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Probabilistic Constraints on the Mass and Composition of Proxima bFeb 08 2017Recent studies regarding the habitability, observability, and possible orbital evolution of the indirectly detected exoplanet Proxima b have mostly assumed a planet with $M \sim 1.3$ $M_\oplus$, a rocky composition, and an Earth-like atmosphere or none ... More

Mapping Directly Imaged Giant ExoplanetsOct 25 2012With the increasing number of directly imaged giant exoplanets the current atmosphere models are often not capable of fully explaining the spectra and luminosity of the sources. A particularly challenging component of the atmosphere models is the formation ... More

On the Mass Function, Multiplicity, and Origins of Wide-Orbit Giant PlanetsApr 12 2019A major outstanding question regarding the formation of planetary systems is whether wide-orbit giant planets form differently than close-in giant planets. We aim to establish constraints on two key parameters that are relevant for understanding the formation ... More

On the Mass Function, Multiplicity, and Origins of Wide-Orbit Giant PlanetsApr 12 2019Apr 16 2019A major outstanding question regarding the formation of planetary systems is whether wide-orbit giant planets form differently than close-in giant planets. We aim to establish constraints on two key parameters that are relevant for understanding the formation ... More

On the Mass Function, Multiplicity, and Origins of Wide-Orbit Giant PlanetsApr 12 2019Apr 23 2019A major outstanding question regarding the formation of planetary systems is whether wide-orbit giant planets form differently than close-in giant planets. We aim to establish constraints on two key parameters that are relevant for understanding the formation ... More

On the Mass Function, Multiplicity, and Origins of Wide-Orbit Giant PlanetsApr 12 2019May 08 2019A major outstanding question regarding the formation of planetary systems is whether wide-orbit giant planets form differently than close-in giant planets. We aim to establish constraints on two key parameters that are relevant for understanding the formation ... More

Atmospheric Compositions of Three Brown Dwarfs and Implications for their Formation ConditionsDec 09 2016The formation mechanisms and chemical compositions of brown dwarfs likely span a diverse range. If they are formed predominantly in isolation by gravitational collapse like dwarf stars then their compositions might follow those of dwarf stars, spanning ... More

On the Mass Function, Multiplicity, and Origins of Wide-Orbit Giant PlanetsApr 12 2019May 20 2019A major outstanding question regarding the formation of planetary systems is whether wide-orbit giant planets form differently than close-in giant planets. We aim to establish constraints on two key parameters that are relevant for understanding the formation ... More

The Transit Light Source Effect: False Spectral Features and Incorrect Densities for M-dwarf Transiting PlanetsNov 15 2017Jan 24 2018Transmission spectra are differential measurements that utilize stellar illumination to probe transiting exoplanet atmospheres. Any spectral difference between the illuminating light source and the disk-integrated stellar spectrum due to starspots and ... More

PHENIX results on Lévy analysis of Bose-Einstein correlation functionsOct 17 2016The nature of the quark-hadron phase transition can be investigated through analyzing the space-time structure of the hadron emission source. For this, the Bose-Einstein or HBT correlations of identified charged particles are among the best observables. ... More

Tractable hypergraph properties for constraint satisfaction and conjunctive queriesNov 04 2009Dec 06 2011An important question in the study of constraint satisfaction problems (CSP) is understanding how the graph or hypergraph describing the incidence structure of the constraints influences the complexity of the problem. For binary CSP instances (i.e., where ... More

Characterizations of centrality by local convexity of certain functions on $C^*$-algebrasSep 11 2017Feb 15 2018We provide a function class which is useful to distinguish central and non-central elements of a $C^*$-algebra in the following sense: for each element $f$ of this function class, a self-adjoint element $a$ of a $C^*$-algebra is central if and only if ... More

Quantum $f$-divergence preserving maps on positive semidefinite operators acting on finite dimensional Hilbert spacesFeb 22 2016Mar 18 2016We determine the structure of all bijections on the cone of positive semidefinite operators which preserve the quantum $f$-divergence for an arbitrary strictly convex function $f$ defined on the positive halfline. It turns out that any such transformation ... More

