Emergent Conformal Boundaries from Finite-Entanglement Scaling in Matrix Product States.

The use of finite entanglement scaling with matrix product states (MPS) has become a crucial tool for studying one-dimensional critical lattice theories, especially those with emergent conformal symmetry. We argue that finite entanglement introduces a relevant deformation in the critical theory. As a result, the bipartite entanglement Hamiltonian defined from the MPS can be understood as a boundary conformal field theory with a physical and an entanglement boundary. We are able to exploit the symmetry properties of the MPS to engineer the physical conformal boundary condition. The entanglement boundary, on the other hand, is related to the concrete lattice model and remains invariant under this relevant perturbation. Using critical lattice models described by the Ising, Potts, and free compact boson conformal field theories, we illustrate the influence of the symmetry and the relevant deformation on the conformal boundaries in the entanglement spectrum.

Extracting the Speed of Light from Matrix Product States.

We provide evidence that the spectrum of the local effective Hamiltonian and the transfer operator in infinite-system matrix product state simulations are identical up to a global rescaling factor, i.e., the speed of light of the system, when the underlying system is described by a 1+1 dimensional CFT. We provide arguments for this correspondence based on a path integral point of view. This observation turns out to yield very precise estimates for the speed of light in practice, confirming exact results to high precision where available, but also allowing us to finally determine the speed of light of the non-integrable, critical SU(2) Heisenberg chains with half-integer spin S>1/2 with unprecedented accuracy. We also show that the same technology applied to doped Hubbard ladders provides highly accurate velocities for a range of dopings. Combined with measurements of compressibilities we present new results for the Luttinger liquid parameter in the Luther-Emery regime of doped Hubbard ladders, outperforming earlier approaches based on the fitting of real-space correlation functions.

Dental and temporomandibular joint pathology of the red fox (Vulpes vulpes).

Skulls from 305 red foxes (Vulpes vulpes) were examined using predefined criteria to assess for the presence and severity of dental and temporomandibular joint (TMJ) pathology. Of the 305 specimens examined, 131 were male (42.9%), 103 were female (33.4%), 71 were of unknown sex (23.3%), 238 were adults (78.03%) and 67 were young adults (21.97%), with juveniles excluded from the study. Of a maximum of 12,810 possible teeth, 12,355 (96.5%) were present for examination, 72 (0.6%) were absent congenitally, 97 (0.8%) were acquired tooth loss and 280 (2.2%) were absent artefactually. Eight teeth (0.06%) in five specimens (1.6%) had abnormal tooth form and four (0.03%) supernumerary teeth were present across four (1.3%) specimens. Ten persistent deciduous teeth were present in seven (2.3%) specimens and six (0.05%) unerupted teeth were found in four (1.1%) specimens. Root number variation was present in 51 (0.4%) teeth, predominantly premolar teeth. Twenty-one (6.9%) specimens had lesions consistent with enamel hypoplasia and 42 (13.8%) showed root fenestrations in the maxillary alveolar bone. Periodontitis and attrition/abrasion were present in most specimens (56.7% and 96.1%, respectively). Three-hundred and eighty (3.1%) teeth were fractured, with the most common fracture type being root fractures. Eleven periapical lesions were found in nine (0.03%) specimens. Six-hundred and eight TMJs were evaluated and many specimens (11.5%) had evidence of low-grade TMJ osteoarthritis. Overall, these red foxes share similar dental pathology to other foxes, but had a higher prevalence of congenital tooth absence, persistent deciduous teeth, TMJ pathology and enamel hypoplasia.

Contrasting pseudocriticality in the classical two-dimensional Heisenberg and RP

Tensor-network methods are used to perform a comparative study of the two-dimensional classical Heisenberg and RP^{2} models. We demonstrate that uniform matrix product states (MPSs) with explicit SO(3) symmetry can probe correlation lengths up to O(10^{3}) sites accurately, and we study the scaling of entanglement entropy and universal features of MPS entanglement spectra. For the Heisenberg model, we find no signs of a finite-temperature phase transition, supporting the scenario of asymptotic freedom. For the RP^{2} model we observe an abrupt onset of scaling behavior, consistent with hints of a finite-temperature phase transition reported in previous studies. A careful analysis of the softening of the correlation length divergence, the scaling of the entanglement entropy, and the MPS entanglement spectra shows that our results are inconsistent with true criticality, but are rather in agreement with the scenario of a crossover to a pseudocritical region which exhibits strong signatures of nematic quasi-long-range order at length scales below the true correlation length. Our results reveal a fundamental difference in scaling behavior between the Heisenberg and RP^{2} models: Whereas the emergence of scaling in the former shifts to zero temperature if the bond dimension is increased, it occurs at a finite bond-dimension independent crossover temperature in the latter.

