1) The document discusses data hiding in mazes using steganography techniques. It describes perfect mazes, imperfect mazes, and how mazes can be represented as graphs.
2) Existing maze-based data hiding methods are described, including representing the solution path as binary 1s and carving walls between embeddable cells and neighboring cells as 0s to hide bits.
3) The proposed method aims to increase data hiding capacity by embedding bits into multiple solution paths in the maze rather than just one path.
This document appears to be a letter from Louay Abdallah to Mr. Jamil Farah. It was written by Louay Abdallah and addressed to Mr. Jamil Farah, but no other details are provided in the document about the purpose or contents of the letter. The summary only includes information explicitly stated in the document.
Presentation by Mahamane Adamou, Agronomist at PPILDA, at the 2012 Agriculture and Rural Development Day (ARDD) in Rio de Janiero, Learning Event No. 9, Session 1: Closing loops and opening minds, nutrients recycling in Aguié, Niger. http://www.agricultureday.org
Este documento resume una reunión sobre la especialización docente en educación y TIC. Explica la interacción entre los coordinadores de sede, el instituto y el equipo central. También detalla los fondos disponibles para gastos operativos y bienes de capital, así como las reglas para los encuentros presenciales de los cursantes.
O documento apresenta os resultados operacionais e financeiros da TPI no 1T12. Destaca-se o crescimento de 21,7% na receita líquida e de 22,2% no EBITDA ajustado. O lucro líquido atingiu R$15 milhões e o lucro base de dividendos foi de R$31,9 milhões. Detalha também investimentos realizados e endividamento da companhia.
1) José contribuiu com R$ 20.000,00 para a empresa, enquanto Marcus contribuiu com R$ 60.000,00 e Roberto com R$ 40.000,00.
2) A probabilidade de ambas as cartas sorteadas no jogo de bisca serem biscas é de 195/7.
3) A área da figura plana formada pelo corte perpendicular do cilindro eqüilátero é de 36 cm2.
El documento presenta un módulo sobre seguridad informática que tiene como objetivos reconocer la importancia de la seguridad, analizar riesgos y vulnerabilidades, diagnosticar riesgos en proyectos tecnológicos, conocer políticas de seguridad y planificar dichas políticas basadas en diagnósticos. Explica conceptos como confidencialidad, integridad y disponibilidad de la información, y medidas para proteger activos informáticos y garantizar estas propiedades.
El documento describe el modelo OSI (Open Systems Interconnection), un marco de referencia de 7 capas para la definición de arquitecturas de red. Cada capa define un segmento del proceso de transmisión de datos a través de una red, desde la capa física hasta la capa de aplicación. El modelo estandariza las interfaces entre capas para facilitar la interoperabilidad.
The Six Highest Performing B2B Blog Post FormatsBarry Feldman
If your B2B blogging goals include earning social media shares and backlinks to boost your search rankings, this infographic lists the size best approaches.
This document appears to be a letter from Louay Abdallah to Mr. Jamil Farah. It was written by Louay Abdallah and addressed to Mr. Jamil Farah, but no other details are provided in the document about the purpose or contents of the letter. The summary only includes information explicitly stated in the document.
Presentation by Mahamane Adamou, Agronomist at PPILDA, at the 2012 Agriculture and Rural Development Day (ARDD) in Rio de Janiero, Learning Event No. 9, Session 1: Closing loops and opening minds, nutrients recycling in Aguié, Niger. http://www.agricultureday.org
Este documento resume una reunión sobre la especialización docente en educación y TIC. Explica la interacción entre los coordinadores de sede, el instituto y el equipo central. También detalla los fondos disponibles para gastos operativos y bienes de capital, así como las reglas para los encuentros presenciales de los cursantes.
O documento apresenta os resultados operacionais e financeiros da TPI no 1T12. Destaca-se o crescimento de 21,7% na receita líquida e de 22,2% no EBITDA ajustado. O lucro líquido atingiu R$15 milhões e o lucro base de dividendos foi de R$31,9 milhões. Detalha também investimentos realizados e endividamento da companhia.
1) José contribuiu com R$ 20.000,00 para a empresa, enquanto Marcus contribuiu com R$ 60.000,00 e Roberto com R$ 40.000,00.
2) A probabilidade de ambas as cartas sorteadas no jogo de bisca serem biscas é de 195/7.
3) A área da figura plana formada pelo corte perpendicular do cilindro eqüilátero é de 36 cm2.
El documento presenta un módulo sobre seguridad informática que tiene como objetivos reconocer la importancia de la seguridad, analizar riesgos y vulnerabilidades, diagnosticar riesgos en proyectos tecnológicos, conocer políticas de seguridad y planificar dichas políticas basadas en diagnósticos. Explica conceptos como confidencialidad, integridad y disponibilidad de la información, y medidas para proteger activos informáticos y garantizar estas propiedades.
El documento describe el modelo OSI (Open Systems Interconnection), un marco de referencia de 7 capas para la definición de arquitecturas de red. Cada capa define un segmento del proceso de transmisión de datos a través de una red, desde la capa física hasta la capa de aplicación. El modelo estandariza las interfaces entre capas para facilitar la interoperabilidad.