The Transit Light Source Effect II: The Impact of Stellar Heterogeneity on Transmission Spectra of Planets Orbiting Broadly Sun-like StarsDec 14 2018Transmission spectra probe exoplanetary atmospheres, but they can also be strongly affected by heterogeneities in host star photospheres through the transit light source effect. Here we build upon our recent study of the effects of unocculted spots and ... More

Cloud Atlas: High-Contrast Time-Resolved Observations of Planetary-Mass CompanionsJan 31 2019Feb 20 2019Directly-imaged planetary-mass companions offer unique opportunities in atmospheric studies of exoplanets. They share characteristics of both brown dwarfs and transiting exoplanets, therefore, are critical for connecting atmospheric characterizations ... More

Stellar-Mass-Dependent Disk Structure in Coeval Planet-Forming DisksJul 21 2010Previous studies suggest that the planet-forming disks around very-low-mass stars/brown dwarfs may be flatter than those around more massive stars, in contrast to model predictions of larger scale heights for gas-disks around lower-mass stars. We conducted ... More

PHENIX results on Bose-Einstein correlation functionsFeb 15 2016Measurement of Bose-Einstein or HBT correlations of identified charged particles provide insight into the space-time structure of particle emitting sources in heavy-ion collisions. In this paper we present the latest results from the RHIC PHENIX experiment ... More

Applications of an intersection formula to dual conesApr 03 2017Oct 19 2017We give a succinct proof of a duality theorem obtained by R\'ev\'esz in 1991 which concerns extremal quantities related to trigonomertic polynomials. The key tool of our new proof is an intersection formula on dual cones in real Banach spaces. We show ... More

Complete intersection quiver settings with one dimensional verticesMay 16 2011Jul 17 2011We describe the class of quiver settings with one dimensional vertices whose semi-simple representations are parametrized by a complete intersection variety. We show that these quivers can be reduced to a one vertex quiver with some combinatorial reduction ... More

Connections between centrality and local monotonicity of certain functions on $C^*$-algebrasAug 18 2016Nov 10 2016In 1955, Ogasawara showed that a $C^*$-algebra $\mathcal{A}$ is commutative if and only if the square function is monotone on the positive cone of $\mathcal{A}.$ It was observed later by Pedersen that the above statement remains true for any power function ... More

Maps on quantum states preserving Bregman and Jensen divergencesJan 25 2016Jul 01 2016We describe the structure of the bijective transformations on the set of density operators which preserve the Bregman $f$-divergence for an arbitrary differentiable strictly convex function $f.$ Furthermore, we determine the preservers of the Jensen $f$-divergence ... More

On a problem of Bauschke and BorweinDec 05 2014Aug 03 2015Consider a differentiable convex function $f: \mathbb{R}^n \supset \mathrm{dom} f \rightarrow \mathbb{R}.$ The induced spectral function $F$ is given by $F=f \circ \lambda,$ where $\lambda: \mathbf{M}_n^{sa} \rightarrow \mathbb{R}^{n}$ is the eigenvalue ... More

Jointly convex quantum Jensen divergencesDec 14 2017Mar 08 2018We investigate the quantum Jensen divergences from the viewpoint of joint convexity. It turns out that the set of the functions which generate jointly convex quantum Jensen divergences on positive matrices coincides with the Matrix Entropy Class which ... More

50+ Metrics for Calendar MiningJan 01 2016In this report we propose 50+ metrics which can be measured by organizations in order to identify improvements in various areas such as meeting efficiency, capacity planning or leadership skills, just to new a few. The notion of calendar mining is introduced ... More

A class of characterizations of central elements in $C^*$-algebrasAug 18 2016Let $\mathcal{A}$ be a unital $C^*$-algebra. We introduce a quite large function class $\mathcal{F}$ (which includes the power function $x \mapsto x^p$ for any $p \in (1, \infty)$), and show that any function $f \in \mathcal{F}$ provides a characterization ... More

