Minimum Light Numbers in the σ\sigma -Game and Lit-Only σ\sigma -Game on Unicyclic and Grid Graphs

Consider a graph each of whose vertices is either in the ON state or in the OFF state and call the resulting ordered bipartition into ON vertices and OFF vertices a configuration of the graph. A regular move at a vertex changes the states of the neighbors of that vertex and hence sends the current configuration to another one. A valid move is a regular move at an ON vertex. For any graph $G,$ let $\mathcal{D}(G)$ be the minimum integer such that given any starting configuration $\bf x$ of $G$ there must exist a sequence of valid moves which takes $\bf x$ to a configuration with at most $\ell +\mathcal{D}(G)$ ON vertices provided there is a sequence of regular moves which brings $\bf x$ to a configuration in which there are $\ell$ ON vertices. The shadow graph $\mathcal{S}(G)$ of a graph $G$ is obtained from $G$ by deleting all loops. We prove that $\mathcal{D}(G)\leq 3$ if $\mathcal{S}(G)$ is unicyclic and give an example to show that the bound $3$ is tight. We also prove that $\mathcal{D}(G)\leq 2$ if $G$ is a two-dimensional grid graph and $\mathcal{D}(G)=0$ if $\mathcal{S}(G)$ is a two-dimensional grid graph but not a path and $G\neq \mathcal{S}(G)$

Does the lit-only restriction make any difference for the σ-game and σ+-game?

AbstractEach vertex in a simple graph is in one of two states: “on” or “off”. The set of all on vertices is called a configuration. In the σ-game, “pushing” a vertex v changes the state of all vertices in the open neighborhood of v, while in the σ+-game pushing v changes the state of all vertices in its closed neighborhood. The reachability question for these two games is to decide whether a given configuration can be reached from a given starting configuration by a sequence of pushes. We consider the lit-only restriction on these two games where a vertex can be pushed only if it is in the on state. We show that the lit-only restriction can make a big difference for reachability in the σ-game, but has essentially no effect in the σ+-game

Self-passivated freestanding superconducting oxide film for flexible electronics

The integration of high-temperature superconducting YBa2Cu3O6+x (YBCO) into flexible electronic devices has the potential to revolutionize the technology industry. The effective preparation of high-quality flexible YBCO films therefore plays a key role in this development. We present a novel approach for transferring water-sensitive YBCO films onto flexible substrates without any buffer layer. Freestanding YBCO film on a polydimethylsiloxane substrate is extracted by etching the Sr3Al2O6 sacrificial layer from the LaAlO3 substrate. In addition to the obtained freestanding YBCO thin film having a Tc of 89.1 K, the freestanding YBCO thin films under inward and outward bending conditions have Tc of 89.6 K and 88.9 K, respectively. A comprehensive characterization involving multiple experimental techniques including high-resolution transmission electron microscopy, scanning electron microscopy, Raman and X-ray Absorption Spectroscopy is conducted to investigate the morphology, structural and electronic properties of the YBCO film before and after the extraction process where it shows the preservation of the structural and superconductive properties of the freestanding YBCO virtually in its pristine state. Further investigation reveals the formation of a YBCO passivated layer serves as a protective layer which effectively preserves the inner section of the freestanding YBCO during the etching process. This work plays a key role in actualizing the fabrication of flexible oxide thin films and opens up new possibilities for a diverse range of device applications involving thin-films and low-dimensional materials.Comment: 22 pages,4 figures,references adde

Retinal ganglion cell-inner plexiform layer, white matter hyperintensities, and their interaction with cognition in older adults

