Welcome to this course on data simulation. We are going to provide a very broad background about the theoretical aspects of data simulation. Our first lecture will be on providing an introduction and an overview. I would like to start with the question what is a simulation? The concept of a simulation in general conjures up various meanings in different disciplines. In biology for example, the human animal plant body assimilates or absorbs food. So, here the word assimilation refers to the process of absorption of food by living organism be human animal or plant. So, here assimilation refers to a biological process. Assimilation also happens within the context of sociology. Immigrants refugees from one country they try to rehabilitate in another country by assimilating into the prevailing culture. In this context assimilation refers to the sociological process. As an example, United States is considered to be an example of social experiment. It is a melting part of sorts where there is continuous simulation of all cultures from all around the world. However, within the context of physical science as an engineering, assimilation refers to the process of fitting models to data. So, in this process the key players are model, data and the process of fitting data to the model. So, this involves 3 different disciplines. One is science of model building. Second one is ability to observe nature and the observations give rise to data. Data is available, model is available, but we need to bring them together. This bringing together that is the assimilation process. That process is also called fitting model to data. Looking from this perspective data assimilation is a very broad and a vast discipline. It is very broad, it is very deep. We would like to develop a very holistic view by looking at various practices that go with different names, but the underlying process is always related to data assimilation. Recall the old saying the whole is greater than the some other parts. So, the process of fitting models to data, the process of various types of assimilation, these are all various parts that come to be called the science of data assimilation. The whole is much bigger than many of its parts. First I would like to talk about data assimilation as a curve fitting or a regression process. The notion of fitting in data assimilation is the same as that is used in deterministic curve fitting or interpolation that is often used in numerical analysis. It is also intimately related to statistical regression analysis. To further understand the relation between data assimilation and other practices, we need to be able to introduce different classifications of models. Please recall models data and the process of fitting are the three components. Now we are going to look into properties of various kinds of model that occur in almost all of sciences and engineering. Models in general can be classified into two types. Type one is called process specific model, type two is called data specific models. Let us first concentrate on type one models. Here we understand the underlying scientific process that is at play. These are developed based on causality. If there is a force there is a reaction to that. There is always a cause and effect relation. In sciences many of these causal relations are nicely captured in the form of conservation laws. Here are some examples of models of type one. The harmonic oscillator that describes the motion of a pendulum in a friction free environment. The shallow water model that can be used to describe the motion of waves in a ocean. The primitive equation model that is the basis for many types of weather forecasting. Geo-strophic vorticity equation in particular. One of the equations which is very generic and has applications. In particular it is the basis for hurricane prediction. So you can see models come from various shapes and forms. Each one of them are developed based on fundamental scientific principles. Causality based, process based. These are essentially statements of conservation laws. As opposed to these the second type of model they are called data specific models. Here there is no underlying causation. There is no cause or effect that is well established. All that we have is the availability of a bunch of data.  Given a bunch of observations of mother nature's behavior at various times it is up to us to be able to mine the underlying information and that mining is done with respect to finding the correlation between the data. This is also called correlation based or similarity based. These models are essentially empirical as opposed to based on physical principles. These models can be either an explicit model or an implicit model. For example I have a time series. The time series could be value of IBM stock over each day. The maximum temperature in Bangalore each day. The unemployment rate in the state of Karnataka every month. This is an example of a time series. We would like to be able to build models for using these time series data to be able to predict how the unemployment will be in a year from now. What will be the maximum temperature in Bangalore in middle of January. These are called explicit models. These are empirical models. These are essentially based on correlation. Machine learning provides again lots of opportunities for model building based on data. Neural network is an example of a specific kind of machine learning process where we try to build a specific neural network to be able to undertake a specific task of being able to classify. Neural network models are essentially implicit models. You give an output. You try to tune the model until you get the required output. You probably may not be able to explain why and how except that if you did the right thing you can make it work. Again these are data specific. For example the time series model that is used for IBM stock price may not be the same type that can be used to predict tomorrow's maximum temperature in Bangalore or unemployment percentage so on and so forth. So each one of these data set has to be looked at separately. For each one of these data set we have to uncover the underlying serial correlation. Here I would like to make a statement about the definite need for correlation. If a collection of data are not correlated means one does not influence the other. If one does not influence the other we cannot we may not be able to predict anything at all. So ultimate aim in model building is to be able to predict. Once you have model I can pull the model solution forward to be able to make predictions. So correlation is very fundamental attribute of data specific models and it is using this correlation the model is able to extrapolate make predictions. Pattern recognition is another example of explicit models that are again data specific. Now another dimension to data simulation I would like to bring to fourth. Data the development of type 1 models and data simulation models for these models are separate processes. For example a physicist may try to develop a primitive equation model. An observation specialist may try to get data from satellites or radar. A data simulation person then comes into play to be able to understand the properties the model understand the data set and to be able to bring them together. So model development and data simulation process are two separate processes. It is the data simulation person is the one who sits in the middle who tries to talk to both the model and the data. The structure of the model in terms of spatio temporal evolution relation among the state variables are specified by the details of the model. Yet many of these models may have several unknowns. For example in a primitive equation model we may have an initial condition we may have a boundary condition. Depending on the type of processes involved different kinds of parameters may also become part of this equation. I know certain class of primitive equation model helps you to predict whether in a particular situation. But to be able to initialize the model to run the model forward I would need initial conditions I would need boundary conditions I would need parameters. So models are specified model low initial conditions boundary conditions and parameters. To be able to run the model forward we need the values of these and how do we get to know the values of these parameters that is where we use the data. So in here the goal of data simulation is to be able to estimate the unknown from the knowledge of the available data that is supposed to contain information about the unknowns. I would like to explain this a little bit further. For example a quasi-geostrophic water city equation is often used to be able to predict the movement of a hurricane. But that is a very generic kind of equation. If I want to be able to use that model to be able to predict the movement of a hurricane I need to know where it is today and what are the coordinates of that what are the pressure differences what are the various other attributes. So somebody has to fly planes into these hurricanes they collect data they bring the data to the office. So that tells you observations about the phenomenon I understand the science the physics behind the hurricane we would like to be able to bring these two together in order to be able to estimate the unknowns initial conditions boundary conditions and parameters. Therefore you can readily see data simulation is closely related to the classical estimation problem. This is fitting the observations of hurricane to the hurricane forecast models that was developed earlier this aspect is related to estimation theory. There is another point of view one can take data simulation has also lot in common with systems identification as used in systems engineering. In systems engineering estimation of parameters of a system to maximize the performance is known as system identification or adaptive identification. So let us look at the picture here this one is an engineering system that is a physical plant the physical plant may be a chemical plant it could be an aircraft it could be a ship or it could be any kind of engineering device it has input it has parameters which are knobs that is meant to control meant to change the behavior of the system. For example if this were to be chemical plant the input could be raw materials the parameters could be the presence of catalyst it could be temperature it could be pressure it could be concentration. So these are all various parameters that one can control. So the output of the plant depends on the physical properties of the engineering system along with parameters and the input I would like to be able to understand the dependence of output of the input. So we try to express that relation in the form of a cost function we would like to be able to maximize or minimize if it is cost is always minimization if it is profit it is generally written as a maximization it is an optimization problem. So we would like to be able to change the input of the parameters in a feedback loop such that I try to maximize the functioning of this plant this often occurs in many of the engineering system you can really see in here data simulation is done online your physical plant is operating it provides an output that is a function of the input I do not know what is the maximum output possible I am going to learn the maximum output by sequentially changing the input and the parameters in the loop based on a pre-specified criterion called the cost function this often happens in all branches of engineering. Now let us come to physically occurring systems such as meteorology such as geophysical sciences there are observations of geophysical sciences we often do the observations geophysical sciences come from satellites radars balloons ships collect information airplane collect information and these days we have ground base stations all around over the ocean we have lots of