Prof. Hsing-Kuo Kenneth Pao

Title Verification and Recognition based on User Trajectories

Many of our activities on computer need a verification step for authorized access. We use the Internet to do bank transactions, talk with friends in the cyber communities, search interesting information, play on-line games, and so on. The usual login-on process is to provide password or biometrics like fingerprint. We propose a general approach for user verification based on user trajectory inputs. The approach is labor-free for users and is likely to avoid the possible copy or simulation from other non-authorized users or even automatic programs like bots. Our study focuses on finding the hidden pattern on the trajectories produced by account users. We adopt a Markov model and a hidden Markov model with Gaussian mixtures in transitions to describe the behavior on the trajectories. To distinguish between two trajectories, we propose a novel dissimilarity measure combined with a manifold learnt tuning for catching the pairwise relationships. Based on the pairwise dissimilarities, we can plug-in any effective classification methods or clustering methods for the detection of unauthorized access. In this work, we focus on solving problems covering many categories of trajectories. That includes handwriting, mouse trace, game trace, and animal movement, etc.


Endah Rokhmati M.P., Ph.D

Title Pricing Financial Derivatives
  1. Subject
    • Introduction to financial derivatives (Options and Stock Loans)
    • Valuation of Options and Stock Loans
  2. Detailed Description
    • Vanilla options, barrier options, stock loans
    • Ito’s Lemma and Black-Scholes model
    • Regime-switching model under Black-Scholes framework
    • Laplace transform method , pseudo-steady-state approximation, and Fourier transform method for valuing options and stock loans
    • Finite difference method

Prof. Laszlo Szalay

Title Application of linear recurrences in number theoretical problems
Subject Introduction to the theory of linear recurrences, application of primitive divisor theorem in diophantine problems, sums in the classical and hyperbolic Pascal triangles
Detailed description
  1. Binary recursions, explicit formula, examples, generating function, associate sequence, identities, linear recurrences of order k, fundamental theorem of linear recurrences, primitive divisor theorem.
  2. Fibonacci numbers which are product of factorials. A variation of Brocard-Ramanujan problem associated with binary recurrences. 
  3. Diagonal sums in Pascal triangle. The concept of hyperbolic Pascal triangles. Number of elements, sum of elements, and power sum of elements of the rows in hyperbolic Pascal trianges with parameter {4,q}.