Maker-Breaker Percolation Games I: Crossing Grids

Motivated by problems in percolation theory, we study the following 2-player positional game. Let $\Lambda_{m \times n}$ be a rectangular grid-graph with $m$ vertices in each row and $n$ vertices in each column. Two players, Maker and Breaker, play in alternating turns. On each of her turns, Maker claims $p$ (as-yet unclaimed) edges of the board $\Lambda_{m \times n}$, while on each of his turns Breaker claims $q$ (as-yet unclaimed) edges of the board and destroys them. Maker wins the game if she manages to claim all the edges of a crossing path joining the left-hand side of the board to its right-hand side, otherwise Breaker wins. We call this game the $(p,q)$-crossing game on $\Lambda_{m \times n}$. Given $m,n\in \mathbb{N}$, for which pairs $(p,q)$ does Maker have a winning strategy for the $(p,q)$-crossing game on $\Lambda_{m \times n}$? The $(1,1)$-case corresponds exactly to the popular game of Bridg-it, which is well understood due to it being a special case of the older Shannon switching game. In this paper, we study the general $(p,q)$-case. Our main result is to establish the following transition: $\bullet$ If $p\geqslant 2q$, then Maker wins the game on arbitrarily long versions of the narrowest board possible, i.e. Maker has a winning strategy for the $(2q, q)$-crossing game on $\Lambda_{m \times(q+1)}$ for any $m\in \mathbb{N}$; $\bullet$ if $p\leqslant 2q-1$, then for every width $n$ of the board, Breaker has a winning strategy for the $(p,q)$-crossing game on $\Lambda_{m \times n}$ for all sufficiently large board-lengths $m$. Our winning strategies in both cases adapt more generally to other grids and crossing games. In addition we pose many new questions and problems.Comment: 29 pages, 7 figure

Student Reactions to a Faculty Strike

Following a three week faculty strike at Dalhousie University in 1988, questionnaires were obtained from 187 students concerning how the strike affected their academic work, emotions and opinions of the university. Results were analyzed separately for first year undergraduates, other undergraduates, and graduate or professional school students. There was much individual variability in reactions, but on average the strike had slightly negative academic and emotional effects but substantial negative effects on opinions about the university. Undergraduate students indicated the most academic disruption, and upper year undergraduates indicated the most negative opinions. There was no correlation, however, between degree of personally experienced academic disruption and degree of negative opinion. Another survey two years after the strike indicated the reestablishment of positive opinions. Implications for ameliorating the effects of a faculty strike are discussed.Une enquête a été menée auprès de 187 étudiants et étudiantes de l'Université Dalhousie visant à évaluer l'effet de la grève de trois semaines du corps professoral de l'Université Dalhousie en 1988 sur le travail académique, les émotions, et l'opinion qu'avaient les étudiants de l'Université. Les résultats furent désagrégés selon trois groupes d'étudiants soit ceux inscrits à la première année du premier cycle, les autres étudiants du premier cycle et les étudiants des cycles supérieurs et des programmes professionnels. Bien qu'on remarque une grande variabilité chez les répondants individuellement, on observe que généralement, la grève n'a eu que de faibles effets négatifs au plans académique et émotif, mais qu'elle a généré de vives réactions négatives quant aux opinions que les étudiants avaient de l'Université. Par rapport à la différenciation par groupes, les étudiants de la première année du premier cycle ont été davantage affecté au plan académique alors que ceux inscrits aux études supérieures ont manifesté le degré le plus élevé d'opinions négatives envers l'Université. Il n'y a toutefois pas de corrélation entre le niveau de perturbation académique personnellement rapporté par les étudiants et les opinions négatives détenues. Une seconde enquête effectuée deux ans plus tard démontre que les opinions des étudiants envers l'Université sont redevenues positives. L'article conclut sur une analyse des implication d'une grève du corps professoral

Theory of the high-frequency chiral optical response in a p_x+ip_y superconductor

