1. Ca’ Foscari University of Venice;
17-18 December 2015, IOS (Center for Innovation, Organization and Strategy),
Ca’ Foscari University of Venice;
1st IOS Conference

2. To find a rhythm of entry and exit...
”We can only preserve our unity by being able to ’open and close’, to participate in and withdraw from the flow of messages. It therefore becomes vital to find a rhythm of entry and exit that allows each of us to communicate meaningfully without nullifying our inner being. Yet in this alternation between noise and silence we need an inner wholeness that must survive through change. To live the discontinuity and variability of time and space we must find a way to unify experience other than by our ’rational’ self.”
Melucci, A., ”Inner Time and Social Time in a World of Uncertainty”, Time Society 7, 179 (1998).

3. Data collection was carried out in June and July 2010
H-art
H-farm
71 assigned to multiple projects.
~ 75 employees and hosted 9 start-ups
employees → functions
employees → start-ups
We analyze face-to-face interactions in two organizations over a period of three weeks. Data on interactions among ca 140 individuals have been collected through a wearable sensors study carried on two start-up organizations in the North-East of Italy.

4. Smaller groups communicate more frequently than larger groups; brief communications are much more common than longer ones.
employees → start-ups
The impression of a power law can result from the superposition of different behaviors.

5. A simple probability model describing the communication behavior < 20 min
-- each interruption of a communication is a statistically independent event;
-- the probability to interrupt an ongoing communication act pT > 0 depends only on the total
expected duration of communication T.
The distribution of communication durations averaged over the observation period is a weighted sum of different exponentials featured by various durations of speaking.
20 min
20 min; difficult to interrupt
Every communication is potentially an extremely time consuming action, time spent in communications has to be invested prudently

6. Intervals between sequent interactions

7. Duration of intervals between sequent communications (min)
Probability
Duration of intervals between sequent communications (min)

8. Duration of intervals between sequent communications (min)
Casual
Probability
Duration of intervals between sequent communications (min)

9. Duration of intervals between sequent communications (min)
Casual
Deliberate
Uniformly random
Fixed during the day
(spontaneous)
Probability
Duration of intervals between sequent communications (min)

10. Duration of intervals between sequent communications (min)
Casual
Deliberate
Uniformly random
Fixed during the day
(spontaneous)
Probability
Mandatory
(institutional)
Duration of intervals between sequent communications (min)

11. Duration dependent communication graphs
Communication durations (min)

12. Duration dependent communication graphs
The degree of communication selectivity:
Communication durations (min)

13. Interaction synchronization: could they all speak altogether?

14. Interaction synchronization: could they all speak altogether?

15. A geometric method for data analysis & representationX Y L
Monge – Kantorovich transport problem
-- the transportation plan L;
-- X , Y probability measures on
a compact space;
K → the transportation metric
-- the (squared) norm of a distribution;
-- the Green function (propagator)
-- the stochastic automorphism /
a diffusion generator;
-- a scalar product of probability measures;
METRIC (60 sec):
The Monge – Kantorovich transportation problem
searches for the optimal transportation plan L over all Borel measures
with marginal measures X and Y on the compact space.
The Kantorovich transportation metric
induces the weak topology on the simplex of probability measures.
However, no explicit formula is known for that in N - dimensions.
We have shown that if the compact space has a structure A
-- being a graph, a network, or a relational database --
the set of transport geodesics can be defined by a diffusion process through the structure.
And the Green function of diffusion process
defines the “path-integral” transportation metric on the data manifold,
in which all possible paths are taken into account,
although some paths are more preferable then others.
The Green function of diffusion process defines the transportation metric on the data manifold

16. A geometric method for data analysis & representation
V.A. Mozart, Eine Kleine Nachtmusik ,G
= ( )
First-passage time ( )T2
Recurrence time ( ) =1/p , p = p G 1
“ “ =
C, “do”:
G major is based on the pitches
G, A, B, C, D, E, and F♯.
Ricci curvature:
ANTICIPATION NEIGHBORHOOD (60 sec):
Anticipation of the future events is possible in the data geometric setting
within the intelligible data neighborhoods of positive Ricci curvature
with respect to the transportation metric.
The one-step transition matrix for a musical composition
defines the transportation metric
on the simplex of probability measures corresponding to the musical notes.
The first-passage time to the note by the random walk
from a note randomly chosen over the musical score
is the norm of the musical note with respect to the transportation metric.
The recurrence time of the walk to any note is approximately equal to
the size of musical octave.
The notes the first-passage times to which are shorter than
recurrence time comprise
the basic pitches of the tonality scale of the musical composition.
If one mistakes a note while performing a musical piece,
we catch it immediately as the pitch would step out the tonality scale of composition.
Anticipation is possible within the data neighborhood of positive Ricci curvature

17. How is the individual communication propensity (a local property) related to global properties?

18. How is the individual communication propensity (a local property) related to global properties?

19. Connectedness exceeds connectivity
How is the individual communication propensity (a local property) related to global properties?
A local property (connectivity)
A global property (connectedness)
Connectedness exceeds connectivity
a “positive Ricci curvature”

20. Conclusion 1: Multilevel communication protocol
Rule of thumb for belonging:
Intervals between communications that last twice as long, occur twice as rare;
→ Simply respect the group discipline
Sample size
Institutions do not die!
Institutional & Spontaneous communications can be resumed at any time!

21. Conclusion 2: Structure affects selectivity
employees → functions
employees → start-ups

22. Conclusion 3: A team exists when connectedness exceeds connectivity
Directed intentional messages traverse the team faster than rumors