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Ice XII
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Ice XII
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It was first obtained by cooling liquid water to 260 K (−13 °C; 8 °F) at a pressure of 0.55 gigapascals (5,400 atm). Ice XII was discovered existing within the phase stability region of ice V. Later research showed that ice XII could be created outside that range. Pure ice XII can be created from ice Ih at 77 K (−196.2 °C; −321.1 °F) by rapid compression (0.81-1.00 GPa/min) or by warming high density amorphous ice at pressures between 0.8 to 1.6 gigapascals (7,900 to 15,800 atm).
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Ice XII
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Ice XII
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While it is similar in density (1.29 g/cm3 at 127 K (−146 °C; −231 °F)) to ice IV (also found in the ice V space) it exists as a tetragonal crystal. Topologically it is a mix of seven- and eight-membered rings, a 4-connected net (4-coordinate sphere packing)—the densest possible arrangement without hydrogen bond interpenetration.
Ordinary water ice is known as ice Ih, (in the Bridgman nomenclature). Different types of ice, from ice II to ice XVI, have been created in the laboratory at different temperatures and pressures.
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Ice XII
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Ice XIV
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When hydrochloric-acid-doped ice XII is cooled down to about 110 K, it undergoes a phase transition into a partially hydrogen-ordered phase, namely ice XIV. The transition entropy from ice XIV to ice XII is estimated to be 60% of Pauling entropy based on DSC measurements. The formation of ice XIV from ice XII is more favoured at high pressure.
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Kirkwood approximation
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Kirkwood approximation
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The Kirkwood superposition approximation was introduced in 1935 by John G. Kirkwood as a means of representing a discrete probability distribution. The Kirkwood approximation for a discrete probability density function P(x1,x2,…,xn) is given by P′(x1,x2,…,xn)=∏i=1n−1[∏Ti⊆Vp(Ti)](−1)n−1−i=∏Tn−1⊆Vp(Tn−1)∏Tn−2⊆Vp(Tn−2)⋮∏T1⊆Vp(T1) where ∏Ti⊆Vp(Ti) is the product of probabilities over all subsets of variables of size i in variable set V . This kind of formula has been considered by Watanabe (1960) and, according to Watanabe, also by Robert Fano. For the three-variable case, it reduces to simply P′(x1,x2,x3)=p(x1,x2)p(x2,x3)p(x1,x3)p(x1)p(x2)p(x3) The Kirkwood approximation does not generally produce a valid probability distribution (the normalization condition is violated). Watanabe claims that for this reason informational expressions of this type are not meaningful, and indeed there has been very little written about the properties of this measure. The Kirkwood approximation is the probabilistic counterpart of the interaction information.
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Kirkwood approximation
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Kirkwood approximation
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Judea Pearl (1988 §3.2.4) indicates that an expression of this type can be exact in the case of a decomposable model, that is, a probability distribution that admits a graph structure whose cliques form a tree. In such cases, the numerator contains the product of the intra-clique joint distributions and the denominator contains the product of the clique intersection distributions.
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Point coordination function
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Point coordination function
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Point coordination function (PCF) is a media access control (MAC) technique used in IEEE 802.11 based WLANs, including Wi-Fi. It resides in a point coordinator also known as access point (AP), to coordinate the communication within the network. The AP waits for PIFS duration rather than DIFS duration to grasp the channel. PIFS is less than DIFS duration and hence the point coordinator always has the priority to access the channel.The PCF is located directly above the distributed coordination function (DCF), in the IEEE 802.11 MAC Architecture. Channel access in PCF mode is centralized and hence the point coordinator sends CF-Poll frame to the PCF capable station to permit it to transmit a frame. In case the polled station does not have any frames to send, then it must transmit null frame.
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Point coordination function
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Point coordination function
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Due to the priority of PCF over DCF, stations that only use DCF might not gain access to the medium. To prevent this, a repetition interval has been designed to cover both (Contention free) PCF & (Contention Based) DCF traffic. The repetition interval which is repeated continuously, starts with a special control frame called Beacon Frame. When stations hear the beacon frame, they start their network allocation vector for the duration of the contention free period of the repetition period. Since most APs have logical bus topologies (they are shared circuits) only one message can be processed at one time (it is a contention based system), and thus a media access control technique is required.
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Point coordination function
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Point coordination function
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Wireless networks may suffer from a hidden node problem where some regular nodes (which communicate only with the AP) cannot see other nodes on the extreme edge of the geographical radius of the network because the wireless signal attenuates before it can reach that far. Thus having an AP in the middle allows the distance to be halved, allowing all nodes to see the AP, and consequentially, halving the maximum distance between two nodes on the extreme edges of a circle-star topology.
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Point coordination function
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Point coordination function
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PCF seems to be implemented only in very few hardware devices as it is not part of the Wi-Fi Alliance's interoperability standard.
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Point coordination function
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PCF Interframe Space
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PCF Interframe Space (PIFS) is one of the interframe space used in IEEE 802.11 based Wireless LANs. PCF enabled access point wait for PIFS duration rather than DIFS to occupy the wireless medium. PIFS duration is less than DIFS and greater than SIFS (DIFS > PIFS > SIFS). Hence AP always has more priority to access the medium.
PIFS duration can be calculated as follows: PIFS = SIFS + Slot time
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Entanglement witness
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Entanglement witness
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In quantum information theory, an entanglement witness is a functional which distinguishes a specific entangled state from separable ones. Entanglement witnesses can be linear or nonlinear functionals of the density matrix. If linear, then they can also be viewed as observables for which the expectation value of the entangled state is strictly outside the range of possible expectation values of any separable state.
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Entanglement witness
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Details
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Let a composite quantum system have state space HA⊗HB . A mixed state ρ is then a trace-class positive operator on the state space which has trace 1. We can view the family of states as a subset of the real Banach space generated by the Hermitian trace-class operators, with the trace norm. A mixed state ρ is separable if it can be approximated, in the trace norm, by states of the form ξ=∑i=1kpiρiA⊗ρiB, where ρiA and ρiB are pure states on the subsystems A and B respectively. So the family of separable states is the closed convex hull of pure product states. We will make use of the following variant of Hahn–Banach theorem: Theorem Let S1 and S2 be disjoint convex closed sets in a real Banach space and one of them is compact, then there exists a bounded functional f separating the two sets.
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Entanglement witness
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Details
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This is a generalization of the fact that, in real Euclidean space, given a convex set and a point outside, there always exists an affine subspace separating the two. The affine subspace manifests itself as the functional f. In the present context, the family of separable states is a convex set in the space of trace class operators. If ρ is an entangled state (thus lying outside the convex set), then by theorem above, there is a functional f separating ρ from the separable states. It is this functional f, or its identification as an operator, that we call an entanglement witness. There is more than one hyperplane separating a closed convex set from a point lying outside of it, so for an entangled state there is more than one entanglement witness. Recall the fact that the dual space of the Banach space of trace-class operators is isomorphic to the set of bounded operators. Therefore, we can identify f with a Hermitian operator A. Therefore, modulo a few details, we have shown the existence of an entanglement witness given an entangled state: Theorem For every entangled state ρ, there exists a Hermitian operator A such that Tr (Aρ)<0 , and Tr (Aσ)≥0 for all separable states σ.
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Entanglement witness
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Details
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When both HA and HB have finite dimension, there is no difference between trace-class and Hilbert–Schmidt operators. So in that case A can be given by Riesz representation theorem. As an immediate corollary, we have: Theorem A mixed state σ is separable if and only if Tr (Aσ)≥0 for any bounded operator A satisfying Tr (A⋅P⊗Q)≥0 , for all product pure state P⊗Q If a state is separable, clearly the desired implication from the theorem must hold. On the other hand, given an entangled state, one of its entanglement witnesses will violate the given condition.
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Entanglement witness
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Details
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Thus if a bounded functional f of the trace-class Banach space and f is positive on the product pure states, then f, or its identification as a Hermitian operator, is an entanglement witness. Such a f indicates the entanglement of some state.
