Unweighted Version Research Articles

Weighted Context-Free-Language Ordered Binary Decision Diagrams

This paper presents a new data structure, called Weighted Context-Free-Language Ordered BDDs (WCFLOBDDs), which are a hierarchically structured decision diagram, akin to Weighted BDDs (WBDDs) enhanced with a procedure-call mechanism. For some functions, WCFLOBDDs are exponentially more succinct than WBDDs. They are potentially beneficial for representing functions of type B n → D , when a function’s image V ⊆ D has many different values. We apply WCFLOBDDs in quantum-circuit simulation, and find that they perform better than WBDDs on certain benchmarks. With a 15-minute timeout, the number of qubits that can be handled by WCFLOBDDs is 1-64× that of WBDDs(and 1-128× that of CFLOBDDs, which are an unweighted version of WCFLOBDDs). These results support the conclusion that for this application—from the standpoint of problem size, measured as the number of qubits—WCFLOBDDs provide the best of both worlds: performance roughly matches whichever of WBDDs and CFLOBDDs is better.(From the standpoint of running time, the results are more nuanced.)

The Teodorescu and the Π-operator in octonionic analysis and some applications

In the development of function theory in octonions, the non-associativity property produces an additional associator term when applying the Stokes formula. To take the non-associativity into account, particular intrinsic weight factors are implemented in the definition of octonion-valued inner products to ensure the existence of a reproducing Bergman kernel. This Bergman projection plays a pivotal role in the L2-space decomposition demonstrated in this paper for octonion-valued functions. In the unit ball, we explicitly show that the intrinsic weight factor is crucial to obtain the reproduction property and that the latter precisely compensates an additional associator term that otherwise appears when leaving out the weight factor.Furthermore, we study an octonionic Teodorescu transform and show how it is related to the unweighted version of the Bergman transform and establish some operator relations between these transformations. We apply two different versions of the Borel-Pompeiu formulae that naturally arise in the context of the non-associativity. Next, we use the octonionic Teodorescu transform to establish a suitable octonionic generalization of the Ahlfors-Beurling operator, also known as the Π-operator. We prove an integral representation formula that presents a unified representation for the Π-operator arising in all prominent hypercomplex function theories. Then we describe some basic mapping properties arising in context with the L2-space decomposition discussed before.Finally, we explore several applications of the octonionic Π-operator. Initially, we demonstrate its utility in solving the octonionic Beltrami equation, which characterizes generalized quasi-conformal maps from R8 to R8 in a specific analytical sense. Subsequently, analogous results are presented for the hyperbolic octonionic Dirac operator acting on the right half-space of R8. Lastly, we discuss how the octonionic Teodorescu transform and the Bergman projection can be employed to solve an eight-dimensional Stokes problem in the non-associative octonionic setting.

Parameterized approximation algorithms for weighted vertex cover

A vertex cover of a graph is a set of vertices of the graph such that every edge has at least one endpoint in it. In this work, we study Weighted Vertex Cover with solution size as a parameter. Formally, in the (k,W)-Vertex Cover problem, given a graph G, an integer k, a positive rational W, and a weight function w:V(G)→Q+, the question is whether G has a vertex cover of size at most k of weight at most W, with k being the parameter. An (a,b)-bi-criteria approximation algorithm for (k,W)-Vertex Cover either produces a vertex cover S such that |S|≤ak and w(S)≤bW, or decides that there is no vertex cover of size at most k of weight at most W. We obtain the following results.•A simple (2,2)-bi-criteria approximation algorithm for (k,W)-Vertex Cover in polynomial time by modifying the standard LP-rounding algorithm.•A simple exact parameterized algorithm for (k,W)-Vertex Cover running in O⁎(1.4656k) time1.•A (1+ϵ,2)-approximation algorithm for (k,W)-Vertex Cover running in O⁎(1.4656(1−ϵ)k) time.•A (1.5,1.5)-approximation algorithm for (k,W)-Vertex Cover running in O⁎(1.414k) time.•A (2−δ,2−δ)-approximation algorithm for (k,W)-Vertex Cover running in O⁎(∑i=δk(1−2δ)1+2δδk(1−2δ)2δ(δk+iδk−2iδ1−2δ)) time for any δ<0.5. For example, for (1.75,1.75) and (1.9,1.9)-approximation algorithms, we get running times of O⁎(1.272k) and O⁎(1.151k) respectively.Our algorithms (expectedly) do not improve upon the running times of the existing algorithms for the unweighted version of Vertex Cover. When compared to algorithms for the weighted version, our algorithms are the first ones to the best of our knowledge which work with arbitrary weights, and they perform well when the solution size is much smaller than the total weight of the desired solution.

