Propagation of generalized vector Helmholtz-Gauss beams through paraxial optical systems

We introduce the generalized vector Helmholtz-Gauss (gVHzG) beams that constitute a general family of localized beam solutions of the Maxwell equations in the paraxial domain. The propagation of the electromagnetic components through axisymmetric ABCD optical systems is expressed elegantly in a coordinate-free and closed-form expression that is fully characterized by the transformation of two independent complex beam parameters. The transverse mathematical structure of the gVHzG beams is form-invariant under paraxial transformations. Any paraxial beam with the same waist size and transverse spatial frequency can be expressed as a superposition of gVHzG beams with the appropriate weight factors. This formalism can be straightforwardly applied to propagate vector Bessel-Gauss, Mathieu-Gauss, and Parabolic-Gauss beams, among others

Tensor Analysis and Fusion of Multimodal Brain Images

Current high-throughput data acquisition technologies probe dynamical systems with different imaging modalities, generating massive data sets at different spatial and temporal resolutions posing challenging problems in multimodal data fusion. A case in point is the attempt to parse out the brain structures and networks that underpin human cognitive processes by analysis of different neuroimaging modalities (functional MRI, EEG, NIRS etc.). We emphasize that the multimodal, multi-scale nature of neuroimaging data is well reflected by a multi-way (tensor) structure where the underlying processes can be summarized by a relatively small number of components or "atoms". We introduce Markov-Penrose diagrams - an integration of Bayesian DAG and tensor network notation in order to analyze these models. These diagrams not only clarify matrix and tensor EEG and fMRI time/frequency analysis and inverse problems, but also help understand multimodal fusion via Multiway Partial Least Squares and Coupled Matrix-Tensor Factorization. We show here, for the first time, that Granger causal analysis of brain networks is a tensor regression problem, thus allowing the atomic decomposition of brain networks. Analysis of EEG and fMRI recordings shows the potential of the methods and suggests their use in other scientific domains.Comment: 23 pages, 15 figures, submitted to Proceedings of the IEE

Patients' with type 2 diabetes willingness to pay for insulin therapy and clinical outcomes

OBJECTIVES: This study assessed patient preferences, using willingness to pay as a method to measure different treatment characteristics or attributes associated with injectable insulin therapy in patients with type 2 diabetes. RESEARCH DESIGN AND METHODS: Adults with type 2 diabetes in 12 countries, diagnosed >6 months prior and receiving insulin for >3 months, were recruited through a representative online panel. Data were collected via online questionnaire and analyzed using a standard choice model for discrete choice experiment. RESULTS: A total of 3758 patients from North America (n=646), South America (n=1537), and Europe (n=1575) completed the study. Mean glycated hemoglobin (HbA1c) levels in North America, South America, and Europe were 63 mmol/mol (7.9%), 75 mmol/mol (9.0%), and 64 mmol/mol (8.0%), respectively. In the three regions, monthly willingness to pay was US$116, US$74, and US$92, respectively, for a 1$99, US$80, and US$104 for one less major hypoglycemic event per year; and US$64, US$37 and US$60 for a 3 kg weight decrease. To avoid preinjection preparation of insulin, the respective values were US$47, US$18, and US$37, and US$25, US$25, and US$24 for one less injection per day. Among respondents on basal-only insulin who had previously tried a more intensive regimen, reasons for switching back included difficulty in handling multiple injections and risk of hypoglycemic events. CONCLUSIONS: Reducing HbA1c, frequency of major hypoglycemic events and weight decrease were the highest valued outcomes in each region. The administrative burden of injections was also considered important

Clash of Titans: The Impact of Cluster Mergers in the Galaxy Cluster Red Sequence

Merging of galaxy clusters are some of the most energetic events in the Universe, and they provide a unique environment to study galaxy evolution. We use a sample of 84 merging and relaxed SPT galaxy clusters candidates, observed with the Dark Energy Camera in the $0.11<z<0.88$ redshift range, to build colour-magnitude diagrams to characterize the impact of cluster mergers on the galaxy population. We divided the sample between relaxed and disturbed, and in two redshifts bin at $z = 0.55$. When comparing the high-z to low-z clusters we find the high-z sample is richer in blue galaxies, independently of the cluster dynamical state. In the high-z bin we find that disturbed clusters exhibit a larger scatter in the Red Sequence, with wider distribution and an excess of bluer galaxies compared to relaxed clusters, while in the low-z bin we find a complete agreement between the relaxed and disturbed clusters. Our results support the scenario in which massive cluster halos at $z<0.55$ galaxies are quenched as satellites of another structure, i.e. outside the cluster, while at $z \geq 0.55$ the quenching is dominated by in-situ processes.Comment: 9 pages, 5 figures, paper accepted in MNRA

NaI(Tl) Scintillator's Response Functions for Point-like and Distributed Gamma-ray Sources

