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control number Books or records relating to a form or its instructions must be retained as long as their contents may become material in the administration of any Internal Revenue law Generally, tax returns and return information are confidential, as required by Code section 6103 The time needed to complete this form will vary depending on individual circumstances The estimated average time is: Recordkeeping, 46 min; Learning about the law or the form, 13 min; Preparing the form, 59 min If you have comments concerning the accuracy of these time estimates or suggestions for making this form simpler, we would be happy to hear from you You can write to the Tax Forms Committee, Western Area Distribution Center, Rancho Cordova, CA 95743-0001 Do not send the tax form to this address Instead, give it to your employer

emergence of a more complex behavior of cluster formation It was further observed that cemeteries are sited around spatial heterogeneities [77, 563] A similar behavior is observed in many ant species, such as Leptothorax unifasciatus, in the way that the colony cares for the brood [77, 912, 913] Larvae are sorted in such a way that di erent brood stages are arranged in concentric rings Smaller larvae are located in the center, with larger larvae on the periphery The concentric clusters are organized in such a way that small larvae receive little individual space, while large larvae receive more space While these behaviors are still not fully understood, a number of studies have resulted in mathematical models to simulate the clustering and sorting behaviors Based on these simulations, algorithms have been implemented to cluster data, to draw graphs, and to develop robot swarms with the ability to sort objects This section discusses these mathematical models and algorithms Section 1721 discusses the basic ant colony clustering (ACC) model, and a generalization of this model is given in Section 1722 A minimal ACC approach is summarized in Section 1723

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The rst algorithmic implementations that simulate cemetery formation were inspired by the studies of Chr tien of the ants Lasius niger [127] Based on physical experie ments, Chr tien derived the probability of an ant dropping a corpse next to an n-cluster e as being proportional to 1 (1 p)n for n 30, where p is a tting parameter [78] Ants cannot, however, precisely determine the size of clusters Instead, the size of clusters is determined by the e ort to transport the corpse (the corpse may catch on other items, making the walk more di cult) It is likely that the corpse is deposited when the e ort becomes too great On the basis of of Chr tien s observations, Deneubourg et al [200] developed a model e to describe the simple behavior of ants The main idea is that items in less dense areas should be picked up and dropped at a di erent location where more of the same type exist The resulting model is referred to as the basic model Assuming only one type of item, all items are randomly distributed on a twodimensional grid, or lattice Each grid-point contains only one item Ants are placed randomly on the lattice, and move in random directions one cell at a time After each move, an unladen ant decides to pick up an item (if the corresponding cell has an item) based on the probability Pp = 1 1 +

We dug a very deep hole for ourselves There were a lot of bad decisions that were made We are cleaning up that mess It s going to be sort of full of ts and starts, in terms of getting the mess cleaned up, but it s going to get cleaned up And we are going to recover, and we are going to emerge more prosperous, more uni ed, and I think more protected from systemic risk

Payroll Taxes and Remittances / 129

(1743)

where is the fraction of items the ant perceives in its neighborhood, and 1 > 0 When there are only a few items in the ant s neighborhood, that is << 1 , then Pp approaches 1; hence, objects have a high probability of being picked up On the other hand, if the ant observes many objects, that is >> 1 , Pp approaches 0, and the probability that the ant will pick up an object is small

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Smart Data: Enterprise Performance Optimization Strategy, by James A George and James A Rodger Copyright 2010 John Wiley & Sons, Inc

(1744)

provided that the corresponding cell is empty; 2 > 0 If a large number of items is observed in the neighborhood, ie >> 2 , then Pd approaches 1, and the probability of dropping the item is high If << 2 , then Pd approaches 0 The fraction of items, , is calculated by making use of a short-term memory for each ant Each ant keeps track of the last T time steps, and is simply the number of items observed during these T time steps, divided by the largest number of items that can be observed during the last T time steps If only one item can be observed during each time step, = n /T , where n is the number of encountered items The basic model is easily expanded to more than one type of item Let A and B denote two types of items Then equations (1743) and (1744) are used as is, but with replaced by A or B depending on the type of item encountered

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