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Share-Based Compensation (Tables)
9 Months Ended
Sep. 30, 2023
Share-Based Payment Arrangement [Abstract]  
Disclosure of Share-Based Compensation Arrangements by Share-Based Payment Award
The following table presents the effects of share-based compensation expense in the Condensed Consolidated Statements of Operations during the periods presented (in thousands):
Three months ended September 30,Nine months ended September 30,
2023202220232022
Cost of revenues$76 $63 $246 $289 
Sales and marketing323 772 2,285 2,447 
Research, development, and engineering840 567 2,581 2,048 
General and administrative5,535 4,984 19,281 16,022 
Total share-based compensation expense$6,774 $6,386 $24,393 $20,806 
Market-Based Restricted Stock Awards, Valuation Assumptions
The weighted-average fair values of market-based restricted stock units granted have been estimated utilizing the following assumptions:
September 30, 2023September 30, 2022
Underlying stock price at valuation date$77.80 $99.32 
Expected volatility32.0 %36.7 %
Risk-free interest rate4.1 %1.8 %
Restricted Stock and Restricted Stock Unit Award Activity
Restricted stock award activity for the nine months ended September 30, 2023 is set forth below:
SharesWeighted-Average
Grant-Date
Fair Value
Nonvested at January 1, 2023311,281 $52.73 
Vested(51,154)$72.40 
Canceled(322)$77.75 
Nonvested at September 30, 2023
259,805 $48.82 
  
Restricted stock unit activity for the nine months ended September 30, 2023 is set forth below:
Number of
Shares

Aggregate
Intrinsic
Value
Outstanding at January 1, 2023464,354 
Granted464,311 
Vested(73,701)
Canceled(36,858)
Outstanding at September 30, 2023818,106 $52,105,171 
Vested and expected to vest at September 30, 2023749,680 $47,747,103 
Schedule of Employee Stock Purchase Plan, Valuation Assumptions
The shared-based compensation expense related to the Purchase Plan has been estimated utilizing the following weighted-average assumptions:
September 30, 2023September 30, 2022
Risk-free interest rate
4.7%1.5%
Expected term (in years)
0.50.5
Expected volatility
35.8%41.6%