Dental and temporomandibular joint pathology of the Arctic fox (Vulpeslagopus).

Museum skull specimens from 224 Arctic foxes (Vulpes lagopus) were examined macroscopically using an established protocol for examination of mammalian skull specimens. Foxes were collected from coastal and island regions of Alaska, USA, except for two individuals. Collection years ranged from 1931 to 2016 with most specimens collected during the 1950s and 1960s. The study population comprised more females (n = 134, 59.8%) than males (n = 83, 37.0%) and individuals of unknown sex (n = 7, 3.1%). There were 108 (48.2%) young adults, 115 (51.3%) adults, and one (0.4%) individual of unknown age. A total of 8,891 teeth (94.5%) were available for examination. The most common types of pathology observed were periodontitis (n = 222, 99.1%), dental fractures (n = 175, 78.1%) and attrition/abrasion (n = 198, 88.4%). Periapical lesions (n = 12, 5.3%), temporomandibular joint (TMJ) osteoarthritis (n = 3, 1.3%) and root number variation (n = 5, 2.2%) were less common. Enamel hypoplasia was noted in eight foxes (3.6%), all of which were discovered on St. Matthew Island, Alaska, in 1963. As in other canid species, periodontitis, attrition/abrasion and tooth fractures are common in the Arctic fox, while TMJ pathology is rare. Loss of tooth crown substance probably reflects the influence of diet, interspecific and conspecific aggression and oral trauma due to trapping and hunting methods. The high prevalence of periodontitis is probably also due to the combined effects of diet, genetics and host immune reaction to oral bacteria.

Dental and temporomandibular joint pathology of the island fox (Urocyon littoralis).

Museum skull specimens from 318 island foxes (Urocyon littoralis) were examined macroscopically according to predefined criteria. The study population included males (n = 129, 40.6%), females (n = 93, 29.3%) and animals of unknown sex (n = 96, 30.2%), and comprised 182 (57.2%) adults, 118 (37.1%) young adults and 18 (5.7%) individuals of unknown age, with juveniles and neonates excluded. The number of teeth present for examination was 11,438 (85.6%) with 1918 (14.4%) absent artefactually, 4 (0.03%) absent congenitally and 243 (1.82%) lost ante mortem through acquired tooth loss. There were seven persistent deciduous teeth (0.05%) in three specimens and 11 supernumerary teeth (0.08%) in 10 specimens. Teeth with extra roots were found in 38 skulls (11.9%) with 0.48% of all teeth affected. Two (0.63%) specimens had one tooth with an abnormal form. Fifty-eight (18.2%) specimens had bone fenestrations. Of the alveoli examined, 5361 (46.9%) displayed bony changes suggestive of periodontitis, with 315 (99.1%) of skulls affected. Of the teeth available for examination in 310 specimens (97.5%), most (n = 6,040, 52.8%) had some degree of attrition or abrasion. Fractures affected 1217 (11.0%) of the teeth present in 266 specimens (83.6%). Twenty-three periapical lesions (0.20%) were present in 16 skulls (5.03%). Evidence of temporomandibular joint osteoarthritis was found in seven specimens (0.02%) on either the mandibular head of the condylar process or on the mandibular fossa of the temporal bone.

Successful Surgical Outcome of Feline Inductive Odontogenic Tumor in Three Cats.

BACKGROUND/AIM: A feline inductive odontogenic tumor (FIOT) is a rare type of tumor that is unique to young cats. CASE REPORT: Herein, we report on three cats (aged 6 months to 2.5 years) that had a bulging mass on the maxilla. On diagnostic imaging, cases 1 and 3 had bone expansion in the affected area, and all three cats were diagnosed with FIOT by histological examination. Maxillectomy and/or incisivectomy techniques were performed according to the tumor site with an intended surgical margin of 5 mm. To increase both precision and safety, a piezoelectric surgical instrument was used. The local advancement flaps were used to repair the surgical sites. The surgical outcomes were excellent, and there were no major complications related to the surgery or tumor recurrences during long-term follow-up (3-5 years) for any of the cats. CONCLUSION: The results from this study were excellent, which may have been due in part to the choice of the surgical instrument that allowed for the implementation of precise and accurate surgical excision and the tension-free flap method for preventing dehiscence of the surgical site.

Tensor Networks Can Resolve Fermi Surfaces.