buoys. So observation comes in various shapes and forms the observation contain secrets about the functioning of the nature the modelers believe that mother nature behaves in a particular way they encapsulate the behavior of the model based on their understanding in the form of the process based models that we talked about the process based models in general can be a dynamic model if it is a dynamic model it can be based on ordinary differential equations or partial differential equations these models have initial conditions boundary conditions and parameters we only know the model describes the overall observations in some specific ways but we would like to be able to fit the model to the data so that a specific model can be used to accommodate the specific set of observation to be able to generate predictions about a particular hurricane a particular tornado a particular natural occurring event so this is how we use the data which are contained in the observation and the model fitting model to data. So this is an alternate view this is the view that often occurs within the geophysical domain oceanography hydrology atmospheric sciences and so on now I would like to talk about how data simulation takes place in empirical models in empirical model there is nothing we do not have physics all that we have is a bunch of data so I have to use this data in two ways so we have a twin task one is to be able to build the model and then once we have a general understanding of the class of models that we can use then we have to do data simulation on these models using the data so let us look at the data mining part the data mining part is the process by which I would like to be able to understand the structure that underlie the creation of the data. So what is that we do we compute the correlations we compute the similarity measures in a given data set based on the correlation we can narrow down a potential class of models to a small subset as an example in the case of time series we may say we are looking at the correlation structure if the correlation persists for a long time that means it has a long memory if the correlation comes down to low values very fast if it decreases for example a correlation could be a correlation structure could be like this here the correlation does not decrease too fast so this these kinds of process supposed to have long memory another could be the correlation comes down to 0 very quickly. So the class of models for this this is one kind of model this is a second kind of model there are guidelines to choose certain kinds of models for correlations of type 1 for correlations of type 2 even here one has to contain with the orders of the model but just by looking at it we cannot say this model work better that model work better so we have to be we have to be flexible try to be able to have at least couple of different ways of looking at it. So once we have narrowed down the size of models it is like having a barotropic vorticity equation it is having a primitive equation so we have to come to the same level as in the process based models by looking at the data to do data mining process we will talk a lot about data mining little later in this lecture series in this introductory chapter now once the model is available again in the case of time series models the models are dynamic given any dynamic model we will have initial conditions we have parameters to be able to pull the model forward we need to be able to know the values of these parameters again so once the set of models are selected we can use the same data set to estimate the unknown parameters by fitting each of the models to the data. So now you can readily see independent of the type of models the process of data assimilation requires the presence of a model the presence of an associated set of data and then the process of fitting that story must come pretty clear by now so here is an added difficulty in the case of empirical thing in the case of process based models for hurricane we know what class of models to use for certain time of atmospheric motions we know what certain type of models to use for oceanography they have a pretty good understanding what type of models to use so a given process has associated with the already understood class of models in the case of empirical model building models of types too there is no such clear cut data association there is no clear cut way to be able to decide this model will work better than that so we have to always content with a class of models so within this context the notion of model selection becomes a very important and a fundamental task there are several methods one can look into to be able to develop and compare the quality of each of these models to a particular given situation and we are not going to indulge into the model selection process those of us who are working in the empirical model building has to be cognizant of the requirement of being able to use very good criteria to be able to select good models for a particular given kind of data set so now you have seen two aspects data mining and data simulation I am going to use time series analysis again to be able to reinforce some of the basic thought process we have already discussed this is an example of an explicit model here data mining step what is the data mining step here given a time series first compute and plot the correlogram and what is the correlogram correlogram is the one that we already saw I am going to give another example of a correlogram this is the time index k this is rho of k so what does k refers to k refers to the separation between two data set time t and time t plus k how are the data are time t and time t plus k are associated with each other for example if I have a maximum temperature tomorrow today how is today's maximum temperature related to yesterday's maximum temperature day before yesterday's 10 days ago you can readily see today's maximum temperature may be related to yesterday's but to a lesser degree day before yesterday to a lesser degree to a week almost no link to a month from today so this correlation of maximum temperature one can think of it like this if you think of again unemployment percentage unemployment percentage do not vary day by day they will repeat of month so today's unemployment is very much related to yesterday's unemployment so what is the correlation between unemployment in time separated by one day one month six months one year where the basic units of time could be one day so k refers to the number of days that separates two time epochs between which I am interested in correlation so this is what is called a correlogram plot of rho of k versus k rho of k is a correlation between data that are case steps apart then what is that we do so this is data dependent so this created from a particular data so this is some sort of a summary of what this data tells us then how do you utilize this mathematicians have helped to create several different types of models for time series analysis these models were called a REMA AR for autoregressive I for integrated MA for moving so it is a three different families of models is called AR model integrated model moving average model ARREMA models these ARREMA models are a very broad class of potential model that one can build mathematicians have helped us to be able to build all these models ahead of time and they have analyzed the underlying correlation properties of each of these models and have cataloged in fact they are they have developed all of them and all of them of properties of correlations of various types of models for example an AR model could be an first order model second order model an MA model could be a first order model second order model and ARMA first order AR second order MA so in general one can have ARMA PQ so P refers to the AR type Q refers to the MA type by changing P is an integer Q is an integer by changing P and Q I can get a whole family of models if each of these models are created I can mathematically compute what their correlation should be and I can plot these correlations and create an album this album is the fundamental basis for almost all of time series analysis how do I use this album you have already cranked out the correlation for a specific data set then you visually compare the given picture the photo with the album that you already have you narrow down which of the pictures in the album close symbol the one that you have that depicts the particular data set you have and that helps you to narrow down maybe it looks like AR 2 and 3 maybe it is AR MA 11 you do not simply say this is it you look at the things that are closed you narrowed on the model to 234 each order will have different kinds of parameterization so use the same data to be able to estimate the various parameters of each of the models on once you fit different models to the same data then you can compute what is called the error in the forecast the error in the model use that error to further select much more finally the appropriate model that could be used in this particular case so the data assimilation step now so that is the so the first one is analysis of data second one is comparison of the given data with the album once a particular data has been narrowed down then you come back to the whole step called the data assimilation step estimate the parameters of the different models using the same data set so here I would like to emphasize the difference in the process based models models are created from by the scientists observations are created by measurement scientist they do not talk to each other but our job is to bring them together so the model building and data assimilation product separate but the case of empirical models while you are given is only the data based on the data you have to develop the model once you develop the model use the same data to be able to assimilate the data into the model and again model selection becomes an important situation in these cases here comparing the album I would like to bring in analogy here all of us happen to go to the doctor once a while in order to understand what happens with your health doctors order different kinds of observations on your blood test just x-ray maybe an MRI or maybe other chemical analysis of your blood once a chemical analysis the blood x-ray MRI all the things are made available a doctor hangs them all together and he looks at various he or she looks at various signals that is observations providers then they go to the anatomy book the anatomy book describes what an ideal body should be they compare the present situation with an ideal situation oh this looks right this looks right oh this looks not that good they try to narrow down a particular possibility and then do for the steps do for the steps do for the steps once they understand then they go for the treatment so to to label you have this disease to label you have that disease you to label you have this problem that is a prediction problem to be able to predict I need to analyze the model and how do they use the model they use them the models or to them the the anatomy textbook so there is a data there is an album they compare the data with the album to be able to generate to be able to make a forecast once the forecast is done with respect to medical diagnosis forecast then leads to a treatment and then recovery in the case of a hurricane forecast we make a forecast then we tell the public that is going to be a 20 drain tomorrow move people up up to the to the to the higher grounds and so on and so forth so the aim of data simulation in general is to be able to fit models to data so that we can generate useful forecast and the forecast can be used in many different ways for public consumption so that is the overall underlying philosophy that will be pursuing in this course so data mining and data simulation dm for data mining da for data simulation they are also used in