Distribution of euptyctimous mite Phthiracarus longulus (Acari: Oribatida) under future climate change in the Palearctic.

The aim of this paper is to prepare, describe and discuss the models of the current and future distribution of Phthiracarus longulus (Koch, 1841) (Acari: Oribatida: Euptyctima), the oribatid mite species widely distributed within the Palearctic. We used the maximum entropy (MAXENT) method to predict its current and future (until the year 2100) distribution based on macroclimatic bio-variables. To our best knowledge, this is the first-ever prediction of distribution in mite species using environmental niche modelling. The main thermal variables that shape the current distribution of P. longulus are the temperature annual range, mean temperature of the coldest quarter and the annual mean temperature, while for precipitation variables the most important is precipitation of the driest quarter. Regardless of the climatic change scenario (SSP1-2.6, SSP2-4.5, SSP5-8.5) our models show generally the northward shift of species range, and in Southern Europe the loss of most habitats with parallel upslope shift. According to our current model, the most of suitable habitats for P. longulus are located in the European part of Palearctic. In general, the species range is mostly affected in Europe. The most stable areas of P. longulus distribution were the Jutland with surrounding southern coasts of Scandinavia, islands of the Danish Straits and the region of Trondheim Fjord.

Fluorescence correlation spectroscopy in the study of the interaction between hyaluronan and positively charged surfactants.

The interaction between fluorescently labeled hyaluronan and cationic surfactants was studied using Fluorescence Correlation Spectroscopy. The hyaluronan was selected at two different molecular weights - specifically, 274 kDa and 710 kDa. Cetyltrimethylammonium bromide and Septonex® were chosen as cationic surfactants to interact with the negatively charged biopolymer. The study focused on changes in the diffusive behavior of a biopolymer that interacts with surfactant molecules in an aqueous environment. Various methods were applied to evaluate the obtained data, these including, among others, the Maximum Entropy Method, which provides the distributional dependences of diffusion coefficients. Without the surfactant, the studied biopolymers showed diffusion behavior comparable to that found in previously published studies. In the presence of surfactants, more intense interaction was observed between Cetyltrimethylammonium bromide and Septonex®. Comparing the molecular weights, the retention of intermolecular aggregates after the precipitation region for the lower weight and the disintegration of these aggregates for the higher weight were observed; moreover, they showed diffusion behavior comparable to the samples without the presence of the surfactant.

SMSP Mainlobe Jamming Suppression with FDA-MIMO Radar Based on FastICA Algorithm.

In the electronic warfare environment, the performance of ground-based radar target search is seriously degraded due to the existence of smeared spectrum (SMSP) jamming. SMSP jamming is generated by the self-defense jammer on the platform, playing an important role in electronic warfare, making traditional radars based on linear frequency modulation (LFM) waveforms face great challenges in searching for targets. To solve this problem, an SMSP mainlobe jamming suppression method based on a frequency diverse array (FDA) multiple-input multiple-output (MIMO) radar is proposed. The proposed method first uses the maximum entropy algorithm to estimate the target angle and eliminate the interference signals from the sidelobe. Then, the range-angle dependence of the FDA-MIMO radar signal is utilized, and the blind source separation (BSS) algorithm is used to separate the mainlobe interference signal and the target signal, avoiding the impact of mainlobe interference on target search. The simulation verifies that the target echo signal can be effectively separated, the similarity coefficient can reach more than 90% and the detection probability of the radar is significantly enhanced at a low signal-to-noise ratio.

Sub-Millisecond Photoinduced Dynamics of Free and EL222-Bound FMN by Stimulated Raman and Visible Absorption Spectroscopies.

Time-resolved femtosecond-stimulated Raman spectroscopy (FSRS) provides valuable information on the structural dynamics of biomolecules. However, FSRS has been applied mainly up to the nanoseconds regime and above 700 cm-1, which covers only part of the spectrum of biologically relevant time scales and Raman shifts. Here we report on a broadband (~200-2200 cm-1) dual transient visible absorption (visTA)/FSRS set-up that can accommodate time delays from a few femtoseconds to several hundreds of microseconds after illumination with an actinic pump. The extended time scale and wavenumber range allowed us to monitor the complete excited-state dynamics of the biological chromophore flavin mononucleotide (FMN), both free in solution and embedded in two variants of the bacterial light-oxygen-voltage (LOV) photoreceptor EL222. The observed lifetimes and intermediate states (singlet, triplet, and adduct) are in agreement with previous time-resolved infrared spectroscopy experiments. Importantly, we found evidence for additional dynamical events, particularly upon analysis of the low-frequency Raman region below 1000 cm-1. We show that fs-to-sub-ms visTA/FSRS with a broad wavenumber range is a useful tool to characterize short-lived conformationally excited states in flavoproteins and potentially other light-responsive proteins.

