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Background: It is undetermined which factors predict return to work after arthroscopic rotator cuff repair. Purpose: To identify which factors predicted return to work at any level and return to preinjury levels of work 6 months after arthroscopic rotator cuff repair. Study Design: Case-control study; Level of evidence, 3. Methods: Multiple logistic regression analysis of prospectively collected descriptive, preinjury, preoperative, and intraoperative data from 1502 consecutive primary arthroscopic rotator cuff repairs, performed by a single surgeon, was performed to identify independent predictors of return to work at 6 months postoperatively. Results: Six months after arthroscopic rotator cuff repair, 76% of patients had returned to work, and 40% had returned to preinjury levels of work. Return to work at 6 months was likely if patients were still working after their injuries but before surgery (Wald statistic [W] = 55, P < .0001), were stronger in internal rotation preoperatively (W = 8, P = .004), had full-thickness tears (W = 9, P = .002), and were female (W = 5, P = .030). Patients who continued working postinjury but presurgery were 1.6 times more likely to return to work at any level at 6 months compared to patients who were not working ( P < .0001). Patients who had a less strenuous preinjury level of work (W = 173, P < .0001), worked at a mild to moderate level post injury but presurgery, had greater preoperative behind-the-back lift-off strength (W = 8, P = .004), and had less preoperative passive external rotation range of motion (W = 5, P = .034) were more likely to return to preinjury levels of work at 6 months postoperatively. Specifically, patients who worked at a mild to moderate level postinjury but presurgery were 2.5 times more likely to return to work than patients who were not working, or who were working strenuously postinjury but presurgery ( p < 0.0001). Patients who nominated their preinjury level of work as “light” were 11 times more likely to return to preinjury levels of work at 6 months compared to those who nominated it as “strenuous” ( P < .0001). Conclusion: Six months after rotator cuff repair, patients who continued to work after injury but presurgery were the most likely to return to work at any level, and patients who had less strenuous preinjury levels of work were the most likely to return to their preinjury levels of work. Greater preoperative subscapularis strength independently predicted return to work at any level and to preinjury levels.

Background: Superior capsule reconstruction (SCR) is an option for the treatment of massive, irreparable rotator cuff tears. However, which materials yield the strongest constructs remains undetermined. Purposes: We sought to investigate whether SCR with polytetrafluoroethylene (PTFE) or human dermal allograft (HDA), 2 or 3 glenoid anchors, and suture or minitape resulted in better failure load properties at the patch-glenoid interface. Methods: We conducted a biomechanical study in 30 glenoid-sided SCR repairs in Sawbones models divided into 5 groups. Each was pulled to failure to assess mode of failure, peak load (N), stiffness (N/mm), yield load (N), peak energy (N m), and ultimate energy (N m). The 5 groups were as follows: group 1—PTFE, 2 anchors, and suture; group 2—PTFE, 2 anchors, and minitape; group 3—HDA, 2 anchors, and suture; group 4—HDA, 2 anchors, and minitape; group 5—PTFE, 3 anchors, and minitape. Results: Repairs failed by button-holing of suture/minitape. Group 5 had greater peak load, stiffness, yield load, and peak energy (384 ± 62 N; 24 ± 3 N/mm; 343 ± 42 N; 4 ± 2 N m) than group 3 (226 ± 67 N; 16 ± 4 N/mm; 194 ± 74 N; 2 ± 1 N m) or group 4 (274 ± 62 N; 17 ± 4 N/mm; 244 ± 50 N; 2 ± 1 N m) and greater ultimate energy (8 ± 3 N m) than all other groups. Conclusions: This biomechanical study of SCR repairs in Sawbones models found that yield load was greater in PTFE than HDA, 3 anchors were better than 2, and minitape was no better than suture.

