Tight Bounds for the Randomized and Quantum Communication Complexities of Equality with Small Error

We investigate the randomized and quantum communication complexities of the well-studied Equality function with small error probability $\epsilon$, getting the optimal constant factors in the leading terms in a number of different models. In the randomized model, 1) we give a general technique to convert public-coin protocols to private-coin protocols by incurring a small multiplicative error, at a small additive cost. This is an improvement over Newman's theorem [Inf. Proc. Let.'91] in the dependence on the error parameter. 2) Using this we obtain a $(\log(n/\epsilon^2)+4)$-cost private-coin communication protocol that computes the $n$-bit Equality function, to error $\epsilon$. This improves upon the $\log(n/\epsilon^3)+O(1)$ upper bound implied by Newman's theorem, and matches the best known lower bound, which follows from Alon [Comb. Prob. Comput.'09], up to an additive $\log\log(1/\epsilon)+O(1)$. In the quantum model, 1) we exhibit a one-way protocol of cost $\log(n/\epsilon)+4$, that uses only pure states and computes the $n$-bit Equality function to error $\epsilon$. This bound was implicitly already shown by Nayak [PhD thesis'99]. 2) We show that any $\epsilon$-error one-way protocol for $n$-bit Equality that uses only pure states communicates at least $\log(n/\epsilon)-\log\log(1/\epsilon)-O(1)$ qubits. 3) We exhibit a one-way protocol of cost $\log(\sqrt{n}/\epsilon)+3$, that uses mixed states and computes the $n$-bit Equality function to error $\epsilon$. This is also tight up to an additive $\log\log(1/\epsilon)+O(1)$, which follows from Alon's result. Our upper bounds also yield upper bounds on the approximate rank and related measures of the Identity matrix. This also implies improved upper bounds on these measures for the distributed SINK function, which was recently used to refute the randomized and quantum versions of the log-rank conjecture.Comment: 16 page

DNA methylation profiling to assess pathogenicity of BRCA1 unclassified variants in breast cancer

Germline pathogenic mutations in BRCA1 increase risk of developing breast cancer. Screening for mutations in BRCA1 frequently identifies sequence variants of unknown pathogenicity and recent work has aimed to develop methods for determining pathogenicity. We previously observed that tumor DNA methylation can differentiate BRCA1-mutated from BRCA1-wild type tumors. We hypothesized that we could predict pathogenicity of variants based on DNA methylation profiles of tumors that had arisen in carriers of unclassified variants. We selected 150 FFPE breast tumor DNA samples [47 BRCA1 pathogenic mutation carriers, 65 BRCAx (BRCA1-wild type), 38 BRCA1 test variants] and analyzed a subset (n=54) using the Illumina 450K methylation platform, using the remaining samples for bisulphite pyrosequencing validation. Three validated markers (BACH2, C8orf31, and LOC654342) were combined with sequence bioinformatics in a model to predict pathogenicity of 27 variants (independent test set). Predictions were compared with standard multifactorial likelihood analysis. Prediction was consistent for c.5194-12G>A (IVS 19-12 G>A) (P>0.99); 13 variants were considered not pathogenic or likely not pathogenic using both approaches. We conclude that tumor DNA methylation data alone has potential to be used in prediction of BRCA1 variant pathogenicity but is not independent of estrogen receptor status and grade, which are used in current multifactorial models to predict pathogenicity

Split buildings of type F₄ in buildings of type E₆

A symplectic polarity of a building of type is a polarity whose fixed point structure is a building of type containing residues isomorphic to symplectic polar spaces (i.e., so-called split buildings of type ). In this paper, we show in a geometric way that every building of type contains, up to conjugacy, a unique class of symplectic polarities. We also show that the natural point-line geometry of each split building of type fully embedded in the natural point-line geometry of arises from a symplectic polarity

On Hierarchy and Equivalence of Relativistic Equations for Massive Fields

A non-canonical correspondence of the complete sets of solutions to the Dirac and Klein-Gordon free equations in Minkowski space-time is established. This allows for a novel viewpoint on the relationship of relativistic equations for different spins and on the origin of spinor transformations. In particular, starting from a solution to the Dirac equation, one obtains a chain of other solutions to both Dirac and Klein-Gordon equations. A comparison with the massless case is performed, and examples of non-trivial singular solutions are presented. A generalization to Riemannian space-time and inclusion of interactions are briefly discussed.Comment: 7 pages, twocolumn. Problem of construction the hierarchy of solutions in the massive case reformulate

Exploring the types of social support exchanged by survivors of pediatric stroke and their families in an online peer support community: a qualitative thematic analysis (Preprint)

