Rational periodic sequences for the Lyness recurrence

Consider the celebrated Lyness recurrence $x_{n+2}=(a+x_{n+1})/x_{n}$ with $a\in\Q$. First we prove that there exist initial conditions and values of $a$ for which it generates periodic sequences of rational numbers with prime periods $1,2,3,5,6,7,8,9,10$ or $12$ and that these are the only periods that rational sequences $\{x_n\}_n$ can have. It is known that if we restrict our attention to positive rational values of $a$ and positive rational initial conditions the only possible periods are $1,5$ and $9$. Moreover 1-periodic and 5-periodic sequences are easily obtained. We prove that for infinitely many positive values of $a,$ positive 9-period rational sequences occur. This last result is our main contribution and answers an open question left in previous works of Bastien \& Rogalski and Zeeman. We also prove that the level sets of the invariant associated to the Lyness map is a two-parameter family of elliptic curves that is a universal family of the elliptic curves with a point of order $n, n\ge5,$ including $n$ infinity. This fact implies that the Lyness map is a universal normal form for most birrational maps on elliptic curves.

On periodic solutions of 2-periodic Lyness difference equations

We study the existence of periodic solutions of the non--autonomous periodic Lyness' recurrence u_{n+2}=(a_n+u_{n+1})/u_n, where {a_n} is a cycle with positive values a,b and with positive initial conditions. It is known that for a=b=1 all the sequences generated by this recurrence are 5-periodic. We prove that for each pair (a,b) different from (1,1) there are infinitely many initial conditions giving rise to periodic sequences, and that the family of recurrences have almost all the even periods. If a is not equal to b, then any odd period, except 1, appears.

Gravity-driven slug motion in capillary tubes

The velocity of a liquid slug falling in a capillary tube is lower than predicted for Poiseuille flow due to presence of menisci, whose shapes are determined by the complex interplay of capillary, viscous, and gravitational forces. Due to the presence of menisci, a capillary pressure proportional to surface curvature acts on the slug and streamlines are bent close to the interface, resulting in enhanced viscous dissipation at the wedges. To determine the origin of drag-force increase relative to Poiseuille flow, we compute the force resultant acting on the slug by integrating Navier-Stokes equations over the liquid volume. Invoking relationships from differential geometry we demonstrate that the additional drag is due to viscous forces only and that no capillary drag of hydrodynamic origin exists (i.e., due to hydrodynamic deformation of the interface). Requiring that the force resultant is zero, we derive scaling laws for the steady velocity in the limit of small capillary numbers by estimating the leading order viscous dissipation in the different regions of the slug (i.e., the unperturbed Poiseuille-like bulk, the static menisci close to the tube axis and the dynamic regions close to the contact lines). Considering both partial and complete wetting, we find that the relationship between dimensionless velocity and weight is, in general, nonlinear. Whereas the relationship obtained for complete-wetting conditions is found in agreement with the experimental data of Bico and Quere [J. Bico and D. Quere, J. Colloid Interface Sci. 243, 262 (2001)], the scaling law under partial-wetting conditions is validated by numerical simulations performed with the Volume of Fluid method. The simulated steady velocities agree with the behavior predicted by the theoretical scaling laws in presence and in absence of static contact angle hysteresis. The numerical simulations suggest that wedge-flow dissipation alone cannot account for the entire additional drag and that the non-Poiseuille dissipation in the static menisci (not considered in previous studies) has to be considered for large contact angles.