Connections between centrality and local monotonicity of certain functions on $C^*$-algebrasAug 18 2016Apr 12 2017We introduce a quite large class of functions (including the exponential function and the power functions with exponent greater than one), and show that for any element $f$ of this function class, a self-adjoint element $a$ of a $C^*$-algebra is central ... More

Retrieval of planetary and stellar properties in transmission spectroscopy with AuraAug 29 2018Transmission spectroscopy provides a powerful probe of the atmospheric properties of transiting exoplanets. To date, studies of exoplanets in transit have focused on inferring their atmospheric properties such as chemical compositions, cloud/haze properties, ... More

A Physical Model-based Correction for Charge Traps in the Hubble Space Telescope's Wide Field Camera 3 Near-IR Detector and Applications to Transiting Exoplanets and Brown DwarfsMar 03 2017Mar 16 2017The Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3) near-IR channel is extensively used in time-resolved observations, especially for transiting exoplanet spectroscopy and brown dwarf and directly imaged exoplanet rotational phase mapping. The ... More

A plurality problem with three colors and query size threeAug 19 2017The Plurality problem - introduced by Aigner \cite{A2004} - has many variants. In this article we deal with the following version: suppose we are given $n$ balls, each of them colored by one of three colors. A \textit{plurality ball} is one such that ... More

Observational Constraints on the Stellar Radiation Field Impinging on Transitional Disk AtmospheresSep 18 2012Mid-infrared atomic and ionic line ratios measured in spectra of pre-main sequence stars are sensitive indicators of the hardness of the radiation field impinging on the disk surface. We present a low-resolution Spitzer IRS search for [Ar II] at 6.98 ... More

Cleaning Interval GraphsMar 05 2010We investigate a special case of the Induced Subgraph Isomorphism problem, where both input graphs are interval graphs. We show the NP-hardness of this problem, and we prove fixed-parameter tractability of the problem with non-standard parameterization, ... More

Structure Theorem and Isomorphism Test for Graphs with Excluded Topological SubgraphsNov 04 2011Nov 13 2014We generalize the structure theorem of Robertson and Seymour for graphs excluding a fixed graph $H$ as a minor to graphs excluding $H$ as a topological subgraph. We prove that for a fixed $H$, every graph excluding $H$ as a topological subgraph has a ... More

Obtaining a Planar Graph by Vertex DeletionDec 29 2008In the k-Apex problem the task is to find at most k vertices whose deletion makes the given graph planar. The graphs for which there exists a solution form a minor closed class of graphs, hence by the deep results of Robertson and Seymour, there is an ... More

The Collins-Roscoe mechanism and D-spacesOct 18 2010We prove that if a space X is well ordered $(\alpha A)$, or linearly semi-stratifiable, or elastic then X is a D-space.

A model with Suslin trees but no minimal uncountable linear orders other than $ω_1$ and $-ω_1$Mar 09 2018Mar 12 2018We show that the existence of a Suslin tree does not necessarily imply that there are uncountable minimal linear orders other than $\omega_1$ and $-\omega_1$, answering a question of J. Baumgartner. This is done by a Jensen-type iteration, proving that ... More

Some inequalities for quantum Tsallis entropy related to the strong subadditivityMar 27 2014Apr 23 2015In this paper we investigate the inequality $S_q(\rho_{123})+S_q(\rho_2)\leq S_q(\rho_{12})+S_q(\rho_{23}) \, (*)$ where $\rho_{123}$ is a state on a finite dimensional Hilbert space $\mathcal{H}_1\otimes \mathcal{H}_2\otimes \mathcal{H}_3,$ and $S_q$ ... More

Two infinite quantities and their surprising relationshipMar 12 2018As early as the 17th century, Galileo Galilei wondered how to compare the sizes of infinite sets. Fast forward almost four hundred years, and in the summer of 2017, at the 6th European Set Theory Conference, a young model theorist, Maryanthe Malliaris, ... More

Quantum Hellinger distances revisitedMar 25 2019May 10 2019This short note aims to study quantum Hellinger distances investigated recently by Bhatia et al. [Lett. Math. Phys. (2019), in press, arXiv:1901.01378] with a particular emphasis on barycenters. We introduce the family of generalized quantum Hellinger ... More

