Brain-wave representation of words by superposition of a few sine waves

Data from three previous experiments were analyzed to test the hypothesis that brain waves of spoken or written words can be represented by the superposition of a few sine waves. First, we averaged the data over trials and a set of subjects, and, in one case, over experimental conditions as well. Next we applied a Fourier transform to the averaged data and selected those frequencies with high energy, in no case more than nine in number. The superpositions of these selected sine waves were taken as prototypes. The averaged unfiltered data were the test samples. The prototypes were used to classify the test samples according to a least-squares criterion of fit. The results were seven of seven correct classifications for the first experiment using only three frequencies, six of eight for the second experiment using nine frequencies, and eight of eight for the third experiment using five frequencies.

Generation of macroscopic superposition states with small nonlinearity

We suggest a scheme to generate a macroscopic superposition state (Schrodinger cat state) of a free-propagating optical field using a beam splitter, homodyne measurement, and a very small Kerr nonlinear effect. Our scheme makes it possible to reduce considerably the required nonlinear effect to generate an optical cat state using simple and efficient optical elements.

Coherent-state linear optical quantum computing gates using simplified diagonal superposition resource states

In this paper we explore the possibility of fundamental tests for coherent-state optical quantum computing gates [ T. C. Ralph et al. Phys. Rev. A 68 042319 (2003)] using sophisticated but not unrealistic quantum states. The major resource required in these gates is a state diagonal to the basis states. We use the recent observation that a squeezed single-photon state [S(r)∣1⟩] approximates well an odd superposition of coherent states (∣α⟩−∣−α⟩) to address the diagonal resource problem. The approximation only holds for relatively small α, and hence these gates cannot be used in a scalable scheme. We explore the effects on fidelities and probabilities in teleportation and a rotated Hadamard gate.

The design of planar gradient coils. Part ll: A weighted superposition method

In this work a superposition technique for designing gradient coils for the purpose of magnetic resonance imaging is outlined, which uses an optimized weight function superimposed upon an initial winding similar to that obtained from the target field method to generate the final wire winding. This work builds on the preliminary work performed in Part I on designing planar insertable gradient coils for high resolution imaging. The proposed superposition method for designing gradient coils results in coil patterns with relatively low inductances and the gradient coils can be used as inserts into existing magnetic resonance imaging hardware. The new scheme has the capacity to obtain images faster with more detail due to the deliver of greater magnetic held gradients. The proposed method for designing gradient coils is compared with a variant of the state-of-the-art target field method for planar gradient coils designs, and it is shown that the weighted superposition approach outperforms the well-known the classical method.

Complex numbers and symmetries in quantum mechanics, and a nonlinear superposition principle for Wigner functions

Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert space, whereas in phase space they are described by real, true representations. Equivalence of the formulations requires that the former representations can be obtained from the latter and vice versa. Examples are given. Equivalence of the two formulations also requires that complex superpositions of state vectors can be described in the phase space formulation, and it is shown that this leads to a nonlinear superposition principle for orthogonal, pure-state Wigner functions. It is concluded that the use of complex numbers in quantum mechanics can be regarded as a computational device to simplify calculations, as in all other applications of mathematics to physical phenomena.

Transfer of nonclassical properties from a microscopic superposition to macroscopic thermal states in the high temperature limit

We present several examples where prominent quantum properties are transferred from a microscopic superposition to thermal states at high temperatures. Our work is motivated by an analogy of Schrodinger's cat paradox, where the state corresponding to the virtual cat is a mixed thermal state with a large average photon number. Remarkably, quantum entanglement can be produced between thermal states with nearly the maximum Bell-inequality violation even when the temperatures of both modes approach infinity.

Observing a coherent superposition of an atom and a molecule

We demonstrate that it is possible, in principle, to perform a Ramsey-type interference experiment to exhibit a coherent superposition of a single atom and a diatomic molecule. This gedanken experiment, based on the techniques of Aharonov and Susskind [Phys. Rev. 155, 1428 (1967)], explicitly violates the commonly accepted superselection rule that forbids coherent superpositions of eigenstates of differing atom number. A Bose-Einstein condensate plays the role of a reference frame that allows for coherent operations analogous to Ramsey pulses. We also investigate an analogous gedanken experiment to exhibit a coherent superposition of a single boson and a fermion, violating the commonly accepted superselection rule forbidding coherent superpositions of states of differing particle statistics. In this case, the reference frame is realized by a multimode state of many fermions. This latter case reproduces all of the relevant features of Ramsey interferometry, including Ramsey fringes over many repetitions of the experiment. However, the apparent inability of this proposed experiment to produce well-defined relative phases between two distinct systems each described by a coherent superposition of a boson and a fermion demonstrates that there are additional, outstanding requirements to fully lift the univalence superselection rule.