On the limits of inferring biophysical parameters of RBP-RNA interactions from in vitro RNA Bind'n Seq data.

We develop a thermodynamic model describing the binding of RNA binding proteins (RBP) to oligomers in vitro. We apply expectation-maximization to infer the specificity of RBPs, represented as position-specific weight matrices (PWMs), by maximizing the likelihood of RNA Bind'n Seq data from the ENCODE project. Analyzing these public data we find sequence motifs that can partly explain the data for more than half of the studied 111 RBPs, and for 48 of the proteins these motifs are consistent with the known specificity. Our code is publicly available, facilitating analysis of RBP binding data.

Quantitative estimation of chemical microheterogeneity through the determination of fuzzy entropy.

Chemical micro-heterogeneity is an attribute of all living systems and most of the soft and crystalline materials. Its characterization requires a plethora of techniques. This work proposes a strategy for quantifying the degree of chemical micro-heterogeneity. First of all, our approach needs the collection of time-evolving signals that can be fitted through poly-exponential functions. The best fit is determined through the Maximum Entropy Method. The pre-exponential terms of the poly-exponential fitting function are used to estimate Fuzzy Entropy. Related to the possibility of implementing Fuzzy sets through the micro-heterogeneity of chemical systems. Fuzzy Entropy becomes a quantitative estimation of the Fuzzy Information that can be processed through micro-heterogeneous chemical systems. We conclude that our definition of Fuzzy Entropy can be extended to other kinds of data, such as morphological and structural distributions, spectroscopic bands and chromatographic peaks. The chemical implementation of Fuzzy sets and Fuzzy logic will promote the development of Chemical Artificial Intelligence.

Revealing heterogeneity in correlation times of EGFP encapsulated in complex coacervate core micelles by analysis of fluorescence anisotropies.

Encapsulation of enhanced green fluorescent protein (EGFP) in complex coacervate core micelles (C3Ms) can be established by mixing EGFP with diblock polymers at equal charge ratio. It has previously been shown that this encapsulation system is highly dynamic, implying existence of different populations; GFP free in solution or complexed with polymers (small complexes) and EGFP encapsulated in C3Ms. We performed time resolved fluorescence anisotropy experiments to determine the relative populations of EGFP encapsulated in C3Ms using three different fluorescence anisotropy decay analysis methods. First, Maximum Entropy Method (MEM) data analysis was employed for five different EGFP concentrations in C3Ms that were mixed with dark fluorescent proteins (10, 20, 30, 40 and 50% EGFP, respectively). In all cases, correlation-time distributions between 0.1 and 100 ns (on a logarithmic timescale) are clearly visible showing bimodal distribution. The distribution between 0.1 and 2.0 ns is due to homo-FRET between EGFP molecules packed in micelles and the distribution between 8 and 30 ns coincides with the correlation-time distribution of free EGFP in solution. The fraction of homo-FRET distribution linearly increases with increase of relative micellar EGFP concentrations. These MEM results were corroborated by two different analysis methods: global population analysis of all five fluorescence anisotropy decays arising from EGFP in micelles together with the one of free EGFP (direct analysis of anisotropies) and global associative population analysis of anisotropies by fitting parallel and perpendicular fluorescence decay components. In contrast to global analyses approaches, the MEM method directly reveals distributions of correlation times without any prior information about the sample. However, global associative analysis of anisotropies by fitting parallel and perpendicular fluorescence decay components is the only method that allows to estimate accurately fractions of free fluorophores in solution and encapsulated fluorophores.

Investigation of Molecular Diffusion at Block Copolymer Thin Films Using Maximum Entropy Method-Based Fluorescence Correlation Spectroscopy and Single Molecule Tracking.

