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1.
Oral Radiol ; 39(3): 455-466, 2023 07.
Artigo em Inglês | MEDLINE | ID: mdl-37058184

RESUMO

The objective of this work was to perform an integrative review of the inspection of peri-implant bone defects using cone beam computed tomography (CBCT). An electronic search was performed in the PubMed database using the following scientific terms: CBCT or Cone Beam computed tomography; dental implant; peri-implant; bone loss; defects. The survey identified 267 studies, of which 18 were considered relevant to this study. These studies provided important data taking into account the accuracy of cone beam computed tomography in the detection and measurement of peri-implant bone defects such as fenestrations, dehiscence and intraosseous circumferential defects. The effectiveness of CBCT in aiding in geometric bone calculations and in the diagnosis of peri-implant defects was influenced by factors such as artefacts, defect size, bone wall thickness, implant material, adjustment of acquisition parameters and observer experience. A not insignificant number of studies compared intraoral radiography to CBCT in the detection of peri-implant bone loss. CBCT was clearly superior to intraoral radiography in the detection of all peri-implant bone defects, except for defects located in the interproximal zone. In general, studies have shown that peri-implant bone measurements adjacent to the implant surface can be correctly determined, as well as the diagnosis of peri-implant bone defects with an average discrepancy of less than 1 mm from the actual measurement of the defect.


Assuntos
Tomografia Computadorizada de Feixe Cônico Espiral , Tomografia Computadorizada de Feixe Cônico/métodos , Osso e Ossos , Artefatos
2.
Actas urol. esp ; 47(3): 172-178, abr. 2023. ilus, tab
Artigo em Espanhol | IBECS | ID: ibc-218407

RESUMO

Introducción Las opciones de tratamiento quirúrgico del cáncer de próstata han experimentado cambios significativos gracias a la expansión de la robótica. Sin embargo, la prostatectomía radical retropúbica abierta (PRA) seguirá realizándose en aquellos entornos con limitaciones económicas o con escaso acceso a la robótica. El objetivo de este estudio fue determinar los resultados oncológicos a largo plazo, clasificar las tasas de complicaciones y examinar las tasas de recuperación temprana de la continencia en pacientes tratados con PRA. Métodos Identificamos a todos los pacientes sometidos a PRA en nuestra institución entre 2000 y 2020. Se utilizó un pad test (prueba de la compresa) estandarizado para determinar las tasas de continencia precoz tras la retirada del catéter; la continencia tardía, alrededor de un año después de la cirugía, se determinó mediante el número de compresas por día. Se utilizó la clasificación de Clavien-Dindo para informar las tasas de complicaciones. Las tasas de supervivencia libre de recidiva bioquímica (RB) y de supervivencia global (SG) se definieron mediante el método de Kaplan-Meier y el análisis log-rank. Se utilizaron modelos multivariantes de regresión de Cox para comprobar el efecto de los distintos factores sobre la recidiva bioquímica. Resultados Se analizaron los datos de 1.095 pacientes. La mediana de seguimiento fue de 93,4 meses. Se encontró una supervivencia global libre de RB a 10años y una SG del 73% y del 82%, respectivamente. Se observó una tasa de complicaciones de Clavien Dindo ≥3 en el 4,8% de los pacientes. La tasa de continencia precoz fue del 81,4% y la tasa de continencia tardía fue del 89,1%. El nivel de PSA preoperatorio, la suma de la puntuación de Gleason, el estadio pT, el estado de los ganglios linfáticos y el estado de los márgenes quirúrgicos fueron predictores independientes de RB (p<0,001). Entre las limitaciones del estudio están su diseño retrospectivo y unicéntrico (AU)


Introduction The surgical treatment options for prostate cancer have changed rapidly, given the expansion of robotics. However, open retropubic radical prostatectomy (ORP) will continue to be performed in areas with financial limitations or with limited access to robotics. The purpose of this study was to determine the long-term oncological outcomes, to categorize complication rates and to examine the early continence rates in patients treated with ORP. Methods We identified all patients who underwent ORP at our institution between 2000 and 2020. A standardized pad test was used to determine the early continence rates upon catheter removal, the late continence around a year after surgery was determined by the number of pads per day. The Clavien-Dindo classification was used to report the complication rates. The biochemical recurrence (BCR)-free survival and overall survival (OS) rates were defined using the Kaplan-Meier method and log-rank analysis. Multivariable Cox-regression models were used to test the effect of different factors on biochemical recurrence. Results We analyzed 1095 patients. The median follow-up was 93.4months. An overall 10-year BCR-free survival and OS of 73% and 82% respectively was found. A complication rate for Clavien Dindo ≥3 was seen in 4.8% of patients. The early continence rate was 81.4% and the late continence 89.1%. Preoperative PSA level, Gleason score sum, pT stage, lymph node status, and surgical margin status were independent predictors of BCR (P<.001). Limitations include retrospective and single centre study design. Conclusions ORP is a surgical procedure that provides excellent oncological- and early continence-rates (AU)


