Limit theorems and absorption problems for quantum radom walks in one dimension

2002 ◽  
Vol 2 (Special) ◽  
pp. 578-595
Author(s):  
N. Konno
Keyword(s):  
Random Walks ◽  
Limit Theorems ◽  
The Other ◽  
One Dimension ◽  
Unitary Matrices ◽  
Quantum Random Walks ◽  
One Dimensional ◽  
The Difference ◽  
The One

In this paper we consider limit theorems, symmetry of distribution, and absorption problems for two types of one-dimensional quantum random walks determined by $2 \times 2$ unitary matrices using our PQRS method. The one type was introduced by Gudder in 1988, and the other type was studied intensively by Ambainis et al. in 2001. The difference between both types of quantum random walks is also clarified.

scholarly journals Assessing a Linear Nanosystem's Limiting Reliability from its Components

2008 ◽  
Vol 45 (03) ◽  
pp. 879-887 ◽  
Author(s):  
Nader Ebrahimi
Keyword(s):  
Present State ◽  
Size Range ◽  
Two Dimensions ◽  
The Other ◽  
One Dimension ◽  
Present Moment ◽  
One Dimensional ◽  
The One ◽  
Fixed Moment ◽  
Nanosized Systems

Nanosystems are devices that are in the size range of a billionth of a meter (1 x 10-9) and therefore are built necessarily from individual atoms. The one-dimensional nanosystems or linear nanosystems cover all the nanosized systems which possess one dimension that exceeds the other two dimensions, i.e. extension over one dimension is predominant over the other two dimensions. Here only two of the dimensions have to be on the nanoscale (less than 100 nanometers). In this paper we consider the structural relationship between a linear nanosystem and its atoms acting as components of the nanosystem. Using such information, we then assess the nanosystem's limiting reliability which is, of course, probabilistic in nature. We consider the linear nanosystem at a fixed moment of time, say the present moment, and we assume that the present state of the linear nanosystem depends only on the present states of its atoms.

scholarly journals Quantum random walks in one dimension via generating functions

2007 ◽  
Vol DMTCS Proceedings vol. AH,... (Proceedings) ◽  
Author(s):  
Andrew Bressler ◽  
Robin Pemantle
Keyword(s):  
Random Walks ◽  
Generating Functions ◽  
Nearest Neighbor ◽  
Function Analysis ◽  
One Dimension ◽  
Quantum Random Walks ◽  
Linear Speed ◽  
One Dimensional ◽  
Asymptotic Term ◽  
International Audience

International audience We analyze nearest neighbor one-dimensional quantum random walks with arbitrary unitary coin-flip matrices. Using a multivariate generating function analysis we give a simplified proof of a known phenomenon, namely that the walk has linear speed rather than the diffusive behavior observed in classical random walks. We also obtain exact formulae for the leading asymptotic term of the wave function and the location probabilities.

Study on Pairwise Bundle Adjustment and One Dimension Wand Calibration for Cameras Group

2013 ◽  
Vol 365-366 ◽  
pp. 702-707
Author(s):  
Xun Luo ◽  
Wei Zhao ◽  
Hai Nan Zhang
Keyword(s):  
Fundamental Matrix ◽  
Bundle Adjustment ◽  
The Other ◽  
One Dimension ◽  
Optimal Solutions ◽  
One Dimensional ◽  
Calibration Methods ◽  
The One ◽  
Dimensional Object ◽  
Couple Method

It is proposed a method of cameras group calibration with pairwise bundle adjustment using one dimensional wand. The one dimensional wand is one of the simplest calibration tools with two distinguishing markers the distance between which is known. The wand with the markers moves unconstrained in the field of cameras group, acquiring the coordinates of the projections of the corresponding marker in each camera. Every two cameras are formed as a couple, which fundamental matrix, focal lengths, rotation matrix, translation matrix and scale factor can be estimated under a few of certain assumptions. Optimal solutions are obtained through the pairwise bundle adjustment. The group calibration result is demonstrated as a sort sequence of all of the couple calibration results in ascending order according to reconstruction errors. The couple as top ranked as possible will be used to reconstruct the object in application procedures. Experimental results show that the dual couple method has much more accuracy and maintain the same feasibility comparing with the other one dimensional object calibration methods.

scholarly journals Assessing a Linear Nanosystem's Limiting Reliability from its Components

2008 ◽  
Vol 45 (3) ◽  
pp. 879-887 ◽  
Author(s):  
Nader Ebrahimi
Keyword(s):  
Present State ◽  
Size Range ◽  
Two Dimensions ◽  
The Other ◽  
One Dimension ◽  
Present Moment ◽  
One Dimensional ◽  
The One ◽  
Fixed Moment ◽  
Nanosized Systems

Nanosystems are devices that are in the size range of a billionth of a meter (1 x 10-9) and therefore are built necessarily from individual atoms. The one-dimensional nanosystems or linear nanosystems cover all the nanosized systems which possess one dimension that exceeds the other two dimensions, i.e. extension over one dimension is predominant over the other two dimensions. Here only two of the dimensions have to be on the nanoscale (less than 100 nanometers). In this paper we consider the structural relationship between a linear nanosystem and its atoms acting as components of the nanosystem. Using such information, we then assess the nanosystem's limiting reliability which is, of course, probabilistic in nature. We consider the linear nanosystem at a fixed moment of time, say the present moment, and we assume that the present state of the linear nanosystem depends only on the present states of its atoms.

