Learning Theory of Distribution Regression with Neural Networks

In this paper, we aim at establishing an approximation theory and a learning theory of distribution regression via a fully connected neural network (FNN). In contrast to the classical regression methods, the input variables of distribution regression are probability measures. Then we often need to perform a second-stage sampling process to approximate the actual information of the distribution. On the other hand, the classical neural network structure requires the input variable to be a vector. When the input samples are probability distributions, the traditional deep neural network method cannot be directly used and the difficulty arises for distribution regression. A well-defined neural network structure for distribution inputs is intensively desirable. There is no mathematical model and theoretical analysis on neural network realization of distribution regression. To overcome technical difficulties and address this issue, we establish a novel fully connected neural network framework to realize an approximation theory of functionals defined on the space of Borel probability measures. Furthermore, based on the established functional approximation results, in the hypothesis space induced by the novel FNN structure with distribution inputs, almost optimal learning rates for the proposed distribution regression model up to logarithmic terms are derived via a novel two-stage error decomposition technique

Extend Wave Function Collapse to Large-Scale Content Generation

Wave Function Collapse (WFC) is a widely used tile-based algorithm in procedural content generation, including textures, objects, and scenes. However, the current WFC algorithm and related research lack the ability to generate commercialized large-scale or infinite content due to constraint conflict and time complexity costs. This paper proposes a Nested WFC (N-WFC) algorithm framework to reduce time complexity. To avoid conflict and backtracking problems, we offer a complete and sub-complete tileset preparation strategy, which requires only a small number of tiles to generate aperiodic and deterministic infinite content. We also introduce the weight-brush system that combines N-WFC and sub-complete tileset, proving its suitability for game design. Our contribution addresses WFC's challenge in massive content generation and provides a theoretical basis for implementing concrete games.Comment: This paper is accepted by IEEE Conference on Games 2023 (nomination of the Best Paper Award

Poly[[diaqua­bis(μ2-isonicotinato-κ2 N:O)bis­(μ3-isonicotinato-κ3 N:O:O′)neodymium(III)disilver(I)] nitrate monohydrate]

In the title complex, {[Ag2Nd(C6H4NO2)4(H2O)2]NO3·H2O}n, the NdIII ion is coordinated by eight O atoms from six isonicotinate ligands and two water mol­ecules in a distorted square anti­prismatic geometry. Each AgI ion is coordinated by two N atoms from two different isonicotinate ligands. The crystal structure exhibits a two-dimensional heterometallic polymeric layer. O—H⋯O hydrogen bonds involving the coordinated and uncoordinated water mol­ecules and intra­layer π–π inter­actions between the pyridine rings [centroid–centroid distances = 3.571 (2) and 3.569 (2) Å] are observed. Each layer inter­acts with two neighboring ones via Ag⋯O(H2O) contacts and inter­layer π–π inter­actions [centroid–centroid distances = 3.479 (3) to 3.530 (3) Å], leading to a three-dimensional supra­molecular network

Poly[[bis(μ2-4-amino­benzene­sul­fon­ato-κ2 N:O)diaqua­manganese(II)] dihydrate]

The title compound, {[Mn(NH2C6H4SO3)2(H2O)2]·2H2O}n, was prepared under mild hydro­thermal conditions. The unique MnII ion is located on a crystallographic inversion center and is coordinated by two –NH2 and two –SO3 groups from four 4-amino­benzene­sulfonate ligands and by two water mol­ecules in the axial positions, forming a slightly distorted octa­hedral coordination environment. The 4-amino­benzene­sulfonate anions behave as μ2-bridging ligands to produce a two-dimensional structure. In the crystal structure, inter­molecular N—H⋯O, O—H⋯O and C—H⋯O hydrogen bonds link the layers into a three-dimensional network

Legal Consideration of Recognizing Dual Nationality in China

Currently, China adopts the principle of non-recognition of dual nationality. However, with the continuous development of society, and increasingly frequent international cooperation and exchanges, Chinese emigrants abroad are crying for state to recognize dual nationality system. And also, the issue of dual nationality has triggered a fierce debate in China. Under new situation in China, limited or targeted recognizing dual nationality meets the requirements of the law and applies theory to practice. China should make appropriate adaptations to the nationality policy so as to meet the demands of current economic and social development better.Key words: Dual nationality; Nationality law; Reciprocal principle; Overseas ChineseRésumé Actuellement, la loi de la naturalisation n’approuve pas la double nationalités. Cependant, avec le développement sans cesse de notre société, l’augmentation de jour en jour de la collaboration et l’échange de la communication avec l’international, La demande des immigrants qui sont des chinois d’origine pour la réforme d’approuvement de la Double nationalités ne cesse de se croitre, le sujet de la Double Nationalité, ce sujet de la Double nationalité a également entrainer des discussions animées. La Chine sous la nouvelle forme, l’approuvement de la double nationalités est limité ou visée, mais ce dernier est conformé aux exigences judicaires et l’application de la pratique. La Chine devrait adjuster un peu ses réformes, afin de mieux s’adapter aux besoins de l’ère du developpement de la société et de l’économie d’actelle.Mots clés: D o u b l e n a t i o n a l i t é s ; L o i d e l a naturalisation; Principe égale; Chinois d’étrange

Diffusion basis spectrum imaging detects axonal loss after transient dexamethasone treatment in optic neuritis mice

Optic neuritis is a frequent first symptom of multiple sclerosis (MS) for which corticosteroids are a widely employed treatment option. The Optic Neuritis Treatment Trial (ONTT) reported that corticosteroid treatment does not improve long-term visual acuity, although the evolution of underlying pathologies is unclear. In this study, we employed non-invasive diffusion basis spectrum imaging (DBSI)-derived fiber volume to quantify 11% axonal loss 2 months after corticosteroid treatment (vs. baseline) in experimental autoimmune encephalomyelitis mouse optic nerves affected by optic neuritis. Longitudinal DBSI was performed at baseline (before immunization), after a 2-week corticosteroid treatment period, and 1 and 2 months after treatment, followed by histological validation of neuropathology. Pathological metrics employed to assess the optic nerve revealed axonal protection and anti-inflammatory effects of dexamethasone treatment that were transient. Two months after treatment, axonal injury and loss were indistinguishable between PBS- and dexamethasone-treated optic nerves, similar to results of the human ONTT. Our findings in mice further support that corticosteroid treatment alone is not sufficient to prevent eventual axonal loss in ON, and strongly support the potential of DBSI as a