Packing odd TT-joins with at most two terminals

Take a graph $G$, an edge subset $\Sigma\subseteq E(G)$, and a set of terminals $T\subseteq V(G)$ where $|T|$ is even. The triple $(G,\Sigma,T)$ is called a signed graft. A $T$-join is odd if it contains an odd number of edges from $\Sigma$. Let $\nu$ be the maximum number of edge-disjoint odd $T$-joins. A signature is a set of the form $\Sigma\triangle \delta(U)$ where $U\subseteq V(G)$ and $|U\cap T)$ is even. Let $\tau$ be the minimum cardinality a $T$-cut or a signature can achieve. Then $\nu\leq \tau$ and we say that $(G,\Sigma,T)$ packs if equality holds here. We prove that $(G,\Sigma,T)$ packs if the signed graft is Eulerian and it excludes two special non-packing minors. Our result confirms the Cycling Conjecture for the class of clutters of odd $T$-joins with at most two terminals. Corollaries of this result include, the characterizations of weakly and evenly bipartite graphs, packing two-commodity paths, packing $T$-joins with at most four terminals, and a new result on covering edges with cuts.Comment: extended abstract appeared in IPCO 2014 (under the different title "the cycling property for the clutter of odd st-walks"

Unlocking the potentials of Micro and Small Enterprises (MSEs) in building local technological capabilities in agro-processing industry

This research was aimed at feeding into the quest for ways that would help advance Africa’s effort to industrialize its economy. Empirical evidence suggests transforming the agro-industry and inserting MSEs into value chains is the most feasible strategy. Inspired by arguments against global value chains (GVCs) orientation of Africa’s industrialization strategies, this research investigated the link between local production and technological capability in Africa using indicators from various international databases and cross-country quantitative analyses. The research also undertook an in-depth qualitative investigation on Ethiopia’s edible oil industry as an important case capable of shedding some light on problems linked to Africa’s agro-processing with a special focus on local production system and technological capability. The finding revealed strong positive linkages between local value chains and technological/innovation capabilities in Africa. Structural constraints, under-developed supply chains, and poor implementation and coordination of policies have limited Africa’s capability to harness potentials inherent in the agro-processing sector.</p

PERJANJIAN WESTPHALIA DAN MOMENTUM PENDIRIAN NEGARA MODERN

The Treaty of Westphalia in 1648 opened a new history for the political constellations of Europe and the world. Based on the results of the Westphalia agreement, the legal concept of sovereignty of the nation-state (state-nation) and the institutionalization of military power and diplomacy were mutually agreed upon by the rulers in Europe through consensus. After the emergence of the Westphalia Treaty, the new structure of the international community was based on national states and was no longer based on kingdoms, empires, and churches. In addition, the composition of the international community is also based on the nature of the state together with its government, which is to separate state power and government from the influence of the church. Various changes in the post-Westphalia international relations system include the growth of representative government, the occurrence of the industrial revolution, the development of international law, the development of diplomacy methods in addition to military strategy, the growth of interdependence among nation states in the economic field, and the birth of procedures - procedures for resolving conflicts peacefully. In short, the Westphalia Treaty has laid the foundation for this form and nature in the composition of the new international community

Idealness and 2-resistant sets

A subset of the unit hypercube {0,1}n is cube-ideal if its convex hull is described by hypercube and generalized set covering inequalities. In this note, we study sets S⊆{0,1}n such that, for any subset X⊆{0,1}n of cardinality at most 2, S∪X is cube-ideal

From coordinate subspaces over finite fields to ideal multipartite uniform clutters

Take a prime power $q$, an integer $n\geq 2$, and a coordinate subspace $S\subseteq GF(q)^n$ over the Galois field $GF(q)$. One can associate with $S$ an $n$-partite $n$-uniform clutter $\mathcal{C}$, where every part has size $q$ and there is a bijection between the vectors in $S$ and the members of $\mathcal{C}$. In this paper, we determine when the clutter $\mathcal{C}$ is ideal, a property developed in connection to Packing and Covering problems in the areas of Integer Programming and Combinatorial Optimization. Interestingly, the characterization differs depending on whether $q$ is $2,4$, a higher power of $2$, or otherwise. Each characterization uses crucially that idealness is a minor-closed property: first the list of excluded minors is identified, and only then is the global structure determined. A key insight is that idealness of $\mathcal{C}$ depends solely on the underlying matroid of $S$. Our theorems also extend from idealness to the stronger max-flow min-cut property. As a consequence, we prove the Replication and $\tau=2$ Conjectures for this class of clutters.Comment: 32 pages, 6 figure

The effect of Punica granatum L. along with aerobic training on resistin, serum adiponectin and insulin resistance in women with type 2 diabetes

