By Bramley A.
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Extra info for Condition that an Electron Describe a Geodesic
For example, when α = 90%, β = 3%, and N = 20, 000, the ratio between the number of bits transmitted by UPE-M (EZB) and Fig. 6 Numbers of bits transmitted when α = 90%, β = 9%, 6% and 3%. 28). 8 show the comparison under different β values when α = 95% and 99%, respectively. Their results are similar to Fig. 6. It should be noted that the number of bits transmitted is not an accurate measurement of the energy cost because it ignores the energy spent to power up the radio and synchronize with the reader.
In the first case, tag x is assigned to a slot by one of those i − 1 hash functions. The probability for this to happen is Pi−1 . In the second case, tag x has not been assigned to any slot and thus it will be considered when the ith hash function is applied. The probability for this to happen is 1 − Pi−1 . Under the condition of the second case, let p be the probability for x to be assigned a slot by the ith hash function. We have Pi = Pi−1 + (1 − Pi−1) × p . 4) Next, we derive p . For tag x to be assigned a slot, it has to be mapped by the ith function to an unoccupied slot, and no other unassigned tag is mapped to the same slot.
If multiple hash functions satisfy the above conditions, the tag only uses the one that has the smallest value of j. When a tag x is mapped to a slot using the jth hash function, if the tag finds that the corresponding element in the hash-selection vector is also j, it means that the reader has assigned a tag to the slot based on the jth function, and moreover the reader will do so only when a single tag is mapped to the slot using the jth function. Tag x can thus conclude that this single tag must be itself.
Condition that an Electron Describe a Geodesic by Bramley A.
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