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Additional file 1: Supplemental Table 1a. Moderately carbohydrate restricted diet meals during crossover phase. Supplemental Table 1b. The goal and the actual values of macronutrients and salt in crossover meals of Moderately carbohydrate restricted diet, per day. Supplemental Table 2a. Healthy Nordic Diet meals during crossover phase. Supplemental Table 2b. The goal and the actual values of macronutrients and salt in crossover meals of Healthy Nordic diet, per day.

Suppose G is a finite group and C(G) denotes the set of all conjugacy classes of G. The normal graph of G, N(G), is a finite simple graph such that V(N(G)) = C(G). Two conjugacy classes A and B in C(G) are adjacent if and only if there is a proper normal subgroup N such that A U B ? N. The aim of this paper is to study the normal graph of a finite group G. It is proved, among other things, that the groups with identical character table have isomorphic normal graphs and so this new graph associated to a group has good relationship by its group structure. The normal graphs of some classes of finite groups are also obtained and some open questions are posed.

Let G be a finite group. The power graph P(G) and its main supergraph S(G) are two simple graphs with the same vertex set G. Two elements x,y ? G are adjacent in the power graph if and only if one is a power of the other. They are joined in S(G) if and only if o(x)|o(y) or o(y)|o(x). The aim of this paper is to compute the characteristic polynomial of these graph for certain finite groups. As a consequence, the spectrum and Laplacian spectrum of these graphs for dihedral, semi-dihedral, cyclic and dicyclic groups were computed.

Low implementation complexity, low delay and close-to-optimal performance over a wide variety of channels are some of the advantages of spatially-coupled low-density parity-check (LDPC) codes. However, the error performance of the sliding window decoding scheme that is used to decode these codes is considerably degraded over channels with memory, such as the correlated erasure channel. Employing a block interleaver to encounter this situation is not always a viable option, since it introduces a large amount of delay and cancels out the low-delay property of the sliding window decoder. Another way to reduce the effects of erasure bursts is to construct a more robust code ensemble by presenting additional code design rules. However, this approach results in additional constraints on the already complicated code construction process. The authors propose a novel communication system that combats the effects of the erasure bursts through the use of a convolutional interleaver. The proposed system combines the inherent convolutional nature of the spatially-coupled LDPC codes with that of a convolutional interleaver to achieve very low overall delay. The performance of the proposed approach is analysed using the density evolution technique and the performance improvement is demonstrated as a function of the interleaving delay via computer simulations.

Our aim was to investigate in a real-life setting the use of machine learning for modelling the postprandial glucose concentrations in morbidly obese patients undergoing Roux-en-Y gastric bypass (RYGB) or one-anastomosis gastric bypass (OAGB). As part of the prospective randomized open-label trial (RYSA), data from obese (BMI ≥35 kg/m2) non-diabetic adult participants were included. Glucose concentrations, measured with FreeStyle Libre, were recorded over 14 preoperative and 14 postoperative days. During these periods, 3-day food intake was self-reported. A machine learning model was applied to estimate glycaemic responses to the reported carbohydrate intakes before and after the bariatric surgeries. Altogether, 10 participants underwent RYGB and 7 participants OAGB surgeries. The glucose concentrations and carbohydrate intakes were reduced postoperatively in both groups. The relative time spent in hypoglycaemia increased regardless of the operation (RYGB, from 9.2 to 28.2%; OAGB, from 1.8 to 37.7%). Postoperatively, we observed an increase in the height of the fitted response curve and a reduction in its width, suggesting that the same amount of carbohydrates caused a larger increase in the postprandial glucose response and that the clearance of the meal-derived blood glucose was faster, with no clinically meaningful differences between the surgeries. A detailed analysis of the glycaemic responses using food diaries has previously been difficult because of the noisy meal data. The utilized machine learning model resolved this by modelling the uncertainty in meal times. Such an approach is likely also applicable in other applications involving dietary data. A marked reduction in overall glycaemia, increase in postprandial glucose response, and rapid glucose clearance from the circulation immediately after surgery are evident after both RYGB and OAGB. Whether nondiabetic individuals would benefit from monitoring the post-surgery hypoglycaemias and the potential to prevent them by dietary means should be investigated.KEY MESSAGESThe use of a novel machine learning model was applicable for combining patient-reported data and time-series data in this clinical study.Marked increase in postprandial glucose concentrations and rapid glucose clearance were observed after both Roux-en-Y gastric bypass and one-anastomosis gastric bypass surgeries.Whether nondiabetic individuals would benefit from monitoring the post-surgery hypoglycaemias and the potential to prevent them by dietary means should be investigated. The use of a novel machine learning model was applicable for combining patient-reported data and time-series data in this clinical study. Marked increase in postprandial glucose concentrations and rapid glucose clearance were observed after both Roux-en-Y gastric bypass and one-anastomosis gastric bypass surgeries. Whether nondiabetic individuals would benefit from monitoring the post-surgery hypoglycaemias and the potential to prevent them by dietary means should be investigated.

Our aim was to investigate in a real-life setting the use of machine learning for modelling the postprandial glucose concentrations in morbidly obese patients undergoing Roux-en-Y gastric bypass (RYGB) or one-anastomosis gastric bypass (OAGB). As part of the prospective randomized open-label trial (RYSA), data from obese (BMI ≥35 kg/m2) non-diabetic adult participants were included. Glucose concentrations, measured with FreeStyle Libre, were recorded over 14 preoperative and 14 postoperative days. During these periods, 3-day food intake was self-reported. A machine learning model was applied to estimate glycaemic responses to the reported carbohydrate intakes before and after the bariatric surgeries. Altogether, 10 participants underwent RYGB and 7 participants OAGB surgeries. The glucose concentrations and carbohydrate intakes were reduced postoperatively in both groups. The relative time spent in hypoglycaemia increased regardless of the operation (RYGB, from 9.2 to 28.2%; OAGB, from 1.8 to 37.7%). Postoperatively, we observed an increase in the height of the fitted response curve and a reduction in its width, suggesting that the same amount of carbohydrates caused a larger increase in the postprandial glucose response and that the clearance of the meal-derived blood glucose was faster, with no clinically meaningful differences between the surgeries. A detailed analysis of the glycaemic responses using food diaries has previously been difficult because of the noisy meal data. The utilized machine learning model resolved this by modelling the uncertainty in meal times. Such an approach is likely also applicable in other applications involving dietary data. A marked reduction in overall glycaemia, increase in postprandial glucose response, and rapid glucose clearance from the circulation immediately after surgery are evident after both RYGB and OAGB. Whether nondiabetic individuals would benefit from monitoring the post-surgery hypoglycaemias and the potential to prevent them by dietary means should be investigated.KEY MESSAGESThe use of a novel machine learning model was applicable for combining patient-reported data and time-series data in this clinical study.Marked increase in postprandial glucose concentrations and rapid glucose clearance were observed after both Roux-en-Y gastric bypass and one-anastomosis gastric bypass surgeries.Whether nondiabetic individuals would benefit from monitoring the post-surgery hypoglycaemias and the potential to prevent them by dietary means should be investigated. The use of a novel machine learning model was applicable for combining patient-reported data and time-series data in this clinical study. Marked increase in postprandial glucose concentrations and rapid glucose clearance were observed after both Roux-en-Y gastric bypass and one-anastomosis gastric bypass surgeries. Whether nondiabetic individuals would benefit from monitoring the post-surgery hypoglycaemias and the potential to prevent them by dietary means should be investigated.