Free mathematically software for linux

Hexagonal Minesweeper is a puzzle game, inspired by famous Minesweeper. HexaMine is puzzle game is based on idea of famous Minesweeper.

Classic Minesweeper quickly becomes boring for experienced player as he remembers most of restricted set of possible game situations, and nothing can challenge him to thing more then 3 seconds any more.

Proprietary MegaMiner by Astatix Software, has introduced mines with variable power to solve this problem, but it created a new one: there were too much situations when player had to guess rather then prove.

HexaMine has taken te idea of MegaMiner a lot further. Here are features, which allow HexaMine to present even most experienced player nontrivial challenging yet solvable game situations:

1) Different mine powers. Exactly as in MegaMiner.
2) Hexagonal grid. This reduces the number is possible situations for any single cell. This also makes surrounding of a cell look nore like a circle, which is more intuitive.
3) Concept of close and far neighborhood. There is nothing new about first one, as it is just sum of mine powers of ajacent cells. Far neighborhood is entirely new concept. Think of real metal detector. It can pick up any mine within small radius, say of 1 meter. This is exactly the close neighborhood. But mentioned metal detector can also pick up larger objects within bigger radius, say 2 meters, although the signal is weaker. This is exactly the concept of far neighborhood. For each empty cell the close neighborhood threat is calculated as mentioned above, although for far neighborhood threat each mine is reduced by 1 category. Smallest mines are not taken into account, larger ones seem smaller. Both threats are specified for open empty cell.
4) In contrast to other known to me Minesweeper-like games, in HexaMine you never know neither number of mines of each power, nor exact total number of mines.
The bottom line, (1) and (4) creates mathematically finite but practically countless number of different game situations, while (2) and (3) give player enough information, although very complicate, to solve vast majority of them without need to guess.

The bottom line, (1) and (4) creates mathematically finite but practically countless number of different game situations, while (2) and (3) give player enough information, although very complicate, to solve vast majority of them without need to guess.

mcl-algorithm is a scalable cluster algorithm for graphs based on stochastic flow.
The flow process employed by the algorithm is mathematically sound and intrinsically tied to cluster structure in graphs, which is revealed as the imprint left by the process.
The threaded implementation has handled graphs of up to one million nodes within hours, and is widely used in the field of protein family analysis. It comes with a wide range of sibling utilities for handling and analyzing graphs, matrices, and clusterings.
The MCL algorithm simulates flow using (alternating) two simple algebraic operations on matrices. Its formulation is simple and elegant. There are no high-level procedural instructions for assembling, joining, or splitting of groups - cluster structure is bootstrapped via a flow process that is inherently affected by any cluster structure present.
The first operation used by MCL is expansion, which coincides with normal matrix multiplication. Expansion models the spreading out of flow, it becoming more homogeneous. The second is inflation, which is mathematically speaking a Hadamard power followed by a diagonal scaling. Inflation models the contraction of flow, it becoming thicker in regions of higher current and thinner in regions of lower current. The MCL process causes flow to spread out within natural clusters and evaporate inbetween different clusters.
- By varying parameters, clusterings on different scales of granularity can be found. The number of clusters can not and need not be specified in advance, but the algorithm can be adapted to different contexts.
- The issue how many clusters? is not dealt with in an arbitrary manner, but rather by strong internal logic. Cluster structure leaves its marks on the flow process simulated by the algorithm, and the flow parameters control the granularity of the cluster imprint.
- The limit of the MCL process (the process simulated by the algorithm) is in general extremely sparse, and the iterands are sparse in a weighted sense. This gives the means to scale the algorithm drastically, leading to a worst-case complexity of order Nk^2, where N is the number of nodes of the input graph, and where k is a threshold for the number of resources allocated per node.
- The rate of convergence of the MCL process, and projection of the iterands afterwards onto the resulting clustering, give hooks for unsupervised parameter adjustment.
- The iterands of the MCL process have structural properties which allow a cluster interpretation, and which generalize the mapping of MCL limits onto clusterings. The mathematics associated with the MCL process shows that there is an intrinsic relationship between the MCL process and cluster structure in graphs. This is very valuable given the many heuristic approaches in cluster analysis.
Enhancements:
- Numerous cleanups in much of the code.
- Improvements in caching intermediate results.