A classification of 3+1D bosonic topological orders (I): the case when point-like excitations are all bosons

Topological orders are new phases of matter beyond Landau symmetry breaking. They correspond to patterns of long-range entanglement. In recent years, it was shown that in 1+1D bosonic systems there is no nontrivial topological order, while in 2+1D bosonic systems the topological orders are classified by a pair: a modular tensor category and a chiral central charge. In this paper, we propose a partial classification of topological orders for 3+1D bosonic systems: If all the point-like excitations are bosons, then such topological orders are classified by unitary pointed fusion 2-categories, which are one-to-one labeled by a finite group $G$ and its group 4-cocycle $\omega_4 \in \mathcal H^4[G;U(1)]$ up to group automorphisms. Furthermore, all such 3+1D topological orders can be realized by Dijkgraaf-Witten gauge theories.Comment: An important new result "Untwisted sector of dimension reduction is the Drinfeld center of E" is added in Sec. IIIC; other minor refinements and improvements; 23 pages, 10 figure

A theory of 2+1D fermionic topological orders and fermionic/bosonic topological orders with symmetries

We propose that, up to invertible topological orders, 2+1D fermionic topological orders without symmetry and 2+1D fermionic/bosonic topological orders with symmetry $G$ are classified by non-degenerate unitary braided fusion categories (UBFC) over a symmetric fusion category (SFC); the SFC describes a fermionic product state without symmetry or a fermionic/bosonic product state with symmetry $G$, and the UBFC has a modular extension. We developed a simplified theory of non-degenerate UBFC over a SFC based on the fusion coefficients $N^{ij}_k$ and spins $s_i$. This allows us to obtain a list that contains all 2+1D fermionic topological orders (without symmetry). We find explicit realizations for all the fermionic topological orders in the table. For example, we find that, up to invertible $p+\hspace{1pt}\mathrm{i}\hspace{1pt} p$ fermionic topological orders, there are only four fermionic topological orders with one non-trivial topological excitation: (1) the $K={\scriptsize \begin{pmatrix} -1&0\\0&2\end{pmatrix}}$ fractional quantum Hall state, (2) a Fibonacci bosonic topological order $2^B_{14/5}$ stacking with a fermionic product state, (3) the time-reversal conjugate of the previous one, (4) a primitive fermionic topological order that has a chiral central charge $c=\frac14$, whose only topological excitation has a non-abelian statistics with a spin $s=\frac14$ and a quantum dimension $d=1+\sqrt{2}$. We also proposed a categorical way to classify 2+1D invertible fermionic topological orders using modular extensions.Comment: 23 pages, 8 table

Tissue Culture and Agrobacterium-Mediated Transformation on Rosa Hybrida L. 'Christian Dior'

Callus induction from leaf explants of Rosa hybrida L. 'Christian Dior' was established. Two types of auxins (2.4-D and NAA) at three concentrations (4.5, 9.0 and 13.5 µM) and two types of cytokinins (kinetin and BA) at three concentrations (2.3, 4.7 and 9.3 µM) were used in a 3 X 4 experimental design. The best caulogenesis and callus maintenance medium was 112 MS + 30 giL sucrose + 9.0 µM NAA + 2.3 µM BA cultured in the dark. Several attempts were carried out to induce shoot organogenesis and/or somatic embryogenesis from callus. None of the media tested induced shoots or somatic embryos. However, there were differences observed for callus growth on the medium tested. Combination of cytokinins (BA and TDZ) at 5.0-10.0 µM with auxins (NAA and IBA) at 1.0-2.0 µM, generally promoted callus proliferation. Callus cultured on cytokinin onlyAmino acids proline and glutamine also enhanced callus proliferation. Observations under the stereo microscope revealed that the callus was globular. Medium without ammonium ion enhanced callus proliferation. TDZ was found to be the better cytokinin for callus proliferation. Observation of cells taken from callus cultured on the various media revealed that there was no meristematic primordias . Agrobacterium-mediated transformation of R. hybrida L . 'Christian Dior' callus produced three transgenic callus lines that were confirmed by dot blot and Southern hybridisation assays. Leaf-derived callus was transformed with Agrobacterium tumefaciens LBA4404 carrying plasmid pBI 121 which contained the B-glucuronidase (GUS) gene and nptII gene coding for kanamycin resistance. The best condition for infection of callus tissues with A. tumefaciens was exposure to 1 X 1 09 cells/ml for 5 minutes. At this condition, GUS activity was found to be the highest (6.39 ± 0.01 pmol MU/h/p.g protein). It was also found that at low Agrobacterium concentration, increasing the exposure period increased GUS transient activity, and at high Agrobacterium concentration, increasing exposure period reduced GUS transient activity . Transformation efficiency improved when callus was cultured for 2 weeks on medium without kanamycin (but with 500 p.g/ml carbenicill in) before transferring the callus to medium with 300 p.g/ml kanamycin + 500 p.g/ml carbenicillin for selection. Carbenicillin served to eliminate Agrobaterium. Kanamycin was also found to be unsuitable for used as a selective marker

Algebraic higher symmetry and categorical symmetry -- a holographic and entanglement view of symmetry