PurposeWe explored the interaction of optical coherence tomography (OCT) parameters and white matter hyperintensities with cognitive measures in our older adult cohort.MethodsThis observational study enrolled participants who underwent a comprehensive neuropsychological battery, structural 3-T brain magnetic resonance imaging (MRI), visual acuity examination, and OCT imaging. Cerebral small vessel disease (CSVD) markers were read on MR images; lacune, cerebral microbleeds (CMB), white matter hyperintensities (WMH), and enlarged perivascular spaces (EPVS), were defined according to the STRIVE standards. Retinal nerve fiber layer (RNFL) and ganglion cell-inner plexiform layer (GCIPL) thicknesses (μm) were measured on the OCT tool.ResultsOlder adults with cognitive impairment (CI) showed lower RNFL (p = 0.001), GCIPL (p = 0.009) thicknesses, and lower hippocampal volume (p = 0.004) when compared to non-cognitively impaired (NCI). RNFL (p = 0.006) and GCIPL thicknesses (p = 0.032) correlated with MoCA scores. GCIPL thickness (p = 0.037), total WMH (p = 0.003), PWMH (p = 0.041), and DWMH (p = 0.001) correlated with hippocampal volume in our older adults after adjusting for covariates. With hippocampal volume as the outcome, a significant interaction (p < 0.05) between GCIPL and PWMH and total WMH was observed in our older adults.ConclusionBoth GCIPL thinning and higher WMH burden (especially PWMH) are associated with hippocampal volume and older adults with both pathologies are more susceptible to subclinical cognitive decline

Direct observation of two-dimensional small polarons at correlated oxide interface

Two-dimensional (2D) perovskite oxide interfaces are ideal systems where diverse emergent properties can be uncovered.The formation and modification of polaronic properties due to short-range strong charge-lattice interactions of 2D interfaces remains hugely intriguing.Here, we report the direct observation of small-polarons at the LaAlO3/SrTiO3 (LAO/STO) conducting interface using high-resolution spectroscopic ellipsometry.First-principles investigations further reveals that strong coupling between the interfacial electrons and the Ti-lattice result in the formation of localized 2D small polarons.These findings resolve the longstanding issue where the excess experimentally measured interfacial carrier density is significantly lower than theoretically predicted values.The charge-phonon induced lattice distortion further provides an analogue to the superconductive states in magic-angle twisted bilayer graphene attributed to the many-body correlations induced by broken periodic lattice symmetry.Our study sheds light on the multifaceted complexity of broken periodic lattice induced quasi-particle effects and its relationship with superconductivity

Minimum light number of lit-only σ-game on a tree. Theoretical Computer Science 381

Abstract Let T be a tree with leaves. Each vertex of T is assigned a state either lit or off. An assignment of states to all the vertices of T is called a configuration. The lit-only σ -game allows the player to pick a lit vertex and change the states of all its neighbours. We prove that for any initial configuration one can make a sequence of allowable moves to arrive at a configuration in which the number of lit vertices is no greater than 2 . We also give examples to show that the bound 2 cannot be relaxed to 2

LH-21, A Peripheral Cannabinoid Receptor 1 Antagonist, Exerts Favorable Metabolic Modulation Including Antihypertensive Effect in KKAy Mice by Regulating Inflammatory Cytokines and Adipokines on Adipose Tissue

Patients with obesity are susceptible to hypertension and diabetes. Over-activation of cannabinoid receptor 1 (CB1R) in adipose tissue is proposed in the pathophysiology of metabolic disorders, which led to the metabolic dysfunction of adipose tissue and deregulated production and secretion of adipokines. In the current study, we determined the impact of LH-21, a representative peripheral CB1R antagonist, on the obesity-accompanied hypertension and explored the modulatory action of LH-21 on the adipose tissue in genetically obese and diabetic KKAy mice. 3-week LH-21 treatment significantly decreased blood pressure with a concomitant reduction in body weight, white adipose tissue (WAT) mass, and a slight loss on food intake in KKAy mice. Meanwhile, glucose handling and dyslipidemia were also markedly ameliorated after treatment. Gene expression of pro-inflammatory cytokines in WAT and the aortae were both attenuated apparently by LH-21, as well the mRNA expression of adipokines (lipocalin-2, leptin) in WAT. Concomitant amelioration on the accumulation of lipocalin-2 was observed in both WAT and aortae. In corresponding with this, serum inflammatory related cytokines (tumor necrosis factor α, IL-6, and CXCL1), and lipocalin-2 and leptin were lowered notably. Thus according to current results, it can be concluded that the peripheral CB1R antagonist LH-21 is effective in managing the obesity-accompanied hypertension in KKAy mice. These metabolic benefits are closely associated with the regulation on the production and secretion of inflammatory cytokines and adipokines in the WAT, particularly alleviated circulating lipocalin-2 and its accumulation in aortae