Differential neuropsychological profiles in Parkinsonian patients with or without vascular lesions.

The purpose of this study is to compare the neuropsychological profile of patients affected by parkinsonism and vascular lesions to that in patients with PD alone (PD) and to evaluate whether the brain vascular lesion load is associated with neuropsychological variables. Thirty-six nondemented patients with parkinsonism were divided into 3 groups of 12 patients each, according to both clinical history and the presence of brain vascular lesions and/or dopaminergic denervation as revealed by magnetic resonance and dopamine transporter imaging, respectively. The first group had vascular lesions without dopaminergic denervation (VP group); the second group had vascular lesions and dopaminergic denervation (DD) (VP+DD group); and the third group consisted of patients with dopaminergic denervation (PD group) without vascular lesions. All patients underwent neurological and neuropsychological assessments. The groups differed in disease duration, age at onset, and cerebrovascular risk factors. The VP and VP+DD groups performed worse than the PD group on frontal/executive tasks. Regardless of the presence of dopaminergic denervation, cerebrovascular lesions in hemispheric white matter, basal ganglia, and cerebellum have an important effect in determining early onset and severity of cognitive impairment in patients with parkinsonism

Differential Privacy in Metric Spaces: Numerical, Categorical and Functional Data Under the One Roof

We study Differential Privacy in the abstract setting of Probability on metric spaces. Numerical, categorical and functional data can be handled in a uniform manner in this setting. We demonstrate how mechanisms based on data sanitisation and those that rely on adding noise to query responses fit within this framework. We prove that once the sanitisation is differentially private, then so is the query response for any query. We show how to construct sanitisations for high-dimensional databases using simple 1-dimensional mechanisms. We also provide lower bounds on the expected error for differentially private sanitisations in the general metric space setting. Finally, we consider the question of sufficient sets for differential privacy and show that for relaxed differential privacy, any algebra generating the Borel $\sigma$-algebra is a sufficient set for relaxed differential privacy.Comment: 18 Page

Differential Geometry from Differential Equations

We first show how, from the general 3rd order ODE of the form z'''=F(z,z',z'',s), one can construct a natural Lorentzian conformal metric on the four-dimensional space (z,z',z'',s). When the function F(z,z',z'',s) satisfies a special differential condition of the form, U[F]=0, the conformal metric possesses a conformal Killing field, xi = partial with respect to s, which in turn, allows the conformal metric to be mapped into a three dimensional Lorentzian metric on the space (z,z',z'') or equivalently, on the space of solutions of the original differential equation. This construction is then generalized to the pair of differential equations, z_ss = S(z,z_s,z_t,z_st,s,t) and z_tt = T(z,z_s,z_t,z_st,s,t), with z_s and z_t, the derivatives of z with respect to s and t. In this case, from S and T, one can again, in a natural manner, construct a Lorentzian conformal metric on the six dimensional space (z,z_s,z_t,z_st,s,t). When the S and T satisfy equations analogous to U[F]=0, namely equations of the form M[S,T]=0, the 6-space then possesses a pair of conformal Killing fields, xi =partial with respect to s and eta =partial with respect to t which allows, via the mapping to the four-space of z, z_s, z_t, z_st and a choice of conformal factor, the construction of a four-dimensional Lorentzian metric. In fact all four-dimensional Lorentzian metrics can be constructed in this manner. This construction, with further conditions on S and T, thus includes all (local) solutions of the Einstein equations.Comment: 37 pages, revised version with clarification

HE4 in the differential diagnosis of ovarian masses

Ovarian masses, a common finding among pre- and post-menopausal women, can be benign or malignant. Ovarian cancer is the leading cause of death from gynecologic malignancy among women living in industrialized countries. According to the current guidelines, measurement of CA125 tumor marker remains the gold standard in the management of ovarian cancer. Recently, HE4 has been proposed as emerging biomarker in the differential diagnosis of adnexal masses and in the early diagnosis of ovarian cancer. Discrimination of benign and malignant ovarian tumors is very important for correct patient referral to institutions specializing in care and management of ovarian cancer. Tumor markers CA125 and HE4 are currently incorporated into the Risk of Ovarian Malignancy Algorithm” (ROMA) with menopausal status for discerning malignant from benign pelvic masses. The availability of a good biomarker such as HE4, closely associated with the differential and early diagnosis of ovarian cancer, could reduce medical costs related to more expensive diagnostic procedures. Finally, it is important to note that HE4 identifies platinum non-responders thus enabling a switch to second line chemotherapy and improved survival

Iterated Differential Forms VI: Differential Equations

We describe the first term of the $\Lambda_{k-1}\mathcal{C}$--spectral sequence (see math.DG/0610917) of the diffiety (E,C), E being the infinite prolongation of an l-normal system of partial differential equations, and C the Cartan distribution on it.Comment: 8 pages, to appear in Dokl. Mat

Differential Chow Form for Projective Differential Variety

In this paper, a generic intersection theorem in projective differential algebraic geometry is presented. Precisely, the intersection of an irreducible projective differential variety of dimension d>0 and order h with a generic projective differential hyperplane is shown to be an irreducible projective differential variety of dimension d-1 and order h. Based on the generic intersection theorem, the Chow form for an irreducible projective differential variety is defined and most of the properties of the differential Chow form in affine differential case are established for its projective differential counterpart. Finally, we apply the differential Chow form to a result of linear dependence over projective varieties given by Kolchin.Comment: 17 page