**Automatic segmentation using shape analysis for rectal cancer radiotherapy**

**Supervisors: Dr. Pieter Slagmolen, Dr. An Elen**

In radiotherapy, the goal is to deliver as much radiation to the target volume as possible while keeping the dose minimum for the surrounding healthy tissues. A correct delineation and identification of this clinical target volume is required to ensure tumor control and limit healthy tis- sue toxicity. In rectal cancer, the target is an anatomical structure called mesorectum and surrounding lymph node regions. An automated delineation of this clinical target volume could be very useful for treatment purposes.

An important class of segmentation methods make use of shape models. However, when large data sets have to be segmented, one shape model might not be enough to represent the entire data. In that case, clustering becomes very significant. The focus of this project is to find a clustering approach for the given data sets. After registration, shapes based on a similarity distance were clustered together. This similarity distance takes into account surface distances and outlier weights. For a data set of 87 shapes, three main clusters and one outlier shape was found. A mean shape for every cluster with associated multiple modes of variations was found using principal component analysis, which take into account the variability existing within a cluster.

**Automated Analysis of cellular signals from Calcium Imaging Data**

**Supervisor: Dr. Vincent Bonin**

In Calcium imaging, the manual analyses to find Region of Interest (ROI) and identifying individual cells require undue labor, particularly when datasets are large. Also, these analyses are prone to cross-talk. This project is based on the automated sorting procedure described by Mukamel et al, for assigning recorded signals to individual cells in Calcium imaging data. The method combines independent component analysis and image segmentation for extracting cells’ locations and their dynamics with minimal human supervision. Both spatial and temporal sparseness of individual cells are used to identify them in Calcium imaging data. The sparseness is quantified by the skewness of amplitude distribution. Data is parsed into a combination of statistically independent signals, each with high sparseness and cell’s location and activities is estimated. The algorithm is extended to do the analysis for astrocytes.

**Biophysics of Membranes_ Voltage and Temperature dependence of a channel**

Supervisor: Dr. Karel Talavera

Supervisor: Dr. Karel Talavera

This project involved studying physiological significance of the dependence of the shift in voltage for half-maximal activation of an ion channel and the gating valence. Part of the project was to calculate opening probability of channels and appreciate how simple laws of thermodynamics lead us to have significant information about structure and conformation of an ion channel.

## Experimental and Simulated Study of Diffusion Limited Aggregation of Magnetic Microspheres

Supervisor: Dr. Fakhar-ul-Inam

Diffusion limited Aggregation (DLA) and its variant forms, such as diffusion limited cluster aggregation (DLCA), is a widely used model to study the growth processes where the growth is mainly guided by the diffusion of constituting species. The model, originally proposed by Witten and Sander in 1981, has been used to study a wide variety of systems, from electrodeposited growth to formation of snow flakes and lightening paths. As our senior year project, we studied aggregation polystyrene micro particles suspended in a liquid medium. We focused on the effects of changing salt concentration and temperature on the fractal dimensions of the resulting aggregates. The study was complemented by simulating the aggregation process using DLA and DLCA models. The full report of the project can be provided on request. The synopsis is uploaded below.

project_synopsis_1.pdf | |

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## Strange Particle Production in p-p collisions at ALICE at CERN

Supervisors: Dr. Adam Jacholkowski and Dr. Jean-Pierre Revol

I did this project during my internship in CERN in summers 2011. I studied production of strange particles in proton-proton collisions at center of mass energy, √s = 7 TeV at ALICE detector at CERN. It involved construction of neutral short Kaon (mesons) and Lambda (baryons) from their decay topologies. Some basic kinematic properties like invariant mass distribution and decay length of neutral kaon was plotted and its life time was calculated. Its multiplicity dependence was also determined. Both real and simulated data sets were used to do analysis and results were compared. The project involved use of different tools like ROOT and AliROOT for data analysis. A detailed Report on analysis work can be seen.

finalreport.pdf | |

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## Consequences of a Nuclear Reactor accident at Karachi Nuclear Power Plant

Supervisor: Dr. Abdul Hameed Nayyar

I did this project currently as my Independent study with Dr. Nayyar. It involves study of basic principles of nuclear reactors as well as a detailed study of working of Karachi nuclear power plant, then creating an accident scenario and discuss its impacts on the atmosphere and living beings around. The project involves detailed study of some dispersal models and simulations of these models as well as the hazards to nearby population center. A similar study of Chashma nuclear power plant can be read here.