Assuntos
Humanos , Masculino , Adulto , Pessoa de Meia-Idade , Idoso , Idoso de 80 Anos ou mais , Prostatectomia/métodos , Neoplasias da Próstata/cirurgia , Recidiva Local de Neoplasia , Resultado do Tratamento , Análise de Sobrevida , Seguimentos , Estadiamento de Neoplasias
3.
Phys Rev E ; 107(1-1): 014301, 2023 Jan.
Artigo em Inglês | MEDLINE | ID: mdl-36797879

RESUMO

The nonbacktracking matrix and the related nonbacktracking centrality (NBC) play a crucial role in models of percolation-type processes on networks, such as nonrecurrent epidemics. Here we study the localization of NBC in infinite sparse networks that contain an arbitrary finite subgraph. Assuming the local tree likeness of the enclosing network, and that branches emanating from the finite subgraph do not intersect at finite distances, we show that the largest eigenvalue of the nonbacktracking matrix of the composite network is equal to the highest of the two largest eigenvalues: that of the finite subgraph and of the enclosing network. In the localized state, when the largest eigenvalue of the subgraph is the highest of the two, we derive explicit expressions for the NBCs of nodes in the subgraph and other nodes in the network. In this state, nonbacktracking centrality is concentrated on the subgraph and its immediate neighborhood in the enclosing network. We obtain simple, exact formulas in the case where the enclosing network is uncorrelated. We find that the mean NBC decays exponentially around the finite subgraph, at a rate which is independent of the structure of the enclosing network, contrary to what was found for the localization of the principal eigenvector of the adjacency matrix. Numerical simulations confirm that our results provide good approximations even in moderately sized, loopy, real-world networks.

4.
Actas Urol Esp (Engl Ed) ; 47(3): 172-178, 2023 04.
Artigo em Inglês, Espanhol | MEDLINE | ID: mdl-36372360

RESUMO

INTRODUCTION: The surgical treatment options for prostate cancer have changed rapidly, given the expansion of robotics. However, open retropubic radical prostatectomy (ORP) will continue to be performed in areas with financial limitations or with limited access to robotics. The purpose of this study was to determine the long-term oncological outcomes, to categorize complication rates and to examine the early continence rates in patients treated with ORP. METHODS: We identified all patients who underwent ORP at our institution between 2000 and 2020. A standardized pad test was used to determine the early continence rates upon catheter removal, the late continence around a year after surgery was determined by the number of pads per day. The Clavien-Dindo classification was used to report the complication rates. The biochemical recurrence (BCR)-free survival and overall survival (OS) rates were defined using the Kaplan-Meier method and log-rank analysis. Multivariable Cox-regression models were used to test the effect of different factors on biochemical recurrence. RESULTS: We analyzed 1095 patients. The median follow-up was 93.4 months. An overall 10-year BCR-free survival and OS of 73% and 82% respectively was found. A complication rate for Clavien Dindo≥3 was seen in 4.8% of patients. The early continence rate was 81.4% and the late continence 89,1%. Preoperative PSA level, Gleason score sum, pT stage, lymph node status, and surgical margin status were independent predictors of BCR (p<0.001, 95% CI). Limitations include retrospective and single center study design. CONCLUSIONS: ORP is a surgical procedure that provides excellent oncological- and early continence-rates.


