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Background The NMDA receptor (NMDAR) plays a key role in the central nervous system, e.g., for synaptic transmission. While synaptic NMDARs are thought to have protective characteristics, activation of extrasynaptic NMDARs might trigger excitotoxic processes linked to neuropsychiatric disorders. Since extrasynaptic NMDARs are typically GluN2B-enriched, the subunit is an interesting target for drug development and treatment monitoring. Recently, the novel GluN2B-specific PET radioligand (R)-[11C]Me-NB1 was investigated in rodents and for the first time successfully translated to humans. To assess whether (R)-[11C]Me-NB1 is a valuable radioligand for (repeated) clinical applications, we evaluated its safety, biodistribution and dosimetry. Methods Four healthy subjects (two females, two males) underwent one whole-body PET/MR measurement lasting for more than 120 min. The GluN2B-specific radioligand (R)-[11C]Me-NB1 was administered simultaneously with the PET start. Subjects were measured in nine passes and six bed positions from head to mid-thigh. Regions of interest was anatomically defined for the brain, thyroid, lungs, heart wall, spleen, stomach contents, pancreas, liver, kidneys, bone marrow and urinary bladder contents, using both PET and MR images. Time-integrated activity coefficients were estimated to calculate organ equivalent dose coefficients and the effective dose coefficient. Additionally, standardized uptake values (SUV) were computed to visualize the biodistribution. Results Administration of the radioligand was safe without adverse events. The organs with the highest uptake were the urinary bladder, spleen and pancreas. Organ equivalent dose coefficients were higher in female in almost all organs, except for the urinary bladder of male. The effective dose coefficient was 6.0 µSv/MBq. Conclusion The GluN2B-specific radioligand (R)-[11C]Me-NB1 was well-tolerated without reported side effects. Effective dose was estimated to 1.8 mSv when using 300 MBq of presented radioligand. The critical organ was the urinary bladder. Due to the low effective dose coefficient of this radioligand, longitudinal studies for drug development and treatment monitoring of neuropsychiatric disorders including neurodegenerative diseases are possible., EJNMMI Research, 12 (1), ISSN:2191-219X

A procedure for determining the overall units of a combination of quantities based on simple additions and subtractions is described. This procedure could be programmed into online-quiz software for student exercises.

The game of cops and robbers is a well-known game played on graphs. In this paper we consider the straight-ahead orientations of 4-regular quadrangulations of the torus and the Klein bottle and we prove that their cop number is bounded by a constant. We also show that the cop number of every k-regularly oriented toroidal grid is at most 13.

A string graph is the intersection graph of a family of continuous arcs in the plane. The intersection graph of a family of plane convex sets is a string graph, but not all string graphs can be obtained in this way. We prove the following structure theorem conjectured by Janson and Uzzell: The vertex set of almost all string graphs on n vertices can be partitioned into five cliques such that some pair of them is not connected by any edge ($$n\rightarrow \infty $$). We also show that every graph with the above property is an intersection graph of plane convex sets. As a corollary, we obtain that almost all string graphs on n vertices are intersection graphs of plane convex sets.

BackgroundPrevious studies suggest that transcranial magnetic stimulation exerts antidepressant effects by altering functional connectivity (FC). However, knowledge about this mechanism is still limited. Here, we aimed to investigate the effect of bilateral sequential theta-burst stimulation (TBS) on FC in treatment-resistant depression (TRD) in a sham-controlled longitudinal study.MethodsTRD patients (n = 20) underwent a three-week treatment of intermittent TBS of the left and continuous TBS of the right dorsolateral prefrontal cortex (DLPFC). Upon this trial’s premature termination, 15 patients had received active TBS and five patients sham stimulation. Resting-state functional magnetic resonance imaging was performed at baseline and after treatment. FC (left and right DLPFC) was estimated for each participant, followed by group statistics (T-tests). Furthermore, depression scores were analyzed (linear mixed models analysis) and tested for correlation with FC.ResultsBoth groups exhibited reductions of depression scores, however, there was no significant main effect of group, or group and time. Anticorrelations between DLPFC and the subgenual cingulate cortex (sgACC) were observed for baseline FC, corresponding to changes in depression severity. Treatment did not significantly change DLPFC-sgACC connectivity, but significantly reduced FC between the left stimulation target and bilateral anterior insula.ConclusionsOur data is compatible with previous reports on the relevance of anticorrelation between DLPFC and sgACC for treatment success. Furthermore, FC changes between left DLPFC and bilateral anterior insula highlight the effect of TBS on the salience network.LimitationsDue to the limited sample size, results should be interpreted with caution and are of exploratory nature.

