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As this example illustrate, units of matter are organized and integrated into levels of increasing complexity; this is a concept referred to as integrative levels of organization. Integrative levels of organization allow researchers to describe evolution from inanimate to animate and social worlds. Higher integrative levels are more complex and demonstrate more variation and characteristics than lower integrative levels. These levels are based upon physical foundation, with the lowest level appearing to consist of subatomic particles. In order to study genetics, however, we don't need to consider objects as tiny as subatomic particles. Rather, spectrum of integrative levels that range from macromolecules to populations is most relevant. A very small change in single macromolecule can have profound effect on organism, or even population, when magnified through levels of complexity. For instance, when disturbance such as genetic mutation is introduced at any level, it can affect all of higher levels of organization. The effect of such a disturbance can be either severe or trivial. For example, mutation, or change, in single DNA base in single gene can result in diseases such as cystic fibrosis and Duchenne muscular dystrophy in humans at organismal level. This means that the mechanism behind an organism's phenotype can be observed at integrative level immediately below it. Likewise, change in matter at a lower level can produce phenotype that is observable at a higher integrative level. Therefore, phenotype must only be defined according to the integrative level under consideration. For example, mutations in genes can be observed as changes in DNA and protein at the macromolecular level. At the tissue level, same mutation could cause changes in histology. Meanwhile, at the level of organism, mutation could result in behavioral changes. For these reasons, each integrative level must be studied with tools available for that level, which are called dimensions of analysis. Moreover, change or changes at any one level must be related to changes at all higher levels. Thus, understanding disease phenotype or behavior at a higher level requires that we study changes at many different integrative levels using appropriate methodologies. For geneticist, chemistry, biochemistry, molecular biology, histology, and physiology are all important. Broad training in all of these techniques allows geneticists to study emergent interactions at multiple levels.

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One of the basic problems in evaluating complex living forms and their changes is how to analyse them quantitatively. Although mathematical thought has not had the same impact on biology and medicine as on physics, mathematician George Boole pointed out that the structure of living matter is subject to numerical relationships in all of its parts, and that all its dynamic actions are measurable and connected by defined numerical relationships. Boole saw human thought in mathematical terms and, given its nature, mathematics holds a fundamental place in human knowledge. The origins of interest of mankind in mathematics of form go back to ancient times, when it coincided with manifestation of specific practical needs and, more generally, need to describe and represent the surrounding world. The use of geometry to describe and understand reality is essential insofar as it makes it possible to reconstruct the inherent rational order of things. According to Pythagoras, real knowledge was necessarily mathematical. This idea continued until the early years of the seventeenth century, when Galileo re - propose observations made by Pythagoras, with no substantial modification, by affirming that the Universe is written in the language of mathematics, whose letters are triangles, circles and other geometric figures. However, during the first half of the twentieth century, it was discovered that the geometric language of Euclid is not only a possible means of making axiomatic formulations, but that other geometries exist that are as self - consistent as classical geometry. This led to the flourishing of new geometrical languages capable of describing new spatial imaginations in rigorous terms. While successive generations of mathematicians were elaborating on large number of new non - Euclidean geometries, beginning of the twentieth century saw the discovery of mathematical objects that seemed at first sight to be little more than curiosities devoid of practical interest. However, in the mid - 1970s, mathematician Benoit Mandelbrot gave them new dignity by defining them as fractal objects and introducing them a new language called fractal geometry. Fractal geometry moves in different developmental directions from non - Euclidean geometries. Whereas the latter is based on collocation of familiar objects in spaces other than Euclidean space, fractal geometry stresses the nature of geometric objects regardless of ambient space. The novelty of fractal objects lies in their infinite morphological complexity, which contrasts with the harmony and simplicity of Euclidean forms but matches the variety and wealth of complex natural forms. Complexity is so pervasive in the anatomical world that it has come to be considered a basic characteristic of anatomical systems. B anatomical entities, viewed at microscopic and macroscopic level of observation, show different degrees of complexity. C complexity can reside in the structure of a system having many diverse parts with varying interactions or intricate architecture or in its behaviour. Often, complexity in structure and behaviour go together. D complex system admit many descriptions ways of looking at system, each of which is only partially true.