On an asymptotic formula for the maximum voltage drop in a on-chip power distribution network

We present a new asymptotic formula for the maximum static voltage in a simplified model for on-chip power distribution networks of array bonded integrated circuits. In this model the voltage is the solution of a Poisson equation in an infinite planar domain whose boundary is an array of circular pads of radius ", and we deal with the singular limit Ɛ → 0 case. In comparison with approximations that appear in the electronic engineering literature, our formula is more complete since we have obtained terms up to order Ɛ15. A procedure will be presented to compute all the successive terms, which can be interpreted as using multipole solutions of equations involving spatial derivatives of functions. To deduce the formula we use the method of matched asymptotic expansions. Our results are completely analytical and we make an extensive use of special functions and of the Gauss constant G

Structural, metamorphic and geochronological relations between the Zanskar Shear Zone and the Miyar Shear Zone (NW Indian Himalaya): Evidence for two distinct tectonic structures and implications for the evolution of the High Himalayan Crystalline of Zanskar

The geologic structures and metamorphic zonation of the northwestern Indian Himalaya contrast significantly with those in the central and eastern parts of the range, where the high-grade metamorphic rocks of the High Himalayan Crystalline (HHC) thrust southward over the weakly metamorphosed sediments of the Lesser Himalaya along the Main Central Thrust (MCT). Indeed, the hanging wall of the MCT in the NW Himalaya mainly consists of the greenschist facies metasediments of the Chamba zone, whereas HHC high-grade rocks are exposed more internally in the range as a large-scale dome called the Gianbul dome. This Gianbul dome is bounded by two oppositely directed shear zones, the NE-dipping Zanskar Shear Zone (ZSZ) on the northern flank and the SW-dipping Miyar Shear Zone (MSZ) on the southern limb. Current models for the emplacement of the HHC in NW India as a dome structure differ mainly in terms of the roles played by both the ZSZ and the MSZ during the tectonothermal evolution of the HHC. In both the channel flow model and wedge extrusion model, the ZSZ acts as a backstop normal fault along which the high-grade metamorphic rocks of the HHC of Zanskar are exhumed. In contrast, the recently proposed tectonic wedging model argues that the ZSZ and the MSZ correspond to one single detachment system that operates as a subhorizontal backthrust off of the MCT. Thus, the kinematic evolution of the two shear zones, the ZSZ and the MSZ, and their structural, metamorphic and chronological relations appear to be diagnostic features for discriminating the different models. In this paper, structural, metamorphic and geochronological data demonstrate that the MSZ and the ZSZ experienced two distinct kinematic evolutions. As such, the data presented in this paper rule out the hypothesis that the MSZ and the ZSZ constitute one single detachment system, as postulated by the tectonic wedging model. Structural, metamorphic and geochronological data are used to present an alternative tectonic model for the large-scale doming in the NW Indian Himalaya involving early NE-directed tectonics, weakness in the upper crust, reduced erosion at the orogenic front and rapid exhumation along both the ZSZ and the MSZ.

The timing of exploratory decision-making revealed by single-trial topographic EEGanalyses.

Decision-making in an uncertain environment is driven by two major needs: exploring the environment to gather information or exploiting acquired knowledge to maximize reward. The neural processes underlying exploratory decision-making have been mainly studied by means of functional magnetic resonance imaging, overlooking any information about the time when decisions are made. Here, we carried out an electroencephalography (EEG) experiment, in order to detect the time when the brain generators responsible for these decisions have been sufficiently activated to lead to the next decision. Our analyses, based on a classification scheme, extract time-unlocked voltage topographies during reward presentation and use them to predict the type of decisions made on the subsequent trial. Classification accuracy, measured as the area under the Receiver Operator's Characteristic curve was on average 0.65 across 7 subjects. Classification accuracy was above chance levels already after 516 ms on average, across subjects. We speculate that decisions were already made before this critical period, as confirmed by a positive correlation with reaction times across subjects. On an individual subject basis, distributed source estimations were performed on the extracted topographies to statistically evaluate the neural correlates of decision-making. For trials leading to exploration, there was significantly higher activity in dorsolateral prefrontal cortex and the right supramarginal gyrus; areas responsible for modulating behavior under risk and deduction. No area was more active during exploitation. We show for the first time the temporal evolution of differential patterns of brain activation in an exploratory decision-making task on a single-trial basis.

