Life on MarsThe possibility of life on Mars is a subject of interest in astrobiology due to the planet's proximity and similarities to Earth. To date, no proof of past or present life has been found on Mars. Cumulative evidence suggests that during the ancient Noachian time period, the surface environment of Mars had liquid water and may have been habitable for microorganisms, but habitable conditions do not necessarily indicate life.
Exploration of MarsThe planet Mars has been explored remotely by spacecraft. Probes sent from Earth, beginning in the late 20th century, have yielded a large increase in knowledge about the Martian system, focused primarily on understanding its geology and habitability potential. Engineering interplanetary journeys is complicated and the exploration of Mars has experienced a high failure rate, especially the early attempts. Roughly sixty percent of all spacecraft destined for Mars failed before completing their missions and some failed before their observations could begin.
Gaussian noiseIn signal processing theory, Gaussian noise, named after Carl Friedrich Gauss, is a kind of signal noise that has a probability density function (pdf) equal to that of the normal distribution (which is also known as the Gaussian distribution). In other words, the values that the noise can take are Gaussian-distributed. The probability density function of a Gaussian random variable is given by: where represents the grey level, the mean grey value and its standard deviation.
Sufficient statisticIn statistics, a statistic is sufficient with respect to a statistical model and its associated unknown parameter if "no other statistic that can be calculated from the same sample provides any additional information as to the value of the parameter". In particular, a statistic is sufficient for a family of probability distributions if the sample from which it is calculated gives no additional information than the statistic, as to which of those probability distributions is the sampling distribution.
Colonization of MarsColonization or settlement of Mars is the theoretical human migration and long-term human establishment of Mars. The prospect has garnered interest from public space agencies and private corporations and has been extensively explored in science fiction writing, film, and art. Organizations have proposed plans for a human mission to Mars, the first step towards any colonization effort, but no person has set foot on the planet, and there have been no return missions.
Additive white Gaussian noiseAdditive white Gaussian noise (AWGN) is a basic noise model used in information theory to mimic the effect of many random processes that occur in nature. The modifiers denote specific characteristics: Additive because it is added to any noise that might be intrinsic to the information system. White refers to the idea that it has uniform power spectral density across the frequency band for the information system. It is an analogy to the color white which may be realized by uniform emissions at all frequencies in the visible spectrum.
Linear algebraLinear algebra is the branch of mathematics concerning linear equations such as: linear maps such as: and their representations in vector spaces and through matrices. Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations. Also, functional analysis, a branch of mathematical analysis, may be viewed as the application of linear algebra to spaces of functions.
Descriptive statisticsA descriptive statistic (in the count noun sense) is a summary statistic that quantitatively describes or summarizes features from a collection of information, while descriptive statistics (in the mass noun sense) is the process of using and analysing those statistics. Descriptive statistics is distinguished from inferential statistics (or inductive statistics) by its aim to summarize a sample, rather than use the data to learn about the population that the sample of data is thought to represent.
StatisticsStatistics (from German: Statistik, () "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal".
Noise reductionNoise reduction is the process of removing noise from a signal. Noise reduction techniques exist for audio and images. Noise reduction algorithms may distort the signal to some degree. Noise rejection is the ability of a circuit to isolate an undesired signal component from the desired signal component, as with common-mode rejection ratio. All signal processing devices, both analog and digital, have traits that make them susceptible to noise.
Map projectionIn cartography, a map projection is any of a broad set of transformations employed to represent the curved two-dimensional surface of a globe on a plane. In a map projection, coordinates, often expressed as latitude and longitude, of locations from the surface of the globe are transformed to coordinates on a plane. Projection is a necessary step in creating a two-dimensional map and is one of the essential elements of cartography. All projections of a sphere on a plane necessarily distort the surface in some way and to some extent.
Summary statisticsIn descriptive statistics, summary statistics are used to summarize a set of observations, in order to communicate the largest amount of information as simply as possible. Statisticians commonly try to describe the observations in a measure of location, or central tendency, such as the arithmetic mean a measure of statistical dispersion like the standard mean absolute deviation a measure of the shape of the distribution like skewness or kurtosis if more than one variable is measured, a measure of statistical dependence such as a correlation coefficient A common collection of order statistics used as summary statistics are the five-number summary, sometimes extended to a seven-number summary, and the associated box plot.
Noise (signal processing)In signal processing, noise is a general term for unwanted (and, in general, unknown) modifications that a signal may suffer during capture, storage, transmission, processing, or conversion. Sometimes the word is also used to mean signals that are random (unpredictable) and carry no useful information; even if they are not interfering with other signals or may have been introduced intentionally, as in comfort noise. Noise reduction, the recovery of the original signal from the noise-corrupted one, is a very common goal in the design of signal processing systems, especially filters.
Linear subspaceIn mathematics, and more specifically in linear algebra, a linear subspace or vector subspace is a vector space that is a subset of some larger vector space. A linear subspace is usually simply called a subspace when the context serves to distinguish it from other types of subspaces. If V is a vector space over a field K and if W is a subset of V, then W is a linear subspace of V if under the operations of V, W is a vector space over K.
MarsMars is the fourth planet and the furthest terrestrial planet from the Sun. The reddish color of its surface is due to finely grained iron(III) oxide dust in the soil, giving it the nickname "the Red Planet". Mars's radius is second smallest among the planets in the Solar System at . The Martian dichotomy is visible on the surface: on average, the terrain on Mars's northern hemisphere is flatter and lower than its southern hemisphere. Mars has a thin atmosphere made primarily of carbon dioxide and two irregularly shaped natural satellites: Phobos and Deimos.
Signal processingSignal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing signals, such as sound, , potential fields, seismic signals, altimetry processing, and scientific measurements. Signal processing techniques are used to optimize transmissions, digital storage efficiency, correcting distorted signals, subjective video quality and to also detect or pinpoint components of interest in a measured signal. According to Alan V. Oppenheim and Ronald W.
RotationRotation or rotational motion is the circular movement of an object around a central line, known as axis of rotation. A plane figure can rotate in either a clockwise or counterclockwise sense around a perpendicular axis intersecting anywhere inside or outside the figure at a center of rotation. A solid figure has an infinite number of possible axes and angles of rotation, including chaotic rotation (between arbitrary orientations), in contrast to rotation around a axis.
Completeness (statistics)In statistics, completeness is a property of a statistic in relation to a parameterised model for a set of observed data. A complete statistic T is one for which any proposed distribution on the domain of T is predicted by one or more prior distributions on the model parameter space. In other words, the model space is 'rich enough' that every possible distribution of T can be explained by some prior distribution on the model parameter space. In contrast, a sufficient statistic T is one for which any two prior distributions will yield different distributions on T.
Mercator projectionThe Mercator projection (mərˈkeɪtər) is a cylindrical map projection presented by Flemish geographer and cartographer Gerardus Mercator in 1569. It became the standard map projection for navigation because it is unique in representing north as up and south as down everywhere while preserving local directions and shapes. The map is thereby conformal. As a side effect, the Mercator projection inflates the size of objects away from the equator. This inflation is very small near the equator but accelerates with increasing latitude to become infinite at the poles.
Equirectangular projectionThe equirectangular projection (also called the equidistant cylindrical projection or la carte parallélogrammatique projection), and which includes the special case of the plate carrée projection (also called the geographic projection, lat/lon projection, or plane chart), is a simple map projection attributed to Marinus of Tyre, who Ptolemy claims invented the projection about AD 100. The projection maps meridians to vertical straight lines of constant spacing (for meridional intervals of constant spacing), and circles of latitude to horizontal straight lines of constant spacing (for constant intervals of parallels).
