Regression Depth and Center Points

We show that, for any set of n points in d dimensions, there exists a hyperplane with regression depth at least ceiling(n/(d+1)). as had been conjectured by Rousseeuw and Hubert. Dually, for any arrangement of n hyperplanes in d dimensions there exists a point that cannot escape to infinity without crossing at least ceiling(n/(d+1)) hyperplanes. We also apply our approach to related questions on the existence of partitions of the data into subsets such that a common plane has nonzero regression depth in each subset, and to the computational complexity of regression depth problems.Comment: 14 pages, 3 figure

Violator Spaces: Structure and Algorithms

Sharir and Welzl introduced an abstract framework for optimization problems, called LP-type problems or also generalized linear programming problems, which proved useful in algorithm design. We define a new, and as we believe, simpler and more natural framework: violator spaces, which constitute a proper generalization of LP-type problems. We show that Clarkson's randomized algorithms for low-dimensional linear programming work in the context of violator spaces. For example, in this way we obtain the fastest known algorithm for the P-matrix generalized linear complementarity problem with a constant number of blocks. We also give two new characterizations of LP-type problems: they are equivalent to acyclic violator spaces, as well as to concrete LP-type problems (informally, the constraints in a concrete LP-type problem are subsets of a linearly ordered ground set, and the value of a set of constraints is the minimum of its intersection).Comment: 28 pages, 5 figures, extended abstract was presented at ESA 2006; author spelling fixe

The fruitless effort of growing a fruitless tree: Early morpho.orthographic and morpho-semantic effects in sentence reading

In this eye-tracking study, we investigated how semantics inform morphological analysis at the early stages of visual word identification in sentence reading. We exploited a feature of several derived Italian words, that is, that they can be read in a \u201cmorphologically transparent\u201d way or in a \u201cmorphologically opaque\u201d way according to the sentence context to which they belong. This way, each target word was embedded in a sentence eliciting either its transparent or opaque interpretation. We analyzed whether the effect of stem frequency changes according to whether the (very same) word is read as a genuine derivation (transparent context) vs. as a pseudo-derived word (opaque context). Analysis of the first fixation durations revealed a stem-word frequency effect in both opaque and transparent contexts, thus showing that stems were accessed whether or not they contributed to word meaning, that is, word decomposition is indeed blind to semantics. However, while the stem-word frequency effect was facilitatory in the transparent context, it was inhibitory in the opaque context, thus showing an early involvement of semantic representations. This pattern of data is revealed by words with short suffixes. These results indicate that derived and pseudo-derived words are segmented into their constituent morphemes also in natural reading; however, this blind- to-semantics process activates morpheme representations that are semantically connote

Consistency measures individuate dissociating semantic modulations in priming paradigms: A new look on semantics in the processing of (complex) words

In human language the mapping between form and meaning is arbitrary, as there is no direct connection between words and the objects that they represent. However, within a given language, it is possible to recognize systematic associations that support productivity and comprehension. In this work, we focus on the consistency between orthographic forms and meaning, and we investigate how the cognitive system may exploit it to process words. We take morphology as our case study, since it arguably represents one of the most notable examples of systematicity in form-meaning mapping. In a series of three experiments, we investigate the impact of form-meaning mapping in word processing by testing new consistency metrics as predictors of priming magnitude in primed lexical decision. In Experiment 1, we re-analyse data from five masked morphological priming studies and show that Orthography-Semantics-Consistency explains independent variance in priming magnitude, suggesting that word semantics is accessed already at early stages of word processing and that crucially semantic access is constrained by word orthography. In Experiment 2 and 3, we investigate whether this pattern is replicated when looking at semantic priming. In Experiment 2, we show that Orthography-Semantics-Consistency is not a viable predictor of priming magnitude with longer SOA. However, in Experiment 3, we develop a new semantic consistency measure based on the semantic density of target neighbourhoods. This measure is shown to significantly predict independent variance in semantic priming effect. Overall our results indicate that consistency measures provide crucial information for the understanding of word processing. Specifically, the dissociation between measures and priming paradigms shows that different priming conditions are associated with the activation of different semantic cohorts

A Multi-signal Variant for the GPU-based Parallelization of Growing Self-Organizing Networks

Among the many possible approaches for the parallelization of self-organizing networks, and in particular of growing self-organizing networks, perhaps the most common one is producing an optimized, parallel implementation of the standard sequential algorithms reported in the literature. In this paper we explore an alternative approach, based on a new algorithm variant specifically designed to match the features of the large-scale, fine-grained parallelism of GPUs, in which multiple input signals are processed at once. Comparative tests have been performed, using both parallel and sequential implementations of the new algorithm variant, in particular for a growing self-organizing network that reconstructs surfaces from point clouds. The experimental results show that this approach allows harnessing in a more effective way the intrinsic parallelism that the self-organizing networks algorithms seem intuitively to suggest, obtaining better performances even with networks of smaller size.Comment: 17 page

new route for tizanidine administration: a pharmacokinetics and light microscope autoradiography study