Changes in distribution of associated molecular targets have been reported across several neuropsychiatric disorders. However, the high-resolution topology of most proteins is unknown and simultaneous in vivo measurement in multi-receptor systems is complicated. To account for the missing proteomic information, mRNA transcripts are typically used as a surrogate. Nonetheless, post-transcriptional and post-translational processes might cause the discrepancy between the final distribution of proteins and gene expression patterns. Therefore, this study aims to investigate ex vivo links between mRNA expression and corresponding receptor density in the human cerebral cortex.To this end, autoradiography data on the density of 15 different receptors in 38 brain regions were correlated with the expression patterns of 50 associated genes derived from microarray data (mA), RNA sequencing data (RNA-Seq) provided by the Allen Human Brain Atlas and predicted mRNA expression patterns (pred-mRNA). Spearman’s rank correlation was used to evaluate the possible links between proteomic data and mRNA expression patterns.Correlations between mRNA and protein density varied greatly between targets: Positive associations were found for e.g. the serotonin 1A (pred-mRNA: rs = 0.708; mA: rs = 0.601) or kainate receptor (pred-mRNA: rs = 0.655; mA: rs = 0.601; RNA-Seq: rs = 0.575), while most of the investigated target receptors showed low or negative correlations.The high variability in the correspondence of mRNA expression and receptor warrants caution when inferring the topology of molecular targets in the brain from transcriptome data. This highlights the longstanding value of molecular imaging data and the need for comprehensive proteomic data.

The clique chromatic number of a graph is the minimum number of colours needed to colour its vertices so that no inclusion-wise maximal clique, which is not an isolated vertex, is monochromatic. We show that every graph of maximum degree ∆ has clique chromatic number O (∆ log ∆ (√ n-vertex graph has clique chromatic number On). We obtain as a corollary that every). Both these results are tight., SCOPUS: ar.j, info:eu-repo/semantics/published

An approximate expression for the visual intensity of the fireball of a nuclear explosion in comparison with the Sun is derived. Results are shown for some warheads of historic and current interest.

Learning-induced neuroplastic changes, further modulated by content and setting, are mirrored in brain functional connectivity (FC). In animal models, selective serotonin reuptake inhibitors (SSRIs) have been shown to facilitate neuroplasticity. This is especially prominent during emotional relearning, such as fear extinction, which may translate to clinical improvements in patients. To investigate a comparable modulation of neuroplasticity in humans, 99 healthy subjects underwent three weeks of emotional (matching faces) or non-emotional learning (matching Chinese characters to unrelated German nouns). Shuffled pairings of the original content were subsequently relearned for the same time. During relearning, subjects received either a daily dose of the SSRI escitalopram or placebo. Resting-state functional magnetic resonance imaging was performed before and after the (re-)learning phases. FC changes in a network comprising Broca's area, the medial prefrontal cortex, the right inferior temporal and left lingual gyrus were modulated by escitalopram intake. More specifically, it increased the bidirectional connectivity between medial prefrontal cortex and lingual gyrus for non-emotional and the connectivity from medial prefrontal cortex to Broca's area for emotional relearning. The context dependence of these effects together with behavioral correlations supports the assumption that SSRIs in clinical practice improve neuroplasticity rather than psychiatric symptoms per se. Beyond expanding the complexities of learning, these findings emphasize the influence of external factors on human neuroplasticity.