We demonstrate that projected entangled-pair states are able to represent ground states of critical, fermionic systems exhibiting both 1d and 0d Fermi surfaces on a 2D lattice with an efficient scaling of the bond dimension. Extrapolating finite size results for the Gaussian restriction of fermionic projected entangled-pair states to the thermodynamic limit, the energy precision as a function of the bond dimension is found to improve as a power law, illustrating that an arbitrary precision can be obtained by increasing the bond dimension in a controlled manner. In this process, boundary conditions and system sizes have to be chosen carefully so that nonanalyticities of the Ansatz, rooted in its nontrivial topology, are avoided.

Scaling Hypothesis for Projected Entangled-Pair States.

We introduce a new paradigm for scaling simulations with projected entangled-pair states (PEPS) for critical strongly correlated systems, allowing for reliable extrapolations of PEPS data with relatively small bond dimensions D. The key ingredient consists of using the effective correlation length ξ for inducing a collapse of data points, f(D,χ)=f(ξ(D,χ)), for arbitrary values of D and the environment bond dimension χ. As such we circumvent the need for extrapolations in χ and can use many distinct data points for a fixed value of D. Here, we need that the PEPSs have been optimized using a fixed-χ gradient method, which can be achieved using a novel tensor-network algorithm for finding fixed points of 2D transfer matrices, or by using the formalism of backwards differentiation. We test our hypothesis on the critical 3D dimer model, the 3D classical Ising model, and the 2D quantum Heisenberg model.

Management of failed stainless steel implants in the oromaxillofacial region of dogs.

Management of complications of fracture fixation in the oromaxillofacial (OMF) region may present a diagnostic and therapeutic challenge. While titanium and stainless steel implants have been utilized in successful fracture fixation in the OMF region, the use of titanium implants is preferred due to the superior intrinsic properties of titanium. Nonetheless, stainless steel materials are still used due to their availability and familiarity. In the present methods report, we describe our approach to the management of failed stainless steel plates and screws used to treat traumatic injuries in the OMF region. Furthermore, we exemplify our approach with five dogs that exhibited complications of stainless steel implants in the OMF region and their subsequent management. In those cases, all failed implants were removed. Reconstruction with a combination of recombinant human bone morphogenetic protein-2 (rhBMP-2) and titanium implants was utilized in two cases while a mandibulectomy was performed in one case. Three cases required removal of the stainless-steel implant with no additional surgical therapy. We conclude that the success of treatment of failed stainless steel implants depends on the use of advanced imaging findings, appropriate antimicrobial therapy, as well as potentially regenerative reconstructive surgery.

Dental and Temporomandibular Joint Pathology of the Steller Sea Lion (Eumetopias jubatus).

Skulls from 112 Steller sea lions (Eumetopias jubatus) were examined according to predefined criteria. Of the specimens, 73 (65.2%) were from males, 29 (25.9%) from females and 10 (8.9%) were of unknown sex, with 50 adults (44.6%), 61 young adults (54.5%) and one of unknown age (0.9%). The number of teeth evaluated was 3,521. Adults had more acquired tooth loss than young adults (P <0.0001). A total of 1,660 teeth (47.1%) from 111 specimens (99.1%) had evidence of attrition or abrasion. Adults displayed more attrition or abrasion than young adults (P <0.0001). A total of 241 teeth (6.8%) from 47 specimens (42%) had tooth fractures. Adults had more fractured teeth than young adults (P <0.0001). Bony changes consistent with periodontitis affected 36.7% of teeth. Adults had more teeth affected by periodontitis than young adults (P <0.0001). Temporomandibular joint osteoarthritis lesions were found in 54 specimens (48.2%) with more in adults than in young adults (P <0.0001). Although the significance of our findings is unknown, the occurrence and severity of these lesions may play an important role in the morbidity and mortality of Steller sea lions.

Systematic Assessment of Mammalian Skull Specimens for Dental and Temporomandibular Joint Pathology.

Museum skull specimens represent a non-invasive, informative, and readily available means to study temporomandibular joint (TMJ) lesions, dental pathology, and anatomic variations in many mammalian species. Studying the teeth and jaws of an array of species can present a challenge requiring attention to detail and understanding of a species' normal anatomy. In the present article, a systematic and precise protocol for examining skull specimens is discussed that has been applied to a variety of mammals to define characteristic diseases in the oromaxillofacial region. The procedure outlined is simultaneously precise, repeatable, and adaptable to the highly differing skull and tooth shapes and anatomy across species. Specifically, specimens are examined for missing teeth, periodontal disease, endodontal disease, TMJ pathology, and anatomical variations. Results gleaned from research on museum specimens may reflect the natural history, health, and disease status of individuals and species. Furthermore, these data can inform ecological and conservation research efforts, as well as the care of captive individuals.