An investigation of the mechanics of wire drawing with the superposition of an oscillatory drawing stress

A number of investigators have studied the application of oscillatory energy to a metal undergoing plastic deformation. Their results have shown that oscillatory stresses reduce both the stress required to initiate plastic deformation and the friction forces between the tool and workpiece. The first two sections in this thesis discuss historically and technically the devolopment of the use of oscillatory energy techniques to aid metal forming with particular reference to wire drawing. The remainder of the thesis discusses the research undertaken to study the effect of applying longitudinal oscillations to wire drawing. Oscillations were supplied from an electric hydraulic vibrator at frequencies in the range 25 to 500 c/s., and drawing tests were performed at drawing speeds up to 50 ft/m. on a 2000 lbf. bull-block. Equipment was designed to measure the drawing force, drawing torque, amplitude of die and drum oscillation and drawing speed. Reasons are given for selecting mild steel, pure and hard aluminium, stainless steel and hard copper as the materials to be drawn, and the experimental procedure and calibration of measuring equipment arc described. Results show that when oscillatory stresses are applied at frequencies within the range investigated : (a) There is no reduction in the maximum drawing load. (b) Using sodium stearate lubricant there is a negligible reduction in the coefficient of friction between the die and wire. (c) Pure aluminium does not absorb sufficient oscillatory energy to ease the movement of dislocations. (d) Hard aluminium is not softened by oscillatory energy accelerating the diffusion process. (e) Hard copper is not cyclically softened. A vibration analysis of the bull-block and wire showed that oscillatory drawiing in this frequency range, is a mechanical process of straining; and unstraining the drawn wire, and is dependent upon the stiffness of the material being drawn and the drawing machine. Directions which further work should take are suggested.

Superposition relations of microfabrics in the northern hanging-wall block

This study reports alternation of D2 extension-related and D3 contraction-related microfabrics in the northern hanging wall block of a gneiss dome-like structure recognized in the Évora Massif (Ossa-Morena Zone). In the Arraiolos – Santo Antonio de Alcorrego traverse high- to low-grade mylonites are dominant. Microfabrics related to D2 ductile deformation and M2 high-amphibolite to greenschist facies characterize an extensional shear zone with telescoping metamorphic isograds. D2 microstructures indicate shear sense with top-to-SE. Superposition of D3 contraction developed under greenschist facies (M3) producing folding of D2 microfabrics, mylonitization of granites along strike-slip shear zones and retrogression of M2 mineral assemblages.

Networks cities and ecological habitats

As the world’s rural populations continue to migrate from farmland to sprawling cities, transport networks form an impenetrable maze within which monocultures of urban form erupt from the spaces in‐between. These urban monocultures are as problematic to human activity in cities as cropping monocultures are to ecosystems in regional landscapes. In China, the speed of urbanisation is exacerbating the production of mono‐functional private and public spaces. Edges are tightly controlled. Barriers and management practices at these boundaries are discouraging the formation of new synergistic relationships, critical in the long‐term stability of ecosystems that host urban habitats. Some urban planners, engineers, urban designers, architects and landscape architects have recognised these shortcomings in contemporary Chinese cities. The ideology of sustainability, while critically debated, is bringing together thinking people in these and other professions under the umbrella of an ecological ethic. This essay aims to apply landscape ecology theory, a conceptual framework used by many professionals involved in land development processes, to a concept being developed by BAU International called Networks Cities: a city with its various land uses arranged in nets of continuity, adjacency, and superposition. It will consider six lesser‐known concepts in relation to creating enhanced human activity along (un)structured edges between proposed nets and suggest new frontiers that might be challenged in an eco‐city. Ecological theory suggests that sustaining biodiversity in regions and landscapes depends on habitat distribution patterns. Flora and fauna biologists have long studied edge habitats and have been confounded by the paradox that maximising the breadth of edges is detrimental to specialist species but favourable to generalist species. Generalist species of plants and animals tolerate frequent change in the landscape, frequenting two or more habitats for their survival. Specialist species are less tolerant of change, having specific habitat requirements during their life cycle. Protecting species richness then may be at odds with increasing mixed habitats or mixed‐use zones that are dynamic places where diverse activities occur. Forman (1995) in his book Land Mosaics however argues that these two objectives of land use management are entirely compatible. He postulates that an edge may be comprised of many small patches, corridors or convoluting boundaries of large patches. Many ecocentrists now consider humans to be just another species inhabiting the ecological environments of our cities. Hence habitat distribution theory may be useful in planning and designing better human habitats in a rapidly urbanising context like China. In less‐constructed environments, boundaries and edges provide important opportunities for the movement of multi‐habitat species into, along and from adjacent land use areas. For instance, invasive plants may escape into a national park from domestic gardens while wildlife may forage on garden plants in adjoining residential areas. It is at these interfaces that human interactions too flow backward and forward between land types. Spray applications of substances by farmers on cropland may disturb neighbouring homeowners while suburban residents may help themselves to farm produce on neighbouring orchards. Edge environments are some of the most dynamic and contested spaces in the landscape. Since most of us require access to at least two or three habitats diurnally, weekly, monthly or seasonally, their proximity to each other becomes critical in our attempts to improve the sustainability of our cities.