Effect of leakage and blockage on the acoustic behavior of particle filters

2019 ◽  
Vol 67 (6) ◽  
pp. 483-492
Author(s):  
Seonghyeon Baek ◽  
Iljae Lee
Keyword(s):  
Transfer Matrix ◽  
Particle Filters ◽  
Acoustic Analysis ◽  
Transmission Loss ◽  
One Dimensional ◽  
Filter System ◽  
The Difference ◽  
The One ◽  
Analytical Approaches ◽  
Good Agreement

The effects of leakage and blockage on the acoustic performance of particle filters have been examined by using one-dimensional acoustic analysis and experimental methods. First, the transfer matrix of a filter system connected to inlet and outlet pipes with conical sections is measured using a two-load method. Then, the transfer matrix of a particle filter only is extracted from the experiments by applying inverse matrices of the conical sections. In the analytical approaches, the one-dimensional acoustic model for the leakage between the filter and the housing is developed. The predicted transmission loss shows a good agreement with the experimental results. Compared to the baseline, the leakage between the filter and housing increases transmission loss at a certain frequency and its harmonics. In addition, the transmission loss for the system with a partially blocked filter is measured. The blockage of the filter also increases the transmission loss at higher frequencies. For the simplicity of experiments to identify the leakage and blockage, the reflection coefficients at the inlet of the filter system have been measured using two different downstream conditions: open pipe and highly absorptive terminations. The experiments show that with highly absorptive terminations, it is easier to see the difference between the baseline and the defects.

scholarly journals EXPERIMENTAL EPIDEMIOLOGY OF TUBERCULOSIS

1930 ◽  
Vol 51 (5) ◽  
pp. 769-776 ◽  
Author(s):  
Max B. Lurie
Keyword(s):  
Guinea Pigs ◽  
Wire Mesh ◽  
The Other ◽  
Tuberculous Infection ◽  
Source Of Infection ◽  
Natural Modes ◽  
The Difference ◽  
The One ◽  
Portal Of Entry ◽  
Human Autopsy Material

Under conditions closely simulating the natural modes of tuberculous infection in man normal guinea pigs have acquired tuberculosis by being exposed under two degrees of crowding to tuberculous cage mates in ordinary cages, where the food became soiled with excreta, bearing tubercle bacilli, and in special cages, with wire-mesh floors, where this source of infection was almost entirely eliminated. Guinea pigs were also exposed in the same room but not in the same cage with tuberculous animals. It was found that the relative tuberculous involvement of the mesenteric and tracheobronchial nodes showed a gradation of change from an almost completely alimentary infection to a completely respiratory infection. The disease involved the mesenteric nodes predominantly in the crowded ordinary cages, with much less or no affection of the tracheobronchial nodes. It was similarly, but less markedly, enteric in origin in the less crowded ordinary cages, the mesenteric nodes again being larger than the tracheobronchial nodes, but the difference in size was not so great. In the more crowded special cages the relative affection of these two groups of nodes alternated, so that in some the mesenteric, in some the tracheobronchial nodes were more extensively tuberculous. A disease characterized by less or no affection of the mesenteric nodes and by extensive lesions of the tracheobronchial nodes was seen in the less crowded special cages. Finally there was a massive tuberculosis of the tracheobronchial nodes with usually no affection of the mesenteric nodes in the frankly air-borne tuberculosis acquired by guinea pigs exposed in the same room but not to tuberculous cage mates. This gradation in the rô1e played by the enteric and respiratory routes of infection, as first the one and then the other becomes the more frequent channel of entrance for tuberculosis, would indicate that the penetration of tubercle bacilli by the one portal of entry inhibits the engrafting of tuberculosis in the tissues by way of the other portal of entry. It is apparent that in the special cages the opportunities for inhaling tubercle bacilli are at most equal to if not much less than in the ordinary cages; for in the latter dust from the bedding, laden with tubercle bacilli, is stirred up almost constantly by the animals, whereas in the special cages there is no bedding at all, and therefore, presumably, no more tubercle bacilli in the air than may occur in any part of the room. Nevertheless the route of infection was predominantly the respiratory tract in the special cages, especially in the less crowded, apparently because the enteric route had been largely eliminated. The greater predominance of the respiratory route amongst guinea pigs that acquired tuberculosis in the less crowded ordinary cages as compared to the lesser significance of this route in the more crowded ordinary cages would point in the same direction. These observations are in harmony with our knowledge that tuberculosis once implanted in an organism confers a certain degree of immunity to the disease. It is noteworthy that in a study of human autopsy material Opie (3) has found that when healed lesions are present in the mesentery focal tuberculosis in the lungs is seldom found, and that when first infection occurs by way of the lungs it tends to prevent the engrafting of the disease by way of the intestinal tract.

