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Understanding how complex systems transition between states requires mapping the energy landscape that governs these changes. Local transition-state networks reveal the barrier architecture that explains observed behaviour and enables…
The transfer of quantum states has played an important role in quantum information processing. In fact, transfer of quantum states from point $A$ to $B$ with unit fidelity is very important for us and we focus on this case. In recent years,…
This article presents a unified approach to simultaneously compute the Jacobians of several singular matrix transformations in the real, complex, quaternion and octonion cases. Formally, these Jacobians are obtained for real normed division…
Motion planning under uncertainty for an autonomous system can be formulated as a Markov Decision Process with a continuous state space. In this paper, we propose a novel solution to this decision-theoretic planning problem that directly…
To realize autonomous collaborative robots, it is important to increase the trust that users have in them. Toward this goal, this paper proposes an algorithm which endows an autonomous agent with the ability to explain the transition from…
Precision matrix estimation is essential in various fields; yet it is challenging when samples for the target study are limited. Transfer learning can enhance estimation accuracy by leveraging data from related source studies. We propose…
For a dynamical system on n-dimensional projective space over a number field or a function field, we show that semi-stable reduction implies the minimality of the resultant. We use this to show that every such dynamical system over a number…
With microwave irradiation, the switching current of a Josephson junction coupled to a microscopic two-level system jumps randomly between two discrete states. We modeled the switching process of the coupled system with quantum jump…
Consider a rational map from a projective space to a product of projective spaces, induced by a collection of linear projections. Motivated by the the theory of limit linear series and Abel-Jacobi maps, we study the basic properties of the…
This paper expands on existing learned models of human behavior via a measured step in structured irrationality. Specifically, by replacing the suboptimality constant $\beta$ in a Boltzmann rationality model with a function over states…
We introduce a new transfer matrix method for calculating the thermodynamic properties of random-tiling models of quasicrystals in any number of dimensions, and describe how it may be used to calculate the phason elastic properties of these…
We review work by the authors on thermal activation in nanoscopic magnetic systems. These systems present unique difficulties in analyzing noise-induced escape over a barrier, including the presence of nonlocal interactions, nongradient…
There are several known constructions of equilibrium states for H\"older continuous potentials in the context of both subshifts of finite type and uniformly hyperbolic systems. In this article we present another method of building such…
A spin-isospin dependent Three-Dimensional formalism based on the momentum vectors for the four-nucleon bound state is presented. The four-nucleon Yakubovsky equations with two- and three-nucleon interactions are formulated as a function of…
A new method of determination entries of the state matrices has been presented. The presented method is based on one-dimensional digraph theory. A procedure for computation of the state matrices has also been proposed. The procedure has…
The paper presents partial-realization theory and realization algorithms for linear switched systems. Linear switched systems are a particular subclass of hybrid systems. We formulate a notion of a partial realization and we present…
We study the time evolution of a single spin excitation state in certain linear spin chains, as a model for quantum communication. Some years ago it was discovered that when the spin chain data (the nearest neighbour interaction strengths…
For the strictly positive case (the suboptimal case) the maximum entropy solution $X$ to the Leech problem $G(z)X(z)=K(z)$ and $\|X\|_\infty=\sup_{|z|\leq 1}\|X(z)\|\leq 1$, with $G$ and $K$ stable rational matrix functions, is proved to be…
The phase-dependent bound states (Andreev levels) of a Josephson junction can cross at the Fermi level, if the superconducting ground state switches between even and odd fermion parity. The level crossing is topologically protected, in the…
We present a new method for computing the transverse transfer matrix through superimposed axisymmetric RF and solenoid field maps. The algorithm constructs the transfer matrix directly from one dimensional RF and solenoid field maps without…