In this paper, we propose TauRieL and target Traveling Salesman Problem (TSP) since it has broad applicability in theoretical and applied sciences. TauRieL utilizes an actor-critic inspired architecture that adopts ordinary feedforward nets to obtain a policy update vector @math . Then, we use @math to improve the state transition matrix from which we generate the policy. Also, the state transition matrix allows the solver to initialize from precomputed solutions such as nearest neighbors. In an online learning setting, TauRieL unifies the training and the search where it can generate near-optimal results in seconds. The input to the neural nets in the actor-critic architecture are raw 2-D inputs, and the design idea behind this decision is to keep neural nets relatively smaller than the architectures with wide embeddings with the tradeoff of omitting any distributed representations of the embeddings. Consequently, TauRieL generates TSP solutions two orders of magnitude faster per TSP instance as compared to state-of-the-art offline techniques with a performance impact of 6.1 in the worst case.
A wide range of TSP variants have been applied to a wide range of domains. Examples include the use of TSP in music for conjunct melody generation in computer-aided composition, as well as for forming automatic playlists and track artist suggestions - now used by Spotify and Tidal @cite_34 . TSP heuristics have also been used for diffractometer guidance in X-ray crystallography @cite_33 ; and for Telescope scheduling in exoplanet discovery @cite_10 as well as in galaxy imaging @cite_24 . It can also be applied to bioinformatics as a genome ordering problem by posing the ordering as a path traveling through each gene marker @cite_3 or as a clustering problem to solve gene expression clustering @cite_18 .
@cite_18 @cite_33 @cite_3 @cite_24 @cite_34 @cite_10
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We present a deterministic (1+√5 2)-approximation algorithm for the s-t path TSP for an arbitrary metric. Given a symmetric metric cost on @math vertices including two prespecified endpoints, the problem is to find a shortest Hamiltonian path between the two endpoints; Hoogeveen showed that the natural variant of Christofides' algorithm is a 5 3-approximation algorithm for this problem, and this asymptotically tight bound in fact had been the best approximation ratio known until now. We modify this algorithm so that it chooses the initial spanning tree based on an optimal solution to the Held-Karp relaxation rather than a minimum spanning tree; we prove this simple but crucial modification leads to an improved approximation ratio, surpassing the 20-year-old barrier set by the natural Christofides' algorithm variant. Our algorithm also proves an upper bound of 1+√5 2 on the integrality gap of the path-variant Held-Karp relaxation. The techniques devised in this paper can be applied to other optimization problems as well: these applications include improved approximation algorithms and improved LP integrality gap upper bounds for the prize-collecting s-t path problem and the unit-weight graphical metric s-t path TSP. For many random constraint satisfaction problems, by now there exist asymptotically tight estimates of the largest constraint density for which solutions exist. At the same time, for many of these problems, all known polynomial-time algorithms stop finding solutions at much smaller densities. For example, it is well-known that it is easy to color a random graph using twice as many colors as its chromatic number. Indeed, some of the simplest possible coloring algorithms achieve this goal. Given the simplicity of those algorithms, one would expect room for improvement. Yet, to date, no algorithm is known that uses (2 - epsiv)chi colors, in spite of efforts by numerous researchers over the years. In view of the remarkable resilience of this factor of 2 against every algorithm hurled at it, we find it natural to inquire into its origin. We do so by analyzing the evolution of the set of k-colorings of a random graph, viewed as a subset of 1,...,k n, as edges are added. We prove that the factor of 2 corresponds in a precise mathematical sense to a phase transition in the geometry of this set. Roughly speaking, we prove that the set of k-colorings looks like a giant ball for k ges 2chi, but like an error-correcting code for k les (2 - epsiv)chi. We also prove that an analogous phase transition occurs both in random k-SAT and in random hypergraph 2-coloring. And that for each of these three problems, the location of the transition corresponds to the point where all known polynomial-time algorithms fail. To prove our results we develop a general technique that allows us to establish rigorously much of the celebrated 1-step replica-symmetry-breaking hypothesis of statistical physics for random CSPs. Motivation: During the last decade, improvements in high-throughput sequencing have generated a wealth of genomic data. Functionally interpreting these sequences and finding the biological signals that are hallmarks of gene function and regulation is currently mostly done using automated genome annotation platforms, which mainly rely on integrated machine learning frameworks to identify different functional sites of interest, including splice sites. Splicing is an essential step in the gene regulation process, and the correct identification of splice sites is a major cornerstone in a genome annotation system. Results: In this paper, we present SpliceRover, a predictive deep learning approach that outperforms the state-of-the-art in splice site