Unitary Systems Research Articles

Quantum-enhanced multi-parameter estimation for unitary photonic systems

Precise device characterisation is a fundamental requirement for a large range of applications using photonic hardware, and constitutes a multi-parameter estimation problem. Estimates based on measurements using single photons or classical light have precision which is limited by shot noise, while quantum resources can be used to achieve sub-shot-noise precision. However, there are many open questions with regard to the best quantum protocols for multi-parameter estimation, including the ultimate limits to achievable precision, as well as optimal choices for probe states and measurements. In this paper, we develop a formalism based on Fisher information to tackle these questions for setups based on linear-optical components and photon-counting measurements. A key ingredient of our analysis is a mapping for equivalent protocols defined for photonic and spin systems, which allows us to draw upon results in the literature for general finite-dimensional systems. Motivated by the protocol in Zhou, et al Optica 2, 510 (2015), we present new results for quantum-enhanced tomography of unitary processes, including a comparison of Holland-Burnett and NOON probe states.

Direct quantification of dual protein adsorption dynamics in three dimensional systems in presence of cells

The biomaterial surface upon exposure to biological fluids is covered by a layer of proteins, which is modified over a period of time and dictates the fate of the biomaterial. In this study, we present and validate a new methodology for quantification of protein adsorption on to a three-dimensional polymer scaffold from unitary and binary systems, using fluorescence molecular tomography, an optical trans-illumination technique with picomolar sensitivity. In additional to being able to follow behavior of two proteins simultaneously, this methodology is also suitable for studying protein uptake in cells situated in a polymer environment. The ability to follow protein adsorption/uptake in a continuous manner opens up new possibilities to study the role of serum proteins in biomaterial compatibility.

Phase rotation symmetry and the topology of oriented scattering networks

We investigate the topological properties of dynamical states evolving on periodic oriented graphs. This evolution, that encodes the scattering processes occurring at the nodes of the graph, is described by a single-step global operator, in the spirit of the Ho-Chalker model. When the successive scattering events follow a cyclic sequence, the corresponding scattering network can be equivalently described by a discrete time-periodic unitary evolution, in line with Floquet systems. Such systems may present anomalous topological phases where all the first Chern numbers are vanishing, but where protected edge states appear in a finite geometry. To investigate the origin of such anomalous phases, we introduce the phase rotation symmetry, a generalization of usual symmetries which only occurs in unitary systems (as opposed to Hamiltonian systems). Equipped with this new tool, we explore a possible explanation of the pervasiveness of anomalous phases in scattering network models, and we define bulk topological invariants suited to both equivalent descriptions of the network model, which fully capture the topology of the system. We finally show that the two invariants coincide, again through a phase rotation symmetry arising from the particular structure of the network model.

Federalism as Compared to What? Sorting Out the Effects of Federalism, Unitary Systems, and Decentralization

Federalism as compared to what? Most American students of federalism rarely compare federal systems to others, and thus lack the ability to say anything meaningful about federalism’s effect on economics, social policies, civic participation, and public welfare. We argue that many of the supposed virtues of federalism are actually the result of decentralization, that unitarism is generally associated with better economic and social outcomes, and that scholars must distinguish between the economic concept of “fiscal federalism” and constitutional federalism. We cite a number of comparative studies from political science, and leverage their data to support our contentions.

Higher education and its contribution to a diverse regional supply of human capital: does the binary/unitary divide matters?

Diversity has been an important topic of research for some time in higher education, though the purposes underlying this attention have varied across national and regional contexts. In many parts of the world, the term diversity has been emphasized with regard to variety among the programs or services provided by academic institutions, and differences among the types of institutions themselves. It is particularly important to discuss whether different dimensions of diversity may influence the degree of effectiveness of higher education (HE) in fulfilling its contribution and relevance to economic and social development. We are particularly interested in analyzing whether unitary or binary systems present significant differences in different dimensions of diversity that may be relevant to enhance higher education institutions’ (HEIs) contribution to territorial cohesion, notably by enhancing the local stock of human capital and contributing to the social and cultural development of their regions. Therefore, we propose the following research questions: *Are there relevant patterns regarding different dimensions of diversity between unitary and binary HE systems? *In the case of binary systems, is it possible to find relevant differences in different dimensions of diversity between universities and more vocational HEIs? By looking at these questions, we aim at contributing both to the literature on HE institutional diversity and to the study of the role played by HEIs on regional development.

