A Nonlinear Plancherel Theorem with Applications to Global Well-Posedness for the Defocusing Davey-Stewartson Equation and to the Inverse Boundary Value Problem of Calderón

We prove a Plancherel theorem for a nonlinear Fourier transform in two dimensions arising in the Inverse Scattering method for the defocusing Davey-Stewartson II equation. We then use it to prove global well-posedness and scattering in $L^2$ for defocusing DSII. This Plancherel theorem also implies global uniqueness in the inverse boundary value problem of Calder\'on in dimension $2$, for conductivities \sigma>0 with $\log \sigma \in \dot H^1$. The proof of the nonlinear Plancherel theorem includes new estimates on classical fractional integrals, as well as a new result on $L^2$-boundedness of pseudo-differential operators with non-smooth symbols, valid in all dimensions

Grover's search with faults on some marked elements

Grover's algorithm is a quantum query algorithm solving the unstructured search problem of size $N$ using $O(\sqrt{N})$ queries. It provides a significant speed-up over any classical algorithm \cite{Gro96}. The running time of the algorithm, however, is very sensitive to errors in queries. It is known that if query may fail (report all marked elements as unmarked) the algorithm needs $\Omega(N)$ queries to find a marked element \cite{RS08}. \cite{AB+13} have proved the same result for the model where each marked element has its own probability to be reported as unmarked. We study the behavior of Grover's algorithm in the model where the search space contains both faulty and non-faulty marked elements. We show that in this setting it is indeed possible to find one of non-faulty marked items in $O(\sqrt{N})$ queries. We also analyze the limiting behavior of the algorithm for a large number of steps and show the existence and the structure of limiting state $\rho_{lim}$.Comment: 17 pages, 6 figure

On the angular momentum transport due to vertical convection in accretion discs

The mechanism of angular momentum transport in accretion discs has long been debated. Although the magnetorotational instability appears to be a promising process, poorly ionized regions of accretion discs may not undergo this instability. In this letter, we revisit the possibility of transporting angular momentum by turbulent thermal convection. Using high-resolution spectral methods, we show that strongly turbulent convection can drive outward angular momentum transport at a rate that is, under certain conditions, compatible with observations of discs. We find however that the angular momentum transport is always much weaker than the vertical heat transport. These results indicate that convection might be another way to explain global disc evolution, provided that a sufficiently unstable vertical temperature profile can be maintained.Comment: 6 pages, 5 figures, accepted in MNRA

Consensus: guidelines: best practices for detection, assessment and management of suspected acute drug-induced liver injury during clinical trials in patients with nonalcoholic steatohepatitis

BACKGROUND: The last decade has seen a rapid growth in the number of clinical trials enrolling patients with nonalcoholic fatty liver disease and nonalcoholic steatohepatitis (NASH). Due to the underlying chronic liver disease, patients with NASH often require different approaches to the assessment and management of suspected drug-induced liver injury (DILI) compared to patients with healthy livers. However, currently no regulatory guidelines or position papers systematically address best practices pertaining to DILI in NASH clinical trials. AIMS: This publication focuses on best practices concerning the detection, monitoring, diagnosis and management of suspected acute DILI during clinical trials in patients with NASH. METHODS: This is one of several papers developed by the IQ DILI Initiative, comprised of members from 15 pharmaceutical companies, in collaboration with DILI experts from academia and regulatory agencies. This paper is based on extensive literature review, and discussions between industry members with expertise in drug safety and DILI experts from outside industry to achieve consensus on common questions related to this topic. RESULTS: Recommended best practices are outlined pertaining to hepatic inclusion and exclusion criteria, monitoring of liver tests, DILI detection, approach to a suspected DILI signal, causality assessment and hepatic discontinuation rules. CONCLUSIONS: This paper provides a framework for the approach to assessment and management of suspected acute DILI during clinical trials in patients with NASH

Narrative-based computational modelling of the Gp130/JAK/STAT signalling pathway.

BACKGROUND: Appropriately formulated quantitative computational models can support researchers in understanding the dynamic behaviour of biological pathways and support hypothesis formulation and selection by "in silico" experimentation. An obstacle to widespread adoption of this approach is the requirement to formulate a biological pathway as machine executable computer code. We have recently proposed a novel, biologically intuitive, narrative-style modelling language for biologists to formulate the pathway which is then automatically translated into an executable format and is, thus, usable for analysis via existing simulation techniques. RESULTS: Here we use a high-level narrative language in designing a computational model of the gp130/JAK/STAT signalling pathway and show that the model reproduces the dynamic behaviour of the pathway derived by biological observation. We then "experiment" on the model by simulation and sensitivity analysis to define those parameters which dominate the dynamic behaviour of the pathway. The model predicts that nuclear compartmentalisation and phosphorylation status of STAT are key determinants of the pathway and that alternative mechanisms of signal attenuation exert their influence on different timescales. CONCLUSION: The described narrative model of the gp130/JAK/STAT pathway represents an interesting case study showing how, by using this approach, researchers can model biological systems without explicitly dealing with formal notations and mathematical expressions (typically used for biochemical modelling), nevertheless being able to obtain simulation and analysis results. We present the model and the sensitivity analysis results we have obtained, that allow us to identify the parameters which are most sensitive to perturbations. The results, which are shown to be in agreement with existing mathematical models of the gp130/JAK/STAT pathway, serve us as a form of validation of the model and of the approach itself

