Lieb–Robinson bounds and growth of correlations in Bose mixtures

For a mixture of interacting Bose gases initially prepared in a regime of condensation (uncorrelation), it is proved that in the course of the time evolution observables of disjoint sets of particles of each species have correlation functions that remain asymptotically small in the total number of particles and display a controlled growth in time. This is obtained by means of ad hoc estimates of Lieb–Robinson type on the propagation of the interaction, established here for the multi-component Bose mixture.

On Weighted Pál Type (0,2)-interpolation on the Unit Circle

In this paper, we study the explicit representation of weighted Pál-type (0,2)-interpolation on two pairwise disjoint sets of nodes on the unit circle, which are obtained by projecting vertically the zeros of (1−x2)Pn(x) and Pn′′(x) respectively, where Pn(x) stands for nth Legendre polynomial.AMS Classification (2000): 41A05, 30E10.

Complexity Assessments for Decidable Fragments of Set Theory. I: A Taxonomy for the Boolean Case*

We report on an investigation aimed at identifying small fragments of set theory (typically, sublanguages of Multi-Level Syllogistic) endowed with polynomial-time satisfiability decision tests, potentially useful for automated proof verification. Leaving out of consideration the membership relator ∈ for the time being, in this paper we provide a complete taxonomy of the polynomial and the NP-complete fragments involving, besides variables intended to range over the von Neumann set-universe, the Boolean operators ∪ ∩ \, the Boolean relators ⊆, ⊈,=, ≠, and the predicates ‘• = Ø’ and ‘Disj(•, •)’, meaning ‘the argument set is empty’ and ‘the arguments are disjoint sets’, along with their opposites ‘• ≠ Ø and ‘¬Disj(•, •)’. We also examine in detail how to test for satisfiability the formulae of six sample fragments: three sample problems are shown to be NP-complete, two to admit quadratic-time decision algorithms, and one to be solvable in linear time.

Distributed Graph Processing System and Processing-in-memory Architecture with Precise Loop-carried Dependency Guarantee

To hide the complexity of the underlying system, graph processing frameworks ask programmers to specify graph computations in user-defined functions (UDFs) of graph-oriented programming model. Due to the nature of distributed execution, current frameworks cannot precisely enforce the semantics of UDFs, leading to unnecessary computation and communication. It exemplifies a gap between programming model and runtime execution. This article proposes novel graph processing frameworks for distributed system and Processing-in-memory (PIM) architecture that precisely enforces loop-carried dependency; i.e., when a condition is satisfied by a neighbor, all following neighbors can be skipped. Our approach instruments the UDFs to express the loop-carried dependency, then the distributed execution framework enforces the precise semantics by performing dependency propagation dynamically. Enforcing loop-carried dependency requires the sequential processing of the neighbors of each vertex distributed in different nodes. We propose to circulant scheduling in the framework to allow different nodes to process disjoint sets of edges/vertices in parallel while satisfying the sequential requirement. The technique achieves an excellent trade-off between precise semantics and parallelism—the benefits of eliminating unnecessary computation and communication offset the reduced parallelism. We implement a new distributed graph processing framework SympleGraph, and two variants of runtime systems— GraphS and GraphSR —for PIM-based graph processing architecture, which significantly outperform the state-of-the-art.

PARTICIPATORY MODELLING OF THE CAUSAL RELATIONSHIP BETWEEN SELF-BELIEFS AND PERSONALITY USING AGGREGATED FUZZYRELATIONAL MAPMODEL AND KOSKO-HAMMING DISTANCE

Fuzzy Relational Map is an efficient tool in establishing the causal relationship between two disjoint sets of concepts. In situations, wherein the data available is unsupervised involving emotions and reasons described in a language that is vague or difficult to interpret, Fuzzy Relational Map is the pertinent approach of choice. Personality is a psychological construct that has different traits and these traits have some unique behavioral beliefs underneath. In this paper, an extension of a fuzzy relational map called aggregatedFuzzyRelational Map is used to study the association between the traits of personality and the behavioral beliefs that influence a certain type of personality. Further, the fixed points are analyzed with the aid of Kosko-Hamming Distance.

The Erdős-Hajnal Property for Graphs with No Fixed Cycle as a Pivot-Minor

We prove that for every integer $k$, there exists $\varepsilon>0$ such that for every $n$-vertex graph with no pivot-minors isomorphic to $C_k$, there exist disjoint sets $A$, $B$ such that $|A|,|B|\ge\varepsilon n$, and $A$ is complete or anticomplete to $B$. This proves the analog of the Erdős-Hajnal conjecture for the class of graphs with no pivot-minors isomorphic to $C_k$.

Reversible Data Hiding for AMBTC Compressed Images Based on Matrix and Hamming Coding

In this paper, we propose a two-layer data hiding method by using the Hamming code to enhance the hiding capacity without causing significantly increasing computation complexity for AMBTC-compressed images. To achieve our objective, for the first layer, four disjoint sets using different combinations of the mean value (AVG) and the standard deviation (VAR) are derived according to the combination of secret bits and the corresponding bitmap, following Lin et al.’s method. For the second layer, these four disjoint sets are extended to eight by adding or subtracting 1, according to a matrix embedding with (7, 4) Hamming code. To maintain reversibility, we must return the irreversible block to its previous state, which is the state after the first layer of data is embedded. Then, to losslessly recover the AMBTC-compressed images after extracting the secret bits, we use continuity feature, the parity of pixels value, and the unique number of changed pixels in the same row to restore AVG and VAR. Finally, in comparison with state-of-the-art AMBTC-based schemes, it is confirmed that our proposed method provided two times the hiding capacity comparing with other six representative AMBTC-based schemes while maintaining acceptable file size of steog-images.

Women and disparities in leadership and wages

The SIGIR'20 Women in IR event, co-organized by SIGIR WIR co-chairs, Nazli Goharian and Suzan Verberne, and local co-chair of SIGIR'20 WIR, Xin Ma, took place on July 27-29 and was attended by ~150 participants from different parts of the earth. Due to Covid-19, SIGIR'20 was held online. To accommodate all the time zones, we organized two sessions (A and B) on the same topics of discussion with two disjoint sets of panelists 1 , each group covering one of two sessions, totaling 19 panelists (17 female and 2 male) from academia and industry. This year we raised two questions for our panellists to discuss, followed by Q&A by the audience. First we discussed the women's status as to holding key leadership roles both in the academia and industry. The second topic was gender inequity in pay, which we had already raised for the first time in our community in SIGIR'19 and was summarized in the WIR at SIGIR'19 Forum 2 .