Internal Edges Research Articles

Comparative finite element analysis of skull mechanical properties following parietal bone graft harvesting in adults

IntroductionParietal bone grafts are commonly used in cranio-maxillo-facial surgery. Both the outer and the internal layer of the calvarium can be harvested. The bone defect created by this harvesting may induce significant weakening of the skull that has not been extensively evaluated. Our aim was to evaluate the consequences of parietal bone graft harvesting on mechanical properties of the skull using a finite element analysis. MethodsFinite elements models of the skull of 3 adult patients were created from CT scans. Parietal external and internal layer harvest models were created. Frontal, lateral, and parietal loading were modeled and von Mises stress distributions were compared. ResultsThe maximal von Mises stress was higher for models of bone harvesting, both on the whole skull and at the harvested site. Maximal von Mises stress was even higher for models with internal layer defect. ConclusionsHarvesting parietal bone modifies the skull's mechanical strength and can increase the risk of skull fracture, mainly on the harvested site. Outer layer parietal graft harvesting is indicated. Graft harvesting located in the upper part of the parietal bone, close to the sagittal suture and with smooth internal edges and corners should limit the risk of fracture.

Optical properties of truncated Au nanocages with different size and shape

The hollow nanostructures are conducive to applications including drug delivery, energy storage and conversion, and catalysis. In the present work, a versatile type of Au nanoparticles, i.e. nanocage with hollow interior, was studied thoroughly. Simulation of the optical properties of nanocages with different sizes and shapes was presented, which is essential for tuning the localized surface plasmon resonance peak. The edge length, side length of triangle, and wall thickness were used as structural parameters of truncated Au nanocage. The dependence of absorption efficiency, resonant wavelength, and absorption quantum yield on the structural parameters were discussed. Meanwhile, the applications of absorption quantum yield in biomedical imaging and laser induced thermal therapy were investigated. It was found that the phenomenon of multipolar plasmon resonances exists on truncated Au nanocage. Furthermore, the electric field distribution at different resonant wavelengths was also investigated. It is found that the electromagnetic field corresponds to the dipolar mode in an individual nanocage is largely distributed at the corners. Whereas, the electromagnetic field corresponds to the multipolar region is mainly located in the internal corners and edges.

On compatibility and incompatibility of collections of unrooted phylogenetic trees

Let P={T1,…,Tk} be a collection of phylogenetic trees over various subsets of a set of species. For each i∈{1,…,k}, let L(Ti) denote the set of species in tree Ti. A supertree for P is a phylogenetic tree with species set ⋃i=1kL(Ti). The tree compatibility problem asks whether there exists a supertree T for P such that, for each i∈{1,…,k}, Ti can be obtained from T|L(Ti) — the minimal subtree of T spanning L(Ti) — by zero or more contractions of internal edges. If the answer is “yes”, then P is said to be compatible; otherwise, P is incompatible.We characterize compatibility via graph triangulations and tree decompositions. We then study how to make an incompatible collection of trees compatible through edge contraction and tree deletion. Finally, we introduce the notion of a phylogenetic minor to study under which conditions edge contraction, tree removal, and species removal/renaming operations preserve compatibility.

Utilizing advances in correlation analysis for community structure detection

Build the connection between correlation analysis and community detection.A framework of utilizing correlation analysis to advance community detection.A novel graphic analysis for selecting methods.Solve the resolution problem through the proposed framework. In the era of big data, some data records are interrelated with each other in many areas, such as marketing, management, health care, and education. These interrelated data can be more naturally represented as networks with nodes and edges. Inside this type of networks, there is usually a hidden community structure where each community represents a relatively independent functional module. Such hidden community structures are useful for many applications, such as word-of-mouth marketing, promoting decentralized social interactions inside organizations, and searching biological pathways related to various diseases. Therefore, how to detect hidden community structures becomes an important task with wide applications. Currently, modularity-based methods are widely-used among many existing community structure detection methods. They detect communities with more internal edges than expected under the null hypothesis of independence. Since research in correlation analysis also searches for patterns which occur more than expected under the null hypothesis of independence, this paper proposed a framework of changing the original modularity function according to different existing correlation functions in the correlation analysis research area. Such a framework can utilize not only the current but also the future potential research progresses in correlation analysis to advance community detection. In addition, a novel graphical analysis on different modified-modularity functions is conducted to analyze their different preferences, which are also validated by our evaluation on both real life and simulated networks. Our work to connect modularity-based methods with correlation analysis has several significant impacts on the community detection research and its applications to expert and intelligent systems. First, the research progress in correlation analysis can be utilized to define a more effective objective function in community detection for better detection results since different real-life applications might need communities with different resolutions. Second, any existing research progress for the modularity function, such as the Louvain method for speeding up the search and different extensions for overlapping community detection, can be applied in a similar way to the new objective function derived from existing correlation functions, because the new objective function is unified within one framework with the modularity function. Third, our framework opens a large unexplored area for the researchers interested in community detection. For example, what is the best heuristic search method for each different objective function? What are the characteristics of each objective function when applied to overlapping community detection? Among different extensions to overlapping community detection, which extension is better for each objective function?