The Six Highest Performing B2B Blog Post FormatsBarry Feldman
If your B2B blogging goals include earning social media shares and backlinks to boost your search rankings, this infographic lists the size best approaches.
The document provides information about electrical engineering vocabulary and grammar related to tenses and passive voice. It includes definitions of electricity and electrical conductors. Questions are provided to test understanding of topics like systems analysis, computer architecture, and electrical insulation materials. Examples cover use of cardinal/ordinal numbers, fractions, decimals, percentages. Guidance is given for writing CVs, job applications, and formal letters.
The document compares exact and approximate structural analysis methods. It provides an overview of various approximate methods described in literature, including simplified storywise summation and assuming inflection point locations. The document then analyzes a 4-story building using both an exact method (STAAD.Pro) and an approximate method. Results are compared to evaluate the approximate method's accuracy, with most errors being less than 5%. The approximate method provides reasonably accurate results with less computation than exact methods.
This document summarizes the design, fabrication, and testing of a microfluidic chip prototype for manipulating particles using dielectrophoresis (DEP). Finite element modeling was used to simulate the electric field distributions around quadrupole and comb electrode geometries. A prototype was fabricated containing these electrode designs in two separate microchannels. Silica microspheres were successfully manipulated within the chip using positive and negative DEP sequences, concentrating particles in the electrode areas. Testing demonstrated the potential of this technique for manipulating and separating microparticles in integrated microfluidic devices.
1997 nucleation of homoepitaxial si chains on si(001) at room temperaturepmloscholte
1) Si dimers initially adsorb at preferred sites on the Si(001) surface, with most occupying C-positions.
2) Interactions between dimers and diffusing adatoms lead to the formation of three-atom clusters like twins and crosses. These can extend into diluted lines of C dimers along [110] and [310] directions.
3) Upon further deposition, the diluted dimer lines transform into epitaxial dimer rows through a process starting at the line ends of reorienting dimers and adding mobile adatoms.
The document discusses various types of imperfections or defects that exist in crystalline materials, including point defects (vacancies, self-interstitials, and substitutional atoms), linear defects, and interfacial defects. Point defects are localized disruptions involving missing or extra atoms. Vacancies occur when an atom is missing from its normal site, while self-interstitials are atoms occupying interstitial sites between normal positions. Substitutional defects involve one atom replacing another. These defects influence material properties and can be introduced intentionally to improve properties like strength.
This document summarizes previous work on comparing the network costs of different interconnection network topologies. It discusses mesh, hexagonal mesh, honeycomb mesh, torus, hexagonal torus, and honeycomb torus networks. Previous studies have calculated the degree, diameter, number of nodes, and network cost (defined as the product of degree and diameter) for each network as the number of nodes or network dimension increases. This paper aims to compare the network costs of the Spidergon and Honeycomb Torus networks based on these parameters.
This document proposes the concept of molecular space frames, which are very light and strong structures composed of struts and nodes repeated in a fractal, self-similar pattern down to the molecular scale. The structures are based on space frame architecture, where nodes are connected by struts arranged in tripodal or tetrapodal configurations. Molecular struts and nodes can be designed by carving out structures from unit cells of crystalline materials like diamond, with the nodes formed from solid blocks of the crystal. These molecular space frames could enable the creation of lightweight aerogels and other highly porous materials with precise atomic control.
This document contains questions and answers related to Chapter 1 - The Solid State from the Class XII Chemistry textbook. It defines amorphous solids and provides examples. It explains the difference between glass and quartz and how quartz can be converted to glass. It also classifies various solids as ionic, metallic, molecular, network or amorphous. It discusses coordination number, unit cells, crystal lattices and void spaces. Finally, it explains the similarities and differences between metallic and ionic crystals and why ionic solids are hard and brittle.
This document describes a research paper that uses a cellular automata model to simulate the spread of rumors. Some key points:
- Cells represent individuals, with white cells meaning individuals who have not heard a rumor and black cells meaning those who have.
- The model has two simple rules: 1) If a white cell has any black neighbor cells, it has a probability of becoming black itself, and 2) Once a cell is black, it remains black.
- This simulates how rumors can spread locally from person to person. Running the model over time steps shows how the rumor can potentially spread through an entire population starting from a single individual.
- Cellular automata models are useful for investigating macro
This document discusses the use of DNA nanotechnology to create new materials. It describes how DNA's base pairing allows it to be used as a programmable component to assemble nanostructures and materials. DNA has been used to construct periodic 2D arrays and 3D shapes like cubes. Future goals include extending these structures to 3D with heterogeneity, incorporating other nanocomponents, and developing self-replicating DNA machines. Achieving these goals will require combining DNA with other materials in compatible systems.