Direct Imaging Discovery of a Jovian Exoplanet Within a Triple Star SystemJul 08 2016Direct imaging allows for the detection and characterization of exoplanets via their thermal emission. We report the discovery via imaging of a young Jovian planet in a triple star system and characterize its atmospheric properties through near-infrared ... More

Evidence Against an Edge-On Disk Around the Extrasolar Planet 2MASS 1207 b and a New Thick Cloud Explanation for its Under-LuminosityMar 09 2011(Abridged) Since the discovery of the first directly-imaged, planetary-mass object, 2MASS 1207 b, several works have sought to explain a disparity between its observed temperature and luminosity. Given its known age, distance, and spectral type, 2MASS ... More

Path-search in the pyramid and in other graphsApr 27 2011We are given an acyclic directed graph with one source, and a subset of its edges which contains exactly one outgoing edge for every non-sink vertex. These edges determine a unique path from the source to a sink. We can think of it as a switch in every ... More

Rounds in a combinatorial search problemNov 30 2016We consider the following combinatorial search problem: we are given some excellent elements of $[n]$ and we should find at least one, asking questions of the following type: "Is there an excellent element in $A \subset [n]$?". G.O.H. Katona proved sharp ... More

Saturation in random graphsOct 30 2015Apr 13 2016A graph $H$ is $K_s$-saturated if it is a maximal $K_s$-free graph, i.e., $H$ contains no clique on $s$ vertices, but the addition of any missing edge creates one. The minimum number of edges in a $K_s$-saturated graph was determined over 50 years ago ... More

Domination in 3-tournamentsFeb 04 2016A 3-tournament is a complete 3-uniform hypergraph where each edge has a special vertex designated as its tail. A vertex set $X$ dominates $T$ if every vertex not in $X$ is contained in an edge whose tail is in $X$. The domination number of $T$ is the ... More

Improved Ramsey-type results in comparability graphsOct 01 2018Several discrete geometry problems are equivalent to estimating the size of the largest homogeneous sets in graphs that happen to be the union of few comparability graphs. An important observation for such results is that if $G$ is an $n$-vertex graph ... More

Finding small patterns in permutations in linear timeJul 11 2013Oct 31 2013Given two permutations $\sigma$ and $\pi$, the \textsc{Permutation Pattern} problem asks if $\sigma$ is a subpattern of $\pi$. We show that the problem can be solved in time $2^{O(\ell^2\log \ell)}\cdot n$, where $\ell=|\sigma|$ and $n=|\pi|$. In other ... More

On the joint convexity of the Bregman divergence of matricesMay 30 2014Apr 23 2015We characterize the functions for which the corresponding Bregman divergence is jointly convex on matrices. As an application of this characterization, we derive a sharp inequality for the quantum Tsallis entropy of a tripartite state, which can be considered ... More

Orientations of graphs with uncountable chromatic numberAug 24 2016Nov 09 2017Motivated by an old conjecture of P. Erd\H{o}s and V. Neumann-Lara, our aim is to investigate digraphs with uncountable dichromatic number and orientations of undirected graphs with uncountable chromatic number. A graph has uncountable chromatic number ... More

Fundamental Analysis of a Developer Support Chat Log for Identifying Process Improvement OpportunitiesMar 18 2015In this report analysis of a support chat log of a development team is shown. Developer support chat is used to provide internal support to other development teams. The report shows how a fundamental data analysis helped to identify gaps and action items ... More

Random walk hierarchy measure: What is more hierarchical, a chain, a tree or a star?Aug 31 2015Signs of hierarchy are prevalent in a wide range of systems in nature and society. One of the key problems is quantifying the importance of hierarchical organisation in the structure of the network representing the interactions or connections between ... More

An exact characterization of tractable demand patterns for maximum disjoint path problemsNov 04 2014We study the following general disjoint paths problem: given a supply graph $G$, a set $T\subseteq V(G)$ of terminals, a demand graph $H$ on the vertices $T$, and an integer $k$, the task is to find a set of $k$ pairwise vertex-disjoint valid paths, where ... More