Fluorescence correlation spectroscopy (FCS) has been widely used to investigate molecular diffusion behavior in various samples. The use of the maximum entropy method (MEM) for FCS data analysis provides a unique means to determine multiple distinct diffusion coefficients without a priori assumption of their number. Comparison of the MEM-based FCS method (MEM-FCS) with another method will reveal its utility and advantage as an analytical tool to investigate diffusion dynamics. Herein, we measured diffusion of fluorescent probes doped into nanostructured thin films using MEM-FCS, and validated the results with single molecule tracking (SMT) data. The efficacy of the MEM code employed was first demonstrated by analyzing simulated FCS data for systems incorporating one and two diffusion modes with broadly distributed diffusion coefficients. The MEM analysis accurately afforded the number of distinct diffusion modes and their mean diffusion coefficients. These results contrasted with those obtained by fitting the simulated data to conventional two-component and anomalous diffusion models, which yielded inaccurate estimates of the diffusion coefficients. Subsequently, the MEM analysis was applied to FCS data acquired from hydrophilic dye molecules incorporated into microphase-separated polystyrene-block-poly(ethylene oxide) (PS-b-PEO) thin films characterized under a water-saturated N2 atmosphere. The MEM analysis revealed distinct fast and slow diffusion components attributable to molecules diffusing on the film surface and inside the film, respectively. SMT studies of the same materials yielded trajectories for mobile molecules that appear to follow the curved PEO microdomains. Diffusion coefficients obtained from the SMT data were consistent with those obtained for the slow diffusion component detected by MEM-FCS. These results highlight the utility of MEM-FCS and SMT for gaining complementary information on molecular diffusion processes in heterogeneous material systems.

Delving into Membrane Heterogeneity Utilizing Fluorescence Lifetime Distribution Analysis.

Lipid bilayer membranes are indispensable parts of cellular architecture. One of the integral properties of bilayer membranes is the environmental heterogeneity over a wide range of spatiotemporal scales. The environmental heterogeneity is a manifestation of the dynamic and compositional anisotropy in the plane of the membrane as well as along the bilayer normal. Fluorescence lifetime distribution analysis provides a spectroscopic tool to quantitatively characterize such heterogeneities. The review discusses recent applications of fluorescence lifetime distribution analysis utilizing the maximum entropy method to characterize horizontal and vertical heterogeneities in membranes.

Modified Maximum Entropy Method and Estimating the AIF via DCE-MRI Data Analysis.

Background: For the kinetic models used in contrast-based medical imaging, the assignment of the arterial input function named AIF is essential for the estimation of the physiological parameters of the tissue via solving an optimization problem. Objective: In the current study, we estimate the AIF relayed on the modified maximum entropy method. The effectiveness of several numerical methods to determine kinetic parameters and the AIF is evaluated-in situations where enough information about the AIF is not available. The purpose of this study is to identify an appropriate method for estimating this function. Materials and Methods: The modified algorithm is a mixture of the maximum entropy approach with an optimization method, named the teaching-learning method. In here, we applied this algorithm in a Bayesian framework to estimate the kinetic parameters when specifying the unique form of the AIF by the maximum entropy method. We assessed the proficiency of the proposed method for assigning the kinetic parameters in the dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI), when determining AIF with some other parameter-estimation methods and a standard fixed AIF method. A previously analyzed dataset consisting of contrast agent concentrations in tissue and plasma was used. Results and Conclusions: We compared the accuracy of the results for the estimated parameters obtained from the MMEM with those of the empirical method, maximum likelihood method, moment matching ("method of moments"), the least-square method, the modified maximum likelihood approach, and our previous work. Since the current algorithm does not have the problem of starting point in the parameter estimation phase, it could find the best and nearest model to the empirical model of data, and therefore, the results indicated the Weibull distribution as an appropriate and robust AIF and also illustrated the power and effectiveness of the proposed method to estimate the kinetic parameters.

Establishing a New Link between Fuzzy Logic, Neuroscience, and Quantum Mechanics through Bayesian Probability: Perspectives in Artificial Intelligence and Unconventional Computing.

Human interaction with the world is dominated by uncertainty. Probability theory is a valuable tool to face such uncertainty. According to the Bayesian definition, probabilities are personal beliefs. Experimental evidence supports the notion that human behavior is highly consistent with Bayesian probabilistic inference in both the sensory and motor and cognitive domain. All the higher-level psychophysical functions of our brain are believed to take the activities of interconnected and distributed networks of neurons in the neocortex as their physiological substrate. Neurons in the neocortex are organized in cortical columns that behave as fuzzy sets. Fuzzy sets theory has embraced uncertainty modeling when membership functions have been reinterpreted as possibility distributions. The terms of Bayes' formula are conceivable as fuzzy sets and Bayes' inference becomes a fuzzy inference. According to the QBism, quantum probabilities are also Bayesian. They are logical constructs rather than physical realities. It derives that the Born rule is nothing but a kind of Quantum Law of Total Probability. Wavefunctions and measurement operators are viewed epistemically. Both of them are similar to fuzzy sets. The new link that is established between fuzzy logic, neuroscience, and quantum mechanics through Bayesian probability could spark new ideas for the development of artificial intelligence and unconventional computing.

