Cyclic Representations Research Articles

Berends-Giele currents in Bern-Carrasco-Johansson gauge for F3- and F4-deformed Yang-Mills amplitudes

We construct new representations of tree-level amplitudes in D-dimensional gauge theories with deformations via higher-mass-dimension operators α′F3 and α′2F4. Based on Berends-Giele recursions, the tensor structure of these amplitudes is compactly organized via off-shell currents. On the one hand, we present manifestly cyclic representations, where the complexity of the currents is systematically reduced. On the other hand, the duality between color and kinematics due to Bern, Carrasco and Johansson is manifested by means of non-linear gauge transformations of the currents. We exploit the resulting notion of Bern-Carrasco-Johansson gauge to provide explicit and manifestly local double-copy representations for gravitational amplitudes involving α′R2 and α′2R3 operators.

The Optimal Control of Two Work-Stealing Deques, Moving One After Another in a Shared Memory

In the parallel work-stealing load balancers, each core owns personal buffer of tasks called deque. One end of the deque is used by its owner to add and retrieve tasks, while the second end is used by other cores to steal tasks. In the paper two representation methods of deques are analyzed: partitioned serial cyclic representation of deques (one of the conventional techniques); and the new approach proposed by our team, without partition of shared memory in advance between deques moving one after another in a circle. Previously we analyzed these methods for representing FIFO queues in network applications, where the “One after another” way gave the best result for some values of the system parameters. Purpose of this research is to construct and analyze models of the process of work with two circular deques located in shared memory, where they movie one after another in a circle. The mathematical model is constructed in the form of a random walk by integer points in the pyramid. The simulation model is constructed using the Monte Carlo method. The used work-stealing strategy is stealing of one element. We propose the mathematical and simulation models of this process and carry out numerical experiments.

Remote state preparation using Einstein–Podolsky–Rosen representations

Because Einstein–Podolsky–Rosen states are well-defined on the Weyl algebra, their canonical cyclic representations are suitable for demonstrating the process of remote state preparation. Local projection-valued measurements and the corresponding recovery unitary operator are formulated in this representation, whereupon generalized equatorial states are prepared remotely and faithfully.

Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra II

This article is a direct continuation of where we begun the study of the transfer matrix spectral problem for the cyclic representations of the trigonometric 6-vertex reflection algebra associated to the Bazhanov-Stroganov Lax operator. There we addressed this problem for the case where one of the KK-matrices describing the boundary conditions is triangular. In the present article we consider the most general integrable boundary conditions, namely the most general boundary KK-matrices satisfying the reflection equation. The spectral analysis is developed by implementing the method of Separation of Variables (SoV). We first design a suitable gauge transformation that enable us to put into correspondence the spectral problem for the most general boundary conditions with another one having one boundary KK-matrix in a triangular form. In these settings the SoV resolution can be obtained along an extension of the method described in . The transfer matrix spectrum is then completely characterized in terms of the set of solutions to a discrete system of polynomial equations in a given class of functions and equivalently as the set of solutions to an analogue of Baxter’s T-Q functional equation. We further describe scalar product properties of the separate states including eigenstates of the transfer matrix.

Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra by quantum separation of variables

In this proceeding, we recall the notion of quantum integrable systems on a lattice and then introduce the Sklyanin’s Separation of Variables method. We sum up the main results for the transfer matrix spectral problem for the cyclic representations of the trigonometric 6-vertex reflection algebra associated to the Bazanov-Stroganov Lax operator. These results apply as well to the spectral analysis of the lattice sine-Gordon model with open boundary conditions. The transfer matrix spectrum (both eigenvalues and eigenstates) is completely characterized in terms of the set of solutions to a discrete system of polynomial equations. We state an equivalent characterization as the set of solutions to a Baxter’s like T-Q functional equation, allowing us to rewrite the transfer matrix eigenstates in an algebraic Bethe ansatz form.

Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra I

We study the transfer matrix spectral problem for the cyclic representations of the trigonometric 6-vertex reflection algebra associated to the Bazanov-Stroganov Lax operator. The results apply as well to the spectral analysis of the lattice sine-Gordon model with integrable open boundary conditions. This spectral analysis is developed by implementing the method of separation of variables (SoV). The transfer matrix spectrum (both eigenvalues and eigenstates) is completely characterized in terms of the set of solutions to a discrete system of polynomial equations in a given class of functions. Moreover, we prove an equivalent characterization as the set of solutions to a Baxter’s like T-Q functional equation and rewrite the transfer matrix eigenstates in an algebraic Bethe ansatz form. In order to explain our method in a simple case, the present paper is restricted to representations containing one constraint on the boundary parameters and on the parameters of the Bazanov-Stroganov Lax operator. In a next article, some more technical tools (like Baxter’s gauge transformations) will be introduced to extend our approach to general integrable boundary conditions.

The Gelfand–Naimark–Segal construction for unitary representations of $\mathbb Z_2^n$-graded Lie supergroups

We establish a Gelfand–Naimark–Segal construction which yields a correspondence between cyclic unitary representations and positive definite superfunctions of a general class of $\mathbb Z_2^n$-graded Lie supergroups.

Good Psychometric Properties of the Addiction Version of the Revised Illness Perception Questionnaire for Health Care Professionals.

BackgroundAddiction, or substance dependence, is nowadays considered a chronic relapsing condition. However, perceptions of addiction vary widely, also among healthcare professionals. Perceptions of addiction are thought to contribute to attitude and stigma towards patients with addiction. However, studies into perceptions of addiction among healthcare professionals are limited and instruments for reliable assessment of their perceptions are lacking. The Illness Perception Questionnaire (IPQ) is widely used to evaluate perceptions of illness. The aim of this study was to evaluate the psychometric properties of the IPQ: factor structure, internal consistency, and discriminant validity, when applied to evaluate healthcare professionals’ perceptions of addiction.MethodsParticipants were 1072 healthcare professionals in training and master students from the Netherlands and Indonesia, recruited from various addiction-training programs. The revised version of the IPQ was adapted to measure perceptions of addiction (IPQ-A). Maximum likelihood method was used to explore the best-fit IPQ factor structure. Internal consistency was evaluated for the final factors. The final factor structure was used to assess discriminant validity of the IPQ, by comparing illness perceptions of addiction between 1) medical students from the Netherlands and Indonesia, 2) medical students psychology students and educational science students from the Netherlands, and 3) participants with different training levels: medical students versus medical doctors.ResultsFactor analysis revealed an eight-factor structure for the perception subscale (demoralization, timeline chronic, consequences, personal control, treatment control, illness coherence, timeline cyclical emotional representations) and a four-factor structure for the attribution subscale (psychological attributions, risk factors, smoking/alcohol, overwork). Internal reliability was acceptable to good. The IPQ-A was able to detect differences in perceptions between healthcare professionals from different cultural and educational background and level of training.ConclusionsThe IPQ-A is a valid and reliable instrument to assess healthcare professionals’ perceptions of addiction.

Development of Cyclic Representations of Senior Preschoolers

Abstract This article is dedicated to the opportunities of development of cyclic representations of preschool children. Cyclic representations are mental structures allowing the reflection of development processes in the world around. An educational experiment is described where the children were suggested to solve some problems that required the application of dialectical mental actions. The evidence obtained as a result of this experiment lead to a conclusion that cyclic representations may be amplified through specifically designed educational program.

Illness Beliefs in End Stage Renal Disease and Associations with Self-Care Modality Choice

BackgroundInterest in self-care haemodialysis (HD) has increased because it improves patients’clinical and quality-of-life outcomes. Patients who undertake self-management for haemodialysis may hold illness beliefs differently to those choosing institutional care at the time of making the modality choice or moulded by their illness and dialysis treatment experience. Illness perceptions amongst predialysis patients and in those undertaking fully-assisted and self-care haemodialysis are being investigated in a combined cross-sectional and longitudinal study.Study DesignThe study data are derived from the BASIC-HHD study, a multicentre observational study on factors influencing home haemodialysis uptake. 535 patients were enrolled into three groups: Predialysis CKD-5 group, prevalent ‘in-centre’ HD and self-care HD groups (93% at home). We explore illness perceptions in the cross-sectional analyses of the three study groups, using the revised Illness Perception Questionnaire (IPQ-R). Predialysis patients’ illness beliefs were reassessed prospectively, typically between 4 and 12 months after dialysis commencement.ResultsIllness belief subscales are significantly different between in-centre and self-care HD groups. In a step-wise hierarchical regression analysis, after adjustment for age, education, marital status, diabetes, dialysis vintage, depression, anxiety scores, and IPQ-R subscales, personal control (p = 0.01) and illness coherence (p = 0.04) are significantly higher in the self-care HD group. In the predialysis group, no significant associations were found between illness representations and modality choices. In prospectively observed predialysis group, scores for personal control, treatment control, timeline cyclical and emotional representations reduced significantly after commencing dialysis and increased significantly for illness coherence.ConclusionsIllness beliefs differ between hospital and self-care haemodialysis patients. Patient’s affect and neurocognitive ability may have an important role in determining illness beliefs. The impact of modality upon illness representations may also be significant and remains to be explored.

