Complex Behavior in the Dynamics of a Polymeric Biocomposite Material—“Liquid Wood”. Experimental and Theoretical Aspects

The purpose of the present paper is to analyze, both experimentally and theoretically, the behavior of the polymeric biocomposite generically known as “liquid wood”, trademarked as Arbofill. The experimental part refers to the mechanical performance in tension and compression, having as finality the possibility of using “liquid wood” as a material suitable for the rehabilitation of degraded wooden elements in civil structures (ex. use in historical buildings, monuments etc.,). The theoretical part refers to computer simulations regarding the mechanical behavior of “liquid wood” as well as to a theoretical model in the paradigm of motion, which describes the same behavior. This model is based on the hypothesis that “liquid wood” can be assimilated, both structurally and functionally, to a multifractal object, situation in which its entities are described through continuous, non-differentiable curves. Then, descriptions of the behavior of “liquid wood”, both in the Schrödinger-type and in hydrodynamic-type representations at various scale resolutions, become operational. Since in the hydrodynamic-type representation, the constitutive law of “liquid wood” can be highlighted, several operational procedures (Ricatti-type gauge, differential geometry in absolute space etc.,) will allow correlations between the present proposed model and the experimental data. The obtained results, both practical (81% bearing capacity in compression and 36% bearing capacity in tension, compared to control samples) and theoretical (validation of material performance in virtual environment simulations, stresses and strains correlations in a theoretical model) indicate that “liquid wood” could be used in the construction industry, as a potential rehabilitation material, but with more development clearly needed.

Ribaucour surfaces of harmonic type

We introduce the class of Ribaucour surfaces of harmonic type (in short HR-surfaces) that generalizes the Ribaucour surfaces related to a problem posed by Élie Cartan. We obtain a Weierstrass-type representation for these surfaces which depends on three holomorphic functions. As application, we classify the HR-surfaces of rotation, present examples of complete HR-surfaces of rotation with at most two isolated singularities and an example of a complete HR-surface of rotation with one catenoid type end and one planar end. Also, we present a 5-parameter family of cyclic HR-surfaces foliated by circles in non-parallel planes. Moreover, we classify the isothermic HR-surfaces with planar lines of curvature.

Unsupervised integration of single-cell multi-omics datasets with disparities in cell-type representation

Integrated analysis of multi-omics data allows the study of how different molecular views in the genome interact to regulate cellular processes; however, with a few exceptions, applying multiple sequencing assays on the same single cell is not possible. While recent unsupervised algorithms align single-cell multi-omic datasets, these methods have been primarily benchmarked on co-assay experiments rather than the more common single-cell experiments taken from separately sampled cell populations. Therefore, most existing methods perform subpar alignments on such datasets. Here, we improve our previous work Single Cell alignment using Optimal Transport (SCOT) by using unbalanced optimal transport to handle disproportionate cell-type representation and differing sample sizes across single-cell measurements. We show that our proposed method, SCOTv2, consistently yields quality alignments on five real-world single-cell datasets with varying cell-type proportions and is computationally tractable. Additionally, we extend SCOTv2 to integrate multiple ($M\geq2$) single-cell measurements and present a self-tuning heuristic process to select hyperparameters in the absence of any orthogonal correspondence information.

Response Ranking with Multi-types of Deep Interactive Representations in Retrieval-based Dialogues

Building an intelligent dialogue system with the ability to select a proper response according to a multi-turn context is challenging in three aspects: (1) the meaning of a context–response pair is built upon language units from multiple granularities (e.g., words, phrases, and sub-sentences, etc.); (2) local (e.g., a small window around a word) and long-range (e.g., words across the context and the response) dependencies may exist in dialogue data; and (3) the relationship between the context and the response candidate lies in multiple relevant semantic clues or relatively implicit semantic clues in some real cases. However, existing approaches usually encode the dialogue with mono-type representation and the interaction processes between the context and the response candidate are executed in a rather shallow manner, which may lead to an inadequate understanding of dialogue content and hinder the recognition of the semantic relevance between the context and response. To tackle these challenges, we propose a representation [ K ] -interaction [ L ] -matching framework that explores multiple types of deep interactive representations to build context-response matching models for response selection. Particularly, we construct different types of representations for utterance–response pairs and deepen them via alternate encoding and interaction. By this means, the model can handle the relation of neighboring elements, phrasal pattern, and long-range dependencies during the representation and make a more accurate prediction through multiple layers of interactions between the context–response pair. Experiment results on three public benchmarks indicate that the proposed model significantly outperforms previous conventional context-response matching models and achieve slightly better results than the BERT model for multi-turn response selection in retrieval-based dialogue systems.

Integrability of Riemann-Type Hydrodynamical Systems and Dubrovin’s Integrability Classification of Perturbed KdV-Type Equations

Dubrovin’s work on the classification of perturbed KdV-type equations is reanalyzed in detail via the gradient-holonomic integrability scheme, which was devised and developed jointly with Maxim Pavlov and collaborators some time ago. As a consequence of the reanalysis, one can show that Dubrovin’s criterion inherits important parts of the gradient-holonomic scheme properties, especially the necessary condition of suitably ordered reduction expansions with certain types of polynomial coefficients. In addition, we also analyze a special case of a new infinite hierarchy of Riemann-type hydrodynamical systems using a gradient-holonomic approach that was suggested jointly with M. Pavlov and collaborators. An infinite hierarchy of conservation laws, bi-Hamiltonian structure and the corresponding Lax-type representation are constructed for these systems.

CrimeVec—Exploring Spatial-Temporal Based Vector Representations of Urban Crime Types and Crime-Related Urban Regions

The traditional categorization of crime types relies on a hierarchical structure, from high-level categories to lower-level subtypes. This tree-based classification treats crime types as mutually independent when they do not branch from the same higher-level category, therefore lacking inter-category semantic relations. The issue then extends over crime distribution analysis of urban regions, often reporting statistics based on crime type counts, but neglecting implicit relations between different crime categories. Our study aims to fill this information gap, providing a more complete understanding of urban crime in both qualitative and quantitative terms. Specifically, we propose a vector-based crime type representation, constructed via unsupervised machine learning on temporal and geographic factors. The general idea is to define crime types as “related” if they often occur in the same area at the same time span, regardless of any initial hierarchical categorization. This opens to a new metric of comparison that goes beyond pre-defined structures, revealing hidden relationships between crime types by generating a vector space in a completely data-driven manner. Crime types are represented as points in this space, and their relative distances disclose stronger or weaker semantic relations. A direct application on urban crime distribution analysis stands out in the form of visualization tools for intuitive data investigations and convenient comparison measures on composite vectors of urban regions. Meaningful insights on crime type distributions and a better understanding of urban crime characteristics determine a valuable asset to urban management and development.