Korntørringsanlæg.

Korntørringsanlæg

On the use of blow up to study regularizations of singularities of piecewise smooth dynamical systems in R3\mathbb{R}^3

In this paper we use the blow up method of Dumortier and Roussarie \cite{dumortier_1991,dumortier_1993,dumortier_1996}, in the formulation due to Krupa and Szmolyan \cite{krupa_extending_2001}, to study the regularization of singularities of piecewise smooth dynamical systems \cite{filippov1988differential} in $\mathbb R^3$. Using the regularization method of Sotomayor and Teixeira \cite{Sotomayor96}, first we demonstrate the power of our approach by considering the case of a fold line. We quickly recover a main result of Bonet and Seara \cite{reves_regularization_2014} in a simple manner. Then, for the two-fold singularity, we show that the regularized system only fully retains the features of the singular canards in the piecewise smooth system in the cases when the sliding region does not include a full sector of singular canards. In particular, we show that every locally unique primary singular canard persists the regularizing perturbation. For the case of a sector of primary singular canards, we show that the regularized system contains a canard, provided a certain non-resonance condition holds. Finally, we provide numerical evidence for the existence of secondary canards near resonance.Comment: To appear in SIAM Journal of Applied Dynamical System

Computation of saddle type slow manifolds using iterative methods

This paper presents an alternative approach for the computation of trajectory segments on slow manifolds of saddle type. This approach is based on iterative methods rather than collocation-type methods. Compared to collocation methods, that require mesh refinements to ensure uniform convergence with respect to $\epsilon$, appropriate estimates are directly attainable using the method of this paper. The method is applied to several examples including: A model for a pair of neurons coupled by reciprocal inhibition with two slow and two fast variables and to the computation of homoclinic connections in the FitzHugh-Nagumo system.Comment: To appear in SIAM Journal of Applied Dynamical System

On the approximation of the canard explosion point in singularly perturbed systems without an explicit small parameter

A canard explosion is the dramatic change of period and amplitude of a limit cycle of a system of nonlinear ODEs in a very narrow interval of the bifurcation parameter. It occurs in slow–fast systems and is well understood in singular perturbation problems where a small parameter epsilon defines the time-scale separation. We present an iterative algorithm for the determination of the canard explosion point which can be applied for a general slow–fast system without an explicit small parameter. We also present assumptions under which the algorithm gives accurate estimates of the canard explosion point. Finally, we apply the algorithm to the van der Pol equations, a Templator model for a self-replicating system and a model for intracellular calcium oscillations with no explicit small parameters and obtain very good agreement with results from numerical simulations.<br/

The regularized visible fold revisited

The planar visible fold is a simple singularity in piecewise smooth systems. In this paper, we consider singularly perturbed systems that limit to this piecewise smooth bifurcation as the singular perturbation parameter $\epsilon\rightarrow 0$. Alternatively, these singularly perturbed systems can be thought of as regularizations of their piecewise counterparts. The main contribution of the paper is to demonstrate the use of consecutive blowup transformations in this setting, allowing us to obtain detailed information about a transition map near the fold under very general assumptions. We apply this information to prove, for the first time, the existence of a locally unique saddle-node bifurcation in the case where a limit cycle, in the singular limit $\epsilon\rightarrow 0$, grazes the discontinuity set. We apply this result to a mass-spring system on a moving belt described by a Stribeck-type friction law

Development and Validation of The SMAP Enhanced Passive Soil Moisture Product

Since the beginning of its routine science operation in March 2015, the NASA SMAP observatory has been returning interference-mitigated brightness temperature observations at L-band (1.41 GHz) frequency from space. The resulting data enable frequent global mapping of soil moisture with a retrieval uncertainty below 0.040 cu m/cu m at a 36 km spatial scale. This paper describes the development and validation of an enhanced version of the current standard soil moisture product. Compared with the standard product that is posted on a 36 km grid, the new enhanced product is posted on a 9 km grid. Derived from the same time-ordered brightness temperature observations that feed the current standard passive soil moisture product, the enhanced passive soil moisture product leverages on the Backus-Gilbert optimal interpolation technique that more fully utilizes the additional information from the original radiometer observations to achieve global mapping of soil moisture with enhanced clarity. The resulting enhanced soil moisture product was assessed using long-term in situ soil moisture observations from core validation sites located in diverse biomes and was found to exhibit an average retrieval uncertainty below 0.040 cu m/cu m. As of December 2016, the enhanced soil moisture product has been made available to the public from the NASA Distributed Active Archive Center at the National Snow and Ice Data Center

Treatment Patterns and Use of Resources in Patients With Tuberous Sclerosis Complex: Insights From the TOSCA Registry