This document provides an overview of topological quantum computing using anyons. It first discusses motivations for alternative computing approaches due to limitations of traditional computing. It then introduces braid theory, including definitions of braids and their equivalence. Braids form a braid group that can represent any braid as a word. Anyons are quasiparticles that emerge in 2D systems and can represent quantum bits in a way that is robust to environmental perturbations. Braids representing the trajectories of anyons over time can encode quantum information and computations in a topological manner.
Paper Explained: Understanding the wiring evolution in differentiable neural ...Devansh16
Read my Explanation of the Paper here: https://medium.com/@devanshverma425/why-and-how-is-neural-architecture-search-is-biased-778763d03f38?sk=e16a3e54d6c26090a6b28f7420d3f6f7
Abstract: Controversy exists on whether differentiable neural architecture search methods discover wiring topology effectively. To understand how wiring topology evolves, we study the underlying mechanism of several existing differentiable NAS frameworks. Our investigation is motivated by three observed searching patterns of differentiable NAS: 1) they search by growing instead of pruning; 2) wider networks are more preferred than deeper ones; 3) no edges are selected in bi-level optimization. To anatomize these phenomena, we propose a unified view on searching algorithms of existing frameworks, transferring the global optimization to local cost minimization. Based on this reformulation, we conduct empirical and theoretical analyses, revealing implicit inductive biases in the cost's assignment mechanism and evolution dynamics that cause the observed phenomena. These biases indicate strong discrimination towards certain topologies. To this end, we pose questions that future differentiable methods for neural wiring discovery need to confront, hoping to evoke a discussion and rethinking on how much bias has been enforced implicitly in existing NAS methods.
Revisiting Projection Methods over Automatic Oct-tree MeshesAbhishek Jain
Above Research Paper can be downloaded from www.zeusnumerix.com
This research aims to use projection methods over automatic oct-tree meshes. This algorithm uses a quick and automatic method to create solver and geometry adaptive oct-tree mesh on a basic Cartesian grid. The non-body fitted type of mesh is independent of geometry topology. The method takes multiple water tight triangulated surface(s) as an input. The software then automatically creates oct-tree based Cartesian grids both outside as well as inside the geometry. The intersection of the cells with the triangles of the geometry is done using a very robust and efficient polygon clipping algorithm allowing the capture of geometry with 100% accuracy. Simulation results show promise while solving simple cases. The mesher can be potentially used for shape optimization and aerodynamic sensitivity simulations. Author - Bharat Agrawal and Saurabh Pandey (Zeus Numerix)
Segmenting Epithelial Cells in High-Throughput RNAi Screens (Miaab 2011)Kevin Keraudren
This document summarizes a proposed method for segmenting epithelial cells in high-throughput RNAi screens using image analysis. The method uses a pipeline that includes pre-processing images using filters to reduce noise and enhance cell structures, segmenting nuclei, generating an edge map of cell-cell contacts, and performing an adaptive watershed segmentation to extract three structures: cell-cell contacts, nuclei, and cell walls. The method is shown to accurately segment these structures and provide reliable quantification of markers in different experimental conditions, distinguishing effects of depleting different actin-binding proteins on cell-cell adhesion receptors and the cytoskeleton.
1) This document discusses semantic networks, which are a knowledge representation technique used in artificial intelligence. Semantic networks represent knowledge through nodes and links, where nodes represent concepts or objects, and links represent relationships between the nodes.
2) As an example, a simple semantic network is presented representing facts about a cat named Jerry - that Jerry is a cat, a mammal, owned by Jay, white in color, and likes cheese.
3) The document outlines different types of semantic networks including definitional, assertional, implicational, and learning networks. It also discusses advantages such as being a natural representation of knowledge, and disadvantages including lack of quantifiers and lack of intelligence.
This document summarizes an article from the International Journal of Electronics and Communication Engineering & Technology. The article discusses algebraic relationships between Boolean functions and their properties in Karnaugh maps. It presents a theorem that any set of simply connected regions in a Karnaugh map can be expressed as the product of the delta derivatives of a Boolean function with respect to each variable. It proves this theorem for a 3-variable Boolean function and notes it can be extended to functions with any number of variables. The paper explores applications of this relationship to better understand Boolean function behavior and decomposition.
This document summarizes an article from the International Journal of Electronics and Communication Engineering & Technology. The article discusses algebraic relationships between Boolean functions and their properties in Karnaugh maps. It presents a theorem that any set of simply connected regions in a Karnaugh map can be expressed as the product of the delta derivatives of a Boolean function with respect to each variable. It proves this theorem for a 3-variable Boolean function and notes it can be extended to functions with any number of variables. The paper explores applications of this relationship to understanding Boolean function behavior and developing new decompositions.
This document summarizes an article from the International Journal of Electronics and Communication Engineering & Technology. The article discusses algebraic relationships between Boolean functions and their properties in Karnaugh maps. It presents a theorem that any set of simply connected regions in a Karnaugh map can be expressed as the product of the delta derivatives of a Boolean function with respect to each variable. It proves this theorem for a 3-variable Boolean function and notes it can be extended to functions with any number of variables. The paper explores applications of this relationship to understanding Boolean function behavior and developing new decompositions.
