Computing Tropical Varieties

The tropical variety of a $d$-dimensional prime ideal in a polynomial ring with complex coefficients is a pure $d$-dimensional polyhedral fan. This fan is shown to be connected in codimension one. We present algorithmic tools for computing the tropical variety, and we discuss our implementation of these tools in the Gr\"obner fan software \texttt{Gfan}. Every ideal is shown to have a finite tropical basis, and a sharp lower bound is given for the size of a tropical basis for an ideal of linear forms.Comment: 22 pages, 2 figure

Functional Health Status in Oropharyngeal Dysphagia

Patient self-evaluations on Functional Health Status (FHS) questionnaires are considered to be part of the assessment of oropharyngeal dysphagia. FHS questionnaires capture the unique personal perception of someone’s health, taking into account social, functional and psychological factors. Many FHS questionnaires have been reported on in literature. This paper describes a selection of FHS questionnaires in more detail; issues concerning the inclusion of Health Related Quality of Life (HRQOL) items, choices in target populations and the distinction between oropharyngeal versus esophageal dysphagia will be discussed. Recommendations are made about the evaluation and use of FHS questionnaires in daily clinical practice. In particular the psychometric properties of FHS questionnaires should be evaluated to determine if they meet quality criteria for measurement properties of health status questionnaires in order to guarantee valid and reliable outcome measurements

Psychometric properties of questionnaires on functional health status in oropharyngeal dysphagia: A systematic literature review

Introduction: Questionnaires on Functional Health Status (FHS) are part of the assessment of oropharyngeal dysphagia. Objective: To conduct a systematic review of the literature on the psychometric properties of English-language FHS questionnaires in adults with oropharyngeal dysphagia. Methods: A systematic search was performed using the electronic databases Pubmed and Embase. The psychometric properties of the questionnaires were determined based on the COSMIN taxonomy of measurement properties and definitions for health-related patient-reported outcomes and the COSMIN checklist using preset psychometric criteria. Results: Three questionnaires were included: the Eating Assessment Tool (EAT-10), the Swallowing Outcome after Laryngectomy (SOAL), and the Self-report Symptom Inventory. The Sydney Swallow Questionnaire (SSQ) proved to be identical to the Modified Self-report Symptom Inventory. All FHS questionnaires obtained poor overall methodological quality scores for most measurement properties. Conclusions: The retrieved FHS questionnaires need psychometric reevaluation; if the overall methodological quality shows satisfactory improvement on most measurement properties, the use of the questionnaires in daily clinic and research can be justified. However, in case of insufficient validity and/or reliability scores, new FHS questionnaires need to be developed using and reporting on preestablished psychometric criteria as recommended in literature

Psychometric properties of questionnaires on functional health status in oropharyngeal dysphagia: A systematic literature review

Introduction: Questionnaires on Functional Health Status (FHS) are part of the assessment of oropharyngeal dysphagia. Objective: To conduct a systematic review of the literature on the psychometric properties of English-language FHS questionnaires in adults with oropharyngeal dysphagia. Methods: A systematic search was performed using the electronic databases Pubmed and Embase. The psychometric properties of the questionnaires were determined based on the COSMIN taxonomy of measurement properties and definitions for health-related patient-reported outcomes and the COSMIN checklist using preset psychometric criteria. Results: Three questionnaires were included: the Eating Assessment Tool (EAT-10), the Swallowing Outcome after Laryngectomy (SOAL), and the Self-report Symptom Inventory. The Sydney Swallow Questionnaire (SSQ) proved to be identical to the Modified Self-report Symptom Inventory. All FHS questionnaires obtained poor overall methodological quality scores for most measurement properties. Conclusions: The retrieved FHS questionnaires need psychometric reevaluation; if the overall methodological quality shows satisfactory improvement on most measurement properties, the use of the questionnaires in daily clinic and research can be justified. However, in case of insufficient validity and/or reliability scores, new FHS questionnaires need to be developed using and reporting on preestablished psychometric criteria as recommended in literature

Computing Linear Matrix Representations of Helton-Vinnikov Curves

Helton and Vinnikov showed that every rigidly convex curve in the real plane bounds a spectrahedron. This leads to the computational problem of explicitly producing a symmetric (positive definite) linear determinantal representation for a given curve. We study three approaches to this problem: an algebraic approach via solving polynomial equations, a geometric approach via contact curves, and an analytic approach via theta functions. These are explained, compared, and tested experimentally for low degree instances.Comment: 19 pages, 3 figures, minor revisions; Mathematical Methods in Systems, Optimization and Control, Birkhauser, Base