Fixed-parameter tractability of multicut parameterized by the size of the cutsetOct 18 2010Sep 03 2013Given an undirected graph $G$, a collection $\{(s_1,t_1),..., (s_k,t_k)\}$ of pairs of vertices, and an integer $p$, the Edge Multicut problem ask if there is a set $S$ of at most $p$ edges such that the removal of $S$ disconnects every $s_i$ from the ... More

Orientations of graphs with uncountable chromatic numberAug 24 2016A graph (digraph) has uncountable chromatic number if its vertices cannot be covered by countably many independent (acyclic) sets. Our aim is to investigate digraphs with uncountable chromatic number and orientations of undirected graphs with uncountable ... More

Toric quiver cellsSep 12 2016It is shown that up to dimension four, the toric ideal of a quiver polytope is generated in degree two, with the only exception of the four-dimensional Birkhoff polytope. As a consequence, B{\o}gvad's conjecture holds for quiver polytopes of dimension ... More

Painlevé test of coupled Gross-Pitaevskii equationsSep 21 2003Painlev\'{e} test of the coupled Gross-Pitaevskii equations has been carried out with the result that the coupled equations pass the P-test only if a special relation containing system parameters (masses, scattering lengths) is satisfied. Computer algebra ... More

Chordal Editing is Fixed-Parameter TractableMay 30 2014Graph modification problems are typically asked as follows: is there a small set of operations that transforms a given graph to have a certain property. The most commonly considered operations include vertex deletion, edge deletion, and edge addition; ... More

Density of 4-edge paths in graphs with fixed edge densityJan 06 2016We investigate the number of 4-edge paths in graphs with a fixed number of vertices and edges. An asymptotically sharp upper bound is given to this quantity. The extremal construction is the quasi-star or the quasi-clique graph, depending on the edge ... More

Extremal results for Berge-hypergraphsMay 29 2015Let $G$ be a graph and $\mathcal{H}$ be a hypergraph both on the same vertex set. We say that a hypergraph $\mathcal{H}$ is a \emph{Berge}-$G$ if there is a bijection $f : E(G) \rightarrow E(\mathcal{H})$ such that for $e \in E(G)$ we have $e \subset ... More

Peeling and Nibbling the Cactus: Subexponential-Time Algorithms for Counting Triangulations and Related ProblemsMar 23 2016Given a set of $n$ points $S$ in the plane, a triangulation $T$ of $S$ is a maximal set of non-crossing segments with endpoints in $S$. We present an algorithm that computes the number of triangulations on a given set of $n$ points in time $n^{(11+ o(1))\sqrt{n} ... More

Uncountable strongly surjective linear ordersJun 30 2017Jan 30 2018A linear order $L$ is strongly surjective if $L$ can be mapped onto any of its suborders in an order preserving way. We prove various results on the existence and non-existence of uncountable strongly surjective linear orders answering questions of Camerlo, ... More

On algebraic endomorphisms of the Einstein gyrogroupJun 20 2015We describe the structure of all continuous algebraic endomorphisms of the open unit ball $\mathbf{B}$ of $\mathbb{R}^3$ equipped with the Einstein velocity addition. We show that any nonzero such transformation originates from an orthogonal linear transformation ... More

Edge-decomposition of graphs into copies of a tree with four edgesMar 08 2012We study edge-decompositions of highly connected graphs into copies of a given tree. In particular we attack the following conjecture by Bar\'at and Thomassen: for each tree $T$, there exists a natural number $k_T$ such that if $G$ is a $k_T$-edge-connected ... More

A characterization theorem for matrix variancesNov 15 2013Jul 01 2014Some recent papers formulated sufficient conditions for the decomposition of matrix variances. A statement was that if we have one or two observables, then the decomposition is possible. In this paper we consider an arbitrary finite set of observables ... More

