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Introduction: Knee dislocations are an uncommon complication following total knee arthroplasty (TKA). There are many causes of TKA dislocation; however, Wernicke-Korsakoff syndrome is one uncommon neurologic condition that increases the risk of TKA dislocation. Case Report: A 71-year-old male with presented to a local community hospital with knee pain due to advanced osteoarthritis of the knee and subsequently underwent an uncomplicated TKA with a cruciate retaining prosthesis. He eventually returned to the hospital due to infection, medical instability, chronic knee instability, and posterior tibiofemoral dislocation. A revision process was required. Throughout the course of management, the patient had altered mental status and was admitted to the intensive care unit. The first procedure involved removing the cruciate retaining prosthesis and replacing it with a static cement antibiotic spacer. This prosthesis was eventually dislocated through the tibia and a second procedure requiring the placement of an intercalary fusion was needed. The patient has not followed up after the hospital admission. Conclusion: Wernicke-Korsakoff Syndrome is an uncommon condition that affects lcoholics and complicates treatment with joint replacement surgery. Patients with Wernicke-Korsakoff syndrome provide a unique set of challenges that may require multiple surgeries and varying prostheses. Chronic posterior tibiofemoral dislocation is one specific complication that may affect the management of these patients. As orthopedic surgeons, it is important to consider alcohol use disorder and Wernicke-Korsakoff Syndrome when treating patients with total joint replacement.

Introduction: Synovial chondromatosis is a condition where the cells lining a joint form benign cartilaginous tumors. This benign cartilage metaplasia results in the formation of multiple intra-articular loose bodies within a joint. Case Report: This case is a 59-year-old female that presented with constant, severe left hip pain that was localized to the groin and began 2 years ago. There were severe limitation of hip flexion, extension, pain on internal rotation, and a half inch left leg shortening. Radiographs demonstrated multiple round opacities surrounding the left femoral neck. MRI showed numerous, small rounded intra-articular loose bodies, measuring about 5–6 mm each within the left hip joint. Surgical Technique: A lateral approach toward the hip was used to perform an osteotomy at the portion of the greater trochanter. The hip capsule was identified and an S-shaped incision was then made through the capsule. Repetitive hip dislocations allowed for improved visualization making further removal of the difficult fragments much easier. The capsule was closed and the osteotomy was reattached. Range of motion was found to be significantly improved compared to preoperatively. No further fixation was necessary and the patient’s subcutaneous tissue was closed in normal fashion. Conclusion: The technique used in our case involves a lateral approach with a trochanteric flip osteotomy to preserve the medial femoral circumflex artery and external rotators. This is similar to the approach described by Ganz in 2001 who used a posterior approach. Following the approach, the hip is then dislocated and exposed anteriorly with full visualization of the joint with a gap of about 11 cm between the femoral head and acetabulum. Surgical dislocation allows for the removal of difficult chondromas and osteophytes around the femoral head-and-neck junction. Multiple studies support the idea of surgical dislocation as an exceptional treatment method for SC.

We consider a class of holographic quantum error-correcting codes, built from perfect tensors in network configurations dual to Bruhat-Tits trees and their quotients by Schottky groups corresponding to BTZ black holes. The resulting holographic states can be constructed in the limit of infinite network size. We obtain a $p$-adic version of entropy which obeys a Ryu-Takayanagi like formula for bipartite entanglement of connected or disconnected regions, in both genus-zero and genus-one $p$-adic backgrounds, along with a Bekenstein-Hawking-type formula for black hole entropy. We prove entropy inequalities obeyed by such tensor networks, such as subadditivity, strong subadditivity, and monogamy of mutual information (which is always saturated). In addition, we construct infinite classes of perfect tensors directly from semiclassical states in phase spaces over finite fields, generalizing the CRSS algorithm, and give Hamiltonians exhibiting these as vacua., 5^3 pages, 20 figures