The Representations and Positive Type Functions of Some Homogenous Spaces

For a homogeneous spaces G=H, we show that the convo- lution on L 1 (G=H) is the same as convolution on L 1 (K), where G is semidirect product of a closed subgroup H and a normal subgroup K of G. Also we prove that there exists a one to one correspondence be- tween nondegenerat -representations of L 1 (G=H) and representations of G=H. We propose a relation between cyclic representations of L 1 (G=H) and positive type functions on G=H. We prove that the Gelfand Raikov theorem for G=H holds if and only if H is normal.

Fixed point theorems for Ciric type generalized contractions defined on cyclic representations

Fixed point theorems for Ciric type generalized contractions defined on cyclic representations

Extending XCS with Cyclic Graphs for Scalability on Complex Boolean Problems.

A main research direction in the field of evolutionary machine learning is to develop a scalable classifier system to solve high-dimensional problems. Recently work has begun on autonomously reusing learned building blocks of knowledge to scale from low-dimensional problems to high-dimensional ones. An XCS-based classifier system, known as XCSCFC, has been shown to be scalable, through the addition of expression tree-like code fragments, to a limit beyond standard learning classifier systems. XCSCFC is especially beneficial if the target problem can be divided into a hierarchy of subproblems and each of them is solvable in a bottom-up fashion. However, if the hierarchy of subproblems is too deep, then XCSCFC becomes impractical because of the needed computational time and thus eventually hits a limit in problem size. A limitation in this technique is the lack of a cyclic representation, which is inherent in finite state machines (FSMs). However, the evolution of FSMs is a hard task owing to the combinatorially large number of possible states, connections, and interaction. Usually this requires supervised learning to minimize inappropriate FSMs, which for high-dimensional problems necessitates subsampling or incremental testing. To avoid these constraints, this work introduces a state-machine-based encoding scheme into XCS for the first time, termed XCSSMA. The proposed system has been tested on six complex Boolean problem domains: multiplexer, majority-on, carry, even-parity, count ones, and digital design verification problems. The proposed approach outperforms XCSCFA (an XCS that computes actions) and XCSF (an XCS that computes predictions) in three of the six problem domains, while the performance in others is similar. In addition, XCSSMA evolved, for the first time, compact and human readable general classifiers (i.e., solving any n-bit problems) for the even-parity and carry problem domains, demonstrating its ability to produce scalable solutions using a cyclic representation.

Cyclic representations of C*-algebras on Fock space

In this paper we characterize C*-algebras generated by semigroups of composition operators acting upon Fock space. With an approach of approximation from nonharmonic analysis, sufficient conditions for cyclic representations are obtained. We also characterize the cyclic representation of a C*-algebra of measures generated by Heisenberg groups.

On the Form Factors of Local Operators in the Bazhanov–Stroganov and Chiral Potts Models

We consider general cyclic representations of the six-vertex Yang–Baxter algebra and analyze the associated quantum integrable systems, the Bazhanov–Stroganov model and the corresponding chiral Potts model on finite size lattices. We first determine the propagator operator in terms of the chiral Potts transfer matrices and we compute the scalar product of separate states (including the transfer matrix eigenstates) as a single determinant formulae in the framework of Sklyanin’s quantum separation of variables. Then, we solve the quantum inverse problem and reconstruct the local operators in terms of the separate variables. We also determine a basis of operators whose form factors are characterized by a single determinant formulae. This implies that the form factors of any local operator are expressed as finite sums of determinants. Among these form factors written in determinant form are in particular those which will reproduce the chiral Potts order parameters in the thermodynamic limit. The results presented here are the generalization to the present models associated to the most general cyclic representations of the six-vertex Yang–Baxter algebra of those we derived for the lattice sine–Gordon model.