In $\mathbb{Z}^d$ with $d\ge 5$, we consider the time constant $\rho_u$ associated to the chemical distance in random interlacements at low intensity $u \ll 1$. We prove an upper bound of order $u^{-1/2}$ and a lower bound of order $u^{-1/2+\varepsilon}$. The upper bound agrees with the conjectured scale in which $u^{1/2}\rho_u$ converges to a constant multiple of the Euclidean norm, as $u\to 0$. Along the proof, we obtain a local lower bound on the chemical distance between the boundaries of two concentric boxes, which might be of independent interest. For both upper and lower bounds, the paper employs probabilistic bounds holding as $u\to 0$; these bounds can be relevant in future studies of the low-intensity geometry., Comment: 39 pages, 8 figures. Several corrections after a major revision

To prospectively compare the effectiveness of three methods for self-assisted shoulder reduction demonstrated using a smartphone video link. Anterior shoulder dislocation is very common among young adults. Patients often seek medical assistance in the emergency department to reduce their shoulder. Many techniques for shoulder reduction had been described, some of which do not require professional assistance and can be performed by patients themselves. Patients admitted with anterior shoulder dislocation were randomized to either the Stimson, Milch or the Boss–Holtzach–Matter technique. Each patient was given a link to watch a short instructional video on his smartphone and instructed to attempt self-reduction. Success of the reduction, pain level, patient satisfaction and complications were recorded. The study cohort consisted of 58 patients (mean age was 31.6 (18–66, median = 27), 82% males, 88% right hand dominant). Success rate using Boss–Holtzach–Matter (10 of 19, 53%) and self-assisted Milch (11 of 20, 55%) were significantly higher than with the self-assisted Stimson method (3 of 19, 16%), p

It is undetermined how effective superior capsule/capsular reconstruction (SCR) is, and which factors influence clinical outcomes.(1) To identify which factors influence outcomes in SCR, (2) to evaluate the effect of graft integrity on clinical outcomes, and (3) to compare SCR to other procedures for irreparable rotator cuff tears.PubMed and EMBASE databases were searched for clinical SCR studies. Data on specific factors that influenced outcomes, that compared outcomes between intact/torn graft groups, or compared SCR to alternative treatments for irreparable tears were extracted by two investigators. Random-effects meta-analysis was performed to compare outcomes between intact vs torn SCR grafts.394 articles were identified. 100 full-text articles were screened. 13 studies were included for scoping review. Eight studies were meta-analyzed. Better clinical scores were found in younger patients, with intact/repairable subscapularis, without acetabulization/arthritis, who played sports. In patients with irreparable tears without arthritis, SCR produced similar clinical scores at 2 years as shoulder arthroplasty and partial infraspinatus repair, and greater improvements in ASES and Constant scores than latissimus dorsi tendon transfer. Intact grafts produced better VAS (mean difference [MD] = 0.97, 95% confidence interval [-1.45-0.50],Patients who underwent SCR for irreparable rotator cuff tears were more likely to have better clinical outcomes if they were younger, had intact/repairable subscapularis, without acetabulization/arthritis, played sports and had intact grafts.

Background: Superior capsular reconstruction (SCR) for massive, irreparable rotator cuff tears involves anchoring a graft between the superior glenoid and the greater tuberosity of the humerus. Optimizing the graft size is important. We aimed (1) to evaluate the reliability of plain film radiography in determining graft size for SCR and (2) to create a database to help predict future graft sizes. Methods: An inter- and intra-rater reliability trial was conducted on 10 and 6 subjects with healthy shoulders, respectively, using plain film radiography to measure the distance between the superior glenoid and the supraspinatus footprint. The subjects were positioned upright with an abduction pillow modified to hold the shoulder at 30° abduction and 45° external rotation, afterwhich a true antero-posterior shoulder radiograph was captured. Thirty subjects were recruited for the database and grouped using the aforementioned protocol. Results: The inter-rater and intra-rater trial agreement was excellent, with intraclass correlation coefficients of 0.94 (95% CI) and 0.76 (95% CI), respectively. Three medio-lateral patch sizes, of 33 mm, 38 mm, and 47 mm, were proposed based on the protocol in 30 subjects. Conclusions: Plain film radiography demonstrated excellent reliability in measuring the distance between the superior glenoid and the supraspinatus footprint. Three ordinal patch sizes are proposed.

