Pendahuluan: Survey penyakit tidak menular (PTM) membuktikan bahwa prevalensi mortalitas dan morbiditas kejadian diabetes mellitus (DM) di Indonesia mengalami peningkatan. Salah satu Program Pengelolaan Penyakit Kronis (PROLANIS), namun angka DM (Diabetes Mellitus) masih meningkat. Karakteristik masyarakat Indonesia yang beragam juga memiliki perbedaan daya penerimaan dan integrasi perilaku masyarakat pedesaaan (rural) dengan masyarakat perkotaan (urban) Pemberian informasi kesehatan dengan basis Health Action Model sangat terkait dengan dampak perubahan perilaku. Metode: Metode yang digunakan dalam pengabdian Masyarakat ini, yaitu menggunakan Implementasi edukasi dengan pendekatan partisipatif, dengan melibatkan kerja sama dengan penanggung Jawab Program PTM dan Kader dalam pelaksanaan program edukasi yang berbasis Health Action Model sehingga bisa mempengaruhi perilaku. Hasil: Hasilnya menunjukkan perubahan yaitu peningkatan signifikan dalam dalam pengetahuan mengontrol dula darah (75%), motivasi dalam menjaga pola makan (60%), serta kebiasaan menerapkan perilaku dengan olahraga/ aktivitas (60%). Meskipun demikian, tantangan utama tetap pada kepatuhan dalam menjaga pola makan makanan manis dan keterbatasan melakukan aktivitas karena keluhan nyeri. Program ini juga berhasil meningkatkan pengetahuan dan pentingnya kesehatan sehingga gula darah bisa terkontrol. Kesimpulan: Kegiatan Edukasi sangat efektif dalam meningkatkan kesadaran dan pengetahuan dalam mengontrol gula darah sehingga dapat mengubah perilaku dalam memilih menu makanan, dan penerapan aktivitas atau olahgara secara rutin. Keberhasilan kegiatan ini dapat di evaluasi dalam penerapan perilaku yang baik jika program ini bisa dilakukan secara berkelanjutan. Evaluasi berkala dan partisipasi instansi terkait dan kader dalam program berkelanjutan kegiatan sangat penting dalam mencapai derajat Kesehatan yang optimal.
We provide a new description of the Pieri rule of the homology of the affine Grassmannian and an affineanalogue of the charge statistics in terms of bounded partitions. This makes it possible to extend the formulation ofthe Kostka–Foulkes polynomials in terms of solvable lattice models by Nakayashiki and Yamada to the affine setting.
We consider a Hopf algebra of simplicial complexes and provide a cancellation-free formula for its antipode. We then obtain a family of combinatorial Hopf algebras by defining a family of characters on this Hopf algebra. The characters of these Hopf algebras give rise to symmetric functions that encode information about colorings of simplicial complexes and their $f$-vectors. We also use characters to give a generalization of Stanley’s $(-1)$-color theorem.
Many results involving Schur functions have analogues involving $k-$Schur functions. Standard strong marked tableaux play a role for $k-$Schur functions similar to the role standard Young tableaux play for Schur functions. We discuss results and conjectures toward an analogue of the hook length formula.
Antonio Bernini, Luca Ferrari, Renzo Pinzani
et al.
We introduce the notion of $\textit{pattern}$ in the context of lattice paths, and investigate it in the specific case of Dyck paths. Similarly to the case of permutations, the pattern-containment relation defines a poset structure on the set of all Dyck paths, which we call the $\textit{Dyck pattern poset}$. Given a Dyck path $P$, we determine a formula for the number of Dyck paths covered by $P$, as well as for the number of Dyck paths covering $P$. We then address some typical pattern-avoidance issues, enumerating some classes of pattern-avoiding Dyck paths. Finally, we offer a conjecture concerning the asymptotic behavior of the sequence counting Dyck paths avoiding a generic pattern and we pose a series of open problems regarding the structure of the Dyck pattern poset.
Art M. Duval, Caroline J. Klivans, Jeremy L. Martin
We study the vector spaces and integer lattices of cuts and flows of an arbitrary finite CW complex, and their relationships to its critical group and related invariants. Our results extend the theory of cuts and flows in graphs, in particular the work of Bacher, de la Harpe and Nagnibeda. We construct explicit bases for the cut and flow spaces, interpret their coefficients topologically, and describe sufficient conditions for them to be integral bases of the cut and flow lattices. Second, we determine the precise relationships between the discriminant groups of the cut and flow lattices and the higher critical and cocritical groups; these are expressed as short exact sequences with error terms corresponding to torsion (co)homology. As an application, we generalize a result of Kotani and Sunada to give bounds for the complexity, girth, and connectivity of a complex in terms of Hermite's constant.
The Little map and the Edelman-Greene insertion algorithm, a generalization of the Robinson-Schensted correspondence, are both used for enumerating the reduced decompositions of an element of the symmetric group. We show the Little map factors through Edelman-Greene insertion and establish new results about each map as a consequence. In particular, we resolve some conjectures of Lam and Little.
In this paper we study finite Eulerian posets which are binomial or Sheffer. These important classes of posets are related to the theory of generating functions and to geometry. The results of this paper are organized as follows: (1) We completely determine the structure of Eulerian binomial posets and, as a conclusion, we are able to classify factorial functions of Eulerian binomial posets; (2) We give an almost complete classification of factorial functions of Eulerian Sheffer posets by dividing the original question into several cases; (3) In most cases above, we completely determine the structure of Eulerian Sheffer posets, a result stronger than just classifying factorial functions of these Eulerian Sheffer posets. We also study Eulerian triangular posets. This paper answers questions posed by R. Ehrenborg and M. Readdy. This research is also motivated by the work of R. Stanley about recognizing the \emphboolean lattice by looking at smaller intervals.
