On the simplest centralizer of a language

Given a finite alphabet Σ and a language L ⊆ ∑+, the centralizer of L is defined as the maximal language commuting with it. We prove that if the primitive root of the smallest word of L (with respect to a lexicographic order) is prefix distinguishable in L then the centralizer of L is as simple as possible, that is, the submonoid L*. This lets us obtain a simple proof of a known result concerning the centralizer of nonperiodic three-word languages

On the Exhaustive Generation of Plane Partitions

We present a CAT (Constant Amortized Time) algorithm for generating all plane partitions of an integer n, that is, all integer matrices with non-increasing rows and columns having sum n

A CAT Algorithm for the Exhaustive Generation of Ice Piles

We present a CAT (constant amortized time) algorithm for generating those partitions of n that are in the ice pile model IPM(k)(n), a generalization of the sand pile model SPM(n). More precisely, for any fixed integer k, we show that the negative lexicographic ordering naturally identifies a tree structure on the lattice IPM(k)(n): this lets us design an algorithm which generates all the ice piles of IPM(k)(n) in amortized time O(1) and in space O(root n)

On Counting L-Convex Polyominoes

A convex polyomino P is L-convex if any two cells of P can be joined by a monotone path inside P with at most one change of direction. In this paper we show that the problem of computing the number of L-convex polyominoes of area n can be solved in polynomial time using O(n^4) space. We designed a C++ program to significantly extend the counting sequence of L-convex polyominoes and to improve the estimate of the associated growth constant

Breakaway oxidation su acciai inossidabili

In questo lavoro sono stati eseguiti trattamenti di ossidazione ad alta temperatura su un acciaio AISI 304L in condizioni controllate per studiare il fenomeno della breakaway oxidation. Esso consiste nella rottura localizzata dello strato di ossido dovuta a shock termici o meccanici, con conseguente esposizione di metallo non ossidato all’atmosfera ossidante. Data la sua natura, si tratta di un fenomeno difficile da prevedere e da monitorare. Sono stati messi a punto metodi per la sua identificazione attraverso tecniche di analisi termica e di microscopia elettronica. E’ stata valutata l’influenza di temperatura, atmosfera ossidante e umidità sulla occorrenza del fenomeno, con riferimento al processo produttivo degli acciai. La possibilità di prevedere nel dettaglio i tempi di trattamento termico ai quali si osserva il fenomeno di breakaway oxidation si conferma limitata

Association of kidney disease measures with risk of renal function worsening in patients with type 1 diabetes

Background: Albuminuria has been classically considered a marker of kidney damage progression in diabetic patients and it is routinely assessed to monitor kidney function. However, the role of a mild GFR reduction on the development of stage 653 CKD has been less explored in type 1 diabetes mellitus (T1DM) patients. Aim of the present study was to evaluate the prognostic role of kidney disease measures, namely albuminuria and reduced GFR, on the development of stage 653 CKD in a large cohort of patients affected by T1DM. Methods: A total of 4284 patients affected by T1DM followed-up at 76 diabetes centers participating to the Italian Association of Clinical Diabetologists (Associazione Medici Diabetologi, AMD) initiative constitutes the study population. Urinary albumin excretion (ACR) and estimated GFR (eGFR) were retrieved and analyzed. The incidence of stage 653 CKD (eGFR < 60 mL/min/1.73 m2) or eGFR reduction > 30% from baseline was evaluated. Results: The mean estimated GFR was 98 \ub1 17 mL/min/1.73m2 and the proportion of patients with albuminuria was 15.3% (n = 654) at baseline. About 8% (n = 337) of patients developed one of the two renal endpoints during the 4-year follow-up period. Age, albuminuria (micro or macro) and baseline eGFR < 90 ml/min/m2 were independent risk factors for stage 653 CKD and renal function worsening. When compared to patients with eGFR > 90 ml/min/1.73m2 and normoalbuminuria, those with albuminuria at baseline had a 1.69 greater risk of reaching stage 3 CKD, while patients with mild eGFR reduction (i.e. eGFR between 90 and 60 mL/min/1.73 m2) show a 3.81 greater risk that rose to 8.24 for those patients with albuminuria and mild eGFR reduction at baseline. Conclusions: Albuminuria and eGFR reduction represent independent risk factors for incident stage 653 CKD in T1DM patients. The simultaneous occurrence of reduced eGFR and albuminuria have a synergistic effect on renal function worsening