In this manuscript we develop the theory of poset pinball, a combinatorial game recently introduced by Harada and Tymoczko for the study of the equivariant cohomology rings of GKM-compatible subspaces of GKM spaces. Harada and Tymoczko also prove that in certain circumstances, a successful outcome of Betti poset pinball yields a module basis for the equivariant cohomology ring of the GKM-compatible subspace. Our main contributions are twofold. First we construct an algorithm (which we call the dimension pair algorithm) which yields the result of a successful outcome of Betti poset pinball for any type A regular nilpotent Hessenberg and any type A nilpotent Springer variety, considered as GKM-compatible subspaces of the flag variety Fℓags(C n ). The definition of the algorithm is motivated by a correspondence between Hessenberg affine cells and certain Schubert polynomials which we learned from Erik Insko. Second, in the special case of the type A regular nilpotent Hessenberg varieties specified by the Hessenberg function h(1) = h(2) = 3 and h(i) = i + 1 for 3 ≤ i ≤ n − 1 and h(n) = n, we prove that the pinball result coming from the dimension pair algorithm is posetupper-triangular; by results of Harada and Tymoczko this implies the corresponding equivariant cohomology classes form a H * S 1 (pt)-module basis for the S 1 -equivariant cohomology ring of the Hessenberg variety.
We prove a Giambelli formula for the Peterson Schubert classes in the S 1 -equivariant cohomology ring of a type A Peterson variety. The proof uses the Monk formula for the equivariant structure constants for the Peterson Schubert classes derived by Harada and Tymoczko. In addition, we give proofs of two facts observed by H. Naruse: firstly, that some constants that appear in the multiplicative structure of the S 1 -equivariant cohomology of Peterson varieties are Stirling numbers of the second kind, and secondly, that the Peterson Schubert classes satisfy a stability property in a sense analogous to the stability of the classical equivariant Schubert classes in the T -equivariant cohomology of the flag variety.
Extraskeletal para-articular osteochondromas of the infrapatellar fat pad are unique soft-tissue tumors whose etiology and clinical history remain poorly understood. We report three cases and a systematic review of the literature. Three females, aged 47, 54, and 70 years, presented with pain and a parapatellar knee mass. All three underwent marginal excision with no complications and no recurrence. In the literature, 32 reports describing 42 cases were identified. Mean age at presentation was 51.1 years (range: 12-75). There were 25 females and 20 males. Seven patients (15.6%) had a history of antecedent trauma. Mean duration of presenting symptoms was 63.9 months (range: 2-300). All patients except for one underwent open excision. Mean follow-up was 14.9 months (range: 3-96). There were no reports of recurrence or malignant transformation. Para-articular extraskeletal osteochondromas of the infrapatellar fat pad have a benign clinical history regardless of whether they are managed by arthroscopic or open marginal excision.
There is evidence that the use of ultrasound-guided regional anesthesia increases the efficacy of peripheral nerve blocks and improves safety while allowing administration of lower volumes of local anesthetics. 1 Onset of the block is also faster, possibly because of visualization of the target nerve in real time and injection of local anesthetic closer to the nerve structures. 2,3 It is logical to hypothesize that these advantages may reduce complications such as nerve injury and local anesthesia systemic toxicity (LAST). We report a case of LAST while performing an ultrasound-guided axillary block that was initially diagnosed by the presence of symptoms of local anesthetic toxicity. The patient provided consent for the publication of this case report.A 63-yr-old woman, American Society of Anesthesiologists' physical status III, presented for a partial amputation of her right middle finger. An axillary block was recommended to her as an appropriate procedure. In the block room, standard monitoring was established, oxygen was applied by nasal prongs at 3 LÁmin -1 , and sedation was given with midazolam 1 mg iv. A 12 MHz linear ultrasound transducer (GE LOGIQ e, Wauwatosa, WI, USA) was placed at the deltopectoral groove. Next, the cross section of the axillary artery and the nerves surrounding it were identified. Under sterile conditions, 1% lidocaine 3 mL was applied to the skin and subcutaneous tissue. Using in-plane visualization, a 5-cm 21G EchoStim Ò needle (Hakko Ò Medical, Japan) connected to a nerve stimulator was directed to the six o'clock position of the artery. After confirmation with neurostimulation (wrist extension that disappeared at 0.3 mA) and negative aspiration, 5% dextrose 2 mL was injected and showed adequate spread around the radial nerve. After negative blood aspiration every 5 mL, 2% lidocaine was injected slowly with appropriate visualization of the spread of the injectate. When a volume of 13 mL was reached, the patient complained of numbness in her lips, a metallic taste in her mouth, and a sensation of fainting. At that point, the injection was interrupted, 100% oxygen via an Ambu Ò face mask was given, and midazolam 2 mg iv was administered. The symptoms resolved after one minute, and the patient was transferred to the operating room where the scheduled procedure was completed. A tourniquet was used and an additional 2% lidocaine 3 mL was needed in the interdigital area. The patient was transferred to the recovery room hemodynamically stable.After surgery, the ultrasound video was reviewed in detail. In the analysis (Figure, Panel A), the needle appeared to be posterolateral to the axillary artery; however, upon closer inspection, the needle tip could be seen as indenting a small anechoic structure posterior to the artery. In the next frame and just before the appearance of LAST symptoms ( Figure, Panel B), local anesthetic spread could be seen as a hypoechoic image posterior to the artery. A portion of local anesthetic was likely deposited into a small vessel characterized by the an...
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