Pasquale del Pezzo, Duke of Caianello, Neapolitan mathematician

This article is dedicated to a reconstruction of some events and achievements, both personal and scientific, in the life of the Neapolitan mathematician Pasquale del Pezzo, Duke of Caianello.

Early auditory processing

ABSTRACT (English)An accurate processing of the order between sensory events at the millisecond time scale is crucial for both sensori-motor and cognitive functions. Temporal order judgment (TOJ) tasks, is the ability of discriminating the order of presentation of several stimuli presented in a rapid succession. The aim of the present thesis is to further investigate the spatio-temporal brain mechanisms supporting TOJ. In three studies we focus on the dependency of TOJ accuracy on the brain states preceding the presentation of TOJ stimuli, the neural correlates of accurate vs. inaccurate TOJ and whether and how TOJ performance can be improved with training.In "Pre-stimulus beta oscillations within left posterior sylvian regions impact auditory temporal order judgment accuracy" (Bernasconi et al., 2011), we investigated if the brain activity immediately preceding the presentation of the stimuli modulates TOJ performance. By contrasting the electrophysiological activity before the stimulus presentation as a function of TOJ accuracy we observed a stronger pre-stimulus beta (20Hz) oscillatory activity within the left posterior sylvian region (PSR) before accurate than inaccurate TOJ trials.In "Interhemispheric coupling between the posterior sylvian regions impacts successful auditory temporal order judgment" (Bernasconi et al., 2010a), and "Plastic brain mechanisms for attaining auditory temporal order judgment proficiency" (Bernasconi et al., 2010b), we investigated the spatio-temporal brain dynamics underlying auditory TOJ. In both studies we observed a topographic modulation as a function of TOJ performance at ~40ms after the onset of the first sound, indicating the engagement of distinct configurations of intracranial generators. Source estimations in the first study revealed a bilateral PSR activity for both accurate and inaccurate TOJ trials. Moreover, activity within left, but not right, PSR correlated with TOJ performance. Source estimations in the second study revealed a training-induced left lateralization of the initial bilateral (i.e. PSR) brain response. Moreover, the activity within the left PSR region correlated with TOJ performance.Based on these results, we suggest that a "temporal stamp" is established within left PSR on the first sound within the pair at early stages (i.e. ~40ms) of cortical processes, but is critically modulated by inputs from right PSR (Bernasconi et al., 2010a; b). The "temporal stamp" on the first sound may be established via a sensory gating or prior entry mechanism.Behavioral and brain responses to identical stimuli can vary due to attention modulation, vary with experimental and task parameters or "internal noise". In a fourth experiment (Bernasconi et al., 2011b) we investigated where and when "neural noise" manifest during the stimulus processing. Contrasting the AEPs of identical sound perceived as High vs. Low pitch, a topographic modulation occurred at ca. 100ms after the onset of the sound. Source estimation revealed activity within regions compatible with pitch discrimination. Thus, we provided neurophysiological evidence for the variation in perception induced by "neural