A 2-adic approach of the human respiratory tree

We propose here a general framework to address the question of trace operators on a dyadic tree. This work is motivated by the modeling of the human bronchial tree which, thanks to its regularity, can be extrapolated in a natural way to an infinite resistive tree. The space of pressure fields at bifurcation nodes of this infinite tree can be endowed with a Sobolev space structure, with a semi-norm which measures the instantaneous rate of dissipated energy. We aim at describing the behaviour of finite energy pressure fields near the end. The core of the present approach is an identification of the set of ends with the ring Z_2 of 2-adic integers. Sobolev spaces over Z_2 can be defined in a very natural way by means of Fourier transform, which allows us to establish precised trace theorems which are formally quite similar to those in standard Sobolev spaces, with a Sobolev regularity which depends on the growth rate of resistances, i.e. on geometrical properties of the tree. Furthermore, we exhibit an explicit expression of the "ventilation operator", which maps pressure fields at the end of the tree onto fluxes, in the form of a convolution by a Riesz kernel based on the 2-adic distance.Comment: 22 page

Aerosol dynamics simulations of the anatomical variability of e-cigarette particle and vapor deposition in a stochastic lung

Electronic cigarette (EC) aerosols are typically composed of a mixture of nicotine, glycerine (VG), propylene glycol (PG), water, acidic stabilizers and a variety of flavors. Inhalation of e-cigarette aerosols is characterized by a continuous modification of particle diameters, concentrations, composition and phase changes, and smoker-specific inhalation conditions, i.e. puffing, mouthhold and bolus inhalation. The dynamic changes of inhaled e-cigarette droplets in the lungs due to coagulation, conductive heat and diffusive heat/convective vapor transport and particle phase chemistry are described by the Aerosol Dynamics in Containment (ADiC) model. For the simulation of the variability of inhaled particle and vapor deposition, the ADiC model is coupled with the IDEAL Monte Carlo code, which is based on a stochastic, asymmetric airway model of the human lung. We refer to the coupled model as "IDEAL/ADIC_v1.0". In this study, two different ecigarettes were compared, one without any acid ("no acid") and the other one with an acidic regulator (benzoic acid) to establish an initial pH level of about 7 ("lower pH"). Corresponding deposition patterns among human airways comprise total and compound-specific number and mass deposition fractions, distinguishing between inhalation and exhalation phases and condensed and vapor phases. Note that the inhaled EC aerosol is significantly modified in the oral cavity prior to inhalation into the lungs. Computed deposition fractions demonstrate that total particle mass is preferentially deposited in the alveolar region of the lung during inhalation. While nicotine deposits prevalently in the condensed phase for the "lower pH" case, vapor phase deposition is dominating the "no acid" case. The significant statistical fluctuations of the particle and vapor deposition patterns illustrate the inherent anatomical variability of the human lung structure.Peer reviewe

Transparent Boundary Conditions for Wave Propagation in Fractal Trees: Approximation by Local Operators

This work is dedicated to the construction and analysis of high-order transparent boundary conditions for the weighted wave equation on a fractal tree, which models sound propagation inside human lungs. This article follows the works [10, 9], aimed at the analysis and numerical treatment of the model, as well as the construction of low-order and exact discrete boundary conditions. The method suggested in this article is based on the truncation of the meromorphic series that approximate the symbol of the Dirichlet-to-Neumann operator, similarly to the absorbing boundary conditions of B. En-gquist and A. Majda. We analyze its stability, convergence and complexity. The error analysis is largely based on spectral estimates of the underlying weighted Laplacian. Numerical results confirm the efficiency of the method