To compare ultrasound examination to false profile radiographs in identification and classification of AIIS morphology. The study hypothesis stated that sonographic imaging of the AIIS correlates well to AIIS morphology seen on false profile radiographs. Fifty-three hips in 30 consecutive patients met the inclusion criteria. A single, fellowship trained, orthopedic surgeon performed an ultrasound on all of the patients to evaluate the AIIS morphology. The patients underwent standing false profile radiographs. The US and radiographic images were independently reviewed and classified according to Hetsroni classification of AIIS morphology by two senior, fellowship trained, orthopedic surgeons. Agreement between the two raters was calculated for each imaging modality (inter-rater agreement) as well as the agreement between the rating in each modality by the same rater (“inter-method” agreement). The agreement between the raters (inter-rater agreement) for morphologic evaluation of the AIIS by means of FP view was 88.8% (p

We present a homogenization theorem for isotropically-distributed point defects, by considering a sequence of manifolds with increasingly dense point defects. The loci of the defects are chosen randomly according to a weighted Poisson point process, making it a continuous version of the first passage percolation model. We show that the sequence of manifolds converges to a smooth Riemannian manifold, while the Levi-Civita connections converge to a non-metric connection on the limit manifold. Thus, we obtain rigorously the emergence of a non-metricity tensor, which was postulated in the literature to represent continuous distribution of point defects.

We present a simple and versatile method for deriving (an)isotropic local laws for general random matrices constructed from independent random variables. Our method is applicable to mean-field random matrices, where all independent variables have comparable variances. It is entirely insensitive to the expectation of the matrix. In this paper we focus on the probabilistic part of the proof -- the derivation of the self-consistent equations. As a concrete application, we settle in complete generality the local law for Wigner matrices with arbitrary expectation.

We consider Diffusion Limited Aggregation (DLA) in a two-dimensional wedge. We prove that if the angle of the wedge is smaller than $��/4$, there is some $a>2$ such that almost surely, for all $R$ large enough, after time $R^a$ all new particles attached to the DLA will be at distance larger than $R$ from the origin. This means that DLA stabilizes in growing balls, thus allowing a definition of the infinite DLA in a wedge via a finite time process., 22 pages, 4 figures

We consider the unique infinite connected component of supercritical bond percolation on the square lattice and study the geometric properties of isoperimetric sets, i.e., sets with minimal boundary for a given volume. For almost every realization of the infinite connected component we prove that, as the volume of the isoperimetric set tends to infinity, its asymptotic shape can be characterized by an isoperimetric problem in the plane with respect to a particular norm. As an application we then show that the anchored isoperimetric profile with respect to a given point as well as the Cheeger constant of the giant component in finite boxes scale to deterministic quantities. This settles a conjecture of Itai Benjamini for the plane., 40 pages, 2 figs; version to appear in Commun. Pure Appl. Math

The calcaneus is the most frequently fractured tarsal bone. Compartment syndrome (CS) complicates fractures and other injuries and is most commonly described in association with the lower leg. The long-term sequelae of CS of the foot can include toe clawing, permanent loss of function, persistent pain, muscle atrophy, contracture, painful warts, weakness, and sensory disturbances. The incidence and clinical significance of untreated CS after calcaneal fractures were questioned. All compliant patients treated by us for a calcaneus fracture underwent a physical examination and medical interview: 47 (49 fractures) were included in the final cohort (36 males, 11 females, mean age 49 ± 14.5 years, mean follow-up 23 ± 16 months). Missed CS sequelae were diagnosed by the presence of claw toes and plantar sensory deficits. The functional outcome and pain at rest and during activity were scored. Five patients (10%) had missed CS, and their functional score was significantly lower than for those without CS (52 ± 21.5 versus 77.4 ± 22 for no CS, p < .05). All missed CS cases were diagnosed in patients with a Sanders type 3 or 4 fracture. Intra-articular fracture was a significant factor associated with developing CS sequelae (p = .045). Untreated CS can cause muscle and nerve injury and contribute to a poor functional outcome. Because CS is more likely to develop after highly comminuted intra-articular fractures, these patients warrant close monitoring for CS development. Early detection and treatment might result in fewer late disabling sequelae of this injury.