The Use of Maximum Entropy to Enhance Wave Intensity Analysis: An Application to Coronary Arteries in Hypertrophic Obstructive Cardiomyopathy.

Background: Wave intensity analysis is useful for analyzing coronary hemodynamics. Much of its clinical application involves the identification of waves indicated by peaks in the wave intensity and relating their presence or absence to different cardiovascular events. However, the analysis of wave intensity peaks can be problematic because of the associated noise in the measurements. This study shows how wave intensity analysis can be enhanced by using a Maximum Entropy Method (MEM). Methods: We introduce a MEM to differentiate between "peaks" and "background" in wave intensity waveforms. We apply the method to the wave intensity waveforms measured in the left anterior descending coronary artery from 10 Hypertrophic Obstructive Cardiomyopathy (HOCM) and 11 Controls with normal cardiac function. We propose a naming convention for the significant waves and compare them across the cohorts. Results: Using a MEM enhances wave intensity analysis by identifying twice as many significant waves as previous studies. The results are robust when MEM is applied to the log transformed wave intensity data and when all of the measured data are used. Comparing waves across cohorts, we suggest that the absence of a forward expansion wave in HOCM can be taken as an indication of HOCM. Our results also indicate that the backward compression waves in HOCM are significantly larger than in Controls; unlike the forward compression waves where the wave energy in Controls is significantly higher than in HOCM. Comparing the smaller secondary waves revealed by MEM, we find some waves that are present in the majority of Controls and absent in almost all HOCM, and other waves that are present in some HOCM patients but entirely absent in Controls. This suggests some diagnostic utility in the clinical measurement of these waves, which can be a positive sign of HOCM or a subgroup with a particular pathology. Conclusion: The MEM enhances wave intensity analysis by identifying many more significant waves. The method is novel and can be applied to wave intensity analysis in all arteries. As an example, we show how it can be useful in the clinical study of hemodynamics in the coronary arteries in HOCM.

Analysis of Indoor Radon Data Using Bayesian, Random Binning, and Maximum Entropy Methods.

Three statistical methods: Bayesian, randomized data binning and Maximum Entropy Method (MEM) are described and applied in the analysis of US radon data taken from the US registry. Two confounding factors-elevation of inhabited dwellings, and UVB (ultra-violet B) radiation exposure-were considered to be most correlated with the frequency of lung cancer occurrence. MEM was found to be particularly useful in extracting meaningful results from epidemiology data containing such confounding factors. In model testing, MEM proved to be more effective than the least-squares method (even via Bayesian analysis) or multi-parameter analysis, routinely applied in epidemiology. Our analysis of the available residential radon epidemiology data consistently demonstrates that the relative number of lung cancers decreases with increasing radon concentrations up to about 200 Bq/m3, also decreasing with increasing altitude at which inhabitants live. Correlation between UVB intensity and lung cancer has also been demonstrated.

Conformational heterogeneity of the voltage sensor loop of KvAP in micelles and membranes: A fluorescence approach.

KvAP is a tetrameric voltage-gated potassium channel that is composed of a pore domain and a voltage-sensing domain (VSD). The VSD is crucial for sensing transmembrane potential and gating. At 0 mV, the VSD adopts an activated conformation in both n-octylglucoside (OG) micelles and phospholipid membranes. Importantly, gating-modifier toxins that bind at S3b-S4 loop of KvAP-VSD exhibit pronounced differences in binding affinity in these membrane-mimetic systems. However, the conformational heterogeneity of this functionally-important sensor loop in membrane mimetics is poorly understood, and is the focus of this work. In this paper, we establish, using intrinsic fluorescence of the uniquely positioned W70 in KvAP-VSD and environment-sensitive NBD (7-nitrobenz-2-oxa-1,3-diazol-4-yl-ethylenediamine) fluorescence of the labelled S3b-S4 loop, that the surface charge of the membrane does not significantly affect the topology and structural dynamics of the sensor loop in membranes. Importantly, the dynamic variability of the sensor loop is preserved in both zwitterionic (POPC) and anionic (POPC/POPG) membranes. Further, the lifetime distribution analysis for the NBD-labelled residues by maximum entropy method (MEM) demonstrates that, in contrast to micelles, the membrane environment not only reduces the relative discrete population of sensor loop conformations, but also broadens the lifetime distribution peaks. Overall, our results strongly suggest that the conformational heterogeneity of the sensor loop is significantly altered in membranes and this correlates well with its environmental heterogeneity. This constitutes the first report demonstrating that MEM-lifetime distribution could be a powerful tool to distinguish changes in conformational heterogeneity in potassium channels with similar architecture and topology.

