Dimensional stability in truncated moment problems

Abstract An approach to truncated moment problems is developed, via the Riesz functional and an assumed dimensional stability of its associated Hilbert spaces. Although equivalent to a concept of atness introduced by R. Curto and L. Fialkow, the dimensional stability discussed in this paper has a dierent geometric aspect and leads to statements parallel to those of Curto and Fialkow, as well as to some newer ones, obtained by simpler arguments. A stability equation, giving a local characterization of the dimensional stability, is also presented

Are N=1 and N=2 supersymmetric quantum mechanics equivalent?

After recalling different formulations of the definition of supersymmetric quantum mechanics given in the literature, we discuss the relationships between them in order to provide an answer to the question raised in the title.Comment: 15 page

Scattering of slow-light gap solitons with charges in a two-level medium

The Maxwell-Bloch system describes a quantum two-level medium interacting with a classical electromagnetic field by mediation of the the population density. This population density variation is a purely quantum effect which is actually at the very origin of nonlinearity. The resulting nonlinear coupling possesses particularly interesting consequences at the resonance (when the frequency of the excitation is close to the transition frequency of the two-level medium) as e.g. slow-light gap solitons that result from the nonlinear instability of the evanescent wave at the boundary. As nonlinearity couples the different polarizations of the electromagnetic field, the slow-light gap soliton is shown to experience effective scattering whith charges in the medium, allowing it for instance to be trapped or reflected. This scattering process is understood qualitatively as being governed by a nonlinear Schroedinger model in an external potential related to the charges (the electrostatic permanent background component of the field).Comment: RevTex, 14 pages with 5 figures, to appear in J. Phys. A: Math. Theo

Translation Representations and Scattering By Two Intervals

Studying unitary one-parameter groups in Hilbert space (U(t),H), we show that a model for obstacle scattering can be built, up to unitary equivalence, with the use of translation representations for L2-functions in the complement of two finite and disjoint intervals. The model encompasses a family of systems (U (t), H). For each, we obtain a detailed spectral representation, and we compute the scattering operator, and scattering matrix. We illustrate our results in the Lax-Phillips model where (U (t), H) represents an acoustic wave equation in an exterior domain; and in quantum tunneling for dynamics of quantum states

Operator theory and function theory in Drury-Arveson space and its quotients

The Drury-Arveson space $H^2_d$, also known as symmetric Fock space or the $d$-shift space, is a Hilbert function space that has a natural $d$-tuple of operators acting on it, which gives it the structure of a Hilbert module. This survey aims to introduce the Drury-Arveson space, to give a panoramic view of the main operator theoretic and function theoretic aspects of this space, and to describe the universal role that it plays in multivariable operator theory and in Pick interpolation theory.Comment: Final version (to appear in Handbook of Operator Theory); 42 page

CLPM: A Cross-Linked Peptide Mapping Algorithm for Mass Spectrometric Analysis

BACKGROUND: Protein-protein, protein-DNA and protein-RNA interactions are of central importance in biological systems. Quadrapole Time-of-flight (Q-TOF) mass spectrometry is a sensitive, promising tool for studying these interactions. Combining this technique with chemical crosslinking, it is possible to identify the sites of interactions within these complexes. Due to the complexities of the mass spectrometric data of crosslinked proteins, new software is required to analyze the resulting products of these studies. RESULT: We designed a Cross-Linked Peptide Mapping (CLPM) algorithm which takes advantage of all of the information available in the experiment including the amino acid sequence from each protein, the identity of the crosslinker, the identity of the digesting enzyme, the level of missed cleavage, and possible chemical modifications. The algorithm does in silico digestion and crosslinking, calculates all possible mass values and matches the theoretical data to the actual experimental data provided by the mass spectrometry analysis to identify the crosslinked peptides. CONCLUSION: Identifying peptides by their masses can be an efficient starting point for direct sequence confirmation. The CLPM algorithm provides a powerful tool in identifying these potential interaction sites in combination with chemical crosslinking and mass spectrometry. Through this cost-effective approach, subsequent efforts can quickly focus attention on investigating these specific interaction sites

