Decision problems in the space of Dehn fillings

Normal surface theory is used to study Dehn fillings of a knot-manifold. We use that any triangulation of a knot-manifold may be modified to a triangulation having just one vertex in the boundary. In this situation, it is shown that there is a finite computable set of slopes on the boundary of the knot-manifold, which come from boundary slopes of normal or almost normal surfaces. This is combined with existence theorems for normal and almost normal surfaces to construct algorithms to determine precisely those manifolds obtained by Dehn filling of a given knot-manifold that: (1) are reducible, (2) contain two-sided incompressible surfaces, (3) are Haken, (4) fiber over S¹, (5) are the 3-sphere, and (6) are a lens space. Each of these algorithms is a finite computation.Moreover, in the case of essential surfaces, we show that the topology of each filled manifold is strongly reflected in the combinatorial properties of a triangulation of the knot-manifold with just one vertex in the boundary. If a filled manifold contains an essential surface then the knot-manifold contains an essential normal vertex solution which caps off to an essential surface of the same type in the filled manifold. (Normal vertex solutions are the premier class of normal surface and are computable.)     

Visible surgery, four-dimensionals-cobordisms and related questions in geometric topology

The visible surgery theory of M. Weiss is used to complete the topological classification of four-dimensionals-cobordisms between three-dimensional spherical spaceforms. Applications to various questions concerning pseudo-isotopies of 3-manifolds, computations of the simple Wall groups of finite periodic groups, and inductive detection of self-homeomorphisms of manifolds are also discussed.The first named author was partially supported by a grant from the Louisiana Board of Regents and National Science Foundation Grants DMS 89-01583 and 91-01575, and the second named author was partially supported by National Science Foundation Grants DMS 86-02543, 89-02622 and 91-02711.     

血液-血管耦合特性与脉搏波传播特性的关系

脉搏波既不可简单地理解为可压缩血液流体中的压力纵波,也不可简单地理解为沿固体血管传播的涨缩位移横波,而是超乎普通想象的流-固耦合和纵波-横波耦合的复杂波。从分析耦合本构关系的新途径出发,本文中提出了一个流-固耦合/纵波-横波耦合的串联模型,可为解读“位数形势”中医脉诊提供更丰富的信息。结果表明,脉搏波耦合系统的等效体积压缩模量K_s以及相应的耦合系统脉搏波传播速度c_s主要依赖于两个无量纲参数：血液-血管模量比K_b(p)/E(p)和薄壁血管径厚比D(p)/h₀,它们因人而异、因人的不同脉搏位置而异。文中定量分析了它们对c_s的影响,显示人体的K_b/E值在10³数量级,从而c_s值在10⁰～10¹ m/s数量级,以适应人体生理生化反应。由临床有创测量,证实脉搏体积横波与脉搏压力纵波是相耦合地以相同速度传播;还显示脉搏波是在其波阵面上具有氧合生化反应的“生物波”。此外,还讨论了“脉压放大”现象与非线性本构关系和与血管分叉处加载增强反射之间的关系,并讨论了Lewis关于重搏波形成的假设。

     

Semi-invariants in surgery

A semi-invariant in surgery is an invariant of a quadratic Poincaré complex which is defined in terms of a null-cobordism. We define five such gadgets: the semicharacteristic, the semitorsion, the cross semitorsion, the torsion semicharacteristic, and the cross torsion semicharacteristic. We describe applications to the evaluation of surgery obstructions, especially in the odd-dimensional case.     

Some insight into characterizations of minimally nonideal matrices

Lehman (Polyhedral combinatorics 1 of DIMACS series in discrete math. and theoretical computer science, pp 101–105, 1990) described some conditions regular minimally nonideal (mni) matrices must satisfy. Although, there are few results on sufficient conditions for mni matrices. In most of these results, the covering polyhedron must have a unique fractional extreme point. This condition corresponds to ask the matrix to be the blocker of a near-ideal matrix, defined by the authors in a previous work (2006). In this paper we prove that, having the blocker of a near-ideal matrix, only a few very easy conditions have to be checked in order to decide if the matrix is regular mni. In doing so, we define the class of quasi mni matrices, containing regular mni matrices, and we find a generalization on the number of integer extreme points adjacent to the fractional extreme point in the covering polyhedron. We also give a relationship between the covering and stability number of regular mni matrices which allows to prove when a regular mni matrix can be a proper minor of a quasi mni. Partially supported by CONICET Grant PIP 2807/2000 (Argentina) and by CNPq/PROSUL Grant 490333/2004-4 (Brasil).     

