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owner decides or is forced to sell the home almost immediately after purchase and pays off the full principal of the loan In line with what we would generally expect, principal payments will likely make their way more meaningfully into the mix of principal-coupon cash flows after some time passes (or, in the jargon of the marketplace, with some seasoning) How can probabilities be assigned to the mortgage product s cash flows over time While we can take the view that we adopted for our callable debenture that at the start of the game every uncertain cash flow has a 50/50 chance of being paid this type of evenly split tactic may not be very practical or realistic for mortgage products For example, a typical home mortgage is a 30-year fixed-rate product.



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might also have an unusual this time increased appetite which is not based upon the distortions of restraint A primary increase in appetite or drive to eat might possibly be present in AN where it would trigger the restraint as a reaction However, there seems to be little evidence for this Such a primary increase is more plausible as a component of the mechanisms of BN and even more so for BED In BN, the model of restraint acting upon an intact but unremarkable appetite is plausible Most BN subjects report that the onset of attempted restraint preceded the onset of binge eating However, this is not the case for a small but interesting minority of BN sufferers and for most of those who suffer with BED Characteristically BED subjects either do not consistently restrain or the onset of their bingeing precedes that of restraint (Mussell et al.





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144 KEY PREDISTRIBUTION Consider a scenario where N number of sensor nodes are dropped from an airplane in the battle eld Thus, the geographical positioning of the nodes cannot be decided a priori However, any two nodes in RF range are expected to be able to communicate securely One option is to maintain different secret keys for each of the pairs Then each of the nodes needs to store N 1 keys Given (i) the huge number of sensor nodes generally deployed, (ii) the memory constraint of the sensor nodes, this solution is not practical On the other hand, online key exchange needs further research as implementation of public key framework demands processing power at the higher end Hence, key predistribution to each of the sensor nodes before deployment is a thrust area of research and the most used mathematical tool for key predistribution is combinatorial design.

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This type of product has been around for some time, and some useful data have been collected to allow for the evaluation of its cash flows over a variety of interest rate and economic environments In short, various patterns can and do emerge with the nature of the cash flows Indeed, a small cottage industry has grown up for the creation and maintenance of models that attempt to divine insight into the expected nature of mortgage product cash flows It is sufficient here merely to note that no model produces a series of expected cash flows from year 1 to year 30 with a 50/50 likelihood attached to each and every payout Happily, this conforms to what we would expect from more of an intuitive or common sense approach Given the importance of prepayment rates when valuing an MBS, several models have been developed to forecast prepayment patterns.

Each of the sensor nodes contains M keys and each key is shared by Q nodes, (thus xing M and Q) such that the encrypted communication between two nodes may be decrypted by at most Q 2 other nodes if they fall within the RF range of the two communicating nodes Similarly, one node can decrypt the communication between any two of at most M(Q 1) nodes if it lies within the RF range of all the nodes who share a key with it Let us present an exact example from the work by Lee and Stinson [28] Take N = 2401, M = 30, Q = 49 The parameters are obtained using a transversal design (TD; for a basic introduction to TD, refer the work by Street and Street [43, p 133] or Section 1441).

Clearly, investors with a superior prepayment model are better equipped to identify fair market value In an attempt to impose a homogeneity across prepayment assumptions, certain market conventions have been adopted These conventions facilitate trades in MBSs since respective buyers and sellers know exactly what assumptions are being used to value various securities..

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