Abstract: A computer implemented method finds a path having a minimal expected cost through a network of nodes connected by arcs, in which the path is from a source node to a destination node, and in which a traversal time for traversing each arc is a random variable. An expected cost of traversing each possible path from the source node to the destination node is determined as an average value of a nonlinear cost function applied to each possible total travel time for traversing the path. The expected cost is weighted according to a probability of each possible total travel time. For each node in the network and for each possible time to start, a particular path from the source node to the node having a minimal expected cost and an optimal time to start on that path is determined.

Abstract: A method constructs a variable multilinear model representing a class of deformable surfaces. First, meshes of deformable surfaces are acquired. The meshes include vertices. The meshes have different identities and different expressions. The meshes can be obtained from images of human faces, where facial features, such as eyes, eyebrows, cheeks, nose, mouth and chin, form the deformable surfaces. The meshes are stored in a memory as elements of a data tensor. The data tensor is selectively flattened to matrices composed of column vectors. An imputative incremental singular value decomposition is applied to each matrix to generate a set of orthogonal bases. Then, the orthogonal bases are applied to the data tensor, via tensor multiplication, to construct a core tensor, which is the variable multilinear model representing the class of surfaces.

Abstract: A method schedules cars of an elevator system in a building. The method begins execution whenever a newly arrived passenger presses an up or down button to generate a call for service. For each car, determine a first waiting time for all existing passengers if the car is assigned to service the call, based on future states of the elevator system. For each car, determine a second waiting time of future passengers if the car is assigned to service the call, based on a landing pattern of the cars. For each car, combine the first and second waiting times to produce an adjusted waiting time, The method ends by assigning a particular car having a lowest adjusted waiting time to service the call and minimize an average waiting time of all passengers.

Abstract: A method determines poses of a sensors distributed in an environment. A signal of the environment is acquired by each sensor. Features in each signal that correspond to the features in at least one other signal are identified. Directions between the sensors and the corresponding features are determined. Nullspaces of the directions are used to construct a matrix. A nullspace eigenvector is determined of the matrix, and then the nullspace eigenvector is reconfigured to a matrix specifying the locations of the sensors.

Abstract: A method determines mappings between high-dimensional measured samples and a reduced-dimensional manifold. Samples are acquired of a physical system. The samples have a high number of dimensions. A low number of dimensions are determined for a manifold embedded in a space of the high-dimensional samples. Local charts having the dimensions of the low number of dimensions of the manifold are fitted to selected high-dimensional samples. The charts are then connected to determine a forward mapping from any high-dimensional sample to a coordinate on the manifold and a reverse mapping from any coordinate on the manifold to a corresponding point in high-dimensional sample space.

Abstract: A method generates a synthetic textured data signal by first acquiring a time-invariant input textured data signal. The input textured data signal is sampled to construct an observation matrix. The observation matrix is eigen-coding and factoring to identify a linear dynamic system modeling the input textured data signal. Then, the linear dynamic system can be run forward from an initial state using a quadratic regulator and a random noise signal to generate the synthetic textured data signal.

Abstract: A method schedules cars of an elevator system in a building. The method begins execution whenever a newly arrived passenger presses an up or down button to generate a call for service. For each car, determine a first waiting time for all existing passengers if the car is assigned to service the call, based on future states of the elevator system. For each car, determine a second waiting time of future passengers if the car is assigned to service the call, based on a landing pattern of the cars. For each car, combine the first and second waiting times to produce an adjusted waiting time, The method ends by assigning a particular car having a lowest adjusted waiting time to service the call and minimize an average waiting time of all passengers.

Abstract: A method controls the distribution of free cars in an elevator system. First, the number of free cars in the elevator system are counted whenever this number changes. At the same time, the arrival/destination rates of passengers at each of the floor is determined. The rates are used to identify up-peak and down-peak traffic patterns. The floors of the building are then assigned to zones. The number of floors in each zone is determined according to the arrival rates, and the free cars are then parked in the zones so that the expected waiting time of the next arriving passenger is minimized.

Abstract: A method and system recommends items such as products and services to consumers. Rating on items are received from consumers as a sequential stream of data. A thin singular value decomposition is updated, one rating at the time, while receiving the ratings. A prediction of a recommendations of particular items for a particular consumer is based on the updated singular value decomposition while receiving the ratings and updating the singular value decomposition. The ratings are discarded after the updating so that a size, structure, and content of an underlying preference matrix is unknown.

