1. Open Problems - Quantiki | Quantum Information Wiki And Portal Sep 9, 2008 List of open problems. This page contains information taken directly from Reinhard Werner s webpage. On this page we collect problems in http://www.quantiki.org/wiki/Open_Problems

@import "/mediawiki/skins/quantiki/mediawiki.css"; @import "/mediawiki/skins/quantiki/style.css"; Portal Forum FAQ Page ... History Open Problems Open Problems Contents List of open problems Suggested further problems Maximal rate function for estimation Problem ... Literature List of open problems This page contains information taken directly from Reinhard Werner's webpage On this page we collect problems in Quantum Information Theory we or our contributors find worthy of attention. The list is ordered by "last submission on top". Numbering is kept stable, so you can refer to the problems by number. Click on the title to find the statement of the problem and some information on known partial results. This information will be updated whenever significant progress is brought to our attention. To make this page interesting we obviously need input from the community, so please contribute good problems. By this we mean problems in Quantum Information Theory, which are stated in a self-contained way in the current terminology of the field, are open to the best of your knowledge, and pose an interesting challenge to other researchers. We will make an effort to publish all good problems quickly, but may reject contributions we find less suitable. Send contributions by email to . The format of contributions is free. Text written in simple LaTeX, and divided into sections such as Problem/ Background/ Partial Results/ Remarks/ Literature creates the smallest workload for us.

2. Category:Open Problems - Wikipedia, The Free Encyclopedia Unsolved problems category for problems of a theoretical nature. http://en.wikipedia.org/wiki/Category:Open_problems

Category:Open problems From Wikipedia, the free encyclopedia Jump to: navigation search Unsolved problems: category for problems of a theoretical nature. See list of unsolved problems Not for factual questions (e.g. Marie Celeste , etc): these belong in Category:Mysteries , or another of its subcategories, like Category:unsolved crimes Not for practical disputes (e.g. pollution Middle East conflict ). Perhaps try Category:Controversies or Category:Conflict Subcategories This category has the following 9 subcategories, out of 9 total. Lists of unsolved problems (13 P) C Uncracked codes and ciphers (3 C, 10 P) Unsolved problems in computer science (12 P) E Economic puzzles (10 P) L Unsolved problems in linguistics (3 C, 4 P) M Unsolved problems in mathematics (3 C, 92 P) N Unsolved problems in neuroscience (1 C, 19 P) P Unsolved problems in physics (25 P) U Unsolved problems in astronomy (3 P) Pages in category "Open problems" The following 7 pages are in this category, out of 7 total. This list may not reflect recent changes ( learn more Open problem List of unsolved problems F Fermi paradox G Great Filter L List of unsolved problems in biology O Origin of water on Earth U Template:Unsolved problems Retrieved from " http://en.wikipedia.org/wiki/Category:Open_problems

3. Open Problems - Discussion And Encyclopedia Article. Who Is Open Problems? What Open problems. Discussion about Open problems. Ecyclopedia or dictionary article about Open problems. http://www.knowledgerush.com/kr/encyclopedia/Open_problems/

4. Game Of Life News: Open Problems Archives Stephen Silver's 81x62 stable reflector discovered on 6 November 1998. Uses a Herschel conduit to repair an imperfect twobeehive reflector found earlier by Paul Callahan. http://pentadecathlon.com/lifeNews/open_problems/

Game of Life News Recent news about Conway's Game of Life Recent Posts The Continuing Search for a Microreflector Site Info Authors H.Koenig Dave Greene Categories Administrative Agars Breeders Discovery ... Main 2010 March 16 Open Problems The Continuing Search for a Microreflector Stephen Silver's 81x62 stable reflector discovered on 6 November 1998. Uses a Herschel conduit to repair an imperfect two-beehive reflector found earlier by Paul Callahan. Ever since Paul Callahan discovered the first stable reflector in 1996, people have continually searched for increasingly smaller reflectors. This has been partially successful , as in the two years that followed the area of stable reflectors decreased by approximately two orders of magnitude. The smallest 90-degree reflector to date was found by Stephen Silver, and has a bounding box of 81*62. The problem is this: Silver's reflector was found over a decade ago, in 1998, and no-one has managed to beat this record. Dave Greene discovered a compact 180-degree reflector, which he dubbed the boojum reflector , in 2001. Recently Adam P. Goucher discovered a slightly smaller and much faster 180-degree reflector (the