prediction. SpliceRover uses convolutional neural networks (CNNs), which have been shown to obtain cutting edge performance on a wide variety of prediction tasks. We adapted this approach to deal with genomic sequence inputs, and show it consistently outperforms already existing approaches, with relative improvements in prediction effectiveness of up to 80.9 when measured in terms of false discovery rate. However, a major criticism of CNNs concerns their 'black box' nature, as mechanisms to obtain insight into their reasoning processes are limited. To facilitate interpretability of the SpliceRover models, we introduce an approach to visualize the biologically relevant information learnt. We show that our visualization approach is able to recover features known to be important for splice site prediction (binding motifs around the splice site, presence of polypyrimidine tracts and branch points), as well as reveal new features (e.g. several types of exclusion patterns near splice sites). Preface Introduction Molecular Biology Mathematics, Statistics, and Computer Science Some Molecular Biology DNA and Proteins The Central Dogma The Genetic Code Transfer RNA and Protein Sequences Genes Are Not Simple Biological Chemistry Restriction Maps Introduction Graphs Interval Graphs Measuring Fragment Sizes Multiple Maps Double Digest Problem Classifying Multiple Solutions Algorithms for DDP Algorithms and Complexity DDP is N P-Complete Approaches to DDP Simulated Annealing: TSP and DDP Mapping with Real Data Cloning and Clone Libraries A Finite Number of Random Clones Libraries by Complete Digestion Libraries by Partial Digestion Genomes per Microgram Physical Genome Maps: Oceans, Islands, and Anchors Mapping by Fingerprinting Mapping by Anchoring An Overview of Clone Overlap Putting It Together Sequence Assembly Shotgun Sequencing Sequencing by Hybridization Shotgun Sequencing Revisited Databases and Rapid Sequence Analysis DNA and Protein Sequence Databases A Tree Representation of a Sequence Hashing a Sequence Repeats in a Sequence Sequence Comparison by Hashing Sequence Comparison with at most l Mismatches Sequence Comparison by Statistical Content Dynamic Programming Alignment of Two Sequences The Number of Alignments Shortest and Longest Paths in a Network Global Distance Alignment Global Similarity Alignment Fitting One Sequence into Another Local Alignment and Clumps Linear Space Algorithms Tracebacks Inversions Map Alignment Parametric Sequence Comparisons Multiple Sequence Alignment The Cystic Fibrosis Gene Dynamic Programming in r-Dimensions Weighted-Average Sequences Profile Analysis Alignment by Hidden Markov Models Consensus Word Analysis Probability and Statistics for Sequence Alignment Global Alignment Local Alignment Extreme Value Distributions The Chein-Stein Method Poisson Approximation and Long Matches Sequence Alignment with Scores Probability and Statistics for Sequence Patterns A Central Limit Theorem Nonoverlapping Pattern Counts Poisson Approximation Site Distributions RNA Secondary Structure Combinatorics Minimum Free-energy Structures Consensus folding Trees and Sequences Trees Distance Parsimony Maximum Likelihood Trees Sources and Perspectives Molecular Biology Physical Maps and Clone Libraries Sequence Assembly Sequence Comparisons Probability and Statistics RNA Secondary Structure Trees and Sequences References Problem Solutions and Hints Mathematical Notation Algorithm Index Author Index Subject Index We present a new efficient algorithm for the search version of the approximate Closest Vector Problem with Preprocessing (CVPP). Our algorithm achieves an approximation factor of O(n sqrt log n ), improving on the previous best of O(n^ 1.5 ) due to Lag arias, Lenstra, and Schnorr hkzbabai . We also show, somewhat surprisingly, that only O(n) vectors of preprocessing advice are sufficient to solve the problem (with the slightly worse approximation factor of O(n)). We remark that this still leaves a large gap with respect to the decisional version of CVPP, where the best known approximation factor is O(sqrt n log n ) due to Aharonov and Regev AharonovR04 . To achieve these results, we show a reduction to the same problem restricted to target points that are close to the lattice and a more efficient reduction to a harder problem, Bounded Distance Decoding with preprocessing (BDDP). Combining either reduction with the previous best-known algorithm for BDDP by Liu, Lyubashevsky, and Micciancio LiuLM06 gives our main result. In the setting of CVP without preprocessing, we also give a reduction from (1+eps)gamma approximate CVP to gamma approximate CVP where the target is at distance at most 1+1 eps times the minimum distance (the length of the shortest non-zero vector) which relies on the lattice sparsification techniques of Dadush and Kun DadushK13 . As our final and most technical contribution, we present a substantially more efficient variant of the LLM algorithm (both in terms of run-time and amount of preprocessing advice), and via an improved analysis, show that it can decode up to a distance proportional to the reciprocal of the smoothing parameter of the dual lattice MR04 . We show that this is never smaller than the LLM decoding radius, and that it can be up to an wide tilde Omega (sqrt n ) factor larger. Genetic algorithms (GA) can be exploited for optimal graph matching. Graphs represent powerful method of a pattern formal description. Globally optimal graph matching is a NP-complete problem. Pattern distortions and noise increase an optimal search difficulty which could be tackled using GA. This paper describes