scholarly journals Η ασυνεχής μέθοδος Galerkin για συστήματα μη-γραμμικών μερικών διαφορικών εξισώσεων παραβολικού τύπου και εφαρμογές

2020 ◽  
Author(s):  
Δημήτριος Κώστας
Keyword(s):  
Type Ii ◽  
Predator Prey ◽  
Type Iii ◽  
Backward Euler ◽  
Boot Strap

Το αντικείμενο της παρούσας διδακτορικής διατριβής αφορά τα προβλήματα Αριθμητικής Ανάλυσης για συστήματα μη γραμμικών παραβολικών εξισώσεων τύπου predator-prey με εφαρμογές στη Βιολογία. Συγκεκριμένα μελετούμε:1)ασυνεχή χρονικά μέθοδο για την χρονική διακριτοποίηση Galerkin σε συνδυασμό με 2)κλασικά πεπερασμένα στοιχεία για την χωρική διακριτοποίηση. Εξετάζουμε τις ιδιότητες ευστάθειας των ανωτέρω διακριτών σχημάτων για ομαλά και μη ομαλά δεδομένα καθώς και την εξάρτηση των εκτιμήσεων αυτών σε σχέση με τις φυσικές παραμέτρους του συστήματος, και ιδιαίτερα σε σχέση με τις παραμέτρους διάχυσης. Επίσης μελετώνται εκτιμήσεις σφαλμάτων για τη διαφορά μεταξύ της διακριτής και της συνεχούς λύσης του συστήματος. Οι εκτιμήσεις αυτές επιβεβαιώνονται από τα εκτεταμένα αριθμητικά αποτελέσματα που παρουσιάζονται στο τελευταίο κεφάλαιο της εργασίας. Το πρόβλημα θηρευτή-θηράματος περιγράφεται ως εξής: Για δοσμένες αρχικές συνθήκες u0,v0 που περιγράφουν την αρχική κατάσταση δύο διαφορετικών πληθυσμών θηρευτή-θηράματος, αναζητούμε λύσεις (u,v) δηλαδή την εξέλιξη των πληθυσμών που ικανοποιεί ένα συζευγμένο σύστημα διαφορικών εξισώσεων. Πιο συγκεκριμένα, ο στόχος της εργασίας είναι η παρουσίαση αποτελεσμάτων και για τις τρεις κύριες μορφές μοντέλων θηρευτή-θηράματος: 1. Συναρτησοειδές του Ivlev: h(au) = 1 − e−au, u > 0,a > 02. Συναρτησοειδές Holling Type II: 3. Συναρτησοειδές Holling Type III: όπου u αντιπροσωπεύει την πυκνότητα των θηραμάτων, v το πλήθος των κυνηγών. Τα κύρια αποτελέσματα της διατριβής: Επισημαίνεται πως η τεχνική που παρουσιάζεται εφαρμόζεται σε πλήρως διακριτοποιημένα σχήματα ανώτερης τάξης, δηλαδή δεν εξετάζεται αποκλειστικά η περίπτωση σχημάτων της μορφής Forward/Backward Euler για την χρονική διακριτοποίηση. Παρόλο που η χρήση πλήρως διακριτοποιημένων σχημάτων ανώτερης τάξης, αυξάνει σημαντικά την τεχνική δυσκολία της ανάλυσης, υπολογιστικά αναμένεται πως μετά από την πάροδο ενός μικρού χρονικού διαστήματος, ο παραβολικός χαρακτήρας του προβλήματος δρα εξομομαλυντικά, επιτρέποντας την χρήση πλήρως διακριτών σχημάτων. Παρ΄ όλα αυτά, οι εκτιμήσεις ευστάθειας που παρουσιάζονται ισχύουν με χαμηλές υποθέσεις ομαλότητας για τα δεδομένα του προβλήματος. Η απόδειξη στηρίζεται σε τεχνικές που έχουν αναπτυχθεί για ασυνεχείς Galerkin σε συνδυασμό με ένα κατάλληλο boot-strap επιχείρημα ώστε να εξασφαλιστεί η αποσύζευξη των δύο εξισώσεων. Στη συνέχεια κατασκευάζοντας κατάλληλες βοηθητικές χωρο-χρονικές προβολές αποδεικνύουμε κατάλληλες εκτιμήσεις σφάλματος της μορφής:||σφάλμα προσέγγισης κατά σημείο ||L2(Ω) + ||σφάλμα||L2(0,T;H1(Ω)) + ||σφάλμα jumps||L2(Ω) ≤ C( ||Σφάλματα βέλτιστης προσέγγισης ||L2(0,T;H1(Ω)) + ||σφάλματα αρχικών τιμών|| . Η ομαλότητα των λύσεων (u,v) είναι η ακόλουθη:(u,v) ∈ L2(0,T;H1(Ω)) ∩ H1(0,T;H1(Ω)∗) ∩ L∞(0,T;L∞(Ω)).Οι εκτιμήσεις της παραπάνω ανισότητας είναι οι βέλτιστες ως προς την ενεργειακή νόρμα.

