On intersections of compacta in Euclidean space : the metastable case

We prove the following theorem: Let f: X→Rn and g:Y→Rn be any maps of copmpacta X and Y into the Euclidean n-space Rn, n≧5. Suppose that dim(X×)0 there exist maps f\u27:X→Rn and g\u27:Y→Rn sucha that d(f,f\u27)<ε, d(g,g\u27)<ε and f\u27(X)∩g\u27(Y)=0

The behavior of solutions of a parametric weighted (p, q)-laplacian equation

We study the behavior of solutions for the parametric equation (Formula presented), under Dirichlet condition, where (Formula presented) is a bounded domain with a C2-boundary (Formula presented) are weighted versions of p-Laplacian and q-Laplacian. We prove existence and nonexistence of nontrivial solutions, when f (z, x) asymptotically as x → ±∞ can be resonant. In the studied cases, we adopt a variational approach and use truncation and comparison techniques. When λ is large, we establish the existence of at least three nontrivial smooth solutions with sign information and ordered. Moreover, the critical parameter value is determined in terms of the spectrum of one of the differential operators

Positive solutions for singular double phase problems

We study the existence of positive solutions for a class of double phase Dirichlet equations which have the combined effects of a singular term and of a parametric superlinear term. The differential operator of the equation is the sum of a p-Laplacian and of a weighted q-Laplacian (q0, the equation has at least two positive solutions

The Covering Homotopy Extension Problem for Compact Transformation Groups

It is shown that the orbit space of universal (in the sense of Palais) G-spaces classifies G-spaces. Theorems on the extension of covering homotopy for G-spaces and on a homotopy representation of the isovariant category ISOV are proved

Constant sign and nodal solutions for parametric anisotropic (p,2)-equations

We consider an anisotropic (Formula presented.) -equation, with a parametric and superlinear reaction term. We show that for all small values of the parameter the problem has at least five nontrivial smooth solutions, four with constant sign and the fifth nodal (sign-changing). The proofs use tools from critical point theory, truncation and comparison techniques, and critical groups

Constructing near-embeddings of codimension one manifolds with countable dense singular sets

The purpose of this paper is to present, for all $n\ge 3$, very simple examples of continuous maps $f:M^{n-1} \to M^{n}$ from closed $(n-1)$-manifolds $M^{n-1}$ into closed $n$-manifold $M^n$ such that even though the singular set $S(f)$ of $f$ is countable and dense, the map $f$ can nevertheless be approximated by an embedding, i.e. $f$ is a {\sl near-embedding}

Association of Thalamic Dysconnectivity and Conversion to Psychosis in Youth and Young Adults at Elevated Clinical Risk

IMPORTANCE: Severe neuropsychiatric conditions, such as schizophrenia, affect distributed neural computations. One candidate system profoundly altered in chronic schizophrenia involves the thalamocortical networks. It is widely acknowledged that schizophrenia is a neurodevelopmental disorder that likely affects the brain before onset of clinical symptoms. However, no investigation has tested whether thalamocortical connectivity is altered in individuals at risk for psychosis or whether this pattern is more severe in individuals who later develop full-blown illness. OBJECTIVES: To determine whether baseline thalamocortical connectivity differs between individuals at clinical high risk for psychosis and healthy controls, whether this pattern is more severe in those who later convert to full-blown illness, and whether magnitude of thalamocortical dysconnectivity is associated with baseline prodromal symptom severity. DESIGN, SETTING, AND PARTICIPANTS: In this multicenter, 2-year follow-up, case-control study, we examined 397 participants aged 12-35 years of age (243 individuals at clinical high risk of psychosis, of whom 21 converted to full-blown illness, and 154 healthy controls). The baseline scan dates were January 15, 2010, to April 30, 2012. MAIN OUTCOMES AND MEASURES: Whole-brain thalamic functional connectivity maps were generated using individuals\u27 anatomically defined thalamic seeds, measured using resting-state functional connectivity magnetic resonance imaging. RESULTS: Using baseline magnetic resonance images, we identified thalamocortical dysconnectivity in the 243 individuals at clinical high risk for psychosis, which was particularly pronounced in the 21 participants who converted to full-blown illness. The pattern involved widespread hypoconnectivity between the thalamus and prefrontal and cerebellar areas, which was more prominent in those who converted to full-blown illness (t(173) = 3.77, P \u3c .001, Hedge g = 0.88). Conversely, there was marked thalamic hyperconnectivity with sensory motor areas, again most pronounced in those who converted to full-blown illness (t(173) = 2.85, P \u3c .001, Hedge g = 0.66). Both patterns were significantly correlated with concurrent prodromal symptom severity (r = 0.27, P \u3c 3.6 x 10(-8), Spearman rho = 0.27, P \u3c 4.75 x 10(-5), 2-tailed). CONCLUSIONS AND RELEVANCE: Thalamic dysconnectivity, resembling that seen in schizophrenia, was evident in individuals at clinical high risk for psychosis and more prominently in those who later converted to psychosis. Dysconnectivity correlated with symptom severity, supporting the idea that thalamic connectivity may have prognostic implications for risk of conversion to full-blown illness

Changes in global and thalamic brain connectivity in LSD-induced altered states of consciousness are attributable to the 5-HT2A receptor

