Non-linear MRD codes from cones over exterior sets

By using the notion of $d$-embedding $\Gamma$ of a (canonical) subgeometry $\Sigma$ and of exterior set with respect to the $h$-secant variety $\Omega_{h}(\mathcal{A})$ of a subset $\mathcal{A}$, $0 \leq h \leq n-1$, in the finite projective space $\mathrm{PG}(n-1,q^n)$, $n \geq 3$, in this article we construct a class of non-linear $(n,n,q;d)$-MRD codes for any $2 \leq d \leq n-1$. A code $\mathcal{C}_{\sigma,T}$ of this class, where $1\in T \subset \mathbb{F}_q^*$ and $\sigma$ is a generator of $\mathrm{Gal}(\mathbb{F}_{q^n}|\mathbb{F}_q)$, arises from a cone of $\mathrm{PG}(n-1,q^n)$ with vertex an $(n-d-2)$-dimensional subspace over a maximum exterior set $\mathcal{E}$ with respect to $\Omega_{d-2}(\Gamma)$. We prove that the codes introduced in [Cossidente, A., Marino, G., Pavese, F.: Non-linear maximum rank distance codes. Des. Codes Cryptogr. 79, 597--609 (2016); Durante, N., Siciliano, A.: Non-linear maximum rank distance codes in the cyclic model for the field reduction of finite geometries. Electron. J. Comb. (2017); Donati, G., Durante, N.: A generalization of the normal rational curve in $\mathrm{PG}(d,q^n)$ and its associated non-linear MRD codes. Des. Codes Cryptogr. 86, 1175--1184 (2018)] are appropriate punctured ones of $\mathcal{C}_{\sigma,T}$ and solve completely the inequivalence issue for this class showing that $\mathcal{C}_{\sigma,T}$ is neither equivalent nor adjointly equivalent to the non-linear MRD code $\mathcal{C}_{n,k,\sigma,I}$, $I \subseteq \mathbb{F}_q$, obtained in [Otal, K., \"Ozbudak, F.: Some new non-additive maximum rank distance codes. Finite Fields and Their Applications 50, 293--303 (2018).]

On the classification of low degree ovoids of Q+(5,q)Q^+(5,q)

Ovoids of the Klein quadric $Q^+(5,q)$ of $\mathrm{PG}(5,q)$ have been studied in the last 40 year, also because of their connection with spreads of $\mathrm{PG}(3,q)$ and hence translation planes. Beside the classical example given by a three dimensional elliptic quadric (corresponding to the regular spread of $\mathrm{PG}(3,q)$) many other classes of examples are known. First of all the other examples (beside the elliptic quadric) of ovoids of $Q(4,q)$ give also examples of ovoids of $Q^+(5,q)$. Another important class of ovoids of $Q^+(5,q)$ is given by the ones associated to a flock of a three dimensional quadratic cone. To every ovoid of $Q^+(5,q)$ two bivariate polynomials $f_1(x,y)$ and $f_2(x,y)$ can be associated. In this paper, we classify ovoids of $Q^+(5,q)$ such that $f_1(x,y)=y+g(x)$ and $\max\{deg(f_1),deg(f_2)\}<(\frac{1}{6.3}q)^{\frac{3}{13}}-1$, that is $f_1(x,y)$ and $f_2(x,y)$ have "low degree" compared with $q$.Comment: Submitted to Journal of Algebraic Combinatorics. arXiv admin note: substantial text overlap with arXiv:2203.1468

On mm-ovoids of Q+(7,q)Q^+(7,q) with qq odd

In this paper, we provide a construction of $(q+1)$-ovoids of the hyperbolic quadric $Q^+(7,q)$, $q$ an odd prime power, by glueing $(q+1)/2$-ovoids of the elliptic quadric $Q^-(5,q)$. This is possible by controlling some intersection properties of (putative) $m$-ovoids of elliptic quadrics. It yields eventually $(q+1)$-ovoids of $Q^+(7,q)$ not coming from a $1$-system. Secondly, we also construct $m$-ovoids for $m \in \{ 2,4,6,8,10\}$ in $Q^+(7,3)$. Therefore we first investigate how to construct spreads of \pg(3,q) that have as many secants to an elliptic quadric as possible

An approach to prevent frailty in community dwelling older adults: a pilot study performed in Campania region in the framework of the PERSSILAA project

We developed and tested an innovative physical training method in older adults that embeds the gym program into everyday life in the most conservative way possible. Physical training was included in the activities of local parishes where older women from Southern Italy spend most of their free time and was delivered by trained physical therapists with the support of an ICT tool known as CoCo. 113 older women (aged 72.0 [69.0-75.0] years) noncompliant to conventional exercise programs participated to the study. 57 of them underwent the final anthropometric assessment and 50 the final physical tests. In study completers handgrip strength and physical performance evaluated with the chair-stand, the two minutes step and the chair-sit and -reach tests significantly improved. Quality of life as evaluated with the EuroQol-5dimension (EQ-5D) questionnaire improved as well. In conclusion, a training program designed to minimally impact on life habits of older people is effective in improving fitness in patients noncompliant to other to physical exercise programs

Infected pancreatic necrosis: outcomes and clinical predictors of mortality. A post hoc analysis of the MANCTRA-1 international study

: The identification of high-risk patients in the early stages of infected pancreatic necrosis (IPN) is critical, because it could help the clinicians to adopt more effective management strategies. We conducted a post hoc analysis of the MANCTRA-1 international study to assess the association between clinical risk factors and mortality among adult patients with IPN. Univariable and multivariable logistic regression models were used to identify prognostic factors of mortality. We identified 247 consecutive patients with IPN hospitalised between January 2019 and December 2020. History of uncontrolled arterial hypertension (p = 0.032; 95% CI 1.135-15.882; aOR 4.245), qSOFA (p = 0.005; 95% CI 1.359-5.879; aOR 2.828), renal failure (p = 0.022; 95% CI 1.138-5.442; aOR 2.489), and haemodynamic failure (p = 0.018; 95% CI 1.184-5.978; aOR 2.661), were identified as independent predictors of mortality in IPN patients. Cholangitis (p = 0.003; 95% CI 1.598-9.930; aOR 3.983), abdominal compartment syndrome (p = 0.032; 95% CI 1.090-6.967; aOR 2.735), and gastrointestinal/intra-abdominal bleeding (p = 0.009; 95% CI 1.286-5.712; aOR 2.710) were independently associated with the risk of mortality. Upfront open surgical necrosectomy was strongly associated with the risk of mortality (p &lt; 0.001; 95% CI 1.912-7.442; aOR 3.772), whereas endoscopic drainage of pancreatic necrosis (p = 0.018; 95% CI 0.138-0.834; aOR 0.339) and enteral nutrition (p = 0.003; 95% CI 0.143-0.716; aOR 0.320) were found as protective factors. Organ failure, acute cholangitis, and upfront open surgical necrosectomy were the most significant predictors of mortality. Our study confirmed that, even in a subgroup of particularly ill patients such as those with IPN, upfront open surgery should be avoided as much as possible. Study protocol registered in ClinicalTrials.Gov (I.D. Number NCT04747990)