Surface Lifshits tails for random quantum Hamiltonians

We consider Schrödinger operators on L2(ℝd)⊗L2(ℝℓ) of the form Hω=H⊥⊗I∥+I⊥⊗H∥+Vω, where H⊥ and H∥ are Schrödinger operators on L2(ℝd) and L2(ℝℓ), respectively, and Vω(x,y):=∑ξ∈ℤdλξ(ω)v(x−ξ,y),x∈ℝd,y∈ℝℓ is a random “surface potential.” We investigate the behavior of the integrated density of surface states of Hω near the bottom of the spectrum and near internal band edges. The main result of the current paper is that, under suitable assumptions, the behavior of the integrated density of surface states of Hω can be read off from the integrated density of states of a reduced Hamiltonian H⊥+Wω where Wω is a quantum mechanical average of Vω with respect to y∈ℝℓ. We are particularly interested in cases when H⊥ is a magnetic Schrödinger operator, but we also recover some of the results from Kirsch and Warzel [J. Funct. Anal. 230, 222–250 (2006)] for non-magnetic H⊥.

A characterization of dissimilarity families of trees

Let T=(T,w) be a weighted finite tree with leaves 1,…,n. For any I≔{i1,…,ik}⊂{1,…,n}, let DI(T) be the weight of the minimal subtree of T connecting i1,…,ik; the DI(T) are called k-weights of T. Let {DI}Ik-subset of {1,…,n} be a family of real numbers. We say that a weighted tree T=(T,w) with leaves 1,…,n realizes the family if DI(T)=DI for any k-subset I of {1,…,n}.In this paper we find some equalities and inequalities characterizing the families of real numbers parametrized by the k-subsets of {1,…,n} that are the families of k-weights of weighted trees whose leaf set is equal to {1,…,n} and whose weights of the internal edges are positive (where we say that an edge e is internal if there exists a path with endpoints of degree greater than 2 and containing e).

Inflammatory cell-induced corrosion in total knee arthroplasty: A retrieval study.

Metal release in patients with joint replacements is associated with local tissue reactions, pain, and ultimately revision of implants. One of the causes of this metal loss is speculated to be due to a mechanism of inflammatory cell-induced corrosion (ICIC). In this knee retrieval study, we aimed to: (1) identify the extent and location of ICI corrosion patterns on our femoral and tibial components and (2) correlate our findings with implant and clinical information. We investigated 28 femoral and 9 tibial components made of polished CoCr for presence of ICIC, using macroscopic and microscopic screening and statistical analyses to identify any significant correlations between our results and clinical information. We found that 71% of femoral and 100% of tibial components showed evidence of ICIC and significantly more was present on non-contacting regions (p < 0.0001). We found a significant correlation between the presence of ICIC and instability (p = 0.0113) and a significant difference between poster stabilized and cruciate retaining designs in the amount of ICIC on internal edges (p = 0.0375). This corrosion pattern was prevalent in our series of knee retrievals and may help explain some of the mechanisms of material loss that may occur in vivo. © 2016 Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater, 106B: 460-467, 2018.

