Forbidden patterns and shift systems

The scope of this paper is two-fold. First, to present to the researchers in combinatorics an interesting implementation of permutations avoiding generalized patterns in the framework of discrete-time dynamical systems. Indeed, the orbits generated by piecewise monotone maps on one-dimensional intervals have forbidden order patterns, i.e., order patterns that do not occur in any orbit. The allowed patterns are then those patterns avoiding the so-called forbidden root patterns and their shifted patterns. The second scope is to study forbidden patterns in shift systems, which are universal models in information theory, dynamical systems and stochastic processes. Due to its simple structure, shift systems are accessible to a more detailed analysis and, at the same time, exhibit all important properties of low-dimensional chaotic dynamical systems (e.g., sensitivity to initial conditions, strong mixing and a dense set of periodic points), allowing to export the results to other dynamical systems via order-isomorphisms.Comment: 21 pages, expanded Section 5 and corrected Propositions 3 and

Random graph model with power-law distributed triangle subgraphs

Clustering is well-known to play a prominent role in the description and understanding of complex networks, and a large spectrum of tools and ideas have been introduced to this end. In particular, it has been recognized that the abundance of small subgraphs is important. Here, we study the arrangement of triangles in a model for scale-free random graphs and determine the asymptotic behavior of the clustering coefficient, the average number of triangles, as well as the number of triangles attached to the vertex of maximum degree. We prove that triangles are power-law distributed among vertices and characterized by both vertex and edge coagulation when the degree exponent satisfies $2<\beta<2.5$; furthermore, a finite density of triangles appears as $\beta=2+1/3$.Comment: 4 pages, 2 figure; v2: major conceptual change

Bulgac-Kusnezov-Nos\'e-Hoover thermostats

In this paper we formulate Bulgac-Kusnezov constant temperature dynamics in phase space by means of non-Hamiltonian brackets. Two generalized versions of the dynamics are similarly defined: one where the Bulgac-Kusnezov demons are globally controlled by means of a single additional Nos\'e variable, and another where each demon is coupled to an independent Nos\'e-Hoover thermostat. Numerically stable and efficient measure-preserving time-reversible algorithms are derived in a systematic way for each case. The chaotic properties of the different phase space flows are numerically illustrated through the paradigmatic example of the one-dimensional harmonic oscillator. It is found that, while the simple Bulgac-Kusnezov thermostat is apparently not ergodic, both of the Nos\'e-Hoover controlled dynamics sample the canonical distribution correctly

Transformational Leadership and Organizational Citizenship Behavior Motives in Teachers

A principal’s leadership is a key part to the success of a school as their leadership guides both instructional and organizational outcomes. Teachers often work beyond their formal duties to see that all their students have their needs met. This is referred to as an Organizational Citizenship Behavior (i.e., when followers display behaviors that benefit the organization or its members beyond their current job requirements). This study investigated the relationship between principal’s transformational leadership and teachers’ Organizational Citizenship Behaviors and related motivating factors. Participants from a suburban school district completed a questionnaire based on their perceptions of their principal’s leadership characteristics and reflections upon their own practices. The results showed the strongest transformational leadership practice is individualized support. This practice demonstrated positive relationships with Organizational Citizenship Behavior, Organizational Concern, and Prosocial Values. The outcomes of this study are intended to assist school leaders in promoting sound citizenship behaviors through leadership practices as well as informing leadership preparation

The impact of intra-operative factors in otosclerosis outcomes: retrospective study in a tertiary centre

The aim of the study was to assess results from a large cohort of patients undergoing otosclerosis surgery with respect to the impact of intra-operative variables on post-operative hearing function and complications. We enrolled 384 patients affected by otosclerosis who were subjected to stapes surgery between 2004 and 2013 at a single institution. Surgery was performed in all cases under local anaesthesia, using a manual perforator and/or microdrill. Teflon-piston prosthesis was used in all patients. Audiological data obtained preoperatively and at last follow-up examination (minimum 12 months) were compared. Statistical analysis was performed using the multiple regression model. Peripheral rim otosclerosis and diffuse otosclerosis were associated with better functional results compared to the obliterative pattern (p &lt; 0.05). Mean post-operative Air-Bone Gap was significantly higher in the 0.4 mm, compared to 0.6 mm piston group at 0.5 kHz (p &lt; 0.001) and 1 kHz (p &lt; 0.02); in the stapedotomy group a statistically significant difference was found between 0.4 and 0.6 mm piston groups, in favour of the latter (p &lt; 0.05). No differences were encountered in terms of average hearing threshold and complications. Intra-operative variables cannot be fully predictable and our data could help in stratification of the results and as a landmark for the surgeon’s decisions

Process performance and precipitate quality of phosphorus recovery by struvite precipitation in a fluidized bed reactor using a MgO industrial by-product