Stanley has conjectured that the h-vector of a matroid complex is a pure O-sequence. We will prove this for cotransversal matroids by using generalized permutohedra. We construct a bijection between lattice points inside a $r$-dimensional convex polytope and bases of a rank $r$ transversal matroid.
We enumerate derangements with descents in prescribed positions. A generating function was given by Guo-Niu Han and Guoce Xin in 2007. We give a combinatorial proof of this result, and derive several explicit formulas. To this end, we consider fixed point $\lambda$-coloured permutations, which are easily enumerated. Several formulae regarding these numbers are given, as well as a generalisation of Euler's difference tables. We also prove that except in a trivial special case, if a permutation $\pi$ is chosen uniformly among all permutations on $n$ elements, the events that $\pi$ has descents in a set $S$ of positions, and that $\pi$ is a derangement, are positively correlated.
The total number of noncrossing partitions of type $\Psi$ is the $n$th Catalan number $\frac{1}{ n+1} \binom{2n}{n}$ when $\Psi =A_{n-1}$, and the binomial coefficient $\binom{2n}{n}$ when $\Psi =B_n$, and these numbers coincide with the correspondent number of nonnesting partitions. For type $A$, there are several bijective proofs of this equality; in particular, the intuitive map, which locally converts each crossing to a nesting, is one of them. In this paper we present a bijection between nonnesting and noncrossing partitions of types $A$ and $B$ that generalizes the type $A$ bijection that locally converts each crossing to a nesting.
The $\textit{hiring problem}$ has been recently introduced by Broder et al. in last year's ACM-SIAM Symp. on Discrete Algorithms (SODA 2008), as a simple model for decision making under uncertainty. Candidates are interviewed in a sequential fashion, each one endowed with a quality score, and decisions to hire or discard them must be taken on the fly. The goal is to maintain a good rate of hiring while improving the "average'' quality of the hired staff. We provide here an alternative formulation of the hiring problem in combinatorial terms. This combinatorial model allows us the systematic use of techniques from combinatorial analysis, e. g., generating functions, to study the problem. Consider a permutation $\sigma :[1,\ldots, n] \to [1,\ldots, n]$. We process this permutation in a sequential fashion, so that at step $i$, we see the score or quality of candidate $i$, which is actually her face value $\sigma (i)$. Thus $\sigma (i)$ is the rank of candidate $i$; the best candidate among the $n$ gets rank $n$, while the worst one gets rank $1$. We define $\textit{rank-based}$ strategies, those that take their decisions using only the relative rank of the current candidate compared to the score of the previous candidates. For these strategies we can prove general theorems about the number of hired candidates in a permutation of length $n$, the time of the last hiring, and the average quality of the last hired candidate, using techniques from the area of analytic combinatorics. We apply these general results to specific strategies like hiring above the best, hiring above the median or hiring above the $m$th best; some of our results provide a complementary view to those of Broder et al., but on the other hand, our general results apply to a large family of hiring strategies, not just to specific cases.
Sampling from a random discrete distribution induced by a 'stick-breaking' process is considered. Under a moment condition, it is shown that the asymptotics of the sequence of occupancy numbers, and of the small-parts counts (singletons, doubletons, etc) can be read off from a limiting model involving a unit Poisson point process and a self-similar renewal process on the half-line.
Let $G$ be a perfectly oriented planar graph. Postnikov's boundary measurement construction provides a rational map from the set of positive weight functions on the edges of $G$ onto the appropriate totally nonnegative Grassmann cell. We establish an explicit combinatorial formula for Postnikov's map by expressing each Plücker coordinate of the image as a ratio of two polynomials in the edge weights, with positive integer coefficients. These polynomials are weight generating functions for certain subsets of edges in $G$.
Philippe Flajolet, Éric Fusy, Olivier Gandouet
et al.
This extended abstract describes and analyses a near-optimal probabilistic algorithm, HYPERLOGLOG, dedicated to estimating the number of \emphdistinct elements (the cardinality) of very large data ensembles. Using an auxiliary memory of m units (typically, "short bytes''), HYPERLOGLOG performs a single pass over the data and produces an estimate of the cardinality such that the relative accuracy (the standard error) is typically about $1.04/\sqrt{m}$. This improves on the best previously known cardinality estimator, LOGLOG, whose accuracy can be matched by consuming only 64% of the original memory. For instance, the new algorithm makes it possible to estimate cardinalities well beyond $10^9$ with a typical accuracy of 2% while using a memory of only 1.5 kilobytes. The algorithm parallelizes optimally and adapts to the sliding window model.
Grown simple families of increasing trees are a subclass of increasing trees, which can be constructed by an insertion process. Three such tree families contained in the grown simple families of increasing trees are of particular interest: $\textit{recursive trees}$, $\textit{plane-oriented recursive trees}$ and $\textit{binary increasing trees}$. Here we present a general approach for the analysis of a number of label-based parameters in a random grown simple increasing tree of size $n$ as, e.g., $\textit{the degree of the node labeled j}$, $\textit{the subtree-size of the node labeled j}$, etc. Further we apply the approach to the random variable $X_{n,j,a}$, which counts the number of size-$a$ branches attached to the node labeled $j$ (= subtrees of size $a$ rooted at the children of the node labeled $j$) in a random grown simple increasing tree of size $n$. We can give closed formulæ for the probability distribution and the factorial moments. Furthermore limiting distribution results for $X_{n,j,a}$ are given dependent on the growth behavior of $j=j(n)$ compared to $n$.