The Traveling Salesman Problem: Low-Dimensionality Implies a Polynomial Time Approximation Scheme

The Traveling Salesman Problem (TSP) is among the most famous NP-hard optimization problems. We design for this problem a randomized polynomial-time algorithm that computes a (1+eps)-approximation to the optimal tour, for any fixed eps>0, in TSP instances that form an arbitrary metric space with bounded intrinsic dimension. The celebrated results of Arora (A-98) and Mitchell (M-99) prove that the above result holds in the special case of TSP in a fixed-dimensional Euclidean space. Thus, our algorithm demonstrates that the algorithmic tractability of metric TSP depends on the dimensionality of the space and not on its specific geometry. This result resolves a problem that has been open since the quasi-polynomial time algorithm of Talwar (T-04)

Efficient Density Estimation via Piecewise Polynomial Approximation

We give a highly efficient "semi-agnostic" algorithm for learning univariate probability distributions that are well approximated by piecewise polynomial density functions. Let $p$ be an arbitrary distribution over an interval $I$ which is $\tau$-close (in total variation distance) to an unknown probability distribution $q$ that is defined by an unknown partition of $I$ into $t$ intervals and $t$ unknown degree-$d$ polynomials specifying $q$ over each of the intervals. We give an algorithm that draws \tilde{O}(t\new{(d+1)}/\eps^2) samples from $p$, runs in time \poly(t,d,1/\eps), and with high probability outputs a piecewise polynomial hypothesis distribution $h$ that is (O(\tau)+\eps)-close (in total variation distance) to $p$. This sample complexity is essentially optimal; we show that even for $\tau=0$, any algorithm that learns an unknown $t$-piecewise degree-$d$ probability distribution over $I$ to accuracy \eps must use \Omega({\frac {t(d+1)} {\poly(1 + \log(d+1))}} \cdot {\frac 1 {\eps^2}}) samples from the distribution, regardless of its running time. Our algorithm combines tools from approximation theory, uniform convergence, linear programming, and dynamic programming. We apply this general algorithm to obtain a wide range of results for many natural problems in density estimation over both continuous and discrete domains. These include state-of-the-art results for learning mixtures of log-concave distributions; mixtures of $t$-modal distributions; mixtures of Monotone Hazard Rate distributions; mixtures of Poisson Binomial Distributions; mixtures of Gaussians; and mixtures of $k$-monotone densities. Our general technique yields computationally efficient algorithms for all these problems, in many cases with provably optimal sample complexities (up to logarithmic factors) in all parameters

Keck Spectra of Brown Dwarf Candidates and a Precise Determination of the Lithium Depletion Boundary in the Alpha Persei Open Cluster

We have identified twenty-seven candidate very low mass members of the relatively young Alpha Persei open cluster from a six square degree CCD imaging survey. Based on their I magnitudes and the nominal age and distance to the cluster, these objects should have masses less than 0.1 Msunif they are cluster members. We have subsequently obtained intermediate resolution spectra of seventeen of these objects using the Keck II telescope and LRIS spectrograph. We have also obtained near-IR photometry for many of the stars. Our primary goal was to determine the location of the "lithium depletion boundary" and hence to derive a precise age for the cluster. We detect lithium with equivalent widths greater than or equal to 0.4 \AA in five of the program objects. We have constructed a color-magnitude diagram for the faint end of the Alpha Persei main sequence. These data allow us to accurately determine the Alpha Persei single-star lithium depletion boundary at M(I$_C$) = 11.47, M(Bol) = 11.42, (R-I)$_{C0}$ = 2.12, spectral type M6.0. By reference to theoretical evolutionary models, this converts fairly directly into an age for the Alpha Persei cluster of 90 $\pm$ 10 Myr. At this age, the two faintest of our spectroscopically confirmed members should be sub-stellar (i.e., brown dwarfs) according to theoretical models.Comment: Accepted Ap

