Abstract: A display system for sensing a finger of a user applied to the display system includes a display panel; a sensor for sensing the finger; a sensing light source configured to emit a first light having a first wavelength W1; and a reflective polarizer disposed between the display panel and the sensor. For a substantially normally incident light, an optical transmittance of the reflective polarizer versus wavelength for a first polarization state has a band edge such that for a first wavelength range extending from a smaller wavelength L1 to a greater wavelength L2 and including W1, where 30 nm?L2?L1?50 nm and L1 is greater than and within about 20 nm of a wavelength L3 corresponding to an optical transmittance of about 50% along the band edge, the optical transmittance has an average of greater than about 75%.

Abstract: Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for determining causal models for controlling environments.

Abstract: A system and methods for multivariant learning and optimization repeatedly generate self-organized experimental units (SOEUs) based on the one or more assumptions for a randomized multivariate comparison of process decisions to be provided to users of a system. The SOEUs are injected into the system to generate quantified inferences about the process decisions. Responsive to injecting the SOEUs, at least one confidence interval is identified within the quantified inferences, and the SOEUs are iteratively modified based on the at least one confidence interval to identify at least one causal interaction of the process decisions within the system. The causal interaction can be used for testing, diagnosis, and optimization of the system performance.

Abstract: An optical film includes a plurality of first layers disposed on a plurality of polymeric second layers. Each of at least 30% of the first layers includes at least 30% by weight of an inorganic material. For a substantially normally incident light, a blue wavelength range extending from about 420 nm to about 480 nm, a green wavelength range extending from about 490 nm to about 560 nm, and a red wavelength range extending from about 590 nm to about 670 nm, the optical film and the plurality of second layers have respective average optical reflectances Rof(b) 10 and R2(b) in the blue wavelength range, Rof(g) and R2(g) in the green wavelength range, and Rof(r) and R2(r) in the red wavelength range, where 0?Rof(b)?R2(b)?25%; Rof(g)?R2(g)>30%; and each of Rof(r) and R2(r) is greater than about 60% and |Rof(r)?R2(r)| is less than about 20%.

Abstract: An optical system including one or more optical lenses, at least one retarder layer, a reflective polarizer, and a partial reflector is provided. The at least one retarder layer may include first and second retarder layers having different wavelength dispersion curves. The at least one retarder layer may include a first retarder layer having a non-uniform fast axis orientation and/or a non-uniform retardance.

Abstract: A method of optimizing a plurality of control signals used in operating a vehicle is described. The operation has a plurality of associated measurable parameters. The method includes: for each control signal, selecting a plurality of potential optimum values from a predetermined set; operating the vehicle in at least a first sequence of operation iterations, where for each pair of sequential first and second operation iterations in the first sequence of operation iterations, the potential optimum value of one control signal in the first operation iteration is replaced in the second operation iteration with a next potential optimum value of the control signal, while the potential optimum values of the remaining control signals are maintained; for each operation iteration, measuring each parameter in the plurality of measurable parameters; and generating confidence intervals for the control signals to determine causal relationships between the control signals and the measurable parameters.

Abstract: Methods for active data center management by injecting randomized controlled signals in the operational controls of the cooling infrastructure of the data center and receiving response signals corresponding with the injected signals. The injected signals are used to adjust the operational controls of the cooling infrastructure, and the response signals relate to the operational conditions in the data center. Based upon the response signals along with independent and external variables, the randomized signals are continually injected into the cooling infrastructure and fine-tuned based upon the response signals. Optimum or improved parameters for controlling the cooling infrastructure of the data center are determined based upon the signal injections and corresponding responses.

Abstract: A display system for sensing a finger of a user applied to the display system includes a display panel; a sensor for sensing the finger; a sensing light source configured to emit a first light having a first wavelength W1; and a reflective polarizer disposed between the display panel and the sensor. For a substantially normally incident light, an optical transmittance of the reflective polarizer versus wavelength for a first polarization state has a band edge such that for a first wavelength range extending from a smaller wavelength L1 to a greater wavelength L2 and including W1, where 30 nm?L2?L1?50 nm and L1 is greater than and within about 20 nm of a wavelength L3 corresponding to an optical transmittance of about 50% along the band edge, the optical transmittance has an average of greater than about 75%.

Abstract: An article includes an optical filter that comprises a wavelength selective reflective layer and at least one wavelength selective absorbing layer. The optical filter has visible transmittance between 400 nm-700 nm of less than about 30% and near infrared transmittance at 830 nm-900 nm greater than about 30%.

Abstract: Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for determining causal models for controlling environments.

Abstract: A system and methods for multivariant learning and optimization repeatedly generate self-organized experimental units (SOEUs) based on the one or more assumptions for a randomized multivariate comparison of process decisions to be provided to users of a system. The SOEUs are injected into the system to generate quantified inferences about the process decisions. Responsive to injecting the SOEUs, at least one confidence interval is identified within the quantified inferences, and the SOEUs are iteratively modified based on the at least one confidence interval to identify at least one causal interaction of the process decisions within the system. The causal interaction can be used for testing, diagnosis, and optimization of the system performance.