New Models for Expert System Design

This thesis presents new work on the analysis of human lung sound. Experimental studies investigated the relationship between the condition of the lungs and the power spectrum of lung sound detected at the chest wall. The conclusion drawn from two clinical studies was that the median frequency of the lung sound power spectrum increases with a decrease in airway calibre. The technique for the analysis of lung sound presented in this thesis is a non-invasive method which may be capable of assessing differences in airway calibre between different lobes of the lung. An expert system for the analysis of lung sound data and pulmonary function data was designed. The expert knowledge was expressed in a belief logic, a system of logic which is more expressive than first order logic. New automated theorem proving methods were developed for the belief logic. The new methods were implemented to form the 'inference engine' of the expert system. The new expert system compared favourably with systems which perform a similar task. The use of belief logic allows introspective reasoning to be carried out. Plausible reasoning, a type of introspective reasoning which allows conclusions to be drawn when the database is incomplete, was proposed and tested. The author concludes that the use of a belief logic in expert system design has significant advantages over conventional approaches. The experimental results of the lung sound research were incorporated into the expert system rule base: the medical and expert system research were complementary

Knowledge Based Systems: A Critical Survey of Major Concepts, Issues, and Techniques

This Working Paper Series entry presents a detailed survey of knowledge based systems. After being in a relatively dormant state for many years, only recently is Artificial Intelligence (AI) - that branch of computer science that attempts to have machines emulate intelligent behavior - accomplishing practical results. Most of these results can be attributed to the design and use of Knowledge-Based Systems, KBSs (or ecpert systems) - problem solving computer programs that can reach a level of performance comparable to that of a human expert in some specialized problem domain. These systems can act as a consultant for various requirements like medical diagnosis, military threat analysis, project risk assessment, etc. These systems possess knowledge to enable them to make intelligent desisions. They are, however, not meant to replace the human specialists in any particular domain. A critical survey of recent work in interactive KBSs is reported. A case study (MYCIN) of a KBS, a list of existing KBSs, and an introduction to the Japanese Fifth Generation Computer Project are provided as appendices. Finally, an extensive set of KBS-related references is provided at the end of the report

Semantic networks

AbstractA semantic network is a graph of the structure of meaning. This article introduces semantic network systems and their importance in Artificial Intelligence, followed by I. the early background; II. a summary of the basic ideas and issues including link types, frame systems, case relations, link valence, abstraction, inheritance hierarchies and logic extensions; and III. a survey of ‘world-structuring’ systems including ontologies, causal link models, continuous models, relevance, formal dictionaries, semantic primitives and intersecting inference hierarchies. Speed and practical implementation are briefly discussed. The conclusion argues for a synthesis of relational graph theory, graph-grammar theory and order theory based on semantic primitives and multiple intersecting inference hierarchies

Local transparent boundary conditions for wave propagation in fractal trees (I). Method and numerical implementation

This work is dedicated to the construction and analysis of high-order transparentboundary conditions for the weighted wave equation on a fractal tree, which models sound propaga-tion inside human lungs. This article follows the works [9, 6], aimed at the analysis and numerical treatment of the model, as well as the construction of low-order and exact discrete boundary conditions. The method suggested in the present work is based on the truncation of the meromorphicseries that represents the symbol of the Dirichlet-to-Neumann operator, in the spirit of the absorbingboundary conditions of B. Engquist and A. Majda. We analyze its stability and convergence, as wellas present computational aspects of the method. Numerical results confirm theoretical finding

Transparent boundary conditions for wave propagation in fractal trees: convolution quadrature approach

International audienceIn this work we propose high-order transparent boundary conditions for the weighted wave equation on a fractal tree, with an application to the modeling of sound propagation in a human lung. This article follows the recent work [29], dedicated to the mathematical analysis of the corresponding problem and the construction of low-order absorbing boundary conditions. The method proposed in this article consists in constructing the exact (trans-parent) boundary conditions for the semi-discretized problem, in the spirit of the convolution quadrature method developed by Ch. Lubich. We analyze the stability and convergence of the method, and propose an efficient algorithm for its implementation. The exposition is concluded with numerical experiments

2010 GREAT Day Program

SUNY Geneseo’s Fourth Annual GREAT Day. This file has a supplement of three additional pages, linked in this record.https://knightscholar.geneseo.edu/program-2007/1004/thumbnail.jp