Recently, with the help of Parisi-Sourlas supersymmetry an intriguing relation was found expressing the four-point scalar conformal block of a (d-2)-dimensional CFT in terms of a five-term linear combination of blocks of a d-dimensional CFT, with constant coefficients. We extend this dimensional reduction relation to all higher-point scalar conformal blocks of arbitrary topology restricted to scalar exchanges. We show that the constant coefficients appearing in the finite term higher-point dimensional reduction obey an interesting factorization property allowing them to be determined in terms of certain graphical Feynman-like rules and the associated finite set of vertex and edge factors. Notably, these rules can be fully determined by considering the explicit power-series representation of just three particular conformal blocks: the four-point block, the five-point block and the six-point block of the so-called OPE/snowflake topology. In principle, this method can be applied to obtain the arbitrary-point dimensional reduction of conformal blocks with spinning exchanges as well. We also show how to systematically extend the dimensional reduction relation of conformal partial waves to higher-points., Comment: 29 pages + appendices, several figures

We conjecture a simple set of "Feynman rules" for constructing $n$-point global conformal blocks in any channel in $d$ spacetime dimensions, for external and exchanged scalar operators for arbitrary $n$ and $d$. The vertex factors are given in terms of Lauricella hypergeometric functions of one, two or three variables, and the Feynman rules furnish an explicit power-series expansion in powers of cross-ratios. These rules are conjectured based on previously known results in the literature, which include four-, five- and six-point examples as well as the $n$-point comb channel blocks. We prove these rules for all previously known cases, as well as for a seven-point block in a new topology and the even-point blocks in the "OPE channel." The proof relies on holographic methods, notably the Feynman rules for Mellin amplitudes of tree-level AdS diagrams in a scalar effective field theory, and is easily applicable to any particular choice of a conformal block., Comment: 59 pages + appendices, several figures

Three related analyses of $\phi^4$ theory with $O(N)$ symmetry are presented. In the first, we review the $O(N)$ model over the $p$-adic numbers and the discrete renormalization group transformations which can be understood as spin blocking in an ultrametric context. We demonstrate the existence of a Wilson-Fisher fixed point using an $\epsilon$ expansion, and we show how to obtain leading order results for the anomalous dimensions of low dimension operators near the fixed point. Along the way, we note an important aspect of ultrametric field theories, which is a non-renormalization theorem for kinetic terms. In the second analysis, we employ large $N$ methods to establish formulas for anomalous dimensions which are valid equally for field theories over the $p$-adic numbers and field theories on $\mathbb{R}^n$. Results for anomalous dimensions agree between the first and second analyses when they can be meaningfully compared. In the third analysis, we consider higher derivative versions of the $O(N)$ model on $\mathbb{R}^n$, the simplest of which has been studied in connection with spatially modulated phases. Our general formula for anomalous dimensions can still be applied. Analogies with two-derivative theories hint at the existence of some interesting unconventional field theories in four real Euclidean dimensions., Comment: 44 pages, 8 figures

We construct a $p$-adic analog to AdS/CFT, where an unramified extension of the $p$-adic numbers replaces Euclidean space as the boundary and a version of the Bruhat-Tits tree replaces the bulk. Correlation functions are computed in the simple case of a single massive scalar in the bulk, with results that are strikingly similar to ordinary holographic correlation functions when expressed in terms of local zeta functions. We give some brief discussion of the geometry of $p$-adic chordal distance and of Wilson loops. Our presentation includes an introduction to $p$-adic numbers., Comment: 53 pages, 6 figures. v2: Improved discussion of normalizations and chordal distance

Conformal blocks play a central role in CFTs as the basic, theory-independent building blocks. However, only limited results are available concerning multipoint blocks associated with the global conformal group. In this paper, we systematically work out the $d$-dimensional $n$-point global conformal blocks (for arbitrary $d$ and $n$) for external and exchanged scalar operators in the so-called comb channel. We use kinematic aspects of holography and previously worked out higher-point AdS propagator identities to first obtain the geodesic diagram representation for the $(n+2)$-point block. Subsequently, upon taking a particular double-OPE limit, we obtain an explicit power series expansion for the $n$-point block expressed in terms of powers of conformal cross-ratios. Interestingly, the expansion coefficient is written entirely in terms of Pochhammer symbols and $(n-4)$ factors of the generalized hypergeometric function ${}_3F_2$, for which we provide a holographic explanation. This generalizes the results previously obtained in the literature for $n=4, 5$. We verify the results explicitly in embedding space using conformal Casimir equations., Comment: 35 pages + appendices + references, several figures. Mathematica notebook containing the main result included as an ancillary file