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Entanglement witness
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Details
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Using the isomorphism between entanglement witnesses and non-completely positive maps, it was shown (by the Horodeckis) that Theorem Assume that HA,HB are finite-dimensional. A mixed state σ∈L(HA)⊗L(HB) is separable if for every positive map Λ from bounded operators on HB to bounded operators on HA , the operator (IA⊗Λ)(σ) is positive, where IA is the identity map on L(HA) , the bounded operators on HA
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Bounded type (mathematics)
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Bounded type (mathematics)
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In mathematics, a function defined on a region of the complex plane is said to be of bounded type if it is equal to the ratio of two analytic functions bounded in that region. But more generally, a function is of bounded type in a region Ω if and only if f is analytic on Ω and log +|f(z)| has a harmonic majorant on Ω, where log max log (x)] . Being the ratio of two bounded analytic functions is a sufficient condition for a function to be of bounded type (defined in terms of a harmonic majorant), and if Ω is simply connected the condition is also necessary.
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Bounded type (mathematics)
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Bounded type (mathematics)
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The class of all such f on Ω is commonly denoted N(Ω) and is sometimes called the Nevanlinna class for Ω . The Nevanlinna class includes all the Hardy classes.
Functions of bounded type are not necessarily bounded, nor do they have a property called "type" which is bounded. The reason for the name is probably that when defined on a disc, the Nevanlinna characteristic (a function of distance from the centre of the disc) is bounded.
Clearly, if a function is the ratio of two bounded functions, then it can be expressed as the ratio of two functions which are bounded by 1: f(z)=P(z)/Q(z) The logarithms of |1/P(z)| and of |1/Q(z)| are non-negative in the region, so log log log log |1/Q(z)| log max log max log log log Q(z)).
The latter is the real part of an analytic function and is therefore harmonic, showing that log +|f(z)| has a harmonic majorant on Ω.
For a given region, sums, differences, and products of functions of bounded type are of bounded type, as is the quotient of two such functions as long as the denominator is not identically zero.
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Bounded type (mathematics)
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Examples
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Polynomials are of bounded type in any bounded region. They are also of bounded type in the upper half-plane (UHP), because a polynomial f(z) of degree n can be expressed as a ratio of two analytic functions bounded in the UHP: f(z)=P(z)/Q(z) with P(z)=f(z)/(z+i)n Q(z)=1/(z+i)n.
The inverse of a polynomial is also of bounded type in a region, as is any rational function.
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Bounded type (mathematics)
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Examples
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The function exp (aiz) is of bounded type in the UHP if and only if a is real. If a is positive the function itself is bounded in the UHP (so we can use Q(z)=1 ), and if a is negative then the function equals 1/Q(z) with exp (|a|iz) Sine and cosine are of bounded type in the UHP. Indeed, sin (z)=P(z)/Q(z) with sin exp (iz) exp (iz) both of which are bounded in the UHP.
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Bounded type (mathematics)
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Examples
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All of the above examples are of bounded type in the lower half-plane as well, using different P and Q functions. But the region mentioned in the definition of the term "bounded type" cannot be the whole complex plane unless the function is constant because one must use the same P and Q over the whole region, and the only entire functions (that is, analytic in the whole complex plane) which are bounded are constants, by Liouville's theorem.
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Bounded type (mathematics)
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Examples
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Another example in the upper half-plane is a "Nevanlinna function", that is, an analytic function that maps the UHP to the closed UHP. If f(z) is of this type, then f(z)=P(z)/Q(z) where P and Q are the bounded functions: P(z)=f(z)f(z)+i Q(z)=1f(z)+i (This obviously applies as well to f(z)/i , that is, a function whose real part is non-negative in the UHP.)
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Bounded type (mathematics)
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Properties
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For a given region, the sum, product, or quotient of two (non-null) functions of bounded type is also of bounded type. The set of functions of bounded type is an algebra over the complex numbers and is in fact a field.
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Bounded type (mathematics)
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Properties
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Any function of bounded type in the upper half-plane (with a finite number of roots in some neighborhood of 0) can be expressed as a Blaschke product (an analytic function, bounded in the region, which factors out the zeros) multiplying the quotient P(z)/Q(z) where P(z) and Q(z) are bounded by 1 and have no zeros in the UHP. One can then express this quotient as exp exp (−V(z)) where U(z) and V(z) are analytic functions having non-negative real part in the UHP. Each of these in turn can be expressed by a Poisson representation (see Nevanlinna functions): U(z)=c−ipz−i∫R(1λ−z−λ1+λ2)dμ(λ) V(z)=d−iqz−i∫R(1λ−z−λ1+λ2)dν(λ) where c and d are imaginary constants, p and q are non-negative real constants, and μ and ν are non-decreasing functions of a real variable (well behaved so the integrals converge). The difference q−p has been given the name "mean type" by Louis de Branges and describes the growth or decay of the function along the imaginary axis: lim sup ln |f(iy)| The mean type in the upper half-plane is the limit of a weighted average of the logarithm of the function's absolute value divided by distance from zero, normalized in such a way that the value for exp (−iz) is 1: lim ln sin θdθ If an entire function is of bounded type in both the upper and the lower half-plane then it is of exponential type equal to the higher of the two respective "mean types" (and the higher one will be non-negative). An entire function of order greater than 1 (which means that in some direction it grows faster than a function of exponential type) cannot be of bounded type in any half-plane.
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Bounded type (mathematics)
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Properties
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We may thus produce a function of bounded type by using an appropriate exponential of z and exponentials of arbitrary Nevanlinna functions multiplied by i, for example: exp exp exp (−i/z) Concerning the examples given above, the mean type of polynomials or their inverses is zero. The mean type of exp (aiz) in the upper half-plane is −a, while in the lower half-plane it is a. The mean type of sin (z) in both half-planes is 1.
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Bounded type (mathematics)
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Properties
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Functions of bounded type in the upper half-plane with non-positive mean type and having a continuous, square-integrable extension to the real axis have the interesting property (useful in applications) that the integral (along the real axis) 12πi∫−∞∞f(t)dtt−z equals f(z) if z is in the upper half-plane and zero if z is in the lower half-plane. This may be termed the Cauchy formula for the upper half-plane.
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Range mode query
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Range mode query
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In data structures, the range mode query problem asks to build a data structure on some input data to efficiently answer queries asking for the mode of any consecutive subset of the input.
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Range mode query
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Problem statement
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Given an array A[1:n]=[a1,a2,...,an] , we wish to answer queries of the form mode(A,i:j) , where 1≤i≤j≤n . The mode mode(S) of any array S=[s1,s2,...,sk] is an element si such that the frequency of si is greater than or equal to the frequency of sj∀j∈{1,...,k} . For example, if S=[1,2,4,2,3,4,2] , then mode(S)=2 because it occurs three times, while all other values occur fewer times. In this problem, the queries ask for the mode of subarrays of the form A[i:j]=[ai,ai+1,...,aj] Theorem 1 Let A and B be any multisets. If c is a mode of A∪B and c∉A , then c is a mode of B Proof Let c∉A be a mode of C=A∪B and fc be its frequency in C . Suppose that c is not a mode of B . Thus, there exists an element b with frequency fb that is the mode of B . Since b is the mode of B and that c∉A , then fb>fc . Thus, b should be the mode of C which is a contradiction.
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Range mode query
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Lower bound
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Any data structure using S cells of w bits each needs log log (Sw/n)) time to answer a range mode query.This contrasts with other range query problems, such as the range minimum query which have solutions offering constant time query time and linear space. This is due to the hardness of the mode problem, since even if we know the mode of A[i:j] and the mode of A[j+1:k] , there is no simple way of computing the mode of A[i:k] . Any element of A[i:j] or A[j+1:k] could be the mode. For example, if mode(A[i:j])=a and its frequency is fa , and mode(A[j+1:k])=b and its frequency is also fa , there could be an element c with frequency fa−1 in A[i:j] and frequency fa−1 in A[j+1:k] . a≠c≠b , but its frequency in A[i:k] is greater than the frequency of a and b , which makes c a better candidate for mode(A[i:k]) than a or b
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Range mode query
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Linear space data structure with square root query time
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This method by Chan et al. uses O(n+s2) space and O(n/s) query time. By setting s=n , we get O(n) and O(n) bounds for space and query time.
