What Sequences obey Benford's Law ?

We propose a new necessary and sufficient condition to test whether a sequence is Benford (base-b) or not and apply this characterization to some kinds of sequences (re)obtaining some well known results, as the fact that the sequence of powers of 2 is Benford (base-10).Benford's law, equidistributed sequences, ergodic endomorphisms

A Modified Galam's Model

In this paper we analyze the stochastic model proposed by Galam in [2], for information spreading in a `word-of-mouth' process among agents, based on a majority rule. Using the communications rules among agents defined in [2], we first perform simulations of the `word-of-mouth' process and compare the results with the theoretical values predicted by Galam's model. Since some dissimilarities arise in particular when a small number of agents is considered, we suggest some enhancements by introducing a new parameter dependent model. We propose a modified Galam's scheme which is asymptotically coincident with the original model in [2]. Furthermore, for relatively small values of the parameter, we provide a numerical experience proving that the modified model often outperforms the original one, in terms of efficiency.Word-of-mouth process, information spreading, agent based simulation

Leading advertisers efficiency evaluated by data envelopment analysis

In this paper we analyze the problem of measuring the advertising efficiency of the Leading US Advertisers during the period 2001-2006. We use the DEA (Data Envelopment Analysis) approach that enables to evaluate the relative efficiency in case of multiple inputs and outputs. In particular, the classical CCR-DEA model is first implemented in each year considered; a windows analysis approach is then used in order to better capture the dynamics of efficiency. Finally, the effect on efficiency of advertising spending over time, is captured by Adstock as an additional variable of the DEA model. The dynamics of Adstock is described by a finite difference equation.

A fractional optimal control problem for maximizing advertising efficiency

We propose an optimal control problem to model the dynamics of the communication activity of a firm with the aim of maximizing its efficiency. We assume that the advertising effort undertaken by the firm contributes to increase the firm's goodwill and that the goodwill affects the firm's sales. The aim is to find the advertising policies in order to maximize the firm's efficiency index which is computed as the ratio between "outputs" and "inputs" properly weighted; the outputs are represented by the final level of goodwill and by the sales achieved by the firm during the period considered, whereas the inputs are represented by the costs undertaken by the firm, fixed costs and advertising costs. The problem considered is formulated as a fractional optimal control problem. In order to find the optimal advertising policies we use the Dinkelbach's algorithm for fractional programming.

An application of Linear Programming to sociophysics models

In this paper we consider a renowned stochastic model from sociophysics reported in [1, 2], which describes the diffusion of information by word-of-mouth processes. This general model has a terrific impact to capture both social dynamics among agents and information percolation, in case interaction among individuals plays a keynote role. Here we generalize this model, by means of Linear Programming (LP) formulations, which exploit to some extent the potentialities of sociophysics from a mathematical programming perspective. Our overall approach aims to formally combine a stochastic model with a Linear Programming framework

Mathematical Programming for the Dynamics of Opinion Diffusion

The focus of this paper is on analyzing the role and the choice of parameters in sociophysics diffusion models, by leveraging the potentialities of sociophysics from a mathematical programming perspective. We first present a generalised version of Galam’s opinion diffusion model (see, e.g. [8,10])). For a given selection of the coefficients in our model, this proposal yields the original Galam’s model. The generalised model suggests guidelines for possible alternative selection of its parameters that allow to foster diffusion. Examples of the parameters selection process as steered by numerical optimisation, taking into account various objectives, are provided

On the Hyperparameters influencing a PINN's generalization beyond the training domain

Physics-Informed Neural Networks (PINNs) are Neural Network architectures trained to emulate solutions of differential equations without the necessity of solution data. They are currently ubiquitous in the scientific literature due to their flexible and promising settings. However, very little of the available research provides practical studies that aim for a better quantitative understanding of such architecture and its functioning. In this paper, we analyze the performance of PINNs for various architectural hyperparameters and algorithmic settings based on a novel error metric and other factors such as training time. The proposed metric and approach are tailored to evaluate how well a PINN generalizes to points outside its training domain. Besides, we investigate the effect of the algorithmic setup on the outcome prediction of a PINN, inside and outside its training domain, to explore the effect of each hyperparameter. Through our study, we assess how the algorithmic setup of PINNs influences their potential for generalization and deduce the settings which maximize the potential of a PINN for accurate generalization. The study that we present returns insightful and at times counterintuitive results on PINNs. These results can be useful in PINN applications when defining the model and evaluating it

