Balian-Low Theorems in Several Variables

Recently, Nitzan and Olsen showed that Balian-Low theorems (BLTs) hold for discrete Gabor systems defined on $\mathbb{Z}_d$. Here we extend these results to a multivariable setting. Additionally, we show a variety of applications of the Quantitative BLT, proving in particular nonsymmetric BLTs in both the discrete and continuous setting for functions with more than one argument. Finally, in direct analogy of the continuous setting, we show the Quantitative Finite BLT implies the Finite BLT.Comment: To appear in Approximation Theory 16 conference proceedings volum

Fault detection and isolation of malicious nodes in MIMO Multi-hop Control Networks

A MIMO Multi-hop Control Network (MCN) consists of a MIMO LTI system where the communication between sensors, actuators and computational units is supported by a (wireless) multi-hop communication network, and data flow is performed using scheduling and routing of sensing and actuation data. We provide necessary and sufficient conditions on the plant dynamics and on the communication protocol configuration such that the Fault Detection and Isolation (FDI) problem of failures and malicious attacks to communication nodes can be solved.Comment: 6 page

On The Weak-Coupling Limit for Bosons and Fermions

In this paper we consider a large system of Bosons or Fermions. We start with an initial datum which is compatible with the Bose-Einstein, respectively Fermi-Dirac, statistics. We let the system of interacting particles evolve in a weak-coupling regime. We show that, in the limit, and up to the second order in the potential, the perturbative expansion expressing the value of the one-particle Wigner function at time $t$, agrees with the analogous expansion for the solution to the Uehling-Uhlenbeck equation. This paper follows in spirit the companion work [\rcite{BCEP}], where the authors investigated the weak-coupling limit for particles obeying the Maxwell-Boltzmann statistics: here, they proved a (much stronger) convergence result towards the solution of the Boltzmann equation

Optimal co-design of control, scheduling and routing in multi-hop control networks

A Multi-hop Control Network consists of a plant where the communication between sensors, actuators and computational units is supported by a (wireless) multi-hop communication network, and data flow is performed using scheduling and routing of sensing and actuation data. Given a SISO LTI plant, we will address the problem of co-designing a digital controller and the network parameters (scheduling and routing) in order to guarantee stability and maximize a performance metric on the transient response to a step input, with constraints on the control effort, on the output overshoot and on the bandwidth of the communication channel. We show that the above optimization problem is a polynomial optimization problem, which is generally NP-hard. We provide sufficient conditions on the network topology, scheduling and routing such that it is computationally feasible, namely such that it reduces to a convex optimization problem.Comment: 51st IEEE Conference on Decision and Control, 2012. Accepted for publication as regular pape

Relative entropy via non-sequential recursive pair substitutions

The entropy of an ergodic source is the limit of properly rescaled 1-block entropies of sources obtained applying successive non-sequential recursive pairs substitutions (see P. Grassberger 2002 ArXiv:physics/0207023 and D. Benedetto, E. Caglioti and D. Gabrielli 2006 Jour. Stat. Mech. Theo. Exp. 09 doi:10.1088/1742.-5468/2006/09/P09011). In this paper we prove that the cross entropy and the Kullback-Leibler divergence can be obtained in a similar way.Comment: 13 pages , 2 figure

Ovarian endometrioid adenocarcinoma diagnosed in pregnancy. a case report

The prevalence of adnexal masses pregnancy is about 0.19-8.8%. The malignancy rate is around 1-6%, and indeed most cases are benign masses. During pregnancy adnexal masses should be accurately evaluated to identify the patients who need surgery from those who need a 'wait-and-see' strategy. The authors report a case of 36-year-old woman (gravida 2, para 2, two vaginal deliveries) referred to the Gynecologic Department with diagnosis of endometrioid ovarian adenocarcinoma. The patient underwent laparotomic surgery with left salpingo-oophorectomy, total hysterectomy, pelvic and para-aortic lymphadenectomy, and peritoneal washing for optimal surgery staging. No ascites or residual tumour in the abdominal cavity were found macroscopically. Histopathology was negative for residual ovarian cancer. Currently the treatment and the management of ovarian cancer are not well established because scientific evidence is limited

Association of endometrioid ovarian carcinoma arising from endometriosis, endometrioid endometrial carcinoma, and high-grade undifferentiated endometrial sarcoma. a case report

Endometriosis is a chronic disease that affects women of reproductive age. Malignant transformation in endometriosis is considered to be an unusual event, only occurring in 0.7-0.1% of cases. However the association between endometriosis and endometrial cancer is not well defined. Also in literature, rare cases of uterine sarcoma, about 3% of all uterine malignancies, associated with endometriosis have been reported. The authors report a case of a 47-years-old Italian woman with histologic diagnosis of endometrioid ovarian carcinoma arising from endometriosis, endometrioid endometrial carcinoma, and undifferentiated endometrial sarcoma. Therefore there have been few studies addressing the relationship between endometrial stromal sarcomas (ESS), and endometriosis. Novel scientific findings are necessary to investigate a possible common pathway and an effective treatment, although complete tumor resection can reduce the recurrence rate

Feedback stabilization of dynamical systems with switched delays

We analyze a classification of two main families of controllers that are of interest when the feedback loop is subject to switching propagation delays due to routing via a wireless multi-hop communication network. We show that we can cast this problem as a subclass of classical switching systems, which is a non-trivial generalization of classical LTI systems with timevarying delays. We consider both cases where delay-dependent and delay independent controllers are used, and show that both can be modeled as switching systems with unconstrained switchings. We provide NP-hardness results for the stability verification problem, and propose a general methodology for approximate stability analysis with arbitrary precision. We finally give evidence that non-trivial design problems arise for which new algorithmic methods are needed