Assuntos
Neoplasias da Próstata , Robótica , Masculino , Humanos , Resultado do Tratamento , Estudos Retrospectivos , Neoplasias da Próstata/patologia , Prostatectomia/métodos
5.
Osteoarthritis Cartilage ; 31(3): 317-339, 2023 03.
Artigo em Inglês | MEDLINE | ID: mdl-36481451

RESUMO

OBJECTIVE: To investigate the effects and mechanotransduction pathways of therapeutic ultrasound on chondrocytes. METHOD: PubMed, EMBASE and Web of Science databases were searched up to 19th September 2021 to identify in vitro studies exploring ultrasound to stimulate chondrocytes for osteoarthritis (OA) treatment. Study characteristics, ultrasound parameters, in vitro setup, and mechanotransduction pathways were collected. Risk of bias was judged using the Risk of Bias Assessment for Non-randomized Studies (RoBANS) tool. RESULTS: Thirty-one studies were included comprising healthy and OA chondrocytes and explants. Most studies had high risk of performance, detection and pseudoreplication bias due to lack of temperature control, setup calibration, inadequate semi-quantitatively analyzes and independent experiments. Ultrasound was applied to the culture plate via acoustic gel, water bath or culture media. Regardless of the setup used, ultrasound stimulated the cartilage production and suppressed its degradation, although the effect size was nonsignificant. Ultrasound inhibited p38, c-Jun N-terminal kinases (JNK) and factor nuclear kappa B (NFκB) pathways in OA chondrocytes to reduce apoptosis, inflammation and matrix degradation, while triggered phosphoinositide-3-kinase/akt (PI3K/Akt), extracellular signal-regulated kinase (ERK), p38 and JNK pathways in healthy chondrocytes to promote matrix synthesis. CONCLUSION: The included studies suggest that ultrasound application induces therapeutic effects on chondrocytes. However, these results should be interpreted with caution because high risk of performance, detection and pseudoreplication bias were identified. Future studies should explore the application of ultrasound on human OA chondrocytes cultures to potentiate the applicability of ultrasound towards cartilage regeneration of knee with OA.


Assuntos
Cartilagem Articular , Osteoartrite , Terapia por Ultrassom , Humanos , Condrócitos/metabolismo , Mecanotransdução Celular , Proteínas Proto-Oncogênicas c-akt/metabolismo , Fosfatidilinositol 3-Quinases/metabolismo , Cartilagem Articular/metabolismo , Osteoartrite/metabolismo
6.
Phys Rev Lett ; 129(20): 208002, 2022 Nov 11.
Artigo em Inglês | MEDLINE | ID: mdl-36462001

RESUMO

We study a model of nonidentical swarmalators, generalizations of phase oscillators that both sync in time and swarm in space. The model produces four collective states: asynchrony, sync clusters, vortexlike phase waves, and a mixed state. These states occur in many real-world swarmalator systems such as biological microswimmers, chemical nanomotors, and groups of drones. A generalized Ott-Antonsen ansatz provides the first analytic description of these states and conditions for their existence. We show how this approach may be used in studies of active matter and related disciplines.


Assuntos
Dispositivos Aéreos não Tripulados
9.
Sci Rep ; 12(1): 3973, 2022 Mar 10.
Artigo em Inglês | MEDLINE | ID: mdl-35273259

RESUMO

Weak multiplex percolation generalizes percolation to multi-layer networks, represented as networks with a common set of nodes linked by multiple types (colors) of edges. We report a novel discontinuous phase transition in this problem. This anomalous transition occurs in networks of three or more layers without unconnected nodes, [Formula: see text]. Above a critical value of a control parameter, the removal of a tiny fraction [Formula: see text] of nodes or edges triggers a failure cascade which ends either with the total collapse of the network, or a return to stability with the system essentially intact. The discontinuity is not accompanied by any singularity of the giant component, in contrast to the discontinuous hybrid transition which usually appears in such problems. The control parameter is the fraction of nodes in each layer with a single connection, [Formula: see text]. We obtain asymptotic expressions for the collapse time and relaxation time, above and below the critical point [Formula: see text], respectively. In the limit [Formula: see text] the total collapse for [Formula: see text] takes a time [Formula: see text], while there is an exponential relaxation below [Formula: see text] with a relaxation time [Formula: see text].