Serum MicroRNA Signatures Identified by Solexa Sequencing Predict Sepsis Patients’ Mortality: A Prospective Observational Study

Sepsis is the leading cause of death in Intensive Care Units. Novel sepsis biomarkers and targets for treatment are needed to improve mortality from sepsis. MicroRNAs (miRNAs) have recently been used as finger prints for sepsis, and our goal in this prospective study was to investigate if serum miRNAs identified in genome-wide scans could predict sepsis mortality.We enrolled 214 sepsis patients (117 survivors and 97 non-survivors based on 28-day mortality). Solexa sequencing followed by quantitative reverse transcriptase polymerase chain reaction assays was used to test for differences in the levels of miRNAs between survivors and non-survivors. miR-223, miR-15a, miR-16, miR-122, miR-193*, and miR-483-5p were significantly differentially expressed. Receiver operating characteristic curves were generated and the areas under the curve (AUC) for these six miRNAs for predicting sepsis mortality ranged from 0.610 (95%CI: 0.523-0.697) to 0.790 (95%CI: 0.719-0.861). Logistic regression analysis showed that sepsis stage, Sequential Organ Failure Assessment scores, Acute Physiology and Chronic Health Evaluation II scores, miR-15a, miR-16, miR-193b*, and miR-483-5p were associated with death from sepsis. An analysis was done using these seven variables combined. The AUC for these combined variables' predictive probability was 0.953 (95% CI: 0.923-0.983), which was much higher than the AUCs for Acute Physiology and Chronic Health Evaluation II scores (0.782; 95% CI: 0.712-0.851), Sequential Organ Failure Assessment scores (0.752; 95% CI: 0.672-0.832), and procalcitonin levels (0.689; 95% CI: 0.611-0.784). With a cut-off point of 0.550, the predictive value of the seven variables had a sensitivity of 88.5% and a specificity of 90.4%. Additionally, miR-193b* had the highest odds ratio for sepsis mortality of 9.23 (95% CI: 1.20-71.16).Six serum miRNA's were identified as prognostic predictors for sepsis patients.ClinicalTrials.gov NCT01207531

First Report of Circulating MicroRNAs in Tumour Necrosis Factor Receptor-Associated Periodic Syndrome (TRAPS)

Tumor necrosis factor-receptor associated periodic syndrome (TRAPS) is a rare autosomal dominant autoinflammatory disorder characterized by recurrent episodes of long-lasting fever and inflammation in different regions of the body, such as the musculo-skeletal system, skin, gastrointestinal tract, serosal membranes and eye. Our aims were to evaluate circulating microRNAs (miRNAs) levels in patients with TRAPS, in comparison to controls without inflammatory diseases, and to correlate their levels with parameters of disease activity and/or disease severity. Expression levels of circulating miRNAs were measured by Agilent microarrays in 29 serum samples from 15 TRAPS patients carrying mutations known to be associated with high disease penetrance and from 8 controls without inflammatory diseases. Differentially expressed and clinically relevant miRNAs were detected using GeneSpring GX software. We identified a 6 miRNAs signature able to discriminate TRAPS from controls. Moreover, 4 miRNAs were differentially expressed between patients treated with the interleukin (IL)-1 receptor antagonist, anakinra, and untreated patients. Of these, miR-92a-3p and miR-150-3p expression was found to be significantly reduced in untreated patients, while their expression levels were similar to controls in samples obtained during anakinra treatment. MiR-92b levels were inversely correlated with the number of fever attacks/year during the 1st year from the index attack of TRAPS, while miR-377-5p levels were positively correlated with serum amyloid A (SAA) circulating levels. Our data suggest that serum miRNA levels show a baseline pattern in TRAPS, and may serve as potential markers of response to therapeutic intervention