We introduce the notion of algebraic higher symmetry, which generalizes higher symmetry and is beyond higher group. We show that an algebraic higher symmetry in a bosonic system in $n$-dimensional space is characterized and classified by a local fusion $n$-category. We find another way to describe algebraic higher symmetry by restricting to symmetric sub Hilbert space where symmetry transformations all become trivial. In this case, algebraic higher symmetry can be fully characterized by a non-invertible gravitational anomaly (i.e. an topological order in one higher dimension). Thus we also refer to non-invertible gravitational anomaly as categorical symmetry to stress its connection to symmetry. This provides a holographic and entanglement view of symmetries. For a system with a categorical symmetry, its gapped state must spontaneously break part (not all) of the symmetry, and the state with the full symmetry must be gapless. Using such a holographic point of view, we obtain (1) the gauging of the algebraic higher symmetry; (2) the classification of anomalies for an algebraic higher symmetry; (3) the equivalence between classes of systems, with different (potentially anomalous) algebraic higher symmetries or different sets of low energy excitations, as long as they have the same categorical symmetry; (4) the classification of gapped liquid phases for bosonic/fermionic systems with a categorical symmetry, as gapped boundaries of a topological order in one higher dimension (that corresponds to the categorical symmetry). This classification includes symmetry protected trivial (SPT) orders and symmetry enriched topological (SET) orders with an algebraic higher symmetry.Comment: 61 pages, 31 figure

User interface for computer-aided product conceptual design

A major objective of this research is to develop a natural sketching interface for designers in conceptual design. Based on the literature review on the sketch-based cognitive process, solutions are developed in this thesis to address two major problems that prevent designers from using computer-aided design tools. First , because the lack of a detailed description of a designer's cognitive model, designers have never been put in the centre of consideration in the development of a CAD tool. This thesis proposes a new approach for the exploration of the designer's cognitive model by applying the axiomatic theory of design modeling. Second , the user mental model underlying the existing CAD tools do not match the actual designer's mental model. To eliminate the gap between two mental models, this thesis develops a prototype of natural interface based on PUI (Perceptual User Interface) theory. This natural interface uses gesture commands to replace menu and button. ANN (Artificial Neural Network) is adopted to recognize the designer's gesture command

Understanding media violence and the development of aggressive behavior of school children

Aggressive behaviour among school children had raised a cause of concern in Malaysia. The development of aggressive behaviour places children at serious risk for future mal-adaptation in the form of continued aggression, conduct problems, and overall difficulties in the domain of social relationships. Therefore, there is a need to study the origins and development of aggressive behaviour. This paper focuses on the nature of aggressive behaviour among school children, the theories that underlying the aggressive behaviour, and the impact of media violence on the development of aggressive behaviour of school children

Investigating the relationship between playing violent video games and viewing violent TV programmes and aggressive behaviour among pre-teens

This study aimed to investigate the relationship between the playing of violent video games and the viewing of violent TV programmes and aggressive behaviour among pre-teens. According to McGahee, Kemp and Tingen (2000), pre-teens referred to preadolescent children who are usually between 9 and 12 years of age. A total of 450 pre-teens aged 11 were randomly selected from nine schools in the state of Selangor, Malaysia, to participate in this study. This study employed a correlation research design and the data were analysed using both descriptive and inferential statistics to address the research objectives. The data were analysed to identify the top 10 favourite video games played by pre-teens in this study. Eight out of 10 video games played by pre-teens were found to be violent in nature. In addition, the top 10 favourite violent TV programmes viewed by pre-teens in this study were also identified. Findings from this study showed that there was a significant difference in the mean score of playing violent video games [t(257)=6.979, p<0.01] and viewing violent TV programmes [t(440)=3.544, p<0.01) between boys and girls who participated in the study. Moreover, the results from this study revealed there was a significant and positive relationship between playing violent video games (r=0.167, p<0.01), viewing violent TV programmes (r=0.126, p=0.000) and aggressive behaviour demonstrated by pre-teens. Multiple regression analysis showed that 39.4% of the variances in pre-teen physical aggression could be explained by both the playing of violent video games and the viewing of violent TV programmes, with the playing of violent video games as a stronger predictor of physical aggressive behaviour in pre-teens (ß=0.238, p=0.025)

Aggression among school children in Malaysia

This study aimed to investigate the level of aggression among primary school children in Malaysia. A total of 450 students aged 11 were randomly selected from nine schools in the Selangor State to participate in this study. Children Aggression Inventory (CAI) was administered to collect data from the respondents. The reliability of the CAI in this study was found to be high (α = 0.90). The data obtained were analyzed using both descriptive and inferential statistics to address the research objectives. Findings from this study showed that the aggression level demonstrated by school children was moderate (M = 2.18, SD = 0.392). The highest mean score for aggressive behaviour exhibited by the children is hostility (M = 1.88, SD= 0.37), followed by anger (M = 1.86, SD = 0.36), verbal aggression (M = 1.71, SD = 0.37), indirect aggression (M = 1.66, SD = 0.38), and physical aggression (M = 1.66, SD = 0.45). Results also indicated a significant difference between the boys and girls in the mean scores of physical aggression [t (443) = 6.034, p < 0.01] and anger [t (445.78) = -3.034, p < 0.01]. Boys were found to be more aggressive than girls in terms of physical aggression while girls were found to be more aggressive than boys in terms of anger