global mean sea surface temperature. Based on a time series of annual changes in cumulative annual counts of major tropical cyclones, the computer system trains a statistical model to make projections of the annual cumulative counts of major tropical cyclones globally. The computer system uses these projections to determine the physical risk to fixed assets. Based the physical risk to the fixed asset, the computer system updates an assumption of a financial model. The computer system analyzes the financial risk of the financial security based on the financial model and the assumption that was updated.

Abstract: A method is provided that comprises collecting financial data points and normalizing the data points into a time series. The time series is merged into aggregates according to sliding windows that comprise different time periods and a sliding step increment. A periodic change in an increasing and convex transformation is computed for each aggregate, and multi-dimensional time-delayed coordinate embedding is applied to each aggregate. The sliding windows are applied to the time-delayed aggregates, and time series of variances and point clouds are derived within each sliding window. Persistence homologies and time series norms are computed for the point clouds, and the time series norms are correlated with the time series of variances. A warning of an impending financial crisis is output if the correlation of the time series norms with the time series of variances exceeds a predefined threshold.

Abstract: A method for performing assisted knowledge discovery includes receiving a dataset. Each of a plurality of analytical techniques is applied to the received data set to generate a plurality of corresponding analytical results. A composite validation metric is applied to each of the plurality of analytical results. The composite validation metric is a single scoring/ranking function that is created from a plurality of different scoring/ranking functions. The plurality of analytical results is presented to a user arranged in accordance with the results of the applying the composite validation metric to each of the plurality of analytical results. A selection from the user from among the plurality of analytical results is recorded. The user's selection is used to modify the composite validation metric such that the analytical techniques responsible for generating the selected analytical result is scored/ranked more highly.

Abstract: A method for performing assisted knowledge discovery includes receiving a dataset. Each of a plurality of analytical techniques is applied to the received data set to generate a plurality of corresponding analytical results. A composite validation metric is applied to each of the plurality of analytical results. The composite validation metric is a single scoring/ranking function that is created from a plurality of different scoring/ranking functions. The plurality of analytical results is presented to a user arranged in accordance with the results of the applying the composite validation metric to each of the plurality of analytical results. A selection from the user from among the plurality of analytical results is recorded. The user's selection is used to modify the composite validation metric such that the analytical techniques responsible for generating the selected analytical result is scored/ranked more highly.

Abstract: A system to determine a direction of arrival of each of a plurality of constituent signals of a superimposed wave includes a tripole radio antenna, a sampling unit, a frequency determining unit, an amplitude and phase determining unit, and a direction determining unit. The sampling unit is configured to periodically sample an output of the tripole radio antenna to generate at least two samples. The frequency determining unit is configured to determine frequencies for each dimension of the constituent signals by performing a unitary matrix pencil method on the at least two samples. The amplitude and phase determining unit is configured to determine x, y, z amplitudes and x, y, z phases for each constituent signal using the determined frequencies. The direction determining unit is configured to determine a direction of arrival for each of the constituent signals from the determined frequencies, amplitudes, and phases.

Abstract: A system to determine a direction of arrival of each of a plurality of constituent signals of a superimposed wave includes a tripole radio antenna, a sampling unit, a frequency determining unit, an amplitude and phase determining unit, and a direction determining unit. The sampling unit is configured to periodically sample an output of the tripole radio antenna to generate at least two samples. The frequency determining unit is configured to determine frequencies for each dimension of the constituent signals by performing a unitary matrix pencil method on the at least two samples. The amplitude and phase determining unit is configured to determine x, y, z amplitudes and x, y, z phases for each constituent signal using the determined frequencies. The direction determining unit is configured to determine a direction of arrival for each of the constituent signals from the determined frequencies, amplitudes, and phases.