Continuous Jordan triple endomorphisms of $\mathbb{P}_2$Jun 20 2015We describe the structure of all continuous Jordan triple endomorphisms of the set $\mathbb{P}_2$ of all positive definite $2\times 2$ matrices thus completing a recent result of ours. We also mention an application concerning sorts of surjective generalized ... More

Trees, ladders and graphsSep 09 2014We introduce a new method to construct uncountably chromatic graphs from non special trees and ladder systems. Answering a question of P. Erd\H{o}s and A. Hajnal from 1985, we construct graphs of chromatic number $\omega_1$ without uncountable $\omega$-connected ... More

Complexity of counting subgraphs: only the boundedness of the vertex-cover number countsJul 10 2014For a class $\mathcal{H}$ of graphs, #Sub$(\mathcal{H})$ is the counting problem that, given a graph $H\in \mathcal{H}$ and an arbitrary graph $G$, asks for the number of subgraphs of $G$ isomorphic to $H$. It is known that if $\mathcal{H}$ has bounded ... More

Prime congruences of idempotent semirings and a Nullstellensatz for tropical polynomialsAug 17 2014Sep 01 2015A new definition of prime congruences in additively idempotent semirings is given using twisted products. This class turns out to exhibit some analogous properties to the prime ideals of commutative rings. In order to establish a good notion of radical ... More

Everything you always wanted to know about the parameterized complexity of Subgraph Isomorphism (but were afraid to ask)Jul 08 2013Aug 25 2013Given two graphs $H$ and $G$, the Subgraph Isomorphism problem asks if $H$ is isomorphic to a subgraph of $G$. While NP-hard in general, algorithms exist for various parameterized versions of the problem: for example, the problem can be solved (1) in ... More

Optimal parameterized algorithms for planar facility location problems using Voronoi diagramsApr 21 2015We study a general family of facility location problems defined on planar graphs and on the 2-dimensional plane. In these problems, a subset of $k$ objects has to be selected, satisfying certain packing (disjointness) and covering constraints. Our main ... More

Quantum Hellinger distances revisitedMar 25 2019This short note aims to study quantum Hellinger distances introduced recently by Bhatia et al. [Lett. Math. Phys. (2019), in press, arXiv:1901.01378] with a particular emphasis on barycenters. We consider a quite large family of generalized quantum Hellinger ... More

Interval Deletion is Fixed-Parameter TractableNov 26 2012May 06 2014We study the minimum \emph{interval deletion} problem, which asks for the removal of a set of at most $k$ vertices to make a graph of $n$ vertices into an interval graph. We present a parameterized algorithm of runtime $10^k \cdot n^{O(1)}$ for this problem, ... More

Triangle-different Hamiltonian pathsAug 18 2016Oct 11 2016Let $G$ be a fixed graph. Two paths of length $n-1$ on $n$ vertices (Hamiltonian paths) are $G$-different if there is a subgraph isomorphic to $G$ in their union. In this paper we prove that the maximal number of pairwise triangle-different Hamiltonian ... More

Quantum Hellinger distances revisitedMar 25 2019Apr 19 2019This short note aims to study quantum Hellinger distances investigated recently by Bhatia et al. [Lett. Math. Phys. (2019), in press, arXiv:1901.01378] with a particular emphasis on barycenters. We introduce the family of generalized quantum Hellinger ... More

A faster FPT algorithm for Bipartite ContractionMay 13 2013Sep 04 2013The \textsc{Bipartite Contraction} problem is to decide, given a graph $G$ and a parameter $k$, whether we can can obtain a bipartite graph from $G$ by at most $k$ edge contractions. The fixed-parameter tractability of the problem was shown by [Heggernes ... More

Forbidden subposet problems with size restrictionsAug 23 2016Upper bounds to the size of a family of subsets of an n-element set that avoids certain configurations are proved. These forbidden configurations can be described by inclusion patterns and some sets having the same size. Our results are closely related ... More