results of simple GA applied on a graph matching problem. As a conclusion, the suitable GA for an optimal graph "isomorphism" and "monomorphism" is proposed. Used coding resembles the travelling salesman problem (TSP). Consequently, performance of ordering operators has been tested. In contrast to the TSP, the fitness function depends on chromosome value positioning not ordering. It results in differences between optimal GA configuration for graph matching and for TSP. > In this work we investigate the applicability of unsupervised feature learning methods to the task of automatic genre prediction of music pieces. More specifically we evaluate a framework that recently has been successfully used to recognize objects in images. We first extract local patches from the time-frequency transformed audio signal, which are then pre-processed and used for unsupervised learning of an overcomplete dictionary of local features. For learning we either use a bootstrapped k-means clustering approach or select features randomly. We further extract feature responses in a convolutional manner and train a linear SVM for classification. We extensively evaluate the approach on the GTZAN dataset, emphasizing the influence of important design choices such as dimensionality reduction, pooling and patch dimension on the classification accuracy. We show that convolutional extraction of local feature responses is crucial to reach high performance. Furthermore we find that using this approach, simple and fast learning techniques such as k-means or randomly selected features are competitive with previously published results which also learn features from audio signals. A major challenge in molecular biology is reverse-engineering the cis-regulatory logic that plays a major role in the control of gene expression. This program includes searching through DNA sequences to identify “motifs” that serve as the binding sites for transcription factors or, more generally, are predictive of gene expression across cellular conditions. Several approaches have been proposed for de novo motif discovery–searching sequences without prior knowledge of binding sites or nucleotide patterns. However, unbiased validation is not straightforward. We consider two approaches to unbiased validation of discovered motifs: testing the statistical significance of a motif using a DNA “background” sequence model to represent the null hypothesis and measuring performance in predicting membership in gene clusters. We demonstrate that the background models typically used are “too null,” resulting in overly optimistic assessments of significance, and argue that performance in predicting TF binding or expression patterns from DNA motifs should be assessed by held-out data, as in predictive learning. Applying this criterion to common motif discovery methods resulted in universally poor performance, although there is a marked improvement when motifs are statistically significant against real background sequences. Moreover, on synthetic data where “ground truth” is known, discriminative performance of all algorithms is far below the theoretical upper bound, with pronounced “over-fitting” in training. A key conclusion from this work is that the failure of de novo discovery approaches to accurately identify motifs is basically due to statistical intractability resulting from the fixed size of co-regulated gene clusters, and thus such failures do not necessarily provide evidence that unfound motifs are not active biologically. Consequently, the use of prior knowledge to enhance motif discovery is not just advantageous but necessary. An implementation of the LR and ALR algorithms is available at http: code.google.com p likelihood-ratio-motifs . Motivation: During the past decade, the new focus on genomics has highlighted a particular challenge: to integrate the different views of the genome that are provided by various types of experimental data. Results: This paper describes a computational framework for integrating and drawing inferences from a collection of genome-wide measurements. Each dataset is represented via a kernel function, which defines generalized similarity relationships between pairs of entities, such as genes or proteins. The kernel representation is both flexible and efficient, and can be applied to many different types of data. Furthermore, kernel functions derived from different types of data can be combined in a straightforward fashion. Recent advances in the theory of kernel methods have provided efficient algorithms to perform such combinations in a way that minimizes a statistical loss function. These methods exploit semidefinite programming techniques to reduce the problem of finding optimizing kernel combinations to a convex optimization problem. Computational experiments performed using yeast genome-wide datasets, including amino acid sequences, hydropathy profiles, gene expression data and known protein--protein interactions, demonstrate the utility of this approach. A statistical learning algorithm trained from all of these data to recognize particular classes of proteins---membrane proteins and ribosomal proteins---performs significantly better than the same algorithm trained on any single type of data. Availability: Supplementary data at http: noble.gs.washington.edu proj sdp-svm In this paper, we propose a new, compact, 4D spatio-temporal “Nebula” feature to improve expression and facial movement analysis performance. Given a spatio-temporal volume, the data is voxelized and fit to a cubic polynomial. A label is assigned based on the principal curvature values, and the