The historical development of the Scandinavian functional approach to transfer of ownership: a tale of change and continuity

In the field of transfer of ownership, the Scandinavian legal systems currently stand out in a European context by applying a approach, rather than a approach, as the rest of European legal systems do. However, the Scandinavian systems have not always stood apart. The development towards the functional approach - which occurred under the influence of legal realist thought- began around the turn of the 20th century and is often considered completed in the second half of the same century. Prior to this Scandinavian legal doctrine agreed upon a unitary approach. This paper discusses the historical development of the functional approach to transfer of ownership in Scandinavian legal systems. The process of transformation is reviewed through the lens of three different sources of law, namely legal doctrine, legislation and case law. It is found that even though the general view of transfer of ownership underwent major changes with the development of the functional approach, only minor changes occurred in the underlying legal framework. In legal scholarship, which was the driving force of the transformation, we observe an image of great change. However, this development was not mirrored in legislation and case law, which present us with an image of continuity. We are thus confronted with conflicting images in legal scholarship on the one hand and legislation and case law on the other. This triggers the question of how such a great paradigm change could occur with only minor changes to the legal framework. How could two vastly different theories on transfer of ownership fit a virtually unchanged legal framework? The paper proposes an explanation to this question. It suggests that the new functional theory fit the existing legal framework because the legal framework at place already contained many features that were -if not directly functional- at least compatible with a functional approach. This suggests that even though the scholars of the time agreed upon the existence of a unitary transfer requirement in both Sweden and Norway it is questionable whether this was the case, at least in the sense of modern unitary legal systems. Further, the paper offers a possible explanation as to why Scandinavian legal scholars of the time insisted upon a unitary rule despite the fact that the legal framework provided little support for such a theory.

A Comparative Study of Energy Consumption for Residential HVAC Systems Using EnergyPlus

Energy conservation and sustainability have become an attractive field for research due to the growth in population and continuing search for better living standards. Heating, Ventilation, and Air Conditioning (HVAC) systems account for almost half of consumed energy in buildings and around 10 to 20% of total energy consumption in developed countries. In general, the trend of installing central HVAC systems increases in residential and commercial buildings. In this research, a study of energy consumption of HVAC systems in residential buildings has been conducted with the aim to compare those systems from an energy consumption point of view. The final goal of this research is to reduce energy requirements of residential buildings sector to save energy and reduce carbon emission. A medium size residential building in the city of Tripoli, Libya, was selected as a case study. EnergyPlus building simulation software along with OpenStudio software were used to model the house and HVAC systems. The results show that the virtual component “ideal air loads” used in EnergyPlus is very easy to use, however, its calculated energy consumption is overestimated compared to other models. Therefore, using that component can be misleading and may result in high monthly and annually energy consumption results. The results also show that in a residential building, unitary systems consume the least annual energy consumption compared to other models. It was concluded that variations in energy consumption of the considered HVAC systems decrease as the coefficient of performance (COP) increases and visa verse.

Board diversity and financial fragility: Evidence from European banks

In the wake of the recent debt crisis in Europe, we investigate the influence of board diversity on financial fragility and performance of European banks. Corporate governance codes in Europe recommend unitary and dual-board systems; therefore, we believe that the influence of board diversity may vary across governance mechanisms and that no other studies have addressed these variations and their influence on financial fragility across European countries. The results show that a critical mass of female representation on both the supervisory board and the board of directors may reduce banks’ vulnerability to financial crisis. However, interestingly, we find evidence that female directors on the management board are not risk averse. We argue that the degree of risk taking for female directors may vary based on their roles (non-executive or executive) and that female and male executive directors may have the same risk taking behaviour. Our empirical results provide guidelines to the regulators in Europe with respect to the recently approved proposal by the European Parliament on female representation.

New investigation on the physical and electrochemical properties of (TAS) thin films grown by electrodeposition technique

Abstract The purpose of this work was to develop a new method on the synthesis of ternary tin antimony sulfide (TAS) thin films on indium tin oxide (ITO) coated glass substrates using one-step electrodeposition route. To explore the mechanism behind, a cyclic voltammetric study was performed in unitary (Sn, Sb, S) systems, binaries (Sn-S, Sb-S) systems, and ternary Sn-Sb-S system. The effect of various deposition potentials (E dep ) on the structural, optical and morphological properties, as well as frequency response has been investigated by X-ray diffraction patterns, UV–vis spectroscopy, scanning electron microscope (SEM), and electrochemical impedance spectroscopy (EIS). From these results, X-ray diffraction demonstrates that the major crystalline phase of the SnSb 2 S 4 orthorhombic phase has been obtained at E dep = −0.7 V (vs. Ag/AgCl). Based on the (SEM) images, it was found that the surface morphology and grain size were strongly influenced by the deposition potential. According to optical measurements, the (TAS) thin films display good optical properties with direct band gap. An equivalent electric circuit model (EECM) is designed for (EIS) data. The fitting curves are aligned well with the experimental curves, suggesting that the proposed equivalent circuit model is an ideal model for (TAS) electrode.