## Zeeman Effect

Supervisor: Dr. Sabieh Anwar

This project was a part of my Experimental Physics 3 course. I observed Zeeman effect defined as splitting of transition lines in the presence of magnetic field. A mercury lamp was used and exciting transition lines were obtained by putting high voltage across the ends. A teflon stand was designed to hold the mercury lamp between the poles of electromagnet and CCD camera was used to view the results. Light from mercury lamp was focussed onto a Fabry Perot interferometer by best possible alignment and resolved light spectrum was viewed on the computer screen. Increasing magnetic field showed the splitting of light. The final report on the experiment is here.

zeeman_effect_rabia.pdf | |

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## Mathematical modelling of Water-borne diseases

Supervisor: Dr. Adnan Khan

In Winter 2010, I started studying mathematical modelling of water-borne diseases with Dr. Adnan Khan. I continued it as my Independent study for Spring 2010. I studied SIR, SIER, SIWR and ordinary differential equation model for each of the model determining fundamental quantities like basic reproductive number, epidemic growth rate, stability analysis and final outbreak size for all of them. The ODEs were solved and results were plotted using Matlab varying different parameters. The paper mainly followed was by Tien and Earn and a chapter from Earn.

## Thermodynamics of Strings and Hagedorn Temperature

Supervisor: Dr. Babar Qureshi

This was the end of semester project for my Statistical Mechanics course. I calculated the partition function of the strings and Hagedorn temperature, the temperature above which partition sum diverges in a system with exponential growth in the density of the states and used results from string theory and ideas of statistical mechanics and thermodynamics to derive entropy of black hole. The project report can be followed.

stat_project.pdf | |

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## Super-symmetric Quantum Mechanics

Supervisor: Dr. Amer Iqbal

In summers of 2010, as part Mathematics department undergraduate summer research program, we studied a simple one-dimensional super-symmetric quantum mechanical system: the harmonic oscillator. It was studied using both operator method and path integral formalism and consistent results were found. We concluded that Schrodinger's equation and path integral formalism for this system gives same results and the ground state of a super-symmetric harmonic oscillator is zero. We gave a poster presentation which stood second among all others. The poster can be seen here.

## Modelling Symbiosis in Biological and Social Systems

Supervisor: Dr. Adnan Khan

Another project we did in undergraduate summers research program was studying mathematical modelling symbiosis in biological and social systems. Based on the paper by Yukalov, Yukalova and Sornette, we introduced general mathematical model of symbiosis between different entities by taking into account the carrying capacities of the others. Our modelling included symbiosis with direct mutual interactions, with asymmetric interactions and without any interactions. We provided a complete classification of all admissible dynamical regimes like convergence to stationary states, unbounded exponential growth, finite-time singularity and finite-time death. The results were produced by Matlab. The poster can be seen here.

## Chaos and R-L Diode

Supervisor: Dr. Sabieh Anwar

As part of my Experimental Physics 2 course, I observed the chaotic behavior using an R-L diode circuit. Chaos defined as a specific kind of deterministic behavior that is very sensitive to initial conditions.I analyzed chaos by phase plots, time series plots, frequency spectrum and poincare maps plotted in Matlab. Chaotic behavior has been observed in the laboratory in a variety of systems including electrical circuits, lasers, oscillating chemical reactions, fluid dynamics, and mechanical and magneto-mechanical devices, as well as computer models of chaotic processes. Chaos theory has been applied in just about every field from aerospace engineering to zoology. The report on this project is here.

chaos_in_rl-diode_circuit.pdf | |

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## Synthesis and Ferroelectric Properties of Potassium Nitrate Film

Supervisor: Dr. Sabieh Anwar

This was again included in Experimental Physics 2. I observed Ferroelectric behavior of Potassium Nitrate film using a Sawyer Tower Circuit as can be seen in report. The hysteresis effect shown by of ferroelectric materials can be used as a memory function, and ferroelectric capacitors are indeed used to make ferroelectric RAM for computers. In these applications, thin films of ferroelectric materials are typically used, as this allows the field required to switch the polarization to be achieved with a moderate voltage.

hysteresis_loop.pdf | |

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## Michelson Interferometry

Supervisor: Dr. Sabieh Anwar

This was also part of Experimental Physics 2. I used Michelson Interferometer to observe the interference pattern, calculated wavelength of laser beam used and measured the refractive index of a glass slide putting it in the configuration of Michelson Interferometer. The report can be seen here.

michelson_interferometer.pdf | |

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## Raman Spectroscopy

Dr. Basit Yameen

This was the final project of the course Spectroscopy I took with Dr. Basit Yameen. As a project I studied Raman Spectroscopy and presented it. The power point presentation can be seen here.