Convex Trace Functions on Quantum Channels and the Additivity Conjecture

We study a natural generalization of the additivity problem in quantum information theory: given a pair of quantum channels, then what is the set of convex trace functions that attain their maximum on unentangled inputs, if they are applied to the corresponding output state? We prove several results on the structure of the set of those convex functions that are "additive" in this more general sense. In particular, we show that all operator convex functions are additive for the Werner-Holevo channel in 3x3 dimensions, which contains the well-known additivity results for this channel as special cases.Comment: 9 pages, 1 figure. Published versio

Significance of solutions of the inverse Biot-Savart problem in thick superconductors

The evaluation of current distributions in thick superconductors from field profiles near the sample surface is investigated theoretically. A simple model of a cylindrical sample, in which only circular currents are flowing, reduces the inversion to a linear least squares problem, which is analyzed by singular value decomposition. Without additional assumptions about the current distribution (e.g. constant current over the sample thickness), the condition of the problem is very bad, leading to unrealistic results. However, any additional assumption strongly influences the solution and thus renders the solutions again questionable. These difficulties are unfortunately inherent to the inverse Biot-Savart problem in thick superconductors and cannot be avoided by any models or algorithms

Towards precision medicine for pain: diagnostic biomarkers and repurposed drugs

We endeavored to identify objective blood biomarkers for pain, a subjective sensation with a biological basis, using a stepwise discovery, prioritization, validation, and testing in independent cohorts design. We studied psychiatric patients, a high risk group for co-morbid pain disorders and increased perception of pain. For discovery, we used a powerful within-subject longitudinal design. We were successful in identifying blood gene expression biomarkers that were predictive of pain state, and of future emergency department (ED) visits for pain, more so when personalized by gender and diagnosis. MFAP3, which had no prior evidence in the literature for involvement in pain, had the most robust empirical evidence from our discovery and validation steps, and was a strong predictor for pain in the independent cohorts, particularly in females and males with PTSD. Other biomarkers with best overall convergent functional evidence for involvement in pain were GNG7, CNTN1, LY9, CCDC144B, and GBP1. Some of the individual biomarkers identified are targets of existing drugs. Moreover, the biomarker gene expression signatures were used for bioinformatic drug repurposing analyses, yielding leads for possible new drug candidates such as SC-560 (an NSAID), and amoxapine (an antidepressant), as well as natural compounds such as pyridoxine (vitamin B6), cyanocobalamin (vitamin B12), and apigenin (a plant flavonoid). Our work may help mitigate the diagnostic and treatment dilemmas that have contributed to the current opioid epidemic

Precision medicine for suicidality: from universality to subtypes and personalization

Suicide remains a clear, present and increasing public health problem, despite being a potentially preventable tragedy. Its incidence is particularly high in people with overt or un(der)diagnosed psychiatric disorders. Objective and precise identification of individuals at risk, ways of monitoring response to treatments and novel preventive therapeutics need to be discovered, employed and widely deployed. We sought to investigate whether blood gene expression biomarkers for suicide (that is, a ‘liquid biopsy’ approach) can be identified that are more universal in nature, working across psychiatric diagnoses and genders, using larger cohorts than in previous studies. Such markers may reflect and/or be a proxy for the core biology of suicide. We were successful in this endeavor, using a comprehensive stepwise approach, leading to a wealth of findings. Steps 1, 2 and 3 were discovery, prioritization and validation for tracking suicidality, resulting in a Top Dozen list of candidate biomarkers comprising the top biomarkers from each step, as well as a larger list of 148 candidate biomarkers that survived Bonferroni correction in the validation step. Step 4 was testing the Top Dozen list and Bonferroni biomarker list for predictive ability for suicidal ideation (SI) and for future hospitalizations for suicidality in independent cohorts, leading to the identification of completely novel predictive biomarkers (such as CLN5 and AK2), as well as reinforcement of ours and others previous findings in the field (such as SLC4A4 and SKA2). Additionally, we examined whether subtypes of suicidality can be identified based on mental state at the time of high SI and identified four potential subtypes: high anxiety, low mood, combined and non-affective (psychotic). Such subtypes may delineate groups of individuals that are more homogenous in terms of suicidality biology and behavior. We also studied a more personalized approach, by psychiatric diagnosis and gender, with a focus on bipolar males, the highest risk group. Such a personalized approach may be more sensitive to gender differences and to the impact of psychiatric co-morbidities and medications. We compared testing the universal biomarkers in everybody versus testing by subtypes versus personalized by gender and diagnosis, and show that the subtype and personalized approaches permit enhanced precision of predictions for different universal biomarkers. In particular, LHFP appears to be a strong predictor for suicidality in males with depression. We also directly examined whether biomarkers discovered using male bipolars only are better predictors in a male bipolar independent cohort than universal biomarkers and show evidence for a possible advantage of personalization. We identified completely novel biomarkers (such as SPTBN1 and C7orf73), and reinforced previously known biomarkers (such as PTEN and SAT1). For diagnostic ability testing purposes, we also examined as predictors phenotypic measures as apps (for suicide risk (CFI-S, Convergent Functional Information for Suicidality) and for anxiety and mood (SASS, Simplified Affective State Scale)) by themselves, as well as in combination with the top biomarkers (the combination being our a priori primary endpoint), to provide context and enhance precision of predictions. We obtained area under the curves of 90% for SI and 77% for future hospitalizations in independent cohorts. Step 5 was to look for mechanistic understanding, starting with examining evidence for the Top Dozen and Bonferroni biomarkers for involvement in other psychiatric and non-psychiatric disorders, as a mechanism for biological predisposition and vulnerability. The biomarkers we identified also provide a window towards understanding the biology of suicide, implicating biological pathways related to neurogenesis, programmed cell death and insulin signaling from the universal biomarkers, as well as mTOR signaling from the male bipolar biomarkers. In particular, HTR2A increase coupled with ARRB1 and GSK3B decreases in expression in suicidality may provide a synergistic mechanistical corrective target, as do SLC4A4 increase coupled with AHCYL1 and AHCYL2 decrease. Step 6 was to move beyond diagnostics and mechanistical risk assessment, towards providing a foundation for personalized therapeutics. Items scored positive in the CFI-S and subtypes identified by SASS in different individuals provide targets for personalized (psycho)therapy. Some individual biomarkers are targets of existing drugs used to treat mood disorders and suicidality (lithium, clozapine and omega-3 fatty acids), providing a means toward pharmacogenomics stratification of patients and monitoring of response to treatment. Such biomarkers merit evaluation in clinical trials. Bioinformatics drug repurposing analyses with the gene expression biosignatures of the Top Dozen and Bonferroni-validated universal biomarkers identified novel potential therapeutics for suicidality, such as ebselen (a lithium mimetic), piracetam (a nootropic), chlorogenic acid (a polyphenol) and metformin (an antidiabetic and possible longevity promoting drug). Finally, based on the totality of our data and of the evidence in the field to date, a convergent functional evidence score prioritizing biomarkers that have all around evidence (track suicidality, predict it, are reflective of biological predisposition and are potential drug targets) brought to the fore APOE and IL6 from among the universal biomarkers, suggesting an inflammatory/accelerated aging component that may be a targetable common denominator

