Abstract: A method includes computing a diffusion vector starting with a seed, querying nodes for connections, reweighting diffusion vector based on the degrees, sorting nodes based upon magnitude in the reweighted diffusion vector which is obtained through wave relaxation solution of a time-dependent initial value problem, detecting a community through a sweep over the nodes according to their rank, and selecting a prefix that minimizes or maximizes an objective function.

Abstract: A method to determine data uncertainty is provided. The method receives a high dimensional data input and a corresponding data output. The method trains a variational autoencoder (VAE) with the high dimensional data input to learn a low dimensional latent space representation of the high dimensional data input. An encoder part of the VAE outputs a set of distributions of the high dimensional dataset in a latent space. The method samples new data samples in the latent space using the set of distributions outputs from the encoder part of the VAE. The method learns a polynomial chaos expansion to map the new data samples in the latent space to the corresponding data output to learn the set of distributions and their relation to perform estimation with high-dimensional dataset under uncertainty such as missing values by estimating the values using the set of distributions.

Abstract: Techniques for generating and managing, including simulating and training, deep tensor neural networks are presented. A deep tensor neural network comprises a graph of nodes connected via weighted edges. A network management component (NMC) extracts features from tensor-formatted input data based on tensor-formatted parameters. NMC evolves tensor-formatted input data based on a defined tensor-tensor layer evolution rule, the network generating output data based on evolution of the tensor-formatted input data. The network is activated by non-linear activation functions, wherein the weighted edges and non-linear activation functions operate, based on tensor-tensor functions, to evolve tensor-formatted input data. NMC trains the network based on tensor-formatted training data, comparing output training data output from the network to simulated output data, based on a defined loss function, to determine an update.

Abstract: The present disclosure relates to a dual-density insole (or sock liner) for a shoe. According to aspects set forth herein, the insole includes a carrier with two cavities. Two inserts with a density or hardness level that is different from that of the carrier are positioned in the cavities for increased performance. The disclosed insole further exhibits a molded geometry marked with shaped protrusions.

Abstract: A method for making a cleated plate member for an article of footwear is described. The method includes a number of steps where various molds are used to form different components of the cleated plate member. A collar receptacle is formed using a first molding process. A cleat member is formed from a non-compatible material with a fastener of the cleat member associated with the collar receptacle using another molding process to form a combined cleat assembly. The combined cleat assembly is placed into corresponding receptacles in a mold used to form the cleated plate member. The cleated plate member is formed using another molding process that embeds the collar receptacle into the body of the cleated plate member. The completed cleated plate member includes releasably attached cleat members.

Abstract: A method for making a cleated plate member for an article of footwear is described. The method includes a number of steps where various molds are used to form different components of the cleated plate member. A collar receptacle is formed using a first molding process. A cleat member is formed from a non-compatible material with a fastener of the cleat member associated with the collar receptacle using another molding process to form a combined cleat assembly. The combined cleat assembly is placed into corresponding receptacles in a mold used to form the cleated plate member. The cleated plate member is formed using another molding process that embeds the collar receptacle into the body of the cleated plate member. The completed cleated plate member includes releasably attached cleat members.

Abstract: A method for making a cleated plate member for an article of footwear is described. The method includes a number of steps where various molds are used to form different components of the cleated plate member. A collar receptacle is formed using a first molding process. A cleat member is formed from a non-compatible material with a fastener of the cleat member associated with the collar receptacle using another molding process to form a combined cleat assembly. The combined cleat assembly is placed into corresponding receptacles in a mold used to form the cleated plate member. The cleated plate member is formed using another molding process that embeds the collar receptacle into the body of the cleated plate member. The completed cleated plate member includes releasably attached cleat members.

Abstract: A method of forming a sole assembly of an article of footwear that includes an interior space that receives a foot of a wearer is disclosed. The article of footwear also includes an exterior surface. The method includes providing a first portion of the sole assembly. The first portion includes a first surface that at least partially defines the interior space. The first portion also includes a first chamber surface that opposes the first surface. Moreover, the method includes providing a second portion of the sole assembly. The second portion includes a second surface that at least partially defines the exterior surface of the article of footwear. The second portion also includes a second chamber surface that opposes the second surface. The method further includes operably securing the first portion to the second portion such that the first chamber surface and the second chamber surface cooperate to at least partially define a substantially sealed chamber within the sole assembly.