polar angles of the direction of least curvature are computed. The labels and angles for each feature are used to build a histogram for each region of the face. The concatenated histograms from each region give us our final feature vector. This feature description is tested on the posed expression database BU-4DFE and on a new 4D spontaneous expression database. Various region configurations, histogram sizes, and feature parameters are tested, including a non-dynamic version of the approach. The LBP-TOP approach on the texture image as well as on the depth image is also tested for comparison. The onsets of the six canonical expressions are classified for 100 subjects in BU-4DFE, while the onset, offset, and non-existence of 12 Action Units (AUs) are classified for 16 subjects from our new spontaneous database. For posed expression recognition, the Nebula feature approach shows improvement over LBPTOP on the depth images and significant improvement over the non-dynamic 3D-only approach. Moreover, the Nebula feature performs better for AU classification than the compared approaches for 11 of the AUs tested in terms of accuracy as well as Area Under Receiver Operating Characteristic Curve (AUC). In this paper, we present the results of a user study on exploratory search activities in a social science digital library. We conducted a user study with 32 participants with a social sciences background—16 postdoctoral researchers and 16 students—who were asked to solve a task on searching related work to a given topic. The exploratory search task was performed in a 10-min time slot. The use of certain search activities is measured and compared to gaze data recorded with an eye tracking device. We use a novel tree graph representation to visualise the users’ search patterns and introduce a way to combine multiple search session trees. The tree graph representation is capable of creating one single tree for multiple users and identifying common search patterns. In addition, the information behaviour of students and postdoctoral researchers is being compared. The results show that search activities on the stratagem level are frequently utilised by both user groups. The most heavily used search activities were keyword search, followed by browsing through references and citations, and author searching. The eye tracking results showed an intense examination of documents metadata, especially on the level of citations and references. When comparing the group of students and postdoctoral researchers, we found significant differences regarding gaze data on the area of the journal name of the seed document. In general, we found a tendency of the postdoctoral researchers to examine the metadata records more intensively with regard to dwell time and the number of fixations. By creating combined session trees and deriving subtrees from those, we were able to identify common patterns like economic (explorative) and exhaustive (navigational) behaviour. Our results show that participants utilised multiple search strategies starting from the seed document, which means that they examined different paths to find related publications. We present a probabilistic generative model for timing deviations in expressive music performance. The structure of the proposed model is equivalent to a switching state space model. The switch variables correspond to discrete note locations as in a musical score. The continuous hidden variables denote the tempo. We formulate two well known music recognition problems, namely tempo tracking and automatic transcription (rhythm quantization) as filtering and maximum a posteriori (MAP) state estimation tasks. Exact computation of posterior features such as the MAP state is intractable in this model class, so we introduce Monte Carlo methods for integration and optimization. We compare Markov Chain Monte Carlo (MCMC) methods (such as Gibbs sampling, simulated annealing and iterative improvement) and sequential Monte Carlo methods (particle filters). Our simulation results suggest better results with sequential methods. The methods can be applied in both online and batch scenarios such as tempo tracking and transcription and are thus potentially useful in a number of music applications such as adaptive automatic accompaniment, score typesetting and music information retrieval. This paper presents an inference algorithm that can discover temporal logic properties of a system from data. Our algorithm operates on finite time system trajectories that are labeled according to whether or not they demonstrate some desirable system properties (e.g. "the car successfully stops before hitting an obstruction"). A temporal logic formula that can discriminate between the desirable behaviors and the undesirable ones is constructed. The formulae also indicate possible causes for each set of behaviors (e.g. "If the speed of the car is greater than 15 m s within 0.5s of brake application, the obstruction will be struck") which can be used to tune designs or to perform on-line monitoring to ensure the desired behavior. We introduce reactive parameter signal temporal logic (rPSTL), a fragment of parameter signal temporal logic (PSTL) that is expressive enough to capture causal, spatial, and temporal relationships in data. We define a partial order over the set of rPSTL formulae that is based on language inclusion. This order enables a directed search over this set, i.e. given a candidate rPSTL formula that does not adequately match the observed data, we can automatically construct a formula that will fit the data at least as well. Two case studies, one involving