Mean-field descriptions of collective migration with strong adhesion

Random walk models based on an exclusion process with contact effects are often used to represent collective migration where individual agents are affected by agent-to-agent adhesion. Traditional mean field representations of these processes take the form of a nonlinear diffusion equation which, for strong adhesion, does not predict the averaged discrete behavior. We propose an alternative suite of mean-field representations, showing that collective migration with strong adhesion can be accurately represented using a moment closure approach.

Improving ultrasound excitation systems using a flexible power supply with adjustable voltage and frequency to drive piezoelectric transducers

The ability of a piezoelectric transducer in energy conversion is rapidly expanding in several applications. Some of the industrial applications for which a high power ultrasound transducer can be used are surface cleaning, water treatment, plastic welding and food sterilization. Also, a high power ultrasound transducer plays a great role in biomedical applications such as diagnostic and therapeutic applications. An ultrasound transducer is usually applied to convert electrical energy to mechanical energy and vice versa. In some high power ultrasound system, ultrasound transducers are applied as a transmitter, as a receiver or both. As a transmitter, it converts electrical energy to mechanical energy while a receiver converts mechanical energy to electrical energy as a sensor for control system. Once a piezoelectric transducer is excited by electrical signal, piezoelectric material starts to vibrate and generates ultrasound waves. A portion of the ultrasound waves which passes through the medium will be sensed by the receiver and converted to electrical energy. To drive an ultrasound transducer, an excitation signal should be properly designed otherwise undesired signal (low quality) can deteriorate the performance of the transducer (energy conversion) and increase power consumption in the system. For instance, some portion of generated power may be delivered in unwanted frequency which is not acceptable for some applications especially for biomedical applications. To achieve better performance of the transducer, along with the quality of the excitation signal, the characteristics of the high power ultrasound transducer should be taken into consideration as well. In this regard, several simulation and experimental tests are carried out in this research to model high power ultrasound transducers and systems. During these experiments, high power ultrasound transducers are excited by several excitation signals with different amplitudes and frequencies, using a network analyser, a signal generator, a high power amplifier and a multilevel converter. Also, to analyse the behaviour of the ultrasound system, the voltage ratio of the system is measured in different tests. The voltage across transmitter is measured as an input voltage then divided by the output voltage which is measured across receiver. The results of the transducer characteristics and the ultrasound system behaviour are discussed in chapter 4 and 5 of this thesis. Each piezoelectric transducer has several resonance frequencies in which its impedance has lower magnitude as compared to non-resonance frequencies. Among these resonance frequencies, just at one of those frequencies, the magnitude of the impedance is minimum. This resonance frequency is known as the main resonance frequency of the transducer. To attain higher efficiency and deliver more power to the ultrasound system, the transducer is usually excited at the main resonance frequency. Therefore, it is important to find out this frequency and other resonance frequencies. Hereof, a frequency detection method is proposed in this research which is discussed in chapter 2. An extended electrical model of the ultrasound transducer with multiple resonance frequencies consists of several RLC legs in parallel with a capacitor. Each RLC leg represents one of the resonance frequencies of the ultrasound transducer. At resonance frequency the inductor reactance and capacitor reactance cancel out each other and the resistor of this leg represents power conversion of the system at that frequency. This concept is shown in simulation and test results presented in chapter 4. To excite a high power ultrasound transducer, a high power signal is required. Multilevel converters are usually applied to generate a high power signal but the drawback of this signal is low quality in comparison with a sinusoidal signal. In some applications like ultrasound, it is extensively important to generate a high quality signal. Several control and modulation techniques are introduced in different papers to control the output voltage of the multilevel converters. One of those techniques is harmonic elimination technique. In this technique, switching angles are chosen in such way to reduce harmonic contents in the output side. It is undeniable that increasing the number of the switching angles results in more harmonic reduction. But to have more switching angles, more output voltage levels are required which increase the number of components and cost of the converter. To improve the quality of the output voltage signal with no more components, a new harmonic elimination technique is proposed in this research. Based on this new technique, more variables (DC voltage levels and switching angles) are chosen to eliminate more low order harmonics compared to conventional harmonic elimination techniques. In conventional harmonic elimination method, DC voltage levels are same and only switching angles are calculated to eliminate harmonics. Therefore, the number of eliminated harmonic is limited by the number of switching cycles. In the proposed modulation technique, the switching angles and the DC voltage levels are calculated off-line to eliminate more harmonics. Therefore, the DC voltage levels are not equal and should be regulated. To achieve this aim, a DC/DC converter is applied to adjust the DC link voltages with several capacitors. The effect of the new harmonic elimination technique on the output quality of several single phase multilevel converters is explained in chapter 3 and 6 of this thesis. According to the electrical model of high power ultrasound transducer, this device can be modelled as parallel combinations of RLC legs with a main capacitor. The impedance diagram of the transducer in frequency domain shows it has capacitive characteristics in almost all frequencies. Therefore, using a voltage source converter to drive a high power ultrasound transducer can create significant leakage current through the transducer. It happens due to significant voltage stress (dv/dt) across the transducer. To remedy this problem, LC filters are applied in some applications. For some applications such as ultrasound, using a LC filter can deteriorate the performance of the transducer by changing its characteristics and displacing the resonance frequency of the transducer. For such a case a current source converter could be a suitable choice to overcome this problem. In this regard, a current source converter is implemented and applied to excite the high power ultrasound transducer. To control the output current and voltage, a hysteresis control and unipolar modulation are used respectively. The results of this test are explained in chapter 7.

