Information geometry of density matrices and state estimation

Given a pure state vector |x> and a density matrix rho, the function p(x|rho)= defines a probability density on the space of pure states parameterised by density matrices. The associated Fisher-Rao information measure is used to define a unitary invariant Riemannian metric on the space of density matrices. An alternative derivation of the metric, based on square-root density matrices and trace norms, is provided. This is applied to the problem of quantum-state estimation. In the simplest case of unitary parameter estimation, new higher-order corrections to the uncertainty relations, applicable to general mixed states, are derived.Comment: published versio

Post‐traumatic stress disorder\u27s relation with positive and negative emotional avoidance: The moderating role of gender

Post‐traumatic stress disorder (PTSD) is characterized by avoidance of trauma‐related emotions. Research indicates that this avoidance may extend to any emotional experience that elicits distress, including those that are unrelated to the trauma. Literature in this area has been limited in its exclusive focus on negative emotions. Despite evidence of gender differences in PTSD and emotional avoidance separately, no studies to date have examined gender as a moderator of their association. The goal of the current study was to extend research by exploring the moderating role of gender in the relation between PTSD symptom severity and positive and negative emotional avoidance. Participants were 276 trauma‐exposed individuals (65.9% female, 65.6% White, Mage = 19.24) from a university in the north‐eastern United States. Moderation results indicated a main effect for PTSD symptom severity on both positive (b = 0.07, p \u3c .001) and negative (b = 0.04, p = .03) emotional avoidance. The interaction of gender and PTSD symptom severity was significant for positive emotion avoidance (b = 0.97, p = .01). Analysis of simple slopes revealed that PTSD symptom severity was significantly associated with positive emotional avoidance for males (b = 0.13, p \u3c .001) but not females (b = 0.03, p = .08). Results suggest the importance of gender‐sensitive recommendations for assessment and treatment of emotional avoidance in PTSD

Research on nonlinear optical materials: an assessment. IV. Photorefractive and liquid crystal materials

This panel considered two separate subject areas: photorefractive materials used for nonlinear optics and liquid crystal materials used in light valves. Two related subjects were not considered due to lack of expertise on the panel: photorefractive materials used in light valves and liquid crystal materials used in nonlinear optics. Although the inclusion of a discussion of light valves by a panel on nonlinear optical materials at first seems odd, it is logical because light valves and photorefractive materials perform common functions

On the dominance of J(P)=0(+) ground states in even-even nuclei from random two-body interactions

Recent calculations using random two-body interactions showed a preponderance of J(P)=0(+) ground states, despite the fact that there is no strong pairing character in the force. We carry out an analysis of a system of identical particles occupying orbits with j=1/2, 3/2 and 5/2 and discuss some general features of the spectra derived from random two-body interactions. We show that for random two-body interactions that are not time-reversal invariant the dominance of 0(+) states in this case is more pronounced, indicating that time-reversal invariance cannot be the origin of the 0(+) dominance.Comment: 8 pages, 3 tables and 3 figures. Phys. Rev. C, in pres

Quantification and expert evaluation of evidence for chemopredictive biomarkers to personalize cancer treatment.

Predictive biomarkers have the potential to facilitate cancer precision medicine by guiding the optimal choice of therapies for patients. However, clinicians are faced with an enormous volume of often-contradictory evidence regarding the therapeutic context of chemopredictive biomarkers.We extensively surveyed public literature to systematically review the predictive effect of 7 biomarkers claimed to predict response to various chemotherapy drugs: ERCC1-platinums, RRM1-gemcitabine, TYMS-5-fluorouracil/Capecitabine, TUBB3-taxanes, MGMT-temozolomide, TOP1-irinotecan/topotecan, and TOP2A-anthracyclines. We focused on studies that investigated changes in gene or protein expression as predictors of drug sensitivity or resistance. We considered an evidence framework that ranked studies from high level I evidence for randomized controlled trials to low level IV evidence for pre-clinical studies and patient case studies.We found that further in-depth analysis will be required to explore methodological issues, inconsistencies between studies, and tumor specific effects present even within high evidence level studies. Some of these nuances will lend themselves to automation, others will require manual curation. However, the comprehensive cataloging and analysis of dispersed public data utilizing an evidence framework provides a high level perspective on clinical actionability of these protein biomarkers. This framework and perspective will ultimately facilitate clinical trial design as well as therapeutic decision-making for individual patients

