Approximations of large trunk line systems under heavy traffic

1994 ◽  
Vol 26 (04) ◽  
pp. 1063-1094
Author(s):  
Harold J. Kushner
Keyword(s):  
Fixed Point ◽  
Heavy Traffic ◽  
Service Capacity ◽  
Mean Values ◽  
Reflected Diffusion ◽  
Trunk Line ◽  
Overflow Traffic ◽  
The Mean ◽  
The Many ◽  
Fully Connected

The paper deals with large trunk line systems of the type appearing in telephone networks. There are many nodes or input sources, each pair of which is connected by a trunk line containing many individual circuits. Traffic arriving at either end of a trunk line wishes to communicate to the node at the other end. If the direct route is full, a rerouting might be attempted via an alternative route containing several trunks and connecting the same endpoints. The basic questions concern whether to reroute, and if so how to choose the alternative path. If the network is ‘large’ and fully connected, then the overflow traffic which is offered for rerouting to any trunk comes from many other trunks in the network with no one dominating. In this case one expects that some sort of averaging method can be used to approximate the rerouting requests and hence simplify the analysis. Essentially, the overflow traffic that a trunk offers the network for rerouting is in some average sense similar to the overflow traffic offered to that trunk. Indeed, a formalization of this idea involves the widely used (but generally heuristic) ‘fixed point' approximation method. One sets up the fixed point equations for appropriate rerouting strategies and then solves them to obtain an approximation to the system loss. In this paper we work in the heavy traffic regime, where the external offered traffic to any trunk is close to the service capacity of that trunk. It is shown that, as the number of links and circuits within each link go to infinity and for a variety of rerouting strategies, the system can be represented by an averaged limit. This limit is a reflected diffusion of the McKean–Vlasov (propagation of chaos) type, where the driving terms depend on the mean values of the solution of the equation. The averages occur due to the symmetry of the network and the averaging effects of the many interactions. This provides a partial justification for the fixed point method. The concrete dynamical systems flavor of the approach and the representations of the limit processes provide a useful way of visualizing the system and promise to be useful for the development of numerical methods and further analysis.

Approximations of large trunk line systems under heavy traffic

1994 ◽  
Vol 26 (4) ◽  
pp. 1063-1094 ◽  
Author(s):  
Harold J. Kushner
Keyword(s):  
Fixed Point ◽  
Heavy Traffic ◽  
Service Capacity ◽  
Mean Values ◽  
Reflected Diffusion ◽  
Trunk Line ◽  
Overflow Traffic ◽  
The Mean ◽  
The Many ◽  
Fully Connected

The paper deals with large trunk line systems of the type appearing in telephone networks. There are many nodes or input sources, each pair of which is connected by a trunk line containing many individual circuits. Traffic arriving at either end of a trunk line wishes to communicate to the node at the other end. If the direct route is full, a rerouting might be attempted via an alternative route containing several trunks and connecting the same endpoints. The basic questions concern whether to reroute, and if so how to choose the alternative path. If the network is ‘large’ and fully connected, then the overflow traffic which is offered for rerouting to any trunk comes from many other trunks in the network with no one dominating. In this case one expects that some sort of averaging method can be used to approximate the rerouting requests and hence simplify the analysis. Essentially, the overflow traffic that a trunk offers the network for rerouting is in some average sense similar to the overflow traffic offered to that trunk. Indeed, a formalization of this idea involves the widely used (but generally heuristic) ‘fixed point' approximation method. One sets up the fixed point equations for appropriate rerouting strategies and then solves them to obtain an approximation to the system loss. In this paper we work in the heavy traffic regime, where the external offered traffic to any trunk is close to the service capacity of that trunk. It is shown that, as the number of links and circuits within each link go to infinity and for a variety of rerouting strategies, the system can be represented by an averaged limit. This limit is a reflected diffusion of the McKean–Vlasov (propagation of chaos) type, where the driving terms depend on the mean values of the solution of the equation. The averages occur due to the symmetry of the network and the averaging effects of the many interactions. This provides a partial justification for the fixed point method. The concrete dynamical systems flavor of the approach and the representations of the limit processes provide a useful way of visualizing the system and promise to be useful for the development of numerical methods and further analysis.