5. Open Problems These are open problems that I ve encountered in the course of my research. Not surprisingly, almost all the problems are geometric in nature. http://compgeom.cs.uiuc.edu/~jeffe/open/

Open Problems These are open problems that I've encountered in the course of my research . Not surprisingly, almost all the problems are geometric in nature. A name in brackets is the first person to describe the problem to me; this may not be original source of the problem. If there's no name, either I thought of the problem myself (although I was certainly not the first to do so), or I just forgot who told me. Problems in bold are described in more detail than the others, and are probably easier to understand without a lot of background knowledge. If you have any ideas about how to solve these problems, or if you have any interesting open problems you'd like me to add, please let me know . I'd love to hear them! Caveat lector! This web page and its children have not been significantly updated since 2001. Many of the problems listed on this page have been partially or even completely solved since then. Please do not cite these pages as evidence that a problem is still open; that makes no more sense than citing a paper published in 2001!

6. Open Problems For Undergraduates A collection of open problems in Discrete Mathematics which are currently being researched by members of the DIMACS community. http://dimacs.rutgers.edu/~hochberg/undopen/

Open Problems for Undergraduates Open Problems by Area Graph Theory Combinatorial Geometry Geometry/Number theory Venn Diagrams Inequalities Polyominos This is a collection of open problems in Discrete Mathematics which are currently being researched by members of the DIMACS community. These problems are easily stated, require little mathematical background, and may readily be understood and worked on by anyone who is eager to think about interesting and unsolved mathematical problems. Some of these problems are quite hard and have been open for a long time. Others are newer. For further information on a particular problem, you may write to the associated researcher. Although these problems are intended for undergraduates, it is expected that high school students, teachers, graduate students and professional mathematicians will be drawn to this collection. This is not discouraged. Each of these problems is associated with some member of DIMACS. If you have any questions, comments, insights or solutions, please send email to the researcher who is listed with the problem. These pages are maintained by Robert Hochberg Last modified Feb. 5, 1997.

7. Open Problems Originally from the Katsiveli 2000 Open Problems Session, now maintained by Sergiy Kolyada. PDF/PS. http://www.math.iupui.edu/~mmisiure/open/

Other sites with this page O pen P roblems in D ynamical S ystems E rgodic T heory Welcome! Katsiveli - 2000 Open Problems Session. New problems are being added to it. If you would like to submit some open problems to this page, please send them to Sergiy Kolyada If you have any remarks about this page, please write to Sergiy Kolyada or Michal Misiurewicz Geometric models of Pisot substitutions and non-commutative arithmetic Submitted by Pierre Arnoux (updated November 29, 2001) Ergodic Ramsey Theory - an update Submitted by Vitaly Bergelson (see also here Dense periodic points in cellular automata Submitted by Francois Blanchard Non-discrete locally compact second countable groups Submitted by Sergey Gefter Martingale convergence and ergodic theorems Submitted by Alexander Kachurovskii The problem is closed (October 21, 2002) Entropy, periodic points and transitivity of maps Submitted by Sergiy Kolyada and Lubomir Snoha (updated October 26, 2002) Natural spectral isomorphisms Submitted by Jan Kwiatkowski Density of periodic orbit measures for piecewise monotonic interval maps Submitted by Peter Raith Polygonal billiards: some open problems Submitted by Pascal Hubert and Serge Troubetzkoy Is any kind of mixing possible in "ToP" N-actions?

8. The Geometry Junkyard: Open Problems Open Problems Antipodes. Jim Propp asks whether the two farthest apart points, as measured by surface distance, on a symmetric convex body must be opposite each other on the body. http://www.ics.uci.edu/~eppstein/junkyard/open.html

Open Problems Antipodes . Jim Propp asks whether the two farthest apart points, as measured by surface distance, on a symmetric convex body must be opposite each other on the body. Apparently this is open even for rectangular boxes. Bounded degree triangulation . Pankaj Agarwal and Sandeep Sen ask for triangulations of convex polytopes in which the vertex or edge degree is bounded by a constant or polylog. Centers of maximum matchings . Andy Fingerhut asks, given a maximum (not minimum) matching of six points in the Euclidean plane, whether there is a center point close to all matched edges (within distance a constant times the length of the edge). If so, it could be extended to more points via Helly's theorem. Apparently this is related to communication network design. I include a response I sent with a proof (of a constant worse than the one he wanted, but generalizing as well to bipartite matching). The chromatic number of the plane . Gordon Royle and Ilan Vardi summarize what's known about the famous open problem of how many colors are needed to color the plane so that no two points at a unit distance apart get the same color. See also another article from Dave Rusin's known math pages.

