Fragment-based shape signature techniques have proven to be powerful tools for computer-aided drug design. They allow scientists to search for target molecules with some similarity to a known active compound. They do not require reference to the full underlying chemical structure, which is essential to deal with chemical databases containing millions of compounds. However, finding the optimal match of a part of the fragmented compound can be time-consuming. In this paper, we use constraint programming to solve this specific problem. It involves finding a weighted assignment of fragments subject to connectivity constraints. Our experiments demonstrate the practical relevance of our approach and open new perspectives, including generating multiple, diverse solutions. Our approach constitutes an original use of a constraint solver in a real time setting, where propagation allows to avoid an enumeration of weighted paths. The model must remain robust to the addition of constraints making some instances not tractable. This particular context requires the use of unusual criteria for the choice of the model: lightweight, standard propagation algorithms, data structures without prohibitive constant cost. The objective is not to design new, complex algorithms to solve difficult instances.
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Community detection refers to the problem of clustering the nodes of a network into groups. Existing inferential methods for community structure mainly focus on unweighted (binary) networks. Many real-world networks are nonetheless weighted and a common practice is to dichotomize a weighted network to an unweighted one which is known to result in information loss. Literature on hypothesis testing in the latter situation is still missing. In this paper, we study the problem of testing the existence of community structure in weighted networks. Our contributions are threefold: (a). We use the (possibly infinite-dimensional) exponential family to model the weights and derive the sharp information-theoretic limit for the existence of consistent test. Within the limit, any test is inconsistent; and beyond the limit, we propose a useful consistent test. (b). Based on the information-theoretic limits, we provide the first formal way to quantify the loss of information incurred by dichotomizing weighted graphs into unweighted graphs in the context of hypothesis testing. (c). We propose several new and practically useful test statistics. Simulation study show that the proposed tests have good performance. Finally, we apply the proposed tests to an animal social network.
We study the stochastic $p$-Laplace system in a bounded domain. We propose two new space-time discretizations based on the approximation of time-averaged values. We establish linear convergence in space and $1/2$ convergence in time. Additionally, we provide a sampling algorithm to construct the necessary random input in an efficient way. The theoretical error analysis is complemented by numerical experiments.
We consider statistical models arising from the common set of solutions to a sparse polynomial system with general coefficients. The maximum likelihood degree counts the number of critical points of the likelihood function restricted to the model. We prove the maximum likelihood degree of a sparse polynomial system is determined by its Newton polytopes and equals the mixed volume of a related Lagrange system of equations.
Given a set $P$ of $n$ points in the plane, the $k$-center problem is to find $k$ congruent disks of minimum possible radius such that their union covers all the points in $P$. The $2$-center problem is a special case of the $k$-center problem that has been extensively studied in the recent past \cite{CAHN,HT,SH}. In this paper, we consider a generalized version of the $2$-center problem called \textit{proximity connected} $2$-center (PCTC) problem. In this problem, we are also given a parameter $\delta\geq 0$ and we have the additional constraint that the distance between the centers of the disks should be at most $\delta$. Note that when $\delta=0$, the PCTC problem is reduced to the $1$-center(minimum enclosing disk) problem and when $\delta$ tends to infinity, it is reduced to the $2$-center problem. The PCTC problem first appeared in the context of wireless networks in 1992 \cite{ACN0}, but obtaining a nontrivial deterministic algorithm for the problem remained open. In this paper, we resolve this open problem by providing a deterministic $O(n^2\log n)$ time algorithm for the problem.
This manuscript gives a theoretical framework for a new Hilbert space of functions, the so called occupation kernel Hilbert space (OKHS), that operate on collections of signals rather than real or complex numbers. To support this new definition, an explicit class of OKHSs is given through the consideration of a reproducing kernel Hilbert space (RKHS). This space enables the definition of nonlocal operators, such as fractional order Liouville operators, as well as spectral decomposition methods for corresponding fractional order dynamical systems. In this manuscript, a fractional order DMD routine is presented, and the details of the finite rank representations are given. Significantly, despite the added theoretical content through the OKHS formulation, the resultant computations only differ slightly from that of occupation kernel DMD methods for integer order systems posed over RKHSs.