Different Patellar Indices and Their Role in Decision-Making: An MRI-Based Study

2020 ◽  
Author(s):  
Sivashanmugam Raju ◽  
Karthikeyan Chinnakkannu ◽  
Balasubramanian Balakumar ◽  
Ramanivas Sundareyan ◽  
Saravanakumar P. Kaliappan ◽  
...  
Keyword(s):  
Decision Making ◽  
Patellofemoral Pain ◽  
Mr Images ◽  
Strong Negative Correlation ◽  
Mean Values ◽  
Patellar Position ◽  
Asymptomatic Patients ◽  
The Mean ◽  
Magnetic Resonance Imaging Mri ◽  
The Many

AbstractMagnetic resonance imaging (MRI) of knee has become the integral part of knee evaluation, hence any MRI based study adds more value if it helps in the decision-making process, especially for surgery in treating patellofemoral pain. We tried to determine normal patellar indices using knee MR images and the correlation between them and also compared the results with different ethnic population. We analyzed the prospectively collected MR images of 117 knees/patients, and Insall–Salvati (IS) index, modified IS index, patellotrochlear (PT) index, and patellophyseal (PP) index were calculated. Two standard deviations from the mean were used to define the normal and abnormal patellar position. Cohen's kappa values were used to assess the agreement between the indices and the correlation between them was analyzed using Pearson's correlation. The mean values for IS index, modified IS index, PT index, and PP index were 1.00, 1.53, 0.40, and 0.58, respectively. There was very good agreement between PT index and PP index. There was weak correlation between all the indices except the one between PT and PP indices which had a strong negative correlation. Based on commonly used methodology, there were 4% of asymptomatic patients who were outside the standardized cut-off values and different indices classified different knees as abnormal. This indicates patellar position should be one among the many other factors, not as a sole factor when making a surgical decision in patellofemoral pain. We also noted that the indices compared fairly with other populations. Further research is needed to determine the clinical applicability of these indices.

Entropy Production of the Willamowski-Rössler Oscillator

2005 ◽  
Vol 60 (8-9) ◽  
pp. 599-9 ◽  
Author(s):  
Jörg W. Stucki ◽  
Robert Urbanczik
Keyword(s):  
Fixed Point ◽  
Entropy Production ◽  
Dynamic Behaviour ◽  
Basin Of Attraction ◽  
Steady States ◽  
Original Model ◽  
Core Component ◽  
Mean Values ◽  
The Mean ◽  
The Basin Of Attraction

Some properties of the Willamowski-Rössler model are studied by numerical simulations. From the original equations a minimal version of the model is derived which also exhibits the characteristic properties of the original model. This minimal model shows that it contains the Volterra-Lotka oscillator as a core component. It thus belongs to a class of generalized Volterra-Lotka systems. It has two steady states, a saddle point, responsible for chaos, and a fixed point, dictating its dynamic behaviour. The chaotic attractor is located close to the surface of the basin of attraction of the saddle node. The mean values of the variables are equal to the (unstable) steady state values during oscillations even under chaos, and the variables are always non-negative as in other generalized Volterra-Lotka systems. Surprisingly this was also the case with the original reversible Willamowski-Rössler model allowing to compare the entropy production during oscillations with the entropy production of the steady states. During oscillations the entropy production was always lower even under chaos. Since under these circumstances less energy is dissipated to produce the same output, the oscillating system is more efficient than the non-oscillatory one.

scholarly journals Monitoring of Air Pollutants Using Plants and Co-Located Soil – Egypt: Characteristics, Pollution, and Toxicity Impact

