Conditional graph entropy as an alternating minimization problem

Conditional graph entropy is known to be the minimal rate for a natural functional compression problem with side information at the receiver. In this paper we show that it can be formulated as an alternating minimization problem, which gives rise to a simple iterative algorithm for numerically computing (conditional) graph entropy. This also leads to a new formula which shows that conditional graph entropy is part of a more general framework: the solution of an optimization problem over a convex corner. In the special case of graph entropy (i.e., unconditioned version) this was known due to Csisz\'ar, K\"orner, Lov\'asz, Marton, and Simonyi. In that case the role of the convex corner was played by the so-called vertex packing polytope. In the conditional version it is a more intricate convex body but the function to minimize is the same. Furthermore, we describe a dual problem that leads to an optimality check and an error bound for the iterative algorithm

A Hybrid Wireless Image Transmission Scheme with Diffusion

We propose a hybrid joint source-channel coding (JSCC) scheme, in which the conventional digital communication scheme is complemented with a generative refinement component to improve the perceptual quality of the reconstruction. The input image is decomposed into two components: the first is a coarse compressed version, and is transmitted following the conventional separation based approach. An additional component is obtained through the diffusion process by adding independent Gaussian noise to the input image, and is transmitted using DeepJSCC. The decoder combines the two signals to produce a high quality reconstruction of the source. Experimental results show that the hybrid design provides bandwidth savings and enables graceful performance improvement as the channel quality improves

Extending Context Window of Large Language Models via Semantic Compression

Transformer-based Large Language Models (LLMs) often impose limitations on the length of the text input to ensure the generation of fluent and relevant responses. This constraint restricts their applicability in scenarios involving long texts. We propose a novel semantic compression method that enables generalization to texts that are 6-8 times longer, without incurring significant computational costs or requiring fine-tuning. Our proposed framework draws inspiration from source coding in information theory and employs a pre-trained model to reduce the semantic redundancy of long inputs before passing them to the LLMs for downstream tasks. Experimental results demonstrate that our method effectively extends the context window of LLMs across a range of tasks including question answering, summarization, few-shot learning, and information retrieval. Furthermore, the proposed semantic compression method exhibits consistent fluency in text generation while reducing the associated computational overhead

A multimodal cell census and atlas of the mammalian primary motor cortex

ABSTRACT We report the generation of a multimodal cell census and atlas of the mammalian primary motor cortex (MOp or M1) as the initial product of the BRAIN Initiative Cell Census Network (BICCN). This was achieved by coordinated large-scale analyses of single-cell transcriptomes, chromatin accessibility, DNA methylomes, spatially resolved single-cell transcriptomes, morphological and electrophysiological properties, and cellular resolution input-output mapping, integrated through cross-modal computational analysis. Together, our results advance the collective knowledge and understanding of brain cell type organization: First, our study reveals a unified molecular genetic landscape of cortical cell types that congruently integrates their transcriptome, open chromatin and DNA methylation maps. Second, cross-species analysis achieves a unified taxonomy of transcriptomic types and their hierarchical organization that are conserved from mouse to marmoset and human. Third, cross-modal analysis provides compelling evidence for the epigenomic, transcriptomic, and gene regulatory basis of neuronal phenotypes such as their physiological and anatomical properties, demonstrating the biological validity and genomic underpinning of neuron types and subtypes. Fourth, in situ single-cell transcriptomics provides a spatially-resolved cell type atlas of the motor cortex. Fifth, integrated transcriptomic, epigenomic and anatomical analyses reveal the correspondence between neural circuits and transcriptomic cell types. We further present an extensive genetic toolset for targeting and fate mapping glutamatergic projection neuron types toward linking their developmental trajectory to their circuit function. Together, our results establish a unified and mechanistic framework of neuronal cell type organization that integrates multi-layered molecular genetic and spatial information with multi-faceted phenotypic properties

Conditional graph entropy as an alternating minimization problem

Conditional graph entropy is known to be the minimal rate for a natural functional compression problem with side information at the receiver. In this paper we show that it can be formulated as an alternating minimization problem, which gives rise to a simple iterative algorithm for numerically computing (conditional) graph entropy. This also leads to a new formula which shows that conditional graph entropy is part of a more general framework: the solution of an optimization problem over a convex corner. In the special case of graph entropy (i.e., unconditioned version) this was known due to Csisz´ar, K¨orner, Lov´asz, Marton, and Simonyi. In that case the role of the convex corner was played by the so-called vertex packing polytope. In the conditional version it is a more intricate convex body but the function to minimize is the same. Furthermore, we describe a dual problem that leads to an optimality check and an error bound for the iterative algorithm