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Range mode query
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Linear space data structure with square root query time
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Preprocessing Let A[1:n] be an array, and D[1:Δ] be an array that contains the distinct values of A, where Δ is the number of distinct elements. We define B[1:n] to be an array such that, for each i , B[i] contains the rank (position) of A[i] in D . Arrays B,D can be created by a linear scan of A Arrays Q1,Q2,...,QΔ are also created, such that, for each a∈{1,...,Δ} , Qa={b|B[b]=a} . We then create an array B′[1:n] , such that, for all b∈{1,...,n} , B′[b] contains the rank of b in QB[b] . Again, a linear scan of B suffices to create arrays Q1,Q2,...,QΔ and B′ It is now possible to answer queries of the form "is the frequency of B[i] in B[i:j] at least q " in constant time, by checking whether QB[i][B′[i]+q−1]≤j The array is split B into s blocks b1,b2,...,bs , each of size t=⌈n/s⌉ . Thus, a block bi spans over B[i⋅t+1:(i+1)t] . The mode and the frequency of each block or set of consecutive blocks will be pre-computed in two tables S and S′ . S[bi,bj] is the mode of bi∪bi+1∪...∪bj , or equivalently, the mode of B[bit+1:(bj+1)t] , and S′ stores the corresponding frequency. These two tables can be stored in O(s2) space, and can be populated in O(s⋅n) by scanning B s times, computing a row of S,S′ each time with the following algorithm: algorithm computeS_Sprime is input: Array B = [0:n - 1], Array D = [0:Delta - 1], Integer s output: Tables S and Sprime let S ← Table(0:n - 1, 0:n - 1) let Sprime ← Table(0:n - 1, 0:n - 1) let firstOccurence ← Array(0:Delta - 1) for all i in {0, ..., Delta - 1} do firstOccurence[i] ← -1 end for for i ← 0:s - 1 do let j ← i × t let c ← 0 let fc ← 0 let noBlock ← i let block_start ← j let block_end ← min{(i + 1) × t - 1, n - 1} while j < n do if firstOccurence[B[j]] = -1 then firstOccurence[B[j]] ← j end if if atLeastQInstances(firstOccurence[B[j]], block_end, fc + 1) then c ← B[j] fc ← fc + 1 end if if j = block_end then S[i * s + noBlock] ← c Sprime[i × s + noBlock] ← fc noBlock ← noBlock + 1 block_end ← min{block_end + t, n - 1} end if end while for all j in {0, ..., Delta - 1} do firstOccurence[j] ← -1 end for end for Query We will define the query algorithm over array B . This can be translated to an answer over A , since for any a,i,j , B[a] is a mode for B[i:j] if and only if A[a] is a mode for A[i:j] . We can convert an answer for B to an answer for A in constant time by looking in A or B at the corresponding index.
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Range mode query
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Linear space data structure with square root query time
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Given a query mode(B,i,j) , the query is split in three parts: the prefix, the span and the suffix. Let bi=⌈(i−1)/t⌉ and bj=⌊j/t⌋−1 . These denote the indices of the first and last block that are completely contained in B . The range of these blocks is called the span. The prefix is then B[i:min{bit,j}] (the set of indices before the span), and the suffix is B[max{(bj+1)t+1,i}:j] (the set of indices after the span). The prefix, suffix or span can be empty, the latter is if bj<bi For the span, the mode c is already stored in S[bi,bj] . Let fc be the frequency of the mode, which is stored in S′[bi,bj] . If the span is empty, let fc=0 . Recall that, by Theorem 1, the mode of B[i:j] is either an element of the prefix, span or suffix. A linear scan is performed over each element in the prefix and in the suffix to check if its frequency is greater than the current candidate c , in which case c and fc are updated to the new value. At the end of the scan, c contains the mode of B[i:j] and fc its frequency.
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Range mode query
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Linear space data structure with square root query time
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Scanning procedure The procedure is similar for both prefix and suffix, so it suffice to run this procedure for both: Let x be the index of the current element. There are three cases: If QB[x][B′[x]−1]≥i , then it was present in B[i:x−1] and its frequency has already been counted. Pass to the next element.
Otherwise, check if the frequency of B[x] in B[i:j] is at least fc (this can be done in constant time since it is the equivalent of checking it for B[x:j] ).
If it is not, then pass to the next element.
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Range mode query
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Linear space data structure with square root query time
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If it is, then compute the actual frequency fx of B[x] in B[i:j] by a linear scan (starting at index B′[x]+fc−1 ) or a binary search in QB[x] . Set := B[x] and := fx .This linear scan (excluding the frequency computations) is bounded by the block size t , since neither the prefix or the suffix can be greater than t . A further analysis of the linear scans done for frequency computations shows that it is also bounded by the block size. Thus, the query time is O(t)=O(n/s)
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Range mode query
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Subquadratic space data structure with constant query time
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This method by uses log log log n) space for a constant time query. We can observe that, if a constant query time is desired, this is a better solution than the one proposed by Chan et al., as the latter gives a space of O(n2) for constant query time if s=n Preprocessing Let A[1:n] be an array. The preprocessing is done in three steps: Split the array A in s blocks b1,b2,...,bs , where the size of each block is t=⌈n/s⌉ . Build a table S of size s×s where S[i,j] is the mode of bi∪bi+1∪...∪bj . The total space for this step is O(s2) For any query mode(A,i,j) , let bi′ be the block that contains i and bj′ be the block that contains j . Let the span be the set of blocks completely contained in A[i:j] . The mode c of the block can be retrieved from S . By Theorem 1, the mode can be either an element of the prefix (indices of A[i:j] before the start of the span), an element of the suffix (indices of A[i:j] after the end of the span), or c . The size of the prefix plus the size of the suffix is bounded by 2t , thus the position of the mode isstored as an integer ranging from 0 to 2t , where [0:2t−1] indicates a position in the prefix/suffix and 2t indicates that the mode is the mode of the span. There are (t2) possible queries involving blocks bi′ and bj′ , so these values are stored in a table of size t2 . Furthermore, there are (2t+1)t2 such tables, so the total space required for this step is O(t2(2t+1)t2) . To access those tables, a pointer is added in addition to the mode in the table S for each pair of blocks.
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Range mode query
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Subquadratic space data structure with constant query time
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To handle queries mode(A,i,j) where i and j are in the same block, all such solutions are precomputed. There are O(st2) of them, they are stored in a three dimensional table T of this size.The total space used by this data structure is O(s2+t2(2t+1)t2+st2) , which reduces to log log log n) if we take log log log n Query Given a query mode(A,i,j) , check if it is completely contained inside a block, in which case the answer is stored in table T . If the query spans exactly one or more blocks, then the answer is found in table S . Otherwise, use the pointer stored in table S at position S[bi′,bj′] , where bi′,bj′ are the indices of the blocks that contain respectively i and j , to find the table Ubi′,bj′ that contains the positions of the mode for these blocks and use the position to find the mode in A . This can be done in constant time.
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Jacqueline Chen
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Jacqueline Chen
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Jacqueline H. Chen is an American mechanical engineer. She works in the Combustion Research Facility of Sandia National Laboratories, where she is a Senior Scientist. Her research applies massively parallel computing to the simulation of turbulent combustion.
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Jacqueline Chen
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Education and career
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Chen grew up as a child of Chinese immigrants in Ohio, and graduated from the Ohio State University with a bachelor's degree in mechanical engineering in 1981. After earning a master's degree in mechanical engineering in 1982 at the University of California, Berkeley, under the mentorship of Boris Rubinsky, she continued at Stanford University for doctoral study in the same subject. She completed her Ph.D. in 1989; her doctoral advisor at Stanford was Brian J. Cantwell.She has worked at Sandia since finishing her education and is a pioneer of massively parallel direct numerical simulation of turbulent combustion with complex chemistry . She has led teams of computer scientists, applied mathematicians and computational engineers on the co-design of combustion simulation software for exascale computing (10^18 flops).
