Abstract: Methods and corresponding apparatus for segmenting an orthodontic treatment path into clinically appropriate substeps for repositioning the teeth of a patient include providing a digital finite element model of the shape and material of each of a sequence of appliances to be applied to a patient; providing a digital finite element model of the teeth and related mouth tissue of the patient; computing the actual effect of the appliances on the teeth by analyzing the finite elements models computationally; and evaluating the effect against clinical constraints. The appliances can be braces, polymeric shells, or other forms of orthodontic appliance.

Abstract: A computer-implemented method of finding a complementary set of parties to begin a negotiation for a trade in an item comprising: creating respective user models, based upon one or more external market factors, to respectively predict behavior of one or more respective users with respect to participation in a transaction in the item; evaluating current external market conditions with respect to the item; based upon respective user models and results of the current external market evaluation, respectively predicting respective current conditions in which respective users are likely to participate in transactions in the item; identifying respective users with respective complementary current conditions; notifying at least one respective user of the existence of at least one other user predicted to currently be likely to be willing to participate in a transaction in the item on conditions that are complementary to conditions on which such at least one notified user is likely to be willing to participate in a tra

Abstract: A computer-implemented method of matching orders comprising: defining a first order for a first item; defining a second order for a second item; defining at least one condition applicable to combined execution of the first and second orders; wherein the at least one condition sets forth a required proportionality measure as between the first order and the second orders; defining a prioritization of first and second orders; and submitting to an electronic marketplace at most one at a time of a new order of only an item of the first order or only an item of the second order: wherein execution of both the first order and the second order meets the conditions applicable to the execution of the first and second orders; and wherein execution of both the first order and the and second order is contingent upon the execution of the at least one order submitted over the electronic marketplace.

Abstract: A computer-implemented method of buying and selling items on an electronic marketplace comprising: providing computer readable media encoded with rules that define multiple tiers of an order for a prescribed quantity of an item; wherein a respective rule for a respective tier sets forth a respective bid or offer for the item that is applicable to the respective tier; wherein a respective rule for a respective tier identifies one or more participants eligible to receive a respective bid or offer applicable to the respective tier; and wherein respective rules define prioritization of respective tiers; providing the order over the network while implementing eligibility rules for the tiers so that respective bids or offers are accessible only to respective participants eligible to receive the respective bids or offers; receiving over the electronic marketplace one or more responsive bids or offers to one or more respective provided offers or bids; matching provided bids or offers with received offers or bids in a