Lossless compression is a class of data compression algorithms that allows the original data to be reconstructed from the compressed data. By contrast, lossy compression permits reconstruction only of an approximation of the original data, though with improved compression rates. Lossless data compression is used in many applications. For example, it is used in the GNU tool gzip, it is often used as a component within lossy data compression technologies. Lossless compression is used in cases where it is important that the original and the decompressed data be identical, or where deviations from the original data would be unfavourable. Typical examples are executable programs, text documents, source code; some image file formats, like PNG or GIF, use only lossless compression, while others like TIFF and MNG may use either lossless or lossy methods. Lossless audio formats are most used for archiving or production purposes, while smaller lossy audio files are used on portable players and in other cases where storage space is limited or exact replication of the audio is unnecessary.

Most lossless compression programs do two things in sequence: the first step generates a statistical model for the input data, the second step uses this model to map input data to bit sequences in such a way that "probable" data will produce shorter output than "improbable" data. The primary encoding algorithms used to produce bit sequences are Huffman coding and arithmetic coding. Arithmetic coding achieves compression rates close to the best possible for a particular statistical model, given by the information entropy, whereas Huffman compression is simpler and faster but produces poor results for models that deal with symbol probabilities close to 1. There are two primary ways of constructing statistical models: in a static model, the data is analyzed and a model is constructed this model is stored with the compressed data; this approach is simple and modular, but has the disadvantage that the model itself can be expensive to store, that it forces using a single model for all data being compressed, so performs poorly on files that contain heterogeneous data.

Adaptive models dynamically update the model. Both the encoder and decoder begin with a trivial model, yielding poor compression of initial data, but as they learn more about the data, performance improves. Most popular types of compression used in practice now use adaptive coders. Lossless compression methods may be categorized according to the type of data they are designed to compress. While, in principle, any general-purpose lossless compression algorithm can be used on any type of data, many are unable to achieve significant compression on data that are not of the form for which they were designed to compress. Many of the lossless compression techniques used for text work reasonably well for indexed images; these techniques take advantage of the specific characteristics of images such as the common phenomenon of contiguous 2-D areas of similar tones. Every pixel but the first is replaced by the difference to its left neighbor; this leads to small values having a much higher probability than large values.

This is also applied to sound files, can compress files that contain low frequencies and low volumes. For images, this step can be repeated by taking the difference to the top pixel, in videos, the difference to the pixel in the next frame can be taken. A hierarchical version of this technique takes neighboring pairs of data points, stores their difference and sum, on a higher level with lower resolution continues with the sums; this is called discrete wavelet transform. JPEG2000 additionally uses data points from other pairs and multiplication factors to mix them into the difference; these factors must be integers. So the values are increased, increasing file size, but the distribution of values is more peaked; the adaptive encoding uses the probabilities from the previous sample in sound encoding, from the left and upper pixel in image encoding, additionally from the previous frame in video encoding. In the wavelet transformation, the probabilities are passed through the hierarchy. Many of these methods are implemented in open-source and proprietary tools LZW and its variants.

Some algorithms are patented in the United States and other countries and their legal usage requires licensing by the patent holder. Because of patents on certain kinds of LZW compression, in particular licensing practices by patent holder Unisys that many developers considered abusive, some open source proponents encouraged people to avoid using the Graphics Interchange Format for compressing still image files in favor of Portable Network Graphics, which combines the LZ77-based deflate algorithm with a selection of domain-specific prediction filters. However, the patents on LZW expired on June 20, 2003. Many of the lossless compression techniques used for text work reasonably well for indexed images, but there are other techniques that do not work for typical text that are useful for some images, other techniques that take advantage of the specific characteristics of images; as mentioned lossless sound com

The Reverend Seymour Mills Spencer was born in Hartford, Connecticut. Son of Moses Roswell Spencer and Alma Flagg, he and his wife Ellen Stanley Spencer followed an ambition to carry out the role of missionary work in New Zealand. He trained for missionary work in England at Islington; the Church Missionary Society was an evangelical organisation, part of the Church of England. The couple sailed on 17 January 1842 to New Zealand on the sailing vessel, Louise Campbell and arrived in Auckland. Spencer was ordained by Bishop Selwyn to be the Deacon for the district of Taupo on 24 September 1843; the ordination ceremony was conducted in the St. John the Baptist Church at Te Waimate mission. Due to scandal over Spencer's purported advances toward a Māori girl, the couple moved from Taupo to Rotorua. From 23 November 1843 he work under the CMS missionary Thomas Chapman at the established CMS mission station at Te Ngae in Rotorua. In 1844 Spencer was at the Maketu mission station near Tauranga. In 1844 the couple established the first missionary post at Lake Tarawera.

