Graph Vertex Model

Cell rearrangements are fundamental mechanisms driving large-scale deformations of living tissues. In three-dimensional (3D) space-filling cell aggregates, cells rearrange through local topological transitions of the network of cell-cell interfaces, which is most conveniently described by the vertex model. Surprisingly, these transitions are not yet mathematically properly formulated due to a rather convoluted architecture of the conventional vertex model. As a result, the vertex model is generally difficult to implement, especially in its full 3D representation. Indeed, the few existing implementations of the full 3D vertex model rely on highly customized and complex software-engineering solutions, which cannot be transparently delineated and are thus mostly non-reproducible. We propose a solution to this outstanding problem by introducing a new formulation of the vertex model, called Graph Vertex Model~(GVM). GVM is based on storing the topology of the cell network into a knowledge graph. Its data structure, uniquely defined by a metagraph, allows performing cell rearrangement events by simple graph transformations, which are themselves represented by graphs. These graph transformations are mathematically well formulated and consist of elementary operations, such as deletions and creations of links between nodes of the knowledge graph, which are straight-forward to implement. Significantly, in the GVM's data representation, complex topological changes in 3D space-filling polyhedral packings can be broken down into a composition of more fundamental T1 transitions. Remarkably, when applied to a 2D system, these transformations reduce to a single T1 transition. This finding unifies topological transitions in 2D and 3D space-filling packings and suggests that the GVM's graph data structure may be the most natural representation of these systems

Digitalna procjena lisne površine krošnje stijenke vinove loze (Vitis vinifera cv. Sauvignon) korištenjem LIDAR mjerne tehnologije

A dosage rate reduction of plant protection products mixed with water, i.e. spray mixture, in a prescribed concentration in the vineyard will only be possible in the future, if the natural characteristics of vine canopy structures (leaf wall area) and canopy management are taken into account. In a practical experiment in the vineyard we evaluated the leaf wall area of the vine cv. Sauvignon on different segments on the left and right side of the vine canopy. We compared the results of manual measurements and laser measuring technology (LIDAR) with the corresponding algorithm, with which we enabled the digital reconstruction of the leaf wall area of the vine. The manual measurement of the leaf wall area was carried out using an automated image analyser. The digital system for measuring the leaf wall area on different segments consisted of a LIDAR sensor and a Differential Global Positioning System (hereinafter DGPS). To determine the exact DGPS position of the LIDAR sensor during the measurement, we set up a DGPS base station. Using the Excel software (CORREL function), we estimated the relationship between the dependent variable (digital number of points in the cloud) and an independent variable (leaf wall area, manually measured). An analysis of six randomly selected vines in the vineyard revealed the maximum value of the correlation coefficient r = 0.80 for the left side and r = 0.90 for the right side of the leaf wall area of the vine, respectively. In the near future the virtual three-dimensional space will provide more even control of spray mixture over the entire structure of the leaf wall area in the vineyard based on autonomous decision-making models.Smanjenje količine utroška sredstava za zaštitu bilja i same smjese za prskanje u budućnosti će biti moguće samo ako se uzmu u obzir prirodne karakteristike krošnje vinove loze tj. lisne površine krošnje trsa. U praktičnom pokusu u vinogradu procijenjena je lisna površinu krošnje vinove loze cv. Sauvignon na različitim segmentima s lijeve i desne strane krošnje uz pomoć ručnih mjerenja i laserske mjerne tehnologije (LIDAR). Dobiveni rezultati uspoređeni su s pripadajućim algoritmom čime je dobivena digitalna rekonstrukcija lisne površine vinove loze. Ručno mjerenje površine listova provedeno je u laboratoriju pomoću digitalnog lisnog skenera nakon što je lišće ručno pobrano s trsova i dopremljeno u sam laboratorij. Digitalni sustav za mjerenje lisne površine na različitim segmentima krošnje sastojao se od LIDAR senzora i DGPS navigacijskog sustava. Da bi se odredio točan DGPS položaj LIDAR senzora tijekom mjerenja, postavljena je DGPS bazna stanica. Pomoću regresijske metode utvrđen je odnos između zavisne varijable (digitalni broj točaka u oblaku) i nezavisne varijable (površina listova izmjerena skenerom). Rezultati analize imeđu dvije uspoređivane metode na šest slučajno odabranih trsova vinove loze otkrivaju vrijednost koeficijenta korelacije r = 0,80 za lijevu i r = 0,90 za desnu stranu krošnje. U bliskoj budućnosti virtualni trodimenzionalni prostor pružit će ravnomjerniju kontrolu smjese raspršivača preko cijele strukture područja stijenke lišča u vinogradu na temelju autonomnih modela odlučivanja