Representations of Conformal Nets, Universal C*-Algebras and K-Theory

We study the representation theory of a conformal net A on the circle from a K-theoretical point of view using its universal C*-algebra C*(A). We prove that if A satisfies the split property then, for every representation \pi of A with finite statistical dimension, \pi(C*(A)) is weakly closed and hence a finite direct sum of type I_\infty factors. We define the more manageable locally normal universal C*-algebra C*_ln(A) as the quotient of C*(A) by its largest ideal vanishing in all locally normal representations and we investigate its structure. In particular, if A is completely rational with n sectors, then C*_ln(A) is a direct sum of n type I_\infty factors. Its ideal K_A of compact operators has nontrivial K-theory, and we prove that the DHR endomorphisms of C*(A) with finite statistical dimension act on K_A, giving rise to an action of the fusion semiring of DHR sectors on K_0(K_A)$. Moreover, we show that this action corresponds to the regular representation of the associated fusion algebra.Comment: v2: we added some comments in the introduction and new references. v3: new authors' addresses, minor corrections. To appear in Commun. Math. Phys. v4: minor corrections, updated reference

Super-KMS functionals for graded-local conformal nets

Motivated by a few preceding papers and a question of R. Longo, we introduce super-KMS functionals for graded translation-covariant nets over R with superderivations, roughly speaking as a certain supersymmetric modification of classical KMS states on translation-covariant nets over R, fundamental objects in chiral algebraic quantum field theory. Although we are able to make a few statements concerning their general structure, most properties will be studied in the setting of specific graded-local (super-) conformal models. In particular, we provide a constructive existence and partial uniqueness proof of super-KMS functionals for the supersymmetric free field, for certain subnets, and for the super-Virasoro net with central charge c>= 3/2. Moreover, as a separate result, we classify bounded super-KMS functionals for graded-local conformal nets over S^1 with respect to rotations.Comment: 30 pages, revised version (to appear in Ann. H. Poincare

Thermal States in Conformal QFT. II

We continue the analysis of the set of locally normal KMS states w.r.t. the translation group for a local conformal net A of von Neumann algebras on the real line. In the first part we have proved the uniqueness of KMS state on every completely rational net. In this second part, we exhibit several (non-rational) conformal nets which admit continuously many primary KMS states. We give a complete classification of the KMS states on the U(1)-current net and on the Virasoro net Vir_1 with the central charge c=1, whilst for the Virasoro net Vir_c with c>1 we exhibit a (possibly incomplete) list of continuously many primary KMS states. To this end, we provide a variation of the Araki-Haag-Kastler-Takesaki theorem within the locally normal system framework: if there is an inclusion of split nets A in B and A is the fixed point of B w.r.t. a compact gauge group, then any locally normal, primary KMS state on A extends to a locally normal, primary state on B, KMS w.r.t. a perturbed translation. Concerning the non-local case, we show that the free Fermi model admits a unique KMS state.Comment: 36 pages, no figure. Dedicated to Rudolf Haag on the occasion of his 90th birthday. The final version is available under Open Access. This paper contains corrections to the Araki-Haag-Kaster-Takesaki theorem (and to a proof of the same theorem in the book by Bratteli-Robinson). v3: a reference correcte

Experimental characterization of thermally-activated artificial muscles based on coiled nylon fishing lines

The discovery of an innovative class of thermally activated actuators based on twisted polymeric fibres has opened new horizons toward the development of effective devices that can be easily manufactured using inexpensive materials such as fishing lines or sewing threads. These new devices show large deformations when heated together with promising performance in terms of energy and power densities. With the aim of providing information and data useful for the future engineering applications, we present the results of a thermo-mechanical characterization conducted on a specific type of twisted polymeric fibre (i.e. nylon-made coiled actuators) that is considered particularly promising. A custom experimental test-bench and procedure have been developed and employed to run isothermal and isometric tensile tests on a set of specimens that are fabricated with a simple and repeatable process. The results of the experiments highlight some important issues related to the response of these actuators such as hysteresis, repeatability, predictability and stored elastic energy