A candidate planetary-mass object with a photoevaporating disk in OrionNov 29 2016In this work, we report the discovery of a candidate planetary-mass object with a photoevaporating protoplanetary disk, Proplyd 133-353, which is near the massive star $\theta^{1}$ Ori C at the center of the Orion Nebula Cluster (ONC). The object was ... More

t-wise Berge and t-heavy hypergraphsFeb 08 2019In many proofs concerning extremal parameters of Berge hypergraphs one starts with analyzing that part of that shadow graph which is contained in many hyperedges. Capturing this phenomenon we introduce two new types of hypergraphs. A hypergraph $\mathcal{H}$ ... More

Global Controllability of Chemical ReactionsAug 13 2015Controllability of chemical reactions is an important problem in chemical engineering science. In control theory, analysis of the controllability of linear systems is well-founded, however the dynamics of chemical reactions is usually nonlinear. Global ... More

Cloud Structure of the Nearest Brown Dwarfs II: High-amplitude variability for Luhman 16 A and B in and out of the 0.99 micron FeH featureSep 21 2015The re-emergence of the 0.99 $\mu$m FeH feature in brown dwarfs of early- to mid-T spectral type has been suggested as evidence for cloud disruption where flux from deep, hot regions below the Fe cloud deck can emerge. The same mechanism could account ... More

Stability results on vertex Turán problems in Kneser graphsApr 11 2018Apr 20 2018The vertex set of the Kneser graph $K(n,k)$ is $V = \binom{[n]}{k}$ and two vertices are adjacent if the corresponding sets are disjoint. For any graph $F$, the largest size of a vertex set $U \subseteq V$ such that $K(n,k)[U]$ is $F$-free, was recently ... More

Stability results on vertex Turán problems in Kneser graphsApr 11 2018Mar 07 2019The vertex set of the Kneser graph $K(n,k)$ is $V = \binom{[n]}{k}$ and two vertices are adjacent if the corresponding sets are disjoint. For any graph $F$, the largest size of a vertex set $U \subseteq V$ such that $K(n,k)[U]$ is $F$-free, was recently ... More

Infinite combinatorics plain and simpleMay 17 2017Feb 05 2018We explore a general method based on trees of elementary submodels in order to present highly simplified proofs to numerous results in infinite combinatorics. While countable elementary submodels have been employed in such settings already, we significantly ... More

Erdös-Pósa property of minor-models with prescribed vertex setsApr 01 2019A minor-model of a graph $H$ in a graph $G$ is a subgraph of $G$ that can be contracted to $H$. We prove that for a positive integer $\ell$ and a non-empty planar graph $H$ with at least $\ell-1$ connected components, there exists a function $f_{H, \ell}:\mathbb{N}\rightarrow ... More

Fixed-parameter algorithms for minimum cost edge-connectivity augmentationApr 24 2013Aug 26 2013We consider connectivity-augmentation problems in a setting where each potential new edge has a nonnegative cost associated with it, and the task is to achieve a certain connectivity target with at most p new edges of minimum total cost. The main result ... More

Constraint satisfaction parameterized by solution sizeJun 21 2012Jan 18 2014In the constraint satisfaction problem (CSP) corresponding to a constraint language (i.e., a set of relations) $\Gamma$, the goal is to find an assignment of values to variables so that a given set of constraints specified by relations from $\Gamma$ is ... More

An Increase in the Mass of Planetary Systems around Lower-Mass StarsOct 08 2015Oct 20 2015Trends in the planet population with host star mass provide an avenue to constrain planet formation theories. We derive the planet radius distribution function for Kepler stars of different spectral types, sampling a range in host star masses. We find ... More

A stellar-mass-dependent drop in planet occurrence ratesJun 28 2014Jan 11 2015The Kepler Spacecraft has discovered a large number of planets up to one-year periods and down to terrestrial sizes. While the majority of the target stars are main-sequence dwarfs of spectral type F, G, and K, Kepler covers stars with effective temperature ... More

Disks around Brown Dwarfs and Cool StarsFeb 10 2007We review the current picture of disks around cool stars and brown dwarfs, including disk fractions, mass estimates, disk structure and dispersal, accretion, dust composition, and the debris disk phase. We discuss these in the framework of recent planet ... More