Nonspecific laryngeal granuloma: A case study of a professional singer

A professional singer with laryngeal granuloma underwent surgery following failed response to conservative treatments. Two primary findings emerged. First, although a sizable lesion was present initially, presurgical voice measures were largely normal or superior. The exception was elevated phonatory effort during singing. Second, postsurgical voice functions were entirely normal or superior (including phonatory effort), despite demanding singing performances a few weeks following surgery. The results add to the limited corpus of quantitative, normative-referenced data on voice in patients with granulomas and are inconsistent with previous reports of voice abnormalities in such patients and poor functional response to surgery.     

Real-Time Tool Detection for Workflow Identification in Open Cranial Vault Remodeling

Deep learning is a recent technology that has shown excellent capabilities for recognition and identification tasks. This study applies these techniques in open cranial vault remodeling surgeries performed to correct craniosynostosis. The objective was to automatically recognize surgical tools in real-time and estimate the surgical phase based on those predictions. For this purpose, we implemented, trained, and tested three algorithms based on previously proposed Convolutional Neural Network architectures (VGG16, MobileNetV2, and InceptionV3) and one new architecture with fewer parameters (CranioNet). A novel 3D Slicer module was specifically developed to implement these networks and recognize surgical tools in real time via video streaming. The training and test data were acquired during a surgical simulation using a 3D printed patient-based realistic phantom of an infant’s head. The results showed that CranioNet presents the lowest accuracy for tool recognition (93.4%), while the highest accuracy is achieved by the MobileNetV2 model (99.6%), followed by VGG16 and InceptionV3 (98.8% and 97.2%, respectively). Regarding phase detection, InceptionV3 and VGG16 obtained the best results (94.5% and 94.4%), whereas MobileNetV2 and CranioNet presented worse values (91.1% and 89.8%). Our results prove the feasibility of applying deep learning architectures for real-time tool detection and phase estimation in craniosynostosis surgeries.     

On the singular PDE's geometry and boundary value problems

A geometric formulation of singular partial differential equations (PDEs) is considered. Surgery techniques and integral bordism groups are utilized, following previous works by Prástaro on PDEs, in order to build global solutions crossing also singular points and to study their stability properties.     

Signature Operators and Surgery Groups over C*-algebras

Let A be a unital complex C^* algebra, L^*(A) the projective symmetric surgery groups, and K_*(A) topological K theory. We define groups B^*(A) of bordism classes of Fredholm complexes over A with Poincaré duality. These generalize the de Rham complex. It is shown that there are isomorphisms B^*(A)K_* (A) and B^*(A) L_*(A) given by abstract versions of the signature operator and symmetric signature. The remaining side of a triangle is formed by an isomorphism due to Mienko.     

Optimal dosage of ultrasound contrast agent for ultrasound surgery: Thermal effect of linear plane wave

The optimal dosage of ultrasound contrast agent model for ultrasound surgery was explored. A specific ultrasound contrast agent Albunex^® was chosen for simulation. The model was developed based on a dilute bubbly liquid model proposed by Ye and Ding [Z. Ye, L. Ding, Acoustic dispersion and attenuation relations in bubbly mixture, J. Acoust. Soc. Am. 98 (3) (1995) 1629–1636]. The numerical simulation suggests that 2 MHz is more efficient than 1 MHz to thermally treat cancer in deep tissue with the optimal dosage of 3 ml. On the other hand, the simulation also suggests 3 MHz center frequency with the optimal dosage of 1.6 ml is adequate for prostate cancer treatment with transrectal equipment. The simulation is expected to valid up to 2 MPa incident pressure due to the limitation of the linearized UCA model. Even though it is developed from a single ultrasound contrast agent, this model is expected to be useful for any ultrasound contrast agent as long as the necessary parameters are provided.