Abstract:
Background: We compared cutting and coagulation of a novel ferromagnetic
tool (FMwand) with modalities currently used in the clinical setting. Methods:
24 F344 rats with 9L gliosarcoma flank tumours were randomized into 2 groups (n
= 12): 1) Five parallel incisions were made into the tumor of each rat using
monopolar electrosurgery (MES) cut mode, MES coagulation (coag) mode, FMwand,
carbon dioxide (CO_{2}) laser and cold scalpel. 2) Two parallel
incisions were made comparing the MES and the FMwand, both with resecting loop
tips. The study was then repeated by a second surgeon. The surgeons applied a
grading scale (1 = worst, 5 = best) based on their observations. Results:
Average scores for FMwand were superior in ease of tissue dissection (3.58),
distortion upon tissues (3.67), and smoke production (2.87). CO_{2} laser led in effectiveness of hemostasis (4.32). MES cut mode had the highest
scores for ease of cleaning of tip (3.17) and speed of dissection (3.92). The
FMwand loop device led in all attributes except for ease of cleaning. Conclusions:
The FMwand outperformed CO_{2} laser significantly in ease and speed.
It was superior compared to MES cut mode for hemostasis and superior compared
to coag mode in ease and speed, distortion upon tissues and smoke production.
The FMwand loop was significantly better compared to MES loop for hemostasis,
distortion, ease and speed. The FMwand was shown to be safe and effective for
hemostatic soft tissue cutting and coagulation.

Abstract:
In this work, a new method is presented for determining the binding constraints
of a general linear maximization problem. The new method uses only
objective function values at points which are determined by simple vector
operations, so the computational cost is inferior to the corresponding cost of
matrix manipulation and/or inversion. This method uses a recently proposed
notion for addressing such problems: the average of each constraint. The
identification of binding constraints decreases the complexity and the dimension
of the problem resulting to a significant decrease of the computational
cost comparing to Simplex-like methods. The new method is highly useful
when dealing with very large linear programming (LP) problems, where only
a relatively small percentage of constraints are binding at the optimal solution,
as in many transportation, management and economic problems, since
it reduces the size of the problem. The method has been implemented and
tested in a large number of LP problems. In LP problems without superfluous
constraints, the algorithm was 100% successful in identifying binding constraints,
while in a set of large scale LP tested problems that included superfluous
constraints, the power of the algorithm considered as statistical tool of
binding constraints identification, was up to 90.4%.

Abstract:
Scattering of the electromagnetic waves by a randomly inhomogeneous electrically gyrotropic slab are studied using the perturbation method. Second order statistical moments of the ordinary and extraordinary waves scattered by the magnetized plasma slab are obtained using the boundary conditions for an arbitrary correlation function of electron density fluctuations. Normalized correlation functions at quasi-longitudinal propagation along the external magnetic field are calculated for the carrier frequency 0.1 MHz and 40 MHz. Isolines of the normalized variance of Faraday angle are constructed for the anisotropic Gaussian correlation function at various anisotropy factors of irregularities. Obtained results are in a good agreement with the experimental data.

Abstract:
Septoku is a Sudoku variant invented by Bruce Oberg, played on a hexagonal grid of 37 cells. We show that up to rotations, reflections, and symbol permutations, there are only six valid Septoku boards. In order to have a unique solution, we show that the minimum number of given values is six. We generalize the puzzle to other board shapes, and devise a puzzle on a star-shaped board with 73 cells with six givens which has a unique solution. We show how this puzzle relates to the unsolved Hadwiger-Nelson problem in combinatorial geometry.

Abstract:
We consider the one-person game of peg solitaire played on a computer. Two popular board shapes are the 33-hole cross-shaped board, and the 15-hole triangle board---we use them as examples throughout. The basic game begins from a full board with one peg missing and the goal is to finish at a board position with one peg. First, we discuss ways to solve the basic game on a computer. Then we consider the problem of quickly distinguishing board positions where the goal can still be reached ("winning" board positions) from those where it cannot. This enables a computer to alert the player if a jump under consideration leads to a dead end. On the 15-hole triangle board, it is possible to identify all winning board positions (from any single vacancy start) by storing a key set of 437 board positions. For the "central game" on the 33-hole cross-shaped board, we can identify all winning board positions by storing 839,536 board positions. By viewing a successful game as a traversal of a directed graph of winning board positions, we apply a simple algorithm to count the number of ways to traverse this graph, and calculate that the total number of solutions to the central game is 40,861,647,040,079,968. Our analysis can also determine how quickly we can reach a "dead board position", where a one peg finish is no longer possible.

Abstract:
We study the classical game of peg solitaire when diagonal jumps are allowed. We prove that on many boards, one can begin from a full board with one peg missing, and finish with one peg anywhere on the board. We then consider the problem of finding solutions that minimize the number of moves (where a move is one or more jumps by the same peg), and find the shortest solution to the "central game", which begins and ends at the center. In some cases we can prove analytically that our solutions are the shortest possible, in other cases we apply A* or bidirectional search heuristics.

Abstract:
This paper presents results on the extent to which mean curvature data can be used to determine a surface in space or its shape. The emphasis is on Bonnet's problem: classify and study the surface immersions in $\R^3$ whose shape is not uniquely determined by the first fundamental form and the mean curvature function. The properties of immersions with umbilics and global rigidity results for closed surfaces are presented in the first part of this paper. The second part of the paper outlines an existence theory for conformal immersions based on Dirac spinors along with its immediate applications to Bonnet's problem. The presented existence paradigm provides insight into the topology of the moduli space of Bonnet immersions of a closed surface, and reveals a parallel between Bonnet's problem and Pauli's exclusion principle.

Abstract:
Global isothermic immersions are defined and studied with the aid of a connection between quadratic differentials and immersions. The applications are two problems stemming from the fundamental question: how much data is needed to identify a surface immersion (Christoffel's problem) or its shape (Bonnet's problem). A short complete solution of Christoffel's problem, including closed surfaces, is given. It is shown that every immersion of an oriented closed surface (genus $\neq$ 1) is uniquely determined up to similitude by its conformal class and the tangent planes map. A classification of all generic Bonnet surfaces follows from a series of papers by Bonnet, Cartan, and Chern. The existence of a new class of Bonnet surfaces is shown here. The understanding of this class is necessary in order to study the rigidity of closed surfaces.

Abstract:
We consider the one-person game of peg solitaire on a triangular board of arbitrary size. The basic game begins from a full board with one peg missing and finishes with one peg at a specified board location. We develop necessary and sufficient conditions for this game to be solvable. For all solvable problems, we give an explicit solution algorithm. On the 15-hole board, we compare three simple solution strategies. We then consider the problem of finding solutions that minimize the number of moves (where a move is one or more consecutive jumps by the same peg), and find the shortest solution to the basic game on all triangular boards with up to 55 holes (10 holes on a side).

Abstract:
In 1979, David Fabian found a complete game of two-person Chinese Checkers in 30 moves (15 by each player) [Martin Gardner, Penrose Tiles to Trapdoor Ciphers, MAA, 1997]. This solution requires that the two players cooperate to generate a win as quickly as possible for one of them. We show, using computational search techniques, that no shorter game is possible. We also consider a solitaire version of Chinese Checkers where one player attempts to move her pieces across the board in as few moves as possible. In 1971, Octave Levenspiel found a solution in 27 moves [Ibid.]; we demonstrate that no shorter solution exists. To show optimality, we employ a variant of A* search, as well as bidirectional search.