Abstract: A quaternion deep neural network (QTDNN) includes a plurality of modular hidden layers, each comprising a set of QT computation sublayers, including a quaternion (QT) general matrix multiplication sublayer, a QT non-linear activations sublayer, and a QT sampling sublayer arranged along a forward signal propagation path. Each QT computation sublayer of the set has a plurality of QT computation engines. In each modular hidden layer, a steering sublayer precedes each of the QT computation sublayers along the forward signal propagation path. The steering sublayer directs a forward-propagating quaternion-valued signal to a selected at least one QT computation engine of a next QT computation subsequent sublayer.

Abstract: A machine-learning system includes a quaternion (QT) computation engine. Input data to the QT computation engine includes quaternion values, each comprising a real component and three imaginary components, represented as a set of real-valued tensors. A single quaternion value is represented as a 1-dimensional real-valued tensor having four real-valued components, wherein a first real-valued component represents the real component of the single quaternion value, and wherein a second, a third, and a fourth real-valued component each respectively represents one of the imaginary components. A quaternion-valued vector having a size N is represented as a 2-dimensional real-valued tensor comprising N 1-dimensional real-valued tensors. A quaternion-valued matrix having N×M dimensions is represented as a 3-dimensional real-valued tensor comprising M 2-dimensional real-valued tensors comprising N 1-dimensional real-valued tensors.

Abstract: A deep neural network (DNN) includes hidden layers arranged along a forward propagation path between an input layer and an output layer. The input layer accepts training data comprising quaternion values, outputs a quaternion-valued signal along the forward path to at least one of the hidden layers. At least some of the hidden layers include quaternion layers to execute consistent quaternion (QT) forward operations based on one or more variable parameters. A loss function engine produces a loss function representing an error between the DNN result and an expected result. QT backpropagation-based training operations include computing layer-wise QT partial derivatives, consistent with an orthogonal basis of quaternion space, of the loss function with respect to a QT conjugate of the one or more variable parameters and of respective inputs to the quaternion layers.

Abstract: A quaternion deep neural network (QTDNN) includes a plurality of modular hidden layers, each comprising a set of QT computation sublayers, including a quaternion (QT) general matrix multiplication sublayer, a QT non-linear activations sublayer, and a QT sampling sublayer arranged along a forward signal propagation path. Each QT computation sublayer of the set has a plurality of QT computation engines. In each modular hidden layer, a steering sublayer precedes each of the QT computation sublayers along the forward signal propagation path. The steering sublayer directs a forward-propagating quaternion-valued signal to a selected at least one QT computation engine of a next QT computation subsequent sublayer.

Abstract: A deep neural network (DNN) includes hidden layers arranged along a forward propagation path between an input layer and an output layer. The input layer accepts training data comprising quaternion values, outputs a quaternion-valued signal along the forward path to at least one of the hidden layers. At least some of the hidden layers include quaternion layers to execute consistent quaternion (QT) forward operations based on one or more variable parameters. A loss function engine produces a loss function representing an error between the DNN result and an expected result. QT backpropagation-based training operations include computing layer-wise QT partial derivatives, consistent with an orthogonal basis of quaternion space, of the loss function with respect to a QT conjugate of the one or more variable parameters and of respective inputs to the quaternion layers.

Abstract: A method of emotive autography includes calculating a plurality of classifiers associated with an individual user. Each of the classifiers indicates a preference of the user for an associated type of multimedia content. Multimedia data is received including video data, audio data and/or image data. The multimedia data is divided into semantically similar segments. A respective preference score is assigned to each of the semantically similar segments by use of the classifiers. The semantically similar segments are arranged in a sequential order dependent upon the preference scores. An emotive autograph is presented based on the semantically similar segments arranged in the sequential order.

Abstract: A machine-learning system includes a quaternion (QT) computation engine. Input data to the QT computation engine includes quaternion values, each comprising a real component and three imaginary components, represented as a set of real-valued tensors. A single quaternion value is represented as a 1-dimensional real-valued tensor having four real-valued components, wherein a first real-valued component represents the real component of the single quaternion value, and wherein a second, a third, and a fourth real-valued component each respectively represents one of the imaginary components. A quaternion-valued vector having a size N is represented as a 2-dimensional real-valued tensor comprising N 1-dimensional real-valued tensors. A quaternion-valued matrix having N×M dimensions is represented as a 3-dimensional real-valued tensor comprising M 2-dimensional real-valued tensors comprising N 1-dimensional real-valued tensors.

Abstract: A method of emotive autography includes calculating a plurality of classifiers associated with an individual user. Each of the classifiers indicates a preference of the user for an associated type of multimedia content. Multimedia data is received including video data, audio data and/or image data. The multimedia data is divided into semantically similar segments. A respective preference score is assigned to each of the semantically similar segments by use of the classifiers. The semantically similar segments are arranged in a sequential order dependent upon the preference scores. An emotive autograph is presented based on the semantically similar segments arranged in the sequential order.

Abstract: The invention provides compounds of the invention pharmaceutical compositions comprising a compound of the invention, processes for preparing compounds of the invention, intermediates useful for preparing compounds of the invention, and therapeutic methods for treating cancer and other topoisomerase mediated conditions.

Abstract: A method and apparatus for optimizing long-term revenues in online auctions of distinguishable units of an item. For example, the item might be a specific keyword in sponsored search where the distinguishable units could be different slots for putting ads. The system can estimate parameters such as relevance and value by using a notion of fairness and can optimize the revenue by effecting the users' incentives and by improving the bidding language. In general, the method and the system can also be used for equivalent offline auctions.

Abstract: The invention provides compounds of the invention pharmaceutical compositions comprising a compound of the invention, processes for preparing compounds of the invention, intermediates useful for preparing compounds of the invention, and therapeutic methods for treating cancer and other topoisomerase mediated conditions.

Abstract: The invention provides compounds of formula I: wherein: R1-R5, “a” and X have any of the meanings defined in the specification and their pharmaceutically acceptable salts. The invention also provides pharmaceutical compositions comprising a compound of formula I, processes for preparing compounds of formula I, intermediates useful for preparing compounds of formula I, and therapeutic methods for treating cancer using compounds of formula I.

Abstract: The invention provides compounds of formula I: wherein R1–R9, W, and X have any of the meanings defined in the specification and their pharmaceutically acceptable salts. The invention also provides pharmaceutical compositions comprising a compound of formula I, processes for preparing compounds of formula I, intermediates useful for preparing compounds of formula I, and therapeutic methods for treating cancer using compounds of formula I.

Abstract: The invention provides compounds of formula I: 1

Abstract: The invention provides compounds of formula I: 1