An essential core function of one's cognitive flexibility is the use of acquired knowledge and skills to adapt to ongoing environmental changes. Animal models have highlighted the influence serotonin has on neuroplasticity. These effects have been predominantly demonstrated during emotional relearning which is theorized as a possible model for depression. However, translation of these mechanisms is in its infancy. To this end, we assessed changes in effective connectivity at rest and during associative learning as a proxy of neuroplastic changes in healthy volunteers. 76 participants underwent 6 weeks of emotional or non-emotional (re)learning (face-matching or Chinese character–German noun matching). During relearning participants either self-administered 10 mg/day of the selective serotonin reuptake inhibitor (SSRI) escitalopram or placebo in a double-blind design. Associative learning tasks, resting-state and structural images were recorded before and after both learning phases (day 1, 21 and 42). Escitalopram intake modulated relearning changes in a network encompassing the right insula, anterior cingulate cortex and right angular gyrus. Here, the process of relearning during SSRI intake showed a greater decrease in effective connectivity from the right insula to both the anterior cingulate cortex and right angular gyrus, with increases in the opposite direction when compared to placebo. In contrast, intrinsic connections and those at resting-state were only marginally affected by escitalopram. Further investigation of gray matter volume changes in these functionally active regions revealed no significant SSRI-induced structural changes. These findings indicate that the right insula plays a central role in the process of relearning and SSRIs further potentiate this effect. In sum, we demonstrated that SSRIs amplify learning-induced effective connections rather than affecting the intrinsic task connectivity or that of resting-state.

The increase in entropy during the volume-doubling free expansion of an ideal gas is a staple example of thermodynamics classes. While the result, Δ S = ( n R ) ln 2 , is correct, the common textbook argument which leads to it can be potentially confusing. An improved but still very simple replacement model is described here and the difficulty in the common argument is discussed.

We study the height of a spanning tree $T$ of a graph $G$ obtained by starting with a single vertex of $G$ and repeatedly selecting, uniformly at random, an edge of $G$ with exactly one endpoint in $T$ and adding this edge to $T$.

Tree-chromatic number is a chromatic version of treewidth, where the cost of a bag in a tree-decomposition is measured by its chromatic number rather than its size. Path-chromatic number is defined analogously. These parameters were introduced by Seymour [JCTB 2016]. In this paper, we survey all the known results on tree- and path-chromatic number and then present some new results and conjectures. In particular, we propose a version of Hadwiger’s Conjecture for tree chromatic number. As evidence that our conjecture may be more tractable than Hadwiger’s Conjecture, we give a short proof that every K5-minor-free graph has tree-chromatic number at most 4, which avoids the Four Colour Theorem. We also present some hardness results and conjectures for computing tree- and path chromatic number.

Random walks on dynamic graphs have received increasingly more attention from different academic communities over the last decade. Despite the relatively large literature, little is known about random walks that construct the graph where they walk while moving around. In this paper we study one of the simplest conceivable discrete time models of this kind, which works as follows: before every walker step, with probability $p$ a new leaf is added to the vertex currently occupied by the walker. The model grows trees and we call it the Bernoulli Growth Random Walk (BGRW). We show that the BGRW walker is transient and has a well-defined linear speed $c(p)>0$ for any $0

Introduction: The early and therapy-specific prediction of treatment success in major depressive disorder is of paramount importance due to high lifetime prevalence, and heterogeneity of response to standard medication and symptom expression. Hence, this study assessed the predictability of long-term antidepressant effects of escitalopram based on the short-term influence of citalopram on functional connectivity. Methods: Twenty nine subjects suffering from major depression were scanned twice with resting-state functional magnetic resonance imaging under the influence of intravenous citalopram and placebo in a randomized, double-blinded cross-over fashion. Symptom factors were identified for the Hamilton depression rating scale (HAM-D) and Beck's depression inventory (BDI) taken before and after a median of seven weeks of escitalopram therapy. Predictors were calculated from whole-brain functional connectivity, fed into robust regression models, and cross-validated. Results: Significant predictive power could be demonstrated for one HAM-D factor describing insomnia and the total score (r = 0.45–0.55). Remission and response could furthermore be predicted with an area under the receiver operating characteristic curve of 0.73 and 0.68, respectively. Functional regions with high influence on the predictor were located especially in the ventral attention, fronto-parietal, and default mode networks. Conclusion: It was shown that medication-specific antidepressant symptom improvements can be predicted using functional connectivity measured during acute pharmacological challenge as an easily assessable imaging marker. The regions with high influence have previously been related to major depression as well as the response to selective serotonin reuptake inhibitors, corroborating the advantages of the current approach of focusing on treatment-specific symptom improvements.

