Abstract: Supervised operator learning is an emerging machine learning paradigm with applications to modeling the evolution maps of spatio-temporal dynamical systems and approximating general black-box relationships between functional data. We propose a novel operator learning method, LOCA (Learning Operators with Coupled Attention), motivated from the attention mechanism. The input functions are mapped to a finite set of features which are then averaged with attention weights that depend on the output query locations. By coupling these attention weights together with an integral transform, LOCA is able to explicitly learn correlations in the target output functions, enabling us to approximate nonlinear operators even when the number of output function measurements is very small.

Abstract: A method for analyzing an object includes modeling the object with a differential equation, such as a linear partial differential equation (PDE), and sampling data associated with the differential equation. The method uses a probability distribution device to obtain the solution to the differential equation. The method eliminates use of discretization of the differential equation.

Abstract: A method for analyzing an object includes modeling the object with a differential equation, such as a linear partial differential equation (PDE), and sampling data associated with the differential equation. The method uses a probability distribution device to obtain the solution to the differential equation. The method eliminates use of discretization of the differential equation.

Abstract: Method of improving the tribological and erosive wear resistance of yankee dryer drums including coating the drum with an iron alloy containing from about 20 to about 47 weight per cent chromium, about 2.5 to about 6.5 weight per cent boron, about 1.7 to about 2.7 weight per cent silicon, and less than about 8 weight per cent molybdenum. The coated yankee dryer drum is long wearing based on the hardness of the coating and smooth wearing as the coating has a consistent composition through its depth at the outset and over time.

Abstract: Aluminizing process guide roll are made longer wearing without surface defects by applying a multilayer coating on the roll surface including a first coating layer of MCrAlY metal of a first, lower porosity effective against corrosion, and a second coating layer of refractory oxide of a second higher porosity effective against surface defect failure generated thermal expansion failure of the layer.

Abstract: A multi-user Time Division Multiplex (TDM) system includes a plurality of stations and at least one erasure node located between groups of the stations. When a station reads the destination identification bits of a received time slot and determines that it is the destination for that slot, it sets the status of a slot-read bit, which follows the destination identification bits, to indicate that the slot has been read. When an erasure node detects a set slot-read bit it erases all or part of the associated slot, thereby enabling the reuse of that slot by subsequent stations. An interface apparatus, which enables the TDM system to connect the other TDM systems, filters intra-system communications from inter-system communications using the slot-read bit. When the interface apparatus detects a set slot-read bit it knows that the slot has been read and, therefore, is an intra-system communication which should be blocked or discarded.

Abstract: A multi-user Time Division Multiplex (TDM) system includes a plurality of stations and at least one erasure node located between groups of the stations. When a station reads the destination identification bits of a received time slot and determines that it is the destination for that slot, it sets the status of a slot-read bit, which follows the destination identification bits, to indicate that the slot has been read. When an erasure node detects a set slot-read bit it erases all or part of the associated slot, thereby enabling the reuse of that slot by subsequent stations. An interface apparatus, which enables the TDM system to connect the other TDM systems, filters intra-system communications from inter-system communications using the slot-read bit. When the interface apparatus detects a set slot-read bit it knows that the slot has been read and, therefore, is an intra-system communication which should be blocked or discarded.