Cuntz–Krieger Algebras and Wavelets on Fractals

We consider representations of Cuntz–Krieger algebras on the Hilbert space of square integrable functions on the limit set, identified with a Cantor set in the unit interval. We use these representations and the associated Perron–Frobenius and Ruelle operators to construct families of wavelets on these Cantor sets

Cuntz-Krieger algebras and wavelets on fractals

We consider representations of Cuntz--Krieger algebras on the Hilbert space of square integrable functions on the limit set, identified with a Cantor set in the unit interval. We use these representations and the associated Perron-Frobenius and Ruelle operators to construct families of wavelets on these Cantor sets.Comment: 37 pages, LaTe

Learning Features that Predict Cue Usage

Our goal is to identify the features that predict the occurrence and placement of discourse cues in tutorial explanations in order to aid in the automatic generation of explanations. Previous attempts to devise rules for text generation were based on intuition or small numbers of constructed examples. We apply a machine learning program, C4.5, to induce decision trees for cue occurrence and placement from a corpus of data coded for a variety of features previously thought to affect cue usage. Our experiments enable us to identify the features with most predictive power, and show that machine learning can be used to induce decision trees useful for text generation.Comment: 10 pages, 2 Postscript figures, uses aclap.sty, psfig.te

Phase-Tunable Thermal Logic: Computation with Heat

Boolean algebra, the branch of mathematics where variables can assume only true or false value, is the theoretical basis of classical computation. The analogy between Boolean operations and electronic switching circuits, highlighted by Shannon in 1938, paved the way to modern computation based on electronic devices. The grow of computational power of such devices, after an exciting exponential -Moore trend, is nowadays blocked by heat dissipation due to computational tasks, very demanding after the chips miniaturization. Heat is often a detrimental form of energy which increases the systems entropy decreasing the efficiency of logic operations. Here, we propose a physical system able to perform thermal logic operations by reversing the old heat-disorder epitome into a novel heat-order paradigm. We lay the foundations of heat computation by encoding logic state variables in temperature and introducing the thermal counterparts of electronic logic gates. Exploiting quantum effects in thermally biased Josephson junctions (JJs), we propound a possible realization of a functionally complete dissipationless logic. Our architecture ensures high operation stability and robustness with switching frequencies reaching the GHz

Sleep-like slow oscillations improve visual classification through synaptic homeostasis and memory association in a thalamo-cortical model

The occurrence of sleep passed through the evolutionary sieve and is widespread in animal species. Sleep is known to be beneficial to cognitive and mnemonic tasks, while chronic sleep deprivation is detrimental. Despite the importance of the phenomenon, a complete understanding of its functions and underlying mechanisms is still lacking. In this paper, we show interesting effects of deep-sleep-like slow oscillation activity on a simplified thalamo-cortical model which is trained to encode, retrieve and classify images of handwritten digits. During slow oscillations, spike-timing-dependent-plasticity (STDP) produces a differential homeostatic process. It is characterized by both a specific unsupervised enhancement of connections among groups of neurons associated to instances of the same class (digit) and a simultaneous down-regulation of stronger synapses created by the training. This hierarchical organization of post-sleep internal representations favours higher performances in retrieval and classification tasks. The mechanism is based on the interaction between top-down cortico-thalamic predictions and bottom-up thalamo-cortical projections during deep-sleep-like slow oscillations. Indeed, when learned patterns are replayed during sleep, cortico-thalamo-cortical connections favour the activation of other neurons coding for similar thalamic inputs, promoting their association. Such mechanism hints at possible applications to artificial learning systems.Comment: 11 pages, 5 figures, v5 is the final version published on Scientific Reports journa

Interferenze fra il "Carmen saeculare" di Orazio e il carme "In laudem Solis" della "Anthologia Latina"

