Exact and Approximate Symmetries and Approximate Conservation Laws of Differential Equations with a Small parameter

The frameworks of Baikov-Gazizov-Ibragimov (BGI) and Fushchich-Shtelen (FS) approximate symmetries have proven useful for many examples where a small perturbation of an ordinary or partial differential equation (ODE, PDE) destroys its local exact symmetry group. For the perturbed model, some of the local symmetries of the unperturbed equation may (or may not) re-appear as approximate symmetries. Approximate symmetries are useful as a tool for systematic construction of approximate solutions. While for algebraic and first-order differential equations, to every point symmetry of the unperturbed equation, there corresponds an approximate point symmetry of the perturbed equation, for second and higher-order ODEs, this is not the case: a point symmetry of the original ODE may be unstable, that is, not have an analogue in the approximate point symmetry classification of the perturbed ODE. We show that such unstable point symmetries correspond to higher-order BGI approximate symmetries of the perturbed ODE, and can be systematically computed. We present a relation between BGI and FS approximate point symmetries for perturbed ODEs. Multiple examples of computations of exact and approximate point and local symmetries are presented, with two detailed examples that include a fourth-order nonlinear Boussinesq ODE reduction. Examples of the use of higher-order approximate symmetries and approximate integrating factors to obtain approximate solutions of higher-order ODEs, including Benjamin-Bona-Mahony ODE reduction are provided. The frameworks of BGI and FS approximate symmetries are used to study symmetry properties of partial differential equations with a small parameter. In general, we show that unlike in the ODE case, unstable point symmetries of an unperturbed PDE do not necessarily yield local approximate symmetries for the perturbed equation. We classify stable point symmetries of a one-dimensional wave model in terms of BGI and FS frameworks. We find a connection between BGI and FS approximate local symmetries for a PDE family. We classify approximate point symmetries for a family of one-dimensional wave equations with a small nonlinear term, and construct a physical approximate solution for a family that includes a one dimensional wave equation describing the wave motion in a hyperelastic material with a single family of fibers. For this model, we find wave breaking times numerically and using the approximate solution. A complete classification of exact and approximate point symmetries of the two-dimensional wave equation with a general small nonlinearity is presented. We investigate approximate conservation laws of systems of perturbed PDEs. We apply the direct mul tiplier method to obtain new approximate conservation laws for perturbed PDEs including nonlinear heat and wave equations. We show that the direct method generalizes the Noether’s theorem for construction of approximate conservation laws by proving that an approximate multiplier corresponds to an approximate local symmetry of an approximately variational problem. We present two formulas relating to construct ad ditional approximate conservation laws for a system of perturbed PDEs. We illustrate these formulas using perturbed wave equation and nonlinear telegraph system. An application for using approximate conservation laws to construct potential systems and approximate potential symmetries is provide

ANALYSIS OF THE ROLES OF HISTONE DEMETHYLASES IN DROSOPHILA MELANOGASTER MALE GERM CELL MAINTENANCE AND DIFFERENTIATION

Adult stem cells reside in microenvironments called niches, where they are regulated by both extrinsic cues such as signaling from neighboring cells and intrinsic factors such as chromatin structure. Here we report that in the Drosophila testis niche, an H3K27me3-specific histone demethylase encoded by ubiquitously transcribed tetratricopeptiderepeat gene on the X chromosome (dUTX) maintains active transcription of Suppressor of cytokine signaling 36E (Socs36E) gene by removing the repressive H3K27me3 modification near its transcription start site. Socs36E encodes an inhibitor of the Janus kinase signal transducer and activator of transcription (JAK-STAT) signaling pathway. While much is known about the niche-to-stem cell signaling, such as the JAK-STAT signaling critical for stem cell identity and activity, our results reveal that stem cells send feedback to niche cells to maintain the proper gene expression and architecture of the niche. We found that dUTX acts in cyst stem cells to maintain hub cell identity through activating Socs36E transcription and preventing hyperactivation of the JAK-STAT signaling. dUTX also acts in germline stem cells to maintain hub structure through regulating DE-Cadherin levels. In addition to the role of dUTX in the testis niche we report that in the Drosophila testis, an H3K4me3-specific histone demethylase encoded by little imaginal discs (lid) maintains germline stem cell self-renewal and prevents premature differentiation. Lid is required cell-autonomously in germ cells for proper expression of the Stat92E transcription factor, the downstream effector of JAK-STAT signaling pathway. Our findings support a germ cell autonomous role for the JAK-STAT pathway in maintaining germline stem cells and place Lid as an upstream regulator of this pathway. Our findings provide new insights into the biological functions of histone demethylases in vivo and shed light on the interaction between epigenetic mechanisms and signaling pathways in regulating stem cell activities. In addition to our studies in the testis niche we report a role for dUTX in spermatocyte maturation. Our findings suggest that dUTX cooperates with the testis-specific homologs of TBP-associated factor (tTAFs) to sequester repressive factors to the nucleolar regions of spermatocytes and allow the transcription of terminal differentiation genes. The readers of this thesis are: Dr. Allan Spradling, Dr. Xin Chen, Dr. Mark Van Doren, and Dr. Daniela Drummond-Barbosa