Introduction: Palatal rugae are irregular and nonidentical mucosal elevations seen on the anterior third of palate. They are arranged in transverse direction on either side of the median palatine raphe (MPR) and are protected from high temperature and trauma because of their rational position in the oral cavity. Their number and patterns are not uniform in all the individuals, and they appear to vary in different population subsets. The study of palatal rugae is termed as “Rugoscopy” or “Palatoscopy”, and it finds its application in various fields such as anthropology, orthodontics, forensic sciences; including forensic odonto-stomatology. Aim: The aim of this study was to evaluate the quantitative and qualitative parameters of palatal rugae using pre-orthodontic study models of Gujarati samples. Objectives: (1) To identify the predominant palatal arch forms in the study samples. (2) To evaluate and correlate the rugae count in both male and female samples with the different palatal arch forms. (3) To assess the symmetry and/or asymmetry in rugae count between the right and left side. (4) To analyze and correlate the qualitative characters such as size, shape, direction, and unification in male and female study samples. Materials and Methods: One hundred pre-orthodontic maxillary dental stone casts of patients with an age range of 17–25 years were selected. The outlines of the rugae were traced using microtip graphite pencil and examined using magnifying glass for different patterns. The quantity and quality of rugae patterns were recorded according to Thomas et al. classification and the data were statistically analyzed by the statistician using SPSS program. Results: Overall, 962 rugae were observed in the study sample. The mean rugae count was 9.86 in males and 9.38 in females. The left side rugae count was more than the right side in both the sexes and it was not statistically significant. Fifty-six percent of the samples showed asymmetry in rugae count between the right and left. Class B palatal arch form was the most common type in the study samples. The number of primary rugae count was more in both the sexes. The distribution of straight (40.2%) and curved (40.4%) types of rugae were almost equal in males but in females, the straight rugae pattern (42.2%) was more than the curved (36.9%), followed by wavy and circular. Of 962 rugae, 36.4% were of horizontal type followed by forward (33.4%) and backward (29.2%). About 1 % of rugae showed perpendicular pattern and only 9.25% showed unification pattern and the divergent type of unification was more common than the convergent type. Conclusion: There is no gender discrimination in relation to any of the metric or non-metric parameters of the palatal rugae in this study samples. No two samples showed similarity in the distribution of palatal rugae patterns. The straight and horizontal rugae distributions were predominant in our Gujarati Study samples.

In this work, we formulate a set of rules for writing down $p$-adic Mellin amplitudes at tree-level. The rules lead to closed-form expressions for Mellin amplitudes for arbitrary scalar bulk diagrams. The prescription is recursive in nature, with two different physical interpretations: one as a recursion on the number of internal lines in the diagram, and the other as reminiscent of on-shell BCFW recursion for flat-space amplitudes, especially when viewed in auxiliary momentum space. The prescriptions are proven in full generality, and their close connection with Feynman rules for real Mellin amplitudes is explained. We also show that the integrands in the Mellin-Barnes representation of both real and $p$-adic Mellin amplitudes, the so-called pre-amplitudes, can be constructed according to virtually identical rules, and that these pre-amplitudes themselves may be re-expressed as products of particular Mellin amplitudes with complexified conformal dimensions., 45 pages + appendices, several figures

Melonic field theories are defined over the p-adic numbers with the help of a sign character. Our construction works over the reals as well as the p-adics, and it includes the fermionic and bosonic Klebanov-Tarnopolsky models as special cases; depending on the sign character, the symmetry group of the field theory can be either orthogonal or symplectic. Analysis of the Schwinger-Dyson equation for the two-point function in the leading melonic limit shows that power law scaling behavior in the infrared arises for fermionic theories when the sign character is non-trivial, and for bosonic theories when the sign character is trivial. In certain cases, the Schwinger-Dyson equation can be solved exactly using a quartic polynomial equation, and the solution interpolates between the ultraviolet scaling controlled by the spectral parameter and the universal infrared scaling. As a by-product of our analysis, we see that melonic field theories defined over the real numbers can be modified by replacing the time derivative by a bilocal kinetic term with a continuously variable spectral parameter. The infrared scaling of the resulting two-point function is universal, independent of the spectral parameter of the ultraviolet theory.