10.
Phys Rev E ; 104(5-1): 054306, 2021 Nov.
Artigo em Inglês | MEDLINE | ID: mdl-34942755

RESUMO

Message-passing theories have proved to be invaluable tools in studying percolation, nonrecurrent epidemics, and similar dynamical processes on real-world networks. At the heart of the message-passing method is the nonbacktracking matrix, whose largest eigenvalue, the corresponding eigenvector, and the closely related nonbacktracking centrality play a central role in determining how the given dynamical model behaves. Here we propose a degree-class-based method to approximate these quantities using a smaller matrix related to the joint degree-degree distribution of neighboring nodes. Our findings suggest that in most networks, degree-degree correlations beyond nearest neighbor are actually not strong, and our first-order description already results in accurate estimates, particularly when message-passing itself is a good approximation to the original model in question, that is, when the number of short cycles in the network is sufficiently low. We show that localization of the nonbacktracking centrality is also captured well by our scheme, particularly in large networks. Our method provides an alternative to working with the full nonbacktracking matrix in very large networks where this may not be possible due to memory limitations.

11.
Chaos Solitons Fractals ; 152: 111359, 2021 Nov.
Artigo em Inglês | MEDLINE | ID: mdl-34483500

RESUMO

We introduce a compartmental model SEIAHRV (Susceptible, Exposed, Infected, Asymptomatic, Hospitalized, Recovered, Vaccinated) with age structure for the spread of the SARAS-CoV virus. In order to model current different vaccines we use compartments for individuals vaccinated with one and two doses without vaccine failure and a compartment for vaccinated individual with vaccine failure. The model allows to consider any number of different vaccines with different efficacies and delays between doses. Contacts among age groups are modeled by a contact matrix and the contagion matrix is obtained from a probability of contagion p c per contact. The model uses known epidemiological parameters and the time dependent probability p c is obtained by fitting the model output to the series of deaths in each locality, and reflects non-pharmaceutical interventions. As a benchmark the output of the model is compared to two good quality serological surveys, and applied to study the evolution of the COVID-19 pandemic in the main Brazilian cities with a total population of more than one million. We also discuss with some detail the case of the city of Manaus which raised special attention due to a previous report of We also estimate the attack rate, the total proportion of cases (symptomatic and asymptomatic) with respect to the total population, for all Brazilian states since the beginning of the COVID-19 pandemic. We argue that the model present here is relevant to assessing present policies not only in Brazil but also in any place where good serological surveys are not available.

12.
Phys Rev E ; 104(2-1): 024313, 2021 Aug.
Artigo em Inglês | MEDLINE | ID: mdl-34525638

RESUMO

We studied the impact of field heterogeneity on entrainment in a system of uniformly interacting phase oscillators. Field heterogeneity is shown to induce dynamical heterogeneity in the system. In effect, the heterogeneous field partitions the system into interacting groups of oscillators that feel the same local field strength and phase. Based on numerical and analytical analysis of the explicit dynamical equations derived from the periodically forced Kuramoto model, we found that the heterogeneous field can disrupt entrainment at different field frequencies when compared to the homogeneous field. This transition occurs when the phase- and frequency-locked synchronization between groups of oscillators is broken at a critical field frequency, causing each group to enter a new dynamical state (disrupted state). Strikingly, it is shown that disrupted dynamics can differ between groups.

13.
Dent Mater ; 37(10): e493-e501, 2021 10.
Artigo em Inglês | MEDLINE | ID: mdl-34479725

RESUMO

OBJECTIVE: Failure of dental implants treatment is frequently the result of bacterial colonization of implants followed by diseases like peri-implantitis. Recent studies have been made regarding the surface treatment of implants components, namely abutments that are in the interface of the living tissue with the implant. This work aimed at evaluating the antimicrobial profile of a silane-based coating with TiO2 adapted to an abutment screw, that was also developed as an anti-loosening agent, to prevent adhesion and migration of Gram + and Gram-bacteria, Staphylococcus aureus, and Escherichia coli, respectively. METHODS: Direct contact antimicrobial studies were conducted on coated and uncoated samples by resazurin fluorescent assay and cytotoxicity assessment was done via MTT indirect method on days 1 and 4. Sterilizations studies by FTIR analysis were also performed to understand the ideal balance between sterilization efficacy and coating functionality subjecting the samples to ethylene oxide, gamma irradiation, and autoclave sterilization, before antimicrobial testing. The implant system as a whole was also studied for its ability to block bacterial migration and preventing microleakage as well as an assessment of initial bacterial adhesion evaluated by scanning electron microscopy. RESULTS: Direct contact studies performed on coated samples showed a very high antimicrobial activity, while cytotoxicity assays revealed the coating to be safe and non-leachable. Sterilizations studies showed that the antimicrobial features of the coating were preserved and interchangeable regardless of the sterilization method. The implant system migration studies demonstrated that the implant system works as an efficient barrier for the studied bacteria. SIGNIFICANCE: The acquired results clearly show that it is possible to obtain a highly functional coating with obvious and marked antimicrobial features that together with an abutment that prevents bacterial migration and versatility in sterilization methodology has a very high potential in the dental implant field.