A semi-hybrid model for malaria with limited superinfection

1998 ◽  
Vol 30 (04) ◽  
pp. 1027-1057 ◽  
Author(s):  
Philippe Picard
Keyword(s):  
Stochastic Model ◽  
Population Size ◽  
Hybrid Model ◽  
Human Population ◽  
Threshold Level ◽  
The Other ◽  
The Difference ◽  
The One

Modelling malaria with consistency necessitates the introduction of at least two families of interconnected processes. Even in a Markovian context the simplest fully stochastic model is intractable and is usually transformed into a hybrid model, by supposing that these two families are stochastically independent and linked only through two deterministic connections. A model closer to the fully stochastic model is presented here, where one of the two families is subordinated to the other and just a unique deterministic connection is required. For this model a threshold theorem can be proved but the threshold level is not the one obtained in a hybrid model. The difference disappears only when the human population size approaches infinity.

Lower Bounds to the Eigenvalues in One-Dimensional Problems by a Shift in the Weight Function

1970 ◽  
Vol 37 (2) ◽  
pp. 267-270 ◽  
Author(s):  
D. Pnueli
Keyword(s):  
Lower Bound ◽  
Weight Function ◽  
Lower Bounds ◽  
Variational Formulation ◽  
Ritz Method ◽  
The Other ◽  
One Dimensional ◽  
Systematic Shift ◽  
The One ◽  
Detailed Computation

A method is presented to obtain both upper and lower bound to eigenvalues when a variational formulation of the problem exists. The method consists of a systematic shift in the weight function. A detailed procedure is offered for one-dimensional problems, which makes improvement of the bounds possible, and which involves the same order of detailed computation as the Rayleigh-Ritz method. The main contribution of this method is that it yields the “other bound;” i.e., the one which cannot be obtained by the Rayleigh-Ritz method.

scholarly journals XXIII.—On the Disruptive Discharge of Electricity: An Experimental Thesis for the Degree of Doctor of Science, Department A

1878 ◽  
Vol 28 (2) ◽  
pp. 633-671 ◽  
Author(s):  
Alexander Macfarlane
Keyword(s):  
Copper Wire ◽  
Late Summer ◽  
The Other ◽  
Straight Line ◽  
Summer Session ◽  
The Difference ◽  
A Chain ◽  
The One ◽  
Metallic Parts ◽  
The University

The experiments to which I shall refer were carried out in the physical laboratory of the University during the late summer session. I was ably assisted in conducting the experiments by three students of the laboratory,—Messrs H. A. Salvesen, G. M. Connor, and D. E. Stewart. The method which was used of measuring the difference of potential required to produce a disruptive discharge of electricity under given conditions, is that described in a paper communicated to the Royal Society of Edinburgh in 1876 in the names of Mr J. A. Paton, M. A., and myself, and was suggested to me by Professor Tait as a means of attacking the experimental problems mentioned below.The above sketch which I took of the apparatus in situ may facilitate tha description of the method. The receiver of an air-pump, having a rod capable of being moved air-tight up and down through the neck, was attached to one of the conductors of a Holtz machine in such a manner that the conductor of the machine and the rod formed one conducting system. Projecting from the bottom of the receiver was a short metallic rod, forming one conductor with the metallic parts of the air-pump, and by means of a chain with the uninsulated conductor of the Holtz machine. Brass balls and discs of various sizes were made to order, capable of being screwed on to the ends of the rods. On the table, and at a distance of about six feet from the receiver, was a stand supporting two insulated brass balls, the one fixed, the other having one degree of freedom, viz., of moving in a straight line in the plane of the table. The fixed insulated ball A was made one conductor with the insulated conductor of the Holtz and the rod of the receiver, by means of a copper wire insulated with gutta percha, having one end stuck firmly into a hole in the collar of the receiver, and having the other fitted in between the glass stem and the hollow in the ball, by which it fitted on to the stem tightly. A thin wire similarly fitted in between the ball B and its insulating stem connected the ball with the insulated half ring of a divided ring reflecting electrometer.

Scenarios as Tools of the Scientific Imagination: The Case of Climate Projections

2021 ◽  
Vol 29 (1) ◽  
pp. 36-61
Author(s):  
Michael Poznic ◽  
Rafaela Hillerbrand
Keyword(s):  
Scientific Community ◽  
Climate Science ◽  
The Other ◽  
Climate Projections ◽  
Public Realm ◽  
The Public ◽  
Other Hand ◽  
The Difference ◽  
The One ◽  
Scientific Imagination

Climatologists have recently introduced a distinction between projections as scenario-based model results on the one hand and predictions on the other hand. The interpretation and usage of both terms is, however, not univocal. It is stated that the ambiguities of the interpretations may cause problems in the communication of climate science within the scientific community and to the public realm. This paper suggests an account of scenarios as props in games of make-belive. With this account, we explain the difference between projections that should be make-believed and other model results that should be believed.

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