Background: Pediatric stroke is relatively rare, under researched and there is little awareness of its occurrence in wider society. There is a paucity of literature on effectiveness of interventions to improve rehabilitation and services available to survivors. Access to online health communities through the internet may be a means of support for pediatric stroke patients and their families during recovery, however little research has been done in this area. Objective: To identify the types of social support provided by an online peer support group to survivors of pediatric stroke and their families. Methods: Qualitative thematic analysis of posts from a pediatric stroke population on a UK online stroke community active between 2004-2011. The population was split into two groups, based upon whether stroke survivors were 18 and under ( 18y) or over 18 (>18y) at the time of posting. The posts were read by two authors who used the adapted Social Support Behaviour Code to analyze the types of social support exchanged. Results: 52 participants who experienced a pediatric stroke were identified, who posted a total of 425 messages to the community. 41 survivors were 18y at the time of posting and written about by others (31/35 mothers), while 11 were >18y and writing about themselves. Survivors and their familes joined together in discussion threads . Support was offered and received by all participants, regardless of age. Of all 425 posts, 193 (45.4%) contained at least one instance of social support. All five types of social support were identified: informational, emotional, network, esteem support and tangible aid. Informational and emotional support were most commonly exchanged. Emotional support was offered more often than informational support among participants 18y at the time of posting, this finding was reversed in the >18y group. Network support and esteem support were less commonly exchanged. Notably, no access support (a sub-category of network support) was exchanged on the community. Tangible aid was the least commonly type of support offered. Conclusions: We found evidence of engagement of childhood stroke survivors and their families in an online stroke community, with peer support being exchanged between both long and short-term survivors of pediatric stroke. Engagement of long-term survivors of pediatric stroke through the online community was key as they were able to offer informational support from lived experience. Further interventional research is needed to assess health and rehabilitation outcomes from engagement with online support groups. Research is also needed to ensure safe, nurturing online communities. Clinical Trial: n/

Centimeter-long electron transport in marine sediments via conductive minerals

© 2015 International Society for Microbial Ecology All rights reserved. Centimeter-long electron conduction through marine sediments, in which electrons derived from sulfide in anoxic sediments are transported to oxygen in surficial sediments, may have an important influence on sediment geochemistry. Filamentous bacteria have been proposed to mediate the electron transport, but the filament conductivity could not be verified and other mechanisms are possible. Surprisingly, previous investigations have never actually measured the sediment conductivity or its basic physical properties. Here we report direct measurements that demonstrate centimeter-long electron flow through marine sediments, with conductivities sufficient to account for previously estimated electron fluxes. Conductivity was lost for oxidized sediments, which contrasts with the previously described increase in the conductivity of microbial biofilms upon oxidation. Adding pyrite to the sediments significantly enhanced the conductivity. These results suggest that the role of conductive minerals, which are more commonly found in sediments than centimeter-long microbial filaments, need to be considered when modeling marine sediment biogeochemistry

Movement-related beta oscillations show high intra-individual reliability

Oscillatory activity in the beta frequency range (15-30Hz) recorded from human sensorimotor cortex is of increasing interest as a putative biomarker of motor system function and dysfunction. Despite its increasing use in basic and clinical research, surprisingly little is known about the test-retest reliability of spectral power and peak frequency measures of beta oscillatory signals from sensorimotor cortex. Establishing that these beta measures are stable over time in healthy populations is a necessary precursor to their use in the clinic. Here, we used scalp electroencephalography (EEG) to evaluate intra-individual reliability of beta-band oscillations over six sessions, focusing on changes in beta activity during movement (Movement-Related Beta Desynchronization, MRBD) and after movement termination (Post-Movement Beta Rebound, PMBR). Subjects performed visually-cued unimanual wrist flexion and extension. We assessed Intraclass Correlation Coefficients (ICC) and between-session correlations for spectral power and peak frequency measures of movement-related and resting beta activity. Movement-related and resting beta power from both sensorimotor cortices was highly reliable across sessions. Resting beta power yielded highest reliability (average ICC=0.903), followed by MRBD (average ICC=0.886) and PMBR (average ICC=0.663). Notably, peak frequency measures yielded lower ICC values compared to the assessment of spectral power, particularly for movement-related beta activity (ICC=0.386-0.402). Our data highlight that power measures of movement-related beta oscillations are highly reliable, while corresponding peak frequency measures show greater intra-individual variability across sessions. Importantly, our finding that beta power estimates show high intra-individual reliability over time serves to validate the notion that these measures reflect meaningful individual differences that can be utilised in basic research and clinical studies

Photobiomodulation Effect of 850 nm Near-infrared Diode Laser on the Release of M1-related Cytokines Inmonocytic THP-1 Cells

Photobiomodulation (PBM) is a form of the use of visible red and Near-infrared (NIR) light at low power, where a laser light photon is absorbed at the electronic level, without heat production. PBM can be applied in wide range of treatment to help the wound, inflammation, edema, and pain reduction. However, there is a lack of scientific documentation regarding its actual effects. Objectives: This study assesses the impact of PBM on the release of M1-related cytokine in monocyte cells with particular emphasis on interleukin-1β (IL-1β) and Tumour Necrosis Factor α (TNF-α). Methods: Tamm-Horsfall Protein 1 (THP-1) macrophages M1 cells have been exposed to the light from the diode laser of 850nmat different doses (0, 0.6, 1.2 and 3.6 J/cm2). The release of cytokines was determined by enzyme-linked immunosorbent assay, after different periods of incubation (0, 12, 24, and 48 hours) post-irradiation. The proliferation of fibroblast cells suspended in irradiated M1-supernatent was evaluated for the same periods of incubation. Results: The results showed that PBM significantly enhanced M1-related cytokine release (p < 0.05). Obviously, IL-1β increased post-irradiation at 1.2 J/cm2 more than other doses for all incubation periods. TNF-α was decreased significantly after two days of irradiation (p < 0.005) for all doses. A significant increase in fibroblast proliferation (p < 0.005) was observed concomitant with the boost of cytokine release. Conclusion: This in vitro study has demonstrated that the PBM of the 850 nm diode laser therapy can enhance M1-related cytokine release, which in turn increases the proliferation of fibroblast cells. Moreover, PBM at 850 nm plays an anti-inflammatory role, which manifested by decreasing the level of TNF-α. Therefore, this therapy may be able to accelerate the wound healing process