“…Using a computational algorithm based on recently developed tools from Persistent Homology theory in the field of algebraic topology, we find that the patterns of neuronal co-firing can, in fact, convey topological information about the environment in a biologically realistic length of time. …”
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“…RESULTS: Here we describe a hidden Markov model (HMM), an algebraic system, and Markov chain Monte Carlo (MCMC) sampling strategies for alignment of multiple sequence motifs. …”
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“…Our hybrid reconstruction technique is based on an algebraic model of data fidelity which substitutes the EID data into the data fidelity term associated with the PCD reconstruction, resulting in a joint reconstruction problem. …”
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“…This is, to the best of our knowledge, the first study that presents an algebraic transformation for simulation of all possible ECG cable reversals, including those with displaced WCT, where most of the leads appear with distorted morphology. …”
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“…We formulate and prove two sufficient conditions yielding [Formula: see text] as injective for given [Formula: see text] and analyze their asymptotic character which forms an important question for [Formula: see text] getting sufficiently dense. The algebraic conditions established herein are also geometrically visualized in 3D plots with the aid of Mathematica. …”
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“…We then prepare various necessary matrix study tools, including a general theory on linear or nonlinear algebraic matrix identities, a group of expansion formulas for calculating ranks of block matrices, two groups of explicit formulas for calculating the maximum and minimum ranks of [Formula: see text] , as well as necessary and sufficient conditions for [Formula: see text] to be invariant with respect to the choice of the generalized inverses, etc. …”
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“…We devise an algorithm where sort as an intrinsic property of both numbers and labels, is used to generate the parameters. Algebraically, point-biserial variation is represented by a Cartesian product of statistical parameters for two sets of [Image: see text] data, and the difference between mean values (δ) corresponds to the representation of variation in the center of mass coordinates, (δ, μ). …”
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“…DBH was estimated by a computationally robust algebraic circle-fitting algorithm through hierarchical cluster analysis (HCA). …”
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“…However, we cannot say that corneal pathological vessels do not contain β2-type adrenergic receptors, because the effect of adrenaline may be an algebraic sum between vasoconstriction produced by stimulating α-adrenergic receptors and vasodilation produced by stimulating β2-adrenergic receptors, but in which the vasodilating effect may be masked by the vasoconstrictor effect given by a higher density of α-adrenergic receptors. …”
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“…By integrating genetics, biophysics, deep learning, and algebraic topology, we reveal that most of the 462 mutations on the receptor-binding domain (RBD) will weaken the binding of S protein and antibodies and disrupt the efficacy and reliability of antibody therapies and vaccines. …”
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“…Then, a trilateration solution can be algebraically acquired from theses ranges, in order to fix user’s actual location. …”
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“…Accordingly, the rectification coefficient can be obtained by solving a simple algebraic expression. There are several structure factors that cause noticeable effects on the thermal rectification properties. …”
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“…On a theoretical level, interpreting ICHD3 differential diagnosis as poset allows for researchers to translate differential diagnoses sets topologically, algebraically, and categorically.…”
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“…We next introduce a method to identify the feasibility parametric regions that allow a system to meet a set of physiological constraints that can be represented in mathematical terms through algebraic equations. This technique is based on applying the outer-approximation based algorithm iteratively over a reduced search space in order to identify regions that contain feasible solutions to the problem and discard others in which no feasible solution exists. …”
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“…Furthermore, total amino-acid concentrations, expressed as the algebraic sum of all amino acids tested, showed a trend toward lower levels in cases vs controls. …”
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“…JSim uses Mathematical Modeling Language (MML) a declarative syntax specifying algebraic and differential equations. Imperative constructs written in other languages (MATLAB, FORTRAN, C++, etc.) are accessed through procedure calls. …”
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“…We have taken spatial learning as our starting point, computationally modeling the activity of place cells using methods derived from algebraic topology, especially persistent homology. …”
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“…CellML is an XML format designed to encode biophysically based systems of ordinary differential equations and both linear and non-linear algebraic equations. A primary design goal of CellML is to allow mathematical models to be encoded in a modular and reusable format to aid reproducibility and interoperability of modeling studies. …”
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“…METHODS: Data were obtained from Yelp that captures a variety of parameters for every business listed in their database as of October 28, 2014, that was tagged as a “hookah bar” and operating in New York State. Two algebraic models were created: one estimated the date of opening of a hookah bar based on the first Yelp review received and the other estimated whether the bar was open or closed based on the date of the most recent Yelp review. …”
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“…There were 28 cases in group A [tube voltage, 100 kV; contrast agent, iohexol (350 mg I/ml), reconstructed by filtered back projection] and 31 cases in group B [tube voltage, 80 kV; contrast agent, iodixanol (270 mg I/ml), reconstructed by algebraic reconstruction technique]. The artery CT value, signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), dose length product, effective dose (ED) of radiation and brain iodine intake of both groups were measured and statistically analyzed. …”
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