Craniomaxillofacial trauma in immature dogs-etiology, treatments, and outcomes.

Treatment of craniomaxillofacial (CMF) trauma in dogs often requires a multidisciplinary approach and a thorough understanding of the CMF anatomical structures involved. This retrospective study aimed to utilize computed tomography (CT) studies of immature dogs evaluated for CMF trauma and to describe common fracture locations, treatment modalities, and complications, as well as the fracture healing outcomes. The medical records and CT studies of 94 dogs under 1 year of age over a 13-year period were evaluated. The skeletal location of CMF fractures, as well as the severity of displacement and fragmentation of each fracture, was recorded. Case demographic data and trauma etiology were also recorded. Animal bites accounted for the majority of trauma (71.0%). The most likely bone or region to be fractured was the maxillary bones, followed by the molar region of the mandibles. Up to 37 bones or specific regions were fractured in any given patient, with an average of 8.8 ± 3.1 fractured bones or regions per dog. Rostral mandibular trauma was associated with intra-articular fractures of the temporomandibular joint (p = 0.016). Patients sustained concomitant injuries in 32% of the cases. Muzzle therapy was the main treatment performed for most dogs (53.2%), followed by soft tissue closure (47.9%) and selective dental extractions (27.6%). Healing complications were recorded in 71.6% of the dogs, with malocclusion being the most reported complication (55.2%), and associated with dentate mandibular jaw fractures (p = 0.05). The average number of complications per dog was 2.4. No statistically significant association was found between treatment modality and healing outcome. There was a positive correlation between the severity of fracture fragmentation and displacement and a negative healing outcome (all rho >0.7). Further treatment was required in 55.6% of the dogs. Additional dental extractions were performed in 77.7% of patients. Healing complications were common in the immature CMF trauma case. Thus, the need for a comprehensive assessment of the entire CMF region during the initial visit, as well as follow-up, preferably using CT or cone beam CT, is underscored.

Biomechanical evaluation of locking versus nonlocking 2.0-mm malleable L-miniplate fixation of simulated caudal mandibular fractures in cats.

OBJECTIVE: To evaluate the biomechanical properties of the mandibles of cats with experimentally created osteotomies simulating oblique ramus fractures, which were stabilized with malleable L-miniplates with either locking screws [locking construct (LC)] or nonlocking screws [nonlocking construct (NLC)], compared with those for intact mandibles. SAMPLES: 20 mandibles from 10 adult cat cadavers. PROCEDURES: A block study design was adopted to allocate the mandibles of each cadaver to 2 of the 3 test groups (LC, NLC, or intact mandible). Mandibles within each cadaver were allocated systematically to a test group. For mandibles assigned to an LC and an NLC, a complete oblique osteotomy was performed from the mid rostral aspect of the ramus in a caudoventral direction. All mandibles were loaded in a single-load-to-failure test through cantilever bending. Load and actuator displacement were recorded simultaneously. Mode of failure and radiographic evidence of damage to tooth roots and the mandibular canal were evaluated. Biomechanical properties were compared among the groups. RESULTS: No iatrogenic tooth root damage was evident, but all mandibles with an LC and an NLC had evidence of screw invasion into the mandibular canal. Plated mandibles had significantly less stiffness and bending moment than intact mandibles. Stiffness was not significantly different between the LC and the NLC; the NLC had a greater bending moment at failure than the LC. The pre-yield stiffness of plated mandibles decreased when the number of screw holes overlapping the mandibular canal increased. CLINICAL RELEVANCE: The use of a malleable L-miniplate in a caudal mandibular fracture model is feasible. Both the LC and the NLC were inferior mechanically to intact mandibles. Type of construct used did not affect the construct stiffness significantly in tested mandibles.

A Retrospective Study on Mandibular Reconstruction Following Excision of Canine Acanthomatous Ameloblastoma.

