A Nonlinear Elliptic PDE with Two Sobolev-Hardy Critical Exponents

In this paper, we consider the following PDE involving two Sobolev-Hardy critical exponents, \label{0.1} {& \Delta u + \lambda\frac{u^{2^*(s_1)-1}}{|x|^{s_1}} + \frac{u^{2^*(s_2)-1}}{|x|^{s_2}} =0 \text{in} \Omega, & u=0 \qquad \text{on} \Omega, where $0 \le s_2 < s_1 \le 2$, $0 \ne \lambda \in \Bbb R$ and $0 \in \partial \Omega$. The existence (or nonexistence) for least-energy solutions has been extensively studied when $s_1=0$ or $s_2=0$. In this paper, we prove that if $0< s_2 < s_1 <2$ and the mean curvature of $\partial \Omega$ at 0 $H(0)<0$, then \eqref{0.1} has a least-energy solution. Therefore, this paper has completed the study of \eqref{0.1} for the least-energy solutions. We also prove existence or nonexistence of positive entire solutions of \eqref{0.1} with \Omega =\rn under different situations of $s_1, s_2$ and $\lambda$

Automating Object Transformations for Dynamic Software Updating via Online Execution Synthesis

Dynamic software updating (DSU) is a technique to upgrade a running software system on the fly without stopping the system. During updating, the runtime state of the modified components of the system needs to be properly transformed into a new state, so that the modified components can still correctly interact with the rest of the system. However, the transformation is non-trivial to realize due to the gap between the low-level implementations of two versions of a program. This paper presents AOTES, a novel approach to automating object transformations for dynamic updating of Java programs. AOTES bridges the gap by abstracting the old state of an object to a history of method invocations, and re-invoking the new version of all methods in the history to get the desired new state. AOTES requires no instrumentation to record any data and thus has no overhead during normal execution. We propose and implement a novel technique that can synthesize an equivalent history of method invocations based on the current object state only. We evaluated AOTES on software updates taken from Apache Commons Collections, Tomcat, FTP Server and SSHD Server. Experimental results show that AOTES successfully handled 51 of 61 object transformations of 21 updated classes, while two state-of-the-art approaches only handled 11 and 6 of 61, respectively

DPAC: An infrastructure for dynamic program analysis of concurrency Java programs

ABSTRACT Concurrency programs are hard to test or debug due to their nondeterministic nature. Existing dynamic program analysis approaches tried to address this by carefully examine a recorded execution trace. However, developing such analysis tools is complicated, requiring to take care of many tedious implementation details, and comparing and evaluating different analysis approaches are also subject to various biases, due to lack of a common base platform. This motivates us to design DPAC, an infrastructure that support in building dynamic program analysis tools for concurrency Java programs. DPAC takes events and their various processing mechanisms as its underlying model to facilitate monitoring and manipulation of program executions as required by dynamic program analysis. Various analysis tools can be implemented by customizing their required event types and processing mechanisms. We show two concrete case studies how our DPAC helps building existing dynamic program analysis approaches, as well as tuning subtle implementation details for supporting customized function implementation and code transformation

Programming by Example Made Easy

Programming by example (PBE) is an emerging programming paradigm that automatically synthesizes programs specified by user-provided input-output examples. Despite the convenience for end-users, implementing PBE tools often requires strong expertise in programming language and synthesis algorithms. Such a level of knowledge is uncommon among software developers. It greatly limits the broad adoption of PBE by the industry. To facilitate the adoption of PBE techniques, we propose a PBE framework called Bee, which leverages an "entity-action" model based on relational tables to ease PBE development for a wide but restrained range of domains. Implementing PBE tools with Bee only requires adapting domain-specific data entities and user actions to tables, with no need to design a domain-specific language or an efficient synthesis algorithm. The synthesis algorithm of Bee exploits bidirectional searching and constraint-solving techniques to address the challenge of value computation nested in table transformation. We evaluated Bee's effectiveness on 64 PBE tasks from three different domains and usability with a human study of 12 participants. Evaluation results show that Bee is easier to learn and use than the state-of-the-art PBE framework, and the bidirectional algorithm achieves comparable performance to domain-specifically optimized synthesizers.Comment: Accepted by ACM Transactions on Software Engineering and Methodolog

Optical Limiting and Theoretical Modelling of Layered Transition Metal Dichalcogenide Nanosheets

Nonlinear optical property of transition metal dichalcogenide (TMDC) nanosheet dispersions, including MoS2, MoSe2, WS2, and WSe2, was performed by using Z-scan technique with ns pulsed laser at 1064 nm and 532 nm. The results demonstrate that the TMDC dispersions exhibit significant optical limiting response at 1064 nm due to nonlinear scattering, in contrast to the combined effect of both saturable absorption and nonlinear scattering at 532 nm. Selenium compounds show better optical limiting performance than that of the sulfides in the near infrared. A liquid dispersion system based theoretical modelling is proposed to estimate the number density of the nanosheet dispersions, the relationship between incident laser fluence and the size of the laser generated micro-bubbles, and hence the Mie scattering-induced broadband optical limiting behavior in the TMDC dispersions

Transcript-indexed ATAC-seq for precision immune profiling.

