scholarly journals Equivalent Analytical Functions of Sums of Sigmoid like Transcendental Functions

2018 ◽  
Vol 3 (2) ◽  
pp. 403-408 ◽  
Author(s):  
J. Takács
Keyword(s):  
Analytical Method ◽  
Computer Assisted ◽  
Mathematical Solution ◽  
Equivalent Function ◽  
Numerical Computer ◽  
Analytical Functions ◽  
Numerical Process ◽  
Transcendental Functions ◽  
Mathematical Operations

AbstractThere is no mathematical solution to adding up transcendental functions other than numerical process. This paper put forward analytical method to model the sum of sigmoid like functions with an equivalent function. The Brillouin and Langevin as well as the error function, the tanh, sigmoid and the tan-1 functions are investigated, their equivalent functions are calculated for four components and the error between the numerical (computer assisted) result and the equivalent function is tested for accuracy. The best modelling function, the most useful to include into mathematical operations, is pointed out finally, based on its performance and convenience. The paper intends to help people involved mostly in modelling hysteresis in Magnetism and other field of research in physics.

Toward Automatic Process Simulators: Part I—Modular Numerical Procedures

1998 ◽  
Vol 120 (1) ◽  
pp. 1-8 ◽  
Author(s):  
E. Sciubba
Keyword(s):  
Process Design ◽  
Process Simulation ◽  
Automatic Process ◽  
Computer Assisted ◽  
Qualitative Synthesis ◽  
Complex Activity ◽  
General Process ◽  
Numerical Process ◽  
Computer Codes ◽  
Quantitative Calculations

This paper presents a general design approach involving automatic, intelligent process simulation procedures. The aim is to derive a general set of design principles and methodologies that can be developed into computer-assisted procedures. This first part deals with numerical, quantitative calculations, i.e., with what commonly goes under the name of “Numerical Process Simulation.” It is argued that the existing design methods can result in computer codes or packages that perform exactly (and deterministically) the numerical operations an engineer would perform. It is also shown that modularity in these codes is dictated by the necessity of automatically implementing numerical procedures that depend on the structure of the process under examination, rather than by user’s convenience and ease of maintenance. An example of a modular, structure-oriented code (CAMEL) is given and discussed in detail, while numerical applications are discussed elsewhere [4]. The second part deals with the more complex qualitative approach to process design, i.e., with the possibility of implementing automatic “expert” procedures that perform the same conceptual tasks as human process engineers. It is shown that by means of Artificial Intelligence techniques it is possible to mimic (to an extent) the “thinking patterns” of a human expert, and to produce process schemes that are both acceptable and realistic. A general process synthesis package (COLOMBO) is described and some of its applications discussed. The main goal of the two parts of the paper is to show that the very complex activity of process design can be executed automatically, not only in principle, but in actual applications, and that both qualitative synthesis and quantitative calculations are possible with the present state of the art of our computational facilities.

scholarly journals Modification of Semi-Analytical Method Applied System of ODE

2020 ◽  
Vol 14 (6) ◽  
pp. 75
Author(s):  
OPhir Nave
Keyword(s):  
Breast Cancer ◽  
Mathematical Model ◽  
Homotopy Analysis Method ◽  
Analytical Method ◽  
Analysis Method ◽  
Analytical Functions ◽  
Ode System ◽  
Homotopy Analysis ◽  
Simulation Results ◽  
The Right

In this study, we modify the well-known semi-analytical method called the Homotopy Analysis Method (HAM), such that the right-hand side of a given ODE system is decomposed to a sum of analytical functions. We called the new semi-analytical method: decomposition of the Homotopy Analysis Method (DHAM). We applied the new method to a breast cancer mathematical model. We compared the DHAM results to HAM and numerical simulations. We concluded that the DHAM results are closer to the numerical simulation results than the HAM.

Densitometric Identification of Primitive Erythroblasts After Reaction With Diaminobenzidine

1973 ◽  
Vol 31 ◽  
pp. 328-329
Author(s):  
John A. Trotter
Keyword(s):  
Red Blood Cells ◽  
Analytical Method ◽  
Blood Cells ◽  
Guinea Pigs ◽  
Specific Protein ◽  
Visual Examination ◽  
Hemoglobin Synthesis ◽  
Peroxidatic Activity ◽  
Small Density

Hemoglobin is the specific protein of red blood cells. Those cells in which hemoglobin synthesis is initiated are the earliest cells that can presently be considered to be committed to erythropoiesis. In order to identify such early cells electron microscopically, we have made use of the peroxidatic activity of hemoglobin by reacting the marrow of erythropoietically stimulated guinea pigs with diaminobenzidine (DAB). The reaction product appeared as a diffuse and amorphous electron opacity throughout the cytoplasm of reactive cells. The detection of small density increases of such a diffuse nature required an analytical method more sensitive and reliable than the visual examination of micrographs. A procedure was therefore devised for the evaluation of micrographs (negatives) with a densitometer (Weston Photographic Analyzer).