pp. 293-319Il carme dell’Anthologia Latina 389 Riese = 385 SB, In laudem Solis, tramandato dai codici Parisinus 8071 (Thuaneus) e Lipsiensis I 74, risulta assente nel Parisinus Latinus 10318 (Salmasianus). L’ipotesi avanzata è che il carme figurasse al termine dell’archetipo e che quindi fosse presente anche nella parte mutila del Salmasiano. L’analisi testuale ha evidenziato le interferenze con il Carmen saeculare di Orazio, attuate sul piano della costituzione del testo in età antica (emendamento del v. 24, ove viene ripristinato ‘aequus’ dei codici ex Hor. Carm. saec. 65) e moderna (emendamento di Haupt di ‘idem’ al v. 58, influenzato dalla memoria oraziana di Carm. saec. 65); su quello del genere letterario dell’innografia politico-religiosa (conservazione delle ipostasi orientali del dio citate da Mart. Cap. Nupt. 2, 190 sgg.); su quello della conservazione culturale di matrice antiquaria in alcune élites pagane (con particolare riferimento a Zosim. Hist. 2, 1-7). Inoltre, ai fini della datatazione del carme antologizzato, ipotizzando un possibile calcolo dei cicli secolari a partire dai ‘ludi’ dell’età dei Severi, si individuerebbe l’anno 534, cui si fa comunemente risalire il termine ultimo per l’assemblaggio della silloge salmasiana. Il contributo si è poi soffermato sulla numerazione romana presente nel Salmasiano, al fine di provare che il suo antigrafo conteneva una silloge più ampia, dalla quale sono stati escerpiti carmi che sono confluiti in esso e nel Thuaneus. Infine, sono stati posti in luce i rapporti fra regno vandalico e impero bizantino (secondo Procopio), utili a contestualizzare il carmen In laudem Solis nel clima politico-intellettuale dell’Africa settentrionale nell’anno 534.The poem of Anthologia Latina 389 Riese = 385 SB, In laudem Solis, handed down by manuscripts Parisinus 8071 (Thuaneus) and Lipsiensis I 74, is absent in Parisinus Latinus 10318 (Salmasianus). The hypothesis maded is that this poem was present in the archetype and so appears originally also in the missing part of Salmasianus. The analysis shows many ‘interferences’ with Orace's Carmen saeculare. Moreover the scholar, hypothesizing a count of cycli saeculares starting from ludi of Severan dynasty, suggests year 534 for a possible dating of the text

Dynamical system analysis of ignition phenomena using the tangential stretching rate concept

We analyze ignition phenomena by resorting to the stretching rate concept formerly introduced in the study of dynamical systems. We construct a Tangential Stretching Rate (TSR) parameter by combining the concepts of stretching rate with the decomposition of the local tangent space in eigen-modes. The main feature of the TSR is its ability to identify unambiguously the most energetic scale at a given space location and time instant. The TSR depends only on the local composition of the mixture, its temperature and pressure. As such, it can be readily computed during the post processing of computed reactive flow fields, both for spatially homogeneous and in-homogenous systems. Because of the additive nature of the TSR, we defined a normalized participation index measuring the relative contribution of each mode to the TSR. This participation index to the TSR can be combined with the mode amplitude participation Index of a reaction to a mode – as defined in the Computational Singular Perturbation (CSP) method – to obtain a direct link between a reaction and TSR. The reactions having both a large participation index to the TSR and a large CSP mode amplitude participation index are those contributing the most to both the explosive and relaxation regimes of a reactive system. This information can be used for both diagnostics and for the simplification of kinetic mechanisms. We verified the properties of the TSR with reference to three nonlinear planar models (one for isothermal branched-chain reactions, one for a non-isothermal, one-step system, and for non-isothermal branched-chain reactions), to one planar linear model (to discuss issues associated with non-normality), and to test problems involving hydro-carbon oxidation kinetics. We demonstrated that the reciprocal of the TSR parameter is the proper characteristic chemical time scale in problems involving multi-step chemical kinetic mechanisms, because (i) it is the most relevant time scale during both the explosive and relaxation regimes and (ii) it is intrinsic to the kinetics, that is, it can be identified without the need of any ad hoc assumption

Predit: A temporal predictive framework for scheduling systems

Scheduling can be formalized as a Constraint Satisfaction Problem (CSP). Within this framework activities belonging to a plan are interconnected via temporal constraints that account for slack among them. Temporal representation must include methods for constraints propagation and provide a logic for symbolic and numerical deductions. In this paper we describe a support framework for opportunistic reasoning in constraint directed scheduling. In order to focus the attention of an incremental scheduler on critical problem aspects, some discrete temporal indexes are presented. They are also useful for the prediction of the degree of resources contention. The predictive method expressed through our indexes can be seen as a Knowledge Source for an opportunistic scheduler with a blackboard architecture

Properzio 2.31.5-6: stile, costituzione del testo e antichità

This paper defends the text transmitted by the most important manuscript tradition of Propertius 2.31.5- 6, on the grounds of grammatical and stylistic arguments, reconstructing (within the editorial history of the text starting from the XViith century) the reasons that led the philologists to emend the text. The transmitted reading can be finally confirmed by the antiquarian witnesses reguarding the arrangement of the monumental complex of apollo’s temple on the Palatine.Si sostiene la difesa del testo tràdito dalla tradizione manoscritta potiore nei vv. 5-6 dell’elegia 2.31 di Properzio sulla base di argomenti grammaticali e stilistici, ricostruendo (nell’ambito della storia ecdotica del testo a partire dal XVii sec.) le motivazioni che hanno indotto i filologi ad intervenire sul testo. la lezione tràdita trova, infine, riscontro nelle testimonianze antiquarie circa l’assetto del complexo monumentale del tempio di apollo sul Palatino