T cells create vast amounts of diversity in the genes that encode their T cell receptors (TCRs), which enables individual clones to recognize specific peptide-major histocompatibility complex (MHC) ligands. Here we combined sequencing of the TCR-encoding genes with assay for transposase-accessible chromatin with sequencing (ATAC-seq) analysis at the single-cell level to provide information on the TCR specificity and epigenomic state of individual T cells. By using this approach, termed transcript-indexed ATAC-seq (T-ATAC-seq), we identified epigenomic signatures in immortalized leukemic T cells, primary human T cells from healthy volunteers and primary leukemic T cells from patient samples. In peripheral blood CD4+ T cells from healthy individuals, we identified cis and trans regulators of naive and memory T cell states and found substantial heterogeneity in surface-marker-defined T cell populations. In patients with a leukemic form of&nbsp;cutaneous T cell lymphoma, T-ATAC-seq enabled identification of leukemic and nonleukemic regulatory pathways in T cells from the same individual by allowing separation of the signals that arose from the malignant clone from the background T cell noise. Thus, T-ATAC-seq is a new tool that enables analysis of epigenomic landscapes in clonal T cells and should be valuable for studies of T cell malignancy, immunity and immunotherapy

The role of Xist-mediated Polycomb recruitment in the initiation of X-chromosome inactivation.

Xist RNA has been established as the master regulator of X-chromosome inactivation (XCI) in female eutherian mammals, but its mechanism of action remains unclear. By creating novel Xist-inducible mutants at the endogenous locus in male mouse embryonic stem (ES) cells, we dissect the role of the conserved A-B-C-F repeats in the initiation of XCI. We find that transcriptional silencing can be largely uncoupled from Polycomb repressive complex 1 and complex 2 (PRC1/2) recruitment, which requires B and C repeats. Xist ΔB+C RNA specifically loses interaction with PCGF3/5 subunits of PRC1, while binding of other Xist partners is largely unaffected. However, a slight relaxation of transcriptional silencing in Xist ΔB+C indicates a role for PRC1/2 proteins in early stabilization of gene repression. Distinct modules within the Xist RNA are therefore involved in the convergence of independent chromatin modification and gene repression pathways. In this context, Polycomb recruitment seems to be of moderate relevance in the initiation of silencing

Heisenberg-limited quantum metrology using 100-photon Fock states

Quantum metrology has emerged as a promising avenue for surpassing the limitations of classical mechanics in high-precision measurements. However, the practical implementation of quantum metrology is hindered by the challenges of manipulating exotic quantum states in large systems. Here, we propose and demonstrate a hardware-efficient approach to achieve Heisenberg-limited quantum metrology using large photon-number Fock states. We have developed a programmable photon number filter that efficiently generates Fock states with up to 100 photons in a high-quality superconducting microwave cavity. Using these highly nontrivial states in displacement and phase measurements, we demonstrate a precision scaling close to the Heisenberg limit and achieve a maximum metrological gain of up to 14.8 dB. Our hardware-efficient quantum metrology can be extended to mechanical and optical systems and provides a practical solution for high metrological gain in bosonic quantum systems, promising potential applications in radiometry and the search for new particles.Comment: Main text: 10 pages, 4 figures; Supplement: 16 pages, 9 figures, 1 tabl

Short Paper: Automatic Configuration for an Optimal Channel Protection in Virtualized Networks

Data confidentiality, integrity and authentication are security properties which are often enforced with the generation of secure channels, such as Virtual Private Networks, over unreliable network infrastructures. Traditionally, the configuration of the systems responsible of encryption operations is performed manually. However, the advent of software-based paradigms, such as Software-Defined Networking and Network Functions Virtualization, has introduced new arms races. In particular, even though network management has become more flexible, the increased complexity of virtual networks is making manual operations unfeasible and leading to errors which open the path to a large number of cyber attacks. A possible solution consists in reaching a trade-off between flexibility and complexity, by automatizing the configuration of the channel protection systems through policy refinement. In view of these considerations, this paper proposes a preliminary study for an innovative methodology to automatically allocate and configure channel protection systems in virtualized networks. The proposed approach would be based on the formulation of a MaxSMT problem and it would be the first to combine automation, formal verification and optimality in a single technique

Beating the break-even point with a discrete-variable-encoded logical qubit

Quantum error correction (QEC) aims to protect logical qubits from noises by utilizing the redundancy of a large Hilbert space, where an error, once it occurs, can be detected and corrected in real time. In most QEC codes, a logical qubit is encoded in some discrete variables, e.g., photon numbers. Such encoding schemes make the codewords orthogonal, so that the encoded quantum information can be unambiguously extracted after processing. Based on such discrete-variable encodings, repetitive QEC demonstrations have been reported on various platforms, but there the lifetime of the encoded logical qubit is still shorter than that of the best available physical qubit in the entire system, which represents a break-even point that needs to be surpassed for any QEC code to be of practical use. Here we demonstrate a QEC procedure with a logical qubit encoded in photon-number states of a microwave cavity, dispersively coupled to an ancilla superconducting qubit. By applying a pulse featuring a tailored frequency comb to the ancilla, we can repetitively extract the error syndrome with high fidelity and perform error correction with feedback control accordingly, thereby exceeding the break-even point by about 16% lifetime enhancement. Our work illustrates the potential of the hardware-efficient discrete-variable QEC codes towards a reliable quantum information processor.Comment: Main text: 8 pages, 3 figures, 1 table; Supplement: 12 pages, 8 figures, 2 table