Euclidean versus hyperbolic congestion in idealized versus experimental networks (2009)
Jonckheere, Edmond, Lou, Mingji, Bonahon, Francis, Baryshnikov, Yuliy
This paper proposes a mathematical justification of the phenomenon of extreme congestion at a very limited number of nodes in very large networks. It is argued that this phenomenon occurs as a...
TARGET ENUMERATION IN SENSOR NETWORKS VIA INTEGRATION WITH RESPECT TO EULER CHARACTERISTIC ∗ (2009)
Yuliy Baryshnikov, Robert Ghrist
Abstract. We solve the problem of counting the total number of observable targets (e.g., persons, vehicles, etc.) in a region based on local counts performed by a network of sensors, each of which...
Sub-Riemannian geometry and periodic orbits in classical billiards (2008)
Yuliy Baryshnikov, Vadim Zharnitsky
Abstract. Classical (Birkhoff) billiards with full 1-parameter families of periodic orbits are considered. It is shown that construction of a convex billiard with a “rational” caustic (i.e....
Experiments in Stochastic Self Assembly (2008)
Yuliy Baryshnikov, Boonsit Yimwadsana
The reaction rate equations of chemical kinetics provide a useful model for molecular self assembly, which can be exhibited as a continuous-time, continuous-space limit under the LLN (law of large...
Two-dimensional quantum random walk (2008)
Baryshnikov, Yuliy, Brady, Wil, Bressler, Andrew, Pemantle, Robin
We analyze several families of two-dimensional quantum random walks. The feasible region (the region where probabilities do not decay exponentially with time) grows linearly with time, as is the case...
Asymptotics of multivariate sequences, part III: quadratic points (2008)
Baryshnikov, Yuliy, Pemantle, Robin
We consider a number of combinatorial problems in which rational generating functions may be obtained, whose denominators have factors with certain singularities. Specifically, there exist points...
On Times to Compute Shapes in 2D Tile Self-Assembly (2008)
Yuliy Baryshnikov, Boonsit Yimwadsana
We study the times to grow structures within the tile self-assembly model proposed by Winfree, and the possible shapes that can be achieved. Our earlier work was confined to the growth of rectangular...
Asymptotics of Damped Periodic Motions with Random Initial Speed (2007)
Yuliy Baryshnikov And, Yuliy Baryshnikov, Wolfgang Stadje
. We consider motion on the circle, possibly with friction and external forces, the initial velocity being a large random variable. We prove that under various assumptions the distribution of the...
Space filling and depletion (2007)
Yuliy Baryshnikov, E. G. Coffman, Predrag Jelenkovi C
Abstract. For a given k 1, subintervals of a given interval [0; X] arrive at random and are accepted (allocated) so long as they overlap fewer than k subintervals already accepted. Subintervals not...
Yuliy Baryshnikov, Robert Ghrist
Abstract. We solve the problem of counting the total number of observable targets (e.g., persons, vehicles, landmarks) in a region using local counts performed by a dense field of sensors, each of...
Localization for Anchoritic Sensor Networks (2007)
Abstract. We introduce a class of anchoritic sensor networks, where communications between sensor nodes are undesirable or infeasible due to, e.g., harsh environments, energy constraints, or security...
Yuliy Baryshnikov, Jing Feng, Vishal Misra
To enhance performance, typical TCP variants propose explicit use of traffic measurements or adjustments to the increase/decrease parameters of the AIMD (additive increase, multiplicative decrease)...
Stochastic yield analysis of self-assembling,single-enzyme reaction networks (2005)
Yuliy Baryshnikov, Teddy Yimwadsana
1 Introduction The goal of this note is to investigate yield patterns in a class of Reaction Networks(RN's) appearing naturally in many biochemical systems, and playing a crucial role in various...
T.: Analysis of self-correcting selfassembly growth models (2005)
Yuliy Baryshnikov, Nadrian Seeman, Teddy Yimwadsana
In many respects, the current state of DNA-based computing resembles the state of standard, electronic computing a half century ago: a fascinating prospect is slow to develop owing to inflexible...
Convolutions of inverse linear functions via multivariate residues (2004)
Yuliy Baryshnikov, Robin Pemantle
lj(z1,...,zd) n j be the quotient of an analytic function by a product of linear functions lj: = 1 − � bijzi. We compute asymptotic formulae for the Taylor coefficients of F via the multivariate...
P.: Phase transitions and control in self assembly (2004)
Yuliy Baryshnikov, Petar Momčilović
Abstract. We introduce a general mathematical model of processes by which self-assembled objects are built from physical (e.g., molecular) units and clusters of these units. We operate within the...
DNA-based computation times (2004)
Yuliy Baryshnikov, Petar Momčilović
Speed of computation and power consumption are the two main parameters of conventional computing devices implemented in microelectronic circuits. As performance of such devices approaches physical...
An asymptotically optimal greedy algorithm for large optical burst switching systems (2003)
Andrew, Lachlan L. H., Baryshnikov, Yuliy, Coffman Jr, E. G., Hanly, Stephen V., White, Jolyon
As the number of wavelengths in OBS systems increases, the utilization achievable for a given blocking probability can be made to approach 100%. This paper shows that this property applies to a...
An asymptotically optimal greedy algorithm for large optical burst switching systems (2003)
Andrew, Lachlan L. H., Baryshnikov, Yuliy, Coffman Jr, E. G., Hanly, Stephen V., White, Jolyon
As the number of wavelengths in OBS systems increases, the utilization achievable for a given blocking probability can be made to approach 100%. This paper shows that this property applies to a...
Supporting Points Processes And Some Of Their Applications (2000)
. We introduce stochastic point process of S-supporting points and prove that upon rescaling it converges to a Gaussian field. The notion of S-supporting points specializes to Pareto (or, more...
Wiener Soccer And Its Generalization (1997)
The trajectory of the ball in a soccer game is modelled by the Brownian motion on a cylinder, subject to elastic reflections at the boundary points (as proposed in [KPY]). The score is then the...
COMMUNICATIONS in PROBABILITY WIENER SOCCER AND ITS GENERALIZATION (1997)
The trajectory of the ball in a soccer game is modelled by the Brownian motion on a cylinder, subject to elastic reflections at the boundary points (as proposed in [KPY]). The score is then the...
Baryshnikov, Yuliy, Eisenberg, Bennett, Stengle, Gilbert
Suppose that the scores of n players are unbounded, independent, integer valued random variables equal in distribution to X. We show that as n --> [infinity], the limiting probability of a tie for...