9. Open Problems In Combinatorics Features links to newsletters, workshops, and papers. http://www.combinatorics.net/problems/

Open Problems in Combinatorics Combinatorial Problems I Like , by Josh Cooper Open Problems - Graph Theory and Combinatorics , by Douglas B. West Open problems in combinatorics (pdf file) , by Alexander Postnikov Positivity Problems and Conjectures in Algebraic Combinatorics , by Richard Stanley Ten Problems in Combinatorics, Lecture given by Gian-Carlo Rota at the Conference on Combinatorics and Physics (CAP'98), held at the Los Alamos National Laboratory, August 10-12, 1998. To be announced. Open Problems from the SIAM Activity Group Newsletter in Discrete Mathematics Problems on the Enumeration of Matchings (ps file) , by James Propp Unsolved Combinatorial Problems, by Zsolt Tuza Open Problems on Perfect Graphs , by Problems in Signed, Gain, and Biased Graphs , compiled by Thomas Zaslavsky Unsolved Problems in Graph Theory , compiled by Stephen C. Locke , by Fan R. K. Chung A list of problems on permutation groups , by Peter J. Cameron A problem on transitive permutation groups , by Peter J. Cameron Some Problems in Matroid Theory , compiled by Thomas Zaslavsky Unsolved Mathematics Problems , compiled by Steven Finch.

10. Some Open Problems Compiled by Jerry Spinrad. http://www.vuse.vanderbilt.edu/~spin/open.html

Send comments or new problems to include to spin@vuse.vanderbilt.edu

11. Problems In Graph Theory And Combinatorics Open problems are listed along with what is known about them, updated as http://www.math.uiuc.edu/~west/openp/

12. Open Problem - Wikipedia, The Free Encyclopedia Important open problems exist in many fields, such as Physics, Chemistry, Biology, Computer science, and Mathematics. For example, one of the most important open problems in http://en.wikipedia.org/wiki/Open_problem

Open problem From Wikipedia, the free encyclopedia Jump to: navigation search "Open question" redirects here. For information on open-ended questions, see closed-ended question In science and mathematics , an open problem or an open question is a known problem that can be accurately stated, and has not yet been solved (no solution for it is known). Notable examples of for-long open problems in mathematics , that have been solved and closed by researchers in the late twentieth century, are Fermat's Last Theorem and the four color map theorem Important open problems exist in many fields, such as Physics Chemistry Biology Computer science , and Mathematics . For example, one of the most important open problems in biochemistry is the protein structure prediction problem – how to predict a protein 's structure from its sequence. It is common in graduate schools to point out open problems to students. Graduate students as well as faculty members often engage in research to solve such problems. edit See also List of unsolved problems (by major field) Hilbert's problems Millennium Prize Problems edit References Faltings, Gerd (July 1995)

13. The Open Problems Project Numerical List of All The Open Problems Project. edited by Erik D. Demaine Joseph S. B. Mitchell - Joseph O'Rourke. Introduction This is the beginning of a project 1 to record open http://maven.smith.edu/~orourke/TOPP/

Next: Numerical List of All The Open Problems Project edited by Erik D. Demaine Joseph S. B. Mitchell Joseph O'Rourke Introduction This is the beginning of a project to record open problems of interest to researchers in computational geometry and related fields. It commenced with the publication of thirty problems in Computational Geometry Column 42 [ ] (see Problems 1-30 ), but has grown much beyond that. We encourage correspondence to improve the entries; please send email to TOPP@cs.smith.edu . If you would like to submit a new problem, please fill out this template Each problem is assigned a unique number for citation purposes. Problem numbers also indicate the order in which the problems were entered. Each problem is classified as belonging to one or more categories. The problems are also available as a single Postscript or PDF file. To begin navigating through the open problems, you may select from a category of interest below, or view a list of all problems sorted numerically Categorized List of All Problems Below, each category lists the problems that are classified under that category. Note that each problem may be classified under several categories.