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The size of the largest organism on Earth has increased by approximately 18 orders of magnitude over the course of the Geozoic. Much of this increase occurs during two major jumps associated with origin of eukaryotic cells approximately 1. 9 Ga and animals approximately 0. 6 Ga. Though increases in largest known organisms have been well document, changes in overall distribution of organismal sizes over Geozoic remain poorly characterize. Evolutionary increases in size correspond to increases in biological complexity. There are two forms of complexity. The first is defined by structural hierarchy, or vertical complexity, which is the number of levels of nestedness or levels of organization in an organism. For example, solitary eukaryotic cells arose historically as an association of prokaryotic cells and are therefore one vertical level above prokaryotes. A Multicellular eukaryotic organism is an association of unicellular protists and is therefore one level higher Vertical complexity contrasts with horizontal complexity, which is the number of part types within give level, such as the number of cell types within an animal. Here, we use the word complexity in its vertical, anatomical sense. The Qualitative trajectory of maximum organismal size over the history of life suggests a connection between complexity and size. However, in the absence of data describing full distribution of organismal sizes, precise nature of the relationship between complexity and other aspects of size distribution, such as minimum, median, mean and range, has remained largely unexplored. Furthermore, there remains the question of whether observed increases in maximum size and complexity are results of driven or passive evolutionary processes. Stanley argues that trends such as increases in mean and maximum organismal size are best explained as increases in variance in systems dominated by passive processes and bound by minimum size, rather than driven trends reflecting selective advantages associated with larger size. This increasing - variance hypothesis predicts a diffusion - like evolutionary process with single constraint on absolute minimum size. If this process operate, organismal size should appear to diffuse away from a single absolute minimum size, and diffusion should be independent of complexity level. Further prediction is that all of life, in aggregate, follows right - skew, unimodal size - frequency distribution. Alternatively, Knoll & Bambach describe the history of life as a sequence of evolutionary megatrajectories, or linked series of discrete trends, that played out during the Geozoic. Their megatrajectories are not purely structuralas vertical complexity, they also have ecological dimension. Adapting their hypothesis to the vertical complexity case, expectation is that variance in size within each megatrajectory increases over geologic time, but is bound by both minimum and maximum constraints imposed by hierarchical structure at each level. For example, smallest possible prokaryotic cella with size minimum for that levelis thought to require a diameter of at least 250 nm, just large enough for a minimum number of ribosomes to mediate gene expression.

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Big O Notation | Name | Example(s) |
---|---|---|

O(1) | Constant | Odd or Even number , Look-up table (on average) |

O(log n) | Logarithmic | Finding element on sorted array with binary search |

O(n) | Linear | Find max element in unsorted array , Duplicate elements in array with Hash Map |

O(n log n) | Linearithmic | Sorting elements in array with merge sort |

O(n 2 ) | Quadratic | Duplicate elements in array (naive) , Sorting array with bubble sort |

O(n 3 ) | Cubic | 3 variables equation solver |

O(2 n ) | Exponential | Find all subsets |

O(n!) | Factorial | Find all permutations of a given set/string |

It is widely acknowledged in machine learning that performance of learning algorithm is dependent on both its parameters and training data. Yet, bulk of algorithmic development has focused on adjusting model parameters without fully understanding data that learning algorithm is modeling. As such, algorithmic development for classification problems has largely been measured by classification accuracy, precision, or similar metrics on benchmark data sets. These metrics, however, only provide aggregate information about the learning algorithm and the task upon which it operate. They fail to offer any information about which instances are misclassified, let alone why they are misclassified. There is some speculation as to why some instances are misclassified, but, to our knowledge, no thorough investigation has taken place. Previous work on instance misclassification, has focused mainly on isolated causes. For example, it has been observed that outliers are often misclassified and can affect classification in other instances. Border points and instances that belong to minority classes have also been found to be more difficult to classify correctly. As these studies have had narrow focus on trying to identify and handle outliers, border points, or minority classes, they have not generally produced an agree - upon definition of what characterizes these instances. At the data set level, previous work has presented measures to characterize the overall complexity of the data set. Data set measures have been used in meta learning as well as to understand under what circumstances a particular learning algorithm will perform well. As with performance metrics, data complexity measures characterize the overall complexity of data set but do not look at instance level and thus cannot say anything about why certain instances are misclassified. It is our contention that identifying which instances are misclassified and understanding why they are misclassified can lead to improvements in machine learning algorithm design and application. Misclassification, for instance, depends on the learning algorithm used to model the task it belongs to and its relationship to other instances in the training set. Hence, any notion of instance hardness, ie, likelihood of instance being misclassified, must be a relative one. However, generalization beyond single learning algorithm can be achieved by aggregating results from multiple learning algorithms. We use this fact to propose an empirical definition of instance hardness based on classification behavior of a set of learning algorithms that have been selected because of their diversity, their utility, and their broad practical applicability. We then present thorough analysis of instance hardness, and provide insight as to why hard instances are frequently misclassified. To the best of our knowledge, our research is first at reporting on systematic and extensive investigation of issue. We analyze instance hardness in over 190 000 instances from 64 classification tasks classified by nine learning algorithms.

