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In this review we consider the performance of the quantum adiabatic algorithm for the solution of decision problems. We divide the possible failure mechanisms into two sets: small gaps due to quantum phase transitions and small gaps due to…
We derive an exact solution for a simple non-autonomous delay differential equation (DDE) over the entire real-time axis, representing it as a sum of Gaussian-shaped dynamics with distinct peak positions. This marks the first explicit…
Time-dependently driven stochastic systems form a vast and manifold class of non-equilibrium systems used to model important applications on small length scales such as bit erasure protocols or microscopic heat engines. One property that…
We discuss global gauge fixing on the lattice, specifically to the lattice Landau gauge, with the goal of understanding the question of why the process becomes extremely slow for large lattices. We construct an artificial "gauge-fixing"…
Phase boundaries in p-T and p-V diagrams are essential in material science researches. Exact analytic knowledge about such phase boundaries are known so far only in two-dimensional (2D) Ising-like models, and only for cases with two phases.…
The chaotic synchronization between two bi-directionally coupled external cavity single-mode semiconductor lasers is investigated. Numerical simulation shows that anticipating synchronization and lag synchronization coexist in certain…
We develop a penalized likelihood estimation framework to estimate the structure of Gaussian Bayesian networks from observational data. In contrast to recent methods which accelerate the learning problem by restricting the search space, our…
We show that an infinite family of odd complex 2-dimensional Galois representations ramified at 5 having nonsolvable projective image are modular, thereby verifying Artin's conjecture for a new case of examples. Such a family contains the…
Linear Temporal Logic (LTL) is the standard specification language for reactive systems and is successfully applied in industrial settings. However, many shortcomings of LTL have been identified in the literature, among them the limited…
In this article, we investigate the maximal smoothness (infinite differentiability) of solutions to thermoelastic models, specifically those where the heat equation is of the ``phase-lag'' or ``parabolic'' type. We derive optimal regularity…
We present the design of an analog circuit which solves linear programming (LP) problems. In particular, the steady-state circuit voltages are the components of the LP optimal solution. The paper shows how to construct the circuit and…
We develop a new generalized coupling approach to the study of stochastic delay equations with H\"older continuous coefficients, for which analytical PDE-based methods are not available. We prove that such equations possess unique weak…
This is not a new result. Purpose of this work is to describe a method to search the analytical expression of the general real solution of the two-dimensional Laplace differential equation. This thing is not easy to find in scientific…
Existence of a new type of oscillating synchronization that oscillates between three different types of synchronizations (anticipatory, complete and lag synchronizations) is identified in unidirectionally coupled nonlinear time-delay…
The optimal control of two-level systems by time-dependent laser fields is studied using a variational theory. We obtain, for the first time, general analytical expressions for the optimal pulse shapes leading to global maximization or…
This paper focuses on the mathematical approaches to the analysis of stability that is a crucial step in the design of dynamical systems. Three methods are presented, namely, absolutely integrable impulse response, Fourier integral, and…
A procedure to derive the Ginzburg-Landau (GL) theory from the multiband BCS Hamiltonian is developed in a general case with an arbitrary number of bands and arbitrary interaction matrix. It combines the standard Gor'kov truncation and a…
Boolean satisfiability (SAT) problem, the first problem proven to be NP-complete, has become a fundamental challenge in computational complexity, with widespread applications in optimization and verification across many domains. Despite…
A new Langevin equation with a field-dependent kernel is proposed to deal with bottomless systems within the framework of the stochastic quantization of Parisi and Wu. The corresponding Fokker-Planck equation is shown to be a diffusion-type…
We present a novel sparsity-based space-time adaptive processing (STAP) technique based on the alternating direction method to overcome the severe performance degradation caused by array gain/phase (GP) errors. The proposed algorithm…