Efficient winning strategies in random-turn Maker-Breaker games

We consider random-turn positional games, introduced by Peres, Schramm, Sheffield and Wilson in 2007. A $p$-random-turn positional game is a two-player game, played the same as an ordinary positional game, except that instead of alternating turns, a coin is being tossed before each turn to decide the identity of the next player to move (the probability of Player I to move is $p$). We analyze the random-turn version of several classical Maker-Breaker games such as the game Box (introduced by Chv\'atal and Erd\H os in 1987), the Hamilton cycle game and the $k$-vertex-connectivity game (both played on the edge set of $K_n$). For each of these games we provide each of the players with a (randomized) efficient strategy which typically ensures his win in the asymptotic order of the minimum value of $p$ for which he typically wins the game, assuming optimal strategies of both players.Comment: 20 page

Linearly Dichroic Plasmonic Lens and Hetero-Chiral Structures

We present theoretical and experimental study of plasmonic Hetero-Chiral structures, comprised of constituents with opposite chirality. We devise, simulate and experimentally demonstrate different schemes featuring selective surface plasmon polariton focusing of orthogonal polarization states and standing plasmonic vortex fields.Comment: 9 pages, 6 figure

Packing, counting and covering Hamilton cycles in random directed graphs

A Hamilton cycle in a digraph is a cycle that passes through all the vertices, where all the arcs are oriented in the same direction. The problem of finding Hamilton cycles in directed graphs is well studied and is known to be hard. One of the main reasons for this is that there is no general tool for finding Hamilton cycles in directed graphs comparable to the so-called Posá ‘rotation-extension’ technique for the undirected analogue. Let D(n, p) denote the random digraph on vertex set [n], obtained by adding each directed edge independently with probability p. Here we present a general and a very simple method, using known results, to attack problems of packing and counting Hamilton cycles in random directed graphs, for every edge-probability p > logC(n)/n. Our results are asymptotically optimal with respect to all parameters and apply equally well to the undirected case

Efficient winning strategies in random-turn Maker-Breaker games

We consider random-turn positional games, introduced by Peres, Schramm, Sheffield and Wilson in 2007. A p-random-turn positional game is a two-player game, played the same as an ordinary positional game, except that instead of alternating turns, a coin is being tossed before each turn to decide the identity of the next player to move (the probability of Player I to move is p). We analyze the random-turn version of several classical MakerBreaker games such as the game Box (introduced by Chvátal and Erdős in 1987), the Hamilton cycle game and the k-vertex-connectivity game (both played on the edge set of K n ). For each of these games we provide each of the players with a (randomized) efficient strategy which typically ensures his win in the asymptotic order of the minimum value of p for which he typically wins the game, assuming optimal strategies of both players

On the Precarious Path of Reverse Neuro-Engineering

In this perspective we provide an example for the limits of reverse engineering in neuroscience. We demonstrate that application of reverse engineering to the study of the design principle of a functional neuro-system with a known mechanism, may result in a perfectly valid but wrong induction of the system's design principle. If in the very simple setup we bring here (static environment, primitive task and practically unlimited access to every piece of relevant information), it is difficult to induce a design principle, what are our chances of exposing biological design principles when more realistic conditions are examined? Implications to the way we do Biology are discussed

Synaptic dynamics contribute to long-term single neuron response fluctuations

Firing rate variability at the single neuron level is characterized by long-memory processes and complex statistics over a wide range of time scales (from milliseconds up to several hours). Here, we focus on the contribution of non-stationary efficacy of the ensemble of synapses-activated in response to a given stimulus-on single neuron response variability. We present and validate a method tailored for controlled and specific long-term activation of a single cortical neuron in vitro via synaptic or antidromic stimulation, enabling a clear separation between two determinants of neuronal response variability: membrane excitability dynamics vs. synaptic dynamics. Applying this method we show that, within the range of physiological activation frequencies, the synaptic ensemble of a given neuron is a key contributor to the neuronal response variability, long-memory processes and complex statistics observed over extended time scales. Synaptic transmission dynamics impact on response variability in stimulation rates that are substantially lower compared to stimulation rates that drive excitability resources to fluctuate. Implications to network embedded neurons are discussed. \ua9 2014 Reinartz, Biro, Gal, Giugliano and Marom

Visualization of both proximal M2-MCA segments in patients (the Tilted-V Sign) with acute M1-MCA occlusion stroke is associated with better procedural and prognostic outcomes

IntroductionWe aimed to assess the clinical significance of M1-MCA occlusion with visualization of both MCA-M2 segments [“Tilted-V sign” (TVS)] on initial CT angiography (CTA) in patients with acute ischemic stroke (AIS) undergoing endovascular thrombectomy (EVT).MethodsData for patients with consecutive AIS undergoing EVT for large vessel occlusion (LVO) in two academic centers are recorded in ongoing databases. Patients who underwent EVT for M1-MCA occlusions ≤ 6 h from symptom onset were included in this retrospective analysis.ResultsA total of 346 patients met the inclusion criteria; 189 (55%) had positive TVS. Patients with positive TVS were younger (68 ± 14 vs. 71 ± 14 years, P = 0.028), with similar rates of vascular risk factors and baseline modified Rankin scores (mRS) 0–2. The rates of achieving thrombolysis in cerebral ischemia (TICI) 2b-3 were similar to the two groups (79%), although successful first-pass recanalization was more common with TVS (64 vs. 36%, p = 0.01). On multivariate analysis, higher collateral score [odds ratio (OR) 1.38 per unit increase, p = 0.008] and lower age (OR 0.98 per year increase, p = 0.046) were significant predictors of TVS. Patients with positive TVS had higher post-procedural Alberta Stroke Program Early CT Score (ASPECTS; 6.9 ± 2.2 vs. 5.2 ± 2.3, p = 0.001), were discharged with lower National Institutes of Health Stroke Score (NIHSS; 6±6 vs. 9±7, p = 0.003) and higher rates of mRS 0–2 (29.5 vs. 12%, p = 0.001), and had lower rates of 90-day mortality (13.2 vs. 21.6%, p = 0.038). However, TVS was not an independent predictor of functional independence (OR 2.51; 95% CI 0.7–8.3).ConclusionTilted-V Sign, an easily identifiable radiological marker, is associated with fewer recanalization attempts, better functional outcomes, and reduced mortality