machine learning in this case the models are implicit we are not going to do much of machine learning in this class we are not going to be doing much of times it in this class that is why I would like to spend a little bit longer time to start with to be able to see the other relations to data simulation so goal is to train a machine say an artificial neural network to classify samples into two classes given a set of for example medical diagnosis for example blood analysis a blood chemist gives the blood chemistry the whole idea is that can you feed this blood chemistry information into a neural network you train the neural network so well to be able to predict yes you have hepatitis a no you have hepatitis b no you have hepatitis c 50 years ago we did not know that there was a disease called hepatitis then they know that there is a disease called hepatitis then they found out hepatitis is not one kind it is a multiple kind a and b then they found out it is not a and b that is also a c have we discovered all aspects of hepatitis the answer is no we never know that could be c d e f g h so once you know that these are the characteristics of the blood that corresponds to a b c we would like to be able to automate the decision process so neural network is essentially a classificatory mechanism into which you feed this chemical information it prints out the particular kind of disease that corresponds to that that is a classification for a typical classification problem another classification problem is in a post office I would like to be able to develop a machine that can read the addresses to be able to sort them human can sort but I would like to automate the sorting process by machines so that is a pattern recognition process but I write in a very different from yours but the machine cannot handle all the ways of handwriting so we are going to say hey if you want to be able to use the machine to classify you have to type in a particular form once you have typed in a particular format a machine can be taught to be able to classify the addresses in different groups that is artificial network making this network do these processes is called learning phase so given a set of samples and their associated classes so what does that mean these corresponds to type a hepatitis these correspond to type b hepatitis these correspond to these type 3 c hepatitis so there must be an expert who already knows a particular analysis also the classification he has labeled them so once I have a sample with their associated classes then what do I do you divide the samples into two groups one large subset called the training data another small subset called the testing data so we use the larger training data to be able to train the machine that is called learning with the teacher we always learn with the teacher there are two times of learning learning with the teacher learning without a teacher in the in case of learning with the teacher you learn by recognizing that you made a mistake in the case of learning with the teacher I already know for this input this must be the output I know for specific so you can train using this data where the known classification an artificial neural network to classify so this is essentially a fitting process in the learning this is called the learning with the teacher during this phase I make sure on this data set this machine behaves in the best possible way then I would like to understand whether the machine will be able to do things that it has not already seen so if I use the same data that I use to teach and then certify that cheating so I would like to be able to test it with the set of data that was not used in the training phase and that is why we have talked about two subsets a smaller subset now you feed the data set that the machine has not seen earlier if on this data set the machine does very well then you have succeeded in making the machine learn though this is from a higher angle you can look at it as a data simulation process we are fitting the behavior of the network to suit the classifications of a given data set so you can see machine learning in data simulation have a very strong interconnection data mining and data simulation in artificial neural network is an implicit model again this is a quick summary of what I already described the data mining phase here what is the data is the choice of the structure of the neural network I simply talked about neural network how do I define the network it has number of stages number of neurons in a given stage the total number of inputs the total number of outputs these essentially describe the topology of the underlying artificial neural network this essentially comes from experience this is the data mining phase the mining relates to a lot of experience that one has should I have two layers should I have one layer should I have five layers should I have one output should I have two output so these are all the decisions that engineer has to make in the design of the networks once the network is designed the structure of the network is designed we are the same level as in the Armagh case I have picked the model we are the same level as I had picked a hurricane I have picked the hurricane model so the model is already fixed in here the data assimilation phase is to fit the chosen structure to the training data by minimizing the error in classification the testing phase is the prediction phase to see whether the artificial neural network handles the new situations very well so you can see the data assimilation is intimately associated with with learning my own background my PhD work was in essentially in machine learning that's why I could jump into data assimilation part rather easily data assimilation is the basis for any and any kind of learning mechanisms or learning devices so different facts about da all in one place now da can be looked at curve fitting da can be looked at estimation theory da can be looked at statistical regression da can also be looked at system identification adaptive optimization so looking at da is like 5 blind man looking at an elephant a person in curve fitting looks at curve fitting only a person in size statistical regression record statistical regression only our job is to be able to bring the big elephant this is what I was trying to tell in the very first slide the sum is greater than the parts the sum the data assimilation to further understand the richness of data assimilation we need to introduce further classifications of both models and data and that's what we are now going to look at until now we classified models only at a broad angle namely process based models or empirical models or data specific models that's the classification at the highest top most level now I need to bring down finer nuances into the classification so models in general can be classified along different dimensions a model can be static or dynamic a model can be deterministic or stochastic a model can be linear or it can be nonlinear a model can be perfect or it can be imperfect almost all the models are imperfect I don't think there is any model that is perfect except few I'm not saying there is no nonexistence for example the model that governs the motion of the planet earth around the sun it's very nearly perfect why how do we know that we are able to predict the loner solar eclipses for the next 100 years and sure enough when we say there will be a lunar eclipse you know like what happens but there are very few systems where we can make such accurate predictions so perfect models are few imperfect models are large a model can operate in discrete time or in continuous time a model can work in discrete space or in continuous space a model can be finite dimensional or model can be infinite dimensional for example a person working in static regression he may be interested only in static deterministic linear nonlinear case a person in system identification may be interested in a dynamic deterministic models linear nonlinear a person working in time series analysis would be interested at dynamics stochastic linear nonlinear imperfect models that operate in discrete time most of the models in geophysical sciences they work in continuous time and continuous space if a model is given by partial differential equation that is infinite dimensional in nature if models are given by ODE they are finite dimensional so you can see data simulation looks at the entire domain of modeling with all its nuances with all its abilities to classify models along these many different dimensions and in our course we are going to take such a global view so what does it mean with this course you can do data simulation in several different walks you can handle any kind of different models so we are looking for the ultimate generality that underlie the notion of what data simulation what models and what is the holistic view of data simulation that is our purpose examples deterministic dynamic continuous time infinite dimensional models ODE XT so I am now going to introduce some notations X is the state of the system T is the continuous time Rn is the set of all vectors of size in real vectors of size n when I say Xt belongs to Rn Xt consists of n components each one of them are functions of time Xn is considered the state of the system for example in meteorological setup what is the current temperature pressure in downtown Bangalore say so time midnight midday 8 o'clock so what is the state how do I describe the state of an atmospheric system temperature pressure humidity wind speed all these constitute different components of the vector and and that's called the state of the system the model also can have a set of parameters alpha that could be p number of them we will use n to be the size of the vector which represents the state p to be the size of the vector that represents the parameter we will use alpha the Greek letter for the parameter the English of X as as as as our our state so the what is the linear model X dot is equal to ax so this is a differential equation X dot dx by dt the rate of change of the system a is a matrix X is a vector X dot is a vector matrix is real matrix of size n by n it needs an initial condition X not so that is the ODE now PDU T is the time variable X is a space variable in the case of ODE there is no space only time P is a function of X and Y that is essentially space no time so P is a function of space but no time two dimensional U is a two dimensional but one is time another space a linear partial differential equation could be a Poisson's equation double derivative of P with respect to X the second derivative of P with respect to Y is equal to minus X X X comma Y it can be it has to be solved under certain kind of boundary conditions a standard nonlinear model is U t of X the time derivative X plus U times the space derivative X must be 0 that is called the burgers equation with a suitable initial or boundary condition oh gosh I think there is a spelling error is called burgers B U R G E R then there is an integral equation f of X 0 to t k X of t M of t dt here f and f and k are given our job is to find yeah so given k k is called the kernel f is called the forcing my job is to be able to find yeah so you can see models of deterministic dynamic continuous time infinite dimensional can occur either as an ODE or a PDE or an integral equation examples of deterministic dynamic discrete time infinite dimensional models replacing the time derivative with suitable discrete time approximation I can express differential equation into a difference equation by replacing an integral by a sum in the standard way that we do in numerical integration we can get a variety of discrete time models the integral equation gives raise to a linear equation A X is equal to B A is known B is known my job is to find X the that is a static model the dynamic model is X k plus 1 is equal to M times X k there is a linear