A Tiny RSA Cryptosystem based on Arduino Microcontroller Useful for Small Scale Networks

AbstractRSA Cryptography is a well-known example of public key cryptographic algorithms that involves robust encryption/decryption processes. In this paper, a microcontroller based RSA is designed and proposed. Arduino Mega2560R3 microcontroller supported with external memory and a screen touch LCD as well as a double keypad has been used under the programming of C language to implement the proposed RSA coprocessor with 32 bits. It was found that the trade of between message size and the encryption time can be drawn as a liner relationship according to the block size of the encryption phase. However, such design with a MCU provided with a small solar cell (and off course with a backup battery) as well as small block sizes is considered useful for the use in wireless sensor network (WSN) applications due to the ease of connecting the MCU to the WSN which as well avoid the processing time of encryption/decryption processes that could be executed by the MCU instead of the life limited sensors

Investigation of the genetic diversity of sheep breeds and their evaluation for designing appropriate conservation schemes

DNA of 31 animals per population, of ten Greek sheep breeds was analysed using 31 polymorphic microsatellite markers. In total, DNA from 310 animals was analysed, in order to investigate the genetic diversity and genetic relationships among these breeds. The breeds under study were Anogeiano, Kalarritiko, Karagouniko, Kefallenias, Kymi, Lesvos, Orino, Piliou, Sfakia and Skopelos. The number of alleles observed in each population ranged from 3-15 (Anogeiano 4-14; Kalarritiko 5-15; Karagouniko 4-14; Kefallenias 4-13; Kymi 5-13; Lesvos 5- 13; Orino 5-15; Piliou 5-12; Sfakia 4-14; Skopelos 3-10). Skopelos showed the lowest values concerning the number of observed alleles (3) and mean number of alleles (6.36). The maximum number of observed alleles was shown in Kalarritiko and Orino (15). This indicates that diversity of alleles was shared by the breeds as a whole. Gene diversity in each breed over all microstaellite loci ranged as following: Anogeiano 0.428-0.886; Kalarritiko 0.576-0.899; Karagouniko 0.485-0.894; Kefallenias 0.513-0.868; Kymi 0.508-0.893; Lesvos 0.482-0.895; Orino 0.481- 0.863; Piliou 0.415-0.873; Sfakia 0.363-0.886 and Skopelos 0.257-0.847. The lowest value of gene diversity (0.257 of OARFCB193 locus) over all populations and over all loci was observed in Skopelos breed, while the highest (0.899 of MAF70 locus) in Kalarritiko, indicating that MAF70 locus showed the greatest variability. The observed heterozygosity ranged between 0.161 (OARCP38 in Kymi) to 1.000 (OARFCB20 in Kalarritiko). The values in the breeds examined overall loci were: Anogeiano 0.290-0.935; Kalarritiko 0.387-1.000; Karagouniko 0.322-0.903; Kefallenias 0.419-0.903; Kymi 0.161-0.871; Lesvos 0.451-0.935; Orino 0.387- 0.903; Piliou 0.354-0.838; Sfakia 0.387-0.903 and Skopelos 0.225-0.838. Nei’s F-statistics were calculated. The range of the values of Ho, Hs, Ht, Gst, Gst' and Gis were as follows: Ho: 0.481-0.835; Hs 0.515-0.859; Ht 0.524-0.873; Gst 0.007-0.054; Gst' 0.007-0.059 and Gis -0.031-0.250. The Nei’s coefficient of differentiation Gst, equivalent to Fst of Wright, was generally low for all loci and also when averaged over all