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Jacqueline Chen
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Recognition
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In 2018, Chen was elected to the National Academy of Engineering "for contributions to the computational simulation of turbulent reacting flows with complex chemistry".
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Jacqueline Chen
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Recognition
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In the same year, the Society of Women Engineers gave her an Achievement Award, their top honor, and the Combustion Institute awarded her the Bernard Lewis Gold Medal, "for her exceptional skill in linking high performance computing and combustion research to deliver fundamental insights into turbulence-chemistry interactions". The Combustion Institute and the American Physical Society also named her as one of its fellows.
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Flöz Mittel Formation
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Flöz Mittel Formation
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The Flöz Mittel Formation is a geologic formation in Germany. It preserves fossils dating back to the Carboniferous period.
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LINC00520
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LINC00520
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Long intergenic non-protein coding RNA 520 is a long non-coding RNA that in humans is encoded by the LINC00520 gene.
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UniHan IME
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UniHan IME
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UniHan IME is an input method based on the framework of IIIMF developed by Hong Kong Sun Wah Hi-Tech Ltd..
UniHan IME is an input method interface that maps the keyboard keys string to the Han character in the latest version of Unicode Table.
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UniHan IME
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UniHan IME
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UniHan is the CJKV characters section which occupied more than half the storage space of the Unicode Table. There are more than 75,000 characters coded in version 6.0.0 in year 2010. The Chinese, Japanese, Korean and Vietnamese shared the Han characters for naming for more than thousand years. The input methods for the Han characters from Unicode are mainly keyboard typing, mouse pointing on screen or hand writing on pad. The popular methods are the pinyin keyboard method and the hand writing method. A complete font set for Unihan version 6.0.0 is yet to come and so is the Unihan IME.
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UniHan IME
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UniHan IME
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A similar IME called 8 Steps Unihan was developed by 8 Steps Unihan company in Melbourne, Australia. The 8StepsA font coupled with Microsoft windows 10 SimSunExtB font are able to display all the characters in Unihan 10.0. which includes the extension F character set. The glyphs that are repeated have been linked together and only one of the linked code is used by the IME so that all the displayable characters are unique.
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Danalite
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Danalite
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Danalite is an iron beryllium silicate sulfide mineral with formula: Fe2+4Be3(SiO4)3S. It is a rare mineral which occurs in granites, tin bearing pegmatites, contact metamorphic skarns, gneisses and in hydrothermal deposits. It occurs in association with magnetite, garnet, fluorite, albite, cassiterite, pyrite, muscovite, arsenopyrite, quartz, and chlorite.Danalite was first described in 1866 from a deposit in Essex County, Massachusetts and named for American mineralogist James Dwight Dana (1813–1895).It has been found in Massachusetts, New Hampshire, Sierra County, New Mexico; Yavapai County, Arizona; Needlepoint Mountain, British Columbia; Walrus Island, James Bay, Quebec; Sweden; Cornwall, England; Imalka and Transbaikal, Russia; Kazakhstan; Somalia; Tasmania; Western Australia and Hiroshima Prefecture, Japan.
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Stepwise regression
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Stepwise regression
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In statistics, stepwise regression is a method of fitting regression models in which the choice of predictive variables is carried out by an automatic procedure. In each step, a variable is considered for addition to or subtraction from the set of explanatory variables based on some prespecified criterion. Usually, this takes the form of a forward, backward, or combined sequence of F-tests or t-tests. The frequent practice of fitting the final selected model followed by reporting estimates and confidence intervals without adjusting them to take the model building process into account has led to calls to stop using stepwise model building altogether or to at least make sure model uncertainty is correctly reflected.
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Stepwise regression
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Stepwise regression
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Alternatives include other model selection techniques, such as adjusted R2, Akaike information criterion, Bayesian information criterion, Mallows's Cp, PRESS, or false discovery rate.
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Stepwise regression
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Main approaches
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The main approaches for stepwise regression are: Forward selection, which involves starting with no variables in the model, testing the addition of each variable using a chosen model fit criterion, adding the variable (if any) whose inclusion gives the most statistically significant improvement of the fit, and repeating this process until none improves the model to a statistically significant extent.
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Stepwise regression
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Main approaches
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Backward elimination, which involves starting with all candidate variables, testing the deletion of each variable using a chosen model fit criterion, deleting the variable (if any) whose loss gives the most statistically insignificant deterioration of the model fit, and repeating this process until no further variables can be deleted without a statistically significant loss of fit.
Bidirectional elimination, a combination of the above, testing at each step for variables to be included or excluded.
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Stepwise regression
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Alternatives
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A widely used algorithm was first proposed by Efroymson (1960). This is an automatic procedure for statistical model selection in cases where there is a large number of potential explanatory variables, and no underlying theory on which to base the model selection. The procedure is used primarily in regression analysis, though the basic approach is applicable in many forms of model selection. This is a variation on forward selection. At each stage in the process, after a new variable is added, a test is made to check if some variables can be deleted without appreciably increasing the residual sum of squares (RSS). The procedure terminates when the measure is (locally) maximized, or when the available improvement falls below some critical value.
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Stepwise regression
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Alternatives
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One of the main issues with stepwise regression is that it searches a large space of possible models. Hence it is prone to overfitting the data. In other words, stepwise regression will often fit much better in sample than it does on new out-of-sample data. Extreme cases have been noted where models have achieved statistical significance working on random numbers. This problem can be mitigated if the criterion for adding (or deleting) a variable is stiff enough. The key line in the sand is at what can be thought of as the Bonferroni point: namely how significant the best spurious variable should be based on chance alone. On a t-statistic scale, this occurs at about log p , where p is the number of predictors. Unfortunately, this means that many variables which actually carry signal will not be included. This fence turns out to be the right trade-off between over-fitting and missing signal. If we look at the risk of different cutoffs, then using this bound will be within a log p factor of the best possible risk. Any other cutoff will end up having a larger such risk inflation.
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Stepwise regression
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Model accuracy
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A way to test for errors in models created by step-wise regression, is to not rely on the model's F-statistic, significance, or multiple R, but instead assess the model against a set of data that was not used to create the model. This is often done by building a model based on a sample of the dataset available (e.g., 70%) – the “training set” – and use the remainder of the dataset (e.g., 30%) as a validation set to assess the accuracy of the model. Accuracy is then often measured as the actual standard error (SE), MAPE (Mean absolute percentage error), or mean error between the predicted value and the actual value in the hold-out sample. This method is particularly valuable when data are collected in different settings (e.g., different times, social vs. solitary situations) or when models are assumed to be generalizable.
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Stepwise regression
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Criticism
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Stepwise regression procedures are used in data mining, but are controversial. Several points of criticism have been made.
The tests themselves are biased, since they are based on the same data. Wilkinson and Dallal (1981) computed percentage points of the multiple correlation coefficient by simulation and showed that a final regression obtained by forward selection, said by the F-procedure to be significant at 0.1%, was in fact only significant at 5%.
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Stepwise regression
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Criticism
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When estimating the degrees of freedom, the number of the candidate independent variables from the best fit selected may be smaller than the total number of final model variables, causing the fit to appear better than it is when adjusting the r2 value for the number of degrees of freedom. It is important to consider how many degrees of freedom have been used in the entire model, not just count the number of independent variables in the resulting fit.
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Stepwise regression
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Criticism
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Models that are created may be over-simplifications of the real models of the data.Such criticisms, based upon limitations of the relationship between a model and procedure and data set used to fit it, are usually addressed by verifying the model on an independent data set, as in the PRESS procedure.