Assuntos
Anti-Infecciosos , Implantes Dentários , Anti-Infecciosos/farmacologia , Bactérias , Parafusos Ósseos , Dente Suporte , Projeto do Implante Dentário-Pivô
14.
J Phys Condens Matter ; 33(43)2021 Aug 13.
Artigo em Inglês | MEDLINE | ID: mdl-34293724

RESUMO

We report the investigation of spin-to-charge current interconversion process in hybrid structures of yttrium iron garnet (YIG)/metallic bilayers by means of two different experimental techniques: spin pumping effect (SPE) and spin Hall magnetoresistance (SMR). We demonstrate the evidence of a correlation between spin-to-charge conversion and SMR in bilayers of YIG/Pd, YIG/Pt, and YIG/IrMn. The correlation was verified directly in the spin Hall angles and the amplitudes of the voltage signals measured by the SPE and SMR techniques. The detection of SMR was carried out using the modulated magnetoresistance technique and lock-in amplifier detection. For these measurements, we present a simple model for the interpretation of the results. The results allow us to conclude that indeed the interface in the YIG/metallic bilayers has a dominant role in the spin-to-charge current conversion and SMR.

15.
Phys Rev E ; 103(2-1): 022321, 2021 Feb.
Artigo em Inglês | MEDLINE | ID: mdl-33736025

RESUMO

Dependency links in single-layer networks offer a convenient way of modeling nonlocal percolation effects in networked systems where certain pairs of nodes are only able to function together. We study the percolation properties of the weak variant of this model: Nodes with dependency neighbors may continue to function if at least one of their dependency neighbors is active. We show that this relaxation of the dependency rule allows for more robust structures and a rich variety of critical phenomena, as percolation is not determined strictly by finite dependency clusters. We study Erdos-Rényi and random scale-free networks with an underlying Erdos-Rényi network of dependency links. We identify a special "cusp" point above which the system is always stable, irrespective of the density of dependency links. We find continuous and discontinuous hybrid percolation transitions, separated by a tricritical point for Erdos-Rényi networks. For scale-free networks with a finite degree cutoff we observe the appearance of a critical point and corresponding double transitions in a certain range of the degree distribution exponent. We show that at a special point in the parameter space, where the critical point emerges, the giant viable cluster has the unusual critical singularity S-S_{c}∝(p-p_{c})^{1/4}. We study the robustness of networks where connectivity degrees and dependency degrees are correlated and find that scale-free networks are able to retain their high resilience for strong enough positive correlation, i.e., when hubs are protected by greater redundancy.

17.
Hernia ; 25(3): 765-774, 2021 06.
Artigo em Inglês | MEDLINE | ID: mdl-32495056

RESUMO

PURPOSE: The enhanced view totally extraperitoneal (eTEP) concept first applied to inguinal hernias has become an important tool in the armamentarium of ventral hernia repair. The purpose of this report is to date the first brazilian robotic-assisted eTEP ventral hernia repair case series. METHODS: A review of a prospectively maintained database was conducted in patients who underwent robotic-assisted enhanced view totally extraperitoneal (eTEP) for ventral hernia repair between June 2018 and January 2020. Patients demographics, preoperative hernia characteristics, intraoperative variables and postoperative outcomes were evaluated. RESULTS: Our review identified 74 patients submitted to the procedure. Thirty-one patients (41.8%) presented primary ventral hernias (PVHs) and 43 patients (58.2%) presented incisional hernias (IHs). Female patients were predominant in both groups PVHs and IHs with 17 (22.9%) and 22 (29.7%) respectively, with a total of 39 patients (52.7%). Mean BMI was 29.1 kg/m2 (range 21.3-48.0 kg/m2) with higher mean BMI rates of 30.3 kg/m2 in the IHs group (range 22-48 years). A lateral dock setup was utilized in 55 cases (74.4%), having the inferior and superior dock setup in 18 (24.3%) and 1 (1.3%) cases respectively. Mean console time was 148.3 (range 75-277 min) and 192.6 min (range 66-301 min) in the PVHs and IHs groups respectively. There were no intraoperative complications or conversions. Average length of stay was 1.5 days. Four patients were readmitted within 30 days of surgery. There were no reoperation or cases of intraparietal herniation in this cohort. No hernia recurrence was verified during the mean 230.7 days of follow up in both groups. CONCLUSION: We present the first brazilian series to-date of the robotic assisted eTEP approach for ventral hernia repairs. Although long term outcomes require further analysis, its feasibility and reproducibility in experienced surgeons hands are evident, with safe and acceptable early postoperative outcomes.