breeds and loci (0.031). This may indicate that these breeds are not differentiated enough and they may have common history of breeding practices. Thus, a small part of the variability at the 28 microsatellite loci analyzed was ascribed to the between-breed variability, while most of the variability was due to within breeds, since 0.969 was the variation related to within breeds or populations. Therefore, it can be recommended that withinbreed diversity is actively maintained to enable these extensively managed stocks to adapt to future demands and conditions.Στην παρούσα διατριβή πραγματοποιήθηκε γονοτυπική ανάλυση δέκα ελληνικών φυλών προβάτων με τη χρησιμοποίηση 31 μικροδορυφορικών δεικτών. Πραγματοποιήθηκαν δειγματοληψίες από 31 ζώα από κάθε φυλή και γονοτυπήθηκαν συνολικά 310 ζώα, με σκοπό τη διερεύνηση της γενετικής ποικιλομορφίας και τις φυλογενετικές σχέσεις μεταξύ των φυλών. Οι φυλές που μελετήθηκαν ήταν οι ακόλουθες: Ανωγείων, Καλαρρύτικη, Καραγκούνικη, Κεφαλληνίας, Κύμης, Λέσβου, Ορεινή Ηπείρου, Πηλίου, Σφακίων και Σκοπέλου. Ο αριθμός αλληλόμορφων γονιδίων που παρατηρήθηκε σε κάθε πληθυσμό, κυμάνθηκε από 3 έως 15 (Ανωγείων 4-14, Καλαρρύτικη 5-15, Καραγκούνικη 4- 14, Κεφαλληνίας 4-13, Κύμης 5-13, Λέσβου 5-13, Ορεινή Ηπείρου 5-15, Πηλίου 5-12, Σφακίων 4-14, Σκοπέλου 3-10). Η φυλή Σκοπέλου παρουσίασε χαμηλότερες τιμές σχετικά με τον αριθμό παρατηρηθέντων αλληλόμορφων γονιδίων (3) και μέσο αριθμό αλληλόμορφων γονιδίων (6,36). Ο μέγιστος αριθμός παρατηρηθέντων αλληλόμορφων γονιδίων παρουσιάστηκε στην Καλαρρύτικη και στην Ορεινή Ηπείρου (15), γεγονός που δείχνει ότι η ποικιλομορφία των αλληλόμορφων γονιδίων μοιράστηκε στο σύνολο των φυλών. Η ποικιλομορφία γονιδίων σε κάθε φυλή, σε όλους τους μικροδορυφορικούς τόπους κυμάνθηκε ως ακολούθως: Ανωγείων 0,428-0,886, Καλαρρύτικη 0,576- 0,899, Καραγκούνικη 0,485-0,894, Κεφαλληνίας 0,513-0,868, Κύμης 0,508- 0,893, Λέσβου 0,482-0,895, Ορεινή Ηπείρου 0,481-0,863, Πηλίου 0,415-0,873, Σφακίων 0,363-0,886 και Σκοπέλου 0,257-0,847. Η χαμηλότερη τιμή, στο σύνολο των πληθυσμών και των μικροδορυφόρων, παρατηρήθηκε στη φυλή Σκοπέλου (0,257 στον μικροδορυφόρο OARFCB193), ενώ η υψηλότερη στην Καλαρρύτικη (0,899 στον μικροδορυφόρο MAF70), δείχνοντας ότι ο μικροδορυφόρος MAF70 παρουσίασε την υψηλότερη παραλλακτικότητα. Η παρατηρηθείσα ετεροζυγωτία κυμάνθηκε μεταξύ 0,161 (OARCP38 στη φυλή Κύμης) έως 1.000 (OARFCB20 στην Καλαρρύτικη φυλή). Οι τιμές στις φυλές που εξετάσθηκαν ήταν: Ανωγείων 0,290-0,935, Καλαρρύτικη 0,387-1,000, Καραγκούνικη 0,322-0,903, Κεφαλληνίας 0,419-0,903, Κύμης 0,161-0,871, Λέσβου 0,451-0,935, Ορεινή Ηπείρου 0,387-0,903, Πηλίου 0,354-0,838, Σφακίων 0,387-0,903 και Σκοπέλου 0,225-0,838. Υπολογίστηκαν οι F-συντελεστές του Nei. O συντελεστής Ho κυμάνθηκε από 0,481 έως 0,835, ο συντελεστής Hs από 0,515 έως 0,859, ο συντελεστής Ht από 0,524 έως 0,873, ο συντελεστής Gst από 0,007 έως 0,054, ο συντελεστής Gst΄ από 0,007 έως 0,059, και τέλος ο συντελεστής Gis κυμάνθηκε από -0,031 έως 0,250. Ο συντελεστής διαφοροποίησης Gst, ήταν χαμηλός στο σύνολο των μικροδορυφόρων, και η μέση τιμή του στο σύνολο των φυλών και των μικροδορυφόρων ήταν 0,031. Κατά συνέπεια ένα μικρό μέρος της παραλλακτικότητας στους μικροδορυφόρους που αναλύθηκαν αποδόθηκε στη παραλλακτικότητα μεταξύ των φυλών, ενώ το μεγαλύτερο τμήμα της παραλλακτικότητας οφειλόταν στην παραλλακτικότητα εντός των φυλών

