Analyzing the relationship between productivity and human communication in an organizational setting

Though it is often taken as a truism that communication contributes to organizational productivity, there are surprisingly few empirical studies documenting a relationship between observable interaction and productivity. This is because comprehensive, direct observation of communication in organizational settings is notoriously difficult. In this paper, we report a method for extracting network and speech characteristics data from audio recordings of participants talking with each other in real time. We use this method to analyze communication and productivity data from seventy-nine employees working within a software engineering organization who had their speech recorded during working hours for a period of approximately 3 years. From the speech data, we infer when any two individuals are talking to each other and use this information to construct a communication graph for the organization for each week. We use the spectral and temporal characteristics of the produced speech and the structure of the resultant communication graphs to predict the productivity of the group, as measured by the number of lines of code produced. The results indicate that the most important speech and network features for predicting productivity include those that measure the number of unique people interacting within the organization, the frequency of interactions, and the topology of the communication network.

A kommunikációs gráfok és a fekete-fehér SAT probléma közti összefüggések vizsgálata

Ebben a cikkben a kommunikációs gráfok és a fekete-fehér SAT probléma közötti összefüggéseket vizsgálom. A kommunikációs gráfok olyan speciális hurokélmentes irányított gráfok, amelyeknek csúcsai logikai változók, az élei pedig a kommunikációt reprezentálják. Ilyen típusú gráfokkal lehet többek között vezeték nélküli szenzorhálózatokat is modellezni. A cikkben bemutatom a fekete-fehér SAT problémát. A fekete-fehér SAT problémák olyan logikai formulák, amelyek majdnem kielégíthetetlenek, csak két megoldásuk van, az úgynevezett fehér hozzárendelés, ahol minden változó igaz, és a fekete hozzárendelés, amelyben minden változó hamis. A fekete-fehér SAT problémák ekvivalensek az olyan konjunktív normálformában lévő logikai formulákkal, amelyekben minden klózban pozitív és negatív literálok vegyesen szerepelnek (például ilyen 3SAT klózok a -++, --+), de sem a fehér klóz, amelyben minden literál pozitív, sem a fekete klóz, amelyben minden literál negatív, nem vezethető le. Továbbá ismertetem, és hatékonyság szempontjából elemzem a kommunikációs gráfok különböző logikai modelljeit (Erős modell, Balatonboglár modell, Egyszerűsített BB modell, Gyenge modell). ----- Investigation of the relationship between communication graphs and the black and white sat ----- In this article, I examine the relationships between communication graphs and the black-andwhite SAT problem. Communication graphs are special loop-free directed graphs whose vertices are logical variables and whose edges represent communication. These types of graphs can be used to model wireless sensor networks (WSNs), among other things. I present the black-and-white SAT problem. Black-and-white SAT problems are logical formulas that are almost unsatisfiable, they have only two solutions, the so-called white assignment, where all variables are true, and the black assignment, in which all variables are false. Black-and-white SAT problems are equivalent to logical formulas in a conjunctive normal form in which positive and negative literals are mixed in each clause (e.g., such 3-SAT clauses are - ++, - +), but not the white clause in which all literals are positive, nor the black clause in which all literals are negative cannot be deduced. I also describe and analyze the different logical models of communication graphs (Strong model, Balatonboglár model, Simplified BB model, Weak model) in terms of efficiency.

Convert a Strongly Connected Directed Graph to a Black-and-White 3-SAT Problem by the Balatonboglár Model

In a previous paper we defined the black and white SAT problem which has exactly two solutions, where each variable is either true or false. We showed that black and white 2-SAT problems represent strongly connected directed graphs. We presented also the strong model of communication graphs. In this work we introduce two new models, the weak model, and the Balatonboglár model of communication graphs. A communication graph is a directed graph, where no self loops are allowed. In this work we show that the weak model of a strongly connected communication graph is a black and white SAT problem. We prove a powerful theorem, the so called transitions theorem. This theorem states that for any model which is between the strong and the weak model, we have that this model represents strongly connected communication graphs as black and white SAT problems. We show that the Balatonboglár model is between the strong and the weak model, and it generates 3-SAT problems, so the Balatonboglár model represents strongly connected communication graphs as black and white 3-SAT problems. Our motivation to study these models is the following: The strong model generates a 2-SAT problem from the input directed graph, so it does not give us a deep insight how to convert a general SAT problem into a directed graph. The weak model generates huge models, because it represents all cycles, even non-simple cycles, of the input directed graph. We need something between them to gain more experience. From the Balatonboglár model we learned that it is enough to have a subset of a clause, which represents a cycle in the weak model, to make the Balatonboglár model more compact. We still do not know how to represent a SAT problem as a directed graph, but this work gives a strong link between two prominent fields of formal methods: the SAT problem and directed graphs.

Convert a Strongly Connected Directed Graph to a Black-and-White 3-SAT Problem by the Balatonboglár Model

In a previous paper we defined the Black-and-White SAT problem which has exactly two solutions, where each variable is either true or false. We showed that Black-and-White $2$-SAT problems represent strongly connected directed graphs. We presented also the strong model of communication graphs. In this work we introduce two new models, the weak model, and the Balatonbogl\'{a}r model of communication graphs. A communication graph is a directed graph, where no self loops are allowed. In this work we show that the weak model of a strongly connected communication graph is a Black-and-White SAT problem. We prove a powerful theorem, the so called Transitions Theorem. This theorem states that for any model which is between the strong and the weak model, we have that this model represents strongly connected communication graphs as Blask-and-White SAT problems. We show that the Balatonbogl\'{a}r model is between the strong and the weak model, and it generates $3$-SAT problems, so the Balatonbogl\'{a}r model represents strongly connected communication graphs as Black-and-White $3$-SAT problems. Our motivation to study these models is the following: The strong model generates a $2$-SAT problem from the input directed graph, so it does not give us a deep insight how to convert a general SAT problem into a directed graph. The weak model generates huge models, because it represents all cycles, even non-simple cycles, of the input directed graph. We need something between them to gain more experience. From the Balatonbogl\'{a}r model we learned that it is enough to have a subset of a clause, which represents a cycle in the weak model, to make the Balatonbogl\'{a}r model more compact. We still do not know how to represent a SAT problem as a directed graph, but this work gives a strong link between two prominent fields of formal methods: SAT problem and directed graphs.