Convex geometric [formula omitted]-quasiplanar representations of semi-bar [formula omitted]-visibility graphs

Semi-bar k-visibility graphs are graphs for which vertices can be drawn as horizontal segments with left endpoints on the y-axis (semi-bars) and edges can be drawn as vertical segments (sightlines) so that two semi-bars are visible to each other if and only if there is a sightline which intersects them and at most k other semi-bars. Cyclic semi-bar k-visibility graphs are graphs for which vertices can be drawn as segments with one endpoint at the origin (semi-bars) and edges can be drawn as arcs of circles centered at the origin (sightlines) so that two semi-bars are visible to each other if and only if there is a sightline which intersects them and at most k other semi-bars. We show that every semi-bar or cyclic semi-bar k-visibility graph can be represented in the plane with vertices drawn as points in convex position and edges drawn as segments so that there are no k+2 pairwise crossing edges. Furthermore, we prove that the class of graphs having cyclic semi-bar k-visibility representations with semi-bars of different lengths is the same as the class of (2k+2)-degenerate graphs that can be represented in the plane with vertices drawn as points in convex position and edges drawn as segments so that there are no k+2 pairwise crossing edges and so that adding any edge would result in k+2 pairwise crossing edges.

Cyclic representations of the periodic Temperley–Lieb algebra, complex Virasoro representations and stochastic processes

An -dimensional representation of the periodic Temperley–Lieb algebra TLL(x) is presented. It is also a representation of the cyclic group ZN. We choose x = 1 and define a Hamiltonian as a sum of the generators of the algebra acting in this representation. This Hamiltonian gives the time evolution operator of a stochastic process. In the finite-size scaling limit, the spectrum of the Hamiltonian contains representations of the Virasoro algebra with complex highest weights. The N = 3 case is discussed in detail. We discuss briefly the consequences of the existence of complex Virasoro representations for the physical properties of the systems.

Using Rasch analysis to evaluate the validity of the diabetes-specific version of the Illness Perception Questionnaire–Revised

This study used Rasch analysis to examine the psychometric validity of the Illness Perception Questionnaire--Revised to assess beliefs about diabetes in 470 participants with Type 2 diabetes and 71 participants with Type 1 diabetes. All Illness Perception Questionnaire--Revised scales had psychometric issues, which included poorly utilised response categories, poor scale precision and multidimensionality. Following re-engineering, only four of the eight scales (Consequences, Illness coherence, Timeline cyclical and Emotional representations) were psychometrically adequate according to the Rasch model. The diabetes-specific version of the Illness Perception Questionnaire--Revised provides suboptimal assessment of beliefs held by patients with diabetes.

Dialectical Thinking as a Mechanism of Construction of Possible Relations for Senior Pre-school Children

Specifics of dialectical thinking consist in handling with oppositions. Current research was meant to check the following hypotheses: dialectical thinking can become a mechanism of construction of possible relations for pre-school children. We based on the assumption that application of dialectical mental acts allows think of possible relations taking in account relations existing in reality. “The possible” thus is created through mental transformation of the real, and is new comparing to that “real”.2 stages of empirical research revealed a correlation between the level of development of dialectical thinking and development of the ability to anticipate s well as with the maturity of cyclic representations. Existence of this connection and qualitative analysis of the responses given by children while completing the tasks of traditional techniques and the ones specially designed by us for examination of dialectical thinking, allows one to suppose commonness of mental mechanisms that help to productively complete those tasks. Dialectical thinking is used as a mechanism of discovering opportunities in the situation and the anticipation is based on assuming and supposing of opportunities and their evaluation. Cyclic representations reflect transformation of the possible to real, demonstrating reality of the “possibility”.

Periodic systems: a sequence algebra approach to realisation, parameterisation and topology

A characterisation of discrete time linear periodic systems is presented, based on a general framework using cyclic projection operators on sequences. Two known liftings of periodic systems to a time invariant one, the monodromy and the cyclic representation, are readily derived in this framework. This approach also leads to the definition of the operational transfer function for such systems, and more generally, the operational transfer inclusion. It is shown that the cyclic realisation allows the multiplexing of individual realisations of a periodic system. These descriptions are useful in the realisation problem and the search for canonical forms. Parameterisations for the class of reachable systems are recalled, and their geometric and topological features are illustrated.