Abstract: A method determines mappings between high-dimensional measured samples and a reduced-dimensional manifold. Samples are acquired of a physical system. The samples have a high number of dimensions. A low number of dimensions are determined for a manifold embedded in a space of the high-dimensional samples. Local charts having the dimensions of the low number of dimensions of the manifold are fitted to selected high-dimensional samples. The charts are then connected to determine a forward mapping from any high-dimensional sample to a coordinate on the manifold and a reverse mapping from any coordinate on the manifold to a corresponding point in high-dimensional sample space.

Abstract: A method controls the distribution of free cars in an elevator system. First, the number of free cars in the elevator system are counted whenever this number changes. At the same time, the arrival/destination rates of passengers at each of the floor is determined. The rates are used to identify up-peak and down-peak traffic patterns. The floors of the building are then assigned to zones. The number of floors in each zone is determined according to the arrival rates, and the free cars are then parked in the zones so that the expected waiting time of the next arriving passenger is minimized.

Abstract: A system for learning a mapping between time-varying signals is used to drive facial animation directly from speech, without laborious voice track analysis. The system learns dynamical models of facial and vocal action from observations of a face and the facial gestures made while speaking. Instead of depending on heuristic intermediate representations such as phonemes or visemes, the system trains hidden Markov models to obtain its own optimal representation of vocal and facial action. An entropy-minimizing training technique using an entropic prior ensures that these models contain sufficient dynamical information to synthesize realistic facial motion to accompany new vocal performances. In addition, they can make optimal use of context to handle ambiguity and relatively long-lasting facial co-articulation effects.

Abstract: A method controls an elevator system including multiple elevator cars and multiple floors. A new passenger at one of the floors signals a hall call. In response to receiving the hall call, the method determines, for each car, a set of all possible future states of the elevator system. The future states depend on the current state of the system, which is defined by passengers already assigned to cars, the direction of travel, position and velocity of the cars. A cost function is evaluated to determine a cost for each set of all possible future states. Then, the car associated with the set having a least cost is assigned to service the hall call. The method is applicable to any type of traffic. It is particularly well-suited for up-peak traffic because it handles efficiently the uncertainty in passenger destinations.

Abstract: A method controls an elevator system including multiple elevator cars and multiple floors. A new passenger at one of the floors signals a hall call. In response to receiving the hall call, the method determines, for each car, a set of all possible future states of the elevator system. The future states depend on the current state of the system, which is defined by passengers already assigned to cars, the direction of travel, position and velocity of the cars. A cost function is evaluated to determine a cost for each set of all possible future states. Then, the car associated with the set having a least cost is assigned to service the hall call. The method is applicable to any type of traffic. It is particularly well-suited for up-peak traffic because it handles efficiently the uncertainty in passenger destinations.

Abstract: A method models data values acquired by measuring a natural phenomena. Samples are acquired of the natural phenomena, each sample is arranged as a vector c of the data values. Some of the data values may be missing. The vectors c are decomposed into five matrices, respectively, a subspace Upxr, singular values srxl, an encoding Vqxr, a subspace rotation U′rxr, an encoding transform V′rxr, where p indicates the number of discrete data values in each sample, q is a number of samples, and r is a rank of a decomposition of the data values. The five matrices can then be multiplied according to UU′diag(s)V′TVT to obtain a best linear approximation of the natural phenomena for any value of r less than both p and q, where T is a matrix transpose operator.

Abstract: A method generates a synthetic textured data signal by first acquiring a time-invariant input textured data signal. The input textured data signal is sampled to construct an observation matrix. The observation matrix is eigen-coding and factoring to identify a linear dynamic system modeling the input textured data signal. Then, the linear dynamic system can be run forward from an initial state using a quadratic regulator and a random noise signal to generate the synthetic textured data signal.

Abstract: A system which observes the world through a video camera and/or other sensors, automatically learns a probabilistic model of normative behavior through the use of a Hidden Markov Model, and uses that model to infer the kind of activity currently under view and detect unusual behavior. The use of hidden Markov models is made possible by entropic training of the model with an &thgr;&thgr; entropic estimator that folds structure learning into the parameter estimation process to remove parameters from the Hidden Markov Model which have little information content, thus to permit real time robust unusual behavior detection. In one embodiment, the system consists of three components: image analysis; model learning; and signal analysis. In image analysis, each frame of video is reduced to a vector of numbers which describe motion of objects in front of the camera, with a sequence of such vectors, one for each frame of video, establishing the “signal.

Abstract: Negative examples are used along with positive examples to modify a Markov Model resulting in lower error rates in classification tasks as compared with conventionally trained Markov models. The subject system is used for identifying particular traits or characteristics of sequences to permit identification of, for instance, inappropriate web page material, hand signing gestures, audio program material type, authorship of a text, with the system also being useful in speech recognition, as well as seismic, medical, and industrial monitoring.