14. Some Open Problems Open problems and conjectures concerning the determination of properties of families of graphs. http://www.eecs.umich.edu/~qstout/constantques.html

Some Open Problems and Conjectures These problems and conjectures concern the determination of properties of families of graphs. For example, one property of a graph is its domination number. For a graph G , a set S of vertices is a dominating set if every vertex of G is in S or adjacent to a member of S . The domination number of G is the minimum size of a dominating set of G . Determining the domination number of a graph is an NP-complete problem, but can often be done for many graphs encountered in practice. One topic of some interest has been to determine the dominating numbers of grid graphs (meshes), which are just graphs of the form P(n) x P(m) , where P(n) is the path of n vertices. Marilynn Livingston and I showed that for any graph G , the domination number of the family G x P(n) has a closed formula (as a function of n ), which can be found computationally. This appears in M.L. Livingston and Q.F. Stout, ``Constant time computation of minimum dominating sets'', Congresses Numerantium (1994), pp. 116-128. Abstract Paper.ps

15. [0707.4558] Open Problems In Algebraic Statistics Abstract Algebraic statistics is concerned with the study of probabilistic models and techniques for statistical inference using methods from algebra and geometry. http://arxiv.org/abs/0707.4558

arXiv.org math Search or Article-id Help Advanced search All papers Titles Authors Abstracts Full text Help pages Full-text links: Download: PDF PostScript Other formats Current browse context: math.ST new recent Change to browse by: math math.AG stat stat.CO ... NASA ADS Bookmark what is this? Mathematics > Statistics Theory Title: Open Problems in Algebraic Statistics Authors: Bernd Sturmfels (Submitted on 31 Jul 2007 ( ), last revised 10 Nov 2007 (this version, v2)) Abstract: Algebraic statistics is concerned with the study of probabilistic models and techniques for statistical inference using methods from algebra and geometry. This article presents a list of open mathematical problems in this emerging field, with main emphasis on graphical models with hidden variables, maximum likelihood estimation, and multivariate Gaussian distributions. This article is based on a lecture presented at the IMA in Minneapolis during the 2006/07 program on Applications of Algebraic Geometry. Comments: 13 pages Subjects: Statistics Theory (math.ST) ; Algebraic Geometry (math.AG); Computation (stat.CO)

16. Graph Theory Open Problems Six problems suitable for undergraduate research projects. http://dimacs.rutgers.edu/~hochberg/undopen/graphtheory/graphtheory.html

Graph Theory Open Problems Index of Problems Unit Distance Graphs-chromatic number Unit Distance Graphs-girth Barnette's Conjecture Crossing Number of K(7,7) ... Square of an Oriented Graph Unit Distance Graphs-chromatic number RESEARCHER: Robert Hochberg OFFICE: CoRE 414 Email: hochberg@dimacs.rutgers.edu DESCRIPTION: How many colors are needed so that if each point in the plane is assigned one of the colors, no two points which are exactly distance 1 apart will be assigned the same color? This problem has been open since 1956. It is known that the answer is either 4, 5, 6 or 7-this is not too hard to show. You should try it now in order to get a flavor for what this problem is really asking. This number is also called ``the chromatic number of the plane.'' A graph which can be embedded in the plane so that vertices correspond to points in the plane and edges correspond to unit-length line segments is called a ``unit-distance graph.'' The question above is equivalent to asking what the chromatic number of unit-distance graphs can be. Here are some warm-up questions, whose answers are known: What complete bipartite graphs are unit-distance graphs? What's the smallest 4-chromatic unit-distance graph? Show that the Petersen graph is a unit-distance graph.

