A method for differentiator-based compression of digital data includes (a) multiplying a tap-weight vector by an original data vector to generate a predicted signal, the original data vector comprising N sequential samples of an original signal, N being an integer greater than or equal to one, (b) using a subtraction module, subtracting the predicted signal from a sample of the original signal to obtain an error signal, (c) using a quantization module, quantizing the error signal to obtain a quantized error signal, and (d) updating the tap-weight vector according to changing statistical properties of the original signal.

A method for approximating a mathematical function defined over a range includes initially dividing at least part of the range into a set of segments. For at least a subset of the segments, the mathematical function is approximated within each segment by a respective approximation polynomial. A series of one or more segment-merging iterations is performed, a given iteration including: selecting adjacent segments as candidates for merging; approximating the mathematical function by a candidate approximation polynomial, over at least a merged segment formed by merging the adjacent segments; and, if approximation of the mathematical function meets a specified condition, updating the set of segments by (i) replacing the adjacent segments with the merged segment and (ii) replacing the approximation polynomials of the adjacent segments with the candidate approximation polynomial.

A method for approximating a mathematical function defined over a range includes initially dividing at least part of the range into a set of segments. For at least a subset of the segments, the mathematical function is approximated within each segment by a respective approximation polynomial. A series of one or more segment-merging iterations is performed, a given iteration including: selecting adjacent segments as candidates for merging; approximating the mathematical function by a candidate approximation polynomial, over at least a merged segment formed by merging the adjacent segments; and, if approximation of the mathematical function meets a specified condition, updating the set of segments by (i) replacing the adjacent segments with the merged segment and (ii) replacing the approximation polynomials of the adjacent segments with the candidate approximation polynomial.

A Heisenberg scaler reduces noise in quantum metrology and includes: a stimulus source that provides physical stimuli; a physical system including quantum sensors that receive a first and second physical stimuli; produces a measured action parameter; receives an perturbation pulse; and produces modal amplitude; an estimation machine that: receives the measured action parameter and produces a zeroth-order value from the measured action parameter; a gradient analyzer that: receives the measured action parameter and produces the measured action parameter and a gradient; the sensor interrogation unit that: receives the modal amplitude; receives the gradient and the measured action parameter; produces the perturbation pulse; and produces a first-order value from the modal amplitude, the gradient, and the measured action parameter; a Heisenberg determination machine that: receives the zeroth-order value; receives the first-order value; and produces a physical scalar from the zeroth-order value and the first-order value.

A Heisenberg scaler reduces noise in quantum metrology and includes: a stimulus source that provides physical stimuli; a physical system including quantum sensors that receive a first and second physical stimuli; produces a measured action parameter; receives an perturbation pulse; and produces modal amplitude; an estimation machine that: receives the measured action parameter and produces a zeroth-order value from the measured action parameter; a gradient analyzer that: receives the measured action parameter and produces the measured action parameter and a gradient; the sensor interrogation unit that: receives the modal amplitude; receives the gradient and the measured action parameter; produces the perturbation pulse; and produces a first-order value from the modal amplitude, the gradient, and the measured action parameter; a Heisenberg determination machine that: receives the zeroth-order value; receives the first-order value; and produces a physical scalar from the zeroth-order value and the first-order value.

A method includes identifying, using at least one processor, a first point associated with an uncertain location of an object in a space and a polynomial curve associated with an uncertain location of a feature in the space. The method also includes determining, using the at least one processor, a probabilistic proximity of the object and the feature. The probabilistic proximity is determined by identifying a second point on the polynomial curve, transforming an uncertainty associated with the polynomial curve into an uncertainty associated with the second point, and identifying the probabilistic proximity of the object and the feature using the first and second points and the uncertainty associated with the second point.

Methods, systems, and devices for automated feature selection and model generation are described. A device (e.g., a server, user device, database, etc.) may perform model generation for an underlying dataset and a specified outcome variable. The device may determine relevance measurements (e.g., stump R-squared values) for a set of identified features of the dataset and can reduce the set of features based on these relevance measurements (e.g., according to a double-box procedure). Using this reduced set of features, the device may perform a least absolute shrinkage and selection operator (LASSO) regression procedure to sort the features. The device may then determine a set of nested linear models—where each successive model of the set includes an additional feature of the sorted features—and may select a “best” linear model for model generation based on this set of models and a model quality criterion (e.g., an Akaike information criterion (AIC)).

Methods, systems, and devices for automated feature selection and model generation are described. A device (e.g., a server, user device, database, etc.) may perform model generation for an underlying dataset and a specified outcome variable. The device may determine relevance measurements (e.g., stump R-squared values) for a set of identified features of the dataset and can reduce the set of features based on these relevance measurements (e.g., according to a double-box procedure). Using this reduced set of features, the device may perform a least absolute shrinkage and selection operator (LASSO) regression procedure to sort the features. The device may then determine a set of nested linear models—where each successive model of the set includes an additional feature of the sorted features—and may select a “best” linear model for model generation based on this set of models and a model quality criterion (e.g., an Akaike information criterion (AIC)).

A spectrum y includes a waveform-of-interest component and a baseline component serving as a wide-band component. An optimum solution of a signal model x is determined according to a first condition to fit a corresponding portion S.sub.IFx of a baseline model Fx with respect to a representative portion y.sub.I of the baseline component, and a second condition to minimize an Lp norm (wherein p≤1) of the signal model x. An estimated baseline component determined from the optimum solution of the signal model x is subtracted from the spectrum y.

A spectrum y includes a waveform-of-interest component and a baseline component serving as a wide-band component. An optimum solution of a signal model x is determined according to a first condition to fit a corresponding portion S.sub.IFx of a baseline model Fx with respect to a representative portion y.sub.I of the baseline component, and a second condition to minimize an Lp norm (wherein p≤1) of the signal model x. An estimated baseline component determined from the optimum solution of the signal model x is subtracted from the spectrum y.