DMTs and Covid-19 severity in MS: a pooled analysis from Italy and France

We evaluated the effect of DMTs on Covid-19 severity in patients with MS, with a pooled-analysis of two large cohorts from Italy and France. The association of baseline characteristics and DMTs with Covid-19 severity was assessed by multivariate ordinal-logistic models and pooled by a fixed-effect meta-analysis. 1066 patients with MS from Italy and 721 from France were included. In the multivariate model, anti-CD20 therapies were significantly associated (OR = 2.05, 95%CI = 1.39–3.02, p < 0.001) with Covid-19 severity, whereas interferon indicated a decreased risk (OR = 0.42, 95%CI = 0.18–0.99, p = 0.047). This pooled-analysis confirms an increased risk of severe Covid-19 in patients on anti-CD20 therapies and supports the protective role of interferon

Mécanismes d'action des lectines sur la muqueuse intestinale du rat. Influence de la dose administrée

International audienc

Peripheral blood lymphocytes muscarinic cholinergic receptor subtypes in Alzheimer's disease: a marker of cholinergic dysfunction?

Muscarinic M2-M5 muscarinic cholinergic receptors were investigated in peripheral blood lymphocytes of patients with mild cognitive impairment of the Alzheimer's type (MCIAT), probable Alzheimer's disease (AD) and probable vascular dementia (VaD). [3H]-N-methyl scopolamine (NMS) in the presence of muscarinic antagonists and Mamba venom to occlude different receptor subtypes was used as radioligand. Analysis of [3H]-NMS binding curves without receptor subtype assessment resulted in a slight decrease of receptor density in AD patients. Evaluation of receptor subtypes in MCIAT and AD patients revealed a decrease of M3 receptor by more than 50%, an increase of M4 receptor expression by about 20% and no changes of M2 or M5 receptors. The expression of M2-M5 receptors was unaltered in VaD patients. Strong positive and negative correlations respectively were found between the density of lymphocyte M3 and M4 receptors and MMSE score in both MCIAT (0.78 for M3 receptor and 0.80 for M4 receptor) and AD (0.82 for M3 receptor and 0.83 for M4 receptor) patients. These findings suggest that changes in the expression of peripheral blood lymphocyte M3 and M4 receptors in AD are related to the degree of cognitive impairment. Assessment of lymphocyte muscarinic receptor subtypes may contribute to characterization of cholinergic impairment in AD

Peripheral blood lymphocytes muscarinic cholinergic receptor subtypes in Alzheimer's disease: a marker of cholinergic dysfunction?

IF 3,35

Stroke Unit: a Cardio-Cerebral Approach

Stroke units are special units where stroke patients receive, simultaneously, medical and physical treatment. Compared to general neurological and medical wards, stroke units show a significant reduction of short- and longtime mortality, and an improvement of long-term quality of life. Nevertheless, mortality in these units is still high (1-year mortality ∼32%; 5-year mortality ∼60%), and consequently, new approaches are needed to control stroke parameters during the acute phase, with the goal to reduce mortality rates. The philosophy of our stroke unit in Fermo (Italy), is to establish a strong association between heart and brain care by approaching each stroke patient as a cardiocerebral patient. In particular, we perform 12-lead Holter ECG monitoring, to prevent the vicious cycle affecting correct cerebral and cardiac functions, and to react to cardiac complications, mostly arrhythmias, that can worsen cerebral damage. Holter ECG monitoring allows a fast physiotherapeutic approach, a better evaluation of metabolic parameters, and collectively, a better global evaluation of the patient during the acute phase of disease. In two years of activity, 80 patients that were admitted to our stroke unit during 1998, and treated as cardio-cerebral patients, were followed-up. This combined treatment decreased the 1-year mortality rate by about 30%, in comparison with the 22% mortality rate reported in the literature. These results confirm the validity of stroke units, as well as of our approach based on cardio-cerebral control of each stroke patient

A doubling dimension threshold Θ(log log n) for augmented graph navigability

Abstract. In his seminal work, Kleinberg showed how to augment meshes using random edges, so that they become navigable; that is, greedy routing computes paths of polylogarithmic expected length between any pairs of nodes. This yields the crucial question of determining wether such an augmentation is possible for all graphs. In this paper, we answer negatively to this question by exhibiting a threshold on the doubling dimension, above which an infinite family of graphs cannot be augmented to become navigable whatever the distribution of random edges is. Precisely, it was known that graphs of doubling dimension at most O(log log n) are navigable. We show that for doubling dimension ≫ log log n, an infinite family of graphs cannot be augmented to become navigable. Finally, we complete our result by studying the special case of square meshes, that we prove to always be augmentable to become navigable