Heat-induced self-assembling of BSA at the isoelectric point.

Materials based on ordered protein aggregates have recently received a lot of attention for their application as drug carriers, due to their biocompatibility and their ability to sequester many biological fluids. Bovine serum albumin (BSA) is a good candidate for this use due to its high availability and tendency to aggregate and gel under acidic conditions. In the present work, we employ spectroscopic techniques to investigate the heat-induced BSA aggregation at the molecular scale, in the 12-84 °C temperature range, at pH = 5 where two different isoforms of the protein are stable. Samples at low and high protein concentration are examined. With the advantage of the combined use of FTIR and CD, we recognize the aggregation-prone species and the different distribution of secondary structures, conformational rearrangements and types of aggregates, of millimolar compared to micromolar BSA solutions. Further, as a new tool, we use the Maximum Entropy Method to fit the kinetic curves to investigate the distribution of kinetic constants of the complex hierarchical aggregation process. Finally, we characterize the activation energy of the initial self-assembling step to observe that the formation of both small and large aggregates is driven by the same interactions.

Improving the depth resolution of STEM-ADF sectioning by 3D deconvolution.

Although the possibility of locating single atom in three dimensions using the scanning transmission electron microscope (STEM) has been discussed with the advent of aberration correction technology, it is still a big challenge. In this report we have developed deconvolution routines based on maximum entropy method (MEM) and Richardson-Lucy algorithm (RLA), which are applicable to the STEM-annular dark-field (ADF) though-focus images to improve the depth resolution. The new three-dimensional (3D) deconvolution routines require a limited defocus-range of STEM-ADF images that covers a whole sample and some vacuum regions. Since the STEM-ADF probe is infinitely elongated along the optical axis, a 3D convolution is performed with a two-dimensional (2D) convolution over xy-plane using the 2D fast Fourier transform in reciprocal space, and a one-dimensional convolution along the z-direction in real space. Using our new deconvolution routines, we have processed simulated focal series of STEM-ADF images for single Ce dopants embedded in wurtzite-type AlN. Applying the MEM, the Ce peaks are clearly localized along the depth, and the peak width is reduced down to almost one half. We also applied the new deconvolution routines to experimental focal series of STEM-ADF images of a monolayer graphene. The RLA gives smooth and high-P/B ratio scattering distribution, and the graphene layer can be easily detected. Using our deconvolution algorithms, we can determine the depth locations of the heavy dopants and the graphene layer within the precision of 0.1 and 0.2 nm, respectively. Thus, the deconvolution must be extremely useful for the optical sectioning with 3D STEM-ADF images.

Gating-related Structural Dynamics of the MgtE Magnesium Channel in Membrane-Mimetics Utilizing Site-Directed Tryptophan Fluorescence.

Magnesium is the most abundant divalent cation present in the cell, and an abnormal Mg2+ homeostasis is associated with several diseases in humans. However, among ion channels, the mechanisms of intracellular regulation and transport of Mg2+ are poorly understood. MgtE is a homodimeric Mg2+-selective channel and is negatively regulated by high intracellular Mg2+ concentration where the cytoplasmic domain of MgtE acts as a Mg2+ sensor. Most of the previous biophysical studies on MgtE have been carried out in detergent micelles and the information regarding gating-related structural dynamics of MgtE in physiologically-relevant membrane environment is scarce. In this work, we monitored the changes in gating-related structural dynamics, hydration dynamics and conformational heterogeneity of MgtE in micelles and membranes using the intrinsic site-directed Trp fluorescence. For this purpose, we have engineered six single-Trp mutants in the functional Trp-less background of MgtE to obtain site-specific information on the gating-related structural dynamics of MgtE in membrane-mimetic systems. Our results indicate that Mg2+-induced gating might involve the possibility of a 'conformational wave' from the cytosolic N-domain to transmembrane domain of MgtE. Although MgtE is responsive to Mg2+-induced gating in both micelles and membranes, the organization and dynamics of MgtE is substantially altered in physiologically important phospholipid membranes compared to micelles. This is accompanied by significant changes in hydration dynamics and conformational heterogeneity. Overall, our results highlight the importance of lipid-protein interactions and are relevant for understanding gating mechanism of magnesium channels in general, and MgtE in particular.