A deconvolution method for deriving the transit time spectrum for ultrasound propagation through cancellous bone replica models

The acceptance of broadband ultrasound attenuation for the assessment of osteoporosis suffers from a limited understanding of ultrasound wave propagation through cancellous bone. It has recently been proposed that the ultrasound wave propagation can be described by a concept of parallel sonic rays. This concept approximates the detected transmission signal to be the superposition of all sonic rays that travel directly from transmitting to receiving transducer. The transit time of each ray is defined by the proportion of bone and marrow propagated. An ultrasound transit time spectrum describes the proportion of sonic rays having a particular transit time, effectively describing lateral inhomogeneity of transit times over the surface of the receiving ultrasound transducer. The aim of this study was to provide a proof of concept that a transit time spectrum may be derived from digital deconvolution of input and output ultrasound signals. We have applied the active-set method deconvolution algorithm to determine the ultrasound transit time spectra in the three orthogonal directions of four cancellous bone replica samples and have compared experimental data with the prediction from the computer simulation. The agreement between experimental and predicted ultrasound transit time spectrum analyses derived from Bland–Altman analysis ranged from 92% to 99%, thereby supporting the concept of parallel sonic rays for ultrasound propagation in cancellous bone. In addition to further validation of the parallel sonic ray concept, this technique offers the opportunity to consider quantitative characterisation of the material and structural properties of cancellous bone, not previously available utilising ultrasound.

An analogy between the double slit experiment and document ranking

In the last years several works have investigated a formal model for Information Retrieval (IR) based on the mathematical formalism underlying quantum theory. These works have mainly exploited geometric and logical–algebraic features of the quantum formalism, for example entanglement, superposition of states, collapse into basis states, lattice relationships. In this poster I present an analogy between a typical IR scenario and the double slit experiment. This experiment exhibits the presence of interference phenomena between events in a quantum system, causing the Kolmogorovian law of total probability to fail. The analogy allows to put forward the routes for the application of quantum probability theory in IR. However, several questions need still to be addressed; they will be the subject of my PhD research