3-D organization of fibrinogen receptors using computer reconstruction and whole-mount microscopy

1988 ◽  
Vol 46 ◽  
pp. 30-31
Author(s):  
E. T. O'Toole ◽  
R. R. Hantgan ◽  
J. C. Lewis
Keyword(s):  
Whole Blood ◽  
Colloidal Gold ◽  
Blood Platelets ◽  
Cell Contact ◽  
Computer Assisted ◽  
Adherent Cells ◽  
Differential Centrifugation ◽  
Computer Reconstruction ◽  
Sds Page ◽  
Whole Mount

Thrombocytes (TC), the avian equivalent of blood platelets, support hemostasis by aggregating at sites of injury. Studies in our lab suggested that fibrinogen (fib) is a requisite cofactor for TC aggregation but operates by an undefined mechanism. To study the interaction of fib with TC and to identify fib receptors on cells, fib was purified from pigeon plasma, conjugated to colloidal gold and used both to facilitate aggregation and as a receptor probe. Described is the application of computer assisted reconstruction and stereo whole mount microscopy to visualize the 3-D organization of fib receptors at sites of cell contact in TC aggregates and on adherent cells.Pigeon TC were obtained from citrated whole blood by differential centrifugation, washed with Ca++ free Hank's balanced salts containing 0.3% EDTA (pH 6.5) and resuspended in Ca++ free Hank's. Pigeon fib was isolated by precipitation with PEG-1000 and the purity assessed by SDS-PAGE. Fib was conjugated to 25nm colloidal gold by vortexing and the conjugates used as the ligand to identify fib receptors.

Bulk standards for low-temperature biological x-ray microanalysis

1984 ◽  
Vol 42 ◽  
pp. 282-283
Author(s):  
P. Echlin ◽  
M. McKoon ◽  
E.S. Taylor ◽  
C.E. Thomas ◽  
K.L. Maloney ◽  
...  
Keyword(s):  
Phase Separation ◽  
Low Temperature ◽  
Analytical Method ◽  
Salt Solutions ◽  
Absolute Concentration ◽  
Cooling Process ◽  
X Ray ◽  
The Absolute ◽  
Analytical Procedures ◽  
Electrical Conductors

Although sections of frozen salt solutions have been used as standards for x-ray microanalysis, such solutions are less useful when analysed in the bulk form. They are poor thermal and electrical conductors and severe phase separation occurs during the cooling process. Following a suggestion by Whitecross et al we have made up a series of salt solutions containing a small amount of graphite to improve the sample conductivity. In addition, we have incorporated a polymer to ensure the formation of microcrystalline ice and a consequent homogenity of salt dispersion within the frozen matrix. The mixtures have been used to standardize the analytical procedures applied to frozen hydrated bulk specimens based on the peak/background analytical method and to measure the absolute concentration of elements in developing roots.

Computer Assisted Image Reconstruction of Oligomer Structure

1976 ◽  
Vol 34 ◽  
pp. 472-473
Author(s):  
A.M. Jones ◽  
A. Max Fiskin
Keyword(s):  
Three Dimensional ◽  
Depth Of Field ◽  
Computer Assisted ◽  
Projection Data ◽  
Two Dimensional ◽  
Single Particles ◽  
Dimensional Reconstruction ◽  
Computer Assisted Image ◽  
The Fourier Transform ◽  
Space Approach

If the tilt of a specimen can be varied either by the strategy of observing identical particles orientated randomly or by use of a eucentric goniometer stage, three dimensional reconstruction procedures are available (l). If the specimens, such as small protein aggregates, lack periodicity, direct space methods compete favorably in ease of implementation with reconstruction by the Fourier (transform) space approach (2). Regardless of method, reconstruction is possible because useful specimen thicknesses are always much less than the depth of field in an electron microscope. Thus electron images record the amount of stain in columns of the object normal to the recording plates. For single particles, practical considerations dictate that the specimen be tilted precisely about a single axis. In so doing a reconstructed image is achieved serially from two-dimensional sections which in turn are generated by a series of back-to-front lines of projection data.

