Matrices over a semiring of binary relations and V -variable fractals

In this paper we prove that V -variable fractal sets are limits of infinite products of matrices over the semiring of binary relations on a compact metric space. © Allerton Press, Inc., 2011

Least-squares fitting of a three-dimensional ellipsoid to noisy data

© 2014 Alexandra Malyugina, Konstantin Igudesman and Dmitry Chickrin. This paper deals with the problem of fitting a three-dimensional ellipsoid to a noisy data point set in the context of three-axis magnit-ometer calibration. It describes methods of ellipsoidal fitting, based on various concepts of ellipsoid representation, error function definition and data simulation. The efficiency of the new approaches is demonstrated through simulations

Peculiarities of elastic wave refraction from the layer with fractal distribution of density

In this study, we underline the peculiarities of the refraction problem of elastic waves from a layer with a fractal density distribution. The refraction problem is reduced to the system of ordinary di erential equations with linear coefficients. Analytic solutions for each of its equations are found. The case for the layer with fractal density distribution is investigated numerically. Characteristic maxima of the reflected wave energy are outlined. Graphs illustrate the dependence of the reflected energy from self-similar properties of the fractal curve

Gut-Brain Interactions: Implications for a Role of the Gut Microbiota in the Treatment and Prognosis of Anorexia Nervosa and Comparison to Type I Diabetes

Anorexia nervosa has poor prognosis and treatment outcomes and is influenced by genetic, metabolic, and psychological factors. Gut microbes interact with gut physiology to influence metabolism and neurobiology, although potential therapeutic benefits remain unknown. Type 1 diabetes is linked to anorexia nervosa through energy dysregulation, which in both disease states is related to the gut microbiota, disordered eating, and genetics

Associations of Dietary Intake with the Intestinal Microbiota and Short-Chain Fatty Acids Among Young Adults with Type 1 Diabetes and Overweight or Obesity

Background: Diet, a key component of type 1 diabetes (T1D) management, modulates the intestinal microbiota and its metabolically active byproducts—including SCFA—through fermentation of dietary carbohydrates such as fiber. However, the diet–microbiome relationship remains largely unexplored in longstanding T1D. Objectives: We evaluated whether increased carbohydrate intake, including fiber, is associated with increased SCFA-producing gut microbes, SCFA, and intestinal microbial diversity among young adults with longstanding T1D and overweight or obesity. Methods: Young adult men and women with T1D for ≥1 y, aged 19–30 y, and BMI of 27.0–39.9 kg/m2 at baseline provided stool samples at baseline and 3, 6, and 9 mo of a randomized dietary weight loss trial. Diet was assessed by 1–2 24-h recalls. The abundance of SCFA-producing microbes was measured using 16S rRNA gene sequencing. GC-MS measured fecal SCFA (acetate, butyrate, propionate, and total) concentrations. Adjusted and Bonferroni-corrected generalized estimating equations modeled associations of dietary fiber (total, soluble, and pectins) and carbohydrate (available carbohydrate, and fructose) with microbiome-related outcomes. Primary analyses were restricted to data collected before COVID-19 interruptions. Results: Fiber (total and soluble) and carbohydrates (available and fructose) were positively associated with total SCFA and acetate concentrations (n = 40 participants, 52 visits). Each 10 g/d of total and soluble fiber intake was associated with an additional 8.8 μmol/g (95% CI: 4.5, 12.8 μmol/g; P = 0.006) and 24.0 μmol/g (95% CI: 12.9, 35.1 μmol/g; P = 0.003) of fecal acetate, respectively. Available carbohydrate intake was positively associated with SCFA producers Roseburia and Ruminococcus gnavus. All diet variables except pectin were inversely associated with normalized abundance of Bacteroides and Alistipes. Fructose was inversely associated with Akkermansia abundance. Conclusions: In young adults with longstanding T1D, fiber and carbohydrate intake were associated positively with fecal SCFA but had variable associations with SCFA-producing gut microbes. Controlled feeding studies should determine whether gut microbes and SCFA can be directly manipulated in T1D

Associations of disordered eating with the intestinal microbiota and short-chain fatty acids among young adults with type 1 diabetes