Painful Birth of Trade Under Classical Monopolistic Competition

In the standard Krugman (1979) non-CES trade model, several asymmetric countries typically lose from increasing trade costs. However, all countries transiently benefit from such increase at the moment of closing trade, under almost-prohibitive trade costs (i.e., near autarky, which is possible only under non-CES preferences). In other words, during trade liberalization the first step from autarky to trade is necessarily harmful. Our explanation rests on market distortion and business destruction effects

Continual proteomic divergence of HepG2 cells as a consequence of long-term spheroid culture

Three-dimensional models are considered a powerful tool for improving the concordance between in vitro and in vivo phenotypes. However, the duration of spheroid culture may infuence the degree of correlation between these counterparts. When using immortalised cell lines as model systems, the assumption for consistency and reproducibility is often made without adequate characterization or validation. It is therefore essential to defne the biology of each spheroid model by investigating proteomic dynamics, which may be altered relative to culture duration. As an example, we assessed the infuence of culture duration on the relative proteome abundance of HepG2 cells cultured as spheroids, which are routinely used to model aspects of the liver. Quantitative proteomic profling of whole cell lysates labelled with tandem-mass tags was conducted using liquid chromatographytandem mass spectrometry (LC–MS/MS). In excess of 4800 proteins were confdently identifed, which were shared across three consecutive time points over 28 days. The HepG2 spheroid proteome was divergent from the monolayer proteome after 14 days in culture and continued to change over the successive culture time points. Proteins representing the recognised core hepatic proteome, cell junction, extracellular matrix, and cell adhesion proteins were found to be continually modulated.The National Research Foundation (NRF) Tuthuka PhD Track Funding Scheme, the NRF Innovation Masters and Doctoral Scholarship Program, University of Pretoria Doctoral Bursary as well as the NRF National Equipment Program.http://www.nature.com/srep/index.htmlpm2022PharmacologyPhysiolog

Biomarkers of browning of white adipose tissue and their regulation during exercise- and diet-induced weight loss

Background: A hypothesis exists whereby an exercise- or dietary-induced negative energy balance reduces human subcutaneous white adipose tissue (scWAT) mass through the formation of brown-like adipocyte (brite) cells. However, the validity of biomarkers of brite formation has not been robustly evaluated in humans, and clinical data that link brite formation and weight loss are sparse. Objectives: We used rosiglitazone and primary adipocytes to stringently evaluate a set of biomarkers for brite formation and determined whether the expression of biomarker genes in scWAT could explain the change in body composition in response to exercise training combined with calorie restriction in obese and overweight women (n = 79). Design: Gene expression was derived from exon DNA microarrays and preadipocytes from obesity-resistant and -sensitive mice treated with rosiglitazone to generate candidate brite biomarkers from a microarray. These biomarkers were evaluated against data derived from scWAT RNA from obese and overweight women before and after supervised exercise 5 d/wk for 16 wk combined with modest calorie restriction (∼0.84 MJ/d). Results: Forty percent of commonly used brite gene biomarkers exhibited an exon or strain-specific regulation. No biomarkers were positively related to weight loss in human scWAT. Greater weight loss was significantly associated with less uncoupling protein 1 expression (P = 0.006, R(2) = 0.09). In a follow-up global analysis, there were 161 genes that covaried with weight loss that were linked to greater CCAAT/enhancer binding protein α activity (z = 2.0, P = 6.6 × 10(−7)), liver X receptor α/β agonism (z = 2.1, P = 2.8 × 10(−7)), and inhibition of leptin-like signaling (z = −2.6, P = 3.9 × 10(−5)). Conclusion: We identify a subset of robust RNA biomarkers for brite formation and show that calorie-restriction–mediated weight loss in women dynamically remodels scWAT to take on a more-white rather than a more-brown adipocyte phenotype