Spasticity could represent a complication of several central nervous system (CNS) disorders. Multiple sclerosis and painful paroxysmal syndromes (e.g. trigeminal neuralgia) are pathologies in which anti-spastic drugs are used to a greater extent . Baclofen, tizanidine (TIZ), benzodiazepines, dantrolene, and, more recently, gabapentin are the pharmacological agents more widely used. Baclofen, TIZ, benzodiazepines, gabapentin, clonidine but not dantrolene are active on CNS. The alpha2 adrenoceptor agonist TIZ is one of the most eff ective and largely used anti-spastic drugs. Oral treatment is the only route of anti-spastics administration, although it may cause problems of bioavailability and/or compliance in spastic patients with impaired deglutition. This study was designed to assess the possibility of develop a new route of administration of TIZ and to identify its targets in the spinal cord. New Zealand rabbits were treated with oral (OR , n=6), intramuscular (IM, n=6) or intranasal (IN, n=6) TIZ (3.2 mg/kg/day). Plasma concentration was measured by HPLC on samples collected at 0, 30, 60, 90, 120 and 480 min after treatment. Curves of average concentrations of TIZ vs. time were constructed. In plasma, TIZ reached a peak between 45-65 min after administration. Cmax was in the range of 268.33–1213.64 ng/ml for IM treatment, of 73.95–135.92 ng/ml for IN treatment and of 16.86–857.25 ng/ml for OR treatment. After pharmacokinetic studies, diff erent spinal cord tracts were removed and used for radioligand binding assay and autoradiography. Using [3H]-RX821002 ([3H]-RX) (0.1-14nM), the Kd and Bmax for every spinal cord segment were calculated. The non-specifi c binding was obtained with 100μM of (-)-epinephrine. [3H]-RX sites were accumulated in the superfi cial laminae of dorsal horn. Dense [3H]-RX binding in control was seen over the superfi cial dorsal horn (laminae I-II) and centrally located lamina X. The ventral horn showed moderate levels of binding. [3H]-RX was displaced after TIZ treatment using diff erent administration routes. The heaviest accumulation of silver grains (lowest displacement of TIZ) occurred after OR administration of the compound, the lowest after IM administration. These results suggest that both IM and IN administration of TIZ may represent routes of administration of the drug alternative to the OR one. Considering predictable adverse eff ects of IM treatment, the IN administration could represent the elective route to administrate this kind of drugs

Obesity-related blood brain barrier changes in obese Zucker rats

The blood brain barrier (BBB) is the site of exchange between blood and the nervous tissue. Damage of it may impair physiological balance between blood stream and nervous tissue. Metabolic syndrome (MetS) is defined by several interconnected physiological, biochemical, and metabolic factors directly related to obesity. It increases the risk of atherosclerotic cardiovascular and cerebrovascular disease and of all cause mortality. Obese Zucker rats (OZRs), with a mutation in leptin receptor, represent a model of obesity exhibiting diabetes and moderate arterial hypertension. In OZRs hyperglycaemia, hyperinsulinaemia and hyperlipidaemia occur simultaneously. This work had characterized BBB and endothelial alterations of OZRs compared to their non-obese cohort lean Zucker rats (LZRs) for assessing the occurrence of an eventual cerebrovascular injury. Brains of male OZRs and LZRs of 12, 16 and 20 weeks were processed for the immunochemical and immunohistochemical detection of different BBB markers. The water channel protein Aquaporin-4 (AQP4) and the glucose transporter protein- 1 (GLUT1) involved in the glucose passage across the BBB endothelial cells were investigated. The expression of adhesion molecules intercellular adhesion molecule-1 (ICAM-1), vascular cell adhesion molecule 1 (VCAM-1) and platelet-endothelial cell adhesion molecule-1 (PECAM-1) was also assessed within cerebrovascular endothelium as a marker of inflammation. In intracerebral arteries of older OZRs, a decrease of lumen area with an increase of wall area was found. BBB of older OZRs revealed an augmented expression of AQP4 probably related to an edema formation. A downregulation of GLUT1 was observed in OZRs of 12 weeks of age. This may represent the adaptive reaction to prevent excessive glucose entering in neurons. On the contrary, in older OZRs an obvious increase in the expression of GLUT1 was found. These phenomena are probably related to vascular inflammation as confirmed by the increase of ICAM-1 and VCAM-1 expression in the endothelium of older OZRs. The above evidence shows that OZRs develope specific BBB changes. This could contribute to clarify the pathophysiology of nervous system damage reported in obese individuals. OZRs may represent an useful animal model for assessing the influence of obesity/MetS on the brain and the possible correlation of it with neurodegenerative disorders

Construction and Analysis of Projected Deformed Products

We introduce a deformed product construction for simple polytopes in terms of lower-triangular block matrix representations. We further show how Gale duality can be employed for the construction and for the analysis of deformed products such that specified faces (e.g. all the k-faces) are ``strictly preserved'' under projection. Thus, starting from an arbitrary neighborly simplicial (d-2)-polytope Q on n-1 vertices we construct a deformed n-cube, whose projection to the last dcoordinates yields a neighborly cubical d-polytope. As an extension of thecubical case, we construct matrix representations of deformed products of(even) polygons (DPPs), which have a projection to d-space that retains the complete (\lfloor \tfrac{d}{2} \rfloor - 1)-skeleton. In both cases the combinatorial structure of the images under projection is completely determined by the neighborly polytope Q: Our analysis provides explicit combinatorial descriptions. This yields a multitude of combinatorially different neighborly cubical polytopes and DPPs. As a special case, we obtain simplified descriptions of the neighborly cubical polytopes of Joswig & Ziegler (2000) as well as of the ``projected deformed products of polygons'' that were announced by Ziegler (2004), a family of 4-polytopes whose ``fatness'' gets arbitrarily close to 9.Comment: 20 pages, 5 figure