The assessment of replicability using the sum of p-values.

Statistical significance of both the original and the replication study is a commonly used criterion to assess replication attempts, also known as the two-trials rule in drug development. However, replication studies are sometimes conducted although the original study is non-significant, in which case Type-I error rate control across both studies is no longer guaranteed. We propose an alternative method to assess replicability using the sum of -values from the two studies. The approach provides a combined -value and can be calibrated to control the overall Type-I error rate at the same level as the two-trials rule but allows for replication success even if the original study is non-significant. The unweighted version requires a less restrictive level of significance at replication if the original study is already convincing which facilitates sample size reductions of up to 10%. Downweighting the original study accounts for possible bias and requires a more stringent significance level and larger sample sizes at replication. Data from four large-scale replication projects are used to illustrate and compare the proposed method with the two-trials rule, meta-analysis and Fisher's combination method.

On the Local Fourier Uniformity Problem for Small Sets

Abstract We consider vanishing properties of exponential sums of the Liouville function $\boldsymbol{\lambda }$ of the form $$ \begin{align*} &amp; \lim_{H\to\infty}\limsup_{X\to\infty}\frac{1}{\log X}\sum_{m\leq X}\frac{1}{m}\sup_{\alpha\in C}\bigg|\frac{1}{H}\sum_{h\leq H}\boldsymbol{\lambda}(m+h)e^{2\pi ih\alpha}\bigg|=0, \end{align*} $$ where $C\subset{{\mathbb{T}}}$. The case $C={{\mathbb{T}}}$ corresponds to the local $1$-Fourier uniformity conjecture of Tao, a central open problem in the study of multiplicative functions with far-reaching number-theoretic applications. We show that the above holds for any closed set $C\subset{{\mathbb{T}}}$ of zero Lebesgue measure. Moreover, we prove that extending this to any set $C$ with non-empty interior is equivalent to the $C={{\mathbb{T}}}$ case, which shows that our results are essentially optimal without resolving the full conjecture. We also consider higher-order variants. We prove that if the linear phase $e^{2\pi ih\alpha }$ is replaced by a polynomial phase $e^{2\pi ih^{t}\alpha }$ for $t\geq 2$ then the statement remains true for any set $C$ of upper box-counting dimension $&amp;lt; 1/t$. The statement also remains true if the supremum over linear phases is replaced with a supremum over all nilsequences coming form a compact countable ergodic subsets of any $t$-step nilpotent Lie group. Furthermore, we discuss the unweighted version of the local $1$-Fourier uniformity problem, showing its validity for a class of “rigid” sets (of full Hausdorff dimension) and proving a density result for all closed subsets of zero Lebesgue measure.

On the parameterized complexity of Sparsest Cut and Small-Set Expansion problems

We present a parameterized dichotomy for the k-Sparsest Cut problem in weighted and unweighted versions. In particular, we show that the weighted k-Sparsest Cut problem is NP-hard for every k≥3 even on graphs with bounded vertex cover number. Also, the unweighted k-Sparsest Cut problem is W[1]-hard when parameterized by the three combined parameters tree-depth, feedback vertex set number, and k. On the positive side, we show that the unweighted k-Sparsest Cut problem is FPT when parameterized by the vertex cover number and k, and when k is fixed, it is FPT with respect to the treewidth. Moreover, we show that the generalized version κ-Small-Set Expansion problem is FPT when parameterized by κ and the maximum degree of the graph, though it is W[1]-hard for each of these parameters separately.

