Google Inc.

Adi Avidor

Noah B Coccaro

Nir Andelman

Mario Tanev

Ivan Davtchev

Michael Roger Marty

Angela Chen

Philip Michael Wells

Peter Michael Klausler

Ariel Krasovsky

Roi Rubins

The expansion of a network by converting the network from a 2-stage folded Clos network to a 3-stage folded Clos network can be cost prohibitive. The system and methods described herein relate to a hybrid network topology. More particularly, the disclosure describes a hybrid topology having internal switches configured in a multidimensional topology configuration. Each of the internal switches are connected to the network hosts with a folded Clos topology.

Hybrid Clos-multidimensional topology for data center networks

Technology is described herein for quickly, efficiently and accurately rendering a plot of the mathematical function within an interactive graph on a web page, such as a search results web page. The technology includes determining a sampling resolution indicating the points of the mathematical function to be plotted within a display region of the plot. The sampling resolution includes a higher number of sample points in sections of the mathematical function with function values that change considerably, and includes a lower number of sample points in sections with function values that change slightly. The interactive graph provides the user with a rich interactive experience that facilitates and encourages the user's understanding of mathematical concepts and underlying principles.

Systems and methods for accurately plotting mathematical functions

Methods, systems, and apparatus, including computer program products, in which input keystroke data can be interpreted using a current mapping and a determination can be made whether the current mapping is valid based upon the characters identified by the mapping and the keystroke data. Invalid mappings can be corrected by identifying a transliteration of the characters in an alternative language.

Automatic correction of user input based on dictionary

Methods, systems, and apparatus, including computer program products, in which input keystroke data can be interpreted by a current mapping and a determination can be made whether the current mapping is valid based upon the characters identified by the mapping and the keystroke data. Invalid mappings can be corrected based upon alternative mapping of the keystroke data.

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Bat Yam, Israel

Adi Avidor