0000000000283087
AUTHOR
Giuseppe Zappalà
Linear quotients of Artinian Weak Lefschetz algebras
Abstract We study the Hilbert function and the graded Betti numbers for “generic” linear quotients of Artinian standard graded algebras, especially in the case of Weak Lefschetz algebras. Moreover, we investigate a particular property of Weak Lefschetz algebras, the Betti Weak Lefschetz Property, which makes possible to completely determine the graded Betti numbers of a generic linear quotient of such algebras.
Low-Frequency Repetitive Transcranial Magnetic Stimulation of the Right Dorsolateral Prefrontal Cortex Enhances Recognition Memory in Alzheimer’s Disease
Background: The lack of effective pharmacological or behavioral interventions for memory impairments associated with Alzheimer’s disease (AD) emphasizes the need for the investigation of approaches based on neuromodulation. Objective: This study examined the effects of inhibitory repetitive transcranial magnetic stimulation (rTMS) of prefrontal cortex on recognition memory in AD patients. Methods: In a first experiment, 24 mild AD patients received sham and real 1Hz rTMS over the left and right dorsolateral prefrontal cortex (DLPFC), in different sessions, between encoding and retrieval phases of a non-verbal recognition memory task. In a second experiment, another group of 14 AD patients u…
Enhancing memory performance with rTMS in healthy subjects and individuals with Mild Cognitive Impairment: the role of the right dorsolateral prefrontal cortex
A debated question in the literature is the degree of anatomical and functional lateralization of the executive control processes subserved by the dorsolateral prefrontal cortex (DLPFC) during recognition memory retrieval. We investigated if transient inhibition and excitation of the left and right DLPFC at retrieval by means of repetitive transcranial magnetic stimulation (rTMS) modulate recognition memory performance in 100 healthy controls (HCs) and in 8 patients with Mild Cognitive Impairment (MCI). Recognition memory tasks of faces, buildings and words were used in different experiments. rTMS-inhibition of the right DLPFC enhanced recognition memory of verbal and non verbal material in…
Tower sets and other configurations with the Cohen-Macaulay property
Abstract Some well-known arithmetically Cohen–Macaulay configurations of linear varieties in P r as k-configurations, partial intersections and star configurations are generalized by introducing tower schemes. Tower schemes are reduced schemes that are a finite union of linear varieties whose support set is a suitable finite subset of Z + c called tower set. We prove that the tower schemes are arithmetically Cohen–Macaulay and we compute their Hilbert function in terms of their support. Afterwards, since even in codimension 2 not every arithmetically Cohen–Macaulay squarefree monomial ideal is the ideal of a tower scheme, we slightly extend this notion by defining generalized tower schemes …