Forgetfulness Can Make You Faster: An O * (8.097 k ) -time Algorithm for Weighted 3-set k -packing

In this article, we study the classic Weighted 3-Set k -Packing problem: given a universe U , a family \( {\mathcal {S}}\) of subsets of size 3 of U , a weight function \(w : {\mathcal {S}} \rightarrow \mathbb {R}\) , \(W \in \mathbb {R}\) , and a parameter \(k \in \mathbb {N}\) , the objective is to decide if there is a subfamily \( {\mathcal {S}}\) ′ ⊆ \( {\mathcal {S}}\) of k disjoint sets and total weight at least W . We present a deterministic parameterized algorithm for this problem that runs in time O * (8.097 k ), where O * hides factors polynomial in the input size. This substantially improves upon the previously best deterministic algorithm for Weighted 3-Set k -Packing , which runs in time O * (12.155 k ) SIDMA [ 18 ], and was also the best deterministic algorithm for the unweighted version of this problem. Our algorithm is based on a novel application of the method of representative sets that might be of independent interest.

From mobile crowdsourcing to crowd-trusted food price in Nigeria: statistical pre-processing and post-sampling

Timely and reliable monitoring of food market prices at high spatial and temporal resolution is essential to understanding market and food security developments and supporting timely policy and decision-making. Mostly, decisions rely on price expectations, which are updated with new information releases. Therefore, increasing the availability and timeliness of price information has become a national and international priority. We present two new datasets in which mobile app-based crowdsourced daily price observations, voluntarily submitted by self-selected participants, are validated in real-time within spatio-temporal markets (pre-processed data). Then, they are reweighted weekly using their geo-location to resemble a formal sample design and allow for more reliable statistical inference (post-sampled data). Using real-time data collected in Nigeria, we assess the accuracy and propose that our reweighted estimates are more accurate with respect to the unweighted version. Results have important implications for governments, food chain actors, researchers and other organisations.

Robust Variable Selection and Regularization in Quantile Regression Based on Adaptive-LASSO and Adaptive E-NET

Robust Variable Selection and Regularization in Quantile Regression Based on Adaptive-LASSO and Adaptive E-NET

Upper and lower bounds on approximating weighted mixed domination

A mixed dominating set of a graph G=(V,E) is a mixed set D of vertices and edges, such that for every edge or vertex, if it is not in D, then it is adjacent or incident to at least one vertex or edge in D. The mixed domination problem is to find a mixed dominating set with a minimum cardinality. It has applications in system control and some other scenarios and it is NP-hard to compute an optimal solution. This paper studies approximation algorithms and hardness of the weighted mixed dominating set problem. The weighted version is a generalization of the unweighted version, where all vertices are assigned the same nonnegative weight wv and all edges are assigned the same nonnegative weight we, and the question is to find a mixed dominating set with a minimum total weight. Although the mixed dominating set problem has a simple 2-approximation algorithm, few approximation results for the weighted version are known. The main contributions of this paper include:1.for we≥wv, a 2-approximation algorithm;2.for we≥2wv, inapproximability within ratio 1.3606 unless P=NP and within ratio 2 under UGC;3.for 2wv>we≥wv, inapproximability within ratio 1.1803 unless P=NP and within ratio 1.5 under UGC;4.for we<wv, inapproximability within ratio (1−ϵ)ln⁡|V| unless P=NP for any ϵ>0.

Weighted geometric set cover with rectangles of bounded integer side lengths

In this article, we study the gradation of the complexity of the weighted set cover problem with axis-parallel rectangles whose side lengths are bounded integers. We show that the mod-one method of Chan and Hu (2015) for unit squares can be extended to these objects to get a polynomial-time approximation scheme (PTAS). We further show that the problem has a polynomial-time algorithm when all rectangles intersect a given horizontal line. On the contrary, we show that even the unweighted version of the problem is NP-hard when every rectangle intersects at least one of two given horizontal lines at the unit vertical distance.

Excluded $t$-Factors in Bipartite Graphs: Unified Framework for Nonbipartite Matchings, Restricted 2-Matchings, and Matroids

We propose a framework for optimal $t$-matchings excluding the prescribed $t$-factors in bipartite graphs. The proposed framework is a generalization of the nonbipartite matching problem and includes several problems, such as the triangle-free $2$-matching, square-free $2$-matching, even factor, and arborescence problems. In this paper, we demonstrate a unified understanding of these problems by commonly extending previous important results. We solve our problem under a reasonable assumption, which is sufficiently broad to include the specific problems listed above. We first present a min-max theorem and a combinatorial algorithm for the unweighted version. We then provide a linear programming formulation with dual integrality and a primal-dual algorithm for the weighted version. A key ingredient of the proposed algorithm is a technique to shrink forbidden structures, which corresponds to the techniques of shrinking odd cycles, triangles, squares, and directed cycles in Edmonds' blossom algorithm, a triangle-free $2$-matching algorithm, a square-free $2$-matching algorithm, and an arborescence algorithm, respectively.

