Topological Recursion and Random Finite Noncommutative Geometries

In this thesis, we investigate a model for quantum gravity on finite noncommutative spaces using the topological recursion method originated from random matrix theory. More precisely, we consider a particular type of finite noncommutative geometries, in the sense of Connes, called spectral triples of type ${(1,0)} \,$, introduced by Barrett. A random spectral triple of type ${(1,0)}$ has a fixed fermion space, and the moduli space of its Dirac operator ${D=\{ H , \cdot \} \, ,}$ ${H \in {\mathcal{H}_N}}$, encoding all the possible geometries over the fermion space, is the space of Hermitian matrices ${\mathcal{H}_N}$. A distribution of the form ${e^{- \mathcal{S} (D)} \mathrm{d} D }$ is considered over the moduli space of Dirac operators. We specify the form of the action functional ${\mathcal{S} (D)}$ such that the topological recursion for a repulsive particles system, introduced by Borot, Eynard and Orantin, holds for the large $N$ topological expansion of the $n$-point correlators ${W_n (x_1 , \cdots , x_n)}$ of our model. In addition, we get the large $N$ topological expansion of the free energy ${F= \log Z_N}$ and the $n$-point correlators of the model in terms of the enumerative combinatorics of the stuffed maps, introduced by Borot, whose elementary 2-cells may have the topology of a disk or of a cylinder. One can compute all the stable coefficients ${W_n^g (x_1 , \cdots , x_n) \, ,}$ ${2g-2+n \u3e0 \, ,}$ ${n \geq 1 \, ,}$ ${g \geq 0}$ of the large $N$ topological expansion of the $n$-point correlators ${W_n (x_1 , \cdots , x_n)}$ of the model using the topological recursion formula, provided the leading order terms ${W_1^0 (x)}$ and ${W_2^0 (x_1 , x_2)}$ are known. We show that, for our model, the leading order term ${W_1^0 (x)}$ satisfies a quadratic algebraic equation ${y^2 + Q(x) \, y - P(x) = 0 \,}$. The spectral curve $\Sigma$ of the model is a genus zero complex algebraic curve, given by the pre-mentioned quadratic equation. We find explicit linear (resp. quadratic) expressions for the coefficients of the polynomial ${Q(x)}$ (resp. ${P(x)}$) in terms of the moments of the jump discontinuity of ${W_1^0 (x) \,}$. We plane to investigate the spectral curve ${(\Sigma , \omega_1^0 , \omega_2^0)}$ of the model in more detail

Adaptive Fuzzy Control of Puma Robot Manipulator in Task Space with Unknown Dynamic and Uncertain Kinematic

A In this paper, an adaptive direct fuzzy control system is presented to control the robot manipulator in task space. It is assumed that robot system has unknown dynamic and uncertain kinematic. The control system and adaption mechanism are firstly designed for joint space tracking. Then by using inverse Jacobian strategy, it is generalized for task space. After that, to overcome the problem of Jacobian matrix uncertainty, an improved adaptive control system is designed. All the design steps are illustrated by simulations

Numerical and Experimental Analysis of the Effect of Faults in Open-Pit Mining Stability

This thesis addresses two main issues in slope stability: 1) effect of faults in the large open pit mines and large rock slopes, and 2) improving stability of tailing dames using Hydro-Jex® technology.Section 1 - Effect of faults in the large open pit mines and large rock slopes: Deep open pit mines and large rock slopes expose many diverse rock lithologies and geological structures in a short period of time. Faulted rock masses reduce the integrity of slopes and can impose significant design challenges for geotechnical engineers. Numerical modeling is a powerful tool for simulating fault response. However, there are few guidelines and methods for calibrating/validating and implementing faults in a numerical model. This study presents a novel laboratory method to calibrate numerical models and highlights the challenges in simulating faults. The weak zone, ubiquitous-joint, and interface techniques are the widely-used methods in the modeling to capture fault slip mechanisms. One of the main issues in reliable modeling of faulted rock structure is the scarcity of experimental analyses in the laboratory under the controlled conditions.Moreover, a comprehensive evaluation of the effect of using the conventional fault modeling methods on the stability of rock structures is required, as well as a benchmarking between theoretical and experimental results. This research combines theory and experiment, in order to fill the existing gaps, using numerical simulation and laboratory measurements. In the numerical simulations, sensitivity and comparative analyses are carried out to investigate the stability of rock slopes on large and small scales (overall open pit slope and bench slope), and the fault zones, employing the methods as mentioned earlier in the FLAC3D software. The factor of safety of the slope is monitored upon variation of the design parameters, such as fault and rock mass mechanical properties, fault types, and modeling framework (e.g., mesh density, convergence ratio). Also, parameters such as shear displacement and shear stress are investigated to deduce the failure mechanism of the studied models. Finally, a laboratory test is performed to calibrate the modeling results and approximate the agreement between theoretical and experimental results. It needs to be mentioned that these analyses/tests are not to favor one method over the other, but rather to emphasize on pros and cons of each within the assumptions of this study. Section 2 - improving stability of tailing dames using Hydro-Jex® technology: Hydro-Jex® is a new enhanced method for heap leach treatments with significantly higher mineral recovery. In this study, the Hydro-Jex operation is case-studied at the Los Filos mine in Mexico for heap leach stability. This is pursued by numerical modeling of the heap leach pad stability and well monitoring of the phreatic surface before and after the Hydro-Jex operation. Experimental and numerical results both indicate an improvement in mineral processing under the influence of Hydro-Jex. Numerical results show an insignificant decrease and significant increase of stability during and after Hydro-Jex, respectively, while the integrity of the liner is maintained in both cases. The injection pressure is found to be negligible compared to the dimensionality of the heap and stability of the structure is not exposed to any significant risk, even up to 25% above the overburden pressure.On the other hand, the heap leach factor of safety increases after Hydro-Jex attributed to the breakdown of the build-up water solution and thus a decrease in the phreatic surface. The injection wells are suggested to be drilled in a wise manner based on accurate geophysical data; in locations where over-compaction of the heap material results in water solution build-ups and pore pressure enhancement. Compared to traditional heap leaching, the Hydro-Jex technique could not only expedite the mining process by increasing the chemical extraction, but also increase the stability of the heap by unclogging drains