NGC 1980 is not a foreground population of Orion: Spectroscopic survey of young stars with low extinction in Orion AMar 20 2017We perform a spectroscopic survey of the foreground population in Orion A with MMT/Hectospec. We use these data, along with archival spectroscopic data and photometric data, to derive spectral types, extinction values, and masses for 691 stars. Using ... More

Generalizations of the Tree Packing ConjectureApr 04 2011Oct 21 2011The Gy\'arf\'as tree packing conjecture asserts that any set of trees with $2,3, ..., k$ vertices has an (edge-disjoint) packing into the complete graph on $k$ vertices. Gy\'arf\'as and Lehel proved that the conjecture holds in some special cases. We ... More

Finding small separators in linear time via treewidth reductionOct 21 2011We present a method for reducing the treewidth of a graph while preserving all of its minimal $s-t$ separators up to a certain fixed size $k$. This technique allows us to solve $s-t$ Cut and Multicut problems with various additional restrictions (e.g., ... More

Known Algorithms on Graphs of Bounded Treewidth are Probably OptimalJul 30 2010We obtain a number of lower bounds on the running time of algorithms solving problems on graphs of bounded treewidth. We prove the results under the Strong Exponential Time Hypothesis of Impagliazzo and Paturi. In particular, assuming that SAT cannot ... More

On subexponential parameterized algorithms for Steiner Tree and Directed Subset TSP on planar graphsJul 07 2017There are numerous examples of the so-called square root phenomenon in the field of parameterized algorithms: many of the most fundamental graph problems, parameterized by some natural parameter $k$, become significantly simpler when restricted to planar ... More

$Extrasolar~Storms$: Pressure-dependent Changes In Light Curve Phase In Brown Dwarfs From Simultaneous $Hubble$ and $Spitzer$ ObservationsMay 09 2016We present $Spitzer$/IRAC Ch1 and Ch2 monitoring of six brown dwarfs during 8 different epochs over the course of 20 months. For four brown dwarfs, we also obtained simulataneous $HST$/WFC3 G141 Grism spectra during two epochs and derived light curves ... More

The LEECH Exoplanet Imaging Survey: Limits on Planet Occurrence Rates Under Conservative AssumptionsOct 24 2018Dec 06 2018We present the results of the largest $L^{\prime}$ ($3.8~\mu$m) direct imaging survey for exoplanets to date, the Large Binocular Telescope Interferometer (LBTI) Exozodi Exoplanet Common Hunt (LEECH). We observed 98 stars with spectral types from B to ... More

Parallaxes and Infrared Photometry of three Y0 dwarfsMar 30 2017We have followed up the three Y0 dwarfs WISEPA J041022.71+150248.5, WISEPA J173835.53+273258.9 and WISEPC J205628.90+145953.3 using the UKIRT/WFCAM telescope/instruments. We find parallaxes that are more consistent and accurate than previously published ... More

ACCESS I: An Optical Transmission Spectrum of GJ 1214b Reveals a Heterogeneous Stellar PhotosphereDec 01 2016GJ 1214b is the most studied sub-Neptune exoplanet to date. Recent measurements have shown its near-infrared transmission spectrum to be flat, pointing to a high-altitude opacity source in the exoplanet's atmosphere, either equilibrium condensate clouds ... More

Fixed-parameter Approximability of Boolean MinCSPsJan 19 2016The minimum unsatisfiability version of a constraint satisfaction problem asks for an assignment where the number of unsatisfied constraints is minimum possible, or equivalently, asks for a minimum-size set of constraints whose deletion makes the instance ... More

Rooted grid minorsJul 30 2013Intuitively, a tangle of large order in a graph is a highly-connected part of the graph, and it is known that if a graph has a tangle of large order then it has a large grid minor. Here we show that for any k, if G has a tangle of large order and Z is ... More

Treewidth reduction for constrained separation and bipartization problemsFeb 22 2009Feb 03 2010We present a method for reducing the treewidth of a graph while preserving all the minimal $s-t$ separators. This technique turns out to be very useful for establishing the fixed-parameter tractability of constrained separation and bipartization problems. ... More