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The simplest non-collision solutions of the N-body problem are the "relative equilibria", in which each body follows a circular orbit around the centre of mass and the shape formed by the N bodies is constant. It is easy to see that the…
The dual problem of optimal transportation in Lorentz-Finsler geometry is studied. It is shown that in general no solution exists even in the presence of an optimal coupling. Under natural assumptions dual solutions are established. It is…
This article describes a bipedal walking algorithm with inverse kinematics resolution based solely on geometric methods, so that all mathematical concepts are explained from the base, in order to clarify the reason for this solution. To do…
Consider a transient near-critical (1,2) random walk on the positive half line. We give a criteria for the finiteness of the number of the skipped points (the points never visited) by the random walk. This result generalizes (partially) the…
We present a new simple method for rounding a semidefinite programming relaxation of a constraint satisfaction problem. We apply it to the problem of approximate angular synchronization. Specifically, we are given directed distances on a…
By following the same construction pattern which Martin Davis proposed in a 1968 paper of his, we have obtained six quaternary quartic Diophantine equations that candidate as `rule-them-all' equations: proving that one of them has only a…
The problem of describing the free motions of three gravitating bodies under each others gravitational influence is one of the oldest of unsolved problems of classical mechanics. Henry Poincare proved in his dictum that due to the nature of…
A combined dynamics consisting of Brownian motion and L\'evy flights is exhibited by a variety of biological systems performing search processes. Assessing the search reliability of ever locating the target and the search efficiency of…
We consider the classical problem of making mobile processes gather or converge at a same position (as performed by swarms of animals in Nature). Existing works assume that each process can see all other processes, or all processes within a…
Self-consistent approaches in many-electron problems typically converge to an unphysical solution in strongly correlated regimes. By deriving the mathematical condition for the stability of the physical solution, we unveil the precise…
This paper looks into the problem of pedestrian tracking using a monocular, potentially moving, uncalibrated camera. The pedestrians are located in each frame using a standard human detector, which are then tracked in subsequent frames.…
This paper shows global uniqueness in two inverse problems for a fractional conductivity equation: an unknown conductivity in a bounded domain is uniquely determined by measurements of solutions taken in arbitrary open, possibly disjoint…
Numerical solutions to Newton's equations of motion for chaotic self gravitating systems of more than 2 bodies are often regarded to be irreversible. This is due to the exponential growth of errors introduced by the integration scheme and…
The continuous evolution of a wide variety of systems, including continuous-time Markov chains and linear hybrid automata, can be described in terms of linear differential equations. In this paper we study the decision problem of whether…
It was recently conjectured that every component of a discrete-time rational dynamical system is a solution to an algebraic difference equation that is linear in its highest-shift term (a quasi-linear equation). We prove that the conjecture…
A small variation of the circular shape of the hodograph theorem states that for every elliptical solution of the two-body problem, it is possible to find an appropriate inertial frame such that the speed of the bodies is constant. We use…
This paper studies the numerical solution of traveling singular sources problems. In such problems, a big challenge is the sources move with different speeds, which are described by some ordinary differential equations. A…
Nearest neighbor (NN) queries in trajectory databases have received significant attention in the past, due to their application in spatio-temporal data analysis. Recent work has considered the realistic case where the trajectories are…
All experiments attempting to verify the invariance of speed of light directly are based on two-way speed measurement. The challenge in one-way speed measurement, the requirement of spatially separated synchronised clocks, can be possibly…
The $n$-body problem with a purely repulsive Coulomb interaction is considered. It is shown that for large times $t$ the distance between any two particles grows linearly in $t$. The trajectory of each particle is asymptotically a straight…