discrete time model X not as initial condition a non-linear model X k plus 1 is equal to M of X k alpha as a parameter in this case I have initial condition I have parameters so I am now giving life to a representation for different kinds of model that we talked about in general now I would like to bring the distinction between model state versus observables observables are related to quantities that I can observe directly for example vorticity but I cannot measure vorticity directly has to be measured indirectly volatility the price changes that is called volatility volatility is a quantity that affects us but I can't measure it directly so there are observables but there are states not every state as observable for example if the observable is pressure I can directly measure pressure if the observable I am sorry if the state is vorticity I cannot measure vorticity directly I have to measure indirectly so I would like to be able to relate the states of the model and what is being observed and relate them so I would like to be able to bring the distinction between the two modeling in spite of all the effort that are gone on for centuries is still an art as well as a science a modeler has full freedom limited only by his her imagination to concoct newer relation between variables of various types so the novelty in modeling relates to the ability limited only by the imagination to be able to describe various relation that are alive between quantities that describes the system so here we can discuss the variables into two types direct variables the right variables direct variables are directly observed pressure temperature the right variables the model needs a direct variable but is not directly observable examples height position velocity temperature energy stock prices interest rate unemployment these are all direct variables which are directly observable vorticity entropy tape volatility inflation some of you may come from meteorological geophysical sciences but my interest comes from applied mathematics to me analysis of time series models in the financial setting is no different from analysis of time series models to analyze climate data underlying mathematics are same that's why I'm trying to give you a broader explanation of variables so vorticity entropy cake this is the convective available potential energy which is very important in severe storms volatility is very fundamental to many things we do in life for example the current deluge in in in Madras in Chennai is because of a low pressure storm they that came and sat in on the top of Madras didn't move at all and dumped it's a very rare event so if you look at the frequency of these events if you look at the intensity of these events this event were a high volatility it's the the the the the the effect was way too much same thing inflation inflation was very high when I when I went to United States in the late 70s we had 14 or 15% interest rate today is close to 0 so inflation in those days was very high inflation there's virtually none inflation affects everybody but inflation something we cannot be measured it has been for so inflation is a derived variable volatility is a derived variable entropy is a derived variable but my model may need these derived variables to be able to make analysis so here I'm going to talk about the relation between state variables and observables dynamics of sea surface temperature in equatorial Pacific that's a state variable this rate variable is a fundamental interest in predicting a linear as we all know we are in a very severe grip we are under the very severe grip with the linear very strong they say the high-temperature they the average temperature is more than 3 to 4 very close to 4 degrees and it is affecting whether in different parts of the world varticity dynamics is another state variable for varticity equation the total water content in a cloud system that's very much needed in in cloud physics speed of a car in a cruise control today we are talking about driverless car google is developing driverless car so I need to be able to measure the speed of a car very accurately to be able to feed back to the control elements all avionics your flight starts from Bangalore airport at 2 a.m. goes to London in 8 hours you cannot see anything everything is automated so the autopilot has to be has to be able to adjust the speed based on various measurements so your plane has tons and tons of observables relating to the situation where it flies the models of the dynamics is already programmed to the autopilot so the autopilot model varies the various control devices based on the observations is that a head when is that a tail when and so on and so forth so to be able to control I need to understand the state variable it could be cease first temperature it could be water dynamics the total water content it could be speed of a car in a cruise control observables how we measure the equatorial Pacific temperature thousand miles west of Hawaii nobody can go it is very difficult to develop a network of buoy systems so we have to measure the temperature essentially from satellites satellite measure only the thermal energy that was radiated in the infrared domain so we have to estimate the temperature based on the thermal energy received by the satellite and invert using the very well-known radiation physics laws Stefan's law Max Planck's law and so on what is the dynamics would use the observables are the prevailing when the UVW component from which you have to essentially compute the water city the total water content in a cloud there is no way to directly measure it is measured through the reflectivity of the radar the raindrops are hanging in the cloud once you send the beam the the radar beam it gets reflected by the the the water droplets so the intensity of the returned reflected beam is displayed in various colors and we can estimate the amount of water that inherent in the cloud by looking at the reflected energy so that is the reflectivity is observable but it is related to the state variable called total water content voltage generated which is proportional to the speed and that is what cruise control uses you sit the speed for 70 if this because the road condition if the speed comes to 68 the accelerator knows that there is a difference it pushes the car forward if the road is smooth if you have set 70 and the current setting it may go 72 it shuts off a little bit to be able to control so I need to be able to measure the speed to be able to to be able to do a good cruise control with the interest in driverless cars this notion of models observation data simulation becomes very fundamental to replace a driver by a computer because we need to know the dynamics of the model we need to know different road conditions so a car is fitted with lots of observing devices measuring device a non-boat computer has to process all the devices almost instantaneously to be able to steer the car in the particular lane and they have to a limited they have obtained a limited success in doing this it's a long way to go but it is the intellectually stimulating project where modeling observations bringing the model almost online to be able to use and to be able to steer the decision there is to be able to steer the decision meteorologist to be able to predict and so you can see the underlying aspects of data simulation again coming along from different directions now I like to we talked a lot about a model I have not talked much about the observations so I am now going to talk a little bit more about observation because it is a one of the three click players in the system observations of physical variables just temperature pressure wind are subject to measurement errors these measurement errors are noise are called noise for example what I may read as 2.5 you may say it is 2.3 one might say is 2.6 so observational errors when humans measure certain things even instruments if you look at any instrument they will say the following so if you buy an ultimate or they will say well it can read from 0 to 100 the accuracy is 10% what does it mean if it says 60 it is plus or minus 10% of 60 and where that error comes in the engineering aspect of the of the design of the instrument itself so that is one way the error can come in the other way the error can come in is how do I calibrate the the the meter shows 60 is it really 60 we have to calibrate a meter against standards so it could be design errors within our design differ there is no design error there is a design differences there are manufacturing differences there is calibration differences then the human being being able to read these all these together lumped into one phase called measurement noise or the measurement error following Gauss one of the very well known mathematicians of all time who lived between 1777 and 1855 he was the first one to be able to analyze the properties of observation noise in fact in his time the only kinds of data that was available was measurements about very many celestial objects made by humans using very simple telescopes that is all that they had they had nothing else so he was to be able to make sense out of these observations and these observations are not consistent these observations contain a lot of errors so by analyzing a given set of observation he modeled the statistical properties of the observation errors and developed the so-called bell curve so what did he show he showed the following if this is 0 the errors from a bell shaped curve on an average the error is 0 but on a given circumstance the probability of an error could be either positive or negative it took a bell shaped curve this is what is called the Gaussian curve and we all know this curve is given by ffx is proportional to e to the power of minus x square by 2 that is a constant of proportionality that comes into play so this curve is a bell shaped curve what one of the most fundamental contributions of Gauss is to be able to establish that observation noise essentially followed this bell shaped curve and we use this to to this date and that is a very enduring aspect of Gauss's discovery so this kind of noise it is also called the white noise what does it mean I measure the temperature today I measure the temperature tomorrow I measure the temperature day after tomorrow by the same instrument the error today is not correlated with the error tomorrow the error is not correlated with the with the error day after tomorrow so that is that there is no correlation when sequence are not correlated there is a particular way to characterize this that is called white Gaussian noise Gaussian refers to the bell shaped curve noise is the error white means they are uncorrelated white noise means errors are uncorrelated these noise are also have a known correlation structure for example if you buy a voltmeter they say a 10% accuracy 15% accuracy 20% accuracy you can measure you calibrate and you can compute the error so observation noise has to be associated with the error properties the error properties have to be related to the known covariance structures of the errors in economics stock prices the interest rate foreign exchange rate they are all intrinsically random pressure temperature there is a variability from night and day that comes because of the phases of the day and night the phases of the moon summer winter autumn spring so these are all the variations induced by season variations induced by the day and night December 31st the maximum temperature in downtown Bangalore this year next year over the past 100 years if you if you plot them there is a natural variability so things could have natural variability things could have underlying stochastic properties so when we talk about random the randomness can come from either from the noise or from intrinsically random variations we will stop here at this moment we will continue these topics in our next lecture thank you.


