A New Approximate Min-Max Theorem with Applications in Cryptography

We propose a novel proof technique that can be applied to attack a broad class of problems in computational complexity, when switching the order of universal and existential quantifiers is helpful. Our approach combines the standard min-max theorem and convex approximation techniques, offering quantitative improvements over the standard way of using min-max theorems as well as more concise and elegant proofs

Approximate Consensus in Highly Dynamic Networks: The Role of Averaging Algorithms

In this paper, we investigate the approximate consensus problem in highly dynamic networks in which topology may change continually and unpredictably. We prove that in both synchronous and partially synchronous systems, approximate consensus is solvable if and only if the communication graph in each round has a rooted spanning tree, i.e., there is a coordinator at each time. The striking point in this result is that the coordinator is not required to be unique and can change arbitrarily from round to round. Interestingly, the class of averaging algorithms, which are memoryless and require no process identifiers, entirely captures the solvability issue of approximate consensus in that the problem is solvable if and only if it can be solved using any averaging algorithm. Concerning the time complexity of averaging algorithms, we show that approximate consensus can be achieved with precision of $\varepsilon$ in a coordinated network model in $O(n^{n+1} \log\frac{1}{\varepsilon})$ synchronous rounds, and in $O(\Delta n^{n\Delta+1} \log\frac{1}{\varepsilon})$ rounds when the maximum round delay for a message to be delivered is $\Delta$. While in general, an upper bound on the time complexity of averaging algorithms has to be exponential, we investigate various network models in which this exponential bound in the number of nodes reduces to a polynomial bound. We apply our results to networked systems with a fixed topology and classical benign fault models, and deduce both known and new results for approximate consensus in these systems. In particular, we show that for solving approximate consensus, a complete network can tolerate up to 2n-3 arbitrarily located link faults at every round, in contrast with the impossibility result established by Santoro and Widmayer (STACS '89) showing that exact consensus is not solvable with n-1 link faults per round originating from the same node

Chemically Cross-Linked Graphene Oxide as a Selective Layer on Electrospun Polyvinyl Alcohol Nanofiber Membrane for Nanofiltration Application.

Graphene oxide (GO) nanosheets were utilized as a selective layer on a highly porous polyvinyl alcohol (PVA) nanofiber support via a pressure-assisted self-assembly technique to synthesize composite nanofiltration membranes. The GO layer was rendered stable by cross-linking the nanosheets (GO-to-GO) and by linking them onto the support surface (GO-to-PVA) using glutaraldehyde (GA). The amounts of GO and GA deposited on the PVA substrate were varied to determine the optimum nanofiltration membrane both in terms of water flux and salt rejection performances. The successful GA cross-linking of GO interlayers and GO-PVA via acetalization was confirmed by FTIR and XPS analyses, which corroborated with other characterization results from contact angle and zeta potential measurements. Morphologies of the most effective membrane (CGOPVA-50) featured a defect-free GA cross-linked GO layer with a thickness of ~67 nm. The best solute rejections of the CGOPVA-50 membrane were 91.01% for Na2SO4 (20 mM), 98.12% for Eosin Y (10 mg/L), 76.92% for Methylene blue (10 mg/L), and 49.62% for NaCl (20 mM). These findings may provide one of the promising approaches in synthesizing mechanically stable GO-based thin-film composite membranes that are effective for solute separation via nanofiltration

Graphene oxide incorporated polysulfone substrate for the fabrication of flat-sheet thin-film composite forward osmosis membranes