Background:Lysergic acid diethylamide (LSD) has agonist activity at various serotonin (5-HT) and dopamine receptors. Despite the therapeutic and scientific interest in LSD, specific receptor contributions to its neurobiological effects remain unknown. Methods: We therefore conducted a double-blind, randomized, counterbalanced, cross-over study (ClinicalTrials.gov, NCT02451072) during which 24 healthy human participants received either (i) placebo+placebo, (ii) placebo+LSD (100 µg po), or (iii) Ketanserin, a selective 5-HT receptor antagonist,+LSD. We quantified resting-state functional connectivity via a data-driven global brain connectivity method and compared it to cortical gene expression maps. Findings: LSD reduced associative, but concurrently increased sensory-somatomotor brain-wide and thalamic connectivity. Ketanserin fully blocked the subjective and neural LSD effects. Whole-brain spatial patterns of LSD effects matched 5-HT receptor cortical gene expression in humans. Conclusion: Together, these results strongly implicate the 5-HT receptor in LSD's neuropharmacology. This study therefore pinpoints the critical role of 5-HT in LSD's mechanism, which informs its neurobiology and guides rational development of psychedelic-based therapeutics. Funding: Swiss National Science Foundation (SNSF, P2ZHP1_161626, KHP), the Swiss Neuromatrix Foundation (2015 - 0103, FXV), the Usona Institute (2015 - 2056, FXV), the NIH (R01MH112746, JDM; DP5OD012109, AA; R01MH108590, AA), the NIAA ( P50AA012870-16, AA & JHK), the NARSAD Independent Investigator Grant (AA), the Yale CTSA grant (UL1TR000142 Pilot Award, AA), and the Slovenian Research Agency (ARRS J7-6829 & ARRS J7-8275, GR)

Computational modelling of EEG and fMRI paradigms indicates a consistent loss of pyramidal cell synaptic gain in schizophrenia

Background Diminished synaptic gain – the sensitivity of postsynaptic responses to neural inputs – may be a fundamental synaptic pathology in schizophrenia. Evidence for this is indirect, however. Furthermore, it is unclear whether pyramidal cells or interneurons (or both) are affected, or how these deficits relate to symptoms. Methods Participants with schizophrenia diagnoses (PScz, n=108), their relatives (n=57), and controls (n=107) underwent three electroencephalography (EEG) paradigms – resting, mismatch negativity, and 40 Hz auditory steady-state response – and resting functional magnetic resonance imaging. Dynamic causal modelling was used to quantify synaptic connectivity in cortical microcircuits. Results Classic group differences in EEG features between PScz and controls were replicated, including increased theta and other spectral changes (resting EEG), reduced mismatch negativity, and reduced 40 Hz power. Across all four paradigms, characteristic PScz data features were all best explained by models with greater self-inhibition (decreased synaptic gain), in pyramidal cells. Furthermore, disinhibition in auditory areas predicted abnormal auditory perception (and positive symptoms) in PScz, in three paradigms. Conclusions First, characteristic EEG changes in PScz in three classic paradigms are all attributable to the same underlying parameter change: greater self-inhibition in pyramidal cells. Second, psychotic symptoms in PScz relate to disinhibition in neural circuits. These findings are more commensurate with the hypothesis that in PScz, a primary loss of synaptic gain on pyramidal cells is then compensated by interneuron downregulation (rather than the converse). They further suggest that psychotic symptoms relate to this secondary downregulation

Ketamine Induces Multiple Individually Distinct Whole-Brain Functional Connectivity Signatures

BACKGROUND Ketamine has emerged as one of the most promising therapies for treatment-resistant depression. However, inter-individual variability in response to ketamine is still not well understood and it is unclear how ketamine's molecular mechanisms connect to its neural and behavioral effects. METHODS We conducted a single-blind placebo-controlled study, with participants blinded to their treatment condition. 40 healthy participants received acute ketamine (initial bolus 0.23 mg/kg, continuous infusion 0.58 mg/kg/hr). We quantified resting-state functional connectivity via data-driven global brain connectivity and related it to individual ketamine-induced symptom variation and cortical gene expression targets. RESULTS We found that: (i) both the neural and behavioral effects of acute ketamine are multi-dimensional, reflecting robust inter-individual variability; (ii) ketamine's data-driven principal neural gradient effect matched somatostatin (SST) and parvalbumin (PVALB) cortical gene expression patterns in humans, while the mean effect did not; and (iii) behavioral data-driven individual symptom variation mapped onto distinct neural gradients of ketamine, which were resolvable at the single-subject level. CONCLUSIONS These results highlight the importance of considering individual behavioral and neural variation in response to ketamine. They also have implications for the development of individually precise pharmacological biomarkers for treatment selection in psychiatry. FUNDING This study was supported by NIH grants DP5OD012109-01 (A.A.), 1U01MH121766 (A.A.), R01MH112746 (J.D.M.), 5R01MH112189 (A.A.), 5R01MH108590 (A.A.), NIAAA grant 2P50AA012870-11 (A.A.); NSF NeuroNex grant 2015276 (J.D.M.); Brain and Behavior Research Foundation Young Investigator Award (A.A.); SFARI Pilot Award (J.D.M., A.A.); Heffter Research Institute (Grant No. 1-190420) (FXV, KHP); Swiss Neuromatrix Foundation (Grant No. 2016-0111) (FXV, KHP); Swiss National Science Foundation under the framework of Neuron Cofund (Grant No. 01EW1908) (KHP); Usona Institute (2015 - 2056) (FXV). CLINICAL TRIAL NUMBER NCT03842800