Reflected Schr\"odinger Bridge for Constrained Generative Modeling

Diffusion models have become the go-to method for large-scale generative models in real-world applications. These applications often involve data distributions confined within bounded domains, typically requiring ad-hoc thresholding techniques for boundary enforcement. Reflected diffusion models (Lou23) aim to enhance generalizability by generating the data distribution through a backward process governed by reflected Brownian motion. However, reflected diffusion models may not easily adapt to diverse domains without the derivation of proper diffeomorphic mappings and do not guarantee optimal transport properties. To overcome these limitations, we introduce the Reflected Schrodinger Bridge algorithm: an entropy-regularized optimal transport approach tailored for generating data within diverse bounded domains. We derive elegant reflected forward-backward stochastic differential equations with Neumann and Robin boundary conditions, extend divergence-based likelihood training to bounded domains, and explore natural connections to entropic optimal transport for the study of approximate linear convergence - a valuable insight for practical training. Our algorithm yields robust generative modeling in diverse domains, and its scalability is demonstrated in real-world constrained generative modeling through standard image benchmarks

High-capacity quantum secure direct communication based on quantum hyperdense coding with hyperentanglement

We present a quantum hyperdense coding protocol with hyperentanglement in polarization and spatial-mode degrees of freedom of photons first and then give the details for a quantum secure direct communication (QSDC) protocol based on this quantum hyperdense coding protocol. This QSDC protocol has the advantage of having a higher capacity than the quantum communication protocols with a qubit system. Compared with the QSDC protocol based on superdense coding with $d$-dimensional systems, this QSDC protocol is more feasible as the preparation of a high-dimension quantum system is more difficult than that of a two-level quantum system at present.Comment: 5 pages, 2 figur

Genome-scale analysis and comparison of gene expression profiles in developing and germinated pollen in Oryza sativa

<p>Abstract</p> <p>Background</p> <p>Pollen development from the microspore involves a series of coordinated cellular events, and the resulting mature pollen has a specialized function to quickly germinate, produce a polar-growth pollen tube derived from the vegetative cell, and deliver two sperm cells into the embryo sac for double fertilization. The gene expression profiles of developing and germinated pollen have been characterised by use of the eudicot model plant <it>Arabidopsis</it>. Rice, one of the most important cereal crops, has been used as an excellent monocot model. A comprehensive analysis of transcriptome profiles of developing and germinated pollen in rice is important to understand the conserved and diverse mechanism underlying pollen development and germination in eudicots and monocots.</p> <p>Results</p> <p>We used Affymetrix GeneChip^®Rice Genome Array to comprehensively analyzed the dynamic changes in the transcriptomes of rice pollen at five sequential developmental stages from microspores to germinated pollen. Among the 51,279 transcripts on the array, we found 25,062 pollen-preferential transcripts, among which 2,203 were development stage-enriched. The diversity of transcripts decreased greatly from microspores to mature and germinated pollen, whereas the number of stage-enriched transcripts displayed a "U-type" change, with the lowest at the bicellular pollen stage; and a transition of overrepresented stage-enriched transcript groups associated with different functional categories, which indicates a shift in gene expression program at the bicellular pollen stage. About 54% of the now-annotated rice F-box protein genes were expressed preferentially in pollen. The transcriptome profile of germinated pollen was significantly and positively correlated with that of mature pollen. Analysis of expression profiles and coexpressed features of the pollen-preferential transcripts related to cell cycle, transcription, the ubiquitin/26S proteasome system, phytohormone signalling, the kinase system and defense/stress response revealed five expression patterns, which are compatible with changes in major cellular events during pollen development and germination. A comparison of pollen transcriptomes between rice and <it>Arabidopsis </it>revealed that 56.6% of the rice pollen preferential genes had homologs in <it>Arabidopsis </it>genome, but 63.4% of these homologs were expressed, with a small proportion being expressed preferentially, in <it>Arabidopsis </it>pollen. Rice and <it>Arabidopsis </it>pollen had non-conservative transcription factors each.</p> <p>Conclusions</p> <p>Our results demonstrated that rice pollen expressed a set of reduced but specific transcripts in comparison with vegetative tissues, and the number of stage-enriched transcripts displayed a "U-type" change during pollen development, with the lowest at the bicellular pollen stage. These features are conserved in rice and <it>Arabidopsis</it>. The shift in gene expression program at the bicellular pollen stage may be important to the transition from earlier cell division to later pollen maturity. Pollen at maturity pre-synthesized transcripts needed for germination and early pollen tube growth. The transcription regulation associated with pollen development would have divergence between the two species. Our results also provide novel insights into the molecular program and key components of the regulatory network regulating pollen development and germination.</p

