The Complexity of Escaping Labyrinths and Enchanted Forests

The board games The aMAZEing Labyrinth (or simply Labyrinth for short) and Enchanted Forest published by Ravensburger are seemingly simple family games. In Labyrinth, the players move though a labyrinth in order to collect specific items. To do so, they shift the tiles making up the labyrinth in order to open up new paths (and, at the same time, close paths for their opponents). We show that, even without any opponents, determining a shortest path (i.e., a path using the minimum possible number of turns) to the next desired item in the labyrinth is strongly NP-hard. Moreover, we show that, when competing with another player, deciding whether there exists a strategy that guarantees to reach one\u27s next item faster than one\u27s opponent is PSPACE-hard. In Enchanted Forest, items are hidden under specific trees and the objective of the players is to report their locations to the king in his castle. Movements are performed by rolling two dice, resulting in two numbers of fields one has to move, where each of the two movements must be executed consecutively in one direction (but the player can choose the order in which the two movements are performed). Here, we provide an efficient polynomial-time algorithm for computing a shortest path between two fields on the board for a given sequence of die rolls, which also has implications for the complexity of problems the players face in the game when future die rolls are unknown

Self-assembling behavior in decane solution of potential wax crystal nucleators based on poly(co-olefins)

The control of the precipitation and gelation of long chain paraffins from oil remains an enduring technological challenge regarding the processing and recovery of refined fuels and waxy crudes. Wax crystal modifiers based on polyethylene -poly(ethylene-propylene) (PE-PEP) diblock copolymers function as efficient nucleators for wax crystals in middle distillate fuels. These diblock polymers self-assemble in oil to form expansive platelike aggregates consisting of a PE core cloaked behind the amorphous PEP brush layer. The PE core thus promotes nucleation of solubilized long chain alkanes. Additional candidate structures for wax crystal nucleators include linear and star copolyolefins where the composition variation signals the alteration between crystalline and amorphous segments. This study focuses upon the self-assembling behavior in solution of these materials. The characteristics of the single chains and the aggregates formed at lower temperatures were determined via small-angle neutron scattering. Both plates and needlelike structures were found. The placement of the amorphous and crystalline blocks in the arms of the star shaped polymers was found to influence the architecture of the self-assembled micelles. As a point of comparison a commercial copolymer of ethylene-vinyl acetate (EVA) was also investigated. The EVA material was found to be relatively "undisciplined" in comparison to the structurally more uniform anionically prepared counterparts

Interaction of paraffin wax gels with random crystalline/amorphous hydrocarbon copolymers

The control mechanisms involved in the modification of wax crystal dimensions in crude oils and refined fuels are of joint scientific and practical interest. An understanding of these mechanisms allows strategies to be developed that lead to decreases in crude oil pour points or (for refined fuels) cold filter plugging points. The attainment of these goals involves the control and modification of wax crystals that spontaneously form in mixed hydrocarbon systems upon decreasing temperature. This work reports on the influence of random crystalline-amorphous block copolymers (ethylene-butene) upon the rheology of model oils. In a parallel fashion small-angle neutron scattering was exploited to gain microscopic insight as to how added poly(ethylene-butene) copolymers modify the wax crystal structures. The copolymers with different contents of polyethylene are highly selective with respect to wax crystal modification. Thus, the copolymer with the highest crystalline tendency is more efficient for the larger wax molecules while the less crystalline one is more efficient for the lower waxes