Quantum Linear Systems Theory

This paper surveys some recent results on the theory of quantum linear systems and presents them within a unified framework. Quantum linear systems are a class of systems whose dynamics, which are described by the laws of quantum mechanics, take the specific form of a set of linear quantum stochastic differential equations (QSDEs). Such sys- tems commonly arise in the area of quantum optics and related disciplines. Systems whose dynamics can be described or ap- proximated by linear QSDEs include interconnections of optical cavities, beam-spitters, phase-shifters, optical parametric am- plifiers, optical squeezers, and cavity quantum electrodynamic systems. With advances in quantum technology, the feedback control of such quantum systems is generating new challenges in the field of control theory. Potential applications of such quantum feedback control systems include quantum computing, quantum error correction, quantum communications, gravity wave detection, metrology, atom lasers, and superconducting quantum circuits. A recently emerging approach to the feedback control of quantum linear systems involves the use of a controller which itself is a quantum linear system. This approach to quantum feedback control, referred to as coherent quantum feedback control, has the advantage that it does not destroy quantum information, is fast, and has the potential for efficient imple- mentation. This paper discusses recent results concerning the synthesis of H-infinity optimal controllers for linear quantum systems in the coherent control case. An important issue which arises both in the modelling of linear quantum systems and in the synthesis of linear coherent quantum controllers is the issue of physical realizability. This issue relates to the property of whether a given set of QSDEs corresponds to a physical quantum system satisfying the laws of quantum mechanics. The paper will cover recent results relating the question of physical realizability to notions occuring in linear systems theory such as lossless bounded real systems and dual J-J unitary systems.

Spaces of Bessel Generators and Characterizations of Bessel Generator Multipliers for Unitary Systems

In this paper, we introduce a set of frame generators for a unitary system which is closed under linear combinations. Certain structural properties of the set are studied. Then we give several sufficient conditions such that an operator is a frame generator multiplier for certain unitary systems. Since there are two natural norms endowed with each Bessel multiplier, i.e., the usual operator norm and the Bessel norm, we compare these norms of Bessel multipliers for some cases.

Wandering subspaces and fusion frame generators for unitary systems

This work is inspired by the study of wandering vectors and frame vectors for unitary systems. We investigate the structure and properties of complete wandering subspaces for unitary systems, and, in particular, we consider the unitary systems with a structure similar to wavelet systems. Given a unitary system with a complete wandering subspace, a necessary and sufficient condition for a closed subspace to be a Parseval fusion frame generator is obtained. Moreover, we study the dilation property for Parseval fusion frame generators for unitary groups.

Canonical dual K-Bessel sequences and dual K-Bessel generators for unitary systems of Hilbert spaces

In this paper, firstly we explore some properties of K-frames in terms of decompositions of operators. Then we pay more attention to characterize the dual K-Bessel sequences of a given K-frames. Since the frame operator for a K-frame may not be invertible, there is no classical canonical dual for a K-frame. We introduce the concept of canonical dual K-Bessel sequence of a K-frame which generalizes the classical dual of a frame. We prove its existence and uniqueness and some other properties. We also give a simple way to construct new K-frames from given ones. For the K-frame generators of a unitary system, we give a condition such that a K-frame generator for a unitary group has a dual K-Bessel generator so that both of them share the same group structure. We characterize the K-frame generators in terms of operators and we also consider the construction of new K-frame generators from given ones.

Evaluation of residual waste char and ash from the Tactical Garbage to Energy Refinery

Abstract The Tactical Garbage to Energy Refinery (TGER) is a hybrid waste to energy system which combines advanced fermentation with thermal decomposition to convert mixed waste products such as plastic, cardboard and food waste, into energy. The hybrid design allows TGER to convert a broader range of waste streams into energy than possible with unitary systems. The waste output is in the form of a dry mix of ash and char, with the char to ash ratio being somewhat higher during initial start-up before the system has reached full efficiency. Samples of the residual material were collected from the initial and final runs and these materials were subjected to elemental analysis and morphological characterization. Visually, the general morphology of the samples resembled generic char with particulate sizes in the range of 5–10 μm. Scanning electron microscopy shows the char to be composed primarily of fibers which retain the general morphology of plant-based fibers. In addition to carbonaceous and organic material, energy dispersive X-ray spectroscopy indicates the presence of the elements Na, Al, Si, Mg, Ca and S, with traces of K, Ti, Fe and F. These are present inhomogeneously as either particulate inclusions or surface particles on fibers. Data indicate that the residual ash and char are generally innocuous and unlikely to pose environmental or health risks. Results will be used to determine the applicability of these materials for reuse in, for example, composite construction materials.

Rational Ignorance is Not Bliss: When do Lazy Voters Learn from Decentralised Policy Experiments?