This document summarizes an article from the International Journal of Electronics and Communication Engineering & Technology. The article discusses algebraic relationships between Boolean functions and their properties in Karnaugh maps. It presents a theorem that any set of simply connected regions in a Karnaugh map can be expressed as the product of the delta derivatives of a Boolean function with respect to each variable. It proves this theorem for a 3-variable Boolean function and notes it can be extended to functions with any number of variables. The paper explores applications of this relationship to better understand Boolean function behavior and decomposition.
The document provides information about electrical engineering vocabulary and grammar related to tenses and passive voice. It includes definitions of electricity and electrical conductors. Questions are provided to test understanding of topics like systems analysis, computer architecture, and electrical insulation materials. Examples cover use of cardinal/ordinal numbers, fractions, decimals, percentages. Guidance is given for writing CVs, job applications, and formal letters.
The document compares exact and approximate structural analysis methods. It provides an overview of various approximate methods described in literature, including simplified storywise summation and assuming inflection point locations. The document then analyzes a 4-story building using both an exact method (STAAD.Pro) and an approximate method. Results are compared to evaluate the approximate method's accuracy, with most errors being less than 5%. The approximate method provides reasonably accurate results with less computation than exact methods.
This document summarizes the design, fabrication, and testing of a microfluidic chip prototype for manipulating particles using dielectrophoresis (DEP). Finite element modeling was used to simulate the electric field distributions around quadrupole and comb electrode geometries. A prototype was fabricated containing these electrode designs in two separate microchannels. Silica microspheres were successfully manipulated within the chip using positive and negative DEP sequences, concentrating particles in the electrode areas. Testing demonstrated the potential of this technique for manipulating and separating microparticles in integrated microfluidic devices.
1997 nucleation of homoepitaxial si chains on si(001) at room temperaturepmloscholte
1) Si dimers initially adsorb at preferred sites on the Si(001) surface, with most occupying C-positions.
2) Interactions between dimers and diffusing adatoms lead to the formation of three-atom clusters like twins and crosses. These can extend into diluted lines of C dimers along [110] and [310] directions.
3) Upon further deposition, the diluted dimer lines transform into epitaxial dimer rows through a process starting at the line ends of reorienting dimers and adding mobile adatoms.
The document discusses various types of imperfections or defects that exist in crystalline materials, including point defects (vacancies, self-interstitials, and substitutional atoms), linear defects, and interfacial defects. Point defects are localized disruptions involving missing or extra atoms. Vacancies occur when an atom is missing from its normal site, while self-interstitials are atoms occupying interstitial sites between normal positions. Substitutional defects involve one atom replacing another. These defects influence material properties and can be introduced intentionally to improve properties like strength.
This document summarizes previous work on comparing the network costs of different interconnection network topologies. It discusses mesh, hexagonal mesh, honeycomb mesh, torus, hexagonal torus, and honeycomb torus networks. Previous studies have calculated the degree, diameter, number of nodes, and network cost (defined as the product of degree and diameter) for each network as the number of nodes or network dimension increases. This paper aims to compare the network costs of the Spidergon and Honeycomb Torus networks based on these parameters.
This document proposes the concept of molecular space frames, which are very light and strong structures composed of struts and nodes repeated in a fractal, self-similar pattern down to the molecular scale. The structures are based on space frame architecture, where nodes are connected by struts arranged in tripodal or tetrapodal configurations. Molecular struts and nodes can be designed by carving out structures from unit cells of crystalline materials like diamond, with the nodes formed from solid blocks of the crystal. These molecular space frames could enable the creation of lightweight aerogels and other highly porous materials with precise atomic control.
This document contains questions and answers related to Chapter 1 - The Solid State from the Class XII Chemistry textbook. It defines amorphous solids and provides examples. It explains the difference between glass and quartz and how quartz can be converted to glass. It also classifies various solids as ionic, metallic, molecular, network or amorphous. It discusses coordination number, unit cells, crystal lattices and void spaces. Finally, it explains the similarities and differences between metallic and ionic crystals and why ionic solids are hard and brittle.
This document describes a research paper that uses a cellular automata model to simulate the spread of rumors. Some key points:
- Cells represent individuals, with white cells meaning individuals who have not heard a rumor and black cells meaning those who have.
- The model has two simple rules: 1) If a white cell has any black neighbor cells, it has a probability of becoming black itself, and 2) Once a cell is black, it remains black.
- This simulates how rumors can spread locally from person to person. Running the model over time steps shows how the rumor can potentially spread through an entire population starting from a single individual.
- Cellular automata models are useful for investigating macro
This document discusses the use of DNA nanotechnology to create new materials. It describes how DNA's base pairing allows it to be used as a programmable component to assemble nanostructures and materials. DNA has been used to construct periodic 2D arrays and 3D shapes like cubes. Future goals include extending these structures to 3D with heterogeneity, incorporating other nanocomponents, and developing self-replicating DNA machines. Achieving these goals will require combining DNA with other materials in compatible systems.