Interaction of paraffin wax gels with ethylene/vinyl acetate copolymers

The commercial grades of ethylene/vinyl acetate (EVA) co-polymers have found application as pour point" depressants in refined fuels. This study focuses on their behavior as additives to crude oils, where the intent is to reduce the yield stress of the gels that can form when the oil exits the reservoir. The model crude oils consisted of 4 wt % wax in decane. At EVA dosage levels of similar to200 ppm, the reduction in yield stress is 3 orders of magnitude for the C-36 wax, whereas the reduction is 1 order of magnitude for C-32 and only 3-fold for the C-28 wax. This decrease in efficiency with decreasing wax carbon number indicates that the EVA materials would not provide an adequate reduction in yield stress to ensure against gelation in pipeline transport. Neutron scattering studies, as a function of temperature, of the self-assembly of the EVA co-polymers show dramatically different aggregated structures in decane. The EVA with the lowest ethylene content shows scattering that increases with a power-law exponent of similar to1.6. This scattering behavior is typical for weakly aggregating polymer gels. In contrast, the EVA with the higher ethylene content shows a transition from surface scattering (found for strongly segregated objects) to a plateau whose height is dependent on temperature. Micrographs of the wax crystal morphology indicate that the ethylene-poor EVA alters the wax crystal habit at higher concentrations more effectively than does its higher-ethylene-content counterpart, whereas the latter EVA grade seems to form more wax crystals at low concentrations

Diazoxide-responsive hyperinsulinemic hypoglycemia caused by HNF4A gene mutations

Objective: The phenotype associated with heterozygous HNF4A gene mutations has recently been extended to include diazoxide responsive neonatal hypoglycemia in addition to maturity-onset diabetes of the young (MODY). To date, mutation screening has been limited to patients with a family history consistent with MODY. In this study, we investigated the prevalence of HNF4A mutations in a large cohort of patients with diazoxide responsive hyperinsulinemic hypoglycemia (HH). Subjects and methods: We sequenced the ABCC8, KCNJ11, GCK, GLUD1, and/or HNF4A genes in 220 patients with HH responsive to diazoxide. The order of genetic testing was dependent upon the clinical phenotype. Results: A genetic diagnosis was possible for 59/220 (27%) patients. KATP channel mutations were most common (15%) followed by GLUD1 mutations causing hyperinsulinism with hyperammonemia (5.9%), and HNF4A mutations (5%). Seven of the 11 probands with a heterozygous HNF4A mutation did not have a parent affected with diabetes, and four de novo mutations were confirmed. These patients were diagnosed with HI within the first week of life (median age 1 day), and they had increased birth weight (median +2.4 SDS). The duration of diazoxide treatment ranged from 3 months to ongoing at 8 years. Conclusions: In this large series, HNF4A mutations are the third most common cause of diazoxide responsive HH. We recommend that HNF4A sequencing is considered in all patients with diazoxide responsive HH diagnosed in the first week of life irrespective of a family history of diabetes, once KATP channel mutations have been excluded

Improving polymeric microemulsions with block copolymer polydispersity

Recent experiments have demonstrated that block copolymers are capable of stabilizing immiscible homopolymer blends producing bicontinuous microemulsion. The stability of these polymeric alloys requires the copolymer to form flexible, nonattractive monolayers along the homopolymer interfaces. We predict that copolymer polydispersity can substantially and simultaneously improve the monolayers in both of these respects. Furthermore, polydispersity should provide similar improvements in systems, such as colloidal suspensions and polymer/clay composites, that utilize polymer brushes to suppress attractive interactions

Bulk and Boundary Critical Behavior at Lifshitz Points

Lifshitz points are multicritical points at which a disordered phase, a homogeneous ordered phase, and a modulated ordered phase meet. Their bulk universality classes are described by natural generalizations of the standard $\phi^4$ model. Analyzing these models systematically via modern field-theoretic renormalization group methods has been a long-standing challenge ever since their introduction in the middle of the 1970s. We survey the recent progress made in this direction, discussing results obtained via dimensionality expansions, how they compare with Monte Carlo results, and open problems. These advances opened the way towards systematic studies of boundary critical behavior at $m$-axial Lifshitz points. The possible boundary critical behavior depends on whether the surface plane is perpendicular to one of the $m$ modulation axes or parallel to all of them. We show that the semi-infinite field theories representing the corresponding surface universality classes in these two cases of perpendicular and parallel surface orientation differ crucially in their Hamiltonian's boundary terms and the implied boundary conditions, and explain recent results along with our current understanding of this matter.Comment: Invited contribution to STATPHYS 22, to be published in the Proceedings of the 22nd International Conference on Statistical Physics (STATPHYS 22) of the International Union of Pure and Applied Physics (IUPAP), 4--9 July 2004, Bangalore, Indi