Background and aims: Disordered eating (DE) in type 1 diabetes (T1D) includes insulin restriction for weight loss with serious complications. Gut microbiota-derived short chain fatty acids (SCFA) may benefit host metabolism but are reduced in T1D. We evaluated the hypothesis that DE and insulin restriction were associated with reduced SCFA-producing gut microbes, SCFA, and intestinal microbial diversity in adults with T1D. Methods and results: We collected stool samples at four timepoints in a hypothesis-generating gut microbiome pilot study ancillary to a weight management pilot in young adults with T1D. 16S ribosomal RNA gene sequencing measured the normalized abundance of SCFA-producing intestinal microbes. Gas-chromatography mass-spectrometry measured SCFA (total, acetate, butyrate, and propionate). The Diabetes Eating Problem Survey—Revised (DEPS-R) assessed DE and insulin restriction. Covariate-adjusted and Bonferroni-corrected generalized estimating equations modeled the associations. COVID-19 interrupted data collection, so models were repeated restricted to pre-COVID-19 data. Data were available for 45 participants at 109 visits, which included 42 participants at 65 visits pre-COVID-19. Participants reported restricting insulin “At least sometimes” at 53.3% of visits. Pre-COVID-19, each 5-point DEPS-R increase was associated with a −0.34 (95% CI -0.56, −0.13, p = 0.07) lower normalized abundance of genus Anaerostipes; and the normalized abundance of Lachnospira genus was −0.94 (95% CI -1.5, −0.42), p = 0.02 lower when insulin restriction was reported “At least sometimes” compared to “Rarely or Never”. Conclusion: DE and insulin restriction were associated with a reduced abundance of SCFA-producing gut microbes pre-COVID-19. Additional studies are needed to confirm these associations to inform microbiota-based therapies in T1D

The Intestinal Microbiota and Short-Chain Fatty Acids in Association with Advanced Metrics of Glycemia and Adiposity Among Young Adults with Type 1 Diabetes and Overweight or Obesity

BACKGROUND: Comanagement of glycemia and adiposity is the cornerstone of cardiometabolic risk reduction in type 1 diabetes (T1D), but targets are often not met. The intestinal microbiota and microbiota-derived short-chain fatty acids (SCFAs) influence glycemia and adiposity but have not been sufficiently investigated in longstanding T1D. OBJECTIVES: We evaluated the hypothesis that an increased abundance of SCFA-producing gut microbes, fecal SCFAs, and intestinal microbial diversity were associated with improved glycemia but increased adiposity in young adults with longstanding T1D. METHODS: Participants provided stool samples at ≤4 time points (NCT03651622: https://clinicaltrials.gov/ct2/show/NCT03651622). Sequencing of the 16S ribosomal RNA gene measured abundances of SCFA-producing intestinal microbes. GC-MS measured total and specific SCFAs (acetate, butyrate, propionate). DXA (body fat percentage and percentage lean mass) and anthropometrics (BMI) measured adiposity. Continuous glucose monitoring [percentage of time in range (70-180 mg/dL), above range (>180 mg/dL), and below range (54-69 mg/dL)] and glycated hemoglobin (i.e., HbA1c) assessed glycemia. Adjusted and Bonferroni-corrected generalized estimating equations modeled the associations of SCFA-producing gut microbes, fecal SCFAs, and intestinal microbial diversity with glycemia and adiposity. COVID-19 interrupted data collection, so models were repeated restricted to pre-COVID-19 visits. RESULTS: Data were available for ≤45 participants at 101 visits (including 40 participants at 54 visits pre-COVID-19). Abundance of Eubacterium hallii was associated inversely with BMI (all data). Pre-COVID-19, increased fecal propionate was associated with increased percentage of time above range and reduced percentage of time in target and below range; and abundances of 3 SCFA-producing taxa (Ruminococcus gnavus, Eubacterium ventriosum, and Lachnospira) were associated inversely with body fat percentage, of which two microbes were positively associated with percentage lean mass. Abundance of Anaerostipes was associated with reduced percentage of time in range (all data) and with increased body fat percentage and reduced percentage lean mass (pre-COVID-19). CONCLUSIONS: Unexpectedly, fecal propionate was associated with detriment to glycemia, whereas most SCFA-producing intestinal microbes were associated with benefit to adiposity. Future studies should confirm these associations and determine their potential causal linkages in T1D.This study is registered at clinical.trials.gov (NCT03651622; https://clinicaltrials.gov/ct2/show/NCT03651622)

Matrices over a semiring of binary relations and V -variable fractals

In this paper we prove that V -variable fractal sets are limits of infinite products of matrices over the semiring of binary relations on a compact metric space. © Allerton Press, Inc., 2011

Matrices over a semiring of binary relations and V -variable fractals

In this paper we prove that V -variable fractal sets are limits of infinite products of matrices over the semiring of binary relations on a compact metric space. © Allerton Press, Inc., 2011

Matrices over a semiring of binary relations and V -variable fractals

In this paper we prove that V -variable fractal sets are limits of infinite products of matrices over the semiring of binary relations on a compact metric space. © Allerton Press, Inc., 2011