Tuberous Sclerosis Complex (TSC) is a rare autosomal-dominant disorder caused by mutations in the TSC1 or TSC2 genes. Patients with TSC may suffer from a wide range of clinical manifestations; however, the burden of TSC and its impact on healthcare resources needed for its management remain unknown. Besides, the use of resources might vary across countries depending on the country-specific clinical practice. The aim of this paper is to describe the use of TSC-related resources and treatment patterns within the TOSCA registry. A total of 2,214 patients with TSC from 31 countries were enrolled and had a follow-up of up to 5 years. A search was conducted to identify the variables containing both medical and non-medical resource use information within TOSCA. This search was performed both at the level of the core project as well as at the level of the research projects on epilepsy, subependymal giant cell astrocytoma (SEGA), lymphangioleiomyomatosis (LAM), and renal angiomyolipoma (rAML) taking into account the timepoints of the study, age groups, and countries. Data from the quality of life (QoL) research project were analyzed by type of visit and age at enrollment. Treatments varied greatly depending on the clinical manifestation, timepoint in the study, and age groups. GAB Aergics were the most prescribed drugs for epilepsy, and mTOR inhibitors are dramatically replacing surgery in patients with SEGA, despite current recommendations proposing both treatment options. mTOR inhibitors are also becoming common treatments in rAML and LAM patients. Forty-two out of the 143 patients (29.4%) who participated in the QoL research project reported inpatient stays over the last year. Data from non-medical resource use showed the critical impact of TSC on job status and capacity. Disability allowances were more common in children than adults (51.1% vs 38.2%). Psychological counseling, social services and social worker services were needed by <15% of the patients, regardless of age. The long-term nature, together with the variability in its clinical manifestations, makes TSC a complex and resource-demanding disease. The present study shows a comprehensive picture of the resource use implications of TSC

Natural clusters of tuberous sclerosis complex (TSC)-associated neuropsychiatric disorders (TAND): new findings from the TOSCA TAND research project.

BACKGROUND: Tuberous sclerosis complex (TSC)-associated neuropsychiatric disorders (TAND) have unique, individual patterns that pose significant challenges for diagnosis, psycho-education, and intervention planning. A recent study suggested that it may be feasible to use TAND Checklist data and data-driven methods to generate natural TAND clusters. However, the study had a small sample size and data from only two countries. Here, we investigated the replicability of identifying natural TAND clusters from a larger and more diverse sample from the TOSCA study. METHODS: As part of the TOSCA international TSC registry study, this embedded research project collected TAND Checklist data from individuals with TSC. Correlation coefficients were calculated for TAND variables to generate a correlation matrix. Hierarchical cluster and factor analysis methods were used for data reduction and identification of natural TAND clusters. RESULTS: A total of 85 individuals with TSC (female:male, 40:45) from 7 countries were enrolled. Cluster analysis grouped the TAND variables into 6 clusters: a scholastic cluster (reading, writing, spelling, mathematics, visuo-spatial difficulties, disorientation), a hyperactive/impulsive cluster (hyperactivity, impulsivity, self-injurious behavior), a mood/anxiety cluster (anxiety, depressed mood, sleep difficulties, shyness), a neuropsychological cluster (attention/concentration difficulties, memory, attention, dual/multi-tasking, executive skills deficits), a dysregulated behavior cluster (mood swings, aggressive outbursts, temper tantrums), and an autism spectrum disorder (ASD)-like cluster (delayed language, poor eye contact, repetitive behaviors, unusual use of language, inflexibility, difficulties associated with eating). The natural clusters mapped reasonably well onto the six-factor solution generated. Comparison between cluster and factor solutions from this study and the earlier feasibility study showed significant similarity, particularly in cluster solutions. CONCLUSIONS: Results from this TOSCA research project in an independent international data set showed that the combination of cluster analysis and factor analysis may be able to identify clinically meaningful natural TAND clusters. Findings were remarkably similar to those identified in the earlier feasibility study, supporting the potential robustness of these natural TAND clusters. Further steps should include examination of larger samples, investigation of internal consistency, and evaluation of the robustness of the proposed natural clusters

Alternating hemiplegia of childhood: Retrospective genetic study and genotype-phenotype correlations in 187 subjects from the US AHCF registry

Mutations in ATP1A3 cause Alternating Hemiplegia of Childhood (AHC) by disrupting function of the neuronal Na+/K+ ATPase. Published studies to date indicate 2 recurrent mutations, D801N and E815K, and a more severe phenotype in the E815K cohort. We performed mutation analysis and retrospective genotype-phenotype correlations in all eligible patients with AHC enrolled in the US AHC Foundation registry from 1997-2012. Clinical data were abstracted from standardized caregivers' questionnaires and medical records and confirmed by expert clinicians. We identified ATP1A3 mutations by Sanger and whole genome sequencing, and compared phenotypes within and between 4 groups of subjects, those with D801N, E815K, other ATP1A3 or no ATP1A3 mutations. We identified heterozygous ATP1A3 mutations in 154 of 187 (82%) AHC patients. Of 34 unique mutations, 31 (91%) are missense, and 16 (47%) had not been previously reported. Concordant with prior studies, more than 2/3 of all mutations are clustered in exons 17 and 18. Of 143 simplex occurrences, 58 had D801N (40%), 38 had E815K (26%) and 11 had G937R (8%) mutations. Patients with an E815K mutation demonstrate an earlier age of onset, more severe motor impairment and a higher prevalence of status epilepticus. This study further expands the number and spectrum of ATP1A3 mutations associated with AHC and confirms a more deleterious effect of the E815K mutation on selected neurologic outcomes. However, the complexity of the disorder and the extensive phenotypic variability among subgroups merits caution and emphasizes the need for further studies