Quantum noise and stochastic reduction

In standard nonrelativistic quantum mechanics the expectation of the energy is a conserved quantity. It is possible to extend the dynamical law associated with the evolution of a quantum state consistently to include a nonlinear stochastic component, while respecting the conservation law. According to the dynamics thus obtained, referred to as the energy-based stochastic Schrodinger equation, an arbitrary initial state collapses spontaneously to one of the energy eigenstates, thus describing the phenomenon of quantum state reduction. In this article, two such models are investigated: one that achieves state reduction in infinite time, and the other in finite time. The properties of the associated energy expectation process and the energy variance process are worked out in detail. By use of a novel application of a nonlinear filtering method, closed-form solutions--algebraic in character and involving no integration--are obtained for both these models. In each case, the solution is expressed in terms of a random variable representing the terminal energy of the system, and an independent noise process. With these solutions at hand it is possible to simulate explicitly the dynamics of the quantum states of complicated physical systems.Comment: 50 page

Martingale Models for Quantum State Reduction

Stochastic models for quantum state reduction give rise to statistical laws that are in most respects in agreement with those of quantum measurement theory. Here we examine the correspondence of the two theories in detail, making a systematic use of the methods of martingale theory. An analysis is carried out to determine the magnitude of the fluctuations experienced by the expectation of the observable during the course of the reduction process and an upper bound is established for the ensemble average of the greatest fluctuations incurred. We consider the general projection postulate of L\"uders applicable in the case of a possibly degenerate eigenvalue spectrum, and derive this result rigorously from the underlying stochastic dynamics for state reduction in the case of both a pure and a mixed initial state. We also analyse the associated Lindblad equation for the evolution of the density matrix, and obtain an exact time-dependent solution for the state reduction that explicitly exhibits the transition from a general initial density matrix to the L\"uders density matrix. Finally, we apply Girsanov's theorem to derive a set of simple formulae for the dynamics of the state in terms of a family of geometric Brownian motions, thereby constructing an explicit unravelling of the Lindblad equation.Comment: 30 pages LaTeX. Submitted to Journal of Physics

Incremental Mutual Information: A New Method for Characterizing the Strength and Dynamics of Connections in Neuronal Circuits

Understanding the computations performed by neuronal circuits requires characterizing the strength and dynamics of the connections between individual neurons. This characterization is typically achieved by measuring the correlation in the activity of two neurons. We have developed a new measure for studying connectivity in neuronal circuits based on information theory, the incremental mutual information (IMI). By conditioning out the temporal dependencies in the responses of individual neurons before measuring the dependency between them, IMI improves on standard correlation-based measures in several important ways: 1) it has the potential to disambiguate statistical dependencies that reflect the connection between neurons from those caused by other sources (e. g. shared inputs or intrinsic cellular or network mechanisms) provided that the dependencies have appropriate timescales, 2) for the study of early sensory systems, it does not require responses to repeated trials of identical stimulation, and 3) it does not assume that the connection between neurons is linear. We describe the theory and implementation of IMI in detail and demonstrate its utility on experimental recordings from the primate visual system

Evaluating Resources for Cancer Caregivers on Cancer Hospital Websites

Background: Over the last 20 years, cancer care has transitioned from long hospitalizations to short inpatient stays or outpatient settings. As patients and their family members increasingly turn to the Internet for health information, cancer hospitals have the opportunity to provide clear, credible information on their websites to cancer patients, families, and informal caregivers. Objective: Recommend improved web content and organization of caregiver information for patients and families at our local comprehensive cancer center. Methods: One librarian and two library science students conducted a cognitive walk-through to assess websites of two cancer hospitals in the Mid-Atlantic Region. Each evaluator independently performed seven tasks distributed among three different caregiver personas to evaluate the presence and accessibility of caregiver information on these cancer hospital websites.Results: Our findings indicate that these websites are not conducive to providing information for cancer caregiver support because of the following: key information is unavailable, navigation on the landing page is limited, broken links, ambiguous page titles, page titles that do not match the content of the page, and lack of contact information (phone number, email) for service access. Conclusion: Opportunities are available to improve cancer caregiver information on cancer hospital websites. Library professionals can help cancer hospitals improve caregiver information on their websites with recommendations for additional content and clearer organization. This is a way to build partnerships between library professionals and cancer hospitals