arXiv subjects

Peter Allen

Publications and source records attributed to Peter Allen.

At least 55 records · Page 3Linked to original sources

arXiv2016

Toward a Science of Autonomy for Physical Systems: Service

A recent study by the Robotic Industries Association has highlighted how service robots are increasingly broadening our horizons beyond the factory floor. From robotic vacuums, bomb retrievers, exoskeletons and drones, to robots used in surgery, space exploration, agriculture, home assistance and construction, service robots are building a formidable resume. In just the last few years we have seen service robots deliver room service meals, assist shoppers in finding items in a large home improvement store, checking in customers and storing their luggage at hotels, and pour drinks on cruise ships. Personal robots are here to educate, assist and entertain at home. These domestic robots can perform daily chores, assist people with disabilities and serve as companions or pets for entertainment. By all accounts, the growth potential for service robotics is quite large.

cs.CY↗

arXiv2016

Chromatic thresholds in dense random graphs

The chromatic threshold $δ_χ(H,p)$ of a graph $H$ with respect to the random graph $G(n,p)$ is the infimum over $d > 0$ such that the following holds with high probability: the family of $H$-free graphs $G \subset G(n,p)$ with minimum degree $δ(G) \ge dpn$ has bounded chromatic number. The study of the parameter $δ_χ(H) := δ_χ(H,1)$ was initiated in 1973 by Erdős and Simonovits, and was recently determined for all graphs $H$. In this paper we show that $δ_χ(H,p) = δ_χ(H)$ for all fixed $p \in (0,1)$, but that typically $δ_χ(H,p) \ne δ_χ(H)$ if $p = o(1)$. We also make significant progress towards determining $δ_χ(H,p)$ for all graphs $H$ in the range $p = n^{-o(1)}$. In sparser random graphs the problem is somewhat more complicated, and is studied in a separate paper.

math.CO↗

arXiv2016

Chromatic thresholds in sparse random graphs

The chromatic threshold $δ_χ(H,p)$ of a graph $H$ with respect to the random graph $G(n,p)$ is the infimum over $d > 0$ such that the following holds with high probability: the family of $H$-free graphs $G \subset G(n,p)$ with minimum degree $δ(G) \ge dpn$ has bounded chromatic number. The study of $δ_χ(H) :=δ_χ(H,1)$ was initiated in 1973 by Erdős and Simonovits. Recently $δ_χ(H)$ was determined for all graphs $H$. It is known that $δ_χ(H,p) =δ_χ(H)$ for all fixed $p \in (0,1)$, but that typically $δ_χ(H,p) \ne δ_χ(H)$ if $p = o(1)$. Here we study the problem for sparse random graphs. We determine $δ_χ(H,p)$ for most functions $p = p(n)$ when $H\in\{K_3,C_5\}$, and also for all graphs $H$ with $χ(H) \not\in \{3,4\}$.

math.CO↗

arXiv2016

Model-Driven Feed-Forward Prediction for Manipulation of Deformable Objects

Robotic manipulation of deformable objects is a difficult problem especially because of the complexity of the many different ways an object can deform. Searching such a high dimensional state space makes it difficult to recognize, track, and manipulate deformable objects. In this paper, we introduce a predictive, model-driven approach to address this challenge, using a pre-computed, simulated database of deformable object models. Mesh models of common deformable garments are simulated with the garments picked up in multiple different poses under gravity, and stored in a database for fast and efficient retrieval. To validate this approach, we developed a comprehensive pipeline for manipulating clothing as in a typical laundry task. First, the database is used for category and pose estimation for a garment in an arbitrary position. A fully featured 3D model of the garment is constructed in real-time and volumetric features are then used to obtain the most similar model in the database to predict the object category and pose. Second, the database can significantly benefit the manipulation of deformable objects via non-rigid registration, providing accurate correspondences between the reconstructed object model and the database models. Third, the accurate model simulation can also be used to optimize the trajectories for manipulation of deformable objects, such as the folding of garments. Extensive experimental results are shown for the tasks above using a variety of different clothing.