Abstract: An optical stack for reflecting and transmitting light in a predetermined wavelength range includes stacked first and second optical films, the predetermined wavelength range defining a first wavelength range and a remaining wavelength range. For normally incident light and for each wavelength in a first wavelength range, the first optical film substantially reflects light having a first polarization state, and substantially transmits light having a second polarization state. For each of the first and second polarization states, for wavelengths in the first wavelength range, the second optical film has a maximum optical transmittance Tmax for light incident at a first incident angle, and an optical transmittance Tmax/2 for light incident at a second incident angle, where the second incident angle is greater than the first incident angle by less than about 50 degrees. For wavelengths in the remaining wavelength range, the second optical film reflects at least 80% of light.

Abstract: An optical film includes a plurality of first layers disposed on a plurality of polymeric second layers. Each of at least 30% of the first layers includes at least 30% by weight of an inorganic material. For a substantially normally incident light, a blue wavelength range extending from about 420 mn to about 480 m, a green wavelength range extending from about 490 nm to about 560 in, and a red wavelength range extending from about 590 nm to about 670 nm, the optical film and the plurality of second layers have respective average optical reflectances Rof(b) and R2(b) in the blue wavelength range, Rof(g) and R2(g) in the green wavelength range, and Rof(r) and R2(r) in the red wavelength range, where 0?Rof(b)?R2(b)?25%; Rof(g)?R2(g)>30%; and each of Rof(r) and R2(r) is greater than about 60% and |Rof(r)?R2(r)| is less than about 20%.

Abstract: Methods for active data center management by injecting randomized controlled signals in the operational controls of the cooling infrastructure of the data center and receiving response signals corresponding with the injected signals. The injected signals are used to adjust the operational controls of the cooling infrastructure, and the response signals relate to the operational conditions in the data center. Based upon the response signals along with independent and external variables, the randomized signals are continually injected into the cooling infrastructure and fine-tuned based upon the response signals. Optimum or improved parameters for controlling the cooling infrastructure of the data center are determined based upon the signal injections and corresponding responses.

Abstract: An optical film includes a plurality of first layers disposed on a plurality of polymeric second layers. Each of at least 30% of the first layers includes at least 30% by weight of an inorganic material. For a substantially normally incident light, a blue wavelength range extending from about 420 nm to about 480 nm, a green wavelength range extending from about 490 nm to about 560 nm, and a red wavelength range extending from about 590 nm to about 670 nm, the optical film and the plurality of second layers have respective average optical reflectances Rof(b) and R2(b) in the blue wavelength range, Rof(g) and R2(g) in the green wavelength range, and Rof(r) and R2(r) in the red wavelength range, where 0?Rof(b)?R2(b)?25%; Rof(g)?R2(g)>30%; and each of Rof(r) and R2(r) is greater than about 60% and |Rof(r)?R2(r)| is less than about 20%.

Abstract: An optical system including one or more optical lenses, at least one retarder layer, a reflective polarizer, and a partial reflector is provided. The at least one retarder layer may include first and second retarder layers having different wavelength dispersion curves. The at least one retarder layer may include a first retarder layer having a non-uniform fast axis orientation and/or a non-uniform retardance.

Abstract: An article includes an optical filter that comprises a wavelength selective reflective layer and at least one wavelength selective absorbing layer. The optical filter has visible transmittance between 400 nm-700 nm of less than about 30% and near infrared transmittance at 830 nm-900 nm greater than about 30%.

Abstract: Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for optimizing a process of manufacturing a product. In one aspect, the method comprises repeatedly performing the following: i) selecting a configuration of input settings for manufacturing a product, based on a causal model that measures causal relationships between input settings and a measure of a quality of the product; ii) determining the measure of the quality of the product manufactured using the configuration of input settings; and iii) adjusting, based on the measure of the quality of the product manufactured using the configuration of input settings, the causal model.

Abstract: An optical stack for reflecting and transmitting light in a predetermined wavelength range includes stacked first and second optical films, the predetermined wavelength range defining a first wavelength range and a remaining wavelength range. For normally incident light and for each wavelength in a first wavelength range, the first optical film substantially reflects light having a first polarization state, and substantially transmits light having a second polarization state. For each of the first and second polarization states, for wavelengths in the first wavelength range, the second optical film has a maximum optical transmittance Tmax for light incident at a first incident angle, and an optical transmittance Tmax/2 for light incident at a second incident angle, where the second incident angle is greater than the first incident angle by less than about 50 degrees. For wavelengths in the remaining wavelength range, the second optical film reflects at least 80% of light.

Abstract: A multilayer partial mirror includes a plurality of alternating first a second polymeric layers numbering at least 50 in total, disposed between, and integrally formed with, opposing first and second polymeric skin layers. For a visible wavelength range extending from about 420 nm to about 680 nm and an incident light propagating in an incident plane that includes a x-direction, and for an s-polarized incident light, the multilayer partial mirror has an average reflectance Rs1 for a first incident angle of less than about 10 degrees, and an average reflectance Rs2 for a second incident angle of greater than about 45 degrees, and for a p-polarized incident light, the multilayer partial mirror has an average reflectance Rp1 for the first incident angle, and an average reflectance Rp2 for the second incident angle. Each of Rs2/Rs1 and Rp2/Rp1 is greater than about 1.15.