A large covariance matrix estimator under intermediate spikiness regimes

The present paper concerns large covariance matrix estimation via composite minimization under the assumption of low rank plus sparse structure. In this approach, the low rank plus sparse decomposition of the covariance matrix is recovered by least squares minimization under nuclear norm plus $l_1$ norm penalization. This paper proposes a new estimator of that family based on an additional least-squares re-optimization step aimed at un-shrinking the eigenvalues of the low rank component estimated at the first step. We prove that such un-shrinkage causes the final estimate to approach the target as closely as possible in Frobenius norm while recovering exactly the underlying low rank and sparsity pattern. Consistency is guaranteed when $n$ is at least $O(p^{\frac{3}{2}\delta})$, provided that the maximum number of non-zeros per row in the sparse component is $O(p^{\delta})$ with $\delta \leq \frac{1}{2}$. Consistent recovery is ensured if the latent eigenvalues scale to $p^{\alpha}$, $\alpha \in[0,1]$, while rank consistency is ensured if $\delta \leq \alpha$. The resulting estimator is called UNALCE (UNshrunk ALgebraic Covariance Estimator) and is shown to outperform state of the art estimators, especially for what concerns fitting properties and sparsity pattern detection. The effectiveness of UNALCE is highlighted on a real example regarding ECB banking supervisory data

Changing ideas about others' intentions: updating prior expectations tunes activity in the human motor system

Predicting intentions from observing another agent’s behaviours is often thought to depend on motor resonance – i.e., the motor system’s response to a perceived movement by the activation of its stored motor counterpart, but observers might also rely on prior expectations, especially when actions take place in perceptually uncertain situations. Here we assessed motor resonance during an action prediction task using transcranial magnetic stimulation to probe corticospinal excitability (CSE) and report that experimentally-induced updates in observers’ prior expectations modulate CSE when predictions are made under situations of perceptual uncertainty. We show that prior expectations are updated on the basis of both biomechanical and probabilistic prior information and that the magnitude of the CSE modulation observed across participants is explained by the magnitude of change in their prior expectations. These findings provide the first evidence that when observers predict others’ intentions, motor resonance mechanisms adapt to changes in their prior expectations. We propose that this adaptive adjustment might reflect a regulatory control mechanism that shares some similarities with that observed during action selection. Such a mechanism could help arbitrate the competition between biomechanical and probabilistic prior information when appropriate for prediction

The quantum time-dependent harmonic oscillator

La presente tesi si propone di mostrare che l’oscillatore armonico quantistico dipendente dal tempo è un sistema risolvibile in maniera esatta. La trattazione è articolata in tre capitoli: nel primo viene richiamata la teoria dell’oscillatore armonico quantistico indipendente dal tempo, al fine di recuperare i concetti e le metodologie che sono comuni anche alla sua controparte dipendente dal tempo. Nel secondo capitolo viene fornita una breve introduzione alla teoria degli operatori invarianti dipendenti dal tempo, di cui ci interessa la loro relazione con le soluzioni dell’equazione di Schrödinger. Infine, nel terzo capitolo viene presentato il problema dell’oscillatore armonico quantistico dipendente dal tempo e discussa la sua soluzione esatta. In aggiunta se ne individuano gli stati coerenti

Crossmodal visual-tactile extinction: Modulation by posture implicates biased competition in proprioceptively reconstructed space

Extinction is a common consequence of unilateral brain injury: contralesional events can be perceived in isolation, yet are missed when presented concurrently with competing events on the ipsilesional side. This can arise crossmodally, where a contralateral touch is extinguished by an ipsilateral visual event. Recent studies showed that repositioning the hands in visible space, or making visual events more distant, can modulate such crossmodal extinction. Here, in a detailed single-case study, we implemented a novel spatial manipulation when assessing crossmodal extinction. This was designed not only to hold somatosensory inputs and hand/arm-posture constant, but also to hold (retinotopic) visual inputs constant, yet while still changing the spatial relationship of tactile and visual events in the external world. Our right hemisphere patient extinguished left-hand touches due to visual stimulation of the right visual field (RVF) when tested in the usual default posture with eyes/head directed straight ahead. But when her eyes/head were turned to the far left (and any visual events shifted along with this), such that the identical RVF retinal stimulation now fell at the same external location as the left-hand touch, crossmodal extinction was eliminated. Since only proprioceptive postural cues could signal this changed spatial relationship for the critical condition, our results show for the first time that such postural cues alone are sufficient to modulate crossmodal extinction. Identical somatosensory and retinal inputs can lead to severe crossmodal extinction, or none, depending on current posture

The Rubber Hand Illusion: Two's a company, but three's a crowd

On the one hand, it is often assumed that the Rubber Hand Illusion (RHI) is constrained by a structural body model so that one cannot implement supernumerary limbs. On the other hand, several recent studies reported illusory duplication of the right hand in subjects exposed to two adjacent rubber hands. The present study tested whether spatial constraints may affect the possibility of inducing the sense of ownership to two rubber hands located side by side to the left of the subject's hand. We found that only the closest rubber hand appeared both objectively (proprioceptive drift) and subjectively (ownership rating) embodied. Crucially, synchronous touch of a second, but farther, rubber hand disrupted the objective measure of the RHI, but not the subjective one. We concluded that, in order to elicit a genuine RHI for multiple rubber hands, the two rubber hands must be at the same distance from the subject's hand/body

The Agent is Right: When Motor Embodied Cognition is Space-Dependent

The role of embodied mechanisms in processing sentences endowed with a first person perspective is now widely accepted. However, whether embodied sentence processing within a third person perspective would also have motor behavioral significance remains unknown. Here, we developed a novel version of the Action-sentence Compatibility Effect (ACE) in which participants were asked to perform a movement compatible or not with the direction embedded in a sentence having a first person (Experiment 1: You gave a pizza to Louis) or third person perspective (Experiment 2: Lea gave a pizza to Louis). Results indicate that shifting perspective from first to third person was sufficient to prevent motor embodied mechanisms, abolishing the ACE. Critically, ACE was restored in Experiment 3 by adding a virtual “body” that allowed participants to know “where” to put themselves in space when taking the third person perspective, thus demonstrating that motor embodied processes are space-dependent. A fourth, control experiment, by dissociating motor response from the transfer verb's direction, supported the conclusion that perspective-taking may induce significant ACE only when coupled with the adequate sentence-response mapping

Paesaggi della memoria e dell’innovazione. Ri-abitare i paesaggi della riforma agraria foggiana

In the firsts decades of the last century, the plain of Foggia was invested by an important intervention of landed property transformation that, on the one hand proposed a significant land reclamation of the Tavoliere delle Puglie and on the other hand, an intense urban activity for the construction of new rural settlements: the suburbs of the Foggia city. This settlement and development policy for the rural centers still characterizes the agrarian landscape in the plain of Foggia today, where it is possible to find vast public properties: large estates, water networks, scattered dwellings, complete suburbs and evocative functionalist architectures. The project proposes a strategy to give value to the local rural landscape and its immense public estate, generating new forms of development that could answer the needs of a “new rurban society”, respecting the identity features of the agrarian reform landscape