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

Periodic Orbits in Rotating Second Degree and Order Gravity Fields

"Periodic orbits in an arbitrary 2nd degree and order uniformly rotating gravity field are studied. We investigate the four equilibrium points in this gravity field. We see that close relation exists between the stability of these equilibria and the existence and stability of their nearby periodic orbits. We check the periodic orbits with non-zero periods. In our searching procedure for these periodic orbits, we remove the two unity eigenvalues from the state transition matrix to find a robust, non-singular linear map to solve for the periodic orbits. The algorithm converges well, especially for stable periodic orbits. Using the searching procedure, which is relatively automatic, we find five basic families of periodic orbits in the rotating second degree and order gravity field for planar motion, and discuss their existence and stability at different central body rotation rates."http://deepblue.lib.umich.edu/bitstream/2027.42/64208/1/chjaa_8_1_012.pd

Irreducible Highest Weight Representations Of The Simple n-Lie Algebra

A. Dzhumadil'daev classified all irreducible finite dimensional representations of the simple n-Lie algebra. Using a slightly different approach, we obtain in this paper a complete classification of all irreducible, highest weight modules, including the infinite-dimensional ones. As a corollary we find all primitive ideals of the universal enveloping algebra of this simple n-Lie algebra.Comment: 24 pages, 24 figures, mistake in proposition 2.1 correcte

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

General Quantum Key Distribution in Higher Dimension

We study a general quantum key distribution protocol in higher dimension. In this protocol, quantum states in arbitrary $g+1$ ($1\le g\le d$) out of all $d+1$ mutually unbiased bases in a d-dimensional system can be used for the key encoding. This provides a natural generalization of the quantum key distribution in higher dimension and recovers the previously known results for $g=1$ and $d$. In our investigation, we study Eve's attack by two slightly different approaches. One is considering the optimal cloner for Eve, and the other, defined as the optimal attack, is maximizing Eve's information. We derive results for both approaches and show the deviation of the optimal cloner from the optimal attack. With our systematic investigation of the quantum key distribution protocols in higher dimension, one may balance the security gain and the implementation cost by changing the number of bases in the key encoding. As a side product, we also prove the equivalency between the optimal phase covariant quantum cloning machine and the optimal cloner for the $g=d-1$ quantum key distribution

Machine Learning Identifies Prognostic Subtypes of the Tumor Microenvironment of NSCLC

The tumor microenvironment (TME) plays a fundamental role in tumorigenesis, tumor progression, and anti-cancer immunity potential of emerging cancer therapeutics. Understanding inter-patient TME heterogeneity, however, remains a challenge to efficient drug development. This article applies recent advances in machine learning (ML) for survival analysis to a retrospective study of NSCLC patients who received definitive surgical resection and immune pathology following surgery. ML methods are compared for their effectiveness in identifying prognostic subtypes. Six survival models, including Cox regression and five survival machine learning methods, were calibrated and applied to predict survival for NSCLC patients based on PD-L1 expression, CD3 expression, and ten baseline patient characteristics. Prognostic subregions of the biomarker space are delineated for each method using synthetic patient data augmentation and compared between models for overall survival concordance. A total of 423 NSCLC patients (46% female; median age [inter quantile range]: 67 [60-73]) treated with definite surgical resection were included in the study. And 219 (52%) patients experienced events during the observation period consisting of a maximum follow-up of 10 years and median follow up 78 months. The random survival forest (RSF) achieved the highest predictive accuracy, with a C-index of 0.84. The resultant biomarker subtypes demonstrate that patients with high PD-L1 expression combined with low CD3 counts experience higher risk of death within five-years of surgical resection

Direct Covalent Chemical Functionalization of Unmodified Two-Dimensional Molybdenum Disulfide