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Stepwise regression
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Criticism
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Critics regard the procedure as a paradigmatic example of data dredging, intense computation often being an inadequate substitute for subject area expertise. Additionally, the results of stepwise regression are often used incorrectly without adjusting them for the occurrence of model selection. Especially the practice of fitting the final selected model as if no model selection had taken place and reporting of estimates and confidence intervals as if least-squares theory were valid for them, has been described as a scandal. Widespread incorrect usage and the availability of alternatives such as ensemble learning, leaving all variables in the model, or using expert judgement to identify relevant variables have led to calls to totally avoid stepwise model selection.
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Orange creamsicle cake
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Orange creamsicle cake
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Orange creamsicle cake is a cake containing orange and vanilla flavors that is named after the Popsicle-brand "Creamsicle" ice cream treat on a stick: a vanilla ice cream center coated in orange-flavored popsicle ice. A traditional version might just be an orange- and vanilla-flavored bundt cake, but there are no-bake versions of the cake made with ice cream and pudding, and other versions made with cakes that are frosted or served with orange marmalade.
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Orange creamsicle cake
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Ice cream cakes
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Some versions of the cake are no bake ice cream cakes made with orange and vanilla layers. The layers can be made with vanilla ice cream and orange sherbet over a vanilla wafer crust, although there is a lot of flexibility in how the cake is assembled, like using gingersnaps or white cake for the crust, or frozen yogurt instead of vanilla ice cream. Pound cake is used in some recipes to line a loaf pan, then the pound cake shell is filled with orange sherbet and the top is covered with pound cake. The sherbet filled pound cake loaf is left in the fridge to set for several hours before it is frosted with vanilla frosting.
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Orange creamsicle cake
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Angel food cake
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Other versions are made with angel food cake which can be flavored with orange-marmalade or orange zest and frosted with an orange and vanilla flavored whipped custard, or simply with orange marmalade.
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Orange creamsicle cake
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Other
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Another version of the cake can be made by frosting orange cake with vanilla pudding frosting.
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Mir-127
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Mir-127
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mir-127 microRNA is a short non-coding RNA molecule with interesting overlapping gene structure. miR-127 functions to regulate the expression levels of genes involved in lung development, placental formation and apoptosis. Aberrant expression of miR-127 has been linked to different cancers.
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Mir-127
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Gene structure
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pri-miR-127 is derived from a separate but overlapping conserved gene cluster coding for miR-433/127. miR-127 and miR-433 are overlapped in a 5'-3' direction. Although the loci could be found on different chromosomes in different species, the structure has been conserved. In mammals including human, chimpanzee, horse, dog, monkey, rat, cow, and mouse, multiple sequence alignments (MSA) between miR-433 and miR127 have shown 95-100% similarity with a conserved distance between miR-433 and miR-127 of 986 to 1007 bp. Moreover, the upstream response elements in the miR-433/127 promoters, including estrogen related receptors response element (ERRE) have been conserved among above species. Data have suggested that that miR-433/127 loci may have evolved from a common gene of origin.
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Mir-127
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Transcription regulation
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Transcription factor binding sites positioned upstream of miRNA precursor play a role in regulating transcription. Activation of miR-127 and miR-433 promoters is mediated by estrogen-related receptor gamma (ERRgamma, NR3B3), which physically associates with their endogenous promoters. Inhibition is regulated by Small heterodimer partner (SHP), which acts in trans. Although miR-127 and miR-433 have common regulatory elements, they have independent promoters and their differential expression pattern is observed.
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Mir-127
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Functional roles
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Down-regulation of the imprinted gene Rtl1 Rtl1 is a key gene in placenta formation and the loss or overexpression of Rlt1 have led to late-fetal or neonatal lethality in mice. miR-127 is located near CpG islands in the imprinted region encoding rtl1 and is normally transcribed in an antisense orientation to the gene. Ectopic expression of miR-127 resulted in a reduction in Rtl1 expression in Human Hela cell and mouse Heppa-1.
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Mir-127
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Functional roles
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Experiments performed in mice showed that Rtl1 was only transcribed from the paternal chromosome, while the maternal allele was degraded. miR-127 and miR-136 however, are only maternally expressed in the somatic cells and thus play a role in antisense regulation of Rtl1 imprinting. Aberrant methylation status of Rtl1 and miR-127 indicated that epigenetic programming is also involved in the process.
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Mir-127
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Functional roles
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Control of fetal lung development miR-127 is highly expressed in late state of fetal development. A disruption to the system by overexpressing miR-127 in a fetal lung organ culture system resulted in defective development shown by a decrease in terminal bud counts and varied bud sizes.
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Mir-127
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Role in disease
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Diffuse large B-cell lymphoma Upregulation of miR-127 caused a downregulation of B-cell lymphoma 6 protein, a proto-oncogene which is usually hypermutated in diffuse large B-cell lymphoma (DLCL). Moreover, differential expression of miR-127 was detected in different type of DLCL. miR-127 levels were significantly higher in the testicular DLCL compared with the nodal and central nervous system DLCL, implying different biological entity of DLCL in different locations.
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Mir-127
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Role in disease
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Hepatocellular carcinoma Inhibition of miR-127 expression is linked with Hepatocellular carcinoma. The mechanistic link was confirmed by a change in BCL6 protein, which is targeted by miR-127.
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Perspective geological correlation
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Perspective geological correlation
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Geological perspective correlation is a theory in geology describing geometrical regularities in the layering of sediments. Seventy percent of the Earth's surface are occupied by sedimentary basins – volumes consisted of sediments accumulated during million years, and alternated by long interruptions in sedimentation (hiatuses). The most noticeable feature of the rocks, which filled the basins, is layering (stratification). Stratigraphy is a part of Geology that investigates the phenomenon of layering. It describes the sequence of layers in the basin as consisted of stratigraphic units. Units are defined on the basis of their lithology and have no clear definition. Geological Perspective Correlation (GPC) is a theory that divided the geological cross-section in units according strong mathematical rule: all borders of layers in this unit obey the law of perspective geometry.Sedimentation layers are mainly created in shallow waters of oceans, seas, and lakes. As new layers are deposited the old ones are sinking deeper due to the weight of accumulating sediments. The content of sedimentary layers (lithological and biological), their order in the sequence, and geometrical characteristics keep records of the history of the Earth, of past climate, sea-level and environment. Most knowledge about the sedimentary basins came from exploration drilling when searching for oil and gas. The essential feature of this information is that each layer is penetrated by the wells in a number of scattered locations. This raises the problem of identifying each layer in all wells – the geological correlation problem The identification is based on comparison of 1) physical and mineralogical characteristics of the particular layer (lithostratigraphy), or 2) petrified remnants in this layer (biostratigraphy). The similarity of layers is decreasing as the distance between the cross-sections increases that leads to ambiguity of the correlation scheme that indicates which layers penetrated at different locations belong to the same body (see A). To improve the results geologists take in consideration the spatial relations between layers, which restricted the number of acceptable correlations. The first restriction was formulated in XVII century: the sequence of layers is the same in any cross-section. The second one was discovered by Haites in 1963: In an undisturbed sequence of layers (strata) the thicknesses (H1 and H2) of any layer observed in two different locations obey the law of perspective geometry, i.e. the perspective ratio K = H1/H2 is the same for all layers in this succession. This theory attracted attention around the world., and particularly in Russia The theory is also a basis of the method of graphical correlation in biostratigraphy widely used in oil and coal industries.
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Perspective geological correlation
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Overview
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The geometry is the main lead to natural resources exploration.For example, the oil geologists are looking for permeable layers of particular geometry, which allows keeping the oil in place (for instance, the domed shape anticlinal trap). The ore geologists are looking for faults in the sediments – the ways, which deliver the melted mantle materials to the upper crust. Knowledge about underground geometry of the sedimentary basins comes from geological observations, geophysical measurements and from drilling. Drilling gives the most detailed information about the position, thickness, physical, chemical and biological characteristics of each layer, but the point is that each well presents all this information in one location on the layer. Because the geometry of a layer can be very complicated it becomes a difficult problem and requires a significant number of drilled wells.