The optical Hall conductivity and the polar Kerr angle are calculated as functions of temperature for a two-dimensional chiral p_x+ip_y superconductor, where the time-reversal symmetry is spontaneously broken. The theoretical estimate for the polar Kerr angle agrees by the order of magnitude with the recent experimental measurement in Sr2RuO4 by Xia et al. cond-mat/0607539. The theory predicts that the Kerr angle is proportional to the square of the superconducting energy gap and is inversely proportional to the cube of frequency, which can be verified experimentally.Comment: 4 pages, no figures, RevTeX. V.2: one reference and discussion of horizontal lines of nodes added. V.3: a typo corrected, and one reference added. V.4: two references added and minor stylistic changes made, as in the published versio

Communication and Cultural Strategies Impacting Ukrainian Refugees and Others Involved

The Russian armed forces moved into Ukraine on February 24, 2022. Immediately and in the months following, millions of Ukrainians left their homes to seek a safe haven elsewhere. The dimensions of the Ukrainian refugee crisis are, in the words of Germany’s representative to the United Nations High Commission on Refugees (UNHCR) Katherina Lumpp, “unprecedented… the refugee movement we are now seeing in Ukraine is unique. It is currently the second largest refugee[1] situation in the world. No situation has developed this rapidly since the Second World War” (Bauer, 2022). As of October 2023, the UN Refugee Agency has officially recorded 6,204,600 Ukrainian refugees (Ukraine Refugee Portal, UN Refugee Agency). In short, the Ukrainian refugee situation presents a dramatic need to accommodate millions of Ukrainians into host or transit countries. Among the many concerns are the cross-cultural differences Ukrainians face as they flee abroad to countries with which they are unfamiliar and whose people may be unacquainted with Ukrainian culture. To that end, the purpose of the current study is to focus on the cross-cultural communication challenges confronted by Ukrainian refugees and those in destination and transit countries interacting with them, such as hosts, paid and volunteer agency staff, school and learning personnel, potential and current employers, and co-workers. The key points covered by this research are cultural complexities; language and language dynamics; managing change; and, loss and grief. Key Words: Ukraine, refugee, communication, culture, hosts, employers, crisis communication, multiculturalism, cross-cultural, emergency, Ukrainian-Russian conflict [1] After the Syrian refugee crisis, although the Syrian war has gone on since 2012, growing over more than a decade, while the Ukrainian refugees have reached this size within a matter of months

Hydrogen-Bonding Linkers Yield a Large-Pore, Non-Catenated, Metal-Organic Framework with pcu Topology

This work is licensed under a Creative Commons Attribution 4.0 International License.Pillared paddle-wheel-based metal-organic framework (MOF) materials are an attractive target as they offer a reliable method for constructing well-defined, multifunctional materials. A drawback of these materials, which has limited their application, is their tendency to form catenated frameworks with little accessible volume. To eliminate this disadvantage, it is necessary to investigate strategies for constructing non-catenated pillared paddle-wheel MOFs. Hydrogen-bonding substituents on linkers have been postulated to prevent catenation in certain frameworks and, in this work, we present a new MOF to further bolster this theory. Using 2,2′-diamino-[1,1′-biphenyl]-4,4′-dicarboxylic acid, BPDC-(NH2)2, linkers and dipyridyl glycol, DPG, pillars, we assembled a MOF with pcu topology. The new material is non-catenated, exhibiting large accessible pores and low density. To the best of our knowledge, this material constitutes the pcu framework with the largest pore volume and lowest density. We attribute the lack of catenation to the presence of H-bonding substituents on both linkers

