Food packing: A case study of dining out in Beijing

the financial project supported by the State Key Program of the National Natural Science Foundation of China （71233007）

Deterministic and Stochastic Fractional-Order Hastings-Powell Food Chain Model

In this paper,a deterministic and stochastic fractional-order model of the tri-trophic food chain model incorporating harvesting is proposed and analysed.The interaction between prey,middle predator and top predator population is investigated.In order to clarify the characteristics of the proposed model,the analysis of existence,uniqueness,non-negativity and boundedness of the solutions of the proposed model are examined.Some sufficient conditions that ensure the local and global stability of equilibrium points are obtained.By using stability analysis of the fractional-order system,it is proved that if the basic reproduction number R_(0)<1,the predator free equilibrium point E_(1) is globally asymptotically stable.The occurrence of local bifurcation near the equilibrium points is investigated with the help of Sotomayor’s theorem.Some numerical examples are given to illustrate the theoretical findings.The impact of harvesting on prey and themiddle predator is studied.We conclude that harvesting parameters can control the dynamics of the middle predator.A numerical approximation method is developed for the proposed stochastic fractional-order model.

A DYNAMIC FOOD CHAIN MODEL FOR HONG KONG BASED ON RADFOOD MODEL AND BIRCHALL－JAMES ALGORITHM

In this paper a dynamic food chain model for Hong Kong which simulates the transfer of radioactive substances from a fallout deposition via the food chain into the human bodies is built. The model is based on the RADFOOD model and the BirchallJames algorithm. The radionuclides 13if and 90Sr representing the short-term and long-term risk situations have been studied as sample cases. Various types of crops,and the dietary pattern of the public have been collsidered. The resulting internal radiation doses have been calculated. The results are obtained for food consumption starting at various time after the fallout deposition and for different consumption durations.

Effect of Particle Phase Volume, Shape and Liquid Phase Concentrations on Rheological Properties of Large Particulate-Liquid Model Food Systems by Using Ball Measuring System

Rheological properties of large particulate-liquid model food systems were studied by using the BMS （ball measuring system）. The model food systems were composed of alginate gel particles （-10mm） and a gelatinised starch solution with 1% w/w sodium chloride as a liquid phase. The effects of particle phase volume （Ф, 0-0.60）, particle shapes （cube, sphere, rod and disc） and starch concentrations （3% and 5% w/w starch） were investigated. The power law model was successfully applied to characterize the flow properties of each system and the consistency K and power law index n were obtained. The K increased and n decreased with increasing # for samples at all particle shapes at 3% w/w starch in the liquid phase. The particle effect on the viscosity is further analysed by means of the Krieger-Dougherty model and the maximum packing fraction #,, and the intrinsic viscosity [η] were obtained in each system. The Фm, depended on the particle shape, as expected. The [7] value depended on particle shape and was largely in the order of 4.04 （cube）, 3.28 （disc）, 2.56 （sphere） and 2.32 （rod） at 3% w/w starch. The [η] also depended on starch concentration and was 1.1 at 5%,6 w/w starch in the liquid phase with spherical particles. The present results show successful application of BMS to study the rheological properties of large particulate liquid food systems at relatively small scale experiment （-0.5 L） and also that existing models for suspension rheology are applicable for such food systems to a great extend.

Dynamics of an autonomous food chain model and existence of global attractor of the associated non-autonomous system

In this paper,we have analyzed a tri-trophic food chain model consisting of phytoplankton,zooplankton and fish population in an aquatic environment.Here,the pelagic water column is divided into two layers namely,the upper layer and the lower layer.The zooplankton population makes a diel vertical migration(DVM)from lower portion to upper portion and vice-versa to trade-off between food source and fear from predator(Fish).Here,mathematical model has been developed and analyzed in a rigorous way.Apart from routine calculations like boundedness and positivity of the solution,local stability of the equilibrium points,we performed Hopf bifurcation analysis of the interior equilibrium point of our model system in a systematic way.It is observed that the migratory behavior of zooplankton plays a crucial role in the dynamics of the model system.Both the upward and downward migration rates of DVM leads the system into Hopf bifurcation.The upward migration rate of zooplankton deteriorates the stable coexistence of all the species in the system,whereas the downward migration rate enhance the stability of the system.FYirther,we analyze the non-autonomous version of the system to capture seasonal effect of environmental variations.We have shown that under certain parametric restrictions periodic coexistence of all the species of our system is possible.Finally,extensive numerical simulation has been performed to support our analytical findings.

Numerical solution of time-fractional three-species food chain model arising in the realm of mathematical ecology

T'his research paper implements the fractional homotopy analysis transform technique to compute the approximate analytical solution of the nonlinear three-species food chain model with time-fractional derivatives.The offered technique is a fantastic blend of homotopy analysis method(HAM)and Laplace transform(LT)operator and has been used fruitfully in the numerical computation of various fractional differential equations(FDEs).This paper involves the fractional derivatives of Caputo style.The numerical solutions of this selected fractional-order food chain model are evaluated by making use of the associated initial conditions.It is revealed by the adopting procedure that the more desirable estimation of the solution can be easily acquired through the calculation of some number of iteration terms only-a fact which authenticates the easiness and soundness of the suggested hybrid scherne.The variations of fractional order of time derivative on the solutions for different specific cases have been depicted through graphical presentations.The outcomes demonstrated through the graphs expound that the adopted scheme is very fantastic and accurate.