This document provides an overview of topological quantum computing using anyons. It first discusses motivations for alternative computing approaches due to limitations of traditional computing. It then introduces braid theory, including definitions of braids and their equivalence. Braids form a braid group that can represent any braid as a word. Anyons are quasiparticles that emerge in 2D systems and can represent quantum bits in a way that is robust to environmental perturbations. Braids representing the trajectories of anyons over time can encode quantum information and computations in a topological manner.
Paper Explained: Understanding the wiring evolution in differentiable neural ...Devansh16
Read my Explanation of the Paper here: https://medium.com/@devanshverma425/why-and-how-is-neural-architecture-search-is-biased-778763d03f38?sk=e16a3e54d6c26090a6b28f7420d3f6f7
Abstract: Controversy exists on whether differentiable neural architecture search methods discover wiring topology effectively. To understand how wiring topology evolves, we study the underlying mechanism of several existing differentiable NAS frameworks. Our investigation is motivated by three observed searching patterns of differentiable NAS: 1) they search by growing instead of pruning; 2) wider networks are more preferred than deeper ones; 3) no edges are selected in bi-level optimization. To anatomize these phenomena, we propose a unified view on searching algorithms of existing frameworks, transferring the global optimization to local cost minimization. Based on this reformulation, we conduct empirical and theoretical analyses, revealing implicit inductive biases in the cost's assignment mechanism and evolution dynamics that cause the observed phenomena. These biases indicate strong discrimination towards certain topologies. To this end, we pose questions that future differentiable methods for neural wiring discovery need to confront, hoping to evoke a discussion and rethinking on how much bias has been enforced implicitly in existing NAS methods.
Revisiting Projection Methods over Automatic Oct-tree MeshesAbhishek Jain
Above Research Paper can be downloaded from www.zeusnumerix.com
This research aims to use projection methods over automatic oct-tree meshes. This algorithm uses a quick and automatic method to create solver and geometry adaptive oct-tree mesh on a basic Cartesian grid. The non-body fitted type of mesh is independent of geometry topology. The method takes multiple water tight triangulated surface(s) as an input. The software then automatically creates oct-tree based Cartesian grids both outside as well as inside the geometry. The intersection of the cells with the triangles of the geometry is done using a very robust and efficient polygon clipping algorithm allowing the capture of geometry with 100% accuracy. Simulation results show promise while solving simple cases. The mesher can be potentially used for shape optimization and aerodynamic sensitivity simulations. Author - Bharat Agrawal and Saurabh Pandey (Zeus Numerix)
Segmenting Epithelial Cells in High-Throughput RNAi Screens (Miaab 2011)Kevin Keraudren
This document summarizes a proposed method for segmenting epithelial cells in high-throughput RNAi screens using image analysis. The method uses a pipeline that includes pre-processing images using filters to reduce noise and enhance cell structures, segmenting nuclei, generating an edge map of cell-cell contacts, and performing an adaptive watershed segmentation to extract three structures: cell-cell contacts, nuclei, and cell walls. The method is shown to accurately segment these structures and provide reliable quantification of markers in different experimental conditions, distinguishing effects of depleting different actin-binding proteins on cell-cell adhesion receptors and the cytoskeleton.
1) This document discusses semantic networks, which are a knowledge representation technique used in artificial intelligence. Semantic networks represent knowledge through nodes and links, where nodes represent concepts or objects, and links represent relationships between the nodes.
2) As an example, a simple semantic network is presented representing facts about a cat named Jerry - that Jerry is a cat, a mammal, owned by Jay, white in color, and likes cheese.
3) The document outlines different types of semantic networks including definitional, assertional, implicational, and learning networks. It also discusses advantages such as being a natural representation of knowledge, and disadvantages including lack of quantifiers and lack of intelligence.
This document summarizes an article from the International Journal of Electronics and Communication Engineering & Technology. The article discusses algebraic relationships between Boolean functions and their properties in Karnaugh maps. It presents a theorem that any set of simply connected regions in a Karnaugh map can be expressed as the product of the delta derivatives of a Boolean function with respect to each variable. It proves this theorem for a 3-variable Boolean function and notes it can be extended to functions with any number of variables. The paper explores applications of this relationship to better understand Boolean function behavior and decomposition.
This document summarizes an article from the International Journal of Electronics and Communication Engineering & Technology. The article discusses algebraic relationships between Boolean functions and their properties in Karnaugh maps. It presents a theorem that any set of simply connected regions in a Karnaugh map can be expressed as the product of the delta derivatives of a Boolean function with respect to each variable. It proves this theorem for a 3-variable Boolean function and notes it can be extended to functions with any number of variables. The paper explores applications of this relationship to understanding Boolean function behavior and developing new decompositions.
This document summarizes an article from the International Journal of Electronics and Communication Engineering & Technology. The article discusses algebraic relationships between Boolean functions and their properties in Karnaugh maps. It presents a theorem that any set of simply connected regions in a Karnaugh map can be expressed as the product of the delta derivatives of a Boolean function with respect to each variable. It proves this theorem for a 3-variable Boolean function and notes it can be extended to functions with any number of variables. The paper explores applications of this relationship to understanding Boolean function behavior and developing new decompositions.
