Related papers: Kolmogorov variation: KAM with knobs (\`a la Kolmo…
An extractor is a function that receives some randomness and either "improves" it or produces "new" randomness. There are statistical and algorithmical specifications of this notion. We study an algorithmical one called Kolmogorov…
Low-resource language translation is a challenging but socially valuable NLP task. Building on recent work adapting the Transformer's normalization to this setting, we propose QKNorm, a normalization technique that modifies the attention…
In this paper, it is proved that the infinite KAM torus with prescribed frequency exists in a sufficiently small neighborhood of a given $ I^{0}$ for nearly integrable and analytic Hamiltonian system $ H(I,\theta) = H_{0}(I)+ \epsilon…
This paper studies a family of convolution quadratures, a numerical technique for efficient evaluation of convolution integrals. We employ the block generalized Adams method to discretize the underlying initial value problem, departing from…
Quantum metrology plays a fundamental role in many scientific areas. However, the complexity of engineering entangled probes and the external noise raise technological barriers for realizing the expected precision of the to-be-estimated…
We present a quantum Viterbi algorithm (QVA) with better than classical performance under certain conditions. In this paper the proposed algorithm is applied to decoding classical convolutional codes, for instance; large constraint length…
Kolmogorov-Smirnov (K-S) test-a non-parametric method to measure the goodness of fit, is applied for automatic modulation classification (AMC) in this paper. The basic procedure involves computing the empirical cumulative distribution…
Our main purpose of this article is to study the convergence and other related properties of q-Bernstein-Kantorovich operators including the shifted knots of real positive numbers. We design the shifted knots of Bernstein-Kantorovich…
We describe a novel switching algorithm based on a ``reverse'' Monte Carlo method, in which the potential is stochastically modified before the system configuration is moved. This new algorithm facilitates a generalized formulation of…
We review Kolmogorov's 1954 fundamental paper {\sl On the Conservation of Conditionally Periodic Motions under Small Perturbation of the Hamiltonian} (Dokl. akad. nauk SSSR,1954, vol. {\bf 98}, pp.527--530), both from the historical and the…
We show that the standard Lanczos algorithm can be efficiently implemented statistically and self consistently improved, using the stochastic reconfigurat ion method, which has been recently introduced to stabilize the Monte Carlo sign…
A fast quantum search algorithm for continuous variables is presented. The result is the quantum continuous variable analog of Grover's algorithm originally proposed for qubits. A continuous variable analog of the Hadamard (i.e., Fourier…
We consider the classical problem of the continuation of periodic orbits surviving to the breaking of invariant lower dimensional resonant tori in nearly integrable Hamiltonian systems. In particular we extend our previous results…
Studying the computational complexity and designing fast algorithms for determining winners under voting rules are classical and fundamental questions in computational social choice. In this paper, we accelerate voting by leveraging quantum…
Post-training quantization (PTQ) has emerged as a practical approach to compress large neural networks, making them highly efficient for deployment. However, effectively reducing these models to their low-bit counterparts without…
We introduce Quantum Time-Frequency Analysis, which expands the approach of Quantum Harmonic Analysis to include modulations of operators in addition to translations. This is done by a projective representation of double-phase space, and we…
Alternating minimization (AM) procedures are practically efficient in many applications for solving convex and non-convex optimization problems. On the other hand, Nesterov's accelerated gradient is theoretically optimal first-order method…
We give a simple proof of the smooth Thom isomorphism for complex bundles for the bivariant K-theories on locally convex algebras considered by Cuntz. We also prove the Thom isomorphism in Kasparov's KK-theory in a form stated without proof…
Quantum machine learning algorithms could provide significant speed-ups over their classical counterparts; however, whether they could also achieve good generalization remains unclear. Recently, two quantum perceptron models which give a…
We apply the general normal form theorems in Kolmogorov spaces to three classical cases: deformations of hypersurface singularities, normal forms of vector fields and invariant tori in Hamiltonian systems.