A popular argument about economic policy under uncertainty states that decentralisation offers the possibility to learn from local or regional policy experiments. We argue that such learning processes are not trivial and do not occur frictionlessly: Voters have an inherent tendency to retain a given stock of policy-related knowledge which was costly to accumulate, so that yardstick competition is improbable to function well particularly for complex issues if representatives' actions are tightly controlled by the electorate. Decentralisation provides improved learning processes compared to unitary systems, but the results we can expect are far from the ideal mechanisms of producing and utilising knowledge often described in the literature.

Comparison of the Straight Adiabatic Capillary Tube Expansion Devices Used in Refrigeration Systems Operating With Refrigerants R134a and R1234yf

Capillary tube expansion devices are used extensively in small refrigeration and unitary air conditioning systems. R1234yf is likely to replace R134a in the next few years in many small refrigeration systems worldwide because of the new environmental regulations being proposed. In this paper, we compare the length and diameter of capillary tube required when R134a and R1234yf are used in a typical small refrigeration system. The minimum diameter of the capillary tube required has been estimated using the speed of sound of the refrigerant leaving the capillary tube in the two-phase state. The two-phase speed of sound routine developed by us can be used with both pure fluids and mixtures.

Minimization of unitary air-conditioning system power with real-time extremum seeking control

Minimization of total system power in single-zone variable air volume unitary AC systems is beneficial for reduction in energy consumption. In this study, a dynamic model of a single-zone variable air volume system including space condition control loops is developed. Two optimal control loops for power minimization utilizing the method of real time optimization by extremum seeking are investigated: supply air leaving-air temperature control and capacity distribution control for two tandem compressors. Supply fan leaving-air temperature control is significantly impacted by the supply fan static pressure, where at low pressures, the optimal leaving-air temperature tends to increase, which may lead to humidity concerns. For the compressor modeled, the compressor capacity distribution control demonstrates a 10.8% power savings over an evenly distributed capacity to two identical compressors.

Topological edge states in two-gap unitary systems: a transfer matrix approach

We construct and investigate a family of two-band unitary systems living on a cylinder geometry and presenting localized edge states. Using the transfer matrix formalism, we solve and investigate in detail such states in the thermodynamic limit. Analytic considerations then suggest the construction of a family of Riemann surfaces associated to the band structure of the system. In this picture, the corresponding edge states naturally wind around non-contractile loops, defining a topological invariant associated to each gap of the system.

SELF SIMILAR TILES ARISING FROM THE UNITARY NUMBER SYSTEMS IN EUCLIDEAN RINGS OF IMAGINARY QUADRATIC INTEGERS

Abstract. In [7], it was shown that Euclidean rings R of imaginary qua-dratic integers admit unitary number systems. In this paper, as an appli-cation of the result, we obtain all self similar tiles arising from the unitarynumber systems of R. 1. IntroductionLet Rbe a ring of imaginary quadratic integers, which consists of all algebraicintegers in the eld Qpdfor some square-free negative integer d, and let bbe an element of Rwhose norm N(b) is greater than one. Then a completerepresentatives Dof R=(b) is called a digit set for a base b, where (b) denotesan ideal generated by b. Then a unitary number system (b;D) in Ris de nedso that all non-zero elements of digits in Dconsist of units of R.From [7] we see that among the nine principal ideal domains of imaginaryquadratic integers, only the ve ringsZp 1; Zp 2; Z1 +p 32; Z1 +p 72; Z1 + 112;equipped with Euclidean functions de ned by norms admit unitary numbersystems. As proposed in [7], the concept of a unitary number system can be re-placement of a ‘universal side divisor’ by Motzkin. Furthermore unitary numbersystems are already available in various applications of complex based numbersystems. In particular, Khmelnik [3] and Penny [6] independently showed thata number system with a base b= 1 +p 1 and a digit set D= f0;1ginZp 1yields so called the twin dragon (see Figure 2 in Appendix). Knuth[5] proposed another binary number system with a base b=p 2 and a digit

Identified Serotonin-Releasing Neurons Induce Behavioral Quiescence and Suppress Mating in Drosophila.

An animal's responsiveness to external stimuli and its various types of endogenously generated, motivated behavior are highly dynamic and change between states of high activity and states of low activity. It remains unclear whether these states are mediated by unitary modulatory systems globally affecting brain activity, or whether distinct neurons modulate specific neuronal circuits underlying particular types of behavior. Using the model organism Drosophila melanogaster, we find that activating large proportions of serotonin-releasing neurons induces behavioral quiescence. Moreover, distinct serotonin-releasing neurons that we genetically isolated and identified negatively affect aspects of mating behavior, but not food uptake. This demonstrates that individual serotoninergic neurons can modulate distinct types of behavior selectively.