Assuntos
Hérnia Ventral , Hérnia Incisional , Laparoscopia , Procedimentos Cirúrgicos Robóticos , Feminino , Hérnia Ventral/cirurgia , Herniorrafia/efeitos adversos , Humanos , Hérnia Incisional/cirurgia , Reprodutibilidade dos Testes , Estudos Retrospectivos , Procedimentos Cirúrgicos Robóticos/efeitos adversos , Telas Cirúrgicas
18.
Entropy (Basel) ; 22(10)2020 Oct 13.
Artigo em Inglês | MEDLINE | ID: mdl-33286918

RESUMO

Compression, filtering, and cryptography, as well as the sampling of complex systems, can be seen as processing information. A large initial configuration or input space is nontrivially mapped to a smaller set of output or final states. We explored the statistics of filtering of simple patterns on a number of deterministic and random graphs as a tractable example of such information processing in complex systems. In this problem, multiple inputs map to the same output, and the statistics of filtering is represented by the distribution of this degeneracy. For a few simple filter patterns on a ring, we obtained an exact solution of the problem and numerically described more difficult filter setups. For each of the filter patterns and networks, we found three key numbers that essentially describe the statistics of filtering and compared them for different networks. Our results for networks with diverse architectures are essentially determined by two factors: whether the graphs structure is deterministic or random and the vertex degree. We find that filtering in random graphs produces much richer statistics than in deterministic graphs, reflecting the greater complexity of such graphs. Increasing the graph's degree reduces this statistical richness, while being at its maximum at the smallest degree not equal to two. A filter pattern with a strong dependence on the neighbourhood of a node is much more sensitive to these effects.

19.
Phys Rev E ; 102(3-1): 032304, 2020 Sep.
Artigo em Inglês | MEDLINE | ID: mdl-33075984

RESUMO

The structure of an evolving network contains information about its past. Extracting this information efficiently, however, is, in general, a difficult challenge. We formulate a fast and efficient method to estimate the most likely history of growing trees, based on exact results on root finding. We show that our linear-time algorithm produces the exact stepwise most probable history in a broad class of tree growth models. Our formulation is able to treat very large trees and therefore allows us to make reliable numerical observations regarding the possibility of root inference and history reconstruction in growing trees. We obtain the general formula 〈lnN〉≅NlnN-cN for the size dependence of the mean logarithmic number of possible histories of a given tree, a quantity that largely determines the reconstructability of tree histories. We also reveal an uncertainty principle: a relationship between the inferability of the root and that of the complete history, indicating that there is a tradeoff between the two tasks; the root and the complete history cannot both be inferred with high accuracy at the same time.

20.
Phys Rev E ; 102(3-1): 032301, 2020 Sep.
Artigo em Inglês | MEDLINE | ID: mdl-33076014

RESUMO

We describe the critical behavior of weak multiplex percolation, a generalization of percolation to multiplex or interdependent networks. A node can determine its active or inactive status simply by referencing neighboring nodes. This is not the case for the more commonly studied generalization of percolation to multiplex networks, the mutually connected clusters, which requires an interconnecting path within each layer between any two vertices in the giant mutually connected component. We study the emergence of a giant connected component of active nodes under the weak percolation rule, finding several nontypical phenomena. In two layers, the giant component emerges with a continuous phase transition, but with quadratic growth above the critical threshold. In three or more layers, a discontinuous hybrid transition occurs, similar to that found in the giant mutually connected component. In networks with asymptotically powerlaw degree distributions, defined by the decay exponent γ, the discontinuity vanishes but at γ=1.5 in three layers, more generally at γ=1+1/(M-1) in M layers.

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