# 2014 I&E Summer Scholars Projects - Science

### 1. COMPUTATIONAL INVESTIGATION OF SIGNALING MOLECULES' BIOLOGICAL EFFECTS AND DETECTION AGENTS

Quantum chemical studies will be employed to elucidate some un-solved problems of the interaction mechanisms of protein complexes with signaling molecules, as well as the molecular design aspects of their efficient molecular probes. These signaling molecules have significant biological effects that may be used in the treatments of many health problems, such as cardiovascular diseases, reduction of neuron damages, and cancers.

Advisor: Dr. Yong Zhang

[email protected]

Ext: 5513

### 2. MECHANISTIC INVESTIGATION OF HIGHLY TUNABLE METALLOPORPHYRIN CATALYSTS

Heme proteins are versatile biocatalysts for numerous biochemical reactions. Their biomimetic metalloporphyrin complexes have also been found to be efficient catalysts for a wide range of organic reactions. Due to abundant C-H bonds in organic molecules, selective C-H functionalization represents a powerful paradigm-shifting strategy in organic synthesis that can streamline and accelerate synthesis of complex organic molecules and libraries of similar compounds to promote development of new drugs with reduced costs. Given the highly tunable nature of metalloporphyrins, a systematic investigation using quantum chemical methods to characterize their reactivity nature and selectivity trends will facilitate development and optimization of highly selective metalloporphyrin catalysts with minimal toxicity and cost.

Advisor: Dr. Yong Zhang

[email protected]

Ext: 5513

### 3. NATURAL GAS CONVERSION OVER ZEOLITE-BASED CATALYSTS

140 billion m3 of natural gas, which is mostly composed of methane, are wastefully flared or vented worldwide annually because there are no efficient technologies for methane conversion. Direct methane conversion into liquid aromatic hydrocarbons over catalysts with metal nanostructures supported on shape selective zeolites is a promising new chemistry that can eliminate this problem of wasteful and environmentally harmful flaring and venting. The project involves synthesis of catalytic materials, reactor testing and data analysis.

Advisor: Prof Simon Podkolzin

[email protected]

Ext: 8074

### 4. CATALYST DEVELOPMENT WITH MOLECULAR MODELING

Molecular modeling for selective hydrogenation of hydrocarbons will be performed in order to identify new patentable catalyst formulations and reaction conditions in order to increase the reaction selectivity. The long-term objective of the program is to establish a synergistic integration between experimental work and molecular modeling, where the role of modeling is to (1) interpret and consolidate existing experimental results and (2) guide future experimental activities in order to minimize the development cycle. The project involves synthesis of catalytic materials, reactor testing and data analysis.

Advisor: Prof Simon Podkolzin

[email protected]

Ext: 8074

### 5. FROM BIOMASS TO FUELS WITH CATALYSTS

Promising new technologies for biomass conversion into fuels and chemical feedstocks rely on production of bio-oils, which need to be upgraded in order to remove oxygen-containing hydrocarbons and water. A high oxygen concentration makes bio-oils acidic and corrosive, unstable during storage, and less energetically valuable per unit weight than petroleum-derived hydrocarbons. New upgrading technologies are, therefore, urgently needed for development of sustainable energy resources. The objective of this project is to develop a molecular model for adsorption and reactivity of selected oxygen-containing hydrocarbons on catalytic bimetallic nano particles.

Advisor: Prof Simon Podkolzin

[email protected]

Ext: 8074

### 6. STEREO VISION FOR DRIVER ASSISTANCE AND AUTONOMOUS NAVIGATION

In parallel with Google driverless car project (http://en.wikipedia.org/wiki/Google_driverless_car) most automobile manufacturers are engaged in research for lower cost solution to assist the driver by sensing the environment and providing real time feedback. Examples include obstacle avoidance, blind spot monitoring, lane departure warnings etc. A key technology for achieving these goals is stereo vision. Using input from two or more cameras the car computer can estimate distances and velocities with much higher accuracy than by using a single camera. Several projects are available in this area, see for example http://www.cvlibs.net/datasets/kitti/, for students with knowledge of C/C++ and geometry.

Advisor: Philippos Mordohai

[email protected]

Ext: 5611

### 7. OPTIMIZATION PROBLEMS WITH CONSTRAINTS ON PROBABLITY OF EVENTS

Deterministic optimization models are usually formulated as problems of mini-mizing or maximizing a certain objective function f(x) over x in a feasible set X of n-dimensional vectors. The sets are usually described by a system of equations and inequalities.

When the objective function or some of the constraint functions contain random data, the formulation of the optimization problem becomes unclear, and new precise deﬁnitions of the ‘objective’ and of the ‘feasible set’ are needed.

One way of dealing with that is to optimize the objective function on average and to require the satisfaction of the constraints with a high probability. Assume that the random data is comprised in a random vector Z.

Our analysis will focus on the following nonlinear optimization problem with probabilistic constraints:

min E[ f(x,Z)]

subject to: P[ gj(x,Z) ≥ 0, j ∈ J] ≥ p,

x ∈ X

Here f : Rn × Rs → R and gj: Rn × Rs → R are continuous functions and X ⊆ Rn is a closed convex set. The vector Z is an s-dimensional random vector. The symbol P denotes probability, and we require that gj(x,Z) ≥ 0,∀ j ∈ J shall hold with some prescribed probability p ∈ (0,1).

This model is in harmony with the principle of statistical decisions, i.e., for a given point x, we do not reject the statistical hypothesis of the constraints g(x,Z) ≥ 0, j ∈ J, being satisﬁed. Imposing constraints on probability of events is particularly appropriate whenever high uncertainty is involved and reliability is a central issue.

We also note that the objective function E[ f(·,Z)] can represent just an expected value or a suitably chosen measure of risk.

Our investigation is motivated by many problems arising in engineering, military logistics, actuarial mathematics, and ﬁnance, where one needs to restrict the probability of certain undesirable events. In engineering, reliability problems are of this type. In mathematical ﬁnance, chance constraints are related to the concept of Value at Risk, which is widely used and has received a lot of attention

The goal of the project is to develop efﬁcient numerical methods for solving problem (1).

There is a lot of literature on this type of models. For an overview of the theory and numerical methods for optimization problems with probabilistic (chance) constraints, we refer to [1, 2, 3] and the references ibid.

The project will require some basic knowledge of optimization on the level of Ma 230. It will start with reading several research papers, and getting familiar with some advanced numerical methods of optimization. You will receive a copy of the necessary papers; the book [3] is available online. At the second stage implementing optimization methods using a CPLEX solver (free for academic purposes) will be necessary and numerical experiments with several methods and data of various dimensions will be conducted. The solver can be used within a C/C ++/C] - program or in a Matlab script. The choice depends on your skills and preferences. Upon completion, the project would result in a publication in a well-ranged journal.

References:

[1] A. Prekopa, ´ Stochastic Programming, Kluwer, Dordrecht, Boston, 1995.

[2] A. Ruszczynski and A. Shapiro (Eds.), ´ Stochastic Programming, Elsevier Science, Amsterdam 2003.

[3] A. Shapiro, D. Dentcheva, and A. Ruszczynski, ´ Lectures on Stochastic Programming: Modeling and Theory, MPS/SIAM Series on Optimization 9, SIAM, Philadelphia, 2009.

Advisor: Darinka Dentcheva

[email protected]

Ext: 8640

### For more information, please contact:

Ms. Sandra Furnbach

Program Manager