a cattle herding scenario and one involving a stochastic hybrid gene circuit model, are presented to illustrate our approach. The problem of obtaining the maximum a posteriori estimate of a general discrete Markov random field (i.e., a Markov random field defined using a discrete set of labels) is known to be NP-hard. However, due to its central importance in many applications, several approximation algorithms have been proposed in the literature. In this paper, we present an analysis of three such algorithms based on convex relaxations: (i) LP-S: the linear programming (LP) relaxation proposed by Schlesinger (1976) for a special case and independently in (2001), (1998), and (2005) for the general case; (ii) QP-RL: the quadratic programming (QP) relaxation of Ravikumar and Lafferty (2006); and (iii) SOCP-MS: the second order cone programming (SOCP) relaxation first proposed by Muramatsu and Suzuki (2003) for two label problems and later extended by (2006) for a general label set. We show that the SOCP-MS and the QP-RL relaxations are equivalent. Furthermore, we prove that despite the flexibility in the form of the constraints objective function offered by QP and SOCP, the LP-S relaxation strictly dominates (i.e., provides a better approximation than) QP-RL and SOCP-MS. We generalize these results by defining a large class of SOCP (and equivalent QP) relaxations which is dominated by the LP-S relaxation. Based on these results we propose some novel SOCP relaxations which define constraints using random variables that form cycles or cliques in the graphical model representation of the random field. Using some examples we show that the new SOCP relaxations strictly dominate the previous approaches. The Cancer Genome Atlas (TCGA) has profiled over 10,000 tumors across 33 different cancer-types for many genomic features, including gene expression levels. Gene expression measurements capture substantial information about the state of each tumor. Certain classes of deep neural network models are capable of learning a meaningful latent space. Such a latent space could be used to explore and generate hypothetical gene expression profiles under various types of molecular and genetic perturbation. For example, one might wish to use such a model to predict a tumor9s response to specific therapies or to characterize complex gene expression activations existing in differential proportions in different tumors. Variational autoencoders (VAEs) are a deep neural network approach capable of generating meaningful latent spaces for image and text data. In this work, we sought to determine the extent to which a VAE can be trained to model cancer gene expression, and whether or not such a VAE would capture biologically-relevant features. In the following report, we introduce a VAE trained on TCGA pan-cancer RNA-seq data, identify specific patterns in the VAE encoded features, and discuss potential merits of the approach. We name our method "Tybalt" after an instigative, cat-like character who sets a cascading chain of events in motion in Shakespeare9s "Romeo and Juliet." From a systems biology perspective, Tybalt could one day aid in cancer stratification or predict specific activated expression patterns that would result from genetic changes or treatment effects. Existing deep convolutional neural networks (CNNs) require a fixed-size (e.g., 224 @math 224) input image. This requirement is “artificial” and may reduce the recognition accuracy for the images or sub-images of an arbitrary size scale. In this work, we equip the networks with another pooling strategy, “spatial pyramid pooling”, to eliminate the above requirement. The new network structure, called SPP-net, can generate a fixed-length representation regardless of image size scale. Pyramid pooling is also robust to object deformations. With these advantages, SPP-net should in general improve all CNN-based image classification methods. On the ImageNet 2012 dataset, we demonstrate that SPP-net boosts the accuracy of a variety of CNN architectures despite their different designs. On the Pascal VOC 2007 and Caltech101 datasets, SPP-net achieves state-of-the-art classification results using a single full-image representation and no fine-tuning. The power of SPP-net is also significant in object detection. Using SPP-net, we compute the feature maps from the entire image only once, and then pool features in arbitrary regions (sub-images) to generate fixed-length representations for training the detectors. This method avoids repeatedly computing the convolutional features. In processing test images, our method is 24-102 @math faster than the R-CNN method, while achieving better or comparable accuracy on Pascal VOC 2007. In ImageNet Large Scale Visual Recognition Challenge (ILSVRC) 2014, our methods rank #2 in object detection and #3 in image classification among all 38 teams. This manuscript also introduces the improvement made for this competition. Background on genetic algorithms, LISP, and genetic programming hierarchical problem-solving introduction to automatically-defined functions - the two-boxes problem problems that straddle the breakeven point for computational effort Boolean parity functions determining the architecture of the program the lawnmower problem the bumblebee problem the increasing benefits of ADFs as problems are scaled up finding an impulse response function artificial ant on the San Mateo trail obstacle-avoiding robot the minesweeper problem automatic discovery of detectors for letter recognition flushes and four-of-a-kinds in a pinochle deck introduction to biochemistry and