On variational formulas on spaces of quadratic differentials

We study the variational formulas for the normalized Abelian differentials and matrix of b-periods on Hurwitz spaces, the moduli spaces of holomorphic Abelian differentials and quadratic differentials over compact Riemann surfaces. As the main result of the thesis, we find a complete set of local vector fields on the non-hyperelliptic connected component of the principal stratum of the moduli space of holomorphic quadratic differentials preserving the moduli of the base Riemann surface

Intra-Dialysis Hypotension in Patients Undergoing Hemodialysis

Introduction: Intra-dialysis hypotension occurs in 20- 55% of hemodialysis sessions. We aimed to define the prevalence and impact of pre-dialysis blood pressure, inter-dialysis weight gain, vasodilator agents, and characteristics of dialysis, serum calcium, and adjusted calcium, sodium, and albumin levels on intra-dialysis hypotension.Materials and Methods: In an observational prospective study, 44 hemodialysis cases aged 4.8-25 years were evaluated in 552 dialysis sessions. A decrease in the mean arterial blood pressure ≥ 10 mm Hg was defined as intra-dialysis hypotension. The characteristics of the patients were compared between cases and those without intra-dialysis hypotension.Results: Intra-dialysis hypotension was noted in 61.4% of the cases and 24.6% of the dialysis sessions. The duration of hemodialysis, weight gain between dialysis sessions, using vasodilator medications, serum sodium and adjusted calcium levels were compared between IDH + and IDH – cases. No significant differences were found in these variables between the 2 groups (P> 0.05 for all). Intra-dialysis hypotension was significantly more prevalent in cases with normal versus high systolic and diastolic blood pressure (P=0.014 and P=0.005 respectively). Intra-dialysis hypotension was significantly more frequent in girls, anuric patients, and patients with a history of transplantation (p=0.022, 0.011 and 0.008 respectively). A Significantly lower serum albumin concentration was found in cases with intra –dialysis hypotension (P=0.021).Conclusions: Intra-dialysis hypotension is a common complication of hemodialysis and is more prevalent in girls, normotensive patients, subjects with lower serum albumin concentrations, cases with a history of transplantation, and anuric patients. Keywords: Hemodialysis; Blood Pressure; Hypotension; Serum Albumin; Serum Calcium

A Review of Coronavirus Disease (COVID-19) in Children

Abstract: Since December 2019, an outbreak of coronavirus disease 2019 (COVID-19) with a high morbidity and mortality rate has spread globally and affected all age groups. Children can carry and transmit the novel coronavirus, but usually do not develop severe disease. The number of children who contracted coronavirus disease 2019 has increased significantly; however, compared to adults, there have been fewer reported cases of COVID-19 in the pediatric population. This review is mainly about the epidemiological features, clinical findings, laboratory tests, imaging, and treatment recommendations in children with COVID-19 disease

Comparative Study of Prophylactic Antibiotic Twice a Week Versus Every Night in Recurrent Urinary Tract Infections in Children

Background and Aim: Urinary tract infection is one of the most common childhood diseases. The results of studies investigating discontinuation or continuation of antibiotics in children with recurrent urinary tract infections and urinary reflux are controversial. Therefore, this study was conducted to compare prophylactic antibiotic treatment twice a week versus every night in the recurrence of urinary tract infections in children. Methods: This clinical trial was conducted using non-random simple sampling. Group A was given a single daily dose of cephalexin 10 mg/kg and group B was given cotrimoxazole at a dose of 5 mg/kg. Both groups were followed for ten months. Recurrences of urinary tract infections were compared between the two groups. Results: The mean age of the participants was 3.53±2.04 years. Most of the subjects were female (n=37, 61.7%). Urinary reflux was unilateral in 65% of the cases (n=39) and bilateral in the rest. There was no significant difference in age distribution, sex, and type of reflux between groups A and B. The frequency of recurrent urinary tract infection was 8.3% in group A and 6.7% in group B indicating no significant difference (p = 0.500). Conclusion: The results of this study showed that the frequency of recurrence of urinary tract infections in children who received prophylactic antibiotic treatment twice a week was not significantly different compared to the group of children who received continuous antibiotic prophylaxis

Streptococcus Pneumonia-Associated Hemolytic Uremic Syndrome: A Case Report

Hemolytic uremic syndrome (HUS), a disease that destroys red blood cells, is the most common cause of sudden, short term acute kidney failure in children. By far, the commonest subgroup (>90% of childhood HUS) is induced by shiga toxin producing bacteria, usually enterohemorrhagic Escherichia coli (EHEC). These patients typically have a prodrome of diarrhea. Another important subgroup that is readily identified on clinical grounds follows invasive Streptococcus pneumonia infection. These infants tend to be younger than those with D + HUS, and the syndrome is very rare after the age of 4 years. They present with pneumonia, empyema, meningitis, and less often, isolated septicemia. Another group of patients may have mutations in complement regulators, and less often, inherited deficiency of von Willebrand protease or an inborn error of cobalamin metabolism. We report a 6-month-old child who developed hemolytic uremic syndrome following S. pneumonia meningitis.Keywords: Hemolytic-Uremic Syndrome; Meningitis; Streptococcus pneumonia; Chil