The successful excision of a locally invasive tumor such as canine acanthomatous ameloblastoma (CAA) typically results in a mandibular contour-derforming, critical-size defect that alters the jaw kinematics, and may affect the patient's quality of life. In this case series, we describe our experience using the regenerative approach of a titanium locking plate and compression resistant matrix infused with rhBMP-2 for the immediate or delayed reconstruction following mandibulectomy for the excision of mandibular CAA in 11 dogs. Surgical planning included computed tomography (CT), with and without contrast, in all cases, and 3D-printed models in four cases. Tumor-free surgical margins were achieved in all dogs. Clinical and diagnostic imaging follow-up (mean, 23.1 months) were performed in-person (11 cases) and with CT/cone-beam computed tomography in most cases, with standard radiography (3 cases) and telemedicine being utilized in 5 cases. At 2 weeks postoperatively, hard tissue was palpable at the defect. Follow-up imaging at 1 month postoperatively revealed evidence of bridging new bone with a heterogeneous appearance, that remodeled over 3-6 months to bone of a similar size, shape and trabecular pattern as native bone. Histological evaluation of regenerated bone was available in two cases, and was supportive of our clinical and imaging findings of normal remodeled bone. Clinically, all dogs returned to a normal lifestyle, rapidly resumed eating and drinking, and exhibited normal occlusion. Complications included wound dehiscence in one dog and self-limiting exuberant bone formation in two dogs. Tumor regrowth, failure of the implant or fracture of the regenerated bone were not observed. We conclude that the mandibular reconstruction using a regenerative approach is safe, feasible, and results in restoration of mandibular contour in dogs following segmental and bilateral rostral mandibulectomy for benign but invasive oral tumors such as CAA.

Critical Lattice Model for a Haagerup Conformal Field Theory.

We use the formalism of strange correlators to construct a critical classical lattice model in two dimensions with the Haagerup fusion category H_{3} as input data. We present compelling numerical evidence in the form of finite entanglement scaling to support a Haagerup conformal field theory (CFT) with central charge c=2. Generalized twisted CFT spectra are numerically obtained through exact diagonalization of the transfer matrix, and the conformal towers are separated in the spectra through their identification with the topological sectors. It is further argued that our model can be obtained through an orbifold procedure from a larger lattice model with input Z(H_{3}), which is the simplest modular tensor category that does not admit an algebraic construction. This provides a counterexample for the conjecture that all rational CFT can be constructed from standard methods.

Corrigendum: Craniomaxillofacial Trauma in Dogs-Part I: Fracture Location, Morphology and Etiology.

[This corrects the article DOI: 10.3389/fvets.2020.00241.].

Radiographic outcome of root canal treatment in dogs: 281 teeth in 204 dogs (2001-2018).

OBJECTIVE: To evaluate the radiographic outcome of root canal treatment (RCT) in dogs and compare outcomes with those reported for a previous study performed at the same institution in 2002. ANIMALS: 204 dogs representing 281 teeth that underwent RCT. PROCEDURES: The medical record database of a veterinary teaching hospital was searched to identify dogs that underwent RCT between 2001 and 2018. Only dogs that had undergone at least 1 radiographic recheck appointment a minimum of 50 days after RCT were included in the study. Dental radiographs were reviewed. Treatment was considered successful if the periapical periodontal ligament space was within reference limits and preexisting external inflammatory root resorption (EIRR), if present, had stabilized. Treatment was considered to show no evidence of failure (NEF) if preoperative EIRR had stabilized and any preoperative periapical lucency (PAL) remained the same or had decreased in size but had not completely resolved. Treatment was considered to have failed if EIRR or a PAL developed after RCT, if a preoperative PAL increased in size, or if preexisting EIRR progressed. RESULTS: Follow-up time ranged from 52 to 3,245 days (mean, 437 days). RCT was classified as successful for 199 (71%) teeth, NEF for 71 (25%) teeth, and failed for 11 (4%) teeth. CONCLUSIONS AND CLINICAL RELEVANCE: Results showed that almost 2 decades after RCT outcome in dogs was first evaluated, during which time numerous advances in dental materials and techniques had been made, the success rate of RCT was virtually unchanged.

Variational Optimization of Continuous Matrix Product States.

Just as matrix product states represent ground states of one-dimensional quantum spin systems faithfully, continuous matrix product states (cMPS) provide faithful representations of the vacuum of interacting field theories in one spatial dimension. Unlike the quantum spin case, however, for which the density matrix renormalization group and related matrix product state algorithms provide robust algorithms for optimizing the variational states, the optimization of cMPS for systems with inhomogeneous external potentials has been problematic. We resolve this problem by constructing a piecewise linear parameterization of the underlying matrix-valued functions, which enables the calculation of the exact reduced density matrices everywhere in the system by high-order Taylor expansions. This turns the variational cMPS problem into a variational algorithm from which both the energy and its backwards derivative can be calculated exactly and at a cost that scales as the cube of the bond dimension. We illustrate this by finding ground states of interacting bosons in external potentials and by calculating boundary or Casimir energy corrections of continuous many-body systems with open boundary conditions.