Correcting the position of piezoelectric transducers during acoustic control of the stressed-strained rolled sections

We used the mirror­shadow method for the diagnostics of stressed­strained state of shaped sections of metal structures. It was found that in the course of implementation of this method there may occur an error that is caused by misalignment of measurement with the dimension of acoustic receiving transducer. The work considers the effect of change in the geometry of shaped sections under the action of maximum permissible stress on the displacement of the point at which a beam of ultrasound wave arrives. We examined a question of influence of the slope of inner edge of the shelf of a shaped section on the displacement of the point of ultrasonic wave’s arrival sideways from the center of receiving transducer. As a result of analytical studies, it was proved that changing geometric dimensions of control object practically does not affect displacement of the point of arrival of the beam from the center of the receiving transducer. It was found that for a number of shaped sections that have slopes of internal edges of the shelves, it is necessary to introduce correction of position of the receiving transducer relative to the emitting transducer by such parameters as angle and distance relative to the anchor point. Performed research is a prerequisite for the development of design of the block of piezoelectric transducers for implementation of the system of acoustic diagnostics of the strained state of shaped sections.

Left Post-Traumatic Diaphragm Rupture Repaired by Reduced Port Laparoscopy

Introduction: Diaphragmatic rupture after high energy blunt trauma occurs in about 5% of cases and overall mortality rate is 31% in a recent series. Left-sided rupture is more common than right-sided1,2 rupture and early diagnosis is made in less than 50% of cases.3 Laparoscopy has been used for diagnosis and treatment. We report the feasibility of reduced port complete laparoscopic repair with special considerations about technical aspects. Materials and Methods: A 30-year-old man was admitted after blunt abdominal trauma; the patient was hemodynamically stable and preoperative work-up showed a left diaphragmatic rupture with transposition of viscera into the left chest. A laparoscopic repair by reduced port surgery (three trocars) was performed. A 10 mm trocar was placed in the umbilical scar, a 5 mm trocar in the right flank, and a 5 mm trocar in the left flank. The exploration of the abdominal cavity confirmed the presence of small bowel, transverse colon, and greater omentum into the left chest. Herniated viscera were reduced into the abdomen. The defect was first repaired by two converting running sutures using nonabsorbable stitches (polypropylene 1). The suture line was later reinforced by a double-face prosthetic mesh (Sepramesh; Bard, Warwick, RI) fixed by 5 mm tacks (Sorbafix; Bard) in the lateral and lower edges and by two Polyglactin 2/0 running sutures in the upper and internal edges. The procedure ended with the closure of the umbilical access and placement of a left chest tube. Results and Conclusions: Operative time was 45 minutes and blood loss of few centiliters. The endotracheal tube was removed on the first postoperative day and the chest tube was removed after 2 days. The postoperative course was uneventful. Laparoscopic repair of traumatic diaphragmatic hernia has been reported.4–8 Here we present our reduced port technique. We prefer laparoscopy instead of thoracoscopy because of the risk of penetrating injury of abdominal organs in the thorax and because single-lung ventilation is not necessary. Moreover laparoscopy permits an easy reduction of abdominal organs and permits exploration of the thorax.4 As observed by other authors,4 we did not experience tension pneumothorax at insufflation. No chest tube is needed during the procedure if CO2 pressure is kept low (10 mm Hg in this case). Preformed knots are useful to save time during the procedure. A mesh can be easily introduced by the optic trocar and a complete repair can be achieved with only three trocars. In stable patients with suspected or demonstrated diaphragmatic rupture, laparoscopy offers all the advantages of minimally invasive surgery, avoiding laparotomy and thoracotomy scars and allowing a complete repair with mesh. Reduced port laparoscopy is feasible and safe and permits to decrease the abdominal trauma. No competing financial interests exist. Runtime of video: 5 mins 37 secs

Regular coronoids and 4-tilings

A benzenoid is a finite connected plane graph with no cut vertices in which every interior region is bounded by a regular hexagon of side length one. A coronoid G is a connected subgraph of a benzenoid such that every edge lies in a hexagon of G and G contains at least one non-hexagon interior face, which should have a size of at least two hexagons. A polyhex is either a benzenoid or a coronoid. A coronoid is said to be regular if it can be generated from a single hexagon by a series of specific additions of hexagons. The vertices of the inner dual I(G) of a polyhex G are the centers of all hexagons of G, two vertices being adjacent if and only if the corresponding hexagons share an edge in G. The graph IS(G) is obtained from I(G) by removing a set of internal edges S. A polyhex G admits a 4-tiling, if every triple of pairwise adjacent hexagons of G belongs to a 4-cycle face of IS(G). We show that a coronoid G admits a 4-tiling if and only if G is regular. This fact enables us to prove that a coronoid G is regular if and only if G can be generated from a single hexagon by a series of normal additions plus corona condensations of mode A2. This result confirms Conjecture 6 stated in [9].