Relationship between Unstable Point Symmetries and Higher-Order Approximate Symmetries of Differential Equations with a Small Parameter

The framework of Baikov–Gazizov–Ibragimov approximate symmetries has proven useful for many examples where a small perturbation of an ordinary or partial differential equation (ODE, PDE) destroys its local exact symmetry group. For the perturbed model, some of the local symmetries of the unperturbed equation may (or may not) re-appear as approximate symmetries. Approximate symmetries are useful as a tool for systematic construction of approximate solutions. For algebraic and first-order differential equations, to every point symmetry of the unperturbed equation, there corresponds an approximate point symmetry of the perturbed equation. For second and higher-order ODEs, this is not the case: a point symmetry of the original ODE may be unstable, that is, not have an analogue in the approximate point symmetry classification of the perturbed ODE. We show that such unstable point symmetries correspond to higher-order approximate symmetries of the perturbed ODE and can be systematically computed. Multiple examples of computations of exact and approximate point and local symmetries are presented, with two detailed examples that include a fourth-order nonlinear Boussinesq equation reduction. Examples of the use of higher-order approximate symmetries and approximate integrating factors to obtain approximate solutions of higher-order ODEs are provided

Epigenetic regulator Lid maintains germline stem cells through regulating JAK-STAT signaling pathway activity

Signaling pathways and epigenetic mechanisms have both been shown to play essential roles in regulating stem cell activity. While the role of either mechanism in this regulation is well established in multiple stem cell lineages, how the two mechanisms interact to regulate stem cell activity is not as well understood. Here we report that in the Drosophila testis, an H3K4me3-specific histone demethylase encoded by little imaginal discs (lid) maintains germline stem cell (GSC) mitotic index and prevents GSC premature differentiation. Lid is required in germ cells for proper expression of the Stat92E transcription factor, the downstream effector of the Janus kinase signal transducer and activator of transcription (JAK-STAT) signaling pathway. Our findings support a germ cell autonomous role for the JAK-STAT pathway in maintaining GSCs and place Lid as an upstream regulator of this pathway. Our study provides new insights into the biological functions of a histone demethylase in vivo and sheds light on the interaction between epigenetic mechanisms and signaling pathways in regulating stem cell activities

Antioxidant and Anti-Urolithiatic Activity of Aqueous and Ethanolic Extracts from Saussurea costus (Falc) Lispich Using Scanning Electron Microscopy