International audience; A well-known conjecture of Erdős and Sós states that every graph with average degree exceeding $m−1$ contains every tree with m edges as a subgraph. We propose a variant of this conjecture, which states that every graph of maximum degree exceeding m and minimum degree at least $[\frac{2m}{3}]$ contains every tree with m edges. As evidence for our conjecture we show (i) for every m there is a g(m) such that the weakening of the conjecture obtained by replacing the first m by g(m) holds, and (ii) there is a $\gamma > 0$ such that the weakening of the conjecture obtained by replacing $[\frac{2m} {3}$ by $(1 − \gamma)m$ holds.

We show that for sufficiently large $d$ and for $t\geq d+1$, there is a graph $G$ with average degree $(1-\varepsilon)\lambda t \sqrt{\ln d}$ such that almost every graph $H$ with $t$ vertices and average degree $d$ is not a minor of $G$, where $\lambda=0.63817\dots$ is an explicitly defined constant. This generalises analogous results for complete graphs by Thomason (2001) and for general dense graphs by Myers and Thomason (2005). It also shows that an upper bound for sparse graphs by Reed and Wood (2016) is best possible up to a constant factor.

We show that Maker wins the Maker-Breaker perfect matching game in $\frac{n}{2}+o(n)$ turns when the bias is at least $\frac{n}{\log{n}}-\frac{f(n)n}{(\log{n})^{5/4}}$, for any $f$ going to infinity with $n$ and $n$ sufficiently large (in terms of $f$)., Comment: 13 pages, 1 figure

Even and odd pairs are important tools in the study of perfect graphs and were instrumental in the proof of the Strong Perfect Graph Theorem. We suggest that such pairs impose a lot of structure also in arbitrary, not just perfect graphs. To this end, we show that the presence of even or odd pairs in graphs imply a special structure of the stable set polytope. In fact, we give a polyhedral characterization of even and odd pairs.

For a fixed degree sequence $\mathcal{D}=(d_1,...,d_n)$, let $G(\mathcal{D})$ be a uniformly chosen (simple) graph on $\{1,...,n\}$ where the vertex $i$ has degree $d_i$. In this paper we determine whether $G(\mathcal{D})$ has a giant component with high probability, essentially imposing no conditions on $\mathcal{D}$. We simply insist that the sum of the degrees in $\mathcal{D}$ which are not 2 is at least $\lambda(n)$ for some function $\lambda$ going to infinity with $n$. This is a relatively minor technical condition, and when $\mathcal{D}$ does not satisfy it, both the probability that $G(\mathcal{D})$ has a giant component and the probability that $G(\mathcal{D})$ has no giant component are bounded away from $1$., Comment: 42 pages, to appear in Probability Theory and Related Fields

In this paper and a companion paper, we prove that, if $m$ is sufficiently large, every graph on $m+1$ vertices that has a universal vertex and minimum degree at least $\lfloor \frac{2m}{3} \rfloor$ contains each tree $T$ with $m$ edges as a subgraph. Our result confirms, for large $m$, an important special case of a recent conjecture by Havet, Reed, Stein, and Wood. The present paper already contains an approximate version of the result., Comment: 59 pages

We prove that, if $m$ is sufficiently large, every graph on $m+1$ vertices that has a universal vertex and minimum degree at least $\lfloor \frac{2m}{3} \rfloor$ contains each tree $T$ with $m$ edges as a subgraph. Our result confirms, for large $m$, an important special case of a conjecture by Havet, Reed, Stein, and Wood. The present paper builds on the results of a companion paper in which we proved the statement for all trees having a vertex that is adjacent to many leaves., Comment: 31 pages

The overall efficiency of a reversible thermodynamic cycle comprising steps around the periphery of back-to-back Carnot cycles is equal to the efficiency-weighted average heat-energy inputs taken over all of the cycles. A proof of this assertion is straightforward and brief enough to be suitable for classroom presentation.