In-Situ Ligand Formation-Driven Preparation of a Heterometallic Metal–Organic Framework for Highly Selective Separation of Light Hydrocarbons and Efficient Mercury Adsorption

By means of the in situ ligand formation strategy and hard-soft acid-base (HSAB) theory, two types of independent In(COO)4 and Cu6S6 clusters were rationally embedded into the heterometallic metal-organic framework (HMOF) {[(CH3)2NH2]InCu4L4·xS}n (BUT-52). BUT-52 exhibits a three-dimensional (3D) anionic framework structure and has sulfur decorating the dumbbell-shaped cages with the external edges of 24 and 14 Å by the internal edges. Remarkably, because of the stronger charge-induced interactions between the charged MOF skeleton and the easily polarized C2 hydrocarbons (C2s), BUT-52 was used for C2s over CH4 and shows both high adsorption heats of C2s and selective separation abilities for C2s/CH4. Furthermore, BUT-52 also displays efficient mercury adsorption resulting from the stronger-binding ability beween the sulfur and the mercury and can remove 92% mercury from methanol solution even with the initial concentration as low as 100 mg/L. The results in this work indicate the feasibility of BUT-52 for the separation of light hydrocarbons and efficient adsorption/removal of mercury.

On the effective size of a non-Weyl graph

We show how to find the coefficient of the leading term of the resonance asymptotics using the method of pseudo-orbit expansion for quantum graphs which do not obey Weyl asymptotics. For a non-Weyl graph we develop a method to reduce the number of edges of a corresponding directed graph. Through this method we prove bounds on the above coefficient depending on the structure of the graph, for graphs with the same lengths of internal edges. We explicitly find the positions of the resolvent resonances.

Hierarchical organization of functional connectivity in the mouse brain: a complex network approach.

This paper represents a contribution to the study of the brain functional connectivity from the perspective of complex networks theory. More specifically, we apply graph theoretical analyses to provide evidence of the modular structure of the mouse brain and to shed light on its hierarchical organization. We propose a novel percolation analysis and we apply our approach to the analysis of a resting-state functional MRI data set from 41 mice. This approach reveals a robust hierarchical structure of modules persistent across different subjects. Importantly, we test this approach against a statistical benchmark (or null model) which constrains only the distributions of empirical correlations. Our results unambiguously show that the hierarchical character of the mouse brain modular structure is not trivially encoded into this lower-order constraint. Finally, we investigate the modular structure of the mouse brain by computing the Minimal Spanning Forest, a technique that identifies subnetworks characterized by the strongest internal correlations. This approach represents a faster alternative to other community detection methods and provides a means to rank modules on the basis of the strength of their internal edges.

Families of multiweights and pseudostars

Let T=(T,w) be a weighted finite tree with leaves 1,…,n. For any I:={i1,…,ik}⊂{1,…,n}, let DI(T) be the weight of the minimal subtree of T connecting i1,…,ik; the DI(T) are called k-weights of T. Given a family of real numbers parametrized by the k-subsets of {1,…,n}, {DI}I∈({1,…,n}k), we say that a weighted tree T=(T,w) with leaves 1,…,n realizes the family if DI(T)=DI for any I.In [14] Pachter and Speyer proved that, if 3≤k≤(n+1)/2 and {DI}I∈({1,…,n}k) is a family of positive real numbers, then there exists at most one positive-weighted essential tree T with leaves 1,…,n that realizes the family (where “essential” means that there are no vertices of degree 2). We say that a tree P is a pseudostar of kind (n,k) if the cardinality of the leaf set is n and any edge of P divides the leaf set into two sets such that at least one of them has cardinality ≥k. Here we show that, if 3≤k≤n−1 and {DI}I∈({1,…,n}k) is a family of real numbers realized by some weighted tree, then there is exactly one weighted essential pseudostar P=(P,w) of kind (n,k) with leaves 1,…,n and without internal edges of weight 0, that realizes the family; moreover we describe how any other weighted tree realizing the family can be obtained from P. Finally we examine the range of the total weight of the weighted trees realizing a fixed family.

The Influence of Running on Foot Posture and In-Shoe Plantar Pressures.

