An original and additional mathematical model characterizing a Bayesian approach to decision theory

We propose an original mathematical model according to a Bayesian approach explaining uncertainty from a point of view connected with vector spaces. A parameter space can be represented by means of random quantities by accepting the principles of the theory of concordance into the domain of subjective probability. We observe that metric properties of the notion of -product mathematically fulfill the ones of a coherent prevision of a bivariate random quantity. We introduce fundamental metric expressions connected with transformed random quantities representing changes of origin. We obtain a posterior probability law by applying the Bayes’ theorem into a geometric context connected with a two-dimensional parameter space

Higher secants of spinor varieties

Let $S_h$ be the even pure spinors variety of a complex vector space $V$ of even dimension $2h$ endowed with a non degenerate quadratic form $Q$ and let $\sigma_k(S_h)$ be the $k$-secant variety of $S_h$. We decribe a probabilistic algorithm which computes the complex dimension of $\sigma_k(S_h)$. Then, by using an inductive argument, we get our main result: $\sigma_3(S_h)$ has the expected dimension except when $h\in \{7,8\}$. Also we provide theoretical arguments which prove that $S_7$ has a defective 3-secant variety and $S_8$ has defective 3-secant and 4-secant varieties.Comment: 23 page

Parallel Tempering for the planted clique problem

The theoretical information threshold for the planted clique problem is $2\log_2(N)$, however no polynomial algorithm is known to recover a planted clique of size $O(N^{1/2-\epsilon})$, $\epsilon>0$. In this paper we will apply a standard method for the analysis of disordered models, the Parallel-Tempering (PT) algorithm, to the clique problem, showing numerically that its time-scaling in the hard region is indeed polynomial for the analyzed sizes. We also apply PT to a different but connected model, the Sparse Planted Independent Set problem. In this situation thresholds should be sharper and finite size corrections should be less important. Also in this case PT shows a polynomial scaling in the hard region for the recovery.Comment: 12 pages, 5 figure

Mortgage Refinancing and Consumption Smoothing

This paper analyses the optimal refinancing decision of an agent whose only asset in the portfolio is the house where she lives in the context of a life-cycle model. The mortgage is modelled as an adjustable rate contract covering the remaining life of te house owner. Thus, refinancing concerns only the size of the mortgage, which can be adjusted in any period subject to a constraint on the amount that can be borrowed: the value of the new mortgage cannot exceed the latest realised price. The paper solves the model analytically and then numerically calibrates the refinancing decision.mortgages, refinancing,consumption smoothing

On the identifiability of ternary forms

We describe a new method to determine the minimality and identifiability of a Waring decomposition $A$ of a specific form (symmetric tensor) $T$ in three variables. Our method, which is based on the Hilbert function of $A$, can distinguish between forms in the span of the Veronese image of $A$, which in general contains both identifiable and not identifiable points, depending on the choice of coefficients in the decomposition. This makes our method applicable for all values of the length $r$ of the decomposition, from $2$ up to the generic rank, a range which was not achievable before. Though the method in principle can handle all cases of specific ternary forms, we introduce and describe it in details for forms of degree $8$

Cyber situational awareness: from geographical alerts to high-level management

This paper focuses on cyber situational awareness and describes a visual analytics solution for monitoring and putting in tight relation data from network level with the organization business. The goal of the proposed solution is to make different security profiles (network security officer, network security manager, and financial security manager) aware of the actual network state (e.g., risk and attack progress) and the impact it actually has on the business tasks, making clear the relationships that exist between the network level and the business level. The proposed solution is instantiated on the ACEA infrastructure, the Italian company that provides power and water purification services to cities in central Italy (millions of end users