Co-localization analysis in fluorescence microscopy via maximum entropy copula.

Co-localization analysis is a popular method for quantitative analysis in fluorescence microscopy imaging. The localization of marked proteins in the cell nucleus allows a deep insight into biological processes in the nucleus. Several metrics have been developed for measuring the co-localization of two markers, however, they depend on subjective thresholding of background and the assumption of linearity. We propose a robust method to estimate the bivariate distribution function of two color channels. From this, we can quantify their co- or anti-colocalization. The proposed method is a combination of the Maximum Entropy Method (MEM) and a Gaussian Copula, which we call the Maximum Entropy Copula (MEC). This new method can measure the spatial and nonlinear correlation of signals to determine the marker colocalization in fluorescence microscopy images. The proposed method is compared with MEM for bivariate probability distributions. The new colocalization metric is validated on simulated and real data. The results show that MEC can determine co- and anti-colocalization even in high background settings. MEC can, therefore, be used as a robust tool for colocalization analysis.

Charge density of 4-methyl-3-[(tetrahydro-2H-pyran-2-yl)oxy]thiazole-2(3H)-thione. A comprehensive multipole refinement, maximum entropy method and density functional theory study.

The structure of 4-methyl-3-[(tetrahydro-2H-pyran-2-yl)oxy]thiazole-2(3H)-thione (MTTOTHP) was investigated using X-ray diffraction and computational chemistry methods for determining properties of the nitrogen-oxygen bond, which is the least stable entity upon photochemical excitation. Experimentally measured structure factors have been used to determine and characterize charge density via the multipole model (MM) and the maximum entropy method (MEM). Theoretical investigation of the electron density and the electronic structure has been performed in the finite basis set density functional theory (DFT) framework. Quantum Theory of Atoms In Molecules (QTAIM), deformation densities and Laplacians maps have been used to compare theoretical and experimental results. MM experimental results and predictions from theory differ with respect to the sign and/or magnitude of the Laplacian at the N-O bond critical point (BCP), depending on the treatment of n values of the MM radial functions. Such Laplacian differences in the N-O bond case are discussed with respect to a lack of flexibility in the MM radial functions also reported by Rykounov et al. [Acta Cryst. (2011), B67, 425-436]. BCP Hessian eigenvalues show qualitatively matching results between MM and DFT. In addition, the theoretical analysis used domain-averaged fermi holes (DAFH), natural bond orbital (NBO) analysis and localized (LOC) orbitals to characterize the N-O bond as a single σ bond with marginal π character. Hirshfeld atom refinement (HAR) has been employed to compare to the MM refinement results and/or neutron dataset C-H bond lengths and to crystal or single molecule geometry optimizations, including considerations of anisotropy of H atoms. Our findings help to understand properties of molecules like MTTOTHP as progenitors of free oxygen radicals.

Mathematical modeling for green supply chain considering product recovery capacity and uncertainty for demand.

Competition in today's market is the most important concern of companies and producers in free markets. Buyers are also looking for higher quality and lower prices. Manufacturers should, therefore, reduce production costs and increase budgets for research and product development. On the other hand, the limitation of mineral resources in each country and in the world in general is a very important factor for increasing the price of raw materials which increases the cost of production of a product. In this study, a green aspect of decision-making, concurrent modeling for inventory-routing, and application of maximum entropy (ME) method for overcoming uncertainties of demands are applied to optimize the usage of raw materials and returning of defective products to the production cycle in a closed-looped supply chain under multi-period planning horizon. Also, dynamic modeling is used to balance the inventory level in all stages of the network that leads to optimum usage of the raw materials. For this purpose, the first objective function reduces production, transportation-routing, and inventory costs, and the second objective reduces greenhouse gas emissions through all levels of the network. Finally, this model is solved by using the exact solution method with the help of Gams software as well as the non-dominated sorting genetic algorithm II (NSGAII) and multi-objective particle swarm optimization (MOPSO) algorithm. Sensitivity analysis has been performed on failure rates, greenhouse gas emissions during recycling and production, and the optimistic-pessimistic coefficient of the ME solution method. Solution methods have been compared using several criteria, and the NSGAII method has finally obtained the best result. The results show that the manager should pay more costs in order to prevent backorder demands. Also, collecting the more defective products leads to increasing production amount since the collective products can return to the production line. Finally, it is required for the managers to control products' failure rate to optimize capacity usage in the model.