Stone 8 theory. That's stone 8 theory. Is that what it's called? Ragatti? Stone 8 theory. Isn't there a theory that the burning bush in Exodus is an analogy for Moses on hallucinogenics and stuff? Yeah, there's a whole belief system that the word Jesus Christ, right, was a code name for hallucinogenics, specifically mushrooms, right? Really, there's a whole, do a little research, just do a little search. The whole, I don't know how legit it is. I like it, right? I know at Christmastime when I used to go to dinner with family and stuff where they used to do a little, you know, do a little prayer thing when it was more confrontational at the period. I would say, I would say cheers. Cheers to the magic mushroom, right? During Christmastime. Why not? Right? Especially when you realize that the whole reindeer thing and the colors of Santa Claus, which is red and white, which is connected to Amanita mascara, which is when the reindeer used to eat these mushrooms and then they go on pee into the, in the snow and their pee would contain, would act as a filter to bring out the hallucinogenic properties of Amanita mascara. So some of the tribal people shaman, shaman there would have followed a reindeer or have a herd of reindeers and they would harvest the pee and then eat that and have their divination journeys and stuff like this. It's been a huge part of humanity. Tripping has been a huge part of humanity since humanity has been in existence, right? It's only been in the last hundred years where centralized governments have come along and banned it, right? Illegal. Wait a second, humans have been doing it for hundreds of thousands. Illegal. Wait, what? No, hundreds of thousands of years. We humans have been using these as tools to understand what's going on in the world and that has brought us to this point in time where we're seeing the industrial revolution. We're about to give birth to computing. Look, a couple of decades from now, we're working on it. Illegal. What? How could you make illegal? Something that goes naturally in the world that has been around since planet Earth had plants growing on it and human beings have been using it since there were little monkey things following little herd animals gathering mushrooms off poop. Illegal. What? Wait, is biblical illegal? The millions, tens of hundreds of millions of lives they've destroyed because of illegal.


We farm about 10,500 acres to give or take cotton, corn, rice, soybeans would be our four mains, a little bit of wheat, and then we're open to trying about anything. We've tried peanuts, we've tried yellow peas, we're trying yellow peas, we looked in the sesame seeds one time, that was a little bit before my time, but you know not not scared to try anything. You know my goal is to be integrated, vertically integrated and very diversified, whether it's crops or you know the truck and company it's a big asset to us when we're harvesting and then when we're not harvesting we're able to run those trucks for other people, so that works out pretty well too. Well as far as we can go back you know I'm gonna be a fifth-generation farm.  Every farmer you know is generational, it's just a matter of how many generations you go back. I'm a fifth generation, I'm a sixth generation and that was almost like a title so to be able to be a part of that is kind of I guess important again you know like you feel like you're carrying on something and keeping it going for your kids and you hope and pray that those kids want to do that and so I hope at least one of our boys wants to do it when he gets older. Our operation is really centered around personalities and getting along in family you know as I told you before our slogan is farmland and these guys that these these members of our team they respect him I would say probably more so or as much as they do me and the reason why is he's in the field you know he's his shadow's in the field all the time so he's not asking them to do something that he hadn't done or willing to do itself and his relationship with with this team is unbelievable you know the things that that we're learning I mean he changes he changes things we do yearly I mean it's not okay well this this is what I'm doing and I'm only gonna do this and so the the innovation in this form I hope to continue I hope to not be doing exactly I mean unless it's absolutely working I hope to not be doing exactly what we're doing now I mean I hope to be able to take take what we're doing and and make it better I mean like he took what his dad and my mom's dad did and make made it better I mean there there's never nothing's ever perfect everything can be improved I just hope that when my boys get it that it's that it's better than was when I got it I hope that they will love it and want to farm and because you don't farm because it's a job you farm because you love it it's a lifestyle and not just a job


Welcome to MIT Supply Chain Frontiers from the MIT Center for Transportation and Logistics. Each episode features center researchers and staff who welcome experts from the field for in-depth conversations about business, education, and beyond. On today's episode, Katie Dade, who leads the Center's Women in Supply Chain initiative, speaks with Julie van de Kamp of US Express and Trisha Branigan of the Hershey Company about how leaders can be champions for positive change within their organizations. Recorded on International Women's Day, the three share insights and challenges of use to anyone who manages a team. Take it away, Katie. Thank you for joining our International Women's Day Leadership Panel, Supply Chain Champions for Change. With us today, we have Julie van de Kamp and Trisha Branigan. Trisha Branigan is the Vice President for Global Procurement for the Hershey Company. In this key leadership role, she is responsible for all aspects of procurement, as well as the responsible sourcing strategies and practices which support the company's sustainability priorities. Trisha has more than 25 years of experience spanning procurement, engineering, and R&D at craft foods, dean foods, and white wave. And she is the chairperson for Hershey's Children's Miracle Network Fundraising and is the leader of the company's Women in Supply Chain and Technology Mentoring and Development Program. Julie van de Kamp is the Vice President of Customer Experience at US Express, where she manages the team, which she handles all customer-facing interactions in a nutshell. Julie and her team create an experience customers have with the organization, which spans across booking freight, service exceptions, collaboration, and coordination with brokerage and OTR operations team, and many other daily touch points. Again, thank you to everyone who is joining us today. My name is Katie Date. I'm the leader of the Women in Supply Chain Initiative at the MIT Center for Transportation and Logistics. We aim to create knowledge and tools for people interested in creating more gender balance in their organizations. So first, I will go to Trisha. Can you tell us a little bit more about yourself and your career? Absolutely. Thanks, Katie, for the introduction and a pleasure to be here with Julie and yourself. I started my career after a chemical engineering degree and I joined Kraft thinking, okay, I'm going to do engineering probably for my career. So if you had asked me 20 plus years ago if I would be in a procurement role, I would have definitely had a lot of questions about that. So it's been quite a journey. After working in engineering, process engineer, product development for some time, I really wanted something different, something that provided me greater exposure to a more, the broader base of the business and really gave me broader exposure to the global operations as well. And so I landed in procurement. I moved over, I did capital equipment procurement, which was kind of like a nice fit and maybe an easy segue for me to get into the function. Thinking that again, you know, it would be a cross functional assignment. I would do this, I would learn a ton and then, you know, I could bring all those learnings back. That was my intent. And I loved it so much. And I just kept finding different roles and different ways to provide high impact within the function. Thrilled to be here at Hershey, I've been here now seven years and have recently taken this role leading our procurement organization last summer. So thanks for having me. Thank you, Trisha. We're so happy to have you. Julie, if you can tell us a little bit more about yourself and your career. Yeah, thanks. So I actually started out in transportation and in trucking while I was still in college at the University of Wisconsin. I grew up around it and I spent my summers and Christmas breaks interning at a trucking company doing anything that needed to be done. And when I say anything, I mean making delivery appointments. This was as we were transitioning to paper lists. So scanning driver logs as their packets came in every day and scanning their fuel receipts and scale tickets and filing paperwork, whatever needed to be done. And after that, I swear would never be in transportation or trucking. I was not into it. And after I graduated from the University of Wisconsin, I actually ended up taking the job right out of college at US Express and our pricing group. Still pretty determined that it would be applicable to any industry so that I would try that out and then take those skills somewhere else. Had no intention of doing this long term. Pretty immediately really fell in love with it. And not just with US Express and with trucking, but with the industry as a whole, with the pace of it, with how I could see how it really affects our economy and our lives. So spent about five years in our pricing group here at US Express helping to evaluate and update and create some of the new tools that our group used. Then I was really lucky to get the opportunity to go over to our brokerage group and focus on business development. That was a really fun time in my career. It was a relatively new part of the company and it was growing very quickly. So I was lucky to have the opportunity to really look around and just see what needed to be done and empowered to be able to jump in and do those things and create new processes and work with our sales team and our operations team to bridge a lot of gaps that kind of a new quickly growing part of the company needed. And then in October 2019, moved into this role, created this new customer experience group and have been managing it since then. That is a little bit about me. Thank you so much. As you both know, we collected questions and one of the questions that kept coming in was why a career in supply chain? Why would I want to go into supply chain? I'm wondering if either one of you have any thoughts about that? You know, one of the reasons I really entered into procurement and then of course, you know, head exposure to broader supply chain work is just really the breadth and impacts that it has on really any organization. So if you think about the key processes of buy, make, ship, sell, we're three of the four. The breadth and the complexity and also the rate of change. I think has been what's really kept me interested and very curious to stay engaged and involved on many levels.  