Running can be considered a high-impact practice, and most people practicing continuous running experience lower-limb injuries. The aim of this study was to determine the influence of 45 min of running on foot posture and plantar pressures. The sample comprised 116 healthy adults (92 men and 24 women) with no foot-related injuries. The mean ± SD age of the participants was 28.31 ± 6.01 years; body mass index, 23.45 ± 1.96; and training time, 11.02 ± 4.22 h/wk. Outcome measures were collected before and after 45 min of running at an average speed of 12 km/h, and included the Foot Posture Index (FPI) and a baropodometric analysis. The results show that foot posture can be modified after 45 min of running. The mean ± SD FPI changed from 6.15 ± 2.61 to 4.86 ± 2.65 (P < .001). Significant decreases in mean plantar pressures in the external, internal, rearfoot, and forefoot edges were found after 45 min of running. Peak plantar pressures in the forefoot decreased after running. The pressure-time integral decreased during the heel strike phase in the internal edge of the foot. In addition, a decrease was found in the pressure-time integral during the heel-off phase in the internal and rearfoot edges. The findings suggest that after 45 min of running, a pronated foot tends to change into a more neutral position, and decreased plantar pressures were found after the run.

Put Three and Three Together

Community detection has arisen as one of the most relevant topics in the field of graph data mining due to its applications in many fields such as biology, social networks, or network traffic analysis. Although the existing metrics used to quantify the quality of a community work well in general, under some circumstances, they fail at correctly capturing such notion. The main reason is that these metrics consider the internal community edges as a set, but ignore how these actually connect the vertices of the community. We propose the Weighted Community Clustering ( WCC ), which is a new community metric that takes the triangle instead of the edge as the minimal structural motif indicating the presence of a strong relation in a graph. We theoretically analyse WCC in depth and formally prove, by means of a set of properties, that the maximization of WCC guarantees communities with cohesion and structure. In addition, we propose Scalable Community Detection (SCD) , a community detection algorithm based on WCC , which is designed to be fast and scalable on SMP machines, showing experimentally that WCC correctly captures the concept of community in social networks using real datasets. Finally, using ground-truth data, we show that SCD provides better quality than the best disjoint community detection algorithms of the state of the art while performing faster.

Sampling and Counting 3-Orientations of Planar Triangulations

Given a planar triangulation, a 3-orientation is an orientation of the internal edges so all internal vertices have out-degree three. Each 3-orientation gives rise to a unique edge coloring known as a Schnyder wood that has proven powerful for various computing and combinatorics applications. We consider natural Markov chains for sampling uniformly from the set of 3-orientations. First, we study a “triangle-reversing” chain on the space of 3-orientations of a fixed triangulation that reverses the orientation of the edges around a triangle in each move. We show that, when restricted to planar triangulations of maximum degree six, this Markov chain is rapidly mixing and we can approximately count 3-orientations. Next, we construct a triangulation with high degree on which this Markov chain mixes slowly. Finally, we consider an “edge-flipping” chain on the larger state space consisting of 3-orientations of all planar triangulations on a fixed number of vertices. We prove that this chain is always rapidly mixing.

Clinical relevance of corrosion patterns attributed to inflammatory cell induced corrosion: A retrieval study

