Multidimensional Scaling on Multiple Input Distance Matrices

Multidimensional Scaling (MDS) is a classic technique that seeks vectorial representations for data points, given the pairwise distances between them. However, in recent years, data are usually collected from diverse sources or have multiple heterogeneous representations. How to do multidimensional scaling on multiple input distance matrices is still unsolved to our best knowledge. In this paper, we first define this new task formally. Then, we propose a new algorithm called Multi-View Multidimensional Scaling (MVMDS) by considering each input distance matrix as one view. Our algorithm is able to learn the weights of views (i.e., distance matrices) automatically by exploring the consensus information and complementary nature of views. Experimental results on synthetic as well as real datasets demonstrate the effectiveness of MVMDS. We hope that our work encourages a wider consideration in many domains where MDS is needed

Impact of delay on HIV-1 dynamics of fighting a virus with another virus

In this paper, we propose a mathematical model for HIV-1 infection with intracellular delay. The model examines a viral-therapy for controlling infections through recombining HIV-1 virus with a genetically modified virus. For this model, the basic reproduction number $\mathcal{R}_0$ are identified and its threshold properties are discussed. When $\mathcal{R}_0 < 1$, the infection-free equilibrium $E_0$ is globally asymptotically stable. When $\mathcal{R}_0 > 1$, $E_0$ becomes unstable and there occurs the single-infection equilibrium $E_s$, and $E_0$ and $E_s$ exchange their stability at the transcritical point $\mathcal{R}_0 =1$. If $1< \mathcal{R}_0 < R_1$, where $R_1$ is a positive constant explicitly depending on the model parameters, $E_s$ is globally asymptotically stable, while when $\mathcal{R}_0 > R_1$, $E_s$ loses its stability to the double-infection equilibrium $E_d$. There exist a constant $R_2$ such that $E_d$ is asymptotically stable if $R_1<\mathcal R_0 < R_2$, and $E_s$ and $E_d$ exchange their stability at the transcritical point $\mathcal{R}_0 =R_1$. We use one numerical example to determine the largest range of $\mathcal R_0$ for the local stability of $E_d$ and existence of Hopf bifurcation. Some simulations are performed to support the theoretical results. These results show that the delay plays an important role in determining the dynamic behaviour of the system. In the normal range of values, the delay may change the dynamic behaviour quantitatively, such as greatly reducing the amplitudes of oscillations, or even qualitatively changes the dynamical behaviour such as revoking oscillating solutions to equilibrium solutions. This suggests that the delay is a very important fact which should not be missed in HIV-1 modelling

Effect of Tempering Moisture and Infrared Heating Temperature on the Functional and Nutritional Properties of Desi Chickpea and Hull-less Barley Flours, and Their Blends

The overall goal of this research was to investigate the effect of tempering moisture and infrared heating surface temperature on the functional and nutritional properties of Desi chickpea and hull-less barley flours, and their blends. Specifically, chickpea (initial moisture content 6.29%) and barley (initial moisture content 6.65%) seeds were tempered to 20% moisture content or left un-tempered followed by infrared heating to reach a surface temperature of 115 or 135oC. The infrared heating process was conducted independently for three times under the same condition to obtain triplicate samples. The seeds were then milled into flour for the subsequent analysis of their physicochemical and functional properties, levels of anti-nutritional compounds and in vitro protein digestibility. In the first study, the impact of infrared heating surface temperature and tempering moisture on the functional properties of Desi chickpea, hull-less barley, and their blends were examined. Neither of the factors was found to significantly affect the proximate composition (i.e., protein, lipid, and ash) of the flours (p>0.05). The content of protein, lipid, and ash was ~25%, 6% and 3% in chickpea flour, and 11%, 2% and 2% in barley flour, respectively. However, the levels of gelatinized starch were found to significantly increase with the combined tempering-heat treatment in each flour (p0.05), which was around 1.1 and 1.3 g/g of chickpea and barley flour respectively, whereas the water hydration capacity was significantly increased from 1.1 and 1.4 to 1.8 and 2.8 g/g of flour in chickpeas and barley respectively (p0.05). Based on the aforementioned results, chickpea and barley flours tempered to 20% moisture and heated to 135oC were subsequently blended at chickpea: barley ratio of 20:80, 40:60, 60:40 and 80:20. The physicochemical and functional properties of the blends showed a gradient change in accordance with their blending ratios. In the second study, the impact of infrared heating surface temperature and tempering moisture on the levels of anti-nutritional factors (i.e., trypsin/chymotrypsin inhibitors, total phenolics and condensed tannins), amino acid composition and in vitro protein digestibility properties of Desi chickpea, hull-less barley, and their blends were examined. Results indicated that both temperature and the tempering/temperature treatment caused a reduction in levels of all anti-nutritional factors for both flours, and the effect was more prominent in the tempering-heat combination (p<0.05). The amino acid composition of both flours was found not to be substantially changed with tempering or infrared heating. The amino acid scores (AAS) of chickpea and barley flours, as determined by the first limiting amino acid using the FAO/WHO reference pattern found in the case of barley to be limiting in lysine with an AAS of ~0.7, whereas for chickpea flour, threonine was limiting and had an AAS of ~0.9. The in vitro protein digestibility of chickpea samples was found to increase from 76% to 79% with the tempering-heat (135oC) combination, whereas barley flour increased from 72% to 79% when directly heated to 135oC (without tempering). In vitro protein digestibility corrected amino acid score (IV-PDCAAS) was found to increase from 0.65 to 0.71 for chickpea flour and 0.44 to 0.52 for barley flour, respectively with tempering-heat (135oC) combination indicating that tempering with infrared heating can improve the nutritional value of both flours. The addition of chickpea flour to the barley flour acted to improve the nutritional properties (IV-PDCAAS), to an extent depending on the concentration of chickpea flour present

Breaking the Barrier 2k2^k for Subset Feedback Vertex Set in Chordal Graphs

The Subset Feedback Vertex Set problem (SFVS), to delete $k$ vertices from a given graph such that any vertex in a vertex subset (called a terminal set) is not in a cycle in the remaining graph, generalizes the famous Feedback Vertex Set problem and Multiway Cut problem. SFVS remains $\mathrm{NP}$-hard even in split and chordal graphs, and SFVS in Chordal Graphs can be considered as a special case of the 3-Hitting Set problem. However, it is not easy to solve SFVS in Chordal Graphs faster than 3-Hitting Set. In 2019, Philip, Rajan, Saurabh, and Tale (Algorithmica 2019) proved that SFVS in Chordal Graphs can be solved in $2^k n^{\mathcal{O}(1)}$, slightly improving the best result $2.076^k n^{\mathcal{O}(1)}$ for 3-Hitting Set. In this paper, we break the "$2^k$-barrier" for SFVS in Chordal Graphs by giving a $1.619^k n^{\mathcal{O}(1)}$-time algorithm. Our algorithm uses reduction and branching rules based on the Dulmage-Mendelsohn decomposition and a divide-and-conquer method.Comment: 27 pages, 8 figures. Full versio