17. Home | Open Problem Garden Welcome to the Open Problem Garden, a collection of unsolved problems in mathematics. Create and edit open problems pages (easy registration required ). http://garden.irmacs.sfu.ca/

@import "/misc/drupal.css"; @import url(/modules/drutex/drutex.css); @import "/modules/administration/administration.css"; @import "/modules/cck/content.css"; @import "/modules/devel/devel.css"; @import "/themes/bluebreeze/style.css"; Open Problem Garden Help About Contact ... login/create account Home Welcome to the Open Problem Garden , a collection of unsolved problems in mathematics. Here you may: Read descriptions of open problems. Post comments on them. Create and edit open problems pages (easy registration required). Help us Grow! We are eager to expand, so we are inviting contributions both large and small from all areas of mathematics. Many thanks to our contributors More about the Garden Structure Purpose Editorial Policy RSS feeds (get what you want delivered to you!) Navigate Subject Algebra Analysis Combinatorics ... more Recent Activity Reflection Disconnected Problem Composition of reloids expressed through atomic reloids Perfect cuboid Lindelöf hypothesis ... more Powered by Drupal Hosted by IRMACS Content distributed under

18. Open Problems In Artificial Life Open Problems in Artificial Life Mark A. Bedau ⁄ ; † JohnS. McCaskill ‡ NormanH. Packard Steen Rasmusse n⁄ ⁄ Chris Adam i† † DavidG. Green ‡‡ Takashi http://mitpress.mit.edu/journals/ARTL/Bedau.pdf

19. Open Problems In Mathematics And Physics - Home OPEN QUESTIONS GENERAL Lists of unsolved problems Science magazine 125 big questions MATHEMATICS (PHYSICIST S PERSPECTIVE) Sir Michael Atiyah s Fields http://www.openproblems.net/

Open Problems In Mathematics And Physics Home Home OPEN QUESTIONS GENERAL Lists of unsolved problems Science magazine 125 big questions Areas long to learn: quantum groups motivic cohomology , local and micro local analysis of large finite groups Exotic areas: infinite Banach spaces , large and inaccessible cardinals Some recent links between mathematics and physics Number theory and physics Conjectured links between the Riemann zeta function and chaotic quantum-mechanical systems Deep and relatively recent ideas in mathematics and physics Standard model and mathematics: Gauge field or connection Dirac operators or fundamental classes in K-theory ( Atiyah-Singer index theorem String theory and mathematics: Mirror symmetry Conformal field theory Mathematics behind supersymmetry Mathematics of M-Theory Chern-Simons theory Higher gauge theory ... Geometric Langlands Program Unified theory: Langlands Program Witten on Langlands Theory of "motives" Lists of unsolved problems ... PRICE P versus NP The Hodge Conjecture The Poincaré Conjecture (solved) The Riemann Hypothesis Yang-Mills Existence and Mass Gap Navier-Stokes Existence and Smoothness The Birch and Swinnerton-Dyer Conjecture Mathworld list Mathematical challenges of the 21st century including moduli spaces and borderland physics Goldbach conjecture Normality of pi digits in an integer base Unsolved problems and difficult to understand areas PRICES Fields Medal and Rolf Nevanlinna Prize Abel Prize PHYSICS Important unsolved problems in physics Quantum gravity Explaining high-Tc superconductors

20. Steiner Trees: Open Problems Of course, there are probably about a zillion open problems related to Steiner trees, but here are a few I've thought about. Full trees. Hwang's theorem allows us to construct an http://ganley.org/steiner/open.html

ganley.org The Steiner Tree Page Open Problems Of course, there are probably about a zillion open problems related to Steiner trees, but here are a few I've thought about. Full trees Hwang's theorem allows us to construct an optimal rectilinear Steiner tree of a full set in linear time. I know of no other metric or type of graph in which computing the optimal Steiner tree of a full set is polynomial-time solvable but computing a general Steiner tree is NP-hard. Note that there isn't even a sufficiently strong analogue of Hwang's theorem for rectilinear Steiner trees in three dimensions. Multidimensional rectilinear Steiner ratio . What is the rectilinear Steiner ratio in arbitrary dimension d ? It is at least 2-1/ d , as the d -dimensional analogue of the "cross" has this ratio. It is obviously at most 2. It is generally believed that the lower bound is correct, but this hasn't been proven. Even an upper bound lower than 2 would be interesting. Rectilinear Steiner arborescence . These are Steiner-like trees on points in the (first quadrant of the) plane, in which every segment in the tree is directed left to right or bottom to top. It is unknown whether computing an RSA is NP-complete. (A good reference to start with is Rao, Sadayappan, Hwang, and Shor

Page 1     1-20 of 131    1  | 2  | 3  | 4  | 5  | 6  | 7  | Next 20