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# Market Research Group

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Daniel Allen

More often in practice, bits are "masked off" (or masked to 0) than "masked on" (or masked to 1). When a bit is ANDed with a 0, the result is always 0, i.e. Y AND 0 = 0. To leave the other bits as they were originally, they can be ANDed with 1 as Y AND 1 = Y

So far the article has covered how to turn bits on and turn bits off, but not both at once. Sometimes it does not really matter what the value is, but it must be made the opposite of what it currently is. This can be achieved using the XOR (exclusive or) operation. XOR returns 1 if and only if an odd number of bits are 1. Therefore, if two corresponding bits are 1, the result will be a 0, but if only one of them is 1, the result will be 1. Therefore inversion of the values of bits is done by XORing them with a 1. If the original bit was 1, it returns 1 XOR 1 = 0. If the original bit was 0 it returns 0 XOR 1 = 1. Also note that XOR masking is bit-safe, meaning that it will not affect unmasked bits because Y XOR 0 = Y, just like an OR.

In programming languages such as C, bit fields are a useful way to pass a set of named boolean arguments to a function. For example, in the graphics API OpenGL, there is a command, glClear() which clears the screen or other buffers. It can clear up to four buffers (the color, depth, accumulation, and stencil buffers), so the API authors could have had it take four arguments. But then a call to it would look like

This technique is used for painting pointing device cursors, in typical 2-D videogames for characters, bullets and so on (the sprites), for GUI icons, and for video titling and other image mixing applications.

In retrospect, relying on laboratory-confirmed cases as the primary outcome may have been unrealistic for a study of this size. ILI in enrolled adults was 17.1%, but laboratory confirmation was modest; the virus was identified in only 34.7% of adult ILI cases (the rate of laboratory diagnosis in children was high at 63.8%). However, even intention-to-treat analysis using ILI outcome shows no significant difference between the groups. We used self-reporting to determine adherence; previous research indicates that patient self-reporting is more reliable than judgments by doctors or nurses when compared against urine drug levels (30). In addition, the significant association between adherence and clinical protection provides internal validation of self-reporting as a measure.

To generate a mask for your case you should exploit the simple mathematical fact that if you add 1 to your mask (the mask having all its least significant bits set to 1 and the rest to 0), you get a value that is a power of 2.

In many circumstances, datasets can be incomplete or tainted by the presenceof invalid data. For example, a sensor may have failed to record a data, orrecorded an invalid value. The numpy.ma module provides a convenientway to address this issue, by introducing masked arrays.

A masked array is the combination of a standard numpy.ndarray and amask. A mask is either nomask, indicating that no value of theassociated array is invalid, or an array of booleans that determines for eachelement of the associated array whether the value is valid or not. When anelement of the mask is False, the corresponding element of the associatedarray is valid and is said to be unmasked. When an element of the mask isTrue, the corresponding element of the associated array is said to bemasked (invalid).

None of these methods is completely satisfactory if some entries have beenmarked as invalid. As a general rule, where a representation of the array isrequired without any masked entries, it is recommended to fill the array withthe filled method.

Another possibility is to use the getmask and getmaskarrayfunctions. getmask(x) outputs the mask of x if x is a maskedarray, and the special value nomask otherwise. getmaskarray(x)outputs the mask of x if x is a masked array. If x has no invalidentry or is not a masked array, the function outputs a boolean array ofFalse with as many elements as x.

When creating a new masked array with a simple, non-structured datatype,the mask is initially set to the special value nomask, thatcorresponds roughly to the boolean False. Trying to set an element ofnomask will fail with a TypeError exception, as a booleandoes not support item assignment.

Unmasking an entry by direct assignment will silently fail if the maskedarray has a hard mask, as shown by the hardmaskattribute. This feature was introduced to prevent overwriting the mask.To force the unmasking of an entry where the array has a hard mask,the mask must first to be softened using the soften_mask methodbefore the allocation. It can be re-hardened with harden_mask:

When accessing a single entry of a masked array with no named fields, theoutput is either a scalar (if the corresponding entry of the mask isFalse) or the special value masked (if the corresponding entry ofthe mask is True):

If the masked array has named fields, accessing a single entry returns anumpy.void object if none of the fields are masked, or a 0d maskedarray with the same dtype as the initial array if at least one of the fieldsis masked.

When accessing a slice, the output is a masked array whosedata attribute is a view of the original data, and whosemask is either nomask (if there was no invalid entries in the originalarray) or a view of the corresponding slice of the original mask. The view isrequired to ensure propagation of any modification of the mask to the original.

Arithmetic and comparison operations are supported by masked arrays.As much as possible, invalid entries of a masked array are not processed,meaning that the corresponding data entriesshould be the same before and after the operation.

The numpy.ma module comes with a specific implementation of mostufuncs. Unary and binary functions that have a validity domain (such aslog or divide) return the maskedconstant whenever the input is masked or falls outside the validity domain:

Masked arrays also support standard numpy ufuncs. The output is then a maskedarray. The result of a unary ufunc is masked wherever the input is masked. Theresult of a binary ufunc is masked wherever any of the input is masked. If theufunc also returns the optional context output (a 3-element tuple containingthe name of the ufunc, its arguments and its domain), the context is processedand entries of the output masked array are masked wherever the correspondinginput fall outside the validity domain:

Some health authorities recommend that masks be worn by ill individuals to prevent onward transmission (source control)4,8. Surgical face masks were originally introduced to protect patients from wound infection and contamination from surgeons (the wearer) during surgical procedures, and were later adopted to protect healthcare workers against acquiring infection from their patients. However, most of the existing evidence on the filtering efficacy of face masks and respirators comes from in vitro experiments with nonbiological particles9,10, which may not be generalizable to infectious respiratory virus droplets. There is little information on the efficacy of face masks in filtering respiratory viruses and reducing viral release from an individual with respiratory infections8, and most research has focused on influenza11,12. 041b061a72