cs.CV↗

arXiv2016

Multi-Sensor Surface Analysis for Robotic Ironing

Robotic manipulation of deformable objects remains a challenging task. One such task is to iron a piece of cloth autonomously. Given a roughly flattened cloth, the goal is to have an ironing plan that can iteratively apply a regular iron to remove all the major wrinkles by a robot. We present a novel solution to analyze the cloth surface by fusing two surface scan techniques: a curvature scan and a discontinuity scan. The curvature scan can estimate the height deviation of the cloth surface, while the discontinuity scan can effectively detect sharp surface features, such as wrinkles. We use this information to detect the regions that need to be pulled and extended before ironing, and the other regions where we want to detect wrinkles and apply ironing to remove the wrinkles. We demonstrate that our hybrid scan technique is able to capture and classify wrinkles over the surface robustly. Given detected wrinkles, we enable a robot to iron them using shape features. Experimental results show that using our wrinkle analysis algorithm, our robot is able to iron the cloth surface and effectively remove the wrinkles.

cs.RO↗

arXiv2015

Folding Deformable Objects using Predictive Simulation and Trajectory Optimization

Robotic manipulation of deformable objects remains a challenging task. One such task is folding a garment autonomously. Given start and end folding positions, what is an optimal trajectory to move the robotic arm to fold a garment? Certain trajectories will cause the garment to move, creating wrinkles, and gaps, other trajectories will fail altogether. We present a novel solution to find an optimal trajectory that avoids such problematic scenarios. The trajectory is optimized by minimizing a quadratic objective function in an off-line simulator, which includes material properties of the garment and frictional force on the table. The function measures the dissimilarity between a user folded shape and the folded garment in simulation, which is then used as an error measurement to create an optimal trajectory. We demonstrate that our two-arm robot can follow the optimized trajectories, achieving accurate and efficient manipulations of deformable objects.

cs.RO↗

arXiv2015

Articulated Pose Estimation Using Hierarchical Exemplar-Based Models

Exemplar-based models have achieved great success on localizing the parts of semi-rigid objects. However, their efficacy on highly articulated objects such as humans is yet to be explored. Inspired by hierarchical object representation and recent application of Deep Convolutional Neural Networks (DCNNs) on human pose estimation, we propose a novel formulation that incorporates both hierarchical exemplar-based models and DCNNs in the spatial terms. Specifically, we obtain more expressive spatial models by assuming independence between exemplars at different levels in the hierarchy; we also obtain stronger spatial constraints by inferring the spatial relations between parts at the same level. As our method strikes a good balance between expressiveness and strength of spatial models, it is both effective and generalizable, achieving state-of-the-art results on different benchmarks: Leeds Sports Dataset and CUB-200-2011.

cs.CV↗

arXiv2015

Triangle-free subgraphs of random graphs

Recently there has been much interest in studying random graph analogues of well known classical results in extremal graph theory. Here we follow this trend and investigate the structure of triangle-free subgraphs of $G(n,p)$ with high minimum degree. We prove that asymptotically almost surely each triangle-free spanning subgraph of $G(n,p)$ with minimum degree at least $\big(\frac{2}{5} + o(1)\big)pn$ is $\mathcal O(p^{-1}n)$-close to bipartite, and each spanning triangle-free subgraph of $G(n,p)$ with minimum degree at least $(\frac{1}{3}+\varepsilon)pn$ is $\mathcal O(p^{-1}n)$-close to $r$-partite for some $r=r(\varepsilon)$. These are random graph analogues of a result by Andrásfai, Erdős, and Sós [Discrete Math. 8 (1974), 205-218], and a result by Thomassen [Combinatorica 22 (2002), 591--596]. We also show that our results are best possible up to a constant factor.

