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diff --git a/README.md b/README.md
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+++ b/README.md
@@ -1,72 +1,72 @@
-# Ripser

-

-Copyright © 2015–2016 [Ulrich Bauer].

-
-

-### Description

-

-Ripser is a lean C++ code for the computation of Vietoris–Rips persistence barcodes. It can do just this one thing, but does it extremely well.

-

-The main features of Ripser:

-

-  - time- and memory-efficient

-  - support for coefficients in prime finite fields

-  - less than 1000 lines of code in a single C++ file

-  - no external dependencies (optional support for Google's [sparsehash])

-

-Currently, Ripser outperforms other codes ([Dionysus], [DIPHA], [GUDHI], [Perseus], [PHAT]) by a factor of at least 40 in computation time and a factor of at least 15 in memory efficiency. (Note that [PHAT] does not contain code for generating Vietoris–Rips filtrations).

-

-Input formats currently supported by Ripser:

-

-  - comma-separated lower triangular distance matrix (preferred)

-  - comma-separated lower triangular distance matrix (MATLAB output from the function `pdist`)

-  - [DIPHA] distance matrix data

-

-Ripser's efficiency is based on a few important concepts and principles:

-  

-  - Compute persistent *co*homology

-  - Don't compute information that is never needed

-    (for the experts: employ the *clearing* optimization, aka *persistence with a twist*)

-  - Don't store information that can be readily recomputed

-  - Take obvious shortcuts (*apparent persistence pairs*)

-

-

-### Version

-[Latest release][latest-release]: 1.0 (July 2016)

-
-

-### Building

-

-Ripser requires a C++11 compiler. Here is how to obtain, build, and run Ripser:

-

-```sh

-git clone https://github.com/Ripser/ripser.git

-cd ripser

-make

-./ripser examples/sphere_3_192.lower_distance_matrix

-```

-
-

-### Options

-

-Ripser supports several compile-time options. They are switched on by defining the C preprocessor macros listed below, either using `#define` in the code or by passing an argument to the compiler. The following options are supported:

-

-  - `ASSEMBLE_REDUCTION_MATRIX`: store the reduction matrix; may speed up computation but will also increase memory usage

-  - `USE_COEFFICIENTS`: enable support for coeffitients in a prime field

-  - `INDICATE_PROGRESS`: indicate the current progress in the console

-  - `PRINT_PERSISTENCE_PAIRS`: output the computed persistence pairs (enabled by default)

-  - `USE_GOOGLE_HASHMAP`: enable support for Google's [sparsehash] data structure; may further reducue memory footprint

-

-Furthermore, one of the following options needs to be chosen to specify the format for the input files:

-

-  - `FILE_FORMAT_LOWER_TRIANGULAR_CSV`: lower triangular distance matrix; a comma separated list of the distance matrix entries below the diagonal, sorted lexicographically by row index and column index

-  - `FILE_FORMAT_UPPER_TRIANGULAR_CSV`: upper triangular distance matrix; similar to the previous, but for the entries above the diagonal; suitable for output from the MATLAB function `pdist`, saved in a CSV file

-  - `FILE_FORMAT_DIPHA`: DIPHA distance matrix as described on the [DIPHA] website

-

-For example, to build with support for coefficients:

-

-```sh

-$ c++ -std=c++11 ripser.cpp -o ripser -Ofast -D NDEBUG -D FILE_FORMAT_LOWER_TRIANGULAR_CSV -D USE_COEFFICIENTS

