Restricted Boltzmann machines (RBMs) are the building blocks of some deep learning networks. However, despite their importance, it is our perception that some very important derivations about the RBM are missing in the literature, and a beginner may feel RBM very hard to understand. We provide here these missing derivations. We cover the classic Bernoulli-Bernoulli RBM and the Gaussian-Bernoulli RBM, but leave out the ``continuous'' RBM as it is believed not as mature as the former two. This tutorial can be used as a companion or complement to the famous RBM paper ``Training restricted Boltzmann machines: An introduction'' by Fisher and Igel.

The efficacy of time-restricted feeding for weight loss has not been established as prior studies were limited by lack of controlled isocaloric designs. This study describes the design and implementation of a controlled feeding study evaluating time-restricted feeding. We designed a randomized, controlled, parallel-arm, feeding study comparing time restricted feeding (TRF) to a usual feeding pattern (UFP) for the primary outcome of weight change. Participants were aged 18-69 years with prediabetes and obesity. TRF consumed 80% of calories by 1300, and UFP consumed ≥50% of calories after 1700. Both arms consumed identical macro- and micro-nutrients, based on a healthy palatable diet. We calculated individual calorie requirements which were maintained throughout the intervention. We randomized 41 participants who all completed the study. The desired distribution of calories across feeding windows in both arms was achieved, as were weekly averages for macronutrients and micronutrients. All randomized participants completed the study. We actively monitored participants and adapted diets to facilitate adherence. We provide the first report, to our knowledge, on the design and implementation of a feeding study that isolated the effect of meal timing on weight, while maintaining constant caloric intake and identical diets during the study period.

Each individual has a unique gut microbiota; therefore the genes in our microbiome outnumber the genes in our genome by about 150 to 1. Perturbation in host nutritional status influences gut microbiome composition and vice versa. The gut microbiome can help in producing vitamins, hormones, and other active metabolites that support the immune system; harvest energy from food; aid in digestion; protect against pathogens; improve gut transit and function; send signals to the brain and other organs, oscillating the circadian rhythm and coordinate with host metabolism through multiple cellular pathways. Gut microbiota can be influenced by host genetics, medications, diet, and lifestyle factors from preterm to aging. So before prescribing a customized treatment, it is crucial to monitor and count the gut flora as a focused biomarker. Many nutritional approaches that have been developed help in maintaining and restoring an optimal microbiome such as specific diet therapy, nutrition interventions and customized eating patterns. One of these approaches is time-restricted feeding/eating (TRF/E), a type of intermittent fasting (IF) in which a subject abstains from food intake for a specific time window. Such a dietary modification might alter and restore the gut microbiome for proper alignment of cellular and molecular pathways throughout the lifespan. In this review, we have highlighted that gut microbiota would be a targeted biomarker and TRF/E would be a targeted approach for restoring the gut microbiome associated molecular pathways like hormonal signaling, the circadian system, metabolic regulators, neural responses, and immune-inflammatory pathways. Consequently, modulation of gut microbiota through TRF/E could contribute in proper utilization and availability of the nutrients and in this way confer protection against diseases for harnessing personalized nutrition approaches to improve human health.

Time-restricted feeding (TRF) showed a potent effect in preventing obesity and improving metabolic outcomes in several animal model of obesity; however, there is, as yet, scarce evidence about its effectiveness against obesogenic challenge that more accurately mimic the human Western diets, such as cafeteria diet. Moreover, the mechanism for its efficacy is poorly understood. White adipose browning has been linked to body weight loss. Herein, we tested whether TRF has the potential to induce browning of inguinal white adipose tissue (iWAT) and to attenuate obesity and associated dyslipidemia in cafeteria diet-induced obesity model. Male Wistar rats, fed normal laboratory chow (NC) or cafeteria diet (CAF) for 16 weeks, were subdivided into two groups that were subjected to either ad libitum (ad lib, A) or TRF (R) for 8 hours per day. Rats under TRF regimen had a lower body weight gain and adiposity compared with their diet-matched ad lib rats, despite equivalent levels of food intake and locomotor activity. In addition, TRF improved the deranged lipid profile [total cholesterol (TC); triglycerides (TG); high density lipoprotein (HDL-c); low density lipoprotein (LDL-c)] and atherogenic indices [atherogenic index of plasma (AIP); atherogenic coefficient (AC); coronary risk index (CRI)] in rats fed CAF diet. Remarkably, TRF resulted in decreased size of adipocytes and induced emergence of multilocular brown-like adipocytes in iWAT of NC- and CAF-fed rats. Protein expression of browning markers, such as uncoupling protein-1 (UCP1) and peroxisome proliferator activated receptor gamma coactivator 1-alpha (PGC1α) in iWAT were also up-regulated in time restricted NC- or CAF-fed rats. These findings suggest that TRF regimen is an effective strategy to improve obesity and associated dyslipidemia induced by CAF-diet, probably via a mechanism involving WAT browning process.

In the paper, the authors find two explicit formulas and recover a recursive formula for the generalized Motzkin numbers. Consequently, the authors deduce two explicit formulas and a recursive formula for the Motzkin numbers, the Catalan numbers, and the restricted hexagonal numbers respectively.

Abstract: The main contribution of this paper is to introduce a new iterative training algorithm for restricted Boltzmann machines. The proposed learning path is inspired from online sequential extreme learning machine one of extreme learning machine variants which deals with time accumulated sequences of data with fixed or varied sizes. Recursive least squares rules are integrated for weights adaptation to avoid learning rate tuning and local minimum issues. The proposed approach is compared to one of the well known training algorithms for Boltzmann machines named “contrastive divergence”, in term of time, accuracy and algorithmic complexity under the same conditions. Results strongly encourage the new given rules during data reconstruction.