Group relations conferences have always been profound experiences for members, and for staff, which clearly affect how participants return to their organizations and begin to behave in new ways in the workplace. The development began in 1968 when we launched the 'Behaviour in the Working Environment' conference, an extended six-month, non-residential course designed to give participants time to become familiar with previously unfamiliar ideas and to apply them while in continuing contact with staff and fellow members. The focus of work is on the client's description of their relatedness to their working organization drawn from their experience of their day to day working relations and the meaning they attach to them. A role in our thinking is a mental regulating principle, based on a person's lived experience of the complex interaction of feelings, ideas, and motivations, aroused in working to the aim of a system, integrated consciously and unconsciously and expressed in purposive behaviour.

In 1998 the second author proved that there is an e>0 such that every graph satisfies i¾?i¾?i¾?1-eΔ+1+eωi¾?. The first author recently proved that any graph satisfying ω>23Δ+1 contains a stable set intersecting every maximum clique. In this note, we exploit the latter result to give a much shorter, simpler proof of the former. Working from first principles, we omit only some five pages of proofs of known intermediate results which appear in an extended version of this paper, and the proofs of Hall's Theorem, Brooks' Theorem, the Lovasz Local Lemma, and Talagrand's Inequality.

Ramsey's theorem says that for every clique $H_1$ and for every graph $H_2$ with no edges, all graphs containing neither of $H_1,H_2$ as induced subgraphs have bounded order. What if, instead, we exclude a graph $H_1$ with a vertex whose deletion gives a clique, and the complement $H_2$ of another such graph? This no longer implies bounded order, but it implies tightly restricted structure that we describe. There are also several related subproblems (what if we exclude a star and the complement of a star? what if we exclude a star and a clique? and so on) and we answer a selection of these.

A vertexuof a graph “t-dominates” a vertexvif there are at mosttvertices different fromu, vthat are adjacent tovand not tou; and a graph is “t-dominating” if for every pair ofdistinct vertices, one of themt-dominates the other. Our main result says that if a graph ist-dominating, then it is close (in an appropriate sense) to being 0-dominating. We also show that an analogous statement for digraphs is false; and discuss some connections with the Erdős-Hajnal conjecture.

For several decades, genetic analysis in Drosophila has made important contributions to the understanding of signaling by Egfr. Egfr has been well characterized with regard to its oncogenic potential but is also being studied for its roles in organismal development. We have recently developed dorsal closure of the Drosophila embryo as a system for characterizing Egfr regulation of events that do not involve proliferation, as no cell divisions occur during this process. Dorsal closure is essentially a developmental wound healing event with parallels to vertebrate developmental epithelial fusions such as neural tube closure and palate fusion. We describe here a set of materials and protocols for studying Egfr signaling during dorsal closure, including assessing effects of altering Egfr signaling on other pathways, gene expression and, using live imaging, morphogenesis and programmed cell death. Although this "tool kit" is designed for looking at Egfr, it can be readily adapted to look at the participation of any signaling molecule in dorsal closure.

We consider the chromatic number of graphs with maximum degree Δ. For sufficiently large Δ, we determine the precise values of k for which the barrier to ( Δ + 1 - k ) -colourability must be a local condition, i.e. a small subgraph. We also show that for Δ constant and sufficiently large, ( Δ + 1 - k ) -colourability is either NP-complete or can be solved in linear time, and we determine precisely which values of k correspond to each case.

We prove a conjecture of Ohba that says that every graph G on at most 2i¾?G+1 vertices satisfies i¾?i¾?G=i¾?G.

We consider the following problem. For every positive integer k there is a smallest integer f ( k ) such that for any two vertices s and t in a non-bipartite f ( k ) -connected graph G, there is an s–t path P in G with specified parity such that G − V ( P ) is k-connected. This conjecture is a variant of the well-known conjecture of Lovasz with the parity condition. Indeed, this conjecture is strictly stronger. Lovasz' conjecture is wide open for k ⩾ 3 . In this paper, we show that f ( 1 ) = 5 and 6 ⩽ f ( 2 ) ⩽ 8 . We also consider a conjecture of Thomassen which says that there exists a function f ( k ) such that every f ( k ) -connected graph with an odd cycle contains an odd cycle C such that G − V ( C ) is k-connected. We show the following strengthening of Thomassen's conjecture for the case k = 2 . Namely; let G be a 5-connected graph and s be a vertex in G such that G − s is not bipartite. Then there is an odd cycle C avoiding s such that G − V ( C ) is 2-connected.