Phosphorus recovery through struvite precipitation has gained interest due to the potential use of struvite as a fertiliser, with fluidised bed reactors being a popular technology for carrying out the process. Struvite precipitation requires a magnesium source and an alkaline reagent. This research uses a low-grade magnesium oxide (LG-MgO) industrial by-product with a 56 wt% of MgO as magnesium source and an alkaline reagent to lower operating costs and value-add an industrial by-product. LG-MgO is poorly soluble in water, but its solubility increases significantly when dissolved in anaerobic digestion supernatants due to its circumneutral pH and high buffer capacity. Phosphorus precipitation was carried out in a laboratory-scale fluidised bed reactor where three operating variables (i.e. P:Mg molar ratio, feed inlet position, and recirculation flow rate) were studied to determine the LG-MgO impact on precipitate struvite content. Experimental results showed a high struvite content in all precipitates, close to the values reported for pure magnesium sources. The P:Mg molar ratio influenced precipitate composition. The percentage of struvite in the precipitate were 75–82 wt%, 85–88 wt%, and 75–76 wt% for the P:Mg ratio of 1:0.5, 1:1 and 1:3, respectively. The feed inlet position (side or bottom) also had an impact on precipitate struvite content when the P:Mg molar ratio was 1:3, but not for the other molar ratios. The recirculation flow rate did not have a significant impact on precipitate struvite content

Secrecy extraction from no-signalling correlations

Quantum cryptography shows that one can guarantee the secrecy of correlation on the sole basis of the laws of physics, that is without limiting the computational power of the eavesdropper. The usual security proofs suppose that the authorized partners, Alice and Bob, have a perfect knowledge and control of their quantum systems and devices; for instance, they must be sure that the logical bits have been encoded in true qubits, and not in higher-dimensional systems. In this paper, we present an approach that circumvents this strong assumption. We define protocols, both for the case of bits and for generic $d$-dimensional outcomes, in which the security is guaranteed by the very structure of the Alice-Bob correlations, under the no-signalling condition. The idea is that, if the correlations cannot be produced by shared randomness, then Eve has poor knowledge of Alice's and Bob's symbols. The present study assumes, on the one hand that the eavesdropper Eve performs only individual attacks (this is a limitation to be removed in further work), on the other hand that Eve can distribute any correlation compatible with the no-signalling condition (in this sense her power is greater than what quantum physics allows). Under these assumptions, we prove that the protocols defined here allow extracting secrecy from noisy correlations, when these correlations violate a Bell-type inequality by a sufficiently large amount. The region, in which secrecy extraction is possible, extends within the region of correlations achievable by measurements on entangled quantum states.Comment: 23 pages, 4 figure

L’analisi della curva di apprendimento della chirurgia dell’otosclerosi può aiutare a predirre i risultati funzionali?

Il numero di interventi per otosclerosi è progressivamente diminuito nel corso degli ultimi 20 anni. Questa riduzione crea difficoltà sia al chirurgo esperto ma soprattutto a quello giovane che inizia il suo percorso di formazione. Abbiamo analizzato in maniera retrospettiva i risultati funzionali ottenuti dopo stapedotomia effettuati da un giovane chirurgo presso la Clinica Otorinolaringoiatrica del Policlinico “A. Gemelli” di Roma. La tecnica impiegata è quella della stapedotomia con laser COe utilizziamo una protesi in teflon e titanio. I risultati funzionali sono stati valutati come riduzione della ipoacusia trasmissiva sulle frequenze comprese tra 250 e 4000 Hz all’ultimo esame eseguito durante il follow-up. L’analisi dei dati non ha evidenziato un momento in cui la curva di apprendimento possa essere considerata conclusa poiché ottimi risultati con una riduzione pressoché completa della ipoacusia trasmissiva si sono alternati con altri i cui risultati funzionali non sono stati altrettanto ottimi. In nessun caso si è comunque registrata una coclearizzazione dell’ipoacusia. Questa analisi supporta l’esistenza di una curva di apprendimento della chirurgia dell’otosclerosi senza però individuare un punto dopo il quale si possa prevedere che i risultati funzionali saranno tutti ottimi. La chirurgia dell’otosclerosi non dovrebbe essere effettuata all’inizio della pratica della chirurgia otologica, data l’aspettativa funzionale che il paziente ripone nell’intervento e la mancanza delle capacità chirurgiche necessarie

Phase-Space Metric for Non-Hamiltonian Systems

We consider an invariant skew-symmetric phase-space metric for non-Hamiltonian systems. We say that the metric is an invariant if the metric tensor field is an integral of motion. We derive the time-dependent skew-symmetric phase-space metric that satisfies the Jacobi identity. The example of non-Hamiltonian systems with linear friction term is considered.Comment: 12 page