Abstract: A method of forming a sole assembly of an article of footwear including an interior space and an exterior surface includes providing a first portion of the sole assembly. The first portion includes a first surface that at least partially defines the interior space and a first chamber surface that opposes the first surface. The first portion is made from a first material. The method also includes providing a second portion of the sole assembly that includes a second surface that at least partially defines the exterior surface of the article of footwear and a second chamber surface that opposes the second surface. The second portion is made from a second material that is different from the first material. The method additionally includes operably securing the first and second portions such that the first chamber surface and the second chamber surface cooperate to at least partially define a chamber.

Abstract: The present disclosure relates to a dual-density insole (or sock liner) for a shoe. According to aspects set forth herein, the insole includes a carrier with two cavities. Two inserts with a density or hardness level that is different from that of the carrier are positioned in the cavities for increased performance. The disclosed insole further exhibits a molded geometry marked with shaped protrusions.

Abstract: A dual-density insole (or sock liner) for a shoe is disclosed. The insole includes a carrier with two cavities. Two inserts with a density or hardness level that is different from that of the carrier are positioned in the cavities for increased performance. The disclosed insole further exhibits a molded geometry marked with shaped protrusions.

Abstract: A method of forming a sole assembly of an article of footwear that includes an interior space that receives a foot of a wearer is disclosed. The article of footwear also includes an exterior surface. The method includes providing a first portion of the sole assembly. The first portion includes a first surface that at least partially defines the interior space. The first portion also includes a first chamber surface that opposes the first surface. Moreover, the method includes providing a second portion of the sole assembly. The second portion includes a second surface that at least partially defines the exterior surface of the article of footwear. The second portion also includes a second chamber surface that opposes the second surface. The method further includes operably securing the first portion to the second portion such that the first chamber surface and the second chamber surface cooperate to at least partially define a substantially sealed chamber within the sole assembly.

Abstract: A method of forming a sole assembly of an article of footwear that includes an interior space that receives a foot of a wearer is disclosed. The article of footwear also includes an exterior surface. The method includes providing a first portion of the sole assembly. The first portion includes a first surface that at least partially defines the interior space. The first portion also includes a first chamber surface that opposes the first surface. Moreover, the method includes providing a second portion of the sole assembly. The second portion includes a second surface that at least partially defines the exterior surface of the article of footwear. The second portion also includes a second chamber surface that opposes the second surface. The method further includes operably securing the first portion to the second portion such that the first chamber surface and the second chamber surface cooperate to at least partially define a substantially sealed chamber within the sole assembly.

Abstract: A method for making a cleated plate member for an article of footwear is described. The method includes a number of steps where various molds are used to form different components of the cleated plate member. A collar receptacle is formed using a first molding process. A cleat member is formed from a non-compatible material with a fastener of the cleat member associated with the collar receptacle using another molding process to form a combined cleat assembly. The combined cleat assembly is placed into corresponding receptacles in a mold used to form the cleated plate member. The cleated plate member is formed using another molding process that embeds the collar receptacle into the body of the cleated plate member. The completed cleated plate member includes releasably attached cleat members.

Abstract: A method for making a cleated plate member for an article of footwear is described. The method includes a number of steps where various molds are used to form different components of the cleated plate member. A collar receptacle is formed using a first molding process. A cleat member is formed from a non-compatible material with a fastener of the cleat member associated with the collar receptacle using another molding process to form a combined cleat assembly. The combined cleat assembly is placed into corresponding receptacles in a mold used to form the cleated plate member. The cleated plate member is formed using another molding process that embeds the collar receptacle into the body of the cleated plate member. The completed cleated plate member includes releasably attached cleat members.

Abstract: The present disclosure relates to a dual-density insole (or sock liner) for a shoe. According to aspects set forth herein, the insole includes a carrier with two cavities. Two inserts with a density or hardness level that is different from that of the carrier are positioned in the cavities for increased performance. The disclosed insole further exhibits a molded geometry marked with shaped protrusions.

Abstract: A method for making a cleated plate member for an article of footwear is described. The method includes a number of steps where various molds are used to form different components of the cleated plate member. A collar receptacle is formed using a first molding process. A cleat member is formed from a non-compatible material with a fastener of the cleat member associated with the collar receptacle using another molding process to form a combined cleat assembly. The combined cleat assembly is placed into corresponding receptacles in a mold used to form the cleated plate member. The cleated plate member is formed using another molding process that embeds the collar receptacle into the body of the cleated plate member. The completed cleated plate member includes releasably attached cleat members.