And so I think anyone who's considering it will, I think, find a lot of opportunity and breadth within the supply chain function to really grow and develop their skills. Yeah, I agree with a lot of those things that, you know, it is integral to our economy and our way of life. One of the things I love the most about it is that it's fast pace. And we're really in an opportunity right now, particularly in the transportation side of it, where it's ripe for innovation and disruption. It's new every day. It's a new challenge, a new problem to solve.  And then I think just the scale of it that you sort of alluded to as well, Trisha, that there, it really opens up a lot of opportunity to lead to affect people's lives and career goals, help your team develop because it is so broad reaching and there's so many different facets of it. You don't necessarily think about how much it affects our everyday lives and all the things that keep us going and everything that you purchase and everything, all of the materials that went to the manufacturing facility to create all the things that you purchase that, that all of that is involved in that. And it's necessary for all of us to keep going. And, and so when you step back and think of it that way a little bit, it's pretty rewarding. So switching gears a little bit. I'm wondering if, if each of you could tell just a short story about how having an ally or a mentor throughout your career kind of helped bolster you to that next level. I don't necessarily have one specific story, but I do kind of, I'm very lucky that I'm on a team right now, where my counterparts who run sort of the other portions of our customer sales marketing pricing group. And I have a really good working relationship and can trust each other and can give each other really candid feedback. And I think that that's a really important part of your career, right? And it's not all negative feedback. It's not all positive feedback. It's constructive. Sometimes it's like, gosh, that was great point in that meeting or, hey, I see your teams doing this, if you did it this way, would it be better, right? And I think it's really important to be able to surround yourself with people who can give you that constructive feedback. It's not always easy to take, right? But if you truly do want to continue to grow personally and professionally, it's immensely important. And I think it's also important to have, you know, allies and learning from the people that you work for, and then in the team that works for you as well, if you're lucky enough to be in a leadership position, and that's what you enjoy, that they should be an ally for you as well, and they should feel like you are for them. I want feedback from my team personally and professionally, and they expect it from me. And I think that that's really an important part of being allies with someone in the workplaces that you can give open, candid praise and, you know, critical feedback. So, and then I think it's important to have allies in your career outside of just your actual workplace. Have, you know, I'm very lucky to have a very supportive husband who's an ally in my personal life and my career, right? I'm very lucky to have a mother-in-law who I admire hugely and can ask for advice and my parents. And then other people I've worked with a long way who might not necessarily work still in the exact same industry or within my organization but who I can still reach out for and get kind of a non-involved opinion when necessary. So, I think it's not necessarily important to just have one specific ally or one specific mentor for your entire career, but kind of a network, both, you know, within your organization and your current role and then within your life outside of work that you can lean on as well. And, Julie, I would just add to that, and I love the way you were thinking about it in terms of, you know, the kind of this whole group of people that help support you throughout your career. Early in my career, I think one of the big leap forward moments that I had was where someone really took a risk on me, put me in a role that I didn't necessarily have 100% of the qualifications to do, but took a chance and really then provided me the support within that role. So, it's one thing to take a chance on someone and then kind of throw them into the mix, but then also really provided me the support, gave me tremendous exposure. So, this was a leader within our organization. It was a critical time. There was a specific initiative at the time that had really company-wide exposure. And this individual, he would literally bring me to these meetings with our senior executives. And I was, you know, five years into my career and the job, and I was like, you sure you want me to come? I'm going to really stand out in that crowd. But it was probably one of the biggest changing moments for me where I really was able to, there was no pressure on me. I was just able to observe and listen and understand the thinking and how people were looking at the situation and then the recommendations to go forward. So, that is a moment for me that really has left an impression and one that I want to make sure that, you know, I can also do for other people. I would just echo what she said and then also, you know, always kind of think about what are those small moments that you might be just an everyday normal part of your role, but could really have a significant impact on someone else if you're to bring them along. Great. Thank you. So, I'd like to kind of twist that question a little bit. Both of you are in leadership roles. So, if there were women in your organization, which I'm sure there are, that are looking up to you and are like, how do I get Trisha or Julie to be my mentor? What advice would you give to them? Because I always tell people that it needs to be something that happens naturally. Totally agree with what you said that, you know, you have to have a natural connection and really that can't be forced. But I would always encourage people to first think of what do you want? What do you want out of the mentor relationship? Is this a person? Is that the best person to help you with that? And maybe that's where you start is just a really kind of informal conversation or a meet and greet and a connection. And it's not so much an ask of, hey, will you be my mentor? But it's an ask of these are things that I'm really curious about or, you know, I'm trying to figure out what the most effective leader looks like. And then letting that sort of lead to really a natural dialogue. And I think, you know, most often you will see that people are very, very willing to help. And so if they're understanding where your needs are and if they feel like they can't help referring you to someone who might be the best person to do that. So that's what I have found effective is just, you know, starting with what do you want and then having a conversation with others who might be able to provide you a perspective on how to see how to find that out. Yeah, I totally agree. And if what you're looking for is career advice, right, or development feedback on what you need to work with to get a certain place, know where it is that you want to go doesn't mean that you want a specific role. I think that I think very often when I'm talking to people, they're like, well, how do I be the next you or how do I get to be the next fellow executive or I want to VP title or I want a director title. I would never approach it that way. Personally, I would make sure that you're always approach it in what attributes do you want in a job that are going to be fulfilling and make you happy? What are you working towards as a career goal? Because you don't even know what roles may become available, you know, and what is out there. And I was kind of trying to think of it and look at it that way as well. Do you want the opportunity to continue to, you know, manage and lead people and grow in that regard? Do you really want something that's especially strategic or, you know, analytical or what part of the roles are fulfilling to you that you want in a career, you know, your future career opportunity versus working towards a specific job or a specific role and ask for feedback on how to develop those things to get you there. I think that that's the most important thing when you're thinking about career growth and what you want to do long term is what attributes of a role do you really want. I love how you brought up to Julie the idea of like moving forward and sort of the skill sets and competencies more so than the role itself. And I have heard from people say, but I don't know what I want. And I actually hear that maybe more often than you might guess. I don't know what I want. So okay, so maybe you need to explore what that looks like or what it could be. And so in those situations, I really advise people to, you know, just sit down.  