noise".ABSTRACT (French)Un traitement précis de l'ordre des événements sensoriels sur une échelle de temps de milliseconde est crucial pour les fonctions sensori-motrices et cognitives. Les tâches de jugement d'ordre temporel (JOT), consistant à présenter plusieurs stimuli en succession rapide, sont traditionnellement employées pour étudier les mécanismes neuronaux soutenant le traitement d'informations sensorielles qui varient rapidement. Le but de cette thèse est d'étudier le mécanisme cérébral soutenant JOT. Dans les trois études présentées nous nous sommes concentrés sur les états du cerveau précédant la présentation des stimuli de JOT, les bases neurales pour un JOT correct vs. incorrect et sur la possibilité et les moyens d'améliorer l'exécution du JOT grâce à un entraînement.Dans "Pre-stimulus beta oscillations within left posterior sylvian regions impact auditory temporal order judgment accuracy" (Bernasconi et al., 2011),, nous nous sommes intéressé à savoir si l'activité oscillatoire du cerveau au pré-stimulus modulait la performance du JOT. Nous avons contrasté l'activité électrophysiologique en fonction de la performance TOJ, mesurant une activité oscillatoire beta au pré-stimulus plus fort dans la région sylvian postérieure gauche (PSR) liée à un JOT correct.Dans "Interhemispheric coupling between the posterior sylvian regions impacts successful auditory temporal order judgment" (Bernasconi et al., 2010a), et "Plastic brain mechanisms for attaining auditory temporal order judgment proficiency" (Bernasconi et al., 2010b), nous avons étudié la dynamique spatio-temporelle dans le cerveau impliqué dans le traitement du JOT auditif. Dans ses deux études, nous avons observé une modulation topographique à ~40ms après le début du premier son, en fonction de la performance JOT, indiquant l'engagement des configurations de générateurs intra- crâniens distincts. La localisation de source dans la première étude indique une activité bilatérale de PSR pour des JOT corrects vs. incorrects. Par ailleurs, l'activité dans PSR gauche, mais pas dans le droit, est corrélée avec la performance du JOT. La localisation de source dans la deuxième étude indiquait une latéralisation gauche induite par l'entraînement d'une réponse initialement bilatérale du cerveau. D'ailleurs, l'activité dans la région PSR gauche corrèlait avec la performance de TOJ.Basé sur ces résultats, nous proposons qu'un « timbre-temporel » soit établi très tôt (c.-à-d. à ~40ms) sur le premier son par le PSR gauche, mais module par l'activité du PSR droite (Bernasconi et al., 2010a ; b). « Le timbre- temporel » sur le premier son peut être établi par le mécanisme neuronal de type « sensory gating » ou « prior entry ».Les réponses comportementales et du cerveau aux stimuli identiques peut varier du à des modulations d'attention ou à des variations dans les paramètres des tâches ou au bruit interne du cerveau. Dans une quatrième expérience (Bernasconi et al. 2011B), nous avons étudié où et quand le »bruit neuronal« se manifeste pendant le traitement des stimuli. En contrastant les AEPs de sons identiques perçus comme aigus vs. grave, nous avons mesuré une modulation topographique à env. 100ms après l'apparition du son. L'estimation de source a révélé une activité dans les régions compatibles avec la discrimination de fréquences. Ainsi, nous avons fourni des preuves neurophysiologiques de la variation de la perception induite par le «bruit neuronal».

