Computer generation of arbitrary functions
Computer generation of data matrixes for arbitrary functions by interpolation series
Fogarty, L. E.↗
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Stochastic journeys of cell progenies through compartments and the role of self-renewal, symmetric and asymmetric division
Abstract Division and differentiation events by which cell populations with specific functions are generated often take place as part of a developmental programme, which can be represented by a sequence of compartments. A compartment is the set of cells with common characteristics; sharing, for instance, a spatial location or a phenotype. Differentiation events are transitions from one compartment to the next. Cells may also die or divide. We consider three different types of division events: (i) where both daughter cells inherit the mother’s phenotype (self-renewal), (ii) where only one of the daughters changes phenotype (asymmetric division), and (iii) where both daughters change phenotype (symmetric division). The self-renewal probability in each compartment determines whether the progeny of a single cell, moving through the sequence of compartments, is finite or grows without bound. We analyse the progeny stochastic dynamics with probability generating functions. In the case of self-renewal, by following one of the daughters after any division event, we may construct lifelines containing only one cell at any time. We analyse the number of divisions along such lines, and the compartment where lines terminate with a death event. Analysis and numerical simulations are applied to a five-compartment model of the gradual differentiation of hematopoietic stem cells and to a model of thymocyte development: from pre-double positive to single positive (SP) cells with a bifurcation to either SP4 or SP8 in the last compartment of the sequence.
Science & Technology - Other Topics↗
Piecewise Linear Membership Function Generator-Divider Approach
In this paper a simple, inexpensive, membership function circuit for fuzzy controllers is presented. The proposed circuit may be used to generate a general trapezoidal membership function. The slope and horizontal shift are fully programmable parameters.
Hart, Ron↗
Crater saturation and equilibrium - A Monte Carlo simulation
Conditions of crater saturation and equilibrium have been simulated with a Monte Carlo computer program which utilizes a generating function of the form N = b x D to the -a. The following conclusions have been deduced from the results of the model: (1) saturation and equilibrium for large craters occur at crater densities substantially greater than those observed on the moon, Mars, and Mercury, an indication that the observed populations are essentially production populations, (2) generating functions with a greater than 2 lead to final crater populations with a = 2, (3) generating functions with a between 2 and 1.5 lead to crater populations with the parameter a approaching 1.0, and (4) changes in the slope of crater populations occur gradually and over a wide interval of crater densities and diameters as saturation is approached.
Woronow, A.↗
Spline methods for approximating quantile functions and generating random samples
Two cubic spline formulations are presented for representing the quantile function (inverse cumulative distribution function) of a random sample of data. Both B-spline and rational spline approximations are compared with analytic representations of the quantile function. It is also shown how these representations can be used to generate random samples for use in simulation studies. Comparisons are made on samples generated from known distributions and a sample of experimental data. The spline representations are more accurate for multimodal and skewed samples and to require much less time to generate samples than the analytic representation.
Schiess, J. R.↗
Improved Blending-Function Algebraic Generation Of Grids
Method of algebraic generation of grids used in computing flows incorporates blending-function techniques to obtain high degree of orthogonality of each grid on its bounding surfaces and to blend grid smoothly, making it conform to all boundaries. Demonstrated in two dimensions, and applied in continuing development of software for real-time interactive generation of three-dimensional grids with color graphical displays. Software used routinely in generating grids for computing flows of practical interest.
Ching-Chung Luh, Raymond↗
Generalized compliant motion primitive
This invention relates to a general primitive for controlling a telerobot with a set of input parameters. The primitive includes a trajectory generator; a teleoperation sensor; a joint limit generator; a force setpoint generator; a dither function generator, which produces telerobot motion inputs in a common coordinate frame for simultaneous combination in sensor summers. Virtual return spring motion input is provided by a restoration spring subsystem. The novel features of this invention include use of a single general motion primitive at a remote site to permit the shared and supervisory control of the robot manipulator to perform tasks via a remotely transferred input parameter set.
