Sensitivity volume as figure-of-merit for maximizing data importance in electrical impedance tomography

Objective.Electrical impedance tomography (EIT) is a noninvasive imaging method whereby electrical measurements on the periphery of a heterogeneous conductor are inverted to map its internal conductivity. The EIT method proposed here aims to improve computational speed and noise tolerance by introducing sensitivity volume as a figure-of-merit for comparing EIT measurement protocols.Approach.Each measurement is shown to correspond to a sensitivity vector in model space, such that the set of measurements, in turn, corresponds to a set of vectors that subtend a sensitivity volume in model space. A maximal sensitivity volume identifies the measurement protocol with the greatest sensitivity and greatest mutual orthogonality. A distinguishability criterion is generalized to quantify the increased noise tolerance of high sensitivity measurements.Main result.The sensitivity volume method allows the model space dimension to be minimized to match that of the data space, and the data importance to be increased within an expanded space of measurements defined by an increased number of contacts.Significance.The reduction in model space dimension is shown to increasecomputational efficiency, accelerating tomographic inversion by several orders of magnitude, while the enhanced sensitivitytolerates higher noiselevels up to several orders of magnitude larger than standard methods.

Quantum Distance Measures Based upon Classical Symmetric Csiszár Divergences

We introduce a new family of quantum distances based on symmetric Csiszár divergences, a class of distinguishability measures that encompass the main dissimilarity measures between probability distributions. We prove that these quantum distances can be obtained by optimizing over a set of quantum measurements followed by a purification process. Specifically, we address in the first place the case of distinguishing pure quantum states, solving an optimization of the symmetric Csiszár divergences over von Neumann measurements. In the second place, by making use of the concept of purification of quantum states, we arrive at a new set of distinguishability measures, which we call extended quantum Csiszár distances. In addition, as it has been demonstrated that a purification process can be physically implemented, the proposed distinguishability measures for quantum states could be endowed with an operational interpretation. Finally, by taking advantage of a well-known result for classical Csiszár divergences, we show how to build quantum Csiszár true distances. Thus, our main contribution is the development and analysis of a method for obtaining quantum distances satisfying the triangle inequality in the space of quantum states for Hilbert spaces of arbitrary dimension.

The Gibbs Paradox and Particle Individuality

A consensus seems to have developed that the Gibbs paradox in classical thermodynamics (the discontinuous drop in the entropy of mixing when the mixed gases become equal to each other) is unmysterious: in any actual situation, two gases can be separated or not, and the associated harmless discontinuity from “yes” to “no” is responsible for the discontinuity. By contrast, the Gibbs paradox in statistical physics continues to attract attention. Here, the problem is that standard calculations in statistical mechanics predict a non-vanishing value of the entropy of mixing even when two gases of the same kind are mixed, in conflict with thermodynamic predictions. This version of the Gibbs paradox is often seen as a sign that there is something fundamentally wrong with either the traditional expression S=klnW or with the way W is calculated. It is the aim of this article to review the situation from the orthodox (as opposed to information theoretic) standpoint. We demonstrate how the standard formalism is not only fully capable of dealing with the paradox, but also provides an intuitively clear picture of the relevant physical mechanisms. In particular, we pay attention to the explanatory relevance of the existence of particle trajectories in the classical context. We also discuss how the paradox survives the transition to quantum mechanics, in spite of the symmetrization postulates.

The Effect of Strong Purifying Selection on Genetic Diversity

Purifying selection reduces genetic diversity, both at sites under direct selection and at linked neutral sites. This process, known as background selection, is thought to play an important role in shaping genomic diversity in natural populations. Yet despite its importance, the effects of background selection are not fully understood. Previous theoretical analyses of this process have taken a backward-time approach based on the structured coalescent. While they provide some insight, these methods are either limited to very small samples or are computationally prohibitive. Here, we present a new forward-time analysis of the trajectories of both neutral and deleterious mutations at a nonrecombining locus. We find that strong purifying selection leads to remarkably rich dynamics: neutral mutations can exhibit sweep-like behavior, and deleterious mutations can reach substantial frequencies even when they are guaranteed to eventually go extinct. Our analysis of these dynamics allows us to calculate analytical expressions for the full site frequency spectrum. We find that whenever background selection is strong enough to lead to a reduction in genetic diversity, it also results in substantial distortions to the site frequency spectrum, which can mimic the effects of population expansions or positive selection. Because these distortions are most pronounced in the low and high frequency ends of the spectrum, they become particularly important in larger samples, but may have small effects in smaller samples. We also apply our forward-time framework to calculate other quantities, such as the ultimate fates of polymorphisms or the fitnesses of their ancestral backgrounds.

On the distinguishability of HRF models in fMRI

Modeling the Hemodynamic Response Function (HRF) is a critical step in fMRI studies of brain activity, and it is often desirable to estimate HRF parameters with physiological interpretability. A biophysically informed model of the HRF can be described by a non-linear time-invariant dynamic system. However, the identification of this dynamic system may leave much uncertainty on the exact values of the parameters. Moreover, the high noise levels in the data may hinder the model estimation task. In this context, the estimation of the HRF may be seen as a problem of model falsification or invalidation, where we are interested in distinguishing among a set of eligible models of dynamic systems. Here, we propose a systematic tool to determine the distinguishability among a set of physiologically plausible HRF models. The concept of absolutely input-distinguishable systems is introduced and applied to a biophysically informed HRF model, by exploiting the structure of the underlying non-linear dynamic system. A strategy to model uncertainty in the input time-delay and magnitude is developed and its impact on the distinguishability of two physiologically plausible HRF models is assessed, in terms of the maximum noise amplitude above which it is not possible to guarantee the falsification of one model in relation to another. Finally, a methodology is proposed for the choice of the input sequence, or experimental paradigm, that maximizes the distinguishability of the HRF models under investigation. The proposed approach may be used to evaluate the performance of HRF model estimation techniques from fMRI data.

Distinguishability and agreement with continuous data

The analysis of concordance among repeated measures has received a huge amount of attention in the statistical literature leading to a range of different approaches. However, because all the approaches are able to assess the closeness among the readings taken on the same subject, the conclusions about the degree of concordance should be similar regardless the approach applied. Here, two indices to assess the concordance among continuous repeated measures, the intraclass correlation coefficient and the total deviation index, are applied and compared in two case examples. The first example concerns the repeatability of individual nutrient allocation strategy assessed by stable isotope analysis. The second example dealt with the assessment of the concordance of functional magnetic resonance imaging data that shows spatial correlation. The results differ depending upon the approach applied leading to contradictory conclusions about the degree of concordance. The reason behind these results is discussed reaching the conclusion that the total deviation index is just assessing agreement among repeated measurements, whereas the intraclass correlation coefficient assesses the concept of distinguishability among subjects that involves agreement among repeated measurements and spread of subjects at once. Therefore, the best way to select the right approach is to understand the right question behind the research hypothesis.