Stochastic Ergodicity Breaking: a Random Walk Approach

The continuous time random walk (CTRW) model exhibits a non-ergodic phase when the average waiting time diverges. Using an analytical approach for the non-biased and the uniformly biased CTRWs, and numerical simulations for the CTRW in a potential field, we obtain the non-ergodic properties of the random walk which show strong deviations from Boltzmann--Gibbs theory. We derive the distribution function of occupation times in a bounded region of space which, in the ergodic phase recovers the Boltzmann--Gibbs theory, while in the non-ergodic phase yields a generalized non-ergodic statistical law.Comment: 5 pages, 3 figure

AgriLOVE: Agriculture, land-use and technical change in an evolutionary, agent-based model

This paper presents a dynamic agent-based model of land use and agricultural production under environmental boundaries, finite available resources and endogenous technical change. In particular, we model a spatially explicit smallholder farming system populated by boundedly-rational agents competing and innovating to fulfill an exogenous demand for food, while coping with a changing environment shaped by their production choices. Given the strong technological and environmental uncertainty, agents learn and adaptively employ heuristics which guide their decisions on engaging in innovation and imitation activities, hiring workers, acquiring new farms, deforesting virgin areas and abandoning unproductive lands. Such activities in turn impact farm productivity, food production, food prices and land use. We firstly show that the model can replicate key stylized facts of the agricultural sector. We then extensively explore its properties across several scenarios featuring different institutional and behavioral settings. Finally, we simulate the model across different applications considering deforestation and land abandonment; human-induced soil degradation; and climate impacts. AgriLOVE offers a flexible simulation environment to study the endogenous emergence of different agricultural production regimes from the interaction of spatially dispersed farms subject to resource constraints, spatial influence and climate change

Dual random fragmentation and coagulation and an application to the genealogy of Yule processes

The purpose of this work is to describe a duality between a fragmentation associated to certain Dirichlet distributions and a natural random coagulation. The dual fragmentation and coalescent chains arising in this setting appear in the description of the genealogy of Yule processes.Comment: 14 page

Time efficiency and efficacy of a centralized computer-aided-design/computer-aided-manufacturing workflow for implant crown fabrication: A prospective controlled clinical study

OBJECTIVE To assess time efficiency and the efficacy of the prosthetic manufacturing for implant crown fabrication in a centralized workflow applying computer aided design and computer aided manufacturing (CAD-CAM). MATERIAL AND METHODS Fifty-nine patients with one posterior implant each, were randomly allocated to either a centralized digital workflow (c-DW, test) or a laboratory digital workflow (l-DW, control). Patients were excluded from efficiency and efficacy analyses, if any additional restoration than this single implant crown had to be fabricated. A customized titanium abutment and a monolithic zirconia crown were fabricated in the c-DW. In the l-DW, models were digitalized for CAD-CAM fabrication of a monolithic zirconia crown using a standardized titanium base abutment. Time for impression, laboratory operating and delivery time were recorded. The efficacy of the prosthetic manufacturing was evaluated at try-in and at delivery. Data was analyzed descriptively. Statistical analyses using student's unpaired t- and paired Wilcoxon were performed (p < 0.05). RESULTS At impression taking, 12 patients (c-DW) and 19 patients (l-DW) were included. The impression time was 9.4±3.5 min (c-DW) and 15.1 ± 4.6 min (l-DW) (p < 0.05). The laboratory operating time was 130 ± 31 min (c-DW) and 218.0±8 min (l-DW) (p < 0.05). The delivery time was significantly longer in the c-DW (5.9 ± 3.5 1 days) as compared to the l-DW (0.5±0.05 days). At try-in and at delivery, efficacy of prosthetic manufacturing was similar high in both workflows. CLINICAL RELEVANCE The c-DW was more time efficient compared to the lab-DW and rendered a similar efficacy of prosthetic manufacturing

Sign-time distribution for a random walker with a drifting boundary

We present a derivation of the exact sign-time distribution for a random walker in the presence of a boundary moving with constant velocity.Comment: 5 page

Cemented versus screw-retained zirconia-based single-implant restorations: 5-year results of a randomized controlled clinical trial

OBJECTIVES To compare cemented and screw-retained one-piece zirconia-based restorations in terms of clinical, radiographic, and technical outcomes 5 years after insertion. MATERIALS AND METHODS Thirty-four patients with single-tooth implants were randomly restored with either a cemented lithium disilicate crown on a one-piece customized zirconia abutment (CEM, 17 patients) or a screw-retained crown based on a directly veneered one-piece customized zirconia abutment (SCREW, 16 patients). All patients were recalled for a baseline examination (7-10 days after crown insertion) and then annually up to 5 years. The following outcomes were assessed: marginal bone level (changes), technical, and clinical (bleeding on probing, plaque control record, probing depth, and keratinized tissue) parameters. The Mann-Whitney U-test was used to assess differences between the two groups. RESULTS At 5 years, 26 patients (13 in each group) were re-examined. The survival rates on the implant and restorative levels were 100% and 82.4% (equally for both groups), respectively. At 5 years, the median marginal bone level was located at -0.15 mm (IQR: -0.89 mm; 0.27 mm) (CEM) and -0.26 mm (IQR: -0.38 mm; 0.01 mm) (SCREW) below the implant shoulder (intergroup p = .9598). The median changes between baseline and the 5-year follow-up amounted to -0.23 mm (CEM; intragroup p = .0002) and -0.15 mm (SCREW; intragroup p = .1465) (intergroup p = .1690). The overall technical complication rate at 5 years was 15.4% (CEM) and 15.4% (SCREW) (intergroup p = 1.00). Clinical parameters remained stable over time (baseline to 5 years). CONCLUSIONS At 5 years, screw-retained and cemented restorations rendered largely the same clinical, technical, and radiographic outcomes. Technical complications were frequent in both groups

The influence of fractional diffusion in Fisher-KPP equations

We study the Fisher-KPP equation where the Laplacian is replaced by the generator of a Feller semigroup with power decaying kernel, an important example being the fractional Laplacian. In contrast with the case of the stan- dard Laplacian where the stable state invades the unstable one at constant speed, we prove that with fractional diffusion, generated for instance by a stable L\'evy process, the front position is exponential in time. Our results provide a mathe- matically rigorous justification of numerous heuristics about this model