Changes in domestic heating fuel use in Greece : Effects on atmospheric chemistry and radiation

For the past 8 years, Greece has been experiencing a major financial crisis which, among other side effects, has led to a shift in the fuel used for residential heating from fossil fuel towards biofuels, primarily wood. This study simulates the fate of the residential wood burning aerosol plume (RWB smog) and the implications on atmospheric chemistry and radiation, with the support of detailed aerosol characterization from measurements during the winter of 2013–2014 in Athens. The applied model system (TNO-MACC_II emissions and COSMO-ART model) and configuration used reproduces the measured frequent nighttime aerosol spikes (hourly PM₁₀  >  75 µg m⁻³) and their chemical profile (carbonaceous components and ratios). Updated temporal and chemical RWB emission profiles, derived from measurements, were used, while the level of the model performance was tested for different heating demand (HD) conditions, resulting in better agreement with measurements for T$_{min}$ < 9 °C. Half of the aerosol mass over the Athens basin is organic in the submicron range, of which 80 % corresponds to RWB (average values during the smog period). Although organic particles are important light scatterers, the direct radiative cooling of the aerosol plume during wintertime is found low (monthly average forcing of –0.4 W m⁻² at the surface), followed by a minor feedback to the concentration levels of aerosol species. The low radiative cooling of a period with such intense air pollution conditions is attributed to the timing of the smog plume appearance, both directly (longwave radiation increases during nighttime) and indirectly (the mild effect of the residual plume on solar radiation during the next day, due to removal and dispersion processes

Q-systems, Heaps, Paths and Cluster Positivity

We consider the cluster algebra associated to the $Q$-system for $A_r$ as a tool for relating $Q$-system solutions to all possible sets of initial data. We show that the conserved quantities of the $Q$-system are partition functions for hard particles on particular target graphs with weights, which are determined by the choice of initial data. This allows us to interpret the simplest solutions of the Q-system as generating functions for Viennot's heaps on these target graphs, and equivalently as generating functions of weighted paths on suitable dual target graphs. The generating functions take the form of finite continued fractions. In this setting, the cluster mutations correspond to local rearrangements of the fractions which leave their final value unchanged. Finally, the general solutions of the $Q$-system are interpreted as partition functions for strongly non-intersecting families of lattice paths on target lattices. This expresses all cluster variables as manifestly positive Laurent polynomials of any initial data, thus proving the cluster positivity conjecture for the $A_r$ $Q$-system. We also give an alternative formulation in terms of domino tilings of deformed Aztec diamonds with defects.Comment: 106 pages, 38 figure

Discrete integrable systems, positivity, and continued fraction rearrangements

In this review article, we present a unified approach to solving discrete, integrable, possibly non-commutative, dynamical systems, including the $Q$- and $T$-systems based on $A_r$. The initial data of the systems are seen as cluster variables in a suitable cluster algebra, and may evolve by local mutations. We show that the solutions are always expressed as Laurent polynomials of the initial data with non-negative integer coefficients. This is done by reformulating the mutations of initial data as local rearrangements of continued fractions generating some particular solutions, that preserve manifest positivity. We also show how these techniques apply as well to non-commutative settings.Comment: 24 pages, 2 figure

The solution of the quantum A1A_1 T-system for arbitrary boundary

We solve the quantum version of the $A_1$ $T$-system by use of quantum networks. The system is interpreted as a particular set of mutations of a suitable (infinite-rank) quantum cluster algebra, and Laurent positivity follows from our solution. As an application we re-derive the corresponding quantum network solution to the quantum $A_1$ $Q$-system and generalize it to the fully non-commutative case. We give the relation between the quantum $T$-system and the quantum lattice Liouville equation, which is the quantized $Y$-system.Comment: 24 pages, 18 figure

Factors influencing the outcome of intrauterine insemination (IUI): age, clinical variables and significant thresholds

The aim was to investigate the influence of various biological factors upon the outcome of intrauterine insemination (IUI). The total IUI history (856 cycles) of 352 couples was studied. Live-birth showed a strong negative correlation with female age but no correlation with male age. Antimullerian hormone (AMH) and antral follicle count (AFC) correlated negatively with female age, and follicle stimulating hormone (FSH) correlated positively. Significant thresholds were found for all three variables, and also for total motile count (TMC) in the prepared sperm. Calculating pregnancy losses per positive pregnancy showed a strong correlation with increasing female age. This was highly significant for biochemical losses but not for fetal heart miscarriages. Male age had no effect on rate of pregnancy loss. In conclusion, female age, FSH, AMH and TMC are good predictive factors for live-birth and therefore relate to essential in vivo steps in the reproductive process