The simulation of multi-body systems with frictional contacts is a fundamental tool for many fields, such as robotics, computer graphics, and mechanics. Hard frictional contacts are particularly troublesome to simulate because they make the differential equations stiff, calling for computationally demanding implicit integration schemes. We suggest to tackle this issue by using exponential integrators, a long-standing class of integration schemes (first introduced in the 60's) that in recent years has enjoyed a resurgence of interest. We show that this scheme can be easily applied to multi-body systems subject to stiff viscoelastic contacts, producing accurate results at lower computational cost than \changed{classic explicit or implicit schemes}. In our tests with quadruped and biped robots, our method demonstrated stable behaviors with large time steps (10 ms) and stiff contacts ($10^5$ N/m). Its excellent properties, especially for fast and coarse simulations, make it a valuable candidate for many applications in robotics, such as simulation, Model Predictive Control, Reinforcement Learning, and controller design.
In this paper we study the finite sample and asymptotic properties of various weighting estimators of the local average treatment effect (LATE), several of which are based on Abadie (2003)'s kappa theorem. Our framework presumes a binary endogenous explanatory variable ("treatment") and a binary instrumental variable, which may only be valid after conditioning on additional covariates. We argue that one of the Abadie estimators, which we show is weight normalized, is likely to dominate the others in many contexts. A notable exception is in settings with one-sided noncompliance, where certain unnormalized estimators have the advantage of being based on a denominator that is bounded away from zero. We use a simulation study and three empirical applications to illustrate our findings. In applications to causal effects of college education using the college proximity instrument (Card, 1995) and causal effects of childbearing using the sibling sex composition instrument (Angrist and Evans, 1998), the unnormalized estimates are clearly unreasonable, with "incorrect" signs, magnitudes, or both. Overall, our results suggest that (i) the relative performance of different kappa weighting estimators varies with features of the data-generating process; and that (ii) the normalized version of Tan (2006)'s estimator may be an attractive alternative in many contexts. Applied researchers with access to a binary instrumental variable should also consider covariate balancing or doubly robust estimators of the LATE.
Recent advances in computer vision has led to a growth of interest in deploying visual analytics model on mobile devices. However, most mobile devices have limited computing power, which prohibits them from running large scale visual analytics neural networks. An emerging approach to solve this problem is to offload the computation of these neural networks to computing resources at an edge server. Efficient computation offloading requires optimizing the trade-off between multiple objectives including compressed data rate, analytics performance, and computation speed. In this work, we consider a "split computation" system to offload a part of the computation of the YOLO object detection model. We propose a learnable feature compression approach to compress the intermediate YOLO features with light-weight computation. We train the feature compression and decompression module together with the YOLO model to optimize the object detection accuracy under a rate constraint. Compared to baseline methods that apply either standard image compression or learned image compression at the mobile and perform image decompression and YOLO at the edge, the proposed system achieves higher detection accuracy at the low to medium rate range. Furthermore, the proposed system requires substantially lower computation time on the mobile device with CPU only.
We recall some of the history of the information-theoretic approach to deriving core results in probability theory and indicate parts of the recent resurgence of interest in this area with current progress along several interesting directions. Then we give a new information-theoretic proof of a finite version of de Finetti's classical representation theorem for finite-valued random variables. We derive an upper bound on the relative entropy between the distribution of the first $k$ in a sequence of $n$ exchangeable random variables, and an appropriate mixture over product distributions. The mixing measure is characterised as the law of the empirical measure of the original sequence, and de Finetti's result is recovered as a corollary. The proof is nicely motivated by the Gibbs conditioning principle in connection with statistical mechanics, and it follows along an appealing sequence of steps. The technical estimates required for these steps are obtained via the use of a collection of combinatorial tools known within information theory as `the method of types.'
Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, DP algorithms are usually non-differentiable, which hampers their use as a layer in neural networks trained by backpropagation. To address this issue, we propose to smooth the max operator in the dynamic programming recursion, using a strongly convex regularizer. This allows to relax both the optimal value and solution of the original combinatorial problem, and turns a broad class of DP algorithms into differentiable operators. Theoretically, we provide a new probabilistic perspective on backpropagating through these DP operators, and relate them to inference in graphical models. We derive two particular instantiations of our framework, a smoothed Viterbi algorithm for sequence prediction and a smoothed DTW algorithm for time-series alignment. We showcase these instantiations on two structured prediction tasks and on structured and sparse attention for neural machine translation.
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