The size - frequency distribution of each vertical level is approximately unimodal. However, there is a hint of bimodality in protists that reflects slight over - representation of Foraminifera, one of the most diverse groups of protists, in our dataset. However, degree of bimodality is low and distributions of Foraminifera and non - foraminiferan protists largely overlap. Aggregate size distribution of all organisms is strongly multimodal; Hartigan's dip test rejects the null hypothesis of unimodality. This multimodality persists so long as protists and animals constitute non - negligible fraction of total diversity. First treatment, where diversity in higher complexity groupings is assumed to be half that of lower levels, remains significantly multimodal. The second treatment, where distributions are adjusted to match estimates of relative diversity in each group, is statistically indistinguishable from unimodality, but this must be the case simply because of extreme weighting of single complexity level: prokaryotes. Neither raw nor corrected size distributions reproduce pattern predicted by Gould. Figure 1. Aggregated distributions of organismal size. Hypothetical unimodal right - skewed distribution of organismal sizes is expected under the Gould model. Observed distribution of organismal sizes in our data. The grey area highlights cumulative distribution of sizes and coloured lines correspond to distributions of individual vertical levels of complexity. Subsampled distributions where protists and multicellular eukaryotes are assumed to be one - half and one - quarter as diverse, respectively, as prokaryotes. Subsampled distributions where relative diversities are assumed to be proportional to estimates for prokaryotes, protists and multicellular eukaryotes. Subsampling our data does not produce unimodal distribution predicted by Gould. Grey areas of and are 50 percentile of 10 000 subsampled distributions. Solid coloured lines are 50 percentiles of individual levels and colour areas bound 5 and 95 percentiles. Regardless of subsampling, overall distribution remains multimodal. Download figure Open in New tab Download powerPoint Three principal patterns emerge when comparing size distributions of genera among complexity levels. First, mean biovolume within each level of complexity is five to eight orders of magnitude larger than at the next lower level; this is also true for medians and size - range midpoints. Tails of adjacent levels overlapsuch that largest simpler organisms are larger than the smallest organisms of each subsequent lower modes are well separate. Figure 2. Distributions of extant organismal size within each of the vertical levels. Colour shade areas highlight the total size range occupied by living genera within give level. As hierarchy ascends from viruses to multicellular eukaryotes, modal size as well as total range in size increases. Download figure Open in New tab Download powerPoint Table 1. Descriptive statistics of size distributions within each level of vertical complexity. All organism sizes were log 10 transform before calculating statistics.

Physicians identified 1126 of their 4302 eligible patients as complex and assigned a mean of 2. 2 domains of complexity per patient. Mental health and substance use were identified as major issues in younger complex patients, whereas medical decision making and care coordination predominate in older patients. Major independent predictors of PCP - define complexity include age, poorly controlled diabetes, use of antipsychotics, alcohol - related diagnoses, and inadequate insurance. Classification agreements for complex patients range from 26. 2% to 56. 0% when PCP assignment was compared with each of the other methods.

In contrast to Dawkins, Stephen Jay Gould comprehensibly discusses complexity and its increasing mode during life expansion. However, he explicitly denies increasing complexity to being driven by natural selection. In referring to the picture of distribution of creatures as skewed curves with simple organisms to the left and the most complex to the right, he states that the right tail is not a fundamental thrust produced by superiority of complex forms under natural selection. Instead, he contends that the most venerable evidence for general progressthe increasing complexity of the most complexbecomes passive consequence of growth in system with no directional bias whatever in motion of its components. For explication of such passively increasing complexity, Gould discusses the kind of diffusion process which he explains by means of metaphor known as drunkards walk that has turned out to have had great general impact. In this metaphor, drunk is staggering along the sidewalk at random. But on one side there is a wall of bar making limit that cause him to stray away from the wall. Gould means that in an analogous way, living organisms are drifting toward higher complexity at random, because there is a limit to minimal complexity. Therefore, Gould maintains, there is no need to drive by natural selection. Apply to my model, this limit of minimal complexity is the time axis in the diagram of Fig. 1, corresponding to zero complexity. However, in Gould's metaphor, nothing prevents drunk from passing over his own previous footprints over and over again, thus occasionally bringing him again close to the wall. This implies, in the evolutionary process, that species of high complexity occasionally revert into previous forms of lower complexity. Such regresses are exceptional, at least in great steps, and are seen to some extent, mainly amongst parasites. But maybe parasitism doesnt necessarily lead to a decrease in complexity. As Conway Morris suggest, interlocking of genomes of hosts and parasites seems to point towards under - appreciated degree of complexity. Another obstruction for species to return to previous level of lower complexity is understood in terms of genomic information content. Return to a lower level of complexity means reduction of information, but information cannot be lost /. / Because mutation corrupting information is purged due to corrupt genomes inferior fitness. In addition, it seems that in many cases when a species is confronted with severe environmental difficulties, it goes extinct instead of changing to a lower level of complexity. Still another difficulty with Gould's metaphor, is that it seems improbable that drunk after staggering to a certain distance from the wall, then suddenly becomes sober enough to be able to follow a straight path parallel to the wall. Likewise, it seems to me improbable that random diffusion processes eventually end up in a steady state situation that is observed in millions of species in millions of years.

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