Background: Factors secreted from adipocytes, such as resistin and adiponectin can affect peripheral insulin resistance and type 2 diabetes. Physical activity and pomegranate, which has both anti-inflammatory and antioxidant properties can affect resistin and adiponectin. The aim of this study was to examine the effect of Punica granatum L. along with aerobic training on serum resistin, adiponectin and insulin resistance in women with type 2 diabetes. Materials and Methods: In this study, 33 diabetic women with type 2 diabetes were selected from Babol city and were randomly divided into four groups (control, P. granatum L., training and P. granatum L.+ training). The training groups participated in an aerobic training for six weeks, three sessions a week (60 to 75 of the reserved heart rate and for 25 to 45 min). The control groups of P. granatum L. and P. granatum L. + training were fed 150 mL of P. granatum L. for six weeks (at about 18 p.m). Two days before and after the protocol, blood samples were taken. Results: The results showed that there was no significant difference in the serum resistin levels among the three experimental groups. Also, the results showed a significant difference between adiponectin levels and insulin resistance in four groups. Conclusions: It seems that aerobic training and P. granatum L. and combination of both can have anti-inflammatory and antioxidant effects on reduction of adiponectin and insulin resistance in women with type 2 diabetes

On packing dijoins in digraphs and weighted digraphs

In this paper, we make some progress in addressing Woodall's Conjecture, and the refuted Edmonds-Giles Conjecture on packing dijoins in unweighted and weighted digraphs. Let $D=(V,A)$ be a digraph, and let $w\in \mathbb{Z}^A_{\geq 0}$. Suppose every dicut has weight at least $\tau$, for some integer $\tau\geq 2$. Let $\rho(\tau,D,w):=\frac{1}{\tau}\sum_{v\in V} m_v$, where each $m_v$ is the integer in $\{0,1,\ldots,\tau-1\}$ equal to $w(\delta^+(v))-w(\delta^-(v))$ mod $\tau$. In this paper, we prove the following results, amongst others: (1) If $w={\bf 1}$, then $A$ can be partitioned into a dijoin and a $(\tau-1)$-dijoin. (2) If $\rho(\tau,D,w)\in \{0,1\}$, then there is an equitable $w$-weighted packing of dijoins of size $\tau$. (3) If $\rho(\tau,D,w)= 2$, then there is a $w$-weighted packing of dijoins of size $\tau$. (4) If $w={\bf 1}$, $\tau=3$, and $\rho(\tau,D,w)=3$, then $A$ can be partitioned into three dijoins. Each result is best possible: (1) and (4) do not hold for general $w$, (2) does not hold for $\rho(\tau,D,w)=2$ even if $w={\bf 1}$, and (3) does not hold for $\rho(\tau,D,w)=3$. The results are rendered possible by a \emph{Decompose, Lift, and Reduce procedure}, which turns $(D,w)$ into a set of \emph{sink-regular weighted $(\tau,\tau+1)$-bipartite digraphs}, each of which is a weighted digraph where every vertex is a sink of weighted degree $\tau$ or a source of weighted degree $\tau,\tau+1$, and every dicut has weight at least $\tau$. Our results give rise to a number of approaches for resolving Woodall's Conjecture, fixing the refuted Edmonds-Giles Conjecture, and the $\tau=2$ Conjecture for the clutter of minimal dijoins. They also show an intriguing connection to Barnette's Conjecture.Comment: 71 page

Intersecting restrictions in clutters

A clutter is intersecting if the members do not have a common element yet every two members intersect. It has been conjectured that for clutters without an intersecting minor, total primal integrality and total dual integrality of the corresponding set covering linear system must be equivalent. In this paper, we provide a polynomial characterization of clutters without an intersecting minor. One important class of intersecting clutters comes from projective planes, namely the deltas, while another comes from graphs, namely the blockers of extended odd holes. Using similar techniques, we provide a poly- nomial algorithm for finding a delta or the blocker of an extended odd hole minor in a given clutter. This result is quite surprising as the same problem is NP-hard if the input were the blocker instead of the clutter

The contribution of the faculty of engineering in Islamizing engineering studies

Islamization as an idea is not a mere process of engagement rather a dynamic and ongoing school of thought; hence, Islamized engineering is a value-laden enterprise and a process reconceptualization. Islamized engineering sciences will generate diverse insights different, to certain a extent, from western conception of engineering. It will connect us to the history of Islamic literature and the salient manifestations of Islamic civilization. This paper aspires to review and evaluate the methodological and epistemological approaches adopted by the Kulliyyah of Engineering in its attempt to infuse Islamic values in the general framework of its activities; from administration to academic and from student's affairs to curriculum development