A semismooth newton method for the nearest Euclidean distance matrix problem

The Nearest Euclidean distance matrix problem (NEDM) is a fundamentalcomputational problem in applications such asmultidimensional scaling and molecularconformation from nuclear magnetic resonance data in computational chemistry.Especially in the latter application, the problem is often large scale with the number ofatoms ranging from a few hundreds to a few thousands.In this paper, we introduce asemismooth Newton method that solves the dual problem of (NEDM). We prove that themethod is quadratically convergent.We then present an application of the Newton method to NEDM with $H$-weights.We demonstrate the superior performance of the Newton method over existing methodsincluding the latest quadratic semi-definite programming solver.This research also opens a new avenue towards efficient solution methods for the molecularembedding problem

Deposition of clusters and nanoparticles onto boron-doped diamond electrodes for electrocatalysis

Metal and metal oxide particles and nanoparticles, differing from each other by their nature and synthesis technique, were deposited onto boron-doped diamond (BDD) thin film electrodes. The applicability in electrocatalysis of thermally decomposed IrO2 and Au nanoparticles, electrodeposited Pt particles, dendrimer-encapsulated Pt nanoparticles (Pt DENs) and microemulsion-synthesized Pt/Ru nanoparticles was studied, once deposited on BDD substrate. In all cases, the electrochemical response of the composite electrodes could be solely attributed to the supported particles. All the particles, with the exception of Pt DENs, exhibited electrocatalytic activity. Pt DENs inactivity has been attributed to insufficient removal of the dendrimer polymer matrix. It was concluded that the BDD electrode is a suitable substrate for the electrochemical investigation of supported catalytic nanoparticle

Correcting datasets leads to more homogeneous early-twentieth-century sea surface warming

Existing estimates of sea surface temperatures (SSTs) indicate that, during the early twentieth century, the North Atlantic and northeast Pacific oceans warmed by twice the global average, whereas the northwest Pacific Ocean cooled by an amount equal to the global average1,2,3,4. Such a heterogeneous pattern suggests first-order contributions from regional variations in forcing or in ocean–atmosphere heat fluxes5,6. These older SST estimates are, however, derived from measurements of water temperatures in ship-board buckets, and must be corrected for substantial biases7,8,9. Here we show that correcting for offsets among groups of bucket measurements leads to SST variations that correlate better with nearby land temperatures and are more homogeneous in their pattern of warming. Offsets are identified by systematically comparing nearby SST observations among different groups10. Correcting for offsets in German measurements decreases warming rates in the North Atlantic, whereas correcting for Japanese measurement offsets leads to increased and more uniform warming in the North Pacific. Japanese measurement offsets in the 1930s primarily result from records having been truncated to whole degrees Celsius when the records were digitized in the 1960s. These findings underscore the fact that historical SST records reflect both physical and social dimensions in data collection, and suggest that further opportunities exist for improving the accuracy of historical SST records9,11

Numerical approximations for the tempered fractional Laplacian: Error analysis and applications

In this paper, we propose an accurate finite difference method to discretize the $d$-dimensional (for $d\ge 1$) tempered integral fractional Laplacian and apply it to study the tempered effects on the solution of problems arising in various applications. Compared to other existing methods, our method has higher accuracy and simpler implementation. Our numerical method has an accuracy of $O(h^\epsilon)$, for $u \in C^{0, \alpha+\epsilon} (\bar{\Omega})$ if $\alpha < 1$ (or $u \in C^{1, \alpha-1+\epsilon} (\bar{\Omega})$ if $\alpha \ge 1$) with $\epsilon > 0$, suggesting the minimum consistency conditions. The accuracy can be improved to $O(h^2)$, for $u \in C^{2, \alpha+\epsilon} (\bar{\Omega})$ if $\alpha < 1$ (or $u \in C^{3, \alpha - 1 + \epsilon} (\bar{\Omega})$ if $\alpha \ge 1$). Numerical experiments confirm our analytical results and provide insights in solving the tempered fractional Poisson problem. It suggests that to achieve the second order of accuracy, our method only requires the solution $u \in C^{1,1}(\bar{\Omega})$ for any $0<\alpha<2$. Moreover, if the solution of tempered fractional Poisson problems satisfies $u \in C^{p, s}(\bar{\Omega})$ for $p = 0, 1$ and $0<s \le 1$, our method has the accuracy of $O(h^{p+s})$. Since our method yields a (multilevel) Toeplitz stiffness matrix, one can design fast algorithms via the fast Fourier transform for efficient simulations. Finally, we apply it together with fast algorithms to study the tempered effects on the solutions of various tempered fractional PDEs, including the Allen-Cahn equation and Gray-Scott equations.Comment: 21 pages, 11 figures, 3 table

A comment on discrete Kalb-Ramond field on orientifold and rank reduction

We show that the rank reduction of the gauge group on orientifolds in presence of non vanishing discrete Kalb-Ramond field can be explained by the presence of an induced field strength in a non trivial bundle on the branes. This field strength is also necessary for the tadpole cancellation and the number of branes is left unchanged by the presence of the discrete Kalb-Ramond background.Comment: v2: added references, improved introduction and corrected misprints; 15 page

Wrapped Magnetized Branes: Two Alternative Descriptions?

We discuss two inequivalent ways for describing magnetized D-branes wrapped N times on a torus T^2. The first one is based on a non-abelian gauge bundle U(N), while the second one is obtained by means of a Narain T-duality transformation acting on a theory with non-magnetized branes. We construct in both descriptions the boundary state and the open string vertices and show that they give rise to different string amplitudes. In particular, the description based on the gauge bundle has open string vertex operators with momentum dependent Chan-Paton factors.Comment: 60 pages, LaTe

Guitar Ensembles

A performance of guitar ensembles at USU.https://digitalcommons.usu.edu/music_programs/1231/thumbnail.jp