2021 ◽  
Author(s):  
Wael M Badawy ◽  
Yasmin Sarhan ◽  
Octavian G Duliu ◽  
Junbeum Kim ◽  
Nikita Yushin ◽  
...  
Keyword(s):  
Tree Species ◽  
Heavy Traffic ◽  
Risk Index ◽  
Urban Pollution ◽  
Major Elements ◽  
Tree Leaves ◽  
Mean Values ◽  
Significant Difference ◽  
Greater Cairo ◽  
The Mean

Abstract The present work was conducted to characterize and monitor the air quality in terms of pollution and toxicity impact using two evergreen tree leaves, Eucalyptus globulus Labill and Ficus benjamina L. as biomonitors. Thirty tree leaves and an equal number of co-located soil samples from different regions of Egypt (urban Greater Cairo Metropolitan GC and rural Menoufia Governorate MG) were collected. The concentrations of 34 and 40 elements were determined using instrumental neutron activation analysis and atomic absorption spectrometer. Bivariate and multivariate statistical analysis were implemented. The air pollution was assessed using enrichment factor, pollution load index, potential ecological risk, and risk index. In addition, human and ecotoxicity were evaluated based on the ReCiPe method. The mean concentration values of the obtained elements in tree leaves in urban Greater Cairo and rural Menoufia Governorate show that the major elements are slightly higher in F. benjamina than in E. globulus. Likewise, the mean values of elements in soil from Greater Cairo and Menoufia Governorate show no significant difference except for major elements (Fe, Al, Mg, K, Na, and Ti) in Menoufia Governorate. The normalized concentrations of tree species and soil show that the accumulated elements by F. benjamina is slightly higher than in E. globulus in Greater Cairo GC and Menoufia Governorate MG. While in terms of the investigated area, the concentrations of elements in MG is considerably higher than in GC. PLI spatial distribution over investigated areas showed that despite high population density, heavy traffic, and urban pollution, the Cairo samples exhibit significantly lower values as compared to those from Menoufia, which is most likely due to the uncontrolled industrial and domestic waste disposal outside Cairo. PER was significant for As in Soil and for As and Cd for tree species. Human toxicity shows higher values in urban locations. Contrariwise, in the terrestrial ecotoxicity aspect, the rural locations are much higher than in urban ones.

Ratio imaging of intracellular ion concentration

1992 ◽  
Vol 50 (2) ◽  
pp. 1160-1161
Author(s):  
Stephen R. Bolsover
Keyword(s):  
Individual Cell ◽  
Video Camera ◽  
Field Of View ◽  
Ion Concentration ◽  
Fluorescence Signal ◽  
Ion Imaging ◽  
Ratiometric Fluorescence ◽  
Ratio Imaging ◽  
The Mean ◽  
The Many

The field of intracellular ion concentration measurement expanded greatly in the 1980's due primarily to the development by Roger Tsien of ratiometric fluorescence dyes. These dyes have many applications, and in particular they make possible to image ion concentrations: to produce maps of the ion concentration within living cells. Ion imagers comprise a fluorescence microscope, an imaging light detector such as a video camera, and a computer system to process the fluorescence signal and display the map of ion concentration.Ion imaging can be used for two distinct purposes. In the first, the imager looks at a field of cells, measuring the mean ion concentration in each cell of the many in the field of view. One can then, for instance, challenge the cells with an agonist and examine the response of each individual cell. Ion imagers are not necessary for this sort of experiment: one can instead use a system that measures the mean ion concentration in a just one cell at any one time. However, they are very much more convenient.

Articulatory Behavior Pre and Post Full-Mouth Tooth Extraction and Alveoloplasty

1980 ◽  
Vol 23 (3) ◽  
pp. 630-645 ◽  
Author(s):  
Gerald Zimmermann ◽  
J.A. Scott Kelso ◽  
Larry Lander
Keyword(s):  
Control Subject ◽  
High Speed ◽  
Tooth Extraction ◽  
Kinematic Parameters ◽  
Experimental Conditions ◽  
Mean Values ◽  
Articulatory Movements ◽  
The Mean ◽  
Experimental Subjects ◽  
Normal Speech