Cascades: A view from Audience

Cascades on online networks have been a popular subject of study in the past decade, and there is a considerable literature on phenomena such as diffusion mechanisms, virality, cascade prediction, and peer network effects. However, a basic question has received comparatively little attention: how desirable are cascades on a social media platform from the point of view of users? While versions of this question have been considered from the perspective of the producers of cascades, any answer to this question must also take into account the effect of cascades on their audience. In this work, we seek to fill this gap by providing a consumer perspective of cascade. Users on online networks play the dual role of producers and consumers. First, we perform an empirical study of the interaction of Twitter users with retweet cascades. We measure how often users observe retweets in their home timeline, and observe a phenomenon that we term the "Impressions Paradox": the share of impressions for cascades of size k decays much slower than frequency of cascades of size k. Thus, the audience for cascades can be quite large even for rare large cascades. We also measure audience engagement with retweet cascades in comparison to non-retweeted content. Our results show that cascades often rival or exceed organic content in engagement received per impression. This result is perhaps surprising in that consumers didn't opt in to see tweets from these authors. Furthermore, although cascading content is widely popular, one would expect it to eventually reach parts of the audience that may not be interested in the content. Motivated by our findings, we posit a theoretical model that focuses on the effect of cascades on the audience. Our results on this model highlight the balance between retweeting as a high-quality content selection mechanism and the role of network users in filtering irrelevant content

Moments of the Proton F2 Structure Function at Low Q2

The Q^2 dependence of inclusive electron-proton scattering F_2 structure function data in both the nucleon resonance region and the deep inelastic region, at momentum transfers below 5 (GeV/c)^2, is investigated. Moments of F_2 are constructed, down to momentum transfers of Q^2 ~ 0.1 (GeV/c)^2. The second moment is only slowly varying with Q^2 down to Q^2 ~ 1 (GeV/c)^2, which is a reflection of duality. Below Q^2 of 1 (GeV/c)^2, the Q^2 dependence of the moments is predominantly governed by the elastic contribution, whereas the inelastic channels still seem governed by local duality.Comment: 11 page paper, 1 LaTeX file, 10 postscript figure file

Scaling of space and timelike response of confined relativistic particles

The response of a relativistic particle bound in a linear confining well is calculated as a function of the momentum and energy transfer, q, \nu. At large values of |q| the response exhibits scaling in the variable y=\nu-|q|, which is proportional to the Nachtmann variable, \xi. The approach to scaling is studied at smaller values of |q|. Scaling occurs at \nu~|q| at relatively small |q|, and its validity extends over the entire \xi range as |q| increases; this behavior is observed in electron-proton scattering. About 10% of the response at large |q| is in the timelike region where \nu>|q|, and it is necessary to include it to fulfill the particle number sum rule. The Gross-Llewellyn Smith and Gottfried sum rules are discussed in the context of these results.Comment: 10 pages, 5 figures; submitted to Physics Letters

Localizability of Wireless Sensor Networks: Beyond Wheel Extension

A network is called localizable if the positions of all the nodes of the network can be computed uniquely. If a network is localizable and embedded in plane with generic configuration, the positions of the nodes may be computed uniquely in finite time. Therefore, identifying localizable networks is an important function. If the complete information about the network is available at a single place, localizability can be tested in polynomial time. In a distributed environment, networks with trilateration orderings (popular in real applications) and wheel extensions (a specific class of localizable networks) embedded in plane can be identified by existing techniques. We propose a distributed technique which efficiently identifies a larger class of localizable networks. This class covers both trilateration and wheel extensions. In reality, exact distance is almost impossible or costly. The proposed algorithm based only on connectivity information. It requires no distance information