Good covers are algorithmically unrecognizable

A good cover in R^d is a collection of open contractible sets in R^d such that the intersection of any subcollection is either contractible or empty. Motivated by an analogy with convex sets, intersection patterns of good covers were studied intensively. Our main result is that intersection patterns of good covers are algorithmically unrecognizable. More precisely, the intersection pattern of a good cover can be stored in a simplicial complex called nerve which records which subfamilies of the good cover intersect. A simplicial complex is topologically d-representable if it is isomorphic to the nerve of a good cover in R^d. We prove that it is algorithmically undecidable whether a given simplicial complex is topologically d-representable for any fixed d \geq 5. The result remains also valid if we replace good covers with acyclic covers or with covers by open d-balls. As an auxiliary result we prove that if a simplicial complex is PL embeddable into R^d, then it is topologically d-representable. We also supply this result with showing that if a "sufficiently fine" subdivision of a k-dimensional complex is d-representable and k \leq (2d-3)/3, then the complex is PL embeddable into R^d.Comment: 22 pages, 5 figures; result extended also to acyclic covers in version

Bounding Helly numbers via Betti numbers

We show that very weak topological assumptions are enough to ensure the existence of a Helly-type theorem. More precisely, we show that for any non-negative integers $b$ and $d$ there exists an integer $h(b,d)$ such that the following holds. If $\mathcal F$ is a finite family of subsets of $\mathbb R^d$ such that $\tilde\beta_i\left(\bigcap\mathcal G\right) \le b$ for any $\mathcal G \subsetneq \mathcal F$ and every $0 \le i \le \lceil d/2 \rceil-1$ then $\mathcal F$ has Helly number at most $h(b,d)$. Here $\tilde\beta_i$ denotes the reduced $\mathbb Z_2$-Betti numbers (with singular homology). These topological conditions are sharp: not controlling any of these $\lceil d/2 \rceil$ first Betti numbers allow for families with unbounded Helly number. Our proofs combine homological non-embeddability results with a Ramsey-based approach to build, given an arbitrary simplicial complex $K$, some well-behaved chain map $C_*(K) \to C_*(\mathbb R^d)$.Comment: 29 pages, 8 figure

Duloxetine Inhibits Effects of MDMA (“Ecstasy") In Vitro and in Humans in a Randomized Placebo-Controlled Laboratory Study

This study assessed the effects of the serotonin (5-HT) and norepinephrine (NE) transporter inhibitor duloxetine on the effects of 3,4–methylenedioxy­methamphetamine (MDMA, ecstasy) in vitro and in 16 healthy subjects. The clinical study used a double-blind, randomized, placebo-controlled, four-session, crossover design. In vitro, duloxetine blocked the release of both 5-HT and NE by MDMA or by its metabolite 3,4-methylenedioxyamphetamine from transmitter-loaded human cells expressing the 5-HT or NE transporter. In humans, duloxetine inhibited the effects of MDMA including elevations in circulating NE, increases in blood pressure and heart rate, and the subjective drug effects. Duloxetine inhibited the pharmacodynamic response to MDMA despite an increase in duloxetine-associated elevations in plasma MDMA levels. The findings confirm the important role of MDMA-induced 5-HT and NE release in the psychotropic effects of MDMA. Duloxetine may be useful in the treatment of psychostimulant dependence

Acute neuropsychological effects of MDMA and ethanol (co-)administration in healthy volunteers

Contains fulltext : 73592.pdf (publisher's version ) (Open Access)RATIONALE: In Western societies, a considerable percentage of young people expose themselves to 3,4-methylenedioxymethamphetamine (MDMA or "ecstasy"). Commonly, ecstasy is used in combination with other substances, in particular alcohol (ethanol). MDMA induces both arousing as well as hallucinogenic effects, whereas ethanol is a general central nervous system depressant. OBJECTIVE: The aim of the present study is to assess the acute effects of single and co-administration of MDMA and ethanol on executive, memory, psychomotor, visuomotor, visuospatial and attention function, as well as on subjective experience. MATERIALS AND METHODS: We performed a four-way, double-blind, randomised, crossover, placebo-controlled study in 16 healthy volunteers (nine male, seven female) between the ages of 18-29. MDMA was given orally (100 mg) and blood alcohol concentration was maintained at 0.6 per thousand by an ethanol infusion regime. RESULTS: Co-administration of MDMA and ethanol was well tolerated and did not show greater impairment of performance compared to the single-drug conditions. Impaired memory function was consistently observed after all drug conditions, whereas impairment of psychomotor function and attention was less consistent across drug conditions. CONCLUSIONS: Co-administration of MDMA and ethanol did not exacerbate the effects of either drug alone. Although the impairment of performance by all drug conditions was relatively moderate, all induced significant impairment of cognitive function