The response functions of a NaI(Tl) detectors have been estimated using Monte Carlo methods. Response functions were calculated for monoenergetic photon sources (0.05 to 3 MeV). Responses were calculated for point-like sources and for sources distributed in Portland cement cylinders. Calculated responses were used to estimate the detector efficiency for point-like and distributed sources. Samples of cylindrical Portland cement were prepared and exposed to the photoneutron field produced by a 15 MV linac used for radiotherapy. Short half-life radioisotopes were induced and the activity was determined by measuring the pulse-height spectra with a NaI(Tl) g-ray spectrometer that was calibrated using point-like sources. Instead of doing corrections due to differences between the geometry, material and solid angle of point-like sources used for calibration, and the Portland cement cylinders, the detection efficiency was determined using the ratio between the efficiencies for the point-like and the distributed sources estimated with the Monte Carlo calculations, and the activity of the induced isotopes in cement was obtained

Semiclassical relativistic strings in S^5 and long coherent operators in N=4 SYM theory

We consider the low energy effective action corresponding to the 1-loop, planar, dilatation operator in the scalar sector of N=4 SU(N) SYM theory. For a general class of non-holomorphic ``long'' operators, of bare dimension L>>1, it is a sigma model action with 8-dimensional target space and agrees with a limit of the phase-space string sigma model action describing generic fast-moving strings in the S^5 part of AdS_5 x S^5. The limit of the string action is taken in a way that allows for a systematic expansion to higher orders in the effective coupling $\lambda/L^2$. This extends previous work on rigid rotating strings in S^5 (dual to operators in the SU(3) sector of the dilatation operator) to the case when string oscillations or pulsations in S^5 are allowed. We establish a map between the profile of the leading order string solution and the structure of the corresponding coherent, ``locally BPS'', SYM scalar operator. As an application, we explicitly determine the form of the non-holomorphic operators dual to the pulsating strings. Using action--angle variables, we also directly compute the energy of pulsating solutions, simplifying previous treatments.Comment: LaTeX, 50 pages, 1 figure. v2: References added, minor corrections. 54 pages. v3: Few changes. One paragraph added at the end of section 3. 55 page

Predicting aging-related decline in physical performance with sparse electrophysiological source imaging

Objective: We introduce a methodology for selecting biomarkers from activation and connectivity derived from Electrophysiological Source Imaging (ESI). Specifically, we pursue the selection of stable biomarkers associated with cognitive decline based on source activation and connectivity patterns of resting-state EEG theta rhythm, used as predictors of physical performance decline in aging individuals measured by a Gait Speed (GS) slowing. Methods: Our two-step methodology involves estimating ESI using flexible sparse-smooth-nonnegative models, from which activation ESI (aESI) and connectivity ESI (cESI) features are derived. The Stable Sparse Classifier method then selects potential biomarkers related to GS changes. Results and Conclusions: Our predictive models using aESI outperform traditional methods such as the LORETA family. The models combining aESI and cESI features provide the best prediction of GS changes. Potential biomarkers from activation/connectivity patterns involve orbitofrontal and temporal cortical regions. Significance: The proposed methodology contributes to the understanding of activation and connectivity of GS-related ESI and provides features that are potential biomarkers of GS slowing. Given the known relationship between GS decline and cognitive impairment, this preliminary work opens novel paths to predict the progression of healthy and pathological aging and might allow an ESI-based evaluation of rehabilitation programs

Preliminary definitions for the sonographic features of synovitis in children

Objectives Musculoskeletal ultrasonography (US) has the potential to be an important tool in the assessment of disease activity in childhood arthritides. To assess pathology, clear definitions for synovitis need to be developed first. The aim of this study was to develop and validate these definitions through an international consensus process. Methods The decision on which US techniques to use, the components to be included in the definitions as well as the final wording were developed by 31 ultrasound experts in a consensus process. A Likert scale of 1-5 with 1 indicating complete disagreement and 5 complete agreement was used. A minimum of 80% of the experts scoring 4 or 5 was required for final approval. The definitions were then validated on 120 standardized US images of the wrist, MCP and tibiotalar joints displaying various degrees of synovitis at various ages. Results B-Mode and Doppler should be used for assessing synovitis in children. A US definition of the various components (i.e. synovial hypertrophy, effusion and Doppler signal within the synovium) was developed. The definition was validated on still images with a median of 89% (range 80-100) of participants scoring it as 4 or 5 on a Likert scale. Conclusions US definitions of synovitis and its elementary components covering the entire pediatric age range were successfully developed through a Delphi process and validated in a web-based still images exercise. These results provide the basis for the standardized US assessment of synovitis in clinical practice and research

Correlation functions of three heavy operators - the AdS contribution

We consider operators in N=4 SYM theory which are dual, at strong coupling, to classical strings rotating in S^5. Three point correlation functions of such operators factorize into a universal contribution coming from the AdS part of the string sigma model and a state-dependent S^5 contribution. Consequently a similar factorization arises for the OPE coefficients. In this paper we evaluate the AdS universal factor of the OPE coefficients which is explicitly expressed just in terms of the anomalous dimensions of the three operators.Comment: 49 pages, 3 figures; v.2 references corrected; v3: corrected discussion in section 5, results unchange