1/8 Doping Anomalies and Oxygen Vacancies in Underdoped Superconducting Cuprates

Measurements of thermal conductivity ($\kappa$) versus temperature and doping for several cuprate superconductors are discussed. Suppressed values of the normal-state $\kappa$ and the slope change in $\kappa$ at $T_c$, observed near 1/8 doping in both YBa$_2$Cu$_3$O$_{6+x}$ and Hg cuprates, are attributed to local lattice distortions and the suppression of the superconducting condensate, respectively. Both phenomena are proposed to arise from small domains of localized planar holes, presumably a manifestation of phase separation. It is suggested that the phase behavior of $\kappa$ reflects stripe dynamics and the 1/8 doping anomalies stripe pinning by oxygen-vacancy clusters.Comment: 6 pages, AIP 6"x9" format, 3 embedded postscript fig.s Proceedings of University of Miami Conference (HTS99), 7-13 Jan., 199

Which groups are amenable to proving exponent two for matrix multiplication?

The Cohn-Umans group-theoretic approach to matrix multiplication suggests embedding matrix multiplication into group algebra multiplication, and bounding $\omega$ in terms of the representation theory of the host group. This framework is general enough to capture the best known upper bounds on $\omega$ and is conjectured to be powerful enough to prove $\omega = 2$, although finding a suitable group and constructing such an embedding has remained elusive. Recently it was shown, by a generalization of the proof of the Cap Set Conjecture, that abelian groups of bounded exponent cannot prove $\omega = 2$ in this framework, which ruled out a family of potential constructions in the literature. In this paper we study nonabelian groups as potential hosts for an embedding. We prove two main results: (1) We show that a large class of nonabelian groups---nilpotent groups of bounded exponent satisfying a mild additional condition---cannot prove $\omega = 2$ in this framework. We do this by showing that the shrinkage rate of powers of the augmentation ideal is similar to the shrinkage rate of the number of functions over $(\mathbb{Z}/p\mathbb{Z})^n$ that are degree $d$ polynomials; our proof technique can be seen as a generalization of the polynomial method used to resolve the Cap Set Conjecture. (2) We show that symmetric groups $S_n$ cannot prove nontrivial bounds on $\omega$ when the embedding is via three Young subgroups---subgroups of the form $S_{k_1} \times S_{k_2} \times \dotsb \times S_{k_\ell}$---which is a natural strategy that includes all known constructions in $S_n$. By developing techniques for negative results in this paper, we hope to catalyze a fruitful interplay between the search for constructions proving bounds on $\omega$ and methods for ruling them out.Comment: 23 pages, 1 figur

Matrix Multiplication via Matrix Groups

In 2003, Cohn and Umans proposed a group-theoretic approach to bounding the exponent of matrix multiplication. Previous work within this approach ruled out certain families of groups as a route to obtaining ? = 2, while other families of groups remain potentially viable. In this paper we turn our attention to matrix groups, whose usefulness within this framework was relatively unexplored. We first show that groups of Lie type cannot prove ? = 2 within the group-theoretic approach. This is based on a representation-theoretic argument that identifies the second-smallest dimension of an irreducible representation of a group as a key parameter that determines its viability in this framework. Our proof builds on Gowers\u27 result concerning product-free sets in quasirandom groups. We then give another barrier that rules out certain natural matrix group constructions that make use of subgroups that are far from being self-normalizing. Our barrier results leave open several natural paths to obtain ? = 2 via matrix groups. To explore these routes we propose working in the continuous setting of Lie groups, in which we develop an analogous theory. Obtaining the analogue of ? = 2 in this potentially easier setting is a key challenge that represents an intermediate goal short of actually proving ? = 2. We give two constructions in the continuous setting, each of which evades one of our two barriers

Matrix multiplication via matrix groups

In 2003, Cohn and Umans proposed a group-theoretic approach to bounding the exponent of matrix multiplication. Previous work within this approach ruled out certain families of groups as a route to obtaining $\omega = 2$, while other families of groups remain potentially viable. In this paper we turn our attention to matrix groups, whose usefulness within this framework was relatively unexplored. We first show that groups of Lie type cannot prove $\omega=2$ within the group-theoretic approach. This is based on a representation-theoretic argument that identifies the second-smallest dimension of an irreducible representation of a group as a key parameter that determines its viability in this framework. Our proof builds on Gowers' result concerning product-free sets in quasirandom groups. We then give another barrier that rules out certain natural matrix group constructions that make use of subgroups that are far from being self-normalizing. Our barrier results leave open several natural paths to obtain $\omega = 2$ via matrix groups. To explore these routes we propose working in the continuous setting of Lie groups, in which we develop an analogous theory. Obtaining the analogue of $\omega=2$ in this potentially easier setting is a key challenge that represents an intermediate goal short of actually proving $\omega = 2$. We give two constructions in the continuous setting, each of which evades one of our two barriers.Comment: 15 page

A review of chronic pectoralis major tears: what options are available?

