Search

Your search keyword '"Przybylowski, P."' showing total 370 results
Start Over Author "Przybylowski, P