Computational and Energy Costs of Cryptographic Algorithms on Handheld Devices

Networks are evolving toward a ubiquitous model in which heterogeneousdevices are interconnected. Cryptographic algorithms are required for developing securitysolutions that protect network activity. However, the computational and energy limitationsof network devices jeopardize the actual implementation of such mechanisms. In thispaper, we perform a wide analysis on the expenses of launching symmetric and asymmetriccryptographic algorithms, hash chain functions, elliptic curves cryptography and pairingbased cryptography on personal agendas, and compare them with the costs of basic operatingsystem functions. Results show that although cryptographic power costs are high and suchoperations shall be restricted in time, they are not the main limiting factor of the autonomyof a device.

Primary γδ T cell lymphoma of the lung: report of a case with features suggesting derivation from intraepithelial γδ T lymphocytes [Primary gammadelta T cell lymphoma of the lung: report of a case with features suggesting derivation from intraepithelial gammadelta T lymphocytes].

T cell lymphoma of γδ T cell origin is a rare disease that mainly involves extranodal sites and shows aggressive clinical behavior. Here, we report a case of primary γδ T cell lymphoma of the lungs with epitheliotropism in the respiratory epithelium, a feature somewhat reminiscent of what is observed in enteropathy-associated T cell lymphoma. A 63-year-old man presented with chest pain and dyspnea on exertion, weight loss, and general weakness. On a positron emission tomography (PET) scan, multiple hypermetabolic lesions were found in both lungs. Microscopic examination of the wedge lung biopsy revealed nodular infiltration of monomorphic, medium- to large-sized atypical lymphocytes with round nuclei, coarse chromatin, and a variable amount of clear to eosinophilic cytoplasm. Of note, intraepithelial lymphocytosis by atypical lymphoid cells was observed in the respiratory epithelium within and around the nodule. Immunohistochemically, the tumor cells were CD3+, TCRβF1-, TCRγ+, CD5-, CD7+, CD20-, CD79a-, CD30-, CD4-, CD8-, CD10-, BCL6-, CD21-, CD56+, CD57-, and CD138-, and expressed cytotoxic molecules. Epstein-Barr virus (EBV) was not detected by an in situ hybridization assay for EBV-encoded RNA. Interestingly, CD103 was expressed by a subset of tumor cells, especially those infiltrating the epithelium. T cell clonality was detected by multiplex PCR analysis of TRG and TRD gene rearrangements. After 2 months of systemic chemotherapy, PET scan showed regression of the size and metabolic activity of the lesions. This case represents a unique γδ T cell lymphoma of the lungs showing epitheliotropism by CD103+ γδ T cells that is suggestive of tissue-resident γδ T cells as the cell of origin.

Designing Digital Filters for Servo Systems

The aim of this work was to select an appropriate digital filter for a servo application and to filter the noise from the measurement devices. Low pass filter attenuates the high frequency noise beyond the specified cut-off frequency. Digital lowpass filters in both IIR and FIR responses were designed and experimentally compared to understand their characteristics from the corresponding step responses of the system. Kaiser Windowing and Equiripple methods were selected for FIR response, whereas Butterworth, Chebyshev, InverseChebyshev and Elliptic methods were designed for IIR case. Limitations in digital filter design for a servo system were analysed. Especially the dynamic influences of each designed filter on the control stabilityof the electrical servo drive were observed. The criterion for the selection ofparameters in designing digital filters for servo systems was studied. Control system dynamics was given significant importance and the use of FIR and IIR responses in different situations were compared to justify the selection of suitableresponse in each case. The software used in the filter design was MatLab/Simulink® and dSPACE's DSP application. A speed controlled Permanent Magnet Linear synchronous Motor was used in the experimental work.

Primääri-sekundäärivuodon tunnistaminen aktiivisuusmittauksin Loviisan voimalaitoksella

Diplomityössä tutkittiin Loviisan voimalaitoksen primääri- ja sekundääripiirin aktiivisuusmittausten kykyä tunnistaa pienet primääri-sekundäärivuodot. Tarkasteltavat primääri-sekundäärivuotojen suuruudet valittiin laitoksen hätätilanne- ja häiriönselvitysohjeiden mukaisesti. Vuodon vaikutuksia arvioitiin erilaisilla primäärijäähdytteen ominaisaktiivisuuksilla. Ominaisaktiivisuudet primääripiirissä määritettiin nuklidikohtaisesti erilaisille polttoainevuototapauksille. Työssä huomioitiin myös transienteissa mahdollisesti esiintyvä primääripiirin aktiivisuustasoa nostava spiking-ilmiö. Vuodon tarkempaa tunnistamista varten työssä laskettiin tarkasteltaville mittareille kalibrointikertoimet. Primääri-sekundäärivuoto mallinnettiin APROS-simulointiohjelmalla laitoksen eri käyttötiloissa ja kahdella eri vuotokoolla. Varsinainen aktiivisuuslaskenta suoritettiin SEKUN-ohjelmalla. Työssä tätä aktiivisuus- ja päästölaskentaohjelmaa muokattiin ohjelmoimalla siihen tarkasteltavat aktiivisuusmittaukset sekä primääripiirin puhdistus ja ulospuhallus. Laskelmien tuloksena saatiin arviot kunkin tarkasteltavana olleen aktiivisuusmittauksen soveltuvuudesta primääri-sekundäärivuodon tunnistamiseen erilaisissa polttoainevuototapauksissa ja reaktorin eri tehotasoilla. Häiriönselvitysohje I3:n käyttöönottoa edellyttävät vuotokoot määritettiin aktiivisuusmittausten havaitseman perusteella. Erityisesti kuumavalmiustilassa tapauksissa, joissa reaktorisydämessä oletetaan olevan tiiveytensä menettäneitä polttoainesauvoja, spikingin vaikutus jäähdytteiden aktiivisuuspitoisuuksiin ja mittaustuloksiin oli merkittävä. Niiltä osin, kuin tulokset käsittelevät ohjeissa vuodon tunnistamiseen käytettyjä aktiivisuusrajoja, tulokset osoittivat aktiivisuusrajat oikeiksi. Kuumavalmiudessa aktiivisuusmittausten mittausalueet saattavat joissakin tapauksissa rajoittaa primääri-sekundäärivuodon tunnistamista.