Backes, Paul G.↗
Analyzing the test process using structural coverage
A large, commercially developed FORTRAN program was modified to produce structural coverage metrics. The modified program was executed on a set of functionally generated acceptance tests and a large sample of operational usage cases. The resulting structural coverage metrics are combined with fault and error data to evaluate structural coverage. It was shown that in the software environment the functionally generated tests seem to be a good approximation of operational use. The relative proportions of the exercised statement subclasses change as the structural coverage of the program increases. A method was also proposed for evaluating if two sets of input data exercise a program in a similar manner. Evidence was provided that implies that in this environment, faults revealed in a procedure are independent of the number of times the procedure is executed and that it may be reasonable to use procedure coverage in software models that use statement coverage. Finally, the evidence suggests that it may be possible to use structural coverage to aid in the management of the acceptance test processed.
Ramsey, James↗
Software Tools for Developing and Simulating the NASA LaRC CMF Motion Base
The NASA Langley Research Center (LaRC) Cockpit Motion Facility (CMF) motion base has provided many design and analysis challenges. In the process of addressing these challenges, a comprehensive suite of software tools was developed. The software tools development began with a detailed MATLAB/Simulink model of the motion base which was used primarily for safety loads prediction, design of the closed loop compensator and development of the motion base safety systems1. A Simulink model of the digital control law, from which a portion of the embedded code is directly generated, was later added to this model to form a closed loop system model. Concurrently, software that runs on a PC was created to display and record motion base parameters. It includes a user interface for controlling time history displays, strip chart displays, data storage, and initializing of function generators used during motion base testing. Finally, a software tool was developed for kinematic analysis and prediction of mechanical clearances for the motion system. These tools work together in an integrated package to support normal operations of the motion base, simulate the end to end operation of the motion base system providing facilities for software-in-the-loop testing, mechanical geometry and sensor data visualizations, and function generator setup and evaluation.
Bryant, Richard B., Jr.↗
Finding the complete path and weight enumerators of convolutional codes
A method for obtaining the complete path enumerator T(D, L, I) of a convolutional code is described. A system of algebraic equations is solved, using a new algorithm for computing determinants, to obtain T(D, L, I) for the (7,1/2) NASA standard code. Generating functions, derived from T(D, L, I) are used to upper bound Viterbi decoder error rates. This technique is currently feasible for constraint length K less than 10 codes. A practical, fast algorithm is presented for computing the leading nonzero coefficients of the generating functions used to bound the performance of constraint length K less than 20 codes. Code profiles with about 50 nonzero coefficients are obtained with this algorithm for the experimental K = 15, rate 1/4, code in the Galileo mission and for the proposed K = 15, rate 1/6, 2-dB code.
Onyszchuk, I.↗
Force-free magnetic fields - Is there a 'loss of equilibrium'?
This paper examines concept in solar physics that is known as loss of equilibrium in which a sequence of force-free magnetic fields, said to represent a possible quasi-static evolution of solar magnetic fields, reaches a critical configuration beyond which no acceptable solution of the prescribed form exists. This concept is used to explain eruptive phenomena ranging from solar flares to coronal mass ejections. Certain sequences of force-free configurations are discussed that exhibit a loss of equilibrium, and it is argued that the concept is devoid of physical significance since each sequence is defined a way that does not represent an acceptable thought experiment. For example, the sequence may be defined in terms of a global constraint on the boundary conditions, or the evolution of the sequence may require the creation of mgnetic flux that is not connected to the photosphere and is not present in the original configuration. The global constraints typically occur in using the so-called generating function method. An acceptance thought experiment is proposed to specify the field configuration in terms of photospheric boundary conditions comprising the normal component of the field and the field-line connectivity. Consider a magnetic-field sequence that, when described in terms of a generating function, exhibits a loss of equilibrium and show that, when one instead defines the sequence in terms of the corresponding boundary conditions, the sequence is well behaved.
Klimchuk, J. A.↗
Generalized serial search code acquisition - The equivalent circular state diagram approach
A transform-domain method for deriving the generating function of the acquisition process resulting from an arbitrary serial search strategy is presented. The method relies on equivalent circular state diagrams, uses Mason's formula from flow-graph theory, and employs a minimum number of required parameters. The transform-domain approach is briefly described and the concept of equivalent circular state diagrams is introduced and exploited to derive the generating function and resulting mean acquisition time for three particular cases of interest, the continuous/center Z search, the broken/center Z search, and the expanding window search. An optimization of the latter technique is performed whereby the number of partial windows which minimizes the mean acquisition time is determined. The numerical results satisfy certain intuitive predictions and provide useful design guidelines for such systems.
