Uniform probability in cosmology.

Problems with uniform probabilities on an infinite support show up in contemporary cosmology. This paper focuses on the context of inflation theory, where it complicates the assignment of a probability measure over pocket universes. The measure problem in cosmology, whereby it seems impossible to pick out a uniquely well-motivated measure, is associated with a paradox that occurs in standard probability theory and crucially involves uniformity on an infinite sample space. This problem has been discussed by physicists, albeit without reference to earlier work on this topic. The aim of this article is both to introduce philosophers of probability to these recent discussions in cosmology and to familiarize physicists and philosophers working on cosmology with relevant foundational work by Kolmogorov, de Finetti, Jaynes, and other probabilists. As such, the main goal is not to solve the measure problem, but to clarify the exact origin of some of the current obstacles. The analysis of the assumptions going into the paradox indicates that there exist multiple ways of dealing consistently with uniform probabilities on infinite sample spaces. Taking a pluralist stance towards the mathematical methods used in cosmology shows there is some room for progress with assigning probabilities in cosmological theories.

Assigning probabilities to non-Lipschitz mechanical systems.

We present a method for assigning probabilities to the solutions of initial value problems that have a Lipschitz singularity. To illustrate the method, we focus on the following toy example: d2r(t)dt2=ra, r(t=0)=0, and dr(t)dt∣r(t=0)=0, with a∈]0,1[. This example has a physical interpretation as a mass in a uniform gravitational field on a frictionless, rigid dome of a particular shape; the case with a=1/2 is known as Norton's dome. Our approach is based on (1) finite difference equations, which are deterministic; (2) elementary techniques from alpha-theory, a simplified framework for non-standard analysis that allows us to study infinitesimal perturbations; and (3) a uniform prior on the canonical phase space. Our deterministic, hyperfinite grid model allows us to assign probabilities to the solutions of the initial value problem in the original, indeterministic model.

Reply to Lucas & Henneberg: Are human faces unique?

This paper offers a response to the 2015 article of Lucas and Henneberg "Are human faces unique?" (Forensic Sci. Int. 257, 514.e1-514.e6), as well as to the subsequent popularization thereof. In the first part, we assess the probabilistic claims made by the authors and find crucial parts to be unsupported. In particular, the authors offer no probabilistic model on which to base their conclusions. Even if we disregard the errors identified in the first part, we find a troubling discrepancy between the published findings and the popular summary.

Infinitesimal Probabilities.

Non-Archimedean probability functions allow us to combine regularity with perfect additivity. We discuss the philosophical motivation for a particular choice of axioms for a non-Archimedean probability theory and answer some philosophical objections that have been raised against infinitesimal probabilities in general. 1 Introduction2 The Limits of Classical Probability Theory 2.1 Classical probability functions 2.2 Limitations 2.3 Infinitesimals to the rescue?3 NAP Theory 3.1 First four axioms of NAP 3.2 Continuity and conditional probability 3.3 The final axiom of NAP 3.4 Infinite sums 3.5 Definition of NAP functions via infinite sums 3.6 Relation to numerosity theory4 Objections and Replies 4.1 Cantor and the Archimedean property 4.2 Ticket missing from an infinite lottery 4.3 Williamson's infinite sequence of coin tosses 4.4 Point sets on a circle 4.5 Easwaran and Pruss5 Dividends 5.1 Measure and utility 5.2 Regularity and uniformity 5.3 Credence and chance 5.4 Conditional probability6 General Considerations 6.1 Non-uniqueness 6.2 InvarianceAppendix .

Measuring Graded Membership: The Case of Color.

This paper considers Kamp and Partee's account of graded membership within a conceptual spaces framework and puts the account to the test in the domain of colors. Three experiments are reported that are meant to determine, on the one hand, the regions in color space where the typical instances of blue and green are located and, on the other hand, the degrees of blueness/greenness of various shades in the blue-green region as judged by human observers. From the locations of the typical blue and typical green regions in conjunction with Kamp and Partee's account follow degrees of blueness/greenness for the color shades we are interested in. These predicted degrees are compared with the judged degrees, as obtained in the experiments. The results of the comparison support the account of graded membership at issue.