Symmetries of the free Schrödinger equation in the non-commutative plane

We study all the symmetries of the free Schr odinger equation in the non-commu- tative plane. These symmetry transformations form an infinite-dimensional Weyl algebra that appears naturally from a two-dimensional Heisenberg algebra generated by Galilean boosts and momenta. These infinite high symmetries could be useful for constructing non-relativistic interacting higher spin theories. A finite-dimensional subalgebra is given by the Schröodinger algebra which, besides the Galilei generators, contains also the dilatation and the expansion. We consider the quantization of the symmetry generators in both the reduced and extended phase spaces, and discuss the relation between both approaches.

Symmetries of the free Schrödinger equation in the non-commutative plane

We study all the symmetries of the free Schrödinger equation in the non-commu- tative plane. These symmetry transformations form an infinite-dimensional Weyl algebra that appears naturally from a two-dimensional Heisenberg algebra generated by Galilean boosts and momenta. These infinite high symmetries could be useful for constructing non-relativistic interacting higher spin theories. A finite-dimensional subalgebra is given by the Schröodinger algebra which, besides the Galilei generators, contains also the dilatation and the expansion. We consider the quantization of the symmetry generators in both the reduced and extended phase spaces, and discuss the relation between both approaches.

Pinnan ominaisuuksien karakterisointi kiiltomittalaitteella ja kiiltomittalaitteen soveltuvuus tuotannon laadunvarmistuksessa

Alahuulten, kärkilistojen, turboputkien ja telapinnoitteiden pinnankarheutta mitataan Rautpohjan tehtaalla nykyään pääosin koskettavalla pinnankarheusprofilometrilla. Profilometrin käyttö on hankalaa ja epäluotettavaa tai käytössä on muita ongelmia. Paperin kuituorientaation mittaamiseen käytetään nykyisin mm. TSO-menetelmää tai repäisymenetelmää. Tämän diplomityön tarkoituksena oli kartoittaa diffraktiiviseen optiseen elementtiin perustuvan kiiltomittalaiteprototyypin mahdollisuuksia karakteroida pinnan ominaisuuksia ja tutkia kiiltomittalaitteen soveltuvuutta tuotannon laadunvarmistuksessa. Alahuuli-, kärkilista-, turboputki-, telapinnoite- ja paperinäytteistä valmistettiinnäytesarjoja, jotka mitattiin nykymenetelmin ja kiiltomittalaitteella. Tulostenkorreloituvuutta tutkittiin ja taloudellista merkitystä arvioitiin investointilaskelmin. Paperin kuituorientaation, paperin pinnan kuituorientaation ja telapinnoitteiden mittaaminen kiiltomittalaitteella osoittautui taloudellisesti erittäin merkittäväksi. Ennen mahdollista kiiltomittalaitteen käyttöönottoa prototyyppiä on kehitettävä, kiillon korreloituvuutta tulee tutkia edelleen ja aiheesta on tehtävä lisätutkimuksia.