Rupture of the pectoralis major muscle typically occurs in the young, active male. Acute management of these injuries is recommended; however, what if the patient presents with a chronic tear of the pectoralis major? Physical exams and magnetic resonance imaging can help identify the injury and guide the physician with a plan for management. Nonoperative management is feasible, but is recommended for elderly, low-demand patients whose functional goals are minimal. Repair of chronic tears should be reserved for younger, healthier patients with high functional demands. Although operative management provides better functional outcomes, operative treatment of chronic pectoralis tears can be challenging. Tendon retraction, poor tendinous substance and quality of tissue, muscle atrophy, scar formation, and altered anatomy make direct repairs complicated, often necessitating auto- or allograft use. We review the various graft options and fixation methods that can be used when treating patients with chronic pectoralis major tears

On cap sets and the group-theoretic approach to matrix multiplication

In 2003, Cohn and Umans described a framework for proving upper bounds on the exponent ω of matrix multiplication by reducing matrix multiplication to group algebra multiplication, and in 2005 Cohn, Kleinberg, Szegedy, and Umans proposed specific conjectures for how to obtain ω = 2. In this paper we rule out obtaining ω = 2 in this framework from abelian groups of bounded exponent. To do this we bound the size of tricolored sum-free sets in such groups, extending the breakthrough results of Croot, Lev, Pach, Ellenberg, and Gijswijt on cap sets. As a byproduct of our proof, we show that a variant of tensor rank due to Tao gives a quantitative understanding of the notion of unstable tensor from geometric invariant theory

Regulation of Intracellular pH Mediates Bax Activation in HeLa Cells Treated with Staurosporine or Tumor Necrosis Factor-α

Induction of apoptosis in HeLa cells with staurosporine produced a rise in the intracellular pH (pH(i)). Intracellular alkalinization was accompanied by translocation of Bax to the mitochondria, cytochrome c release, and cell death. The chloride channel inhibitor furosemide prevented intracellular alkalinization, Bax translocation, cytochrome c release, and cell death. Translocation of full-length Bid to the mitochondria was also prevented by furosemide. The cleavage product of Bid degradation (truncated Bid, tBid) was not detectable in the mitochondria. Its accumulation in the cytosol was prevented by furosemide. Apoptosis induced by tumor necrosis factor-alpha (TNF) lowered pH(i), an effect also accompanied by Bax translocation, cytochrome c release, and cell killing. Furosemide prevented all of these events. TNF induced a depletion of full-length Bid from the mitochondria and the cytosol but induced an accumulation of mitochondrial tBid. Furosemide only delayed full-length Bid depletion and tBid accumulation. The caspase 8 inhibitor IETD did not prevent the translocation of Bax. Although IETD did inhibit the cleavage of Bid and the accumulation of tBid, cell killing was reduced only slightly. It is concluded that with either staurosporine or TNF a furosemide-sensitive change in pH(i) is linked to Bax translocation, cytochrome c release, and cell killing. With TNF Bax translocation occurs as Bid is depleted and can be dissociated from the accumulation of tBid. With staurosporine a role for full-length Bid in Bax translocation cannot be excluded but is not necessary as evidenced by the data with TNF

Risk factors for unexpected admission following arthroscopic and open treatment of shoulder instability: a national database study of 11,230 cases

Background Shoulder instability procedures have low morbidity; however, complications can arise that result in readmission to an inpatient healthcare facility. The purpose of this study is to identify the demographics and risk factors associated with unplanned 30-day readmission and reoperation following arthroscopic and open treatment for shoulder instability. Methods The American College of Surgeons National Surgical Quality Improvement Program database was queried to find patients who underwent shoulder instability surgery from 2015 to 2019. Independent sample Student t-tests, chi-square, and (where appropriate) Fisher’s exact tests were used in univariate analyses to identify demographic, lifestyle, and perioperative variables related to 30-day readmission and reoperation following repair for shoulder instability. Multivariate logistic regression modeling was subsequently performed. Results Of the 11,230 cases included in our sample, only 0.54% were readmitted, and 0.23% underwent reoperation within the 30-day postoperative period. Multivariate logistic regression modeling confirmed that the following patient variables were associated with statistically significantly increased odds of readmission and reoperation: open repair, congestive heart failure (CHF), and hospital length of stay. Conclusions Unplanned 30-day readmission and reoperation after shoulder instability surgery is infrequent. Patients with American Society of Anesthesiologists class II, CHF, longer than average hospital length of stay, or an open procedure have higher odds of readmission than patients without those factors. Patients who have CHF, longer than average hospital length of stay, and open surgery have higher odds of reoperation than others. Arthroscopic procedures should be used to manage shoulder instability, if possible. Level of evidence III

A Clinical Decision Support System for Malignant Pleural Effusion Analysis

Pleural effusion occurs when fluid accumulates in the pleural cavity surrounding the lung. This condition is commonly caused by infection, but can also be associated with the presence of a metastatic tumor. Samples of pleural fluid are used to analyze the morphologies of mesothelial cells and can typically be used to make a diagnosis between benignity and malignancy. Atypical pleural effusion samples are not easily identified as benign or malignant due to a lack of differentiable visual features, and such a problem has a significant influence in clinicians\u27 decision making. In this paper, the goal is to develop a clinical decision support system (CDSS) using computer imaging and machine learning techniques for diagnosing atypical pleural effusion. The proposed approach involves four steps for analyzing slides of pleural effusion samples: image processing, feature measurement, feature selection, and classification. Processing and measurement of images produced a preliminary data set of 500 samples; each is described by 398 features. A genetic algorithm was applied for feature selection and identified a subset of 39 important features. The experimental results showed that the selected features can distinguish atypical nuclei as benign or malignant with a five-fold cross validation accuracy of 91%