On the relevance of non-standard theories of uncertainty in modeling and pooling expert opinions

Wu, Apostolakis and Okrent¹ have recently analyzed the current status of emerging alternatives to classical probabilistic methods in the modeling and pooling of expert opinions in safety analysis of engineering systems. They have pointed out some difficulties faced by these theories, due to their relative lack of maturity. This paper pursues the investigation so as to clarify some aspects of belief functions and possibility theories, and also to point out the need for further research. A comparison between the mathematical models of expert opinion pooling offered by Bayesian probabilities, belief functions and possibility theory is carried out. It is proved that the Bayesian approach that these authors advocate suffers from the same numerical stability problems as possibilistic and evidential rules of combination in the presence of strongly conflicting information due to their strong structural similarities. The problem of dependence between experts is briefly addressed. The other main point of this paper is that a single combination rule cannot reasonably address all situations where expert opinions must be pooled. It is suggested that the framework of possibility and evidence theories offers a more flexible framework for representing and combining subjective uncertain judgments than the one of subjective probability alone although some progress is required to reach the maturity of the Bayesian theory.     

Application of ultrafiltration to the preparation of defined hydrolysates of bovine haemoglobin

Many uses of protein hydrolysates have been developed and applied to areas such as nutritional therapy, culture media, and the isolation of biologically active peptides. All these applications need carefully controlled and characterized hydrolysates. In order to produce such a type of hydrolysate, it is possible to use haemoglobin which is a very well defined and constant protein source. Enzymic hydrolysis of haemoglobin by pepsin was carried out at pilot-plant scale in an ultrafiltration reactor with mineral membranes. The object was to obtain a reproducible, decolorized, salt-free enzymic hydrolysate. Two types of membranes were tested having 10000 dalton (M5 type) and 20000 dalton (M4 type) cut-offs. Little significant difference was observed in the final products when both types of membranes were used. Reproducibility of hydrolysates was verified by amino acid analysis and gel filtration chromatography. The haemoglobin hydrolysates produced contained more than 90% protein and are especially suitable for fine applications.     

Preliminary investigations of weak non-adiabatic effects in materials from simulations on model clusters

According to earlier work, excited electronic states, despite their very small concentrations in wide-gap systems, might be involved in the initiation of energetic materials. To get further insight into the non-adiabatic electronic behaviour under intense mechanical perturbations, a simple approach is suggested, using finite clusters as models for materials. Preliminary calculations are carried out for isolated clusters undergoing vibrations. Electronic populations in excited states obtained from these simulations are much larger than expected on the basis of statistical mechanics. Therefore, an extension of the present scheme to the canonical NVT ensemble would be desirable.     

Characterization of PVA cryogel for intravascular ultrasound elasticity imaging

The present study characterizes the mechanical properties of polyvinyl alcohol (PVA) cryogel in order to show its utility for intravascular elastography. PVA cryogel becomes harder with an increasing number of freeze-thaw cycles, and Young's modulus and Poisson's ratio are measured for seven samples. Mechanical tests were performed on cylindrical samples with a pressure column and on a hollow cylinder with the calculation of an intravascular elastogram. An image of the Young's modulus was obtained from the elastogram using cylinder geometry properties. Results show the mechanical similitude of PVA cryogel with the biological tissues present in arteries. A good agreement between Young's modulus obtained from pressure column and from elastogram was also observed.     

Possibility Theory, Probability Theory and Multiple-Valued Logics: A Clarification

There has been a long-lasting misunderstanding in the literature of artificial intelligence and uncertainty modeling, regarding the role of fuzzy set theory and many-valued logics. The recurring question is that of the mathematical and pragmatic meaningfulness of a compositional calculus and the validity of the excluded middle law. This confusion pervades the early developments of probabilistic logic, despite early warnings of some philosophers of probability. This paper tries to clarify this situation. It emphasizes three main points. First, it suggests that the root of the controversies lies in the unfortunate confusion between degrees of belief and what logicians call degrees of truth. The latter are usually compositional, while the former cannot be so. This claim is first illustrated by laying bare the non-compositional belief representation embedded in the standard propositional calculus. It turns out to be an all-or-nothing version of possibility theory. This framework is then extended to discuss the case of fuzzy logic versus graded possibility theory. Next, it is demonstrated that any belief representation where compositionality is taken for granted is bound to at worst collapse to a Boolean truth assignment and at best to a poorly expressive tool. Lastly, some claims pertaining to an alleged compositionality of possibility theory are refuted, thus clarifying a pervasive confusion between possibility theory axioms and fuzzy set basic connectives.     

Globally Optimal Estimates for Geometric Reconstruction Problems

We introduce a framework for computing statistically optimal estimates of geometric reconstruction problems. While traditional algorithms often suffer from either local minima or non-optimality—or a combination of both—we pursue the goal of achieving global solutions of the statistically optimal cost-function. Our approach is based on a hierarchy of convex relaxations to solve non-convex optimization problems with polynomials. These convex relaxations generate a monotone sequence of lower bounds and we show how one can detect whether the global optimum is attained at a given relaxation. The technique is applied to a number of classical vision problems: triangulation, camera pose, homography estimation and last, but not least, epipolar geometry estimation. Experimental validation on both synthetic and real data is provided. In practice, only a few relaxations are needed for attaining the global optimum.     

基于Livermore模型CT图片构建人体躯干数字体模及其在肺部计数器虚拟刻度中的应用

基于Livermore 人体躯干物理模型CT图片构建数字体模,并结合蒙特卡罗程序MCNP对一套由四个宽能高纯锗探测器(BEGe)构成的肺部计数器进行了虚拟刻度.首先,利用点源(241Am,137Cs,60Co,54Mn,57Co,109Cd) 实验数据,对高纯锗晶体尺寸进行调整以获得正确的探测器几何参数,在γ射线能量13.9 keV～1332.5 keV范围内,调整后四个探测器全能峰效率实验测量的平均值与蒙特卡罗计算值的差别在±10%范围内.之后,对不同胸壁厚度(CWT=19 mm, 25 mm, 30 mm, 43 mm)躯干体模进行CT扫描获得其CT图片,利用Dosigray软件对CT图片进行分割后,连同探测器几何描述文件输入到OEDIPE软件,生成数字体模虚拟刻度用MCNP输入程序.最后,利用241Am、152Eu肺部源对数字体模虚拟刻度结果进行了实验验证,结果表明:在59.5 keV～1408 keV能量范围内,虚拟刻度结果与实验结果的差别在±10%之间;对于17.5 keV能量,差别在±30%之间.     

Credible autocoding of convex optimization algorithms

The efficiency of modern optimization methods, coupled with increasing computational resources, has led to the possibility of real-time optimization algorithms acting in safety-critical roles. There is a considerable body of mathematical proofs on on-line optimization algorithms which can be leveraged to assist in the development and verification of their implementation. In this paper, we demonstrate how theoretical proofs of real-time optimization algorithms can be used to describe functional properties at the level of the code, thereby making it accessible for the formal methods community. The running example used in this paper is a generic semi-definite programming solver. Semi-definite programs can encode a wide variety of optimization problems and can be solved in polynomial time at a given accuracy. We describe a top-down approach that transforms a high-level analysis of the algorithm into useful code annotations. We formulate some general remarks on how such a task can be incorporated into a convex programming autocoder. We then take a first step towards the automatic verification of the optimization program by identifying key issues to be addressed in future work.