Linear-Time Algorithms for Maximum-Weight Induced Matchings and Minimum Chain Covers in Convex Bipartite Graphs

A bipartite graph G=(U,V,E) is convex if the vertices in V can be linearly ordered such that for each vertex uin U, the neighbors of u are consecutive in the ordering of V. An induced matchingH of G is a matching for which no edge of E connects endpoints of two different edges of H. We show that in a convex bipartite graph with n vertices and mweighted edges, an induced matching of maximum total weight can be computed in O(n+m) time. An unweighted convex bipartite graph has a representation of size O(n) that records for each vertex uin U the first and last neighbor in the ordering of V. Given such a compact representation, we compute an induced matching of maximum cardinality in O(n) time. In convex bipartite graphs, maximum-cardinality induced matchings are dual to minimum chain covers. A chain cover is a covering of the edge set by chain subgraphs, that is, subgraphs that do not contain induced matchings of more than one edge. Given a compact representation, we compute a representation of a minimum chain cover in O(n) time. If no compact representation is given, the cover can be computed in O(n+m) time. All of our algorithms achieve optimal linear running time for the respective problem and model, and they improve and generalize the previous results in several ways: The best algorithms for the unweighted problem versions had a running time of O(n^2) (Brandstädt et al. in Theor. Comput. Sci. 381(1–3):260–265, 2007. https://doi.org/10.1016/j.tcs.2007.04.006). The weighted case has not been considered before.

Upper and lower degree-constrained graph orientation with minimum penalty

In the degree-constrained graph orientation problem, the input is an unweighted, undirected graph G=(V,E) and nonnegative integers av and bv (with av≤bv) for each v∈V, and the objective is to assign a direction to every edge in E in such a way that for each v∈V, the number of outgoing edges in the resulting directed graph lies in the interval [av,bv]. When such an orientation does not exist, it is desirable to find an orientation that best fits the condition instead. In this paper, we consider the problem of finding an orientation that minimizes the total penalty ∑v∈Vcv, where cv is a penalty incurred whenever a vertex v violates its degree constraints. As penalty functions, convex, concave, and step functions are considered in this paper. We show that the problem with any convex penalty function can be solved in O(|E|1.5min⁡{log⁡(|E|⋅C),|E|0.5log⁡Δlog⁡|E|}) time, where Δ and C are the maximum degree and the largest magnitude of a penalty, respectively. In contrast, we show APX-hardness of the problem with step or concave functions. For trees and graphs with treewidth τ, the problem with any penalty function can be solved exactly in O(|V|log⁡Δ) time and O(τ2Δ2τ+2|V|) time, respectively. Finally, we consider the generalization of the problem to edge-weighted graphs and establish strong bounds on its inapproximability that hold even in the special case of stars. On the positive side, we can extend our algorithms for unweighted version of the problem to obtain pseudo-polynomial-time algorithms for the edge-weighted problem variant when restricted to trees and graphs with bounded treewidth. Also, we design a PTAS and a linear-time algorithm for stars with further restrictions on the degree constraints and edge weights.

Gentrification and Food Retail Instability: A Census Tract Analysis of the Bronx, New York, 2008 and 2017

As food retailers open, close, and change ownership, the resulting instability in local food environments can affect food access and health. Gentrification, and its associated socioeconomic changes, can be a factor in destabilizing food environments. This study examined food retail in lower income, gentrifying, and higher income census tracts in the Bronx, New York, in 2008 and 2017 to analyze the level of instability of retailers over this period. We created an instability index and tested unweighted and weighted variants to examine disruptions in food retail over time, within and across different food retail segments. We argue that, compared to an unweighted version of the index, a weighted index better captures meaningful food environment changes. The results of this weighted index show that although the odds of food retail change varied among segments and census tract types, gentrifying neighborhoods were not particularly vulnerable to food retail changes in the Bronx compared to lower income and higher income neighborhoods. Our weighted instability index can be applied to other contexts and commercial sectors to track the status of retailers over time and across neighborhoods.