math.CO↗

arXiv2014

Tight cycles and regular slices in dense hypergraphs

We study properties of random subcomplexes of partitions returned by (a suitable form of) the Strong Hypergraph Regularity Lemma, which we call regular slices. We argue that these subcomplexes capture many important structural properties of the original hypergraph. Accordingly we advocate their use in extremal hypergraph theory, and explain how they can lead to considerable simplifications in existing proofs in this field. We also use them for establishing the following two new results. Firstly, we prove a hypergraph extension of the Erdős-Gallai Theorem: for every $δ>0$ every sufficiently large $k$-uniform hypergraph with at least $(α+δ)\binom{n}{k}$ edges contains a tight cycle of length $αn$ for each $α\in[0,1]$. Secondly, we find (asymptotically) the minimum codegree requirement for a $k$-uniform $k$-partite hypergraph, each of whose parts has $n$ vertices, to contain a tight cycle of length $αkn$, for each $0<α<1$.

math.CO↗

arXiv2014

An extension of Turán's Theorem, uniqueness and stability

We determine the maximum number of edges of an $n$-vertex graph $G$ with the property that none of its $r$-cliques intersects a fixed set $M\subset V(G)$. For $(r-1)|M|\ge n$, the $(r-1)$-partite Turan graph turns out to be the unique extremal graph. For $(r-1)|M|<n$, there is a whole family of extremal graphs, which we describe explicitly. In addition we provide corresponding stability results.

math.CO↗

arXiv2014

A density Corrádi-Hajnal Theorem

We find, for all sufficiently large $n$ and each $k$, the maximum number of edges in an $n$-vertex graph which does not contain $k+1$ vertex-disjoint triangles. This extends a result of Moon [Canad. J. Math. 20 (1968), 96-102] which is in turn an extension of Mantel's Theorem. Our result can also be viewed as a density version of the Corradi-Hajnal Theorem.

math.CO↗

arXiv2014

Powers of Hamilton cycles in pseudorandom graphs

We study the appearance of powers of Hamilton cycles in pseudorandom graphs, using the following comparatively weak pseudorandomness notion. A graph $G$ is $(\varepsilon,p,k,\ell)$-pseudorandom if for all disjoint $X$ and $Y\subset V(G)$ with $|X|\ge\varepsilon p^kn$ and $|Y|\ge\varepsilon p^\ell n$ we have $e(X,Y)=(1\pm\varepsilon)p|X||Y|$. We prove that for all $β>0$ there is an $\varepsilon>0$ such that an $(\varepsilon,p,1,2)$-pseudorandom graph on $n$ vertices with minimum degree at least $βpn$ contains the square of a Hamilton cycle. In particular, this implies that $(n,d,λ)$-graphs with $λ\ll d^{5/2 }n^{-3/2}$ contain the square of a Hamilton cycle, and thus a triangle factor if $n$ is a multiple of $3$. This improves on a result of Krivelevich, Sudakov and Szabó [Triangle factors in sparse pseudo-random graphs, Combinatorica 24 (2004), no. 3, 403--426]. We also extend our result to higher powers of Hamilton cycles and establish corresponding counting versions.

math.CO↗

arXiv2013

Tight Hamilton cycles in random hypergraphs

We give an algorithmic proof for the existence of tight Hamilton cycles in a random r-uniform hypergraph with edge probability p=n^{-1+eps} for every eps>0. This partly answers a question of Dudek and Frieze [Random Structures Algorithms], who used a second moment method to show that tight Hamilton cycles exist even for p=omega(n)/n (r>2) where omega(n) tends to infinity arbitrary slowly, and for p=(e+o(1))/n (r>3). The method we develop for proving our result applies to related problems as well.

math.CO↗

arXiv2013

Maximum planar subgraphs in dense graphs

Kühn, Osthus and Taraz showed that for each γ>0 there exists C such that any n-vertex graph with minimum degree γn contains a planar subgraph with at least 2n-C edges. We find the optimum value of C for all γ<1/2 and sufficiently large n.

