## Time-Weighted Average Price (TWAP): A New Approach

**The Time-Weighted Average Price (TWAP) is defined
as the average price of a security over the course of a specified period of time. The TWAP is traditionally calculated by
first averaging the open, high, low, and close prices for each bar and then calculating the average of those averages as time
progresses. The problem is that there is often a difference between the open, high, low, and close prices and where a security
actually spends the most time in any given bar. Therefore, the traditional TWAP may at times be incorrect, especially in the
short run. For instance, how accurate would the TWAP calculation be if the trading range for a given bar is wide, but the
security spent most of the time in the upper portion of the bar? In that case, the traditional TWAP value would be lower than
it should be. The technical indicator introduced in this paper reveals a new approach to the TWAP calculation intended to
improve its accuracy. **LINK

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**Firefly inspired Heartbeat Synchronization: in a paper entitled Fireﬂy-inspired
Heartbeat ****Synchronization in Overlay Networks by the University
of Bologna - Trento Italy along with the University of Szeged, Hungary: “Heartbeat synchronization strives to
have nodes in a distributed system generate periodic, local “heartbeat” events approximately at the same
time. Many useful distributed protocols rely on the existence of such heartbeats for driving their cycle- based execution..
The heartbeat synchronization protocol for overlay networks is inspired by mathematical models of ﬂash synchronization
in certain species of ﬁre ﬂies. Nodes send ﬂash messages to their neighbors when a local heartbeat
triggers. Fireflies adjust the phase of their next heartbeat based on incoming ﬂash messages using an algorithm
inspired by mathematical models of ﬁre-ﬂy synchronization. Heartbeat synchronization strives to have
nodes in a distributed system generate periodic, local “heartbeat” events approximately at the same time.
It differs from classical clock synchronization in that nodes are not interested in counting cycles and agreeing
on a ID of a current cycle. There is no requirement regarding the length of a cycle with respect to real time as long
as a length is bounded and all nodes agree on it eventually. The goal is to guarantee that all nodes start and end
their cycles at the same time, with an error that is at least one, but preferably more, orders of magnitude smaller
than a chosen cycle length.**

**Firefly inspired stochastic
harmonization combined with cycle Heart Beacon Cycle: Fireflies adjust the phase of their next heartbeat based on
incoming ﬂash messages using an algorithm inspired by mathematical models of ﬁreﬂy synchronization.
There is no requirement regarding the length of a cycle with respect to real time as long as a length is bounded and
all nodes agree on it eventually. What we are interested in guaranteeing is that all nodes start and end their cycles
at the same time, with an error that is at least one, but preferably more, orders of magnitude smaller than a chosen
cycle length. Firefly heartbeat synchronization reduces uncertainty in stochastic networks" -- especially when
firefly's near consensus (statistical mean) that is matched to nearest Heartbeat Beacon micro-cycle schedule news-casted
over wide areas.**