Polydoros, A.↗
Immobilizing a Lehn-Type Catalyst with Nitrocyclocondensation Chemistries: CO 2 Reduction on Silicon Hybrid Photoelectrodes
Here, we present the first examples of installing a redox reporter and CO 2 reduction (CO 2 R) catalyst onto freshly HF-etched Si (photo)electrodes using a solution-phase nitrocyclocondensation (NCC) reaction. Previous studies detailed the mechanism of NCC reactions on Si under ultrahigh vacuum conditions but have not applied these chemistries to generate functional (photo)electrodes. Installing 4-nitrophenyl ferrocene (4-NpFc) molecules directly onto degenerately doped p + Si allowed us to evaluate the effects of different NCC reaction conditions on coverage (e.g., 3.6 ± 1.2 × 10 –11 mol/cm 2 ) and electrochemical reversibility. The 4-NpFc molecules remained immobilized under the reducing potentials (−2.0 V vs Fc +/0 in acetonitrile) needed to drive molecular CO 2 R catalysts. Installing 4-nitroaniline (4-NA) molecules onto low-doped pSi allowed us to couple Lehn-type Re(I) catalysts with pendant carboxylic acids. The CO Faradaic efficiency of CO production under 1-sun illumination (−2.15 V vs Fc +/0 ) was 23% in CO 2 -saturated electrolyte, a value that surpasses previous examples of CO 2 R catalyst monolayers on Si. These two examples highlight the versatility of solution-phase NCC attachment chemistries for generating functional Si (photo)electrodes.
catalysis↗
Scattering neutrinos, spin models, and permutations
We consider a class of Heisenberg all-to-all coupled spin models inspired by neutrino interactions in a supernova with N degrees of freedom. These models are characterized by a coupling matrix that is relatively simple in the sense that there are only a few, relative to N , nontrivial eigenvalues, in distinction to the classic Heisenberg spin-glass models, leading to distinct behavior in both the high-temperature and low-temperature regimes. When the momenta of the neutrinos are uniform and random in directions, we can calculate the large- N partition function for the quantum Heisenberg model. In particular, the high-temperature partition function predicts a non-Gaussian density of states, providing interesting counterexamples showing the limits of general theorems on the density of states for quantum spin models. We can repeat the same argument for classical Heisenberg models, also known as rotor models, and we find the high-temperature expansion is completely controlled by the eigenvalues of the coupling matrix, and again predicts non-Gaussian behavior for the density of states as long as the number of eigenvalues does not scale linearly with N . Indeed, we derive the amusing fact that these partition functions are essentially the generating function for counting permutations in the high-temperature regime. Finally, for the case relevant to neutrinos in a supernova, we identify the low-temperature phase as a unique state with the direction of the momenta of the neutrino dictating its coherent state in flavor-space, a state we dub the “flavor-momentum-locked” state. Published by the American Physical Society 2025
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Research in methods of generating Liapunov functions Final report
Liapunov functions for nonlinear systems of differential equations
Drake, R.↗
Topological formulation of network functions without generation of k-trees.
Linear network analysis by topological formulas for derivation of k-tree terms without generation of k-trees of graph
Chan, S. P.↗
Multivariant function model generation
The development of computer programs applicable to space vehicle guidance was conducted. The subjects discussed are as follows: (1) determination of optimum reentry trajectories, (2) development of equations for performance of trajectory computation, (3) vehicle control for fuel optimization, (4) development of equations for performance trajectory computations, (5) applications and solution of Hamilton-Jacobi equation, and (6) stresses in dome shaped shells with discontinuities at the apex.
Source record↗
Lyapunov function gradient generated robust control in the absence of the nominal stabilizing control
A relevant facet of the application of Lyapunov gradient-generated robust control to unstable linear autonomous plants is explored. It is demonstrated that if the plant, the output, and the nominal stabilizing control satisfy certain conditions, then the robust component alone stabilizes the nominal plant. An example characterized by two zero eigenvalues and two negative real value poles is presented. These results assure that the robust component will fulfill the role of nominal stabilization successfully so long as the possible magnitude of the robust component can overcome the contribution of the instability to positiveness of the Lyapunov rate.
Blackwell, C. C.↗