3,4-Methylenedioxymethamphetamine (MDMA) neurotoxicity in rats: a reappraisal of past and present findings

RATIONALE: 3,4-Methylenedioxymethamphetamine (MDMA) is a widely abused illicit drug. In animals, high-dose administration of MDMA produces deficits in serotonin (5-HT) neurons (e.g., depletion of forebrain 5-HT) that have been interpreted as neurotoxicity. Whether such 5-HT deficits reflect neuronal damage is a matter of ongoing debate. OBJECTIVE: The present paper reviews four specific issues related to the hypothesis of MDMA neurotoxicity in rats: (1) the effects of MDMA on monoamine neurons, (2) the use of “interspecies scaling” to adjust MDMA doses across species, (3) the effects of MDMA on established markers of neuronal damage, and (4) functional impairments associated with MDMA-induced 5-HT depletions. RESULTS: MDMA is a substrate for monoamine transporters, and stimulated release of 5-HT, NE, and DA mediates effects of the drug. MDMA produces neurochemical, endocrine, and behavioral actions in rats and humans at equivalent doses (e.g., 1–2 mg/kg), suggesting that there is no reason to adjust doses between these species. Typical doses of MDMA causing long-term 5-HT depletions in rats (e.g., 10–20 mg/kg) do not reliably increase markers of neurotoxic damage such as cell death, silver staining, or reactive gliosis. MDMA-induced 5-HT depletions are accompanied by a number of functional consequences including reductions in evoked 5-HT release and changes in hormone secretion. Perhaps more importantly, administration of MDMA to rats induces persistent anxiety-like behaviors in the absence of measurable 5-HT deficits. CONCLUSIONS: MDMA-induced 5-HT depletions are not necessarily synonymous with neurotoxic damage. However, doses of MDMA which do not cause long-term 5-HT depletions can have protracted effects on behavior, suggesting even moderate doses of the drug may pose risks

Pach's Selection Theorem Does Not Admit a Topological Extension

Let U1,…,Ud+1 be n-element sets in Rd . Pach’s selection theorem says that there exist subsets Z1⊂U1,…,Zd+1⊂Ud+1 and a point u∈Rd such that each |Zi|≥c1(d)n and u∈conv{z1,…,zd+1} for every choice of z1∈Z1,…,zd+1∈Zd+1 . Here we show that this theorem does not admit a topological extension with linear size sets Zi . However, there is a topological extension where each |Zi| is of order (logn)1/d

First passage distributions for long memory processes

We study the distribution of first passage time for Levy type anomalous diffusion. A fractional Fokker-Planck equation framework is introduced.For the zero drift case, using fractional calculus an explicit analytic solution for the first passage time density function in terms of Fox or H-functions is given. The asymptotic behaviour of the density function is discussed. For the nonzero drift case, we obtain an expression for the Laplace transform of the first passage time density function, from which the mean first passage time and variance are derived

Nonlinear measures of respiration: Respiratory irregularity and increased chaos of respiration in patients with panic disorder

Background. Respiratory irregularity has been previously reported in patients with panic disorder using time domain measures. However, the respiratory signal is not entirely linear and a few previous studies used approximate entropy (APEN), a measure of regularity of time series. We have been studying APEN and other nonlinear measures including a measure of chaos, the largest Lyapunov exponent (LLE) of heart rate time series, in some detail. In this study, we used these measures of respiration to compare normal controls (n = 18) and patients with panic disorder (n = 22) in addition to the traditional time domain measures of respiratory rate and tidal volume. Methods: Respiratory signal was obtained by the Respitrace system using a thoracic and an abdominal belt, which was digitized at 500 Hz. Later, the time series were constructed at 4 Hz, as the highest frequency in this signal is limited to 0.5 Hz. We used 256 s of data (1,024 points) during supine and standing postures under normal breathing and controlled breathing at 12 breaths/min. Results: APEN was significantly higher in patients in standing posture during normal as well as controlled breathing (p = 0.002 and 0.02, respectively). LLE was also significantly higher in standing posture during normal breathing (p = 0.009). Similarly, the time domain measures of standard deviations and the coefficient of variation (COV) of tidal volume (TV) were significantly higher in the patient group (p = 0.02 and 0.004, respectively). The frequency of sighs was also higher in the patient group in standing posture (p = 0.02). In standing posture, LLE (p < 0.05) as well as APEN (p < 0.01) contributed significantly toward the separation of the two groups over and beyond the linear measure, i.e. the COV of TV. Conclusion: These findings support the previously described respiratory irregularity in patients with panic disorder and also illustrate the utility of nonlinear measures such as APEN and LLE as additional measures toward a better understanding of the abnormalities of respiratory physiology in similar patient populations as the correlation between LLE, APEN and some of the time domain measures only explained up to 50-60% of the variation. Copyright (C) 2002 S. Karger AG, Basel