Two-dimensional semiconducting transition metal dichalcogenides (TMDCs) like molybdenum disulfide (MoS2) are generating significant excitement due to their unique electronic, chemical, and optical properties. Covalent chemical functionalization represents a critical tool for tuning the properties of TMDCs for use in many applications. However, the chemical inertness of semiconducting TMDCs has thus far hindered the robust chemical functionalization of these materials. Previous reports have required harsh chemical treatments or converting TMDCs into metallic phases prior to covalent attachment. Here, we demonstrate the direct covalent functionalization of the basal planes of unmodified semiconducting MoS2 using aryl diazonium salts without any pretreatments. Our approach preserves the semiconducting properties of MoS2, results in covalent C-S bonds, is applicable to MoS2 derived from a range of different synthesis methods, and enables a range of different functional groups to be tethered directly to the MoS2 surface. Using density functional theory calculations including van der Waals interactions and atomic-scale scanning probe microscopy studies, we demonstrate a novel reaction mechanism in which cooperative interactions enable the functionalization to propagate along the MoS2 basal plane. The flexibility of this covalent chemistry employing the diverse aryl diazonium salt family is further exploited to tether active proteins to MoS2, suggesting future biological applications and demonstrating its use as a versatile and powerful chemical platform for enhancing the utility of semiconducting TMDCsComment: To appear in Chemistry Materials (In press

FDLS: A Deep Learning Approach to Production Quality, Controllable, and Retargetable Facial Performances

Visual effects commonly requires both the creation of realistic synthetic humans as well as retargeting actors' performances to humanoid characters such as aliens and monsters. Achieving the expressive performances demanded in entertainment requires manipulating complex models with hundreds of parameters. Full creative control requires the freedom to make edits at any stage of the production, which prohibits the use of a fully automatic ``black box'' solution with uninterpretable parameters. On the other hand, producing realistic animation with these sophisticated models is difficult and laborious. This paper describes FDLS (Facial Deep Learning Solver), which is Weta Digital's solution to these challenges. FDLS adopts a coarse-to-fine and human-in-the-loop strategy, allowing a solved performance to be verified and edited at several stages in the solving process. To train FDLS, we first transform the raw motion-captured data into robust graph features. Secondly, based on the observation that the artists typically finalize the jaw pass animation before proceeding to finer detail, we solve for the jaw motion first and predict fine expressions with region-based networks conditioned on the jaw position. Finally, artists can optionally invoke a non-linear finetuning process on top of the FDLS solution to follow the motion-captured virtual markers as closely as possible. FDLS supports editing if needed to improve the results of the deep learning solution and it can handle small daily changes in the actor's face shape. FDLS permits reliable and production-quality performance solving with minimal training and little or no manual effort in many cases, while also allowing the solve to be guided and edited in unusual and difficult cases. The system has been under development for several years and has been used in major movies.Comment: DigiPro '22: The Digital Production Symposiu

Directed Diffusion: Direct Control of Object Placement through Attention Guidance

Text-guided diffusion models such as DALLE-2, Imagen, and Stable Diffusion are able to generate an effectively endless variety of images given only a short text prompt describing the desired image content. In many cases the images are of very high quality. However, these models often struggle to compose scenes containing several key objects such as characters in specified positional relationships. The missing capability to "direct" the placement of characters and objects both within and across images is crucial in storytelling, as recognized in the literature on film and animation theory. In this work, we take a particularly straightforward approach to providing the needed direction. Drawing on the observation that the cross-attention maps for prompt words reflect the spatial layout of objects denoted by those words, we introduce an optimization objective that produces ``activation'' at desired positions in these cross-attention maps. The resulting approach is a step toward generalizing the applicability of text-guided diffusion models beyond single images to collections of related images, as in storybooks. To the best of our knowledge, our Directed Diffusion method is the first diffusion technique that provides positional control over multiple objects, while making use of an existing pre-trained model and maintaining a coherent blend between the positioned objects and the background. Moreover, it requires only a few lines to implement.Comment: Our project page: https://hohonu-vicml.github.io/DirectedDiffusion.Pag