Abstract:
lveolar fractal box dimension inversely correlates with mean linear intercept in mice with elastase-induced emphysema Original Research (1638) Total Article Views Authors: Andersen MP, Parham AR, Waldrep JC, McKenzie WN, Dhand R Published Date March 2012 Volume 2012:7 Pages 235 - 243 DOI: http://dx.doi.org/10.2147/COPD.S26493 Received: 23 September 2011 Accepted: 01 November 2011 Published: 27 March 2012 Mary P Andersen1, A Read Parham1, J Clifford Waldrep1,2, Wayland N McKenzie1, Rajiv Dhand1,2 1Division of Pulmonary, Critical Care, and Environmental Medicine, Department of Internal Medicine, University of Missouri, 2Research Services, Harry S Truman Memorial VA Hospital, Columbia, MO, USA Rationale: A widely applicable model of emphysema that allows efficient and sensitive quantification of injury is needed to compare potential therapies. Objectives: To establish such a model, we studied the relationship between elastase dose and the severity of emphysema in female C57BL/6J mice. We compared alveolar fractal box dimension (DB), a new measure which is an assessment of the complexity of the tissue, with mean linear intercept (Lm), which is commonly used to estimate airspace size, for sensitivity and efficiency of measurement. Methods: Emphysema was induced in female C57BL/6J mice by administering increasing intratracheal doses of porcine pancreatic elastase (PPE). Changes in morphology and static lung compliance (CL) were examined 21 days later. Correlation of DB with Lm was determined in histological sections of lungs exposed to PPE. The inverse relationship between DB and Lm was supported by examining similar morphological sections from another experiment where the development of emphysema was studied 1 to 3 weeks after instillation of human neutrophil elastase (HNE). Results: Lm increased with PPE dose in a sigmoidal curve. CL increased after 80 or 120 U/kg body weight (P < 0.05), but not after 40 U/kg, compared with the control. DB progressively declined from 1.66 ± 0.002 (standard error of the mean) in controls, to 1.47 ± 0.006 after 120 U PPE/kg (P < 0.0001). After PPE or HNE instillation, DB was inversely related to Lm (R = –0.95, P < 0.0001 and R = –0.84, P = 0.01, respectively), with a more negative slope of the relationship using HNE (P < 0.0001). Conclusion: Intratracheal instillation of increasing doses of PPE yields a scale of progression from mild to severe emphysema. DB correlates inversely with Lm after instillation of either PPE or HNE and yields a rapid, sensitive measure of emphysema after elastase instillation.

Abstract:
Young's lattice $L(m,n)$ consists of partitions having $m$ parts of size at most $n$, ordered by inclusion of the corresponding Ferrers diagrams. K. O'Hara gave the first constructive proof of the unimodality of the Gaussian polynomials by expressing the underlying ranked set of $L(m,n)$ as a disjoint union of products of centered rank-unimodal subsets. We construct a finer decomposition which is compatible with the partial order on Young's lattice, at the cost of replacing the cartesian product with a more general poset extension. As a corollary, we obtain an explicit chain decomposition which exhibits the rank-unimodality of $L(m,n)$. Moreover, this set of chains is closed under the natural rank-flipping involution given by taking complements of Ferrers diagrams.

Abstract:
The category of perverse sheaves on the affine Grassmannian of a complex reductive group $G$ gives a canonical geometric construction of the split form of the Langlands dual group $\check G_\bZ$ over the integers. Given a field $k$, we give a Tannakian construction of the quasi-split forms of $\check G_k$, as well as a construction of the gerbe associated to an inner form of $\check G_k$.

Abstract:
Young's partition lattice $L(m,n)$ consists of unordered partitions having $m$ parts where each part is at most $n$. Using methods from complex algebraic geometry, R. Stanley proved that $L(m,n)$ is rank-symmetric, unimodal, and strongly Sperner. Moreover, he conjectured that $L(m,n)$ has a stronger property called symmetric chain decomposition. Despite many efforts, this conjecture has only been proved for $\min(m,n)\leq 4$. In this paper, we decompose $L(m,n)$ into level sets for certain tropical polynomials derived from the secant varieties of the rational normal curve in projective space, and we find that the resulting subposets have an elementary raising and lowering algorithm. As a corollary, we obtain a symmetric chain decomposition for the subposet of $L(m,n)$ consisting of "sufficiently generic" partitions.

Abstract:
A finite ranked poset is called a symmetric chain order if it can be written as a disjoint union of rank-symmetric, saturated chains. If $P$ is any symmetric chain order, we prove that $P^n/\mathbb{Z}_n$ is also a symmetric chain order, where $\mathbb{Z}_n$ acts on $P^n$ by cyclic permutation of the factors.