Adverse Drug Event Prediction Using Noisy Literature-Derived Knowledge Graphs: Algorithm Development and Validation.

BackgroundAdverse drug events (ADEs) are unintended side effects of drugs that cause substantial clinical and economic burdens globally. Not all ADEs are discovered during clinical trials; therefore, postmarketing surveillance, called pharmacovigilance, is routinely conducted to find unknown ADEs. A wealth of information, which facilitates ADE discovery, lies in the growing body of biomedical literature. Knowledge graphs (KGs) encode information from the literature, where the vertices and the edges represent clinical concepts and their relations, respectively. The scale and unstructured form of the literature necessitates the use of natural language processing (NLP) to automatically create such KGs. Previous studies have demonstrated the utility of such literature-derived KGs in ADE prediction. Through unsupervised learning of the representations (features) of clinical concepts from the KG, which are used in machine learning models, state-of-the-art results for ADE prediction were obtained on benchmark data sets.ObjectiveDue to the use of NLP to infer literature-derived KGs, there is noise in the form of false positive (erroneous) and false negative (absent) nodes and edges. Previous representation learning methods do not account for such inaccuracies in the graph. NLP algorithms can quantify the confidence in their inference of extracted concepts and relations from the literature. Our hypothesis, which motivates this work, is that by using such confidence scores during representation learning, the learned embeddings would yield better features for ADE prediction models.MethodsWe developed methods to use these confidence scores on two well-known representation learning methods—DeepWalk and Translating Embeddings for Modeling Multi-relational Data (TransE)—to develop their weighted versions: Weighted DeepWalk and Weighted TransE. These methods were used to learn representations from a large literature-derived KG, the Semantic MEDLINE Database, which contains more than 93 million clinical relations. They were compared with Embedding of Semantic Predications, which, to our knowledge, is the best reported representation learning method using the Semantic MEDLINE Database with state-of-the-art results for ADE prediction. Representations learned from different methods were used (separately) as features of drugs and diseases to build classification models for ADE prediction using benchmark data sets. The methods were compared rigorously over multiple cross-validation settings.ResultsThe weighted versions we designed were able to learn representations that yielded more accurate predictive models than the corresponding unweighted versions of both DeepWalk and TransE, as well as Embedding of Semantic Predications, in our experiments. There were performance improvements of up to 5.75% in the F1-score and 8.4% in the area under the receiver operating characteristic curve value, thus advancing the state of the art in ADE prediction from literature-derived KGs.ConclusionsOur classification models can be used to aid pharmacovigilance teams in detecting potentially new ADEs. Our experiments demonstrate the importance of modeling inaccuracies in the inferred KGs for representation learning.

On Recovery Guarantees for Angular Synchronization

The angular synchronization problem of estimating a set of unknown angles from their known noisy pairwise differences arises in various applications. It can be reformulated as an optimization problem on graphs involving the graph Laplacian matrix. We consider a general, weighted version of this problem, where the impact of the noise differs between different pairs of entries and some of the differences are erased completely; this version arises for example in ptychography. We study two common approaches for solving this problem, namely eigenvector relaxation and semidefinite convex relaxation. Although some recovery guarantees are available for both methods, their performance is either unsatisfying or restricted to the unweighted graphs. We close this gap, deriving recovery guarantees for the weighted problem that are completely analogous to the unweighted version.