It could be very a simple discussion on what do you think makes people successful in this organization? Or, you know, what have you seen others do really well and are there pitfalls you suggest to me that I should avoid? And maybe that just starts it. Maybe you just start to learn and meet with different leaders all on this quest of learning versus trying to achieve something. And so if you are in that place of I don't know what I want, I just I want to figure that out. That might be a place to start. That's a great piece of advice. Megan Carr wrote in and she is asking the two of you, how do you rebalance personal and professional life components? Yeah, I don't know that there's a great answer for this. And I don't know that there really is a true balance. If I'm going to be totally transparent, I think it's kind of a juggling act to an extent. And I think that it's a matter of one, hopefully working in a place that's supportive of your life. Our company has really looked at people as people and I make sure that I really try to do that with my team as well. Obviously, there are certain roles that have to be eight to five. But the fact that we can do that from home now in this world makes makes a huge difference. And then I would also say that even more than work being supportive, you've got to have the right support beyond that. You know, I'm very fortunate to have a husband who's very supportive and who we share a lot of our household and particularly the responsibilities of our children, right? And I'm very fortunate. I also work very hard at making sure that we have the right resources set up to help us support having the appropriate childcare for our kids, but can't be perfect at everything.  I think it's a matter of sitting down and deciding like, what really matters? What has to be done? What has to be done well? And what doesn't really matter? Like, do I have to be in this meeting today? Or can someone on my team sit in for me who's equally as qualified who can give me, you know, a brief summary of it, which would likely be good career opportunity for them to sit on a meeting like this so that I can go to whatever Halloween party that probably will matter to me in six months versus this meeting might not. So I think it's really a matter of like keeping perspective and then deciding what really has to be done and what's important because life is busy and crazy and work is always going to be busy and crazy and really prioritizing what's important in giving that some thought versus like getting stuck in the whirlwind every day of all of the things that just have to be done. Yeah, I love it. And one of the, one of the mantras that I have is the, and Julie was really hitting on this, is the do-dump delegate model. So being very choice-full, this I need to do. Is it my 80%? Is it my 100%? You can decide on all those things and when you need to get it done, but this is something I've got to do. The dump, I would call it in two buckets. They may be the things that you're just not going to do. You're not going to do right now. It's just not going to happen. The stack of books on my shelf that need to get cleaned out so I can, you know, put the kids' papers, it's just not going to happen. The dump is, in my opinion, less about what you're not doing but more the permission you're giving yourself to not do it. My daughter came into my office at home the other day. I think it was like one or two o'clock or something. She said, what are you going to be done? I was like, okay, we have this conversation every day. And today it's happening earlier. It's like one or two. I said, it's not going to be for a while. I will tell you that. I talked to her and I said, look, I hope that this is actually setting a good example where you can see your mom working and really delivering, you know, that hopefully I'm setting an example by also setting the boundaries is what I'm trying to say. So sometime is just giving yourself the permission, setting the boundaries, being okay with that and then following through. And likewise, likewise, if there's two hours, I might be able to, you know, sneak in the walk with the dog or taking, you know, Joe to his basketball game or whatever it may be. I'm not going to feel guilty about it at all. And giving myself the permission to just do it because I don't know when I'm going to get those two hours again. So just make it happen and take advantage of the moment. That's great. I'm hearing so many great themes coming out of this. The biggest thing I'm hearing is letting go of that need to be perfect and knowing that no matter what we're doing the best we can. And like you said, putting great, great things out into the universe and setting a great example for your employees, setting a great example for your children. I think that's, that's so important to give everyone a little bit of grace and a little bit of flexibility. So moving on to the next topic. So I'm wondering if, if the two of you can share a story of a time either you've challenged yourself or you've chose to challenge norms or chose to challenge someone who has maybe pushed your boundaries a little bit. This is a daily event. I think that all of us have, whether we're challenging a work norm or challenging a project or our own selves for that matter. So I work very closely with many of our suppliers and our supply base. Those might be material supplier service providers, the whole gamut. Through the course of the year, Hershey has an amazing inclusive culture and there's always room for improvement. But also being, you know, with third parties, I also see many other cultures and many other practices and behaviors. My example is when I was with one of my leaders in the organization and it was the first time I was being introduced to a specific supplier. We had a conversation. There were four of us. They were introducing me to kind of the need of this particular business unit and the entire conversation. This man never once made eye contact with me and looked directly at the person who was his primary contact on my team. That person happens to be a man, but never even almost acknowledged my presence. And just the whole thing was so odd. I think these are all opportunities for all of us. And so I went to the person on my staff afterward and I said, Hey, did you notice that behavior by the way? Like at all. No, he didn't notice. Did notice it at all. It was a wrapped up and a conversation and never even occurred to me. And I said, No, it wasn't that you needed to necessarily do anything, but but here's the moment. I think the moment is recognized. I'm fine. I can stand on my own and I will make sure that this relationship is off on the right foot.  And so I would just ask, this is such a great moment for you. I would just ask that you think about that when you're interacting with others. And it wasn't a criticism in any way. It was just kind of this like heart to heart that we had afterward. And I think finding those opportunities for the learning moments and a level when people do that with me as well is is is probably the most impactful way we can challenge each other, especially in the in the spirit of equity and inclusion. Yeah. Did you notice any shifts in like the next meeting that you were in? I really took it upon myself, right? So the next meeting, okay, I've been introduced, I saw this dynamic sort of happening. And so, so then it's up to me, right? Then it's on me to really make sure, okay, I'm now educated myself on the business or beyond the introduction capacity, then I can create my own seat at the table. I think what hopefully has been more impactful was maybe less with the supplier, but more on my team member, right, to just continuing to sort of recognize that these are all possibilities, whether it's in a in a meeting with a third party or whether it's a meeting internally. And so that I think Katie is where it was most impactful. That's great.  And I think that that's an important point also is honestly challenging the status quo. It really just means looking around and seeing what needs to be better and asking the right questions, right? So my current role I started in October 2019, it was a new department that the organization decided we were going to create. And I went out on maternity leave in May of 2019, within a week of being home from the hospital, my my boss at the time called me and said, Hey, so I know this is crazy timing. And I don't want to add stress on your, you know, maternity leave, but I also would never want to not consider, you know, talk to you about it, which I found very, you know, really fortunate that I was in that opportunity. How do you feel about coming back and considering this role coming out of maternity leave and the timing and all of that? And then I wouldn't want to, you know, sell your time away from work and how fortunate that I was that they still, you know, walked that kind of almost uncomfortable line of still considering me for the role, talking to me about it openly. And I think that part of that story really the important part to me is that I challenged myself then and thought, Oh my God, like, do I really want to do this at this time of my life with all that coming on, you know, going on? But I thought, you know, vice versa, if they'd called my husband a week after us having a son, there would be no question, right? This great job opportunity comes up and he would do it in a heartbeat. And I would support it in doing it. And he was very supportive of me doing it as well. So I think that you can undertake a lot. And I think that either way. And I gave a lot of thought. And I, like I mentioned earlier, have a really good family to bounce ideas off of.  