Abstract:
Pak and Panova recently proved that the $q$-binomial coefficient ${m+n \choose m}_q$ is a strictly unimodal polynomial in $q$ for $m,n \geq 8$, via the representation theory of the symmetric group. We give a direct combinatorial proof of their result by characterizing when a product of chains is strictly unimodal and then applying O'Hara's structure theorem for the partition lattice $L(m,n)$. In fact, we prove a stronger result: if $m, n \geq 8d$, and $2d \leq r \leq mn/2$, then the $r$-th rank of $L(m,n)$ has at least $d$ more elements that the next lower rank.

Abstract:
A 53-year-old man reported a 4-month history of increasing dyspnea and weight loss. He had a long history of smoking and admission chest X-ray revealed a density in the right hemithorax. Computed tomography confirmed a probable mass with further speculated opacities in both lung fields suspicious for malignant spread. Biopsies obtained using endobronchial ultrasound-guided aspiration returned negative for malignancy and showed bronchial epithelial cells with foreign body giant cell reaction and polarizable birefringent talc crystals.This case demonstrates a rare presentation of talc granulomatosis three decades after the last likely exposure. The history and imaging findings in a chronic smoker were initially strongly suggestive of malignant disease, and we recommend that talc-induced lung disease is considered in any patient with multiple scattered pulmonary lesions and a history of intravenous drug use. Confirmation of the disease by biopsy is essential, but unfortunately there are few successful proven management options for patients with worsening disease.Pulmonary talc granulomatosis is a rare disorder characterized by the development of foreign body granuloma secondary to talc exposure. Several case reports have documented the disease in known intravenous drug abusers who present with respiratory symptoms. We present the diagnosis in a patient with a remote history of intravenous heroin use, and initial symptoms and imaging suggestive of malignancy.A 53-year-old man presented with increasing dyspnea and a weight loss of 3 kg over a 4-month period. Past medical history was significant for emphysema, seizure disorder and hepatitis C. Medications included albuterol and dilantin. The patient was unemployed and had a 35-pack/year history of smoking. He also reported intravenous heroin abuse 30 years previously (undertaken for a period of 10 years).Laboratory results including complete blood count, renal function and liver function tests were all within normal limit

Abstract:
Any lossless transformation on $n_{s}$ spatial and $n_{p}$ internal modes of light can be described by an $n_{s}n_{p}\times n_{s}n_{p}$ unitary matrix, but there is no known procedure to effect an arbitrary $n_{s}n_{p}\times n_{s}n_{p}$ unitary matrix on light in $n_{s}$ spatial and $n_{p}$ internal modes. We devise an algorithm to realize an arbitrary discrete unitary transformation on the combined spatial and internal degrees of freedom of light. Our realization uses beamsplitters and operations on internal modes to effect arbitrary linear transformations. The number of beamsplitters required to realize a unitary transformation is reduced as compared to existing realization by a factor $n_{p}^2/2$ at the cost of increasing the number of internal optical elements by a factor of two. Our algorithm thus enables the optical implementation of higher dimensional unitary transformations.

Abstract:
The Trotter-Suzuki decomposition is an important tool for the simulation and control of physical systems. We provide evidence for the stability of the Trotter-Suzuki decomposition. We model the error in the decomposition and determine sufficiency conditions that guarantee the stability of this decomposition under this model. We relate these sufficiency conditions to precision limitations of computing and control in both classical and quantum cases. Furthermore we show that bounded-error Trotter-Suzuki decomposition can be achieved by a suitable choice of machine precision.

Abstract:
Myotonic dystrophy type 1 (DM1) is the commonest muscular dystrophy in adults, affecting multiple organs in addition to skeletal muscles. Cardiac conduction system abnormalities are well recognized as an important component of DM1 phenotype; however, primary structural myocardial abnormalities, which may predispose these patients to congestive heart failure, are not as well characterized. We reviewed the retrospective analysis of the clinical and echocardiographic findings in adult patients with DM1. Among 27 patients (16 male; age 19-61 years) with DM1, the echocardiogram (ECHO) was abnormal in 10 (37%) including one of 6 patients (16%) with congenital myotonic dystrophy. Reduced left ventricular ejection fraction (LVEF ≤50%) was noted in 5, diastolic dysfunction in 4, left atrial dilatation in 3, left ventricular hypertrophy in 2, apical hypokinesia in 1 and mitral valve prolapse in 3 patients. One patient had paradoxical septal movement in the setting of left bundle branch block. Echocardiographic abnormalities significantly correlated with older age; however, patients with systolic dysfunction on echocardiogram ranged in age from 27 to 52 years including 2 patients aged 27 and 34 years. We can conclude that echocardiographic abnormalities are frequent in adult patients with DM1. The incidence is similar in the classical and congenital type of DM1. Overall, echocardiographic abnormalities in DM1 correlate with increasing age; however, reduced LVEF is observed even at young age. Cardiac assessment and monitoring in adult patients with DM1 should include evaluation for primary myocardial involvement.