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Due to the limitations of the acquisition procedure (limited measure range, occlusions due to the object shape, etc)., not all pixel positions i∈I may have a valid corresponding point p i ∈R, therefore only a subset I V ⊆ I of valid points is acquired for each image.
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Formally, an up-to-date pattern is a pair with the itemset and its valid corresponding lifetime in which the user-defined minimum support threshold must be satisfied.
In order to invert the quantization process, an adversary who possesses the biohash (b) of a valid system user and corresponding random projection matrix (R) uses an arbitrary biometric feature vector x f to simulate the biometric hashing procedure through random projection and obtain an intermediate vector z f =R x f.
With the help of a huge database of biometric features along with the biohash vector of a valid user and the corresponding secret key, a biometric image that creates a sufficiently close biohash to the desired one is found and used for illegitimate authentication.
For the reverse direction, we know that T spans all vertices of G and therefore is a valid clonal tree with corresponding clonal matrix B. Lemma 5 tells us that B, and hence also T, generate F. Thus, there is a 1-1 correspondence between spanning arborescences in G that satisfy the sum condition and solutions to the VAFFP.
For the reverse direction, we know that T spans all vertices of G and therefore is a valid clonal tree with corresponding clonal matrix B. Lemma 5 tells us that B, and hence also T, generate F. T generates F = [ f p j ] if and only if T is a spanning arborescence of G such that Equation (2) holds for all f pj.
For the given value of, if the solution of (23a)–(23d) satisfies (23c) with equality, the corresponding solution represents a valid power partitioning and this value of corresponds to twice a weighted sum of achievable rates.
Each conflict graph is corresponding to a valid assignment of licensed channels to the requesting OBU pairs.
Here, we assume that an adversary gains access to the biohash vector of a valid system user and the corresponding secret key and estimates a new real-valued feature vector from the binary biohash in order to authenticate to the system.
A phenotype is defined as the set, or sets, of concentrations and fluxes corresponding to a valid combination of dominant processes functioning within a system.
Here we first describe two linear-time algorithms that, given a valid Lyndon array λ, compute a corresponding string — one for an alphabet of size n, the other for a smaller alphabet.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com