scholarly journals Warming can destabilise predator-prey interactions by shifting the functional response from Type III to Type II

2018 ◽  
Author(s):  
Uriah Daugaard ◽  
Owen Petchey ◽  
Frank Pennekamp
Keyword(s):  
Population Dynamics ◽  
Functional Response ◽  
Conversion Efficiency ◽  
Trophic Interactions ◽  
Clearance Rate ◽  
Temperature Effects ◽  
Type Ii ◽  
Predator Prey ◽  
Type Iii ◽  
Population Dynamic Model

The potential for climate change and temperature shifts to affect community stability remains relatively unknown. One mechanism by which temperature may affect stability is by altering trophic interactions. The functional response quantifies the per capita resource consumption by the consumer as a function of resource abundance and is a suitable framework for the description of nonlinear trophic interactions. We studied the effect of temperature on a ciliate predator-prey pair (Spathidium sp. and Dexiostoma campylum) by estimating warming effects on the functional response and on the associated conversion efficiency of the predator. We recorded prey and predator dynamics over 24 hours and at three temperature levels (15, 20 and 25 C). To these data we fitted a population dynamic model including the predator functional response, such that the functional response parameters (space clearance rate, handling time, and density dependence of space clearance rate) were estimated for each temperature separately. To evaluate the ecological significance of temperature effects on the functional response parameters we simulated predator-prey population dynamics. We considered the predator-prey system to be destabilised, if the prey was driven extinct by the predator. Effects of increased temperature included a transition of the functional response from a Type III to a Type II and an increase of the conversion efficiency of the predator. The simulated population dynamics showed a destabilisation of the system with warming, with greater risk of prey extinction at higher temperatures likely caused by the transition from a Type III to a Type II functional response. Warming-induced shifts from a Type III to II are not commonly considered in modelling studies that investigate how population dynamics respond to warming. Future studies should investigate the mechanism and generality of the effect we observed and simulate temperature effects in complex food webs including shifts in the type of the functional response as well as consider the possibility of a temperature dependent conversion efficiency.

scholarly journals Warming can destabilize predator–prey interactions by shifting the functional response from Type III to Type II

2019 ◽  
Vol 88 (10) ◽  
pp. 1575-1586 ◽  
Author(s):  
Uriah Daugaard ◽  
Owen L. Petchey ◽  
Frank Pennekamp
Keyword(s):  
Functional Response ◽  
Type Ii ◽  
Predator Prey ◽  
Type Iii

Does altering patch number and connectivity change the predatory functional response type? Experiments and simulations in an acarine predator–prey system

2005 ◽  
Vol 83 (6) ◽  
pp. 797-806 ◽  
Author(s):  
P J Lester ◽  
J M Yee ◽  
S Yee ◽  
J Haywood ◽  
H MA Thistlewood ◽  
...  
Keyword(s):  
Functional Response ◽  
Panonychus Ulmi ◽  
Type Ii ◽  
Response Type ◽  
Predator Prey ◽  
Amblyseius Fallacis ◽  
Type Iii ◽  
Prey Interaction ◽  
Patch Connectivity

