k-means with nonnegative, proportions, or Boolean vectors. Suppose that the vectors x1, . . . , xN are clustered using k-means, with group representatives z1, . . . , zk. (a) Suppose the original vectors xi are nonnegative, i. e., their entries are nonnegative. Explain why the representatives zj are also nonnegative. (b) Suppose the original vectors xi represent proportions, i. e., their entries are nonneg- ative and sum to one. (This is the case when xi are word count histograms, for example.) Explain why the representatives zj also represent proportions, i. e., their entries are nonnegative and sum to one. (c) Suppose the original vectors xi are Boolean, i. e., their entries are either 0 or 1. Give an interpretation of (zj)i, the ith entry of the j group representative.

Local area networks use many of the same network technologies and the internet, only on a smaller scale. devices that access lans are equipped with a network interface that contains circuitry for wireless or wired connections. devices also have a physical address, in addition to the ip addresses acquired from a dhcp server. the most popular wired technology is . the most popular wireless technology is , which can be configured as a(n) or star topology. setting up a lan and configuring its router is fairly easy. the first step is to change the standard to one that is secure. next, create a(n) that uniquely identifies the network by name. it is also important to activate wireless to prevent wireless signals from being intercepted during transmission. a limited-access network can be created for visitors to use. by activating , the router will be able to assign ip addresses to each device that joins the network. to connect to a secure lan that is protected by encryption, an encryption , or password, is required. lans can be used to access data collected by iot devices and the networks that tie these devices together. technologies such as rfid, nfc, bluetooth smart, zigbee, and z-wave offer -power links, essential for battery-powered devices that can’t expend excess amounts of energy transmitting data.