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Perspective geological correlation
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Overview
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The challenge is identifying in each well the interval that belongs to the same layer now or in the past (see A). To do this geologists use all available characteristics of the layer. Only after this it is possible to begin the recovery of the geometry of the layer (to be more precise – the geometry of the top and bottom surfaces of the layer). This procedure is called geological correlation, and the results are presented as acorrelation scheme (A). It is natural that at the beginning of the exploration, when the number of wells is small, the correlation scheme contains expensive mistakes.
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Perspective geological correlation
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Basics of geological correlation
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The Danish scientist Nicolas Steno (1638–1686) is credited with three principles of sedimentation superposition: in undeformed stratigraphic sequences the oldest strata will be at the bottom of the succession, original horizontality: layers of sediment are originally deposited horizontally, lateral continuity: layers of sediments initially extend laterally in all directions.The principles 1 allows defining the temporary relations between neighboring geological bodies, the principle 2 organizes the geometrical pattern of the succession of layers, the principle 3 helps uniting the parts of the layer found in separated geological cross-sections.
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Perspective geological correlation
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Basics of geological correlation
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Practical correlation has a lot of difficulties: fuzzy borders of the layers, variations in composition and structure of the rocks in the layer, unconformities in the sequence of layers, etc. This is why errors in correlation schemes are not seldom. When the distances between available cross-sections are decreasing (for example, by drilling new wells) the quality of correlation is improving, but meanwhile the wrong geological decisions could be made that increases the expenses of geological projects. From Steno's principle of initial horizontality follows that the top borders of the layers (tops) were initially flat, and remained flat until the complete succession stays undisturbed by subsequent tectonic movements, but no regularities about the geometric relations between these flat surfaces in the succession were known. The first to shed light on the problem was Canadian geologist Binner Heites: in 1963 he published the Geological Perspective Correlation hypothesis. Perspective geological correlation is a theory that establishes strong geometrical restrictions on the geometry of the layers in sedimentary deposits.
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Perspective geological correlation
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Perspective geometry in undisturbed succession of layers
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In 1963 the Canadian geologist Binner Heites discovered a strong regularity of the layering in sedimentary basins: the thicknesses of layers within each stratigraphic unit are governed by the law of perspective correspondence. It means that in undisturbed succession on the correlation scheme the straight lines drawn through the border points of the same layer in two cross-sections intersect in one point – center of perspectivity (see B). For geological purposes more convenient geometrical presentation of perspective relations is the correlation plot proposed by Jekhowsky (see C): the depths of the layer's borders in one geologic cross-section are plotted along axis h′ (h1′, h2′, h3′,...), and the position of the same layers in another cross-section are plotted along axis h′′ (h1′′, h2′′, h3′′, ...). Points 1, 2, 3 ... with coordinates (h1′, h1′′), (h2′, h2′′), and (h3′, h3′′), accordingly, are called correlation points, and a curve drawn through these points, a correlation line. Black dots (connectors) represent the relative position of correlated borders on the plot. When the layers geometry satisfies the conditions of perspective correspondence the correlation line is a straight line. In the particular case of parallel layers the inclination of the correlation line is 450. The Perspective Geological Correlation also states that each sedimentary basin consists of a number of stratigraphic units (sequence of layers without unconformities), and in each unit the relations between the thicknesses of the layers in two cross-sections satisfy the perspective geometry conditions with individual ratios K.Heites also concludes that all strata in each unit were governed by the same rate of deposition, and their borders are synchronous time-planes. Each layer has different thicknesses in different locations, but they lasted equally long. It was a significant input in chronostratigraphy.
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Perspective geological correlation
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Perspective geometry in undisturbed succession of layers
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The following are consequences of the basic statements: In different stratigraphic horizons the slopes of the correlation lines are different.
If two adjacent sections have the same slope then both sections belong to the same stratigraphic horizon. The gap between the lines indicates a fault.
If on the correlation line that presents the undisturbed stratigraphic succession one correlation point doesn't fit the line it means thata) the correlation of the tops of the corresponding layer is wrong, or b) lithologic replacement.
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Perspective geological correlation
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Connections to traditional lithostratigraphy
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The Perspective Geological Correlation is well grounded in traditional geology. The method of convergence maps serves for determining the structure of the layer based on the known structure of the layers lying above. It is based on the assumption that the layers are close to parallel. Convergence map shows lines of equal distance (isopach lines) between key layer and target layer. If the layers are parallel the distance between these layers is constant, the structures of both layers are identical, and to determine depths of the target horizon it is enough to get only one deep well, which reached the target layer. But in reality such conditions are extremely rare. In reality restoring the geometry of the target horizon demands a number of deep wells in the area. In this case the standard procedure for calculating the distance between the target layer and key layer in any point in the area is linear interpolation between the known wells. The reliability of the result (the geometrical structure of the target horizon) is estimated by the analysis of the trend of the distances between key horizon and target horizon (isopachs): if the trend is regular, for example, the distances are monotonically changing in one direction, it is a sign of reliability of the reconstruction. In the simplest case the surface of the target horizon is a plain in general position, and the linear interpolation gives the correct result. The assumptions of the convergence method are consequences of the perspective correlations theory, so, the method obtains the theoretical background. The theory also gave an additional criteria for the validity of the reconstructed surface. It defines the stratigraphic interval where layers were deposited without interruption, and where the layers' thicknesses satisfy the law of perspective geometry.The convergence maps deliver the correct result only when the layers belong to such stratigraphic unit.
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Perspective geological correlation
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Testing
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The description of the theory was supplied by a number of cases in support of the theory.
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Perspective geological correlation
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Testing
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The plot (D) shows the correlation plot for two wells in Alberta (Canada): Innisfail 15-8-35-1W5 and Innisfail 7-33-25-lW5 . The cross-section of Innisfail field contains a middle Proterozoic to Paleocene sedimentary succession in excess of 6 km in thickness. The graph shows that the relations between thicknesses of all corresponding layers in these two cross-sections are located on the straight line, i.e. submit to the law of geometrical perspective with the same perspective ratio K. The markers are from conventional correlation scheme.The deviation of the correlation points from the straight line is about 5 feet on average. .The plot (E) demonstrates that Perspective Geological Correlation works at long distances as well. The plot shows the correlation between two wells in Canada 300 miles apart (Saskatchewan and Manitoba) in Silur-Ordovician carbonates (the tilt angle 530 corresponds to K = 1.6).