This document summarizes an article from the International Journal of Electronics and Communication Engineering & Technology. The article discusses algebraic relationships between Boolean functions and their properties in Karnaugh maps. It presents a theorem that any set of simply connected regions in a Karnaugh map can be expressed as the product of the delta derivatives of a Boolean function with respect to each variable. It proves this theorem for a 3-variable Boolean function and notes it can be extended to functions with any number of variables. The paper explores applications of this relationship to better understand Boolean function behavior and decomposition.
1. T.Sukumar, Dr.K.R.Santha / International Journal of Engineering Research and Applications
(IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 4, July-August 2012, pp.499-504
Maze Based Data Hiding Using Back Tracker Algorithm
T.Sukumar1, Dr.K.R.Santha2
Department of IT, SVCE, Anna University, India
Department of EEE, SVCE, Anna University, India
I INTRODUCTION
Steganography is an art and science of writing most puzzles appearing in websites are rectangle and
hidden messages in such a way that no one, apart from perfect. For security consideration, the created maze
the sender and intended recipient, suspects the should look like a common one hence; here we only
existence of the message, a form of security through deal with rectangular perfect mazes. Regarding cells as
obscurity. A word steganography is of Greek origin nodes, carved invisible walls as links.
and means "concealed writing" from the Greek
word stegano means "covered or protected",
and graphic means "writing". classically, the hidden
message may be an invisible link between the visible
lines of a private letter [1] and [2].
Steganography includes the concealment of
information within computer files. In digital
steganography, electronic communications may
include steganographic coding inside of a transport
layer, such as a document file, image file, program or
protocol. Media files are ideal for steganographic
transmission because of their large size. As a simple
Fig.2.2. A 16×12 perfect maze
example, a sender might start with an innocent image
file and adjust the color of every 100th pixel to
correspond to a letter in the alphabet, a change so
subtle that someone not specifically looking for it is
unlikely to notice it [2].
A maze (See Fig 2.1) basically contains cells,
walls, a starting cell and an end cell. Logically, a maze
is a puzzle with complex multipath network, and a
player is to find a solution path from the Starting cell to
the end cell. A rectangular maze has m cells in width
and n cells in height and is denoted as m x n maze, it is
called perfect if there exists one and only one path
between any two cells [1].
Fig.2.3. A 16×12 imperfect maze
II PREVIOUS WORKS
A. Maze Generation C. Expressing Maze As A Graph
We can express a maze as a graph. Fig.2.4 shows an
example, a number attached to a link connecting two
nodes S and E.
Fig.2.1. An example to illustrate a maze structure
B. Perfect Maze And An Imperfect Maze
Figs. 2.2 and 2.3 show a perfect maze and an
imperfect maze, respectively. From our observation, Fig.2.4 Correspondence between an imperfect maze
and a graph
499 | P a g e
2. T.Sukumar, Dr.K.R.Santha / International Journal of Engineering Research and Applications
(IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 4, July-August 2012, pp.499-504
Based on this representation, we can find that a perfect
maze corresponds to a tree (see Fig. 2.5), such relation
can be used to prove whether a generated maze is
perfect.
Fig 2.7 the capacities of different sizes of mazes.
Fig.2.5. Correspondence between a perfect maze and a
tree. The main idea of the existing method is to
consider multipath rather than only the solution path to
D. Existing Approaches gain more embedding capacity. Before Describing the
In this section, we will first introduce a typical proposed method, we will define “embeddable cell”
maze generator, then a steganographic method based which will be used to embed a bit. Suppose the HKMG
on this generator is described. algorithm is used to generate a perfect maze, and the
Hunt-and-Kill maze generating (HKMG) algorithm solution path from the starting cell to the end cell is
There are a number of maze generating located. All cells on the path are marked as I cells, the
algorithms, Hunt-and-Kill maze generating algorithm other cells are reset to be O cells, and all walls are
is typical. The HKMG algorithm generates a maze by rebuilt, except those in the path (see Fig.2.8).
carving walls. Fig. 2.6 shows a maze generated by the Definition 1. An embeddable cell, A, is an I cell,
HKMG algorithm. which is in the solution path with exact two O cells in
its 4-neighbors, and each O cell should not be a
neighbor of another embeddable cell which appears
before A. Fig. 2.8 shows an example. In Fig. 2.8(b), the
cells with black triangles are embeddable ones and the
gray cell is an O cell and is the overlapped neighbor of
two I cells, thus the cell with a black solid circle is not
an embeddable cell. Based on the definition, all
embeddable cells can be located. According to the
embedding bit, we carve the wall between an
embeddable cell and one O cell around it, and mark the
O cell as I cell. There are six kinds of embeddable cells
shown in Fig. 2.9.
Fig 2.6 An maze generated by HKMG algorithm.
HKMG algorithm, there are three types of cells defined
as follows:
• „In‟ cell (I): a cell that has been processed and always
keeps its type.