© 2015 Elsevier B.V. The preparation and performances of the newly synthesized thin film composite (TFC) forward osmosis (FO) membranes with graphene oxide (GO)-modified support layer are presented in this study. GO nanosheets were incorporated in the polysulfone (PSf) to obtain PSf/GO composite membrane support layer. Polyamide (PA) active layer was subsequently formed on the PSf/GO by interfacial polymerization to obtain the TFC-FO membranes. Results reveal that at an optimal amount of GO addition (0.25wt%), a PSf/GO composite support layer with favorable structural property measured in terms of thickness, porosity and pore size can be achieved. The optimum incorporation of GO in the PSF support layer not only significantly improved water permeability but also allowed effective PA layer formation, in comparison to that of pure PSf support layer which had much lower water permeability. Thus, a TFC-FO membrane with high water flux (19.77Lm-2h-1 against 6.08Lm-2h-1 for pure PSf) and reverse flux selectivity (5.75Lg-1 against 3.36Lg-1 for pure PSf) was obtained under the active layer facing the feed solution or AL-FS membrane orientation. Besides the improved structural properties (reduced structural parameter, S) of the support layer, enhanced support hydrophilicity also contributed to the improved water permeability of the membrane. Beyond a certain point of GO addition (≥0.5wt%), the poor dispersion of GO in dope solution and significant structure change resulted in lower water permeation and weaker mechanical properties in support as well as FO flux/selectivity of consequent TFC membrane. Overall, this study suggests that GO modification of membrane supports could be a promising technique to improve the performances of TFC-FO membranes

I_MDS: an inflammatory bowel disease molecular activity score to classify patients with differing disease-driving pathways and therapeutic response to anti-TNF treatment

Crohn's disease and ulcerative colitis are driven by both common and distinct underlying mechanisms of pathobiology. Both diseases, exhibit heterogeneity underscored by the variable clinical responses to therapeutic interventions. We aimed to identify disease-driving pathways and classify individuals into subpopulations that differ in their pathobiology and response to treatment. We applied hierarchical clustering of enrichment scores derived from gene set variation analysis of signatures representative of various immunological processes and activated cell types, to a colonic biopsy dataset that included healthy volunteers, Crohn's disease and ulcerative colitis patients. Patient stratification at baseline or after anti-TNF treatment in clinical responders and non-responders was queried. Signatures with significantly different enrichment scores were identified using a general linear model. Comparisons to healthy controls were made at baseline in all participants and then separately in responders and non-responders. Fifty-nine percent of the signatures were commonly enriched in both conditions at baseline, supporting the notion of a disease continuum within ulcerative colitis and Crohn's disease. Signatures included T cells, macrophages, neutrophil activation and poly:IC signatures, representing acute inflammation and a complex mix of potential disease-driving biology. Collectively, identification of significantly enriched signatures allowed establishment of an inflammatory bowel disease molecular activity score which uses biopsy transcriptomics as a surrogate marker to accurately track disease severity. This score separated diseased from healthy samples, enabled discrimination of clinical responders and non-responders at baseline with 100% specificity and 78.8% sensitivity, and was validated in an independent data set that showed comparable classification. Comparing responders and non-responders separately at baseline to controls, 43% and 70% of signatures were enriched, respectively, suggesting greater molecular dysregulation in TNF non-responders at baseline. This methodological approach could facilitate better targeted design of clinical studies to test therapeutics, concentrating on patient subsets sharing similar underlying pathobiology, therefore increasing the likelihood of clinical response

Convergence rates and source conditions for Tikhonov regularization with sparsity constraints

This paper addresses the regularization by sparsity constraints by means of weighted $\ell^p$ penalties for $0\leq p\leq 2$. For $1\leq p\leq 2$ special attention is payed to convergence rates in norm and to source conditions. As main result it is proven that one gets a convergence rate in norm of $\sqrt{\delta}$ for $1\leq p\leq 2$ as soon as the unknown solution is sparse. The case $p=1$ needs a special technique where not only Bregman distances but also a so-called Bregman-Taylor distance has to be employed. For $p<1$ only preliminary results are shown. These results indicate that, different from $p\geq 1$, the regularizing properties depend on the interplay of the operator and the basis of sparsity. A counterexample for $p=0$ shows that regularization need not to happen

Cortico-autonomic local arousals and heightened somatosensory arousability during NREMS of mice in neuropathic pain.