Event Abstract Back to Event Clinical relevance of corrosion patterns attributed to inflammatory cell induced corrosion: A retrieval study Anna Di Laura1*, Harry Hothi1*, Jay Meswania1*, Robert Whittaker1*, Danielle De Villiers1*, Gordon Blunn1, John Skinner1* and Alister Hart1* 1 University College London, Institute of Orthopaedics and Musculoskeletal Science (IOMS), United Kingdom Introduction: Cobalt Chromium (CoCr) alloys are the most commonly used materials in orthopaedics. In vitro studies have shown that human osteoclasts can corrode Stainless Steel and Titanium forming resorption pits that lead to the production of metal ions responsible for inflammatory reactions [1],[2]. Moreover, traces of cellular activities on metal orthopaedic explants have recently been reported as Inflammatory Cell-Induced (ICI) corrosion being the result of the cells sealing on the metal surfaces and releasing Reactive Oxygen Species through Fenton-like reactions [3]. We aimed to better understand the clinical relevance of this phenomenon. Our objectives were 1) to determine the extent of ICI corrosion patterns observed in a large cohort of retrieved hip implants,2) to give a 3Dimensional characterisation to the corroded regions, 3) to correlate our findings with clinical data. Materials: This was a retrieval study involving 100 failed hip implants received at our centre with metal-on-metal (MOM) bearings. We selected Durom modular heads [n=25], Durom resurfacing [n=25] as well as ASR modular heads [n=25] and ASR resurfacing [n=25] for inspection, so that we included both metallurgical features for Co-Cr alloys: wrought and cast. Methods: Initial screening included macroscopic and microscopic analysis of both cups and heads with the aid of a stereomicroscope (Leica) and a digital microscope (Keyence). A scanning electron microscope (Jeol) was used to perform detailed analysis of specific areas of interest highlighted from the initial visual screening. Second and Backscattered Electron Imaging ranging from low (4-5) to high (10-15) kV were used. Energy dispersive X-ray spectrometry (EDS) assessed the elemental composition and organic biocorrosion products on the implant surface. A 3D optical microscope (Bruker) showed both depth of pits and deposition of material in µm.The significance of any univariable associations between the presence of ICI corrosion and key implant and clinical variables were assessed using simple linear regression models. Results: 59 % of implants had evidence of corrosion patterns as described by Gilbert et al. Haziness, pits and streaks were visible on the: polished regions of the heads as well as on internal edges of cups; and machining marks of acetabular rims and head rims (Figure1). Higher magnification images showed crater-like spots surrounded by a frosted pattern of a ruffled topography. SEM images confirmed the presence of the features probably derived from different cellular mechanisms . Further confirmation of this was achieved by the optical profilometer. Scaled maps gave information about depth of pits that ranged from 0.5 to 3µm. There was a significant association between ICI corrosion and aseptic loosening for the ASR modular (r=-0.488, p=0.016) and the Durom modular (r=0.454, p=0.026) explants. EDS analysis revealed the presence of iron in correspondence of corroded regions, the element was only detectable in proximity of the corrosion patterns. Discussion: Corrosion patterns potentially attributable to cell induced corrosion were found on 59% of retrieved hips. There was no difference between cast and wrought microstructures but there was a correlation between implants revised due to aseptic loosening and presence of cellular corrosion. Iron is also in accordance with the presence of phagocytic cells on the metal surfaces due to Fenton-like reaction taking place. We recommend further work to determine the role and type of cells in the corrosion damage patterns observed. This may help understand which patient factors are involved in hip implant failure: and whether some patients more prone to failure of CoCr implants?

Leaders in communities of real-world networks

Community structures have important influence on the properties and dynamic characteristics of the complex networks. However, to the best of our knowledge, there is not much attention given to investigating the internal structure of communities in the literature. In this paper, we study community structures of more than twenty existing networks using ten commonly used community-detecting methods, and discovery that most communities have several leaders whose degrees are particularly large. We use statistical parameter, variance, to classify the communities as leader communities and self-organized communities. In a leader community, we defined the nodes with largest 10% degree as its leaders. In our experiences, when removing the leaders, on average community’s internal edges are reduced by more than 40% and inter-communities edges are reduced by more than 20%. In addition, community’s average clustering coefficient decreases. These facts suggest that the leaders play an important role in keeping communities denser and more clustered, and it is the leaders that are more likely to link to other communities. Moreover, similar results for several random networks are obtained, and a theoretical lower bound of the lost internal edges is given. Our study shed the light on the further understanding and application of the internal community structure in complex networks.

A TQFT of Turaev–Viro Type on Shaped Triangulations

A shaped triangulation is a finite triangulation of an oriented pseudo-three-manifold where each tetrahedron carries dihedral angles of an ideal hyperbolic tetrahedron. To each shaped triangulation, we associate a quantum partition function in the form of an absolutely convergent state integral which is invariant under shaped 3–2 Pachner moves and invariant with respect to shape gauge transformations generated by total dihedral angles around internal edges through the Neumann–Zagier Poisson bracket. Similarly to Turaev–Viro theory, the state variables live on edges of the triangulation but take their values on the whole real axis. The tetrahedral weight functions are composed of three hyperbolic gamma functions in a way that they enjoy a manifest tetrahedral symmetry. We conjecture that for shaped triangulations of closed three-manifolds, our partition function is twice the absolute value squared of the partition function of Techmuller TQFT defined by Andersen and Kashaev. This is similar to the known relationship between the Turaev–Viro and the Witten–Reshetikhin–Turaev invariants of three-manifolds. We also discuss interpretations of our construction in terms of three-dimensional supersymmetric field theories related to triangulated three-dimensional manifolds.