Institutions do not die Networks & Communication

What is a network?

How are the local and global properties related to each other? Local, immediate properties Global, long-time, large-scale properties Geometry Topology

Transportation metrics on networks & databases X 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

Transportation (Ricci) curvature

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

Can we see the first-passage times? (Mean) First passage time Tax assessment value of land ($) Manhattan, 2005 Federal Hall SoHo East Village Bowery East Harlem 10 100 1,000 5,000 10,000 (Mean) first-passage times in the city graph of Manhattan

Why are mosques located close to railways? NEUBECKUM: Social isolation vs. structural isolation

Organizations: why do we think that the majority is always right? We like to be a part of a majority, as ”if many believe so, it is so” – The drive towards a majority is that of an insurance policy against the risks with which the daily life is fraught. The position of the majority is always perceived as fair.

Social time is unfolding through the switching between communication and withdrawing ”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.” Melucci, A., ”Inner Time and Social Time in a World of Uncertainty”, Time Society 7, 179 (1998).

Communication Patterns in Organizations We have presented the first study integrating the analysis of temporal patterns of interaction, interaction preferences and the local vs. global structure of communication in two organizations over a period of three weeks. The data suggest that there are three regimes of interaction arising from the organizational context of our observations: casual, spontaneous (or deliberate) and institutional interaction. We show that institutions never die, as once interrupted communication can be resumed anytime

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 four 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.

The radio-frequency identification sensors reported on occasions of physical proximity

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.

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 (“sticky”), time spent in communications has to be invested prudently

Intervals between sequent interactions

Duration of intervals between sequent communications (min) Probability The distribution of intervals between the sequent communication events is remarkably skewed, indicating a significant proportion of the abnormally long periods of inactivity. Duration of intervals between sequent communications (min)

Duration of intervals between sequent communications (min) Casual Probability The normal distribution can be interpreted as an average outcome of many statistically independent processes that determine the majority of casual interactions characterized by the very short intervals between them lasting not longer than 4 mins. Duration of intervals between sequent communications (min)

Duration of intervals between sequent communications (min) Casual The most probable interval between sequent communications lasts 2 min. Probability Although time is a scarce resource, short time intervals go largely unmanaged in organizations. Duration of intervals between sequent communications (min)

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

Duration of intervals between sequent communications (min) Casual Deliberate Uniformly random Fixed during the day (spontaneous) Probability The simplest time management strategy is to postpone or avoid unimportant or unwanted meetings Duration of intervals between sequent communications (min)

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)

Duration of intervals between sequent communications (min) Casual Mandatory institutional communications may include urgent, exigent contacts made in emergency, as well as some common rites and rituals that serve important functions for all team members. Deliberate Uniformly random Fixed during the day (spontaneous) Probability Mandatory (institutional) A logic of institutional interaction prevails, where top-down, almost mandatory interaction occurs Duration of intervals between sequent communications (min)

Duration dependent communication graphs 1 2 3 4 5 6 Communication durations (min)

Duration dependent communication graphs In order to analyze how interaction propensities and the duration of interaction affect each other, we use mutual information as a statistical measure of pairwise interaction propensities. If during the observation period A and B participated in meetings independently, 1 2 3 4 5 6 Communication durations (min)

Duration dependent communication graphs The degree of communication selectivity: How much knowing the fact of that X is communicating during time t would reduce uncertainty about that Y is communicating 1 2 3 4 5 6 Communication durations (min)

Duration dependent communication graphs The degree of communication selectivity: How much knowing the fact of that X is communicating during time t would reduce uncertainty about that Y is communicating 1 2 3 4 5 6 Communication durations (min) The performed analysis of mutual information shows that the degree of selectivity in both companies monotonously increases with the interaction duration, until their maximum values are attained; People are essentially selective in choosing partners for communications lasting between 10 and 20 min; For particularly long interactions, perhaps involving many group members at once, the values of mutual information is particularly small.

Duration dependent communication graphs The degree of communication selectivity: How much knowing the fact of that X is communicating during time t would reduce uncertainty about that Y is communicating 1 2 3 4 5 6 Communication durations (min) The functional structure of organization matters essentially for the communications of short duration (1-5 min): departmental structure evokes more selectivity in short communications

Time-dependent interaction graphs (Networks) The main objective of analysis is to understand how the ”local”, individual interaction propensities described by the connectivity of subjects as nodes of a communication graph determine the ”global”, connectedness property of the entire communication process described by the ensemble of communication graphs for all communication durations.

Time-dependent interaction graphs (Networks) In order to address this problem in relation to all communication graphs, let us consider a model of simple random walks, a statistical metaphor of message transmission in a working team. We suppose that a message (requiring t time units to be transmitted) is passed on by each subject X to another one – Y , selected at random among all available companions accordingly to the connection probability T(t)XY determined by the communication graph of communication duration t.

Interaction synchronization: could they all speak altogether? Then the minimal amount of information required to record a single random transition of a message in the entire communication graph correspondent to the duration t is defined by the entropy rate of random walks

Interaction synchronization: could they all speak altogether?

Interaction synchronization: could they all speak altogether? Excess entropy/ complexity/ past-future mutual information:

Interaction synchronization: could they all speak altogether?

Interaction synchronization: could they all speak altogether? The functional structure of organization matters essentially for individuals of low connectivity (subordinates): departmental structure evokes more schedules/organization shaping interactions between subordinates

Interaction synchronization: could they all speak altogether? Individuals communicating with 10-12 people are evolved in the maximum number of communicating groups; Individuals communicating with more than 10-12 people organize meetings themselves

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

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

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”

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

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!

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

Conclusion 2: Structure affects selectivity employees → functions employees → start-ups more schedules/ structure

Conclusion 3: A team exists when connectedness exceeds connectivity “Positive Ricci curvature”: Directed intentional messages traverse the team faster than rumors