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Perspective geological correlation
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Testing
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The first review of Heites' publication appeared at 1964 in Russia. It describes in the details the hypothesis and estimates very high its potential. The idea attracted the programmers working on automation of correlation on computers: the known rules of correlation were fuzzy, and it was impossible to formalize them and transform them into algorithms. The restrictions of the geometry of layering observed by Heites allowed compensating the lack of nonformal human knowledge.A group of Russian scientists (Guberman, Ovchinnikova, Maximov) positively tested Heites' hypothesis in different oil-bearing province using the computer program (in Central Asia, Volga-Ural province, West and East Siberia, and Russian Platform). For example, see plot (F). The activity of this group continued in 2000th, and covers new geological provinces around the globe Canada, Kansas, Louisiana, South Welsh. O. Karpenko demonstrated an effective use of perspective correlation in resolving very practical problems of oil exploration. The law of perspective accordance allowed to discover the boundaries of changing the paleotectonic regime in the thin-layered sedimentary rocks, while the regular correlation technic didn't work. At the example of Rubanivsk gas field author demonstrated that the Dashava deposits of Precarpathian External Zone depression can be divided into number of zones of stable sediment accumulation in different conditions. Some zones correlate with the intervals of enhanced gas flow rate. These works show that the hypothesis is correct in the wide variety of geological conditions, it works at long distances, it can serve as a solid test for stratigraphic schemes made by geologists, it reviles the unconformity of layers as small as 1° (G–I), and faults with the amplitude of displacement as small as 1–2 m (G–II), the number of correctly correlated tops in the stratigraphic unit without unconformities has to be not less than three, and as bigger is this number the bigger is the reliability of the result, it is an instrument for correcting the mistakes. Since the publication of Heites' theory in 1963 it was republished in a number of reviews on quantitative methods of correlation (including automatic correlation). Some of the reports (Hansen, Salin, Barinova) demonstrate that the perspective correlation allowed to achieve better reconstruction of the geological structure at the early stages of geological exploration. Hansen describes the controversial history of investigating the complicated Patapsco formation in Maryland and Virginia (USA), and claims that “an adaptation of Heites' (1963) technique of perspective correlation is used to subdivide the Patapsco Formation into consistently defied mapping units”. Salin was able to simplify the stratigraphic description of Khatyr depression (Siberia) by applying perspective correlation. Barinova analysed the structure of Osipovichy gas underground storage (East Europe)) by automatic correlation program baswed on Haites principles. Because of the high resolving power of the method it was recognized the existence of a number of geological faults that break the leakproofness. Because of small displacements of the faults they were not found by the traditional methods of correlation, and rejected by the geological service of the project. Very soon after the storage started functioning significant leakage of gas was recognized
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Perspective geological correlation
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Extension to biostratigraphy
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In 1964 Shaw proposed the method of correlating fossiliferous stratigraphic profiles using the two-axis graph (H). The markers on each axis are the observed depths of lowest (FAD) and highest (LAD) occurrences of a specially defined group of fossils (taxa). The appearances/ disappearances of taxa are regarded as synchronous and used as markers of correlation. When projected on a graph, the corresponding points of two compared profiles form the Line of Correlation (LOC). Shaw showed that the ideal LOC consists of linear segments (H). Such conditions occur when the number of collected fossils is big, and one can be sure that the material covers the complete range of fossils appearance, and FADs and LADs can be accurately determined. In the reality, some sampled ranges will be shorter than true ranges, and this can disturb the linearity of the LOC.
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Perspective geological correlation
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Extension to biostratigraphy
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In every stratigraphic interval correlated ends of the range (FAD or LAD) belong to the same time surface, and in each geological cross-section (well or outcrop) this interval has identical duration but different thickness. It means that accumulation rates (thickness-to-duration ratio = tg β) are different in different locations. From the fact that the relation of durations of the units and their thicknesses are linear follows that in the limits of the linear section of LOC all strata have the same accumulation rate.
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Perspective geological correlation
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Extension to biostratigraphy
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The reliability and accuracy of Shaw's method have been tested by Edwards, using a computer simulation on hypothetical data sets, and by Rubel and Pak in terms of the formal logic and stochastic theory.
The graphical correlation became a very important tool of stratigraphy in coal and oil industries.
In 1988 Nemec showed the equivalence of Haites' perspective correlation, and Shaw's graphical correlation
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Perspective geological correlation
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Sedimentation model
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Based on the theory of perspective correlation in 1986 S. Guberman proposed a model of the process of sedimentation According Haites’ theory in the given sedimentary basin in each stratigraphic unit the condition of perspective correspondence are satisfied in any pair of wells. From this follows that the tops and bases of the layers in this stratigraphic unit satisfy the conditions of perspective correspondence in 3-D space (K). Any three points of a plane define the complete plane. It means that if in three wells the thicknesses of layers belonging to the same stratigraphic unit are known, then the thicknesses of these layers can be calculated for any location in the basin. Accordingly, if the structure of the top border of the stratigraphic unit is known, the structure of any other border in this unit can be calculated.
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Perspective geological correlation
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Sedimentation model
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The model of creating such sophisticated geometrical pattern is based on the first Steno's principle: the strata are originally horizontal, i.e. are planes. It occurs in the shallow waters due to the turbulence of the undersurface layer of water. The second Steno's principle, which indicates the creation of a series of sedimentary layers lying on top of each others, supposes the subsidence of the basin. The sinking of the basin follows the strong geometrical restrictions: the tectonic bloc, which carry the basin, is rotating around the straight line parallel to the water surface, and located onshore (L). As a result, until the moment of main tectonic disturbance all borders of the layers remain flat and the geometrical inter-relations are described as perspective correspondence. In the future the tectonic movements will distort the shape of the layers – the borders will no more be planes, but in majority of cases the changes are smooth and the perspective relations are maintained.
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Perspective geological correlation
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Sedimentation model
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This model allows specifying some geological terms. The Steno's horizontality principle has to state: the top surface of the sediments is horizontal.The conformity is a fundamental notion in stratigraphy. Until now this term is used in two different meanings: a surface between two stratigraphic sequances, and the relationship between two stratigraphic units. Sometimes both were used in the same paragraph (see, page 84).Perspective correlation principle allows to define the notion of conformity: sequence of layers that obey the conditions of geometrical perspective is a unit of conformity. Two neighboring units of conformity are in relation of unconformity. Here is an example that shows that the borders of undisturbed stratigraphic unit in the Middle Carboniferous (Volga-Ural oil province, Russia) initially were plains. In the central part of the area (about 100 km in diameter) were chosen three wells at distances of 10 – 15 km.. The three tops of the stratigraphic unit in the three wells are points in 3D space with coordinates x, y, z, where x and y are present the position of the well on the surface (M), and z is the thickness of the stratigraphic unit in this location. They determine the top plain of the unit as it was at the time of its creation. The three bases determine the bottom plane of the unit at it was at the same time. This allowed calculating the thickness of the stratigraphic unit at any point in the area. Because the area was well enough drilled the calculated numbers can be compared with the real numbers. The average difference equals 2%.
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Momoiro Clover Z
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Momoiro Clover Z
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Momoiro Clover Z (ももいろクローバーZ, Momoiro Kurōbā Zetto) is a Japanese idol girl group, commonly abbreviated as MCZ or Momoclo (ももクロ, Momokuro).
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Momoiro Clover Z
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Momoiro Clover Z
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The four members of MCZ are known for energetic performances, incorporating elements of ballet, gymnastics, and action movies.MCZ is notable for being the first female group to hold a solo concert at National Olympic Stadium in Japan, as well as providing theme music for anime television series such as Sailor Moon, Dragon Ball, and Pokémon.In 2013, the group grossed the fourth highest total sales revenue by a music artist in Japan, with over ¥5.2 billion. During 2016, about 636,000 people attended their live concerts, the most ever for a Japanese female group. MCZ was ranked as the most popular female Japanese group from 2013 to 2018, and 2020 to 2022.MCZ has collaborated with other performers, including a 2015 recording with American hard rock band KISS, marking KISS's first collaborative recording. In 2016, their first overseas tour titled Trans America Ultra Live was held in Hawaii, Los Angeles, and New York. They sold more than 3 million physical copies in Japan.
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Momoiro Clover Z
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Members
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On stage, Momoiro Clover Z members are easily distinguished by the colors of their clothes, similar to the characters from Super Sentai or Power Rangers. In some songs and music videos, the group loosely parodies them.
Before the group made its debut, other girls were in the lineup: Sumire Fujishiro, Manami Ikura, Yukina Kashiwa (later a member of Nogizaka46), Tsukina Takai (later became a member of SKE48), Miyū Wagawa, and Runa Yumikawa.
Timeline
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Momoiro Clover Z
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History
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2008-2009: Conception and beginnings The group was formed in the spring of 2008 as a 5-member unit, originally named Momoiro Clover ("Pink Clover" or, literally, "Peach-Colored Clover"). The name was chosen to imply that the group was composed of innocent girls who wanted to bring happiness to people. Ariyasu Momoka joined the group after their first single. Later in 2011, after the departure of Akari Hayami from the group, management added the letter "Z" to the group's name. The group's slogan is "Idols you can meet right now" (いま、会えるアイドル, Ima, aeru aidoru).