The theory of $k$-regular graphs is closely related to group theory. Every $k$-regular, bipartite graph is a Schreier graph with respect to some group $G$, a set of generators $S$ (depending only on $k$) and a subgroup $H$. The goal of this paper is to begin to develop such a framework for $k$-regular simplicial complexes of general dimension $d$. Our approach does not directly generalize the concept of a Schreier graph, but still presents an extensive family of $k$-regular simplicial complexes as quotients of one universal object: the $k$-regular $d$-dimensional arboreal complex, which is itself a simplicial complex originating in one specific group depending only on $d$ and $k$. Along the way we answer a question from [PR12] on the spectral gap of higher dimensional Laplacians and prove a high dimensional analogue of Leighton's graph covering theorem. This approach also suggests a random model for $k$-regular $d$-dimensional multicomplexes., 40 pages, 7 figures

Nous considerons un modele de marches aleatoires en milieu aleatoire ayant pour sommets un sous-ensemble aleatoire de ${\mathbb{Z} }^{d}$ et une probabilite de transition uniforme sur $2d$ points (les plus proches voisins dans chacune des directions des coordonnees). Nous prouvons que la vitesse de ce type de marches est presque surement zero, donnons une caracterisation partielle de transience et recurrence dans les differentes dimensions et prouvons un theoreme central limite (CLT) pour de telles marches sous une condition concernant la distance entre plus proches voisins.

In this work, we discuss certain ballistic random walks in random environments on $\mathbb{Z}^d$, and prove the equivalence between the static and dynamic points of view in dimension $d\geq4$. Using this equivalence, we also prove a version of a local limit theorem which relates the local behavior of the quenched and annealed measures of the random walk by a prefactor., Published at http://dx.doi.org/10.1214/15-AOP1038 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Random walks on a graph reflect many of its topological and spectral properties, such as connectedness, bipartiteness and spectral gap magnitude. In the first part of this paper we define a stochastic process on simplicial complexes of arbitrary dimension, which reflects in an analogue way the existence of higher dimensional homology, and the magnitude of the high-dimensional spectral gap originating in the works of Eckmann and Garland. The second part of the paper is devoted to infinite complexes. We present a generalization of Kesten's result on the spectrum of regular trees, and of the connection between return probabilities and spectral radius. We study the analogue of the Alon-Boppana theorem on spectral gaps, and exhibit a counterexample for its high-dimensional counterpart. We show, however, that under some assumptions the theorem does hold - for example, if the codimension-one skeletons of the complexes in question form a family of expanders. Our study suggests natural generalizations of many concepts from graph theory, such as amenability, recurrence/transience, and bipartiteness. We present some observations regarding these ideas, and several open questions.

We study nearest neighbor random walks in fixed environments of $\mathbb{Z}$ composed of two point types : $(\frac{1}{2},\frac{1}{2})$ and$(p,1-p)$ for $p>\frac{1}{2}$. We show that for every environmentwith density of $p$ drifts bounded by $\lambda$ we have $\limsup_{n\rightarrow\infty}\frac{X_n}{n}\leq (2p-1)\lambda$, where $X_n$ is a random walk in the environment. In addition up to some integereffect the environment which gives the greatest speed is given byequally spaced drifts.

In graph theory there are intimate connections between the expansion properties of a graph and the spectrum of its Laplacian. In this paper we define a notion of combinatorial expansion for simplicial complexes of general dimension, and prove that similar connections exist between the combinatorial expansion of a complex, and the spectrum of the high dimensional Laplacian defined by Eckmann. In particular, we present a Cheeger-type inequality, and a high-dimensional Expander Mixing Lemma. As a corollary, using the work of Pach, we obtain a connection between spectral properties of complexes and Gromov's notion of geometric overlap. Using the work of Gundert and Wagner, we give an estimate for the combinatorial expansion and geometric overlap of random Linial-Meshulam complexes.