A Characterization of Bispecial Sturmian Words

A finite Sturmian word w over the alphabet {a,b} is left special (resp. right special) if aw and bw (resp. wa and wb) are both Sturmian words. A bispecial Sturmian word is a Sturmian word that is both left and right special. We show as a main result that bispecial Sturmian words are exactly the maximal internal factors of Christoffel words, that are words coding the digital approximations of segments in the Euclidean plane. This result is an extension of the known relation between central words and primitive Christoffel words. Our characterization allows us to give an enumerative formula for bispecial Sturmian words. We also investigate the minimal forbidden words for the set of Sturmian words.Comment: Accepted to MFCS 201

Shortest Repetition-Free Words Accepted by Automata

We consider the following problem: given that a finite automaton $M$ of $N$ states accepts at least one $k$-power-free (resp., overlap-free) word, what is the length of the shortest such word accepted? We give upper and lower bounds which, unfortunately, are widely separated.Comment: 12 pages, conference pape

Some computations in the cyclic permutations of completely rational nets

In this paper we calculate certain chiral quantities from the cyclic permutation orbifold of a general completely rational net. We determine the fusion of a fundamental soliton, and by suitably modified arguments of A. Coste , T. Gannon and especially P. Bantay to our setting we are able to prove a number of arithmetic properties including congruence subgroup properties for $S, T$ matrices of a completely rational net defined by K.-H. Rehren .Comment: 30 Pages Late

Interprofessional collaboration between different health care professions in emilia romagna

Background and aim of the work: Interprofessional collaboration in the healthcare sector contributes to the delivery of high quality and safe services to patients across different subdivisions of the healthcare system which is faced with constant challenges. The international literature offers a plethora of tools for assessing the collaboration between health workers, but only a few of these have been validated in the Italian language. One that has undergone such validation is the interprofessional collaboration (IPC) scale, which measures the perception of collaboration among health professionals. An advantage of this scale is that is addresses all workers within the system, and is not limited to specific professions. The aim of the present study was to apply the validated Italian version of the IPC scale, to a context different to the one used for its validation, to measure the level of collaboration between different health care workers. Method: A questionnaire-based study was conducted on a sample consisting of 329 health professionals working at Azienda USL-IRCCS in Reggio Emilia. The categorical and continuous variables were analysed using descriptive statistics (frequen-cies, percentages and standard deviations). Results: The IPC scale showed physicians to express the highest level of collaboration with other professionals, in line with the results of other studies in the literature. The values calculated for the factors “accommodation” and “communication” were higher than for “isolation”, de-picting a good level collaboration. The only case in which the isolation factor, which describes an absence of collaboration, was equal to the other two factors was in relation to the evaluation of midwives by nursing aides/orderlies. Conclusions: In conclusion, the Italian version of the IPC scale provides a useful instrument for measuring interprofessional collaboration between workers in the healthcare sector. In the present study, it revealed a satisfactory level of collaboration between health professionals in an organization located in Emilia Romagna, Italy. (www.actabiomedica.it)

Soft capacitor fibers using conductive polymers for electronic textiles

A novel, highly flexible, conductive polymer-based fiber with high electric capacitance is reported. In its crossection the fiber features a periodic sequence of hundreds of conductive and isolating plastic layers positioned around metallic electrodes. The fiber is fabricated using fiber drawing method, where a multi-material macroscopic preform is drawn into a sub-millimeter capacitor fiber in a single fabrication step. Several kilometres of fibers can be obtained from a single preform with fiber diameters ranging between 500um -1000um. A typical measured capacitance of our fibers is 60-100 nF/m and it is independent of the fiber diameter. For comparison, a coaxial cable of the comparable dimensions would have only ~0.06nF/m capacitance. Analysis of the fiber frequency response shows that in its simplest interrogation mode the capacitor fiber has a transverse resistance of 5 kOhm/L, which is inversely proportional to the fiber length L and is independent of the fiber diameter. Softness of the fiber materials, absence of liquid electrolyte in the fiber structure, ease of scalability to large production volumes, and high capacitance of our fibers make them interesting for various smart textile applications ranging from distributed sensing to energy storage