molecular biology prediction of transmembrane domains in proteins prediction of omega loops in proteins lookahead version of the transmembrane problem evolutionary selection of the architecture of the program evolution of primitives and sufficiency evolutionary selection of terminals evolution of closure simultaneous evolution of architecture, primitive functions, terminals, sufficiency, and closure the role of representation and the lens effect. Appendices: list of special symbols list of special functions list of type fonts default parameters computer implementation annotated bibliography of genetic programming electronic mailing list and public repository. We prove the approximation ratio 8 5 for the metric s,t -path-TSP, and more generally for shortest connected T-joins. The algorithm that achieves this ratio is the simple "Best of Many" version of Christofides' algorithm (1976), suggested by An, Kleinberg and Shmoys (2012), which consists in determining the best Christofides s,t -tour out of those constructed from a family @math of trees having a convex combination dominated by an optimal solution x* of the Held-Karp relaxation. They give the approximation guarantee @math for such an s,t -tour, which is the first improvement after the 5 3 guarantee of Hoogeveen's Christofides type algorithm (1991). Cheriyan, Friggstad and Gao (2012) extended this result to a 13 8-approximation of shortest connected T-joins, for |T|≥4. The ratio 8 5 is proved by simplifying and improving the approach of An, Kleinberg and Shmoys that consists in completing x* 2 in order to dominate the cost of "parity correction" for spanning trees. We partition the edge-set of each spanning tree in @math into an s,t -path (or more generally, into a T-join) and its complement, which induces a decomposition of x*. This decomposition can be refined and then efficiently used to complete x* 2 without using linear programming or particular properties of T, but by adding to each cut deficient for x* 2 an individually tailored explicitly given vector, inherent in x*. A simple example shows that the Best of Many Christofides algorithm may not find a shorter s,t -tour than 3 2 times the incidentally common optima of the problem and of its fractional relaxation. A new improved hybrid optimization algorithm - PGATS algorithm, which is based on toy off-lattice model, is presented for dealing with three-dimensional protein structure prediction problems. The algorithm combines the particle swarm optimization (PSO), genetic algorithm (GA), and tabu search (TS) algorithms. Otherwise, we also take some different improved strategies. The factor of stochastic disturbance is joined in the particle swarm optimization to improve the search ability; the operations of crossover and mutation that are in the genetic algorithm are changed to a kind of random liner method; at last tabu search algorithm is improved by appending a mutation operator. Through the combination of a variety of strategies and algorithms, the protein structure prediction (PSP) in a 3D off-lattice model is achieved. The PSP problem is an NP-hard problem, but the problem can be attributed to a global optimization problem of multi-extremum and multi-parameters. This is the theoretical principle of the hybrid optimization algorithm that is proposed in this paper. The algorithm combines local search and global search, which overcomes the shortcoming of a single algorithm, giving full play to the advantage of each algorithm. In the current universal standard sequences, Fibonacci sequences and real protein sequences are certified. Experiments show that the proposed new method outperforms single algorithms on the accuracy of calculating the protein sequence energy value, which is proved to be an effective way to predict the structure of proteins. Markov chains are a well known tool to model temporal properties of many phenomena, from text structure to fluctuations in economics. Because they are easy to generate, Markovian sequences, i.e. temporal sequences having the Markov property, are also used for content generation applications such as text or music generation that imitate a given style. However, Markov sequences are traditionally generated using greedy, left-to-right algorithms. While this approach is computationally cheap, it is fundamentally unsuited for interactive control. This paper addresses the issue of generating steerable Markovian sequences. We target interactive applications such as games, in which users want to control, through simple input devices, the way the system generates a Markovian sequence, such as a text, a musical sequence or a drawing. To this aim, we propose to revisit Markov sequence generation as a branch and bound constraint satisfaction problem (CSP). We propose a CSP formulation of the basic Markovian hypothesis as elementary Markov Constraints (EMC). We propose algorithms that achieve domain-consistency for the propagators of EMCs, in an event-based implementation of CSP. We show how EMCs can be combined to estimate the global Markovian probability of a whole sequence, and accommodate for different species of Markov generation such as fixed order, variable-order, or smoothing. Such a formulation, although more costly than traditional greedy generation algorithms, yields the immense advantage of being naturally steerable, since control specifications can be represented by arbitrary additional constraints, without any modification of the generation algorithm. We illustrate our approach on simple yet combinatorial chord sequence and melody generation problems and give some performance results.