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Generalized Chinese Remainder Theorem (CRT) has been shown to be a powerful approach to solve the ambiguity resolution problem. However, with its close relationship to number theory, study in this area is mainly from a coding theory…
Recent trends of ab initio studies and progress in methodologies for electronic structure calculations of strongly correlated electron systems are discussed. The interest for developing efficient methods is motivated by recent discoveries…
An outstanding challenge in chemical computation is the many-electron problem where computational methodologies scale prohibitively with system size. The energy of any molecule can be expressed as a weighted sum of the energies of…
The population annealing algorithm is a population-based equilibrium version of simulated annealing. It can sample thermodynamic systems with rough free-energy landscapes more efficiently than standard Markov chain Monte Carlo alone. A…
Recent advances in the fields of robotics and automation have spurred significant interest in robust state estimation. To enable robust state estimation, several methodologies have been proposed. One such technique, which has shown…
Electrical impedance tomography aims at reconstructing the conductivity inside a physical body from boundary measurements of current and voltage at a finite number of contact electrodes. In many practical applications, the shape of the…
I summarise a method to quantitatively assess the consistency of power-counting proposals in Effective Field Theories which are non-perturbative at leading order. It uses the fact that the Renormalisation Group evolution of an observable…
Generalized Chinese Remainder Theorem (CRT) is a well-known approach to solve ambiguity resolution related problems. In this paper, we study the robust CRT reconstruction for multiple numbers from a view of statistics. To the best of our…
Electrical impedance tomography is an imaging modality for extracting information on the conductivity distribution inside a physical body from boundary measurements of current and voltage. In many practical applications, it is a priori…
Electronic phase behavior in correlated-electron systems is a fundamental problem of condensed matter physics. We argue here that the change in the phase behavior near the surface and interface, i.e., {\em electronic reconstruction}, is the…
While the Ising model remains essential to understand physical phenomena, its natural connection to combinatorial reasoning makes it also one of the best models to probe complex systems in science and engineering. We bring a computational…
Using Monte Carlo techniques and a star-triangle transformation, Ising models with random, 'strong' and 'weak', nearest-neighbour ferromagnetic couplings on a square lattice with a (1,1) surface are studied near the phase transition. Both…
The design and optimization of Reconfigurable Intelligent Surfaces (RISs) are key challenges for future wireless communication systems. RISs are devices that can manipulate electromagnetic (EM) waves in a programmable way, thus enhancing…
Understanding how recurrent neural circuits can learn to implement dynamical systems is a fundamental challenge in neuroscience. The credit assignment problem, i.e. determining the local contribution of each synapse to the network's global…
The reconfigurable intelligent surface is an emerging technology for wireless communications. We model it as an inhomogeneous boundary of surface impedance, and consider various optimization problems that offer different tradeoffs in terms…
We present novel information-theoretic limits on detecting sparse changes in Ising models, a problem that arises in many applications where network changes can occur due to some external stimuli. We show that the sample complexity for…
The strong mixing of many-electron basis states in excited atoms and ions with open $f$ shells results in very large numbers of complex, chaotic eigenstates that cannot be computed to any degree of accuracy. Describing the processes which…
A semilinear parabolic equation with constraint modeling the dynamics of a microelectromechanical system (MEMS) is studied. In contrast to the commonly used MEMS model, the well-known pull-in phenomenon occurring above a critical potential…
We prove stability estimates for the ENO reconstruction and ENO interpolation procedures. In particular, we show that the jump of the reconstructed ENO pointvalues at each cell interface has the same sign as the jump of the underlying cell…
In order to identify a system (module) embedded in a dynamic network, one has to formulate a multiple-input estimation problem that necessitates certain nodes to be measured and included as predictor inputs. However, some of these nodes may…