So no, it's not too much to take on with a brand new baby or coming back from maternity leave. And so glad that I did challenge myself and make that decision. It would have been really easy to just say, no, there's too much change going on in my life right now. I'll stick with what I'm comfortable with because, you know, I want to adjust at home. But so glad that I didn't. And that I continued to challenge myself, you know, personally and professionally at the same time and challenge kind of what people think you need to maybe be focused on when you first have a new baby.  You need to do what you can challenge yourself to do and feel comfortable with. Yeah, I totally agree. You know, as you thought about, you know, what would my husband do if he was coming back from parental leave? I think that's I think that's a great way to frame it. And actually, that kind of leads into another question that we got. They asked, what are your suggestions for ladies who are preparing and upgrading to go back to work after a sabbatical? I think the first and foremost, and we're sort of been heading in this direction is don't apologize. Don't apologize for being away. Don't apologize as if you've missed something. And actually, I would think of it all in terms of what has us done to enhance everything that you're now doing moving forward, reposition it in your head that it's not a challenge or something you're going to have to struggle with. But it's actually an advantage. Now, having said that with that right mindset going in, I would absolutely be over-prepared for anything and everything that could come your way. So that doesn't negate the need to make sure that you're up to speed. Has anything changed? Have you networked? Have you looked at what's happening within your space, your field or your industry? Because that's also critically important. So your interviewer or your supervisor, whatever the case may be, is going to want to make sure you're committed and you're in and you're engaged. And that's one way to demonstrate that. Thank you. So I have two questions that are specifically addressed to each of you. So the first one is for Julie. And they're asking, so you've worked in a male-dominated sector transportation for the majority of your career. Can you talk a little bit about how you developed the leadership skills to grow within your career? First and foremost, being a female in a male-dominated industry has not in any way been a hindrance to me. If anything, I feel like it's been an asset. Part of it is I guess I've never felt that there's nothing that I can't do as well within the industry. And I think that that's really important. But I think that there are some things that I can look back on that I kind of did develop and grow into through my career. Developing leadership skills and growing in your career, I think that you can learn from everyone around you. And I think it's really important that you take every opportunity to do that. I've gotten the opportunity to work for a lot of really, really amazing people and learn good and bad from each of them, right? And as long as you can distinguish which is which and pick up some of the very best traits that each of them have or some of the very best leadership styles or skills that each of them have that will work for you, then that's really important in developing your your leadership ability as well, right? You can learn from your colleagues, your counterparts. Get that feedback from from your team and the people who work for you as you're as you're learning to be a leader so that you can improve and then also really keep your eyes open and learn from the people who you get the opportunity to work for as well. That's great advice. Thanks, Julie. Procurement isn't as male dominated, Trisha, but I don't know if you have any thoughts on that. You know, it really depends on the area though, Katie. I think the function may not be, but then there's specific industries and verticals that are that we work with, especially, you know, agriculture, perhaps dairy, you know, and while they're still growing segments, I would say, you know, I think part of what all of us try to do is to reach out in ways that we can connect and also bring others along. So that's what I personally try to do, whether it's, you know, women and dairy programs or whether it's other venues and events where we can, again, create those connections, create those networks and kind of raise all votes with the type. Building on that supplier diversity and inclusion has taken kind of a front of the house stage over the last year. Can you talk a little bit about Hershey's program? Because I know you do a lot to source from diversifiers. Yeah, absolutely. We've had tremendous progress over the past four to five years. We've more than doubled our diversity spend. And what's even more amazing is that women-owned businesses in particular have a pretty large share of spend. So that could be because of, you know, kind of the types of work that they're in, or it could be just that that seems to be where we're able to create value mutually. But we've got about a third of our total diversity spend is made above women-owned businesses. We have a long way to go. Look, like there's nothing perfect about this and there still is room for growth. And I think one of the things that we have found to be tremendously successful is to just start. And that sounds basic and simple. And actually that's the beauty of it is just to start. What gets to be difficult with a company of our size is that, you know, you're sending out bids and you're looking at proposals that are for pretty large portions of spend. And not all of the privately-owned and diversifiers really have the scale to support a large portion of that or a smaller portion of that. So what we have found to work very, very well in building this up is one just to start somewhere. It could be $500,000 worth of business out of the $20 million category. It could be a million out of the $50 million. But whatever it is, is to start to have the two of us, the two companies gain experience, really create those lessons learned and then build from there in a successful way. That way, sort of no one gets thrown in over their ski tips and, you know, the setup for failure. So I think that's one thing. The second thing is where there may not be opportunity, where we're working with really large public companies, because of the type of product it is or the capital intensity nature of the raw material or something like that, we encourage those providers to be sourcing diversely. So maybe we can't necessarily in that specific vertical find a diverse supplier, but we certainly can influence our partners and expect more. And this is yet another area where we continue to raise the bar and say we've all got to do more. That's great. Thank you so much. We did have another question. Any advice that you have for young women in college looking to enter this field? And then also, what would you tell yourself when you were back in the beginning of your career to help you to kind of focus and look forward? I think one of the most important things we can do for other women and for other groups who are underrepresented is be visible. You know, it's important for me to show up today on International Women's Day. I'm thrilled to be a part of the MIT session with Julie, but I think part of it is really being visible. And if I were to give myself advice, I think I would say continue to be open. I always took the philosophy of trying not to close doors, whatever that sort of looked like at the time and whatever decision that was. And you certainly need to move on, but not shutting a door such that it was locked forever. So what are the things and what are the areas where I can gain experience, but I'm not necessarily closing something off and try to do that for as long as possible? One, I think it's a great way to gain experience. Two, you never know what you may find. You truly have a passion around until you try it. And then three, gaining that breadth of experience is critical in supply chain. There's so many moving components as we talked about earlier and the complexity and that's the great part of it. That's the fun and giving yourself that room and that time to learn and grow and being open to that. So hope that helps. So I don't know that I have anything hugely profound to close on. Trisha, thank you for doing this with us. I honestly took notes on a lot of the things that you said. I agree with being visible and I agree with as you have the opportunity to lift others up. I think that's the most important thing we can do for any of our colleagues, but particularly for other women who are coming out of school and who are looking for careers like this and wanting advice. The other advice I would give is, in addition to the cliche, things like work hard. I think be aware of your perception, but don't over question yourself. I think women have a tendency and Katie, I think you even referred to it a little bit earlier of shying away from stepping up, from speaking up, from doing a lot of those things and questioning their reaction to everything. And I would say that as long as you feel like it is a professionally appropriate reaction, don't over question everything that you're doing. And other than that, I mean, I really think it's just a matter of use data to make your decisions. In addition to your instinct, we have it for a reason. Like I mentioned earlier, I think for me more than a hindrance, it's really been an asset to use a lot of my natural abilities in being a woman and the way that I can look at things a little bit differently in a male dominated career and go with that and use it to your advantage versus trying to suppress it so much. Thank you so much. And thank you both. I hope that all of you take this beyond International Women's Day and really go out into your organizations. As Trisha mentioned, you know, lift kind of as you rise.  So with that, thank you so much. All right, everyone. Thank you for listening. I hope you enjoyed this edition of MIT Supply Chain Frontiers. My name is Arthur Grau, Communications Officer for the Center. I invite you to visit us anytime at ctl.mit.edu or search for MIT Supply Chain Frontiers on your favorite listening platform. Until next time.