Epidemic spreading in a weighted pig trade network

The inclusion of edge weights can add valuable insights in the spreading processes within trade networks and may identify factors influencing the final epidemic size. The aim of the study was to evaluate the effect of different network versions on the outcome of an epidemiological model. The weighted network versions included the number of trade contacts (A), the sum of delivered livestock (B) and the mean number of delivered livestock per trade contact (C). Furthermore, other factors, e.g. transmission probability and farm type of primary outbreak, were tested for their impact on the final epidemic size. From 2013–2014, data from a pig trade network in Northern Germany was recorded containing 678 farms connected by 1,018 directed edges. An epidemiological model was implemented considering a higher probability of disease spread for edges with a higher weight for each of the combinations between network version and transmission probability. Only transmission routes following the network structure were considered for disease transmission. The outcome of the epidemiological model (number of infected farms) was tested with a generalized linear mixed model including the fixed effects network version (unweighted, A, B, C), transmission probability and farm type of primary outbreak (breeding farm, farrowing farm, finishing farm, farrow-to-finishing farm, unknown) as well as all twofold interactions. The results revealed that all fixed effects as well as all twofold interactions were significant (p ≤ 0.05), i.e. in the following only the impact of the interactions on the number of infected farms can be interpreted. Network versions B and C showed in all combinations the highest number of infected farms independent of the underlying transmission probability. The unweighted network and network version A showed a significant increase of infected farms with increasing transmission probability. All interactions including the farm type of primary outbreak revealed a significant higher number of infected farms for farm types located at the beginning of the production chain, e.g. breeding farms. These farm types reached also more other farms in 1–4 steps compared to farm types located near to the end of the production chain. The inclusion of edge weights has a significant effect on the outcome of epidemiological models and dependent on the chosen edge weight the results need to be interpreted accordingly.

On new algorithmic techniques for the weighted vertex coloring problem

The classical NP-hard weighted vertex coloring problem consists in minimizing the number of colors in colorings of vertices of a given graph so that, for each vertex, the number of its colors equals a given weight of the vertex and adjacent vertices receive distinct colors. The weighted chromatic number is the smallest number of colors in these colorings. There are several polynomial-time algorithmic techniques for designing efficient algorithms for the weighted vertex coloring problem. For example, standard techniques of this kind are the modular graph decomposition and the graph decomposition by separating cliques. This article proposes new polynomial-time methods for graph reduction in the form of removing redundant vertices and recomputing weights of the remaining vertices so that the weighted chromatic number changes in a controlled manner. We also present a method of reducing the weighted vertex coloring problem to its unweighted version and its application. This paper contributes to the algorithmic graph theory.

Mbend: an R package for bending non-positive-definite symmetric matrices to positive-definite

BackgroundR package mbend was developed for bending symmetric non-positive-definite matrices to positive-definite (PD). Bending is a procedure of transforming non-PD matrices to PD. The covariance matrices used in multi-trait best linear unbiased prediction (BLUP) should be PD. Two bending methods are implemented in mbend. The first is an unweighted bending with small positive values in a descending order replacing negative eigenvalues (LRS14), and the second method is a weighted (precision-based) bending with a custom small positive value (ϵ) replacing smaller eigenvalues (HJ03). Weighted bending is beneficial, as it relaxes low precision elements to change and it reduces or prohibits the change in high precision elements. Therefore, a weighted version of LRS14 was developed in mbend. In cases where the precision of matrix elements is unknown, the package provides an unweighted version of HJ03. Another unweighted bending method (DB88) was tested, by which all eigenvalues are changed (eigenvalues less than ϵ replaced with 100 × ϵ), and it is originally designed for correlation matrices.ResultsDifferent bending procedures were conducted on a 5 × 5 covariance matrix (V), V converted to a correlation matrix (C) and an ill-conditioned 1000 × 1000 genomic relationship matrix (G). Considering weighted distance statistics between matrix elements before and after bending, weighting considerably improved the bending quality. For weighted and unweighted bending of V and C, HJ03–4 (HJ03, ϵ = 10−4) performed the best. HJ03–2 (HJ03, ϵ = 10−2) ranked better than LRS14 for V, but not for C. Though the differences were marginal, LRS14 performed the best for G. DB88–4 (DB88, ϵ = 10−4) was used for unweighted bending and it ranked the last. This method could perform considerably better with a lower ϵ.ConclusionsR package mbend provides necessary tools for transforming symmetric non-PD matrices to PD, using different methods and parameters. There were benefits in both weighted bending and small positive values in a descending order replacing negative eigenvalues. Thus, weighted LRS14 was implemented in mbend. Different bending methods might be preferable for different matrices, depending on the matrix type (covariance vs. correlation), number and the magnitude of negative eigenvalues, and the matrix size.