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Momoiro Clover Z
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History
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Momoiro Clover began as a street act in 2008, performing for bystanders in Tokyo's Yoyogi Park. As most members were students attending school on weekdays, the group was active mainly on weekends, leading them to be nicknamed "Weekend Heroines" (週末ヒロイン, Shūmatsu Hiroin). In a one-year period, Momoiro Clover had a number of line-up changes. In March 2009, they became a five-member unit composed of Reni Takagi, Kanako Momota, Akari Hayami, Shiori Tamai, and Ayaka Sasaki.To support and promote their first indie single, "Momoiro Punch", Momoiro Clover took advantage of school holidays from May to August and went by minibus on a long tour across Japan. They gave a total of 104 concerts in 24 electronic stores of the Yamada Denki network. The girls slept in the minivan, and group's managers drove. In the middle of the tour, Momoka Ariyasu was added to the group as a sixth member. The single was sold only at the group's live events and those sales were enough for it to place 11th in the Oricon Daily Singles Chart and 23rd in the weekly chart.
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Momoiro Clover Z
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History
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2010: Major debut In March 2010, the girls stated their goals: to take first place on Oricon, to participate in Kōhaku Uta Gassen, to perform at Budokan. They usually performed in a small club with live music or on a roof of a department store. They sometimes set a simulated stage of National Olympic Stadium, where notable musicians are allowed to perform.Their first major-label single "Ikuze! Kaitō Shōjo" was released in May. The single debuted on Japan's Oricon Daily Singles Chart at the first position, and at number 3 for the week. Momoiro Clover then moved to King Records. The group's first single with King was "Pinky Jones", composed by Narasaki from the Japanese rock band Coaltar of the Deepers with a "more chaotic" approach than previous songs. December 24 marked Momoiro Clover's first solo concert at a concert hall. Nihon Seinenkan, a venue with a capacity of 1,300 seats, was sold out in 30 minutes.
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Momoiro Clover Z
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History
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2011: Shift to Momoiro Clover "Z" In January 2011 at the release event for a new song, sub-leader Akari Hayami stated that she had decided to withdraw from the group in April. Hayami explained that her character was not suited to being an idol and that her dream was to become an actress. At the April 10 Akari Hayami "graduation" concert, the group's management announced the name change to Momoiro Clover Z after Hayami's departure. In Japan, Z(ゼット) symbolizes ultimateness and this letter is often appended to a title (e.g., Mazinger Z and Dragon Ball Z). Z is officially pronounced as (non-US pronunciation) when the name is used in spoken English. The band has gone on record saying in an interview that the Z in the title is a reference to the famous anime series, Dragon Ball Z stating "The Z in our name is a very obvious reference to Dragon Ball Z" and that "It's a awesome and very influential series".
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Momoiro Clover Z
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History
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Momoiro Clover Z's first single after Hayami's departure was "Z Densetsu: Owarinaki Kakumei", accompanied by a new group image and stage performance. The girls wore outfits with helmets and so-called "transformation belts" reminiscent of Japanese superhero movies, and the music video also borrowed from such "Super Sentai" imagery. In July, Momoiro Clover Z released their first album, Battle and Romance. Later in December, Hotexpress described the band as the number-one breakthrough idol artist of 2011 and stated that the album became a big turning point for them. Next February, Battle and Romance won the Grand Prix at the CD Shop Awards as the best CD of the year selected by music shop employees from all over the country. Momoiro Clover Z was the first idol group to win the award. On Christmas Day, 2011, Momoiro Clover Z gave a concert at Saitama Super Arena to their biggest audience to date: all 10,000 tickets were sold out.
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Momoiro Clover Z
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History
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2012: Rising popularity in Japan In May 2012, Momoiro Clover Z performed in Putrajaya, Malaysia. The former Prime Minister, Najib Razak, personally greeted the group. In June, Momoiro Clover Z opened a national tour, which closed with a sold-out show at Seibu Dome in August to a capacity crowd of 37,000 fans. Both dates were broadcast live to selected cinemas across Japan, the latter also to Taiwan and Hong Kong.
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Momoiro Clover Z
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History
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The group recorded an ending theme song for Pokémon's Best Wishes series (titled "Mite Mite Kocchichi" and included in the eighth single "Otome Sensō" as a coupling track). In July, Momoiro Clover Z performed at Japan Expo 2012 in Paris.Momoiro Clover Z's ninth single "Saraba, Itoshiki Kanashimitachi yo", which appeared in November, topped the Billboard Japan Hot 100 chart, becoming their first single to do so. They contributed to the anime Joshiraku with "Nippon Egao Hyakkei" as the ending theme which was released on 5 September with a prior early release in iTunes Japan on 22 August.On December 31, Momoiro Clover Z performed at Kōhaku Uta Gassen, an annual New-Year-Eve music show hosted by NHK, for the first time. Going to Kōhaku had been the group's goal for a long time. During the January 1 Ustream broadcast, Momoiro Clover Z made several announcements: that the band set a new goal for itself — to give a concert at the National Olympic Stadium, an arena with 60–70,000 capacity, that they would release a new album in spring, and that Momoka Ariyasu had to undergo a throat treatment and she would not sing or even talk until the end of January. The treatment was subsequently prolonged for another month, until the end of February. During the group's live Ustream broadcasts, Momoka communicated by drawing and writing on a markerboard. At live performances, other members took turns in singing her parts.
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Momoiro Clover Z
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History
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2013: 5th Dimension Momoiro Clover Z's second full-length album 5th Dimension was released in April. It sold 180,000 copies in the first week and debuted on top of the Oricon charts, with the first album Battle and Romance resurging to number two. Finally, it won a platinum disk award. In August, Momoiro Clover Z held a concert at Nissan Stadium. It has the largest capacity in Japan.
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Momoiro Clover Z
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History
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2014: Dream come true In March, the group held a solo concert at National Olympic Stadium, realizing one of their dreams since the debut. Such solo concerts had only been performed by six groups until then. Momoiro Clover Z was the first female group and also became the fastest group ever, which achieved that in six years. As a two-day concert, a total of 150,000 people watched in the stadium and at live viewing venues.In May, the group released their 11th single "Naite mo Iin Da yo"; B-side "My Dear Fellow" made its debut at Yankee Stadium when it was used for Masahiro Tanaka's warm up for his first game with the New York Yankees. The group also provided the theme music for the anime Sailor Moon Crystal. The title is "Moon Pride" (the group's 12th single released in July).In August, the group performed at Lady Gaga's concert as an opening act. It was a part of Gaga's world tour named "ArtRave: The Artpop Ball" and held in Japan. Momoiro Clover Z was selected by Gaga herself.
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Momoiro Clover Z
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History
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2015: Collaboration with KISS On January 28, 2015, Momoiro Clover Z released a collaboration single with the American hard rock band KISS, titled "Yume no Ukiyo ni Saitemina". It was the first time for KISS to release a collaboration CD with another artist. In Japan, it was released physically in two versions: Momoiro Clover Z edition (CD+Blu-ray) and KISS edition (CD only). An alternate mix of the single's title song was also included as an opening track on the Japanese-only SHM-CD album Best of KISS 40, released in Japan on the same day.In February 2015, Momoiro Clover Z were removed from a television performance due to controversy surrounding an appearance in blackface alongside Rats & Star.Momoiro Clover Z provided the theme song, "Z no Chikai" which was released as their fifteenth single on April 29, 2015, for the Dragon Ball Z: Resurrection 'F' theatrical anime film. The group also voiced the Angels at the end of the film.
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Momoiro Clover Z
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History
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2016: Amaranthus/Hakkin no Yoake and Trans America Ultra Live The group released their third studio album Amaranthus and fourth studio album Hakkin no Yoake in a double release in Japan on February 17, 2016. The albums debuted at #1 and #2 in the Oricon weekly albums chart. The group held a dome trek tour for the two albums.In early April 2016, the group announced their first overseas tour titled Trans America Ultra Live and appeared in Hawaii, Los Angeles and New York 2017: MTV Unplugged 2018: 10th Anniversary Best Album On January 21, Momoka Ariyasu graduated from the group, leaving MCZ with only four members. In April, they released their 18th single, "Xiao yi Xiao". On May 23, they released a new best of album for their tenth anniversary called Momo mo Juu, Bancha mo Debana.
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