Frequent nightly arousals typical for sleep disorders cause daytime fatigue and present health risks. As such arousals are often short, partial, or occur locally within the brain, reliable characterization in rodent models of sleep disorders and in human patients is challenging. We found that the EEG spectral composition of non-rapid eye movement sleep (NREMS) in healthy mice shows an infraslow (~50 s) interval over which microarousals appear preferentially. NREMS could hence be vulnerable to abnormal arousals on this time scale. Chronic pain is well-known to disrupt sleep. In the spared nerve injury (SNI) mouse model of chronic neuropathic pain, we found more numerous local cortical arousals accompanied by heart rate increases in hindlimb primary somatosensory, but not in prelimbic, cortices, although sleep macroarchitecture appeared unaltered. Closed-loop mechanovibrational stimulation further revealed higher sensory arousability. Chronic pain thus preserved conventional sleep measures but resulted in elevated spontaneous and evoked arousability. We develop a novel moment-to-moment probing of NREMS vulnerability and propose that chronic pain-induced sleep complaints arise from perturbed arousability

Universal Geometric Graphs

We introduce and study the problem of constructing geometric graphs that have few vertices and edges and that are universal for planar graphs or for some sub-class of planar graphs; a geometric graph is \emph{universal} for a class $\mathcal H$ of planar graphs if it contains an embedding, i.e., a crossing-free drawing, of every graph in $\mathcal H$. Our main result is that there exists a geometric graph with $n$ vertices and $O(n \log n)$ edges that is universal for $n$-vertex forests; this extends to the geometric setting a well-known graph-theoretic result by Chung and Graham, which states that there exists an $n$-vertex graph with $O(n \log n)$ edges that contains every $n$-vertex forest as a subgraph. Our $O(n \log n)$ bound on the number of edges cannot be improved, even if more than $n$ vertices are allowed. We also prove that, for every positive integer $h$, every $n$-vertex convex geometric graph that is universal for $n$-vertex outerplanar graphs has a near-quadratic number of edges, namely $\Omega_h(n^{2-1/h})$; this almost matches the trivial $O(n^2)$ upper bound given by the $n$-vertex complete convex geometric graph. Finally, we prove that there exists an $n$-vertex convex geometric graph with $n$ vertices and $O(n \log n)$ edges that is universal for $n$-vertex caterpillars.Comment: 20 pages, 8 figures; a 12-page extended abstracts of this paper will appear in the Proceedings of the 46th Workshop on Graph-Theoretic Concepts in Computer Science (WG 2020

Optimized T1- and T2-weighted volumetric brain imaging as a diagnostic tool in very preterm neonates.

BACKGROUND: T1- and T2-W MR sequences used for obtaining diagnostic information and morphometric measurements in the neonatal brain are frequently acquired using different imaging protocols. Optimizing one protocol for obtaining both kinds of information is valuable. OBJECTIVE: To determine whether high-resolution T1- and T2-W volumetric sequences optimized for preterm brain imaging could provide both diagnostic and morphometric value. MATERIALS AND METHODS: Thirty preterm neonates born between 24 and 32 weeks' gestational age were scanned during the first 2 weeks after birth. T1- and T2-W high-resolution sequences were optimized in terms of signal-to-noise ratio, contrast-to-noise ratio and scan time and compared to conventional spin-echo-based sequences. RESULTS: No differences were found between conventional and high-resolution T1-W sequences for diagnostic confidence, image quality and motion artifacts. A preference for conventional over high-resolution T2-W sequences for image quality was observed. High-resolution T1 images provided better delineation of thalamic myelination and the superior temporal sulcus. No differences were found for detection of myelination and sulcation using conventional and high-resolution T2-W images. CONCLUSION: High-resolution T1- and T2-W volumetric sequences can be used in clinical MRI in the very preterm brain to provide both diagnostic and morphometric information