An Integrated Autoencoder-Based Filter for Sparse Big Data

We propose a novel filter for sparse big data, called an integrated autoencoder (IAE), which utilizes auxiliary information to mitigate data sparsity. The proposed model achieves an appropriate balance between prediction accuracy, convergence speed, and complexity. We implement experiments on a GPS trajectory dataset, and the results demonstrate that the IAE is more accurate and robust than some state-of-the-art methods

Uncertainty Quantification and Composition Optimization for Alloy Additive Manufacturing Through a CALPHAD-based ICME Framework

During powder production, the pre-alloyed powder composition often deviates from the target composition leading to undesirable properties of additive manufacturing (AM) components. Therefore, we developed a method to perform high-throughput calculation and uncertainty quantification by using a CALPHAD-based ICME framework (CALPHAD: calculations of phase diagrams, ICME: integrated computational materials engineering) to optimize the composition, and took the high-strength low-alloy steel (HSLA) as a case study. We analyzed the process-structure-property relationships for 450,000 compositions around the nominal composition of HSLA-115. Properties that are critical for the performance, such as yield strength, impact transition temperature, and weldability, were evaluated to optimize the composition. With the same uncertainty as the initial composition, an optimized average composition has been determined, which increased the probability of achieving successful AM builds by 44.7%. The present strategy is general and can be applied to other alloy composition optimization to expand the choices of alloy for additive manufacturing. Such a method also calls for high-quality CALPHAD databases and predictive ICME models.Comment: 37 pages, 10 figure, 11 table

On blowup of classical solutions to the compressible Navier-Stokes equations

We study the finite time blow up of smooth solutions to the Compressible Navier-Stokes system when the initial data contain vacuums. We prove that any classical solutions of viscous compressible fluids without heat conduction will blow up in finite time, as long as the initial data has an isolated mass group (see definition in the paper). The results hold regardless of either the size of the initial data or the far fields being vacuum or not. This improves the blowup results of Xin (1998) by removing the crucial assumptions that the initial density has compact support and the smooth solution has finite total energy. Furthermore, the analysis here also yields that any classical solutions of viscous compressible fluids without heat conduction in bounded domains or periodic domains will blow up in finite time, if the initial data have an isolated mass group satisfying some suitable conditions.Comment: 13 pages, Submitte

Static Quantum Computation

Tailoring many-body interactions among a proper quantum system endows it with computing ability by means of static quantum computation in the sense that some of the physical degrees of freedom can be used to store binary information and the corresponding binary variables satisfy some given logic relations if and only if the system is in the ground state. Two theorems are proved showing that the universal static quantum computer can encode the solutions for any P and NP problem into its ground state using only polynomial number (in the problem input size) of logic gates. The second step is to read out the solutions by relaxing the system. The time complexity is relevant when one tries to read out the solution by relaxing the system, therefore our model of static quantum computation provides a new connection between the computational complexity and the dynamics of a complex system.Comment: 8 pages, 3 ps figure

Tailoring Many-Body Interactions to Solve Hard Combinatorial Problems

A quantum machine consisting of interacting linear clusters of atoms is proposed for the 3SAT problem. Each cluster with two relevant states of collective motion can be used to register a Boolean variable. Given any 3SAT Boolean formula the interactions among the clusters can be so tailored that the ground state(s) (possibly degenerate) of the whole system encodes the satisfying truth assignment(s) for it. This relates the 3SAT problem to the dynamics of the properly designed glass system.Comment: Latex 7 pages, 3 ps figure

Covering Radius of Permutation Groups with Infinity-Norm

The covering radius of permutation group codes are studied in this paper with $l_{\infty}$-metric. We determine the covering radius of the $(p,q)$-type group, which is a direct product of two cyclic transitive groups. We also deduce the maximum covering radius among all the relabelings of this group under conjugation, that is, permutation groups with the same algebraic structure but with relabelled members. Finally, we give a lower bound of the covering radius of the dihedral group code, which differs from the trivial upper bound by a constant at most one. This improves the result of Karni and Schwartz in 2018, where the gap between their lower and upper bounds tends to infinity as the code length grows.Comment: 13 pages, 0 figure

Single Molecule Magnetic Resonance and Quantum Computation

It is proposed that nuclear (or electron) spins in a trapped molecule would be well isolated from the environment and the state of each spin can be measured by means of mechanical detection of magnetic resonance. Therefore molecular traps make an entirely new approach possible for spin-resonance quantum computation which can be conveniently scaled up. In the context of magnetic resonance spectroscopy, a molecular trap promises the ultimate sensitivity for single spin detection and an unprecedented spectral resolution as well

A class of generalized positive linear maps on matrix algebras

We construct a class of positive linear maps on matrix algebras. We find conditions when these maps are atomic, decomposable and completely positive. We obtain a large class of atomic positive linear maps. As applications in quantum information theory, we discuss the structural physical approximation and optimality of entanglement witness associated with these maps

Uniform Spanning Forests and the bi-Laplacian Gaussian field

We construct a natural discrete random field on $\mathbb{Z}^{d}$, $d\geq 5$ that converges weakly to the bi-Laplacian Gaussian field in the scaling limit. The construction is based on assigning i.i.d. Bernoulli random variables on each component of the uniform spanning forest, thus defines an associated random function. To our knowledge, this is the first natural discrete model (besides the discrete bi-Laplacian Gaussian field) that converges to the bi-Laplacian Gaussian field

A protein structural alphabet and its substitution matrix CLESUM

By using a mixture model for the density distribution of the three pseudobond angles formed by $C_\alpha$ atoms of four consecutive residues, the local structural states are discretized as 17 conformational letters of a protein structural alphabet. This coarse-graining procedure converts a 3D structure to a 1D code sequence. A substitution matrix between these letters is constructed based on the structural alignments of the FSSP database.Comment: 10 page