System Justification and the Defense of Committed Relationship Ideology

A consequential ideology in Western society is the uncontested belief that a committed relationship is the most important adult relationship and almost all people want to marry or seriously couple (DePaulo & Morris, 2005). In the present article, I investigated the extent to which the system justification motive may contribute to the adoption of this ideology. In Studies 1 and 2, I examined whether a heightened motive to maintain the status quo would increase defense of committed relationship values. In Study 3, I examined the reverse association, that is, whether a threat to committed relationship ideology would also affect socio-political system endorsement. As past research has found that the justification of political systems depends upon how much these systems are perceived as having control over life outcomes, in Study 4 I tested whether the defense of the system of committed relationships would also increase when framed as controlling. Results from Studies 1–4 were consistent with my hypotheses, but only for men. In Study 5, using cross-cultural data, I sought to replicate these findings correlationally and probe for a cause of the gender effect. Results from over 33 000 respondents indicated a relationship (for men) between defense of the socio-political system and defense of marriage in countries where the traditional advantages of men over women were most threatened. In Studies 6 and 7, I investigated when the gender difference found in the earlier studies disappears. Results revealed that when I measured (Study 6) or manipulated (Study 7) personal relationship identity (i.e., how much relationships are part of the active self-concept), rather than relationship ideology, effects also emerge for women

Imbuing Aqueous Solubility to Amphotericin B and Nystatin with a Vitamin

Aqueous solubilities of many drugs in current clinical use are very low, necessitating formulations that often present problems for parenteral administration, including toxicities due to the excipients used. Recognizing that pharmacologically active compounds frequently possess amines, we asked whether pyridoxal phosphate (PLP), an inoccuous, water-soluble vitamin, could be utilized to form prodrug-like complexes via the formation of imine or iminium adducts, and whether the vitamin would impart solubilizing properties to such complexes. Direct spectroscopic and crystallographic data obtained using model primary and secondary amines showed that PLP forms stable imine adducts with primary amines under entirely aqueous conditions and at physiologic pH, while no reaction was observed for secondary amines; the basis of the exceptional stability appears to be a consequence of favorable H-bond interactions of the imine nitrogen with the 5-OH group of PLP. Amphotericin B and nystatin in their native forms display marked aqueous insolubility, and possess lone primary amines. We were able to utilize PLP in achieving excellent solubilization of both these antifungal agents, surpassing aqueous solubilities of 100 mg/mL. In in vitro bioassays, both polyenes in their PLP-adducted form display attenuated antifungal potencies which is attributable to ‘prodrug-like’ complexes. These results point to the utility of excipient-free, entirely aqueous formulations of amphotericin B for parenteral use, and may also be extended to other primary amine-bearing compounds exhibiting poor aqueous solubility

Reaction Landscape of a Pentadentate N5-Ligated MnII Complex with O2•− and H2O2 Includes Conversion of a Peroxomanganese(III) Adduct to a Bis(μ-oxo)dimanganese(III,IV) Species

Herein we describe the chemical reactivity of the mononuclear [MnII(N4py)(OTf)](OTf) (1) complex with hydrogen peroxide and superoxide. Treatment of 1 with one equivalent superoxide at −40 °C in MeCN formed the peroxomanganese(III) adduct, [MnIII(O2)(N4py)]+ (2) in ~30% yield. Complex 2 decayed over time and the formation of the bis(μ-oxo)dimanganese(III,IV) complex, [MnIIIMnIV(μ-O)2(N4py)2]3+ (3) was observed. When 2 was formed in higher yields (~60%) using excess superoxide, the [MnIII(O2)(N4py)]+ species thermally decayed to MnII species and 3 was formed in no greater than 10% yield. Treatment of [MnIII(O2)(N4py)]+ with 1 resulted in the formation of 3 in ~90% yield, relative to the concentration of [MnIII(O2)(N4py)]+. This reaction mimics the observed chemistry of Mn-ribonucleotide reductase, as it features the conversion of two MnII species to an oxo-bridged MnIIIMnIV compound using O2− as oxidant. Complex 3 was independently prepared through treatment of 1 with H2O2 and base at −40 °C. The geometric and electronic structures of 3 were probed using electronic absorption, electron paramagnetic resonance (EPR), magnetic circular dichroism (MCD), variable-temperature, variable-field MCD (VTVH-MCD), and X-ray absorption (XAS) spectroscopies. Complex 3 was structurally characterized by X-ray diffraction (XRD), which revealed the N4py ligand bound in an unusual tetradentate fashion