Abstract: A network is designed based on its topology and the expected flow patterns in the network. The use of the latter can lead to efficient use of network resources and can reduce or even minimize waste. Non-interference properties of the expected flows can yield an improved or even optimal design.

Abstract: A processor-implemented method for simultaneously tracking one or more objects includes receiving, via a dynamical system with a set of sensors, a first set of unlabeled measurements from one or more objects. Each of the measurements is a function of time. A set of candidate tracks is determined for the one or more objects. Probabilities of each of the first set of unlabeled measurements being assigned to each of the set of candidate tracks are computed. A track from the set of candidate tracks is determined for each of the one or more objects based on a joint probability distribution of track attributes and the probabilistic assignment of each of the first set of unlabeled measurements to each of the set of candidate tracks.

Abstract: Techniques are presented for designing a network based on its topology and the expected flow patterns in the network. The use of the latter can lead to efficient use of network resources and can minimize waster. Non-interference property of the expected flows can yield an optimal design.

Abstract: A network is designed based on its topology and the expected flow patterns in the network. The use of the latter can lead to efficient use of network resources and can reduce or even minimize waste. Non-interference properties of the expected flows can yield an improved or even optimal design.

Abstract: A processor-implemented method for simultaneously tracking one or more objects includes receiving, via a dynamical system with a set of sensors, a first set of unlabeled measurements from one or more objects. Each of the measurements is a function of time. A set of candidate tracks is determined for the one or more objects. Probabilities of each of the first set of unlabeled measurements being assigned to each of the set of candidate tracks are computed. A track from the set of candidate tracks is determined for each of the one or more objects based on a joint probability distribution of track attributes and the probabilistic assignment of each of the first set of unlabeled measurements to each of the set of candidate tracks.

Abstract: A processor-implemented method includes approximating an optimization problem for training an artificial neural network as a nested polynomial optimization problem. The method also includes dividing the nested polynomial optimization problem into a sequence of sub-problems. The method further includes hierarchically solving the sequence of sub-problems to train the artificial neural network.

Abstract: A processor-implemented method includes receiving as input, a global polynomial optimization problem that approximates a training problem of a neural network. The method also includes relaxing the global polynomial optimization problem including polynomial constraints with multiple semi-definite programs. The method further includes solving the semi-definite programs based on a pre-defined structure and outputting a solution indicating a location of a global optimum of the optimization problem. The method includes performing inference with the neural network based on the solution.

Abstract: A processor-implemented method includes receiving, as input, an array of values characterizing a polynomial feasibility problem representing a physical system for solving a computational problem. The method also includes reducing dimensions of the polynomial feasibility problem by transforming the polynomial feasibility problem into a high-dimensional linear feasibility problem and a non-linear feasibility problem. The method further includes solving the high-dimensional linear feasibility problem to obtain a first set of interim solutions. The method includes solving the non-linear feasibility problem based on the first set of interim solutions to obtain a result of the non-linear feasibility problem. The method also includes outputting parameters characterizing the physical system, with a ground state corresponding to an output solution of the computational problem based on the result obtained from solving the non-linear feasibility problem.

Abstract: Methods, apparatus, and computer software product for making a decision based on the semantics of formal logic are provided. In an exemplary embodiment, two custom computing apparatuses are used to resolve the satisfiability of a logical formula and provide an example. In this embodiment, the two custom computing apparatuses operate in concert to explore the space of possible satisfying examples. This Abstract is provided for the sole purpose of complying with the Abstract requirement rules. This Abstract is submitted with the explicit understanding that it will not be used to interpret or to limit the scope or the meaning of the claims.