In multipatch landscapes, understanding the role of patch number and connectivity is key for the conservation of species under processes such as predation. The functional response is the most basic form of the predator–prey interaction. Two common response types exist: a decelerating curvilinear increase in prey consumption with prey density to a plateau (type II) and a sigmoidal-shaped curve (type III). Type II responses have been observed for a variety of predators, though only type III responses allow long-term persistence and are demographically stabilizing. We tested the hypothesis that the functional response type can change from a type II to a type III with increasing patch number and (or) decreasing connectivity. The predatory mite Amblyseius fallacis (Garman, 1948) has previously been shown to have a type II response when feeding on Panonychus ulmi (Koch, 1839). We examined this predator–prey interaction using experiments that varied in patch number, and simulations that varied in both patch number and connectivity. In no experimental or simulation trial did altering patch number or connectivity change the predator's functional response from type II to type III, even with an 80-fold decrease in patch connectivity. How do predators with this demographically destabilizing functional response persist? Hypotheses regarding metapopulations and alternative prey are discussed.

Labelling of non-A, non-B hepatitis infected chimpanzee hepatocytes with nuclease-gold conjugates

1984 ◽  
Vol 42 ◽  
pp. 250-251
Author(s):  
G. D. Gagne ◽  
M. F. Miller ◽  
D. A. Peterson
Keyword(s):  
Endoplasmic Reticulum ◽  
Experimental Infection ◽  
Uranyl Acetate ◽  
Type I ◽  
Cellular Injury ◽  
Type Ii ◽  
Tubular Structures ◽  
Type Iii ◽  
Type Iv ◽  
Infected Chimpanzee

Experimental infection of chimpanzees with non-A, non-B hepatitis (NANB) or with delta agent hepatitis results in the appearance of characteristic cytoplasmic alterations in the hepatocytes. These alterations include spongelike inclusions (Type I), attached convoluted membranes (Type II), tubular structures (Type III), and microtubular aggregates (Type IV) (Fig. 1). Type I, II and III structures are, by association, believed to be derived from endoplasmic reticulum and may be morphogenetically related. Type IV structures are generally observed free in the cytoplasm but sometimes in the vicinity of type III structures. It is not known whether these structures are somehow involved in the replication and/or assembly of the putative NANB virus or whether they are simply nonspecific responses to cellular injury. When treated with uranyl acetate, type I, II and III structures stain intensely as if they might contain nucleic acids. If these structures do correspond to intermediates in the replication of a virus, one might expect them to contain DNA or RNA and the present study was undertaken to explore this possibility.

The global dynamics of stochastic Holling type II predator-prey models with non constant mortality rate

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5811-5825
Author(s):  
Xinhong Zhang
Keyword(s):  
Mortality Rate ◽  
Stochastic Model ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Global Dynamics ◽  
Type Ii ◽  
Predator Prey ◽  
Persistence In The Mean ◽  
The Mean ◽  
Predator Prey Models

In this paper we study the global dynamics of stochastic predator-prey models with non constant mortality rate and Holling type II response. Concretely, we establish sufficient conditions for the extinction and persistence in the mean of autonomous stochastic model and obtain a critical value between them. Then by constructing appropriate Lyapunov functions, we prove that there is a nontrivial positive periodic solution to the non-autonomous stochastic model. Finally, numerical examples are introduced to illustrate the results developed.

scholarly journals Perforator preservation technologies (PPT) based on a new neuro-interventional classification in endovascular treatment of perforator involving aneurysms (piANs)

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Chen Li ◽  
Ao-Fei Liu ◽  
Han-Cheng Qiu ◽  
Xianli Lv ◽  
Ji Zhou ◽  
...  
Keyword(s):  
Endovascular Therapy ◽  
Saccular Aneurysm ◽  
Type I ◽  
Type Ii ◽  
Fusiform Aneurysm ◽  
Type Iii ◽  
Perforating Artery ◽  
Protection Technology ◽  
Perforating Arteries