In 1844 Spencer was suspended from the CMS for impropriety with a Māori woman. He rejoined the CMS in 1849 and was stationed at Opotiki until about 1855. Sometime after 1855 the couple returned to the Te Wairoa mission and remained there until 1870. Spencer visited Rotomahana and Te Ariki many times during his 35-year term with the CMS, his work with the local Māori helped develop the area, he was instrumental in assisting explorers and traders in the vicinity of Rotorua and Lake Tarawera. Ellen Stanley Spencer died at Maketu in 1882 at the age of 65. On 10 June 1886, Mount Tarawera erupted burying the surrounding communities including Kariri. Spencer was buried at Maketu, their son, Frederick H. Spencer, build a Spencer Family Mausoleum at Kariri.

Sonnet 101 is one of 154 sonnets written by the English playwright and poet William Shakespeare. It is a member of the Fair Youth sequence; the three other internal sequences include the procreation sonnets, the Rival Poet sequence and the Dark Lady sequence. While the exact date of composition of Sonnet 101 is unknown, scholars agree that the group of Sonnets 61–103 was written in the first half of the 1590s and was not revised before being published with the complete sequence of sonnets in the 1609 Quarto; the Muse is chided for her neglect of praise for the youth. The poet-speaker goes further, imagining the Muse responding that truth and beauty need no additions or explanations; the Muse is implored by the poet to praise the youth. The poet will teach her. Sonnet 101 is an Shakespearean sonnet; the English sonnet has three quatrains, followed by a final rhyming couplet. It follows the typical rhyme scheme of the form ABAB CDCD EFEF GG and is composed in iambic pentameter, a type of poetic metre based on five pairs of metrically weak/strong syllabic positions.

The 11th line exemplifies a regular iambic pentameter: × / × / × / × / × / To make him much outlive a gilded tomb / = ictus, a metrically strong syllabic position. × = nonictus. The 7th line has a common metrical variation, an initial reversal: / × × / × / × / × / Beauty no pencil, beauty's truth to lay; the parallelism of "seem" and "shows" in the final line suggest a rightward movement of the fourth ictus: × / × / × / × × / / To make him seem, long hence, as he shows now. While Petrarchan sonnets by tradition have a volta at the end of line eight, in Shakespeare's sonnets this can occur as late as line 12 and sometimes not at all. In Sonnet 101, a volta seems to occur at the end of line eight, as the poet-speaker, in a role-reversal with the Muse, begins to lead the Muse towards the couplet and there provides the Muse with a solution to the problem of "what to say and how to say it" thus ensuring that memory of youth will endure. In addition to Sonnet 100, Sonnet 101 is recognized as one of the only two sonnets in the complete sequence which directly invokes the Muse.

These two sonnets in turn are part of the group of four sonnets, 100–103, wherein the poet-speaker deflects blame for his silence from himself onto the Muse, making excuses for having not written or if writing, not writing adequately. Dubrow notes the use here of occupatio, that rhetorical method of announcing a topic which one will not discuss and by that announcement commencing a discussion of it. On the other hand, Stirling has noted the differences of 100–101 from 102–103 and from the larger group 97–104, that by removing them, one creates a more cohesive sequence tied together by "the theme of absence and'return'". A new position for 100–101 is suggested as the introduction to a sequence which develops with its "twin ideas of Time the destroyer—Verse the preserver."As mentioned above, the large group 61–103 was written in the first half of the 1590s, presented unrevised in 1609. Together with two other groups, 1–60 and 104-26 they make up the largest subsection known as the Fair Youth Sonnets.

The other three internal sequences of note are the Procreation sequence, the Rival Poet sequence and the Dark Lady sequence. The two most candidates for the Fair Youth are Henry Wriothesley, 3rd Earl of Southampton, an early patron of Shakespeare, William Herbert, 3rd Earl of Pembroke, a patron. Duncan-Jones argues that Pembroke is the more candidate, she suggests that John Davies of Hereford, Samuel Daniel, George Chapman, Ben Jonson are all plausible candidates for the role of Rival Poet in Sonnets 78-86. Atkins argues that pursuing a biographical context to the poems in Shakespeare's sequence is nonsensical and that a more productive focus of attention might be on the literary society of the time—which may have included small literary associations or academies, for one of these, the sonnets were composed; the popular themes would have included the Renaissance philosophy of platonic ideas of Truth and Beauty and Love and the relationship of each to the others. In Shakespeare's time, the word'pencil,' means paintbrush, though it can mean style, or level of skill in painting, or "an agent or medium which brushes, delineates, or colors."

Dundas describes the fascination of the English Renaissance poets with painting. Sonnet 24 uses the painter and painting as the extended conceit, pointing out the limits of the painter to capture the accurate image of beauty, then that the visual image may show no knowledge of the inward beauty of the heart. Sonnet 101 builds on that philosophy, that neither the painter nor the poet can accurately reflect the truth of the loved one's beauty so why not remain silent. Martz extends the discussion by suggesting that the work of Sidney and Shakespeare is analogous to the transition from High Renaissance to Mannerist styles in that they may refer to the ideals of harmonious composition, but focus on the tensions and anxieties and darker moods in the images of the subjects depicted in the