We formulate a Euclidean theory of edge length dynamics based on a notion of Ricci curvature on graphs with variable edge lengths. In order to write an explicit form for the discrete analog of the Einstein-Hilbert action, we require that the graph should either be a tree or that all its cycles should be sufficiently long. The infinite regular tree with all edge lengths equal is an example of a graph with constant negative curvature, providing a connection with $p$-adic AdS/CFT, where such a tree takes the place of anti-de Sitter space. We compute simple correlators of the operator holographically dual to edge length fluctuations. This operator has dimension equal to the dimension of the boundary, and it has some features in common with the stress tensor., Comment: 42 pages, 6 figures

Geodesic bulk diagrams were recently shown to be the geometric objects which compute global conformal blocks. We show that this duality continues to hold in $p$-adic AdS/CFT, where the bulk is replaced by the Bruhat-Tits tree, an infinite regular graph with no cycles, and the boundary is described by $p$-adic numbers, rather than reals. We apply the duality to evaluate the four-point function of scalar operators of generic dimensions using tree-level bulk diagrams. Relative to standard results from the literature, we find intriguing similarities as well as significant simplifications. Notably, all derivatives disappear in the conformal block decomposition of the four-point function. On the other hand, numerical coefficients in the four-point function as well as the structure constants take surprisingly universal forms, applicable to both the reals and the $p$-adics when expressed in terms of local zeta functions. Finally, we present a minimal bulk action with nearest neighbor interactions on the Bruhat-Tits tree, which reproduces the two-, three-, and four-point functions of a free boundary theory., 28 pages, 5 figures. v2: Added reference, appendix on computational details

We present new exact solutions describing motions of closed segmented strings in $AdS_3$ in terms of elliptic functions. The existence of analytic expressions is due to the integrability of the classical equations of motion, which in our examples reduce to instances of the McMillan map. We also obtain a discrete evolution rule for the motion in $AdS_3$ of arbitrary bound states of fundamental strings and D1-branes in the test approximation., 18 pages

We study pairs of co-axial vortex rings starting from the action for a classical bosonic string in a three-form background. We complete earlier work on the phase diagram of classical orbits by explicitly considering the case where the circulations of the two vortex rings are equal and opposite. We then go on to study perturbations, focusing on cases where the relevant four-dimensional transfer matrix splits into two-dimensional blocks. When the circulations of the rings have the same sign, instabilities are mostly limited to wavelengths smaller than a dynamically generated length scale at which single-ring instabilities occur. When the circulations have the opposite sign, larger wavelength instabilities can occur., 62 pages, 21 figures

We initiate a study of correlation functions of gauge-invariant operators in N=4 super Yang-Mills theory using the light-cone superspace formalism. Our primary aim is to develop efficient methods to compute perturbative corrections to correlation functions. This analysis also allows us to examine potential subtleties which may arise when calculating off-shell quantities in light-cone gauge. We comment on the intriguing possibility that the manifest N=4 supersymmetry in this approach may allow for a compact description of entire multiplets and their correlation functions., Comment: 35 pages, several figures

We derive a manifestly MHV Lagrangian for the N=4 supersymmetric Yang-Mills theory in light-cone superspace. This is achieved by constructing a canonical redefinition which maps the N=4 superfield and its conjugate to a new pair of superfields. In terms of these new superfields the N=4 Lagrangian takes a (non-polynomial) manifestly MHV form, containing vertices involving two superfields of negative helicity and an arbitrary number of superfields of positive helicity. We also discuss constraints satisfied by the new superfields, which ensure that they describe the correct degrees of freedom in the N=4 supermultiplet. We test our derivation by showing that an expansion of our superspace Lagrangian in component fields reproduces the correct gluon MHV vertices.

We treat string propagation and interaction in the presence of a background Neveu–Schwarz three-form field strength, suitable for describing vortex rings in a superfluid or low-viscosity normal fluid. A circular vortex ring exhibits instabilities which have been recognized for many years, but whose precise boundaries we determine for the first time analytically in the small core limit. Two circular vortices colliding head-on exhibit stronger instabilities which cause splitting into many small vortices at late times. We provide an approximate analytic treatment of these instabilities and show that the most unstable wavelength is parametrically larger than a dynamically generated length scale which in many hydrodynamic systems is close to the cutoff. We also summarize how the string construction we discuss can be derived from the Gross–Pitaevskii Lagrangian, and also how it compares to the action for giant gravitons.