Abstract Background Treatment of perforator involving aneurysm (piAN) remains a challenge to open and endovascular neurosurgeons. Our aim is to demonstrate a primary outcome of endovascular therapy for piANs with the use of perforator preservation technologies (PPT) based on a new neuro-interventional classification. Methods The piANs were classified into type I: aneurysm really arises from perforating artery, type II: saccular aneurysm involves perforating arteries arising from its neck (IIa) or dome (IIb), and type III: fusiform aneurysm involves perforating artery. Stent protection technology of PPT was applied in type I and III aneurysms, and coil-basket protection technology in type II aneurysms. An immediate outcome of aneurysmal obliteration after treatment was evaluated (satisfactory obliteration: the saccular aneurysm body is densely embolized (I), leaving a gap in the neck (IIa) or dome (IIb) where the perforating artery arising; fusiform aneurysm is repaired and has a smooth inner wall), and successful perforating artery preservation was defined as keeping the good antegrade flow of those perforators on postoperative angiography. The periprocedural complication was closely monitored, and clinical and angiographic follow-ups were performed. Results Six consecutive piANs (2 ruptured and 4 unruptured; 1 type I, 2 type IIa, 2 type IIb, and 1 type III) in 6 patients (aged from 43 to 66 years; 3 males) underwent endovascular therapy between November 2017 and July 2019. The immediate angiography after treatment showed 6 aneurysms obtained satisfactory obliteration, and all of their perforating arteries were successfully preserved. During clinical follow-up of 13–50 months, no ischemic or hemorrhagic event of the brain occurred in the 6 patients, but has one who developed ischemic event in the territory of involving perforators 4 h after operation and completely resolved within 24 h. Follow-up angiography at 3 to 10M showed patency of the parent artery and perforating arteries of treated aneurysms, with no aneurysmal recurrence. Conclusions Our perforator preservation technologies on the basis of the new neuro-interventional classification seem feasible, safe, and effective in protecting involved perforators while occluding aneurysm.

scholarly journals Outcomes of one-stage reconstruction for chronic multiligament injuries of knee

2021 ◽  
Vol 33 (1) ◽  
Author(s):  
Tarun Goyal ◽  
Souvik Paul ◽  
Sushovan Banerjee ◽  
Lakshmana Das
Keyword(s):  
Cruciate Ligament ◽  
Lysholm Score ◽  
Activity Level ◽  
Type Ii ◽  
Hamstring Tendons ◽  
Peroneus Longus ◽  
Type Iii ◽  
Type Iv ◽  
Ikdc Score

Abstract Purpose This article aims to evaluate patterns of chronic multiligament injuries and outcomes of treatment with single-stage reconstruction using autografts. Methods All patients with clinicoradiologically diagnosed multiligament knee injury (MKI) were included in this prospective observational study. As the time since injury was more than 6 weeks in all of the patients, they were categorized as having chronic MKI. Patients were assessed clinically for laxity, and the diagnosis was confirmed radiologically. Ipsilateral hamstring tendons were used for medial collateral ligament (MCL) or posterolateral corner reconstruction in a patient with Schenck knee dislocation (KD) type III. In these cases, the posterior cruciate ligament (PCL) and anterior cruciate ligament (ACL) were reconstructed by using the peroneus longus and contralateral hamstring tendons respectively. Ipsilateral hamstring tendons were used for ACL reconstruction and an ipsilateral peroneus longus tendon graft was used for reconstruction of the PCL in a KD type II injury. In two cases of KD type IV injury, the lateral laxity was only grade II and was managed conservatively; the rest of the ligaments were addressed like a KD type III injury. Outcome evaluation was done using a visual analogue scale (VAS) for pain, International Knee Documentation Committee (IKDC) score, Lysholm score, and Tegner activity level, preoperatively and postoperatively at 2 years’ follow-up. Results A total of 27 patients of mean age 33.48 ± 9.9 years with MKI were included in the study. The patients were classified as eight KD type II, 17 KD type III, and two KD type IV. The majority of the patients had associated meniscal (59.2%) or chondral (40.7%) injuries. At the 2 years’ follow-up visit, there were significant improvements in VAS score (p = 0.0001) IKDC score (p = 0.0001), Lysholm score (p = 0.0001), and range of motion (p = 0.001). None of the patients had residual laxity on clinical examination of the knee joint at the 2 years’ follow-up. All but two of the patients went back to their previous activity level. These two patients had progressive knee arthritis and needed knee arthroplasty. Conclusion Single-stage surgical reconstruction for chronic MKI has favourable functional outcomes. Level of evidence Level IV, case series.