• „Frontier‟ cell (F): a cell that is processed and is a 4-
neighbor of a certain “I” cell.
• „Out‟ cell (O): a cell not yet processed.
The HKMG algorithm described as follows
1. Mark all cells as O cells.
2. Mark the starting cell as I cell, and mark each O cell
in the 4-neighborhood of Fig. 2.8. One example to illustrate embeddable cells.
the I cell as F cell. (a) The white path stands for the solution path. (b)
3. Choose an F cell around an I cell, and carve the wall Embeddable cells marked by black triangles.
between the F cell and the I cell. Mark the F cell as I
cell, and mark each O cell in the 4-neighborhood of the
I cell as F cell. Repeat step 3 until there is no F cell.
4. End
500 | P a g e
3. T.Sukumar, Dr.K.R.Santha / International Journal of Engineering Research and Applications
(IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 4, July-August 2012, pp.499-504
Fig. 2.9 Six kinds of embeddable cells.
Each embeddable cell has two neighboring O
cells marked as 1 and 0. If a “1” bit is embedded, then
the wall between the embeddable cell and the cell
marked “1” is carved, and the “1” cell is marked as I
cell. Otherwise the wall between the embeddable cell Fig.2.10 An example of using existing method to
and the cell marked as “0” is carved, and the “0” cell is embed data in a perfect maze
marked as I cell. To increase embedding capacity, we
can embed bits into multipath instead of only one path. Table 3.1 Comparison of Algorithms
In the existing method, we first generate a perfect maze
with HKMG algorithm. Subsequently, we choose some
cells as the start cells and one cell as the common end
one of the multipaths. Finally, we solve the perfect
maze to obtain the corresponding multipath. This
multipath sometimes will merge at some cells. The two
solution paths start at different cells respectively they
should have the common end cell E. The second path
from maze is merged into the first path from S to E at
cell A as shown in the figure Fig 2.10(d). Note that the
number of solution paths and all the start cells and one
end cell are chosen through a random number
generator and a seed, which will be considered as the
secret key [5]&[6].
(a) A perfect maze generated by HKMG algorithm. III IMPLEMENTATION
(b) Two paths from S to E and T to E in (a) located with The main idea of the proposed method is to
merged points A. consider SOLUTION PATH rather than only MULTI
(c) The result after performing Step 3 of the proposed PATH to gain more embedding capacity. Before define the
embedding algorithm to (b). proposed work., we first discuss some available list of
(d) All embeddable cells located. maze generation algorithms, that meet out requirement to
(e) The result after embedding data in embeddable cells gain more embedding capacity.
with D cells marked.
(f) The result of applying HKMG algorithm to process F From the above table, Recursive Backtracker is
cells. the algorithm gives higher river factor comparatively from
(g) The immediate result of applying Step 8 of the Hunt and Kill algorithm. Recursive backtracker gives
proposed embedding algorithm to (f). larger solution path than the HKMG, and also the dead end
(h) The perfect maze generated after processing all Ds. gets decreased by one percent , by this for the same size of
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4. T.Sukumar, Dr.K.R.Santha / International Journal of Engineering Research and Applications (IJERA)
ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 4, July-August 2012, pp.499-504
maze that with same start cell and same end cell by do not set the cell on boundary to be embeddable
Recursive backtracker gives higher embeddable cell than cell even if the cell is embeddable.
by HKMG.
E. Embedding Algorithm
The details of the proposed embedding algorithm are
described as follows:
1. Creating a maze using the Recursive Backtracker
algorithm.
Fig 3.3 After finding the embeddable cells
5. For each embeddable cell, if the embedding bit is 1
(0), the wall between the embeddable cell and its
neighboring O cell marked 1 (0) is carved and the
cell marked 1 (0) is set as I cell, the other
Fig 3.1Generated perfect maze by recursive neighboring O cell marked 0 (1) is set as D cell (see
backtracker D stands for the D cell).Then write the binary
2. Choose one cell as start cells and one cell as the end representation of the processed cell to a file
cell. Solve solution path from these starting cells to 6. Set those O cells around I cells to be F cells.
the end cell 7. Process these F cells using recursive backtracker
3. Reset all cells to be O cells and all walls as visible. algorithm, O stands for the O cell.
Set those cells On solution path to be I cells. Carve
each wall between two I cells
Fig 3.4 After embedding with d cell remains unprocessed
Fig 3.2 After finding the solution path 8. Process the D cells.(a) Scan the maze, and check if
any D cell exists. If none, go to step 9. Otherwise,
4. Find all embeddable cells in solution path and order choose a D cell with one of its neighbors being an
them according to the path sequence. Note that we un-embeddable I cell and carve the wall between the
D cell and the un-embeddable I cell. Mark the D cell
as I cell, and mark each O cell in the 4-
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5. T.Sukumar, Dr.K.R.Santha / International Journal of Engineering Research and Applications (IJERA)
ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 4, July-August 2012, pp.499-504
neighborhood of the I cell as F cell (b) Check if any
F cell exists. If yes, go to step 7. If none, go to step
8.