High speed cinefluorography was used to track articulatory movements preceding and following full-mouth tooth extraction and alveoloplasty in two subjects. Films also were made of a control subject on two separate days. The purpose of the study was to determine the effects of dramatically altering the structural dimensions of the oral cavity on the kinematic parameters of speech. The results showed that the experimental subjects performed differently pre and postoperatively though the changes were in different directions for the two subjects. Differences in both means and variabilities of kinematic parameters were larger between days for the experimental (operated) subjects than for the control subject. The results for the Control subject also showed significant differences in the mean values of kinematic variables between days though these day-to-day differences could not account for the effects found pre- and postoperatively. The results of the kinematic analysis, particularly the finding that transition time was most stable over the experimental conditions for the operated subjects, are used to speculate about the coordination of normal speech.

Comparative Study of Intranasal, Subcutaneous and Intravenous Administration of Desamino-D-Arginine Vasopressin (DDAVP)

1986 ◽  
Vol 55 (01) ◽  
pp. 108-111 ◽  
Author(s):  
M Köhler ◽  
P Hellstern ◽  
C Miyashita ◽  
G von Blohn ◽  
E Wenzel
Keyword(s):  
Factor Viii ◽  
Von Willebrand Factor ◽  
Factor Xii ◽  
Additional Advantage ◽  
Mean Values ◽  
Routes Of Administration ◽  
The Mean ◽  
Von Willebrand ◽  
Willebrand Factor ◽  
Factor Antigen

SummaryThis study was performed to evaluate the influence of different routes of administration on the efficacy of DDAVP treatment. Ten healthy volunteers received DDAVP intranasally (i.n.), subcutaneously (s.c.) and intravenously (i.v.) in a randomized cross-over trial. Factor XII and high molecular weight (HMW)-kininogen levels increased only slightly after DDAVP administration. The mean increase of factor VIII: C was 3.1 (i. v.), 2.3 (s. c.), and 1.3 (i.n.) - fold over baseline. Ristocetin cofactor (von Willebrand factor antigen) increased 3.1 (2.5), 2.0 (2.3) and 1.2 (1.2) - fold over baseline mean values after i.v., s.c. and i.n. DDAVP, respectively. The half-disappearance time of factor VIII and von Willebrand factor (vWF) after DDAVP ranged from five (factor VIII: C) to eight hours (vWF). The mean increase of fibrinolytic activity was more pronounced after i.v. DDAVP. The antidiuretic effect was moderate with no apparent differences between the routes of application. This study provides further evidence that both i.v. and s.c. DDAVP administration result in an appropriate and reliable stimulation of haemostasis. An additional advantage of s. c. administration is its suitability for home treatment.

Comparative Study of effectiveness of mobilization with movement (MWM) and End range mobilization (ERM) techniques in frozen shoulder

2018 ◽  
Vol 4 (4) ◽  
pp. 519-522
Author(s):  
Jeyakumar S ◽  
Jagatheesan Alagesan ◽  
T.S. Muthukumar
Keyword(s):  
Range Of Motion ◽  
Frozen Shoulder ◽  
Type I ◽  
Mean Values ◽  
Functional Activities ◽  
Group A ◽  
The Mean ◽  
Group B

Background: Frozen shoulder is disorder of the connective tissue that limits the normal Range of motion of the shoulder in diabetes, frozen shoulder is thought to be caused by changes to the collagen in the shoulder joint as a result of long term Hypoglycemia. Mobilization is a therapeutic movement of the joint. The goal is to restore normal joint motion and rhythm. The use of mobilization with movement for peripheral joints was developed by mulligan. This technique combines a sustained application of manual technique “gliding” force to the joint with concurrent physiologic motion of joint, either actively or passively. This study aims to find out the effects of mobilization with movement and end range mobilization in frozen shoulder in Type I diabetics. Materials and Methods: 30 subjects both male and female, suffering with shoulder pain and clinically diagnosed with frozen shoulder was recruited for the study and divided into two groups with 15 patients each based on convenient sampling method. Group A patients received mobilization with movement and Group B patients received end range mobilization for three weeks. The outcome measurements were SPADI, Functional hand to back scale, abduction range of motion using goniometer and VAS. Results: The mean values of all parameters showed significant differences in group A as compared to group B in terms of decreased pain, increased abduction range and other outcome measures. Conclusion: Based on the results it has been concluded that treating the type 1 diabetic patient with frozen shoulder, mobilization with movement exercise shows better results than end range mobilization in reducing pain and increase functional activities and mobility in frozen shoulder.