Shock Diffraction by Convex Cornered Wedges for the Nonlinear Wave System

We are concerned with rigorous mathematical analysis of shock diffraction by two-dimensional convex cornered wedges in compressible fluid flow governed by the nonlinear wave system. This shock diffraction problem can be formulated as a boundary value problem for second-order nonlinear partial differential equations of mixed elliptic-hyperbolic type in an unbounded domain. It can be further reformulated as a free boundary problem for nonlinear degenerate elliptic equations of second order. We establish a first global theory of existence and regularity for this shock diffraction problem. In particular, we establish that the optimal regularity for the solution is $C^{0,1}$ across the degenerate sonic boundary. To achieve this, we develop several mathematical ideas and techniques, which are also useful for other related problems involving similar analytical difficulties.Comment: 50 pages;7 figure

Broad-lined type Ic supernova iPTF16asu: A challenge to all popular models

It is well-known that ordinary supernovae (SNe) are powered by 56Ni cascade decay. Broad-lined type Ic SNe (SNe Ic-BL) are a subclass of SNe that are not all exclusively powered by 56Ni decay. It was suggested that some SNe Ic-BL are powered by magnetar spin-down. iPTF16asu is a peculiar broad-lined type Ic supernova discovered by the intermediate Palomar Transient Factory. With a rest-frame rise time of only 4 days, iPTF16asu challenges the existing popular models, for example, the radioactive heating (56Ni-only) and the magnetar+56Ni models. Here we show that this rapid rise could be attributed to interaction between the SN ejecta and a pre-existing circumstellar medium ejected by the progenitor during its final stages of evolution, while the late-time light curve can be better explained by energy input from a rapidly spinning magnetar. This model is a natural extension to the previous magnetar model. The mass-loss rate of the progenitor and ejecta mass are consistent with a progenitor that experienced a common envelope evolution in a binary. An alternative model for the early rapid rise of the light curve is the cooling of a shock propagating into an extended envelope of the progenitor. It is difficult at this stage to tell which model (interaction+magnetar+56Ni or cooling+magnetar+56Ni) is better for iPTF16asu. However, it is worth noting that the inferred envelope mass in the cooling+magnetar+56Ni is very high.Comment: 11 pages, 4 figures, 3 table

Probabilistic teleportation of unknown two-particle state via POVM

We propose a scheme for probabilistic teleportation of unknown two-particle state with partly entangled four-particle state via POVM. In this scheme the teleportation of unknown two-particle state can be realized with certain probability by performing two Bell state measurements, a proper POVM and a unitary transformation.Comment: 5 pages, no figur

Efficient inhibition of lung cancer in murine model by plasmid-encoding VEGF short hairpin RNA in combination with low-dose DDP

<p>Abstract</p> <p>Background</p> <p>VEGF is a well-validated target for antiangiogenic intervention in cancer. To date, RNAi technology has been proven to be a promising approach for targeted therapy. DDP is frequently used as a first-line drug in chemotherapy for lung cancer but usually causes severe toxicity. In this study, we investigated a novel strategy of administering and combining RNAi mediated VEGF-targeted therapy with DDP for treatment of lung cancer, with the aim of increasing efficacy and decreasing toxicity.</p> <p>Methods</p> <p>In this study, a plasmid encoding VEGF shRNA was constructed to knockdown VEGF both in vitro and in vivo. In vitro, specificity and potency of the targeting sequence were validated in A549 lung adenocarcinoma cells by RT-PCR and ELISA assays. In vivo, therapy experiments were conducted on nude mice bearing A549 xenograft tumors. The VEGF shRNA expressing plasmids were administered systemically in combination with low-dose DDP on a frequent basis. The tumor volume and weight were measured. MVD, the number of apoptotic cells and proliferation index in tumor tissues were assessed by CD31, TUNEL and PCNA immunostaining.</p> <p>Results</p> <p>The VEGF shRNA was highly effective in attenuating VEGF expression both in vitro and in vivo. The treatment with the VEGF shRNA alone reduced the mean tumor weight by 49.40% compared with the blank control (P < 0.05). The treatment with the VEGF shRNA plus DDP yielded maximal benefits by reducing the mean tumor weight by 83.13% compared with the blank control (P < 0.01). The enhanced antitumor efficacy was associated with decreased angiogenesis and increased induction of apoptosis.</p> <p>Conclusions</p> <p>Our study demonstrated synergistic antitumor activity of combined VEGF shRNA expressing plasmids and low-dose DDP with no overt toxicity, suggesting potential applications of the combined approach in the treatment of lung cancer.</p