`
Fig 3.7 Stegomaze Architecture
Fig 3.5 After processing of all cells with Marking
G. Maze Generation
Basically a maze is a collection of cells., so first
generate the cells upto mentioned maze size. then address
each cell to identify them. generating different mazes at
every time is our objective here., so we use a random
number generator and seed to achieve this. the random
number generator generates the unique pattern of results
for unique seed., by using the pattern the corresponding
unique maze gets generated. hence the same maze will be
generated for same seed any number of times.
H. Locate Embeddable Cells
After the maze gets generated, we first find the
solution path where the secret data to be embed. For that
we have to feed the starting cell and the end cell. From the
start cell, find the next cell from its four neighbors and
there is no wall between the current cell and next cell.
Process till it reaches the end cell. Push the solution cells in
a separate stack.
Fig 3.6 After processing of all cells without Marking Rebuild the walls of all cells except the cells from
9. End the solution path. Mark the cells in the solution path as
embeddable cells if the cell contains two neighbors and the
F. Extraction Algorithm neighbors should not be a neighbor of any other cell. Push
To extract the embedded bits, the receiver must the embeddable cells in a separate stack.
know the start and end cells of solution path which can be
extracted through the secret key and a pseudo random I. Embedding Data
number generator. Since the generated maze is perfect, the The embeddable cells are used to embed the secret
receiver can get the original solution path accurately data. Using the random number generator, mark one of the
according to these start and end cells. Then, the receiver neighbor for zero bit and the another for one bit. the secret
can locate all embeddable cells. Then use the Binary data should be converted into binary form. the binary data
Representation of the maze to redraw the maze as in the is to be embed into the maze. if the zero bit is to be embed,
sender side finally according to the direction of the branch carve the walls between the embeddable cell and its zero
in each embeddable cell, secret data can be extracted bit , else carve the walls between the embeddable cell and
successfully. its one bit. after embedding , the binary representation of
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6. T.Sukumar, Dr.K.R.Santha / International Journal of Engineering Research and Applications (IJERA)
ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 4, July-August 2012, pp.499-504
the embeddable cells is stored in the file. After that process (ICMLC), 2011 IEEE Transactions on , vol.1, no.,
all the remaining cells so that it looks like a maze. pp.61-67, 10-13 July 2011
[3] Hopper, N.; von Ahn, L.; Langford, J.; , "Provably
J. Encrypting File Secure Steganography," Computers, IEEE
The stored binary representation of the maze is then Transactions on , vol.58, no.5, pp.662-676, May
encrypted using DES encryption standard. Read the 8 bit 2009
key from the user and by using that encrypt the file. Finally [4] Artz, D."Digital steganography: hiding data within
the encrypted file and the key alone is shared with the data," Internet Computing, IEEE , vol.5, no.3,
ultimate receiver. pp.75-80, May 2007
[5] Andrew D. Ker "Steganalysis of Embedding in Two
K. Decrypting File And Extract T Original Data Least-Significant Bits," Information Forensics and
By using the same secret key and the encrypted Security, IEEE Transactions on , vol.2, no.1, pp.46-
file as input decrypt using same DES and get the binary 54, March 2007
representation of the maze. By using the seed from the [6] Anderson, R.J.; Petitcolas, F.A.P.; , "On the limits of
decrypted file, the original maze gets generated. Then steganography," Selected Areas in Communications,
using the binary representation of the maze, the original IEEE Journal on , vol.16, no.4, pp.474-481, May
maze after embedding will be regenerated. Then use the 2006
start cell and end cell to find the solution path. Then find [7] http://www.msdn.com
the embeddable cells, and depends on the branching on [8] http://www.social.msdn.com
every embeddable cells, the binary bits gets extracted. [9] http://www.dotnetpearls.com
Then the extracted binary data is converted to ASCII value [10] http://www.stackoverflow.com
to get the character equivalent of the binary. Thus the
original data can be extracted successfully.
IV CONCLUSION
We proposed an enhancement in existing method to
embed secret data into mazes. It generates perfect mazes
that cannot be distinguished visually by humans from other
perfect mazes commonly used. Hence, it significantly
improves security over the existing HKMG embedding
algorithm by providing encryption to sharing Data. When
embedding bits into one solution path our new method
provides approximately twice the embedding capacity of
the one-path HKMG algorithm.
FUTURE ENHANCEMENT
With larger mazes our algorithm can utilize
multiple paths for embedding to further increase capacity,
while maintaining its “undetectability” from human vision.
Data compression can be used to increase the embedding
capacity. In this project we are working with maze, in
future other puzzle games can be used for hiding the Data.
ACKNOWLEDGMENT
The authors would like to thank the anonymous
reviewers for their valued comments which helped to
improve the manuscript.
REFERENCES
[1] Hui-Lung Lee, Chia-Feng Lee, Ling-Hwei Chen,”A
perfect maze based steganographic method” The
Journal of Systems and Software, August 2010
[2] Zhan-He Ou; Ling-Hwei Chen; , "Hiding data in
Tetris," Machine Learning and Cybernetics
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