Optimal Spreading Sequences for Chaos-Based Communication Systems

As a continuation from [2], some higherorder statistical dependency aspects of chaotic spreading sequences used in communication systems are presented. The autocorrelation function (ACF) of the mean-adjusted squares, termed the quadratic autocorrelation function, forms the building block of nonlinear dependence assessment of the family of spreading sequences under investigation. Explicit results are provided for the theoretical lower bound, the so-called Fr´echet lower bound, of the quadratic ACF of that family. A method for producing a spreading sequence which attains the Fr´echet bound is introduced

Higher order Dependency of Chaotic Maps

Some higher-order statistical dependency aspects of chaotic maps are presented. The autocorrelation function (ACF) of the mean-adjusted squares, termed the quadratic autocorrelation function, is used to access nonlinear dependence of the maps under consideration. A simple analytical expression for the quadratic ACF has been found in the case of fully stretching piece-wise linear maps. A minimum bit energy criterion from chaos communications is used to motivate choosing maps with strong negative quadratic autocorrelation. A particular map in this class, a so-called deformed circular map, is derived which performs better than other well-known chaotic maps when used for spreading sequences in chaotic shift-key communication systems

Combinatorial Complexes:Bridging the Gap Between Cell Complexes and Hypergraphs

Graph-based signal processing techniques have become essential for handling data in non-Euclidean spaces. However, there is a growing awareness that these graph models might need to be expanded into ‘higher-order’ domains to effectively represent the complex relations found in high-dimensional data. Such higher-order domains are typically modeled either as hypergraphs, or as simplicial, cubical or other cell complexes. In this context, cell complexes are often seen as a subclass of hypergraphs with additional algebraic structure that can be exploited, e.g., to develop a spectral theory. In this article, we promote an alternative perspective. We argue that hypergraphs and cell complexes emphasize different types of relations, which may have different utility depending on the application context. Whereas hypergraphs are effective in modeling set-type, multi-body relations between entities, cell complexes provide an effective means to model hierarchical, interior-to-boundary type relations. We discuss the relative advantages of these two choices and elaborate on the previously introduced concept of a combinatorial complex that enables co-existing set-type andhierarchical relations. Finally, we provide a brief numerical experiment to demonstrate that this modelling flexibility can be advantageous in learning tasks

TopoBenchmarkX: A Framework for Benchmarking Topological Deep Learning

This work introduces TopoBenchmarkX, a modular open-source library designed to standardize benchmarking and accelerate research in Topological Deep Learning (TDL). TopoBenchmarkX maps the TDL pipeline into a sequence of independent and modular components for data loading and processing, as well as model training, optimization, and evaluation. This modular organization provides flexibility for modifications and facilitates the adaptation and optimization of various TDL pipelines. A key feature of TopoBenchmarkX is that it allows for the transformation and lifting between topological domains. This enables, for example, to obtain richer data representations and more fine-grained analyses by mapping the topology and features of a graph to higher-order topological domains such as simplicial and cell complexes. The range of applicability of TopoBenchmarkX is demonstrated by benchmarking several TDL architectures for various tasks and datasets

Combinatorial drug screening identifies Ewing sarcoma-specific sensitivities

Improvements in survival for Ewing sarcoma pediatric and adolescent patients have been modest over the past 20 years. Combinations of anticancer agents endure as an option to overcome resistance to single treatments caused by compensatory pathways. Moreover, combinations are thought to lessen any associated adverse side effects through reduced dosing, which is particularly important in childhood tumors. Using a parallel phenotypic combinatorial screening approach of cells derived from three pediatric tumor types, we identified Ewing sarcoma-specific interactions of a diverse set of targeted agents including approved drugs. We were able to retrieve highly synergistic drug combinations specific for Ewing sarcoma and identified signaling processes important for Ewing sarcoma cell proliferation determined by EWS-FLI1 We generated a molecular target profile of PKC412, a multikinase inhibitor with strong synergistic propensity in Ewing sarcoma, revealing its targets in critical Ewing sarcoma signaling routes. Using a multilevel experimental approach including quantitative phosphoproteomics, we analyzed the molecular rationale behind the disease-specific synergistic effect of simultaneous application of PKC412 and IGF1R inhibitors. The mechanism of the drug synergy between these inhibitors is different from the sum of the mechanisms of the single agents. The combination effectively inhibited pathway crosstalk and averted feedback loop repression, in EWS-FLI1-dependent manner. Mol Cancer Ther; 16(1); 88-101. ©2016 AACR