Biodegradable polyester neuroprostheses promote the reconnection of separated peripheral nerve stubs

1992 ◽  
Vol 50 (2) ◽  
pp. 1094-1095
Author(s):  
Beverly L. Giammara ◽  
Jennifer S. Stevenson ◽  
Peggy E. Yates ◽  
Robert H. Gunderson ◽  
Jacob S. Hanker
Keyword(s):  
Image Analysis ◽  
Basement Membrane ◽  
Periodic Acid ◽  
Light And Electron Microscopy ◽  
Computer Assisted ◽  
Type Iii Collagen ◽  
Image Analysis System ◽  
Biodegradable Polyester ◽  
Adult Rats ◽  
Type Iv

An 11mm length of sciatic nerve was removed from 10 anesthetized adult rats and replaced by a biodegradable polyester Vicryl™ mesh sleeve which was then injected with the basement membrane gel, Matrigel™. It was noted that leg sensation and movement were much improved after 30 to 45 days and upon sacrifice nerve reconnection was noted in all animals. Epoxy sections of the repaired nerves were compared with those of the excised segments by the use of a variation of the PAS reaction, the PATS reaction, developed in our laboratories for light and electron microscopy. This microwave-accelerated technique employs periodic acid, thiocarbohydrazide and silver methenamine. It stains basement membrane or Type IV collagen brown and type III collagen (reticulin), axons, Schwann cells, endoneurium and perineurium black. Epoxy sections of repaired and excised nerves were also compared by toluidine blue (tb) staining. Comparison of the sections of control and repaired nerves was done by computer-assisted microscopic image analysis using an Olympus CUE-2 Image Analysis System.

High-resolution measurement of birefringent fine structure in living cells using a new polarized light microscope

1995 ◽  
Vol 53 ◽  
pp. 54-55
Author(s):  
Rudolf Oldenbourg
Keyword(s):  
Light Microscope ◽  
Fluorescent Dyes ◽  
Polarized Light ◽  
Processing System ◽  
Video Camera ◽  
Molecular Organization ◽  
Computer Assisted ◽  
Image Recording ◽  
Birefringent Crystal ◽  
Technological Advances

The recent renaissance of the light microsope is fueled in part by technological advances in components on the periphery of the microscope, such as the laser as illumination source, electronic image recording (video), computer assisted image analysis and the biochemistry of fluorescent dyes for labeling specimens. After great progress in these peripheral parts, it seems timely to examine the optics itself and ask how progress in the periphery facilitates the use of new optical components and of new optical designs inside the microscope. Some results of this fruitful reflection are presented in this symposium.We have considered the polarized light microscope, and developed a design that replaces the traditional compensator, typically a birefringent crystal plate, with a precision universal compensator made of two liquid crystal variable retarders. A video camera and digital image processing system provide fast measurements of specimen anisotropy (retardance magnitude and azimuth) at ALL POINTS of the image forming the field of view. The images document fine structural and molecular organization within a thin optical section of the specimen.

Computer-Assisted Analysis of Multi-Color Confocal Microscopic Datasets: Automated Light Microscopic Discrimination of Synaptic Relationships

1996 ◽  
Vol 54 ◽  
pp. 284-285
Author(s):  
M Wessendorf ◽  
A Beuning ◽  
D Cameron ◽  
J Williams ◽  
C Knox
Keyword(s):  
Nerve Fibers ◽  
Confocal Scanning Laser Microscopy ◽  
Computer Assisted ◽  
Nerve Terminals ◽  
Neuronal Somata ◽  
Scanning Laser Microscopy ◽  
Confocal Scanning ◽  
Entire Cell ◽  
Confocal Scanning Laser ◽  
Assisted Analysis

Multi-color confocal scanning-laser microscopy (CSLM) allows examination of the relationships between neuronal somata and the nerve fibers surrounding them at sub-micron resolution in x,y, and z. Given these properties, it should be possible to use multi-color CSLM to identify relationships that might be synapses and eliminate those that are clearly too distant to be synapses. In previous studies of this type, pairs of images (e.g., red and green images for tissue stained with rhodamine and fluorescein) have been merged and examined for nerve terminals that appose a stained cell (see, for instance, Mason et al.). The above method suffers from two disadvantages, though. First, although it is possible to recognize appositions in which the varicosity abuts the cell in the x or y axes, it is more difficult to recognize them if the apposition is oriented at all in the z-axis—e.g., if the varicosity lies above or below the neuron rather than next to it. Second, using this method to identify potential appositions over an entire cell is time-consuming and tedious.

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