+# Ripser
+
+Copyright © 2015–2016 [Ulrich Bauer].
+
+
+### Description
+
+Ripser is a lean C++ code for the computation of Vietoris–Rips persistence barcodes. It can do just this one thing, but does it extremely well.
+
+The main features of Ripser:
+
+  - time- and memory-efficient
+  - support for coefficients in prime finite fields
+  - less than 1000 lines of code in a single C++ file
+  - no external dependencies (optional support for Google's [sparsehash])
+
+Currently, Ripser outperforms other codes ([Dionysus], [DIPHA], [GUDHI], [Perseus], [PHAT]) by a factor of more than 40 in computation time and a factor of more than 15 in memory efficiency. (Note that [PHAT] does not contain code for generating Vietoris–Rips filtrations).
+
+Input formats currently supported by Ripser:
+
+  - comma-separated lower triangular distance matrix (preferred)
+  - comma-separated lower triangular distance matrix (MATLAB output from the function `pdist`)
+  - [DIPHA] distance matrix data
+
+Ripser's efficiency is based on a few important concepts and principles:
+  
+  - Compute persistent *co*homology
+  - Don't compute information that is never needed
+    (for the experts: employ the *clearing* optimization, aka *persistence with a twist*)
+  - Don't store information that can be readily recomputed
+  - Take obvious shortcuts (*apparent persistence pairs*)
+
+
+### Version
+[Latest release][latest-release]: 1.0 (July 2016)
+
+
+### Building
+
+Ripser requires a C++11 compiler. Here is how to obtain, build, and run Ripser:
+
+```sh
+git clone https://github.com/Ripser/ripser.git
+cd ripser
+make
+./ripser examples/sphere_3_192.lower_distance_matrix
+```
+
+
+### Options
+
+Ripser supports several compile-time options. They are switched on by defining the C preprocessor macros listed below, either using `#define` in the code or by passing an argument to the compiler. The following options are supported:
+
+  - `ASSEMBLE_REDUCTION_MATRIX`: store the reduction matrix; may speed up computation but will also increase memory usage
+  - `USE_COEFFICIENTS`: enable support for coefficients in a prime field
+  - `INDICATE_PROGRESS`: indicate the current progress in the console
+  - `PRINT_PERSISTENCE_PAIRS`: output the computed persistence pairs (enabled by default)
+  - `USE_GOOGLE_HASHMAP`: enable support for Google's [sparsehash] data structure; may further reducue memory footprint
+
+Furthermore, one of the following options needs to be chosen to specify the format for the input files:
+
+  - `FILE_FORMAT_LOWER_TRIANGULAR_CSV`: lower triangular distance matrix; a comma separated list of the distance matrix entries below the diagonal, sorted lexicographically by row index and column index
+  - `FILE_FORMAT_UPPER_TRIANGULAR_CSV`: upper triangular distance matrix; similar to the previous, but for the entries above the diagonal; suitable for output from the MATLAB function `pdist`, saved in a CSV file
+  - `FILE_FORMAT_DIPHA`: DIPHA distance matrix as described on the [DIPHA] website
+
+For example, to build with support for coefficients:
+
+```sh
+$ c++ -std=c++11 ripser.cpp -o ripser -Ofast -D NDEBUG -D FILE_FORMAT_LOWER_TRIANGULAR_CSV -D USE_COEFFICIENTS
 ```
 
 The following options are supported at the command line:
@@ -75,27 +75,27 @@ The following options are supported at the command line:
   - `--threshold t`: compute Rips complexes up to diameter *t*
   - `--modulus p`: compute homology with coefficients in the prime field Z/*p*Z (only available when build with the option `USE_COEFFICIENTS`)
 
-

-### Planned features

-

-The following features are currently planned for future versions:

-

- - support for point clouds

- - computation of representative cycles for persistent homology (currenly only *co*cycles are computed)

- - support for sparse distance matrices

-
-

-### License

-

-[LGPL] 3.0

-

-

-[Ulrich Bauer]: <http://ulrich-bauer.org>

-[latest-release]: <https://github.com/Ripser/ripser/releases/latest>

-[Dionysus]: <http://www.mrzv.org/software/dionysus/>

-[DIPHA]: <http://git.io/dipha>

-[PHAT]: <http://git.io/dipha>

-[Perseus]: <http://www.sas.upenn.edu/~vnanda/perseus/>

-[GUDHI]: <http://gudhi.gforge.inria.fr>

-[sparsehash]: <https://github.com/sparsehash/sparsehash>

+
+### Planned features
+
+The following features are currently planned for future versions:
+
+ - support for point clouds
+ - computation of representative cycles for persistent homology (currenly only *co*cycles are computed)
+ - support for sparse distance matrices
+
+
+### License
+
+[LGPL] 3.0
+
+
+[Ulrich Bauer]: <http://ulrich-bauer.org>
+[latest-release]: <https://github.com/Ripser/ripser/releases/latest>
+[Dionysus]: <http://www.mrzv.org/software/dionysus/>
+[DIPHA]: <http://git.io/dipha>
+[PHAT]: <http://git.io/dipha>
+[Perseus]: <http://www.sas.upenn.edu/~vnanda/perseus/>
+[GUDHI]: <http://gudhi.gforge.inria.fr>
+[sparsehash]: <https://github.com/sparsehash/sparsehash>
 [LGPL]: <https://www.gnu.org/licenses/lgpl>
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