Topological Deep Learning: Going Beyond Graph Data

Topological deep learning is a rapidly growing field that pertains to the development of deep learning models for data supported on topological domains such as simplicial complexes, cell complexes, and hypergraphs, which generalize many domains encountered in scientific computations. In this paper, we present a unifying deep learning framework built upon a richer data structure that includes widely adopted topological domains. Specifically, we first introduce combinatorial complexes, a novel type of topological domain. Combinatorial complexes can be seen as generalizations of graphs that maintain certain desirable properties. Similar to hypergraphs, combinatorial complexes impose no constraints on the set of relations. In addition, combinatorial complexes permit the construction of hierarchical higher-order relations, analogous to those found in simplicial and cell complexes. Thus, combinatorial complexes generalize and combine useful traits of both hypergraphs and cell complexes, which have emerged as two promising abstractions that facilitate the generalization of graph neural networks to topological spaces. Second, building upon combinatorial complexes and their rich combinatorial and algebraic structure, we develop a general class of message-passing combinatorial complex neural networks (CCNNs), focusing primarily on attention-based CCNNs. We characterize permutation and orientation equivariances of CCNNs, and discuss pooling and unpooling operations within CCNNs in detail. Third, we evaluate the performance of CCNNs on tasks related to mesh shape analysis and graph learning. Our experiments demonstrate that CCNNs have competitive performance as compared to state-of-the-art deep learning models specifically tailored to the same tasks. Our findings demonstrate the advantages of incorporating higher-order relations into deep learning models in different applications

New genetic loci link adipose and insulin biology to body fat distribution.

Body fat distribution is a heritable trait and a well-established predictor of adverse metabolic outcomes, independent of overall adiposity. To increase our understanding of the genetic basis of body fat distribution and its molecular links to cardiometabolic traits, here we conduct genome-wide association meta-analyses of traits related to waist and hip circumferences in up to 224,459 individuals. We identify 49 loci (33 new) associated with waist-to-hip ratio adjusted for body mass index (BMI), and an additional 19 loci newly associated with related waist and hip circumference measures (P < 5 × 10(-8)). In total, 20 of the 49 waist-to-hip ratio adjusted for BMI loci show significant sexual dimorphism, 19 of which display a stronger effect in women. The identified loci were enriched for genes expressed in adipose tissue and for putative regulatory elements in adipocytes. Pathway analyses implicated adipogenesis, angiogenesis, transcriptional regulation and insulin resistance as processes affecting fat distribution, providing insight into potential pathophysiological mechanisms

ICML 2023 Topological Deep Learning Challenge:Design and Results

This paper presents the computational challenge on topological deep learning that was hosted within the ICML 2023 Workshop on Topology and Geometry in Machine Learning. The competition asked participants to provide open-source implementations of topological neural networks from the literature by contributing to the python packages TopoNetX (data processing) and TopoModelX (deep learning). The challenge attracted twenty-eight qualifying submissions in its two-month duration. This paper describes the design of the challenge and summarizes its main findings

A genome-wide screen for interactions reveals a new locus on 4p15 modifying the effect of waist-to-hip ratio on total cholesterol.

Recent genome-wide association (GWA) studies described 95 loci controlling serum lipid levels. These common variants explain and#8764;25% of the heritability of the phenotypes. To date, no unbiased screen for gene-environment interactions for circulating lipids has been reported. We screened for variants that modify the relationship between known epidemiological risk factors and circulating lipid levels in a meta-analysis of genome-wide association (GWA) data from 18 population-based cohorts with European ancestry (maximum N=32,225). We collected 8 further cohorts (N=17,102) for replication, and rs6448771 on 4p15 demonstrated genome-wide significant interaction with waist-to-hip-ratio (WHR) on total cholesterol (TC) with a combined P-value of 4.79x10-9. There were two potential candidate genes in the region, PCDH7 and CCKAR, with differential expression levels for rs6448771 genotypes in adipose tissue. The effect of WHR on TC was strongest for individuals carrying two copies of G allele, for whom a one standard deviation (sd) difference in WHR corresponds to 0.19 sd difference in TC concentration, while for A allele homozygous the difference was 0.12 sd. Our findings may open up possibilities for targeted intervention strategies for people characterized by specific genomic profiles. However, more refined measures of both body-fat distribution and metabolic measures are needed to understand how their joint dynamics are modified by the newly found locus

Zero variance differential geometric markov chain monte carlo algorithms

Differential geometric Markov Chain Monte Carlo (MCMC) strategies exploit the geometry of the target to achieve convergence in fewer MCMC iterations at the cost of increased computing time for each of the iterations. Such computational complexity is regarded as a potential shortcoming of geometric MCMC in practice. This paper suggests that part of the additional computing required by Hamiltonian Monte Carlo and Metropolis adjusted Langevin algorithms produces elements that allow concurrent implementation of the zero variance reduction technique for MCMC estimation. Therefore, zero variance geometric MCMC emerges as an inherently unified sampling scheme, in the sense that variance reduction and geometric exploitation of the parameter space can be performed simultaneously without exceeding the computational requirements posed by the geometric MCMC scheme alone. A MATLAB package is provided, which implements a generic code framework of the combined methodology for a range of models. © 2014 International Society for Bayesian Analysis