Approximate solutions to large nonsymmetric differential Riccati problems with applications to transport theory

In the present paper, we consider large scale nonsymmetric differential matrix Riccati equations with low rank right hand sides. These matrix equations appear in many applications such as control theory, transport theory, applied probability and others. We show how to apply Krylov-type methods such as the extended block Arnoldi algorithm to get low rank approximate solutions. The initial problem is projected onto small subspaces to get low dimensional nonsymmetric differential equations that are solved using the exponential approximation or via other integration schemes such as Backward Differentiation Formula (BDF) or Rosenbrok method. We also show how these technique could be easily used to solve some problems from the well known transport equation. Some numerical experiments are given to illustrate the application of the proposed methods to large-scale problem

Recovery of an embedded obstacle and the surrounding medium for Maxwell's system

In this paper, we are concerned with the inverse electromagnetic scattering problem of recovering a complex scatterer by the corresponding electric far-field data. The complex scatterer consists of an inhomogeneous medium and a possibly embedded perfectly electric conducting (PEC) obstacle. The far-field data are collected corresponding to incident plane waves with a fixed incident direction and a fixed polarisation, but frequencies from an open interval. It is shown that the embedded obstacle can be uniquely recovered by the aforementioned far-field data, independent of the surrounding medium. Furthermore, if the surrounding medium is piecewise homogeneous, then the medium can be recovered as well. Those unique recovery results are new to the literature. Our argument is based on low-frequency expansions of the electromagnetic fields and certain harmonic analysis techniques.Comment: 15 page

Study identification and selection flowchart.

ObjectiveThe prevalence of obesity and type 2 diabetes is rapidly increasing worldwide, posing serious threats to human health. This study aimed to evaluate the role of FMT in the treatment of obesity and/or metabolic syndrome and its impact on clinically important parameters.MethodsWe searched Medline, Embase, and Cochrane Library databases up to April 31, 2022 and further assessed articles that met the eligibility criteria. Mean differences and 95% confidence intervals were used to analyze continuous data. The I2 statistic was used to measure study heterogeneity. Univariate meta-regression or subgroup analyses were performed to explore the covariates that might contribute to heterogeneity. Potential publication bias was assessed using the Egger’s test. We used the GRADEpro guideline development tool to assess the quality of the evidence.ResultsNine studies, comprising 303 participants, were included in the meta-analysis. In the short-term outcomes (ConclusionsFMT, as an adjunctive therapy, does not produce any serious adverse effects and may be useful in the treatment of metabolic syndrome, especially in improving HbA1c, insulin sensitivity, and HDL cholesterol. However, there was no significant difference between the FMT group and the placebo group in terms of weight reduction.</div

Evaluation of study quality.

ObjectiveThe prevalence of obesity and type 2 diabetes is rapidly increasing worldwide, posing serious threats to human health. This study aimed to evaluate the role of FMT in the treatment of obesity and/or metabolic syndrome and its impact on clinically important parameters.MethodsWe searched Medline, Embase, and Cochrane Library databases up to April 31, 2022 and further assessed articles that met the eligibility criteria. Mean differences and 95% confidence intervals were used to analyze continuous data. The I2 statistic was used to measure study heterogeneity. Univariate meta-regression or subgroup analyses were performed to explore the covariates that might contribute to heterogeneity. Potential publication bias was assessed using the Egger’s test. We used the GRADEpro guideline development tool to assess the quality of the evidence.ResultsNine studies, comprising 303 participants, were included in the meta-analysis. In the short-term outcomes (ConclusionsFMT, as an adjunctive therapy, does not produce any serious adverse effects and may be useful in the treatment of metabolic syndrome, especially in improving HbA1c, insulin sensitivity, and HDL cholesterol. However, there was no significant difference between the FMT group and the placebo group in terms of weight reduction.</div

Subgroup analysis based on FMT use method in short-term outcomes.

Subgroup analysis based on FMT use method in short-term outcomes.</p

Forest plot of short-term factor results.

1) Weight (Kg), 2) BMI (Kg/m2), 3) Fasting glucose (mmol/L), 4) HbA1C, 5) HOMA-IR, 6) Insulin (pmol/L), 7) Cholesterol (mmol/L), 8) HDL (mmol/L), 9) LDL (mmol/L), 10) Triglycerides (mmol/L).</p

Summary of data for each study objective.

ObjectiveThe prevalence of obesity and type 2 diabetes is rapidly increasing worldwide, posing serious threats to human health. This study aimed to evaluate the role of FMT in the treatment of obesity and/or metabolic syndrome and its impact on clinically important parameters.MethodsWe searched Medline, Embase, and Cochrane Library databases up to April 31, 2022 and further assessed articles that met the eligibility criteria. Mean differences and 95% confidence intervals were used to analyze continuous data. The I2 statistic was used to measure study heterogeneity. Univariate meta-regression or subgroup analyses were performed to explore the covariates that might contribute to heterogeneity. Potential publication bias was assessed using the Egger’s test. We used the GRADEpro guideline development tool to assess the quality of the evidence.ResultsNine studies, comprising 303 participants, were included in the meta-analysis. In the short-term outcomes (ConclusionsFMT, as an adjunctive therapy, does not produce any serious adverse effects and may be useful in the treatment of metabolic syndrome, especially in improving HbA1c, insulin sensitivity, and HDL cholesterol. However, there was no significant difference between the FMT group and the placebo group in terms of weight reduction.</div

Funnel plot test for publication bias.

ObjectiveThe prevalence of obesity and type 2 diabetes is rapidly increasing worldwide, posing serious threats to human health. This study aimed to evaluate the role of FMT in the treatment of obesity and/or metabolic syndrome and its impact on clinically important parameters.MethodsWe searched Medline, Embase, and Cochrane Library databases up to April 31, 2022 and further assessed articles that met the eligibility criteria. Mean differences and 95% confidence intervals were used to analyze continuous data. The I2 statistic was used to measure study heterogeneity. Univariate meta-regression or subgroup analyses were performed to explore the covariates that might contribute to heterogeneity. Potential publication bias was assessed using the Egger’s test. We used the GRADEpro guideline development tool to assess the quality of the evidence.ResultsNine studies, comprising 303 participants, were included in the meta-analysis. In the short-term outcomes (ConclusionsFMT, as an adjunctive therapy, does not produce any serious adverse effects and may be useful in the treatment of metabolic syndrome, especially in improving HbA1c, insulin sensitivity, and HDL cholesterol. However, there was no significant difference between the FMT group and the placebo group in terms of weight reduction.</div

Forest plot of long-term factor result.

1) Weight (Kg), 2) BMI (Kg/m2), 3) Fasting glucose (mmol/L), 4) HbA1C, 5) HOMA-IR, 6) Insulin (pmol/L), 7) Cholesterol (mmol/L), 8) HDL (mmol/L), 9) LDL (mmol/L), 10) Triglycerides (mmol/L).</p