Reversibility in Chemical Reactions

open access bookIn this chapter we give an overview of techniques for the modelling and reasoning about reversibility of systems, including outof- causal-order reversibility, as it appears in chemical reactions. We consider the autoprotolysis of water reaction, and model it with the Calculus of Covalent Bonding, the Bonding Calculus, and Reversing Petri Nets. This exercise demonstrates that the formalisms, developed for expressing advanced forms of reversibility, are able to model autoprotolysis of water very accurately. Characteristics and expressiveness of the three formalisms are discussed and illustrated

From Business to IT with SEAM: J2EE Pet Store Example

Business and IT alignment demands clear traceability between the applications to be developed and the business requirements. SEAM is a systemic visual approach for modeling systems, including information systems and organizations. This paper illustrates how we represent the business role of an IT application and its platform-specific realization in SEAM. We use the Java Pet Store sample application as an example

Magnetically Torqued Thin Accretion Disks

We compute the properties of a geometrically thin, steady accretion disk surrounding a central rotating, magnetized star. The magnetosphere is assumed to entrain the disk over a wide range of radii. The model is simplified in that we adopt two (alternate) ad hoc, but plausible, expressions for the azimuthal component of the magnetic field as a function of radial distance. We find a solution for the angular velocity profile tending to corotation close to the central star, and smoothly matching a Keplerian curve at a radius where the viscous stress vanishes. The value of this ''transition'' radius is nearly the same for both of our adopted B-field models. We then solve analytically for the torques on the central star and for the disk luminosity due to gravity and magnetic torques. When expressed in a dimensionless form, the resulting quantities depend on one parameter alone, the ratio of the transition radius to the corotation radius. For rapid rotators, the accretion disk may be powered mostly by spin-down of the central star. These results are independent of the viscosity prescription in the disk. We also solve for the disk structure for the special case of an optically thick alpha disk. Our results are applicable to a range of astrophysical systems including accreting neutron stars, intermediate polar cataclysmic variables, and T Tauri systems.Comment: 9 sharper figs, updated reference

Identification of MS-specific serum miRNAs in an international multicenter study.

ObjectiveTo identify circulating microRNAs (miRNAs) linked to disease, disease stage, and disability in MS across cohorts.MethodsSamples were obtained from the Comprehensive Longitudinal Investigation of Multiple Sclerosis (CLIMB, Boston, MA), EPIC (San Francisco, CA), AMIR (Beirut, Lebanon) as part of the SUMMIT consortium, and Stockholm Prospective Assessment of Multiple Sclerosis (Stockholm, Sweden) cohorts. Serum miRNA expression was measured using locked nucleic acid-based quantitative PCR. Four groups were compared: (1) MS vs healthy control (HC), (2) relapsing-remitting (RR) vs HC, (3) secondary progressive (SP) vs HC, and (4) RR vs SP. A Wilcoxon rank-sum test was used for the comparisons. The association between each miRNA and the Expanded Disability Status Scale (EDSS) score was assessed using the Spearman correlation coefficient. For each comparison, the p values were corrected for multiple comparisons using the approach of Benjamini and Hochberg to control the false discovery rate.ResultsIn the CLIMB cohort, 5 miRNAs (hsa-miR-484, hsa-miR-140-5p, hsa-miR-320a, hsa-miR-486-5p, and hsa-miR-320c) showed a significant difference between patients with MS and healthy individuals; among these, miR-484 remained significant after accounting for multiple comparisons (p = 0.01). When comparing RRMS with HCs, hsa-miR-484 showed a significant difference (p = 0.004) between the groups after accounting for multiple group comparisons. When SP and HC were compared, 6 miRNAs (hsa-miR-484, hsa-miR-140-5p, hsa-miR-142-5p, hsa-miR-320a, hsa-miR-320b, and hsa-miR-320c) remained significantly different after accounting for multiple comparisons. Disability correlation analysis with miRNA provided 4 miRNAs (hsa-miR-320a, hsa-miR-337-3p, hsa-miR-199a-5p, and hsa-miR-142-5p) that correlated with the EDSS during the internal reproducibility phase. Among these, hsa-miR-337-3p was the most statistically significant miRNA that negatively correlated with the EDSS in three of the MS cohorts tested.ConclusionsThese findings further confirm the use of circulating serum miRNAs as biomarkers to diagnose and monitor disease status in MS.Classification of evidenceThis study provides Class III evidence that levels of circulating miRNAs identify patients with MS

Computational Indistinguishability between Quantum States and Its Cryptographic Application

We introduce a computational problem of distinguishing between two specific quantum states as a new cryptographic problem to design a quantum cryptographic scheme that is "secure" against any polynomial-time quantum adversary. Our problem, QSCDff, is to distinguish between two types of random coset states with a hidden permutation over the symmetric group of finite degree. This naturally generalizes the commonly-used distinction problem between two probability distributions in computational cryptography. As our major contribution, we show that QSCDff has three properties of cryptographic interest: (i) QSCDff has a trapdoor; (ii) the average-case hardness of QSCDff coincides with its worst-case hardness; and (iii) QSCDff is computationally at least as hard as the graph automorphism problem in the worst case. These cryptographic properties enable us to construct a quantum public-key cryptosystem, which is likely to withstand any chosen plaintext attack of a polynomial-time quantum adversary. We further discuss a generalization of QSCDff, called QSCDcyc, and introduce a multi-bit encryption scheme that relies on similar cryptographic properties of QSCDcyc.Comment: 24 pages, 2 figures. We improved presentation, and added more detail proofs and follow-up of recent wor