The plant Saussurea costus (Falc) Lipsch has many biological activities and a strong curative and preventive power against a variety of diseases including cancer, diabetes, and hemorrhoids. In the current study, phytochemical screening was carried out as well as an investigation of the antilithiatic and antioxidant activities of aqueous and ethanolic extracts of this plant. The results showed that aqueous and ethanolic extracts were effective in reducing cystine stone mass and that the aqueous extract of Saussurea costus (Falc) Lipsch had the highest percentage of dissolution (6.756 ± 1.024) (p < 0.05). A turbidimetric method and a crystallization test were used to evaluate the antilithiatic activity of an aqueous and ethanolic extract of this plant on calcium oxalate crystallization. The results of these methods revealed that the ethanolic extract of this plant has a significant inhibitory effect on calcium oxalate crystallization, with a percentage inhibition of (91.017 ± 0.299) (p < 0.05) for a concentration of 2 mg mL−1. The DPPH method revealed that the ethanolic extract of Saussurea costus (Falc) Lipsch with a concentration of (IC50 = 0.12325 mg mL−1) had the highest IC50, whereas the FRAP method revealed that the aqueous extract of Saussurea costus (Falc) Lipsch with a concentration of 300 µg mL−1 has the most significant reducing power with (OD = 0.56 ± 0.05). These findings indicate that aqueous and ethanolic extracts of Saussurea costus (Falc) Lipsch had a significant effect on whewellite and weddellite and a greater free radical scavenging effect but had no effect on cystine dissolution

Physicochemical characterization, antioxidant and antifungal activities of essential oils of Urginea maritima and Allium sativum

This study aims to contribute to the valorizing of aromatic and medicinal plants of Morocco by studying the antioxidant and antifungal properties of the essential oils (EOs) of Allium sativum (AS) (garlic) and Urginea maritima (Syn. Drimia maritima) tested in vitro. After the hydrodistillation of EOs, we determined their physicochemical indices according to an international standard (Moroccan ISO standard), and the chemical composition of the oils was studied by gas chromatography coupled with mass spectrometry (GC-MS). Then, the antioxidant properties were determined using the free radical scavenging capacity of 2,2-diphenyl-1-picrylhydrazyl and the ferric-reducing antioxidant power of these oils. The evaluation of the antifungal activity was carried out by the direct contact method against two fungal strains, Fusarium oxysporum and Fusarium equiseti. GC-MS analysis revealed a significant percentage of terpenes in U. maritima EO, with terpinolene (21.82%) and estragole (6.24%) as the main compounds. Biological tests have demonstrated the remarkable antioxidant activities of this EO compared with AS EO, with an IC50 of 1.03 mg/mL and an RP0.5 of 1.60 mg/mL. On the other hand, while A. sativum (garlic) EO showed exceptional antifungal activities, with 100% inhibition and MICs of 0.5 µL/mL for F. equiseti and 2.5 µL/mL for F. oxysporum. Also, regardless of its antioxidant properties being moderate, this EO stands out for its efficacy against fungal infections of the Fusarium genus. In summary, the results suggest that U. maritima EO could be used as a natural source of antioxidants, while garlic EO could be considered a potentially effective treatment against fungal infections caused by Fusarium fungi

Phytochemical Compounds, Acute Toxicity, Anti-Inflammatory and Antioxidant Activities of Thymus leptobotrys Murb Essential Oil

The present study was conducted to evaluate the acute toxicity and anti-inflammatory effect in vivo, as well as the antioxidant activity, of the essential oil of Thymus leptobotrys Murb. The results indicate that the tested essential oil is non-toxic, with an estimated LD50 of 2500 mg kg−1 of mice body weight. The anti-inflammatory test revealed that, at a dose of 200 mg kg−1, the essential oil reduced rat paw edemas by 89.59% within 3 h of oral administration, this reduction in edema size was greater than that obtained with indomethacin (75.78%). The antioxidant activity (IC50) of Thymus leptobotrys Murb essential oil was 346.896 µg mL−1 and 861.136 mg Trolox equivalent/g essential oil in the 2.2-diphenyl1-picryl-hydrazyl radical scavenging capacity (DPPH) and Trolox equivalent antioxidant capacity (TEAC) assays, respectively. The toxicity test reveals an LD50 greater than 2500 mg kg−1 of body weight of mice which classifies it within category 5 of non-toxic substances that can be administered orally. These results suggest that the essential oil of Thymus leptobotrys Murb is not toxic, and it represents a valuable source of anti-inflammatory and antioxidant metabolites