Rationality: a social-epistemology perspective.

Both in philosophy and in psychology, human rationality has traditionally been studied from an "individualistic" perspective. Recently, social epistemologists have drawn attention to the fact that epistemic interactions among agents also give rise to important questions concerning rationality. In previous work, we have used a formal model to assess the risk that a particular type of social-epistemic interactions lead agents with initially consistent belief states into inconsistent belief states. Here, we continue this work by investigating the dynamics to which these interactions may give rise in the population as a whole.

Nanocrystalline diamond impedimetric aptasensor for the label-free detection of human IgE.

Like antibodies, aptamers are highly valuable as bioreceptor molecules for protein biomarkers because of their excellent selectivity, specificity and stability. The integration of aptamers with semiconducting materials offers great potential for the development of reliable aptasensors. In this paper we present an aptamer-based impedimetric biosensor using a nanocrystalline diamond (NCD) film as a working electrode for the direct and label-free detection of human immunoglobulin E (IgE). Amino (NH(2))-terminated IgE aptamers were covalently attached to carboxyl (COOH)-modified NCD surfaces using carbodiimide chemistry. Electrochemical impedance spectroscopy (EIS) was applied to measure the changes in interfacial electrical properties that arise when the aptamer-functionalized diamond surface was exposed to IgE solutions. During incubation, the formation of aptamer-IgE complexes caused a significant change in the capacitance of the double-layer, in good correspondence with the IgE concentration. The linear dynamic range of IgE detection was from 0.03 µg/mL to 42.8 µg/mL. The detection limit of the aptasensor reached physiologically relevant concentrations (0.03 µg/mL). The NCD-based aptasensor was demonstrated to be highly selective even in the presence of a large excess of IgG. In addition, the aptasensor provided reproducible signals during six regeneration cycles. The impedimetric aptasensor was successfully tested on human serum samples, which opens up the potential of using EIS for direct and label-free detection of IgE levels in blood serum.

DNA sensors with diamond as a promising alternative transducer material.

Bio-electronics is a scientific field coupling the achievements in biology with electronics to obtain higher sensitivity, specificity and speed. Biosensors have played a pivotal role, and many have become established in the clinical and scientific world. They need to be sensitive, specific, fast and cheap. Electrochemical biosensors are most frequently cited in literature, often in the context of DNA sensing and mutation analysis. However, many popular electrochemical transduction materials, such as silicon, are susceptible to hydrolysis, leading to loss of bioreceptor molecules from the surface. Hence, increased attention has been shifted towards diamond, which surpasses silicon on many levels.

Structural and optical properties of DNA layers covalently attached to diamond surfaces.

Label-free detection of DNA molecules on chemically vapor-deposited diamond surfaces is achieved with spectroscopic ellipsometry in the infrared and vacuum ultraviolet range. This nondestructive method has the potential to yield information on the average orientation of single as well as double-stranded DNA molecules, without restricting the strand length to the persistence length. The orientational analysis based on electronic excitations in combination with information from layer thicknesses provides a deeper understanding of biological layers on diamond. The pi-pi* transition dipole moments, corresponding to a transition at 4.74 eV, originate from the individual bases. They are in a plane perpendicular to the DNA backbone with an associated n-pi* transition at 4.47 eV. For 8-36 bases of single- and double-stranded DNA covalently attached to ultra-nanocrystalline diamond, the ratio between in- and out-of-plane components in the best fit simulations to the ellipsometric spectra yields an average tilt angle of the DNA backbone with respect to the surface plane ranging from 45 degrees to 52 degrees . We comment on the physical meaning of the calculated tilt angles. Additional information is gathered from atomic force microscopy, fluorescence imaging, and wetting experiments. The results reported here are of value in understanding and optimizing the performance of the electronic readout of a diamond-based label-free DNA hybridization sensor.