A COMPARISON OF TWO METHODS FOR MEASUREMENT OF ALDOSTERONE SECRETION RATE IN MAN

1966 ◽  
Vol 53 (2) ◽  
pp. 177-188 ◽  
Author(s):  
P. Lund-Johansen ◽  
T. Thorsen ◽  
K. F. Støa
Keyword(s):  
Urinary Excretion ◽  
Normal Subjects ◽  
Secretion Rate ◽  
Aldosterone Secretion ◽  
Simple Method ◽  
Mean Values ◽  
Pathological Conditions ◽  
Significant Difference ◽  
Derivative Method ◽  
The Mean

ABSTRACT A comparison has been made between (A), a relatively simple method for the measurement of aldosterone secretion rate, based on paper chromatography and direct densitometry of the aldosterone spot and (B) a more elaborate isotope derivative method. The mean secretion rate in 9 normal subjects was 112 ± 26 μg per 24 hours (method A) and 135 ± 35 μg per 24 hours (method B). The »secretion rate« in one adrenalectomized subject after the intravenous injection of 250 μg of aldosterone was 230 μg per 24 hours (method A) and 294 μg per 24 hours (method B). There was no significant difference in the mean values, and correlation between the two methods was good (r = 0.80). It is concluded that the densitometric method is suitable for clinical purposes as well as research, being more rapid and less expensive than the isotope derivative method. Method A also measures the urinary excretion of the aldosterone 3-oxo-conjugate, which is of interest in many pathological conditions. The densitometric method is obviously the less sensitive and a prerequisite for its use is an aldosterone secretion of 20—30 μg per 24 hours. Lower values are, however, rare in adults.

EFFECT OF OESTRONE-PELLET IMPLANTATION ON PLASMA LEVELS OF PROLACTIN

1970 ◽  
Vol 64 (2) ◽  
pp. 265-272 ◽  
Author(s):  
A. A. van der Gugten ◽  
M. Sala ◽  
H. G. Kwa
Keyword(s):  
Plasma Levels ◽  
Male Rats ◽  
Mean Values ◽  
The Mean ◽  
Dose Levels ◽  
Higher Doses ◽  
Primary Break

ABSTRACT Eight female and eight male rats were castrated at the age of 8 to 10 weeks. Four spayed and four orchidectomized rats received one oestrone/cholesterol pellet (200 μg oestrone) on the day of operation (day 0), a second pellet on day 11 and a third on day 23. The remaining animals received four oestrone/cholesterol pellets at these times. The fluctuations in the prolactin levels in the circulation induced by the oestrogen challenges in these animals were followed during 31 days by radioimmunoassays performed on days 3, 7, 9, 14, 15, 17, 23, 24, 25, 28 and 31. The results suggested that the homoeostatic mechanism regulating plasma levels of prolactin was capable of withstanding the three time-spaced oestrogen challenges only in the spayed animals receiving the lower doses of oestrogen, since it allowed the mean values of the prolactin levels to remain fairly constant during the first 4 weeks. The levels in this group rose to much higher levels only on day 31. The higher doses of oestrone in the spayed rats and both dose levels of oestrone in the orchidectomized animals apparently resulted in a primary break-down of the homoeostatic mechanism, since the prolactin levels in the animals of these groups rose to much higher levels either on day 7 or on day 9. This was followed by a period during which the prolactin levels appeared to be more or less under control, until a second and probably definitive failure of the homoeostatic mechanism allowed the mean levels to rise sharply again.

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