scholarly journals Intracellular and Extracellular Markers of Lethality in Osteogenesis Imperfecta: A Quantitative Proteomic Approach

2021 ◽  
Vol 22 (1) ◽  
pp. 429
Author(s):  
Luca Bini ◽  
Domitille Schvartz ◽  
Chiara Carnemolla ◽  
Roberta Besio ◽  
Nadia Garibaldi ◽  
...  
Keyword(s):  
Osteogenesis Imperfecta ◽  
Type I Collagen ◽  
Type I ◽  
Tandem Mass ◽  
Type Ii ◽  
Type Iii ◽  
Bioinformatic Tools ◽  
Proteomic Approach ◽  
Fibrillin 1 ◽  
Heritable Disorder

Osteogenesis imperfecta (OI) is a heritable disorder that mainly affects the skeleton. The inheritance is mostly autosomal dominant and associated to mutations in one of the two genes, COL1A1 and COL1A2, encoding for the type I collagen α chains. According to more than 1500 described mutation sites and to outcome spanning from very mild cases to perinatal-lethality, OI is characterized by a wide genotype/phenotype heterogeneity. In order to identify common affected molecular-pathways and disease biomarkers in OI probands with different mutations and lethal or surviving phenotypes, primary fibroblasts from dominant OI patients, carrying COL1A1 or COL1A2 defects, were investigated by applying a Tandem Mass Tag labeling-Liquid Chromatography-Tandem Mass Spectrometry (TMT LC-MS/MS) proteomics approach and bioinformatic tools for comparative protein-abundance profiling. While no difference in α1 or α2 abundance was detected among lethal (type II) and not-lethal (type III) OI patients, 17 proteins, with key effects on matrix structure and organization, cell signaling, and cell and tissue development and differentiation, were significantly different between type II and type III OI patients. Among them, some non–collagenous extracellular matrix (ECM) proteins (e.g., decorin and fibrillin-1) and proteins modulating cytoskeleton (e.g., nestin and palladin) directly correlate to the severity of the disease. Their defective presence may define proband-failure in balancing aberrances related to mutant collagen.

scholarly journals Brachial supporting structure of Spiriferida (Brachiopoda)

2020 ◽  
pp. 1-15
Author(s):  
Zhiwei Yuan ◽  
Wen Guo ◽  
Dan Lyu ◽  
Yuanlin Sun
Keyword(s):  
Mantle Cavity ◽  
Family Type ◽  
Type I ◽  
Type Ii ◽  
Feeding Apparatus ◽  
Single Family ◽  
Supporting Structure ◽  
Type Iii ◽  
Type Iv ◽  
Evolutionary Lineages

Abstract The filter-feeding organ of some extinct brachiopods is supported by a skeletal apparatus called the brachidium. Although relatively well studied in Atrypida and Athyridida, the brachidial morphology is usually neglected in Spiriferida. To investigate the variations of brachidial morphology in Spiriferida, 65 species belonging to eight superfamilies were analyzed. Based on the presence/absence of the jugal processes and normal/modified primary lamellae of the spiralia, four types of brachidium are recognized. Type-I (with jugal processes) and Type-II (without jugal processes), both having normal primary lamellae, could give rise to each other by losing/re-evolving the jugal processes. Type-III, without jugal processes, originated from Type-II through evolution of the modified lateral-convex primary lamellae, and it subsequently gave rise to Type-IV by evolving the modified medial-convex primary lamellae. The evolution of brachidia within individual evolutionary lineages must be clarified because two or more types can be present within a single family. Type-III and Type-IV are closely associated with the prolongation of the crura, representing innovative modifications of the feeding apparatus in response to possible shift in the position of the mouth towards the anterior, allowing for more efficient feeding on particles entering the mantle cavity from the anterior gape. Meanwhile, the modified primary lamellae adjusted/regulated the feeding currents. The absence of spires in some taxa with Type-IV brachidium might suggest that they developed a similar lophophore to that in some extant brachiopods, which can extend out of the shell.

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