math.CO↗

arXiv2012

Turan numbers for bipartite graphs plus an odd cycle

For an odd integer $k$, let $\mathcal{C}_k = \{C_3,C_5,...,C_k\}$ denote the family of all odd cycles of length at most $k$ and let $\mathcal{C}$ denote the family of all odd cycles. Erdős and Simonovits \cite{ESi1} conjectured that for every family $\mathcal{F}$ of bipartite graphs, there exists $k$ such that $\ex{n}{\mathcal{F} \cup \mathcal{C}_k} \sim \ex{n}{\mathcal{F} \cup \mathcal{C}}$ as $n \rightarrow \infty$. This conjecture was proved by Erdős and Simonovits when $\mathcal{F} = \{C_4\}$, and for certain families of even cycles in \cite{KSV}. In this paper, we give a general approach to the conjecture using Scott's sparse regularity lemma. Our approach proves the conjecture for complete bipartite graphs $K_{2,t}$ and $K_{3,3}$: we obtain more strongly that for any odd $k \geq 5$, \[ \ex{n}{\mathcal{F} \cup \{C_k\}} \sim \ex{n}{\mathcal{F} \cup \mathcal{C}}\] and we show further that the extremal graphs can be made bipartite by deleting very few edges. In contrast, this formula does not extend to triangles -- the case $k = 3$ -- and we give an algebraic construction for odd $t \geq 3$ of $K_{2,t}$-free $C_3$-free graphs with substantially more edges than an extremal $K_{2,t}$-free bipartite graph on $n$ vertices. Our general approach to the Erdős-Simonovits conjecture is effective based on some reasonable assumptions on the maximum number of edges in an $m$ by $n$ bipartite $\mathcal{F}$-free graph.

math.CO↗

arXiv2011

A Spitzer IRAC Imaging Survey for T Dwarf Companions Around M, L, and T Dwarfs: Observations, Results, and Monte Carlo Population Analyses

We report observational techniques, results, and Monte Carlo population analyses from a Spitzer Infrared Array Camera imaging survey for substellar companions to 117 nearby M, L, and T dwarf systems (median distance of 10 pc, mass range of 0.6 to \sim0.05 M\odot). The two-epoch survey achieves typical detection sensitivities to substellar companions of [4.5 μm] \leq 17.2 mag for angular separations between about 7" and 165". Based on common proper motion analysis, we find no evidence for new substellar companions. Using Monte Carlo orbital simulations (assuming random inclination, random eccentricity, and random longitude of pericenter), we conclude that the observational sensitivities translate to an ability to detect 600-1100K brown dwarf companions at semimajor axes greater than ~35 AU, and to detect 500-600K companions at semimajor axes greater than ~60 AU. The simulations also estimate a 600-1100K T dwarf companion fraction of < 3.4% for 35-1200 AU separations, and < 12.4% for the 500-600K companions, for 60-1000 AU separations.

astro-ph.SR↗

arXiv2011

An improved error term for minimum H-decompositions of graphs

We consider partitions of the edge set of a graph G into copies of a fixed graph H and single edges. Let ϕ_H(n) denote the minimum number p such that any n-vertex G admits such a partition with at most p parts. We show that ϕ_H(n)=ex(n,K_r)+Θ(biex(n,H)) for χ(H)>2, where biex(n,H) is the extremal number of the decomposition family of H. Since biex(n,H)=O(n^{2-γ}) for some γ>0 this improves on the bound ϕ_H(n)=ex(n,H)+o(n^2) by Pikhurko and Sousa [J. Combin. Theory Ser. B 97 (2007), 1041-1055]. In addition it extends a result of Özkahya and Person [J. Combin. Theory Ser. B, to appear].

math.CO↗

arXiv2011

The chromatic thresholds of graphs

The chromatic threshold delta_chi(H) of a graph H is the infimum of d>0 such that there exists C=C(H,d) for which every H-free graph G with minimum degree at least d|G| satisfies chi(G) 2. We moreover characterise the graphs H with a given chromatic threshold, and thus determine delta_chi(H) for every graph H. This answers a question of Erdős and Simonovits [Discrete Math. 5 (1973), 323-334], and confirms a conjecture of Łuczak and Thomassé [preprint (2010), 18pp].

math.CO↗