OVERTAKING OPTIMAL HARVESTING FOR AN AGE-DEPENDENT n-DIMENSIONAL FOOD CHAIN MODEL

This paper is concerned with an optimal harvesting problem over an infinite horizon for age-dependent n-dimensional food chain model and the analysis of long-term behaviors of the optimal-controlled system. The existence of overtaking optimal policy is proved and a maximum principle is carefully derived by means of Dubovitskii-Milyutin functional analytical extremum theory. Weak and strong turnpike properties of optimal trajectories are established.

Using Machine Learning to Identify and Optimize Sensitive Parameters in Urban Flood Model Considering Subsurface Characteristics

This study presents a novel method for optimizing parameters in urban flood models,aiming to address the tedious and complex issues associated with parameter optimization.First,a coupled one-dimensional pipe network runoff model and a two-dimensional surface runoff model were integrated to construct an interpretable urban flood model.Next,a principle for dividing urban hydrological response units was introduced,incorporating surface attribute features.The K-means algorithm was used to explore the clustering patterns of the uncertain parameters in the model,and an artificial neural network(ANN)was employed to identify the sensitive parameters.Finally,a genetic algorithm(GA) was used to calibrate the parameter thresholds of the sub-catchment units in different urban land-use zones within the flood model.The results demonstrate that the parameter optimization method based on K-means-ANN-GA achieved an average Nash-Sutcliffe efficiency coefficient(NSE) of 0.81.Compared to the ANN-GA and K-means-deep neural networks(DNN) methods,the proposed method better characterizes the runoff generation and flow processes.This study demonstrates the significant potential of combining machine learning techniques with physical knowledge in parameter optimization research for flood models.

Evaluating the Influence of Multisource Typhoon Precipitation Data on Multiscale Urban Pluvial Flood Modeling

Based on station precipitation observations,radar quantitative precipitation estimates(QPE), and radar fusion data during Typhoon Fitow(2013), the influence of multisource precipitation data on multiscale urban typhoon pluvial flood modeling is studied. Using Shanghai, China,as the study area, a simplified 2D hydrodynamic model is applied to simulations. Combined with actual flood incidents reported by the public and soil moisture data, we perform multiscale verifications and determine the applicability of three precipitation datasets in the modeling. The results are as follows:(1) At the city scale, although QPE have higher spatial resolution, these estimates are lower than station observations. Radar fusion data have both high accuracy and high spatial resolution. For flood depths above 5 cm, the radar fusion precipitation scenario can improve the matching probability by 6%.(2) At the neighborhood scale, the radar fusion precipitation scenario can effectively mitigate the problems of an uneven spatial distribution of stations and a weak QPE to accurately capture pluvial details.(3)One fixed-point assessment shows that different precipitation data have little influence on the temporal characteristics of the modeling result-all three types of data can accurately reflect flood occurrence times. This work can provide a scientific basis for constructing effective urban pluvial flood monitoring systems.

Removal of aflatoxin M1 from milk and aqueous medium by indigenously isolated strains of W.confusa H1 and L.plantarum S2

Employing LAB and/or their metabolites to reduce aflatoxins from food products is one of the fascinating areas of research.Therefore,in the present work an attempt was made to study the effect of isolated lactic acid bacteria(LAB)on the reduction of aflatoxin M1(AFM1)from phosphate buffer saline(PBS)and reconstituted skim milk(RSM).Out of 68 isolates,nine strains of LAB isolated from food products were examined to bind and reduce AFM1.The isolates were incubated with AFM1 at different time and temperature(24 h,48 h,and 72 h at 37℃ and 4℃)and later the residual toxin in the supernatant was determined.The preliminary results through thin layer chromatography(TLC)revealed that all isolates were able to bind AFM1 in PBS.However,based on the intensity of spots observed in TLC sheets,it was indicated that two isolates,H1 and S2 genotypically identified as W.confusa and L.plantarum shown better AFM1 binding ability as compared to other isolates.Further,the heat treated cells of both the selected strains did not show significant difference to AFM1 binding ability as compared to live cells.Results of high performance liquid chromatography(HPLC)observed that W.confusa H1 and L.plantarum had shown 78% and 72%AFM1 binding in PBS at 37℃ after 72 h.There was a significant difference(P<0.05)in AFM1 binding ability of L.plantarum S2 at 37℃&4℃,but such difference was not observed for W.confusa H1.Moreover,these isolates also observed reduction of naturally present AFM1 in 10%RSM.This is the first study reporting the AFM1 binding capability of the genus Weissella(strain W.confusa H1)and Enterococcus durans.These results showed that indigenous strains of LAB are able to bind AFM1 effectively.