Joint work with Anna Scaglione.
Each time the PSP exceeds a threshold, the neuron produces an efferent spike that propagates along its axon to some 10,000 recipient neurons. Immediately after each spike emission, the neuron's PSP is reset to zero. There follows a brief refractory period during which the neuron is virtually incapable of producing another spike even if its PSP builds up above the threshold.
We assume that the PSP decays exponentially after each afferent contribution until the next contribution arrives. This, in conjunction with the times of occurrence of said contributions constituting a Poisson process, makes the process of efferent spike times a renewal process. That is, in this model successive efferent pulses are separated by interspike intervals (ISI's), or gaps, whose random durations, G_1, G_2, ... are i.i.d.r.v. We seek the probability distribution common to these gap durations, call it F_G(g) = P[G < g], where Grepresents a generic G_i.
The key step toward finding an analytical expression for F_G(g) is to derive and then solve a partial differential equation (PDE) for q_{R|X}(r|x), the probability density function of the residual time R to first passage through the threshold conditional on the PSP's current value X. With the R|X subscript repressed, this PDE reads
where \alpha is the PSP decay constant, \lambda is the afferent Poisson arrival rate, and \bar A is the mean algebraic value of a contribution to the PSP.
We show how to solve this PDE with the refractory period explicitly taken into account, and we describe how F_G(g) follows therefrom. The mean and standard deviation of G are evaluated both computationally and via simulation as functions of the model parameters \alpha, \lambda and \bar A. The neuroscientific significance of the findings is then discussed.
Topic 1: A Semidefinite Programming Approach for Network Coding. The first topic can be related to the vector quantization problem. We have a real point that we want to transmit, under rate constraint, over a communication network. We assume that due to length limitation of the input packets, our encoding will be split into smaller packets. Furthermore, we assume that the network will lose packets, and that hard delay constraints disable retransmission. We address the question of designing codes for this problem.
Topic 2: Algebraic Codes for the Rayleigh Fading Channel. The second topic is inspired by work of Boutros et al. They consider communication over the Rayleigh fading channel. Instead of using error-correcting codes, they introduced modulation schemes with intrinsic diversity, based on lattice constellations. Using algebraic methods, we build several families of these lattice constellations. Furthermore, we give explicit formulas to evaluate their performance over the Rayleigh fading Channel.
The first topic is joint work with Sergio Servetto. The second is joint work with Emanuele Viterbo (Politecnico di Torino)
Collaboration with: Sueli I. R. Costa and N. J. A. Sloane.
Bio: Vinay A. Vaishampayan received the B.Tech degree from the Indian Institute of Technology, Delhi, India, in 1981, the M.S. and Ph.D. degrees from the University of Maryland, College Park, Maryland, in 1986 and 1989, respectively. He works on research problems in the areas of communications, signal processing, statistics and information theory and has a strong interest in geometric aspects of such problems. He works at AT\&T Labs-Research, Shannon Laboratory, Florham Park, NJ, where he heads the Communication Sciences Research Department. Previous experience includes academia, teaching Electrical Engineering at Texas A\&M University, and the oil industry, for Schlumberger Technical Services.
Note: this will be a re-run of my talk presented two weeks ago at CISS.
This is a dry run for a talk that will be presented at ISIT 2003. Joint work with Sergio Servetto.
This is a dry run for a talk that will be presented at MobiHoc 2003. Joint work with Sergio Servetto.
Borrowing an information-theoretic and machine-learning framework, we define the attenuation of an estimator as the ratio between the probability assigned to each symbol in a sequence by any distribution, and the corresponding probability assigned by the estimator. We show that the Good Turing estimator performs well in the sense that its attenuation is at most 2, however it is suboptimal in the sense that for some sequences its attenuation is at least 1.39. We then derive an estimator whose attenuation approaches 1, namely, as the length of any sequence increases, the ratio between the probability assigned to each symbol by any distribution, and that assigned by the estimator is at most one.
To better understand the behavior of the estimator, we study the probability it assigns to several simple sequences. We show that for some sequences this probability agrees with our intuition, while for others it is quite unintuitive.
Joint work with N. Prasad Santhanam and Junan Zhang.
Biography: Alon Orlitsky received B.Sc. degrees in Mathematics and Electrical Engineering from Ben Gurion University in 1980 and 1981, and M.Sc. and Ph.D. degrees in electrical engineering from Stanford University in 1982 and 1986.
From 1986 to 1996, Dr. Orlitsky was with the Communications Analysis Research Department of Bell Laboratories. From 1996 to 1997 he was a quantitative analyst at D.E. Shaw and Company, an investment firm in New York City. In 1997 he joined the University of California in San Diego where he is currently a professor of Electrical and Computer Engineering and of Computer Science and Engineering.
Dr. Orlitsky's research concerns information theory, learning, and speech recognition. He is a recipient of the 1981 ITT International Fellowship and of the 1992 IEEE W.R.G. Baker Paper Award.
We derive lower bounds on the achievable rate for the high-rate source by this decision directed structure. These bounds are given as functions of the low-rate message error probability \gamma, which characterizes the impact of \gamma on the performance of the system. It is shown that, in terms of the achievable rate for the high-rate information, the decision directed scheme achieves the performance of the known-training scheme as \gamma goes to zero.
Joint work with Lang Tong.