Unsymmetrical Growth Synthesis of Nontraditional Dendrimers

Developing highly complex molecules is of great significance in science and technology. Here we present an unprecedented type of dendrimer assembled from linear ABB-type monomer. The construction of this nontraditional ramified architecture was facilely achieved through one simple convergent strategy established on the iridium-catalyzed cycloaddition of organic azides with internal 1-thioalkynes (IrAAC). By virtue of the unsymmetrically growing fashion in this process, diverse functional groups could be conveniently distributed on both of its exterior and interior layers. Syntheses of two dendrons from the cooperation of one linear alkyne motif with different azides were presented to demonstrate the efficiency and fidelity of this protocol. Post-modifications on their core or periphery were further conducted, resulting in diverse newly functionalized dendrimers with up to ~16.0 kDa molecular weight. The identity and purity of these unsymmetrical dendritic macromolecules were well confirmed by 1H NMR, MS and SEC analysis

Generalizing K\"orner's graph entropy to graphons

K\"orner introduced the notion of graph entropy in 1973 as the minimal code rate of a natural coding problem where not all pairs of letters can be distinguished in the alphabet. Later it turned out that it can be expressed as the solution of a minimization problem over the so-called vertex-packing polytope. In this paper we generalize this notion to graphons. We show that the analogous minimization problem provides an upper bound for graphon entropy. We also give a lower bound in the shape of a maximization problem. The main result of the paper is that for most graphons these two bounds actually coincide and hence precisely determine the entropy in question. Furthermore, graphon entropy has a nice connection to the fractional chromatic number and the fractional clique number

A Certificateless Anonymous Cross-Domain Authentication Scheme Assisted by Blockchain for Internet of Vehicles

With the development of the Internet of Things and the increase of intelligent vehicles, the Internet of Vehicles (IoVs) have been widely used in the information communication such as road and traffic conditions. However, heavy overhead of certificate management, high computing load of identity and message authentication, and the privacy disclosure of vehicle nodes have hindered the development of intelligent transportation. In this study, we propose a certificateless cross-domain anonymous authentication scheme based on blockchain for IoVs. Specifically, the vehicle identity information is authenticated by the first roadside unit (RSU), and transactions are recorded permanently and immutably in the blockchain to reduce the repeated authentication load of other RSUs. To achieve conditional privacy, the trusted authority (TA) generates pseudonyms for each registered user. The relation between the pseudonym and the real identity is kept confidential by the TA and only can only be revealed in case of disputes. Meanwhile, the private key of the vehicle is generated anonymously on the basis of certificateless technology and the pairing-free signature verification. Correctness and security proof demonstrate that our proposed scheme is provably secure and can withstand different types of attacks. A simulation environment has been built to test the packet loss rate and delay of messages in the network. Results show that the proposed scheme is more efficient than the related schemes

Investigation of the Effects of Glabridin on the Proliferation, Apoptosis, and Migration of the Human Colon Cancer Cell Lines SW480 and SW620 and Its Mechanism Based on Reverse Virtual Screening and Proteomics

Colon cancer is a relatively common malignant tumor of the digestive tract. Currently, most colon cancers originate from adenoma carcinogenesis. By screening various licorice flavonoids with anticancer effects, we found that glabridin (GBN) has a prominent anticolon cancer effect. First, we initially explored whether GBN can inhibit proliferation, migration, and invasion and induce apoptosis in SW480 and SW620 cells. Next, we exploited reverse virtual and proteomics technologies to screen out closely related target pathways on the basis of a drug and target database. At the same time, we constructed the structure of the GBN target pathway in colon cancer. We predicted that GBN can regulate the phosphatidylinositol 3-kinase (PI3K)–protein kinase B (AKT)–mammalian target of the rapamycin pathway (mTOR) pathway to fight colon cancer. Finally, through Western blot analysis and qRT-PCR, we verified that the expression levels of the PI3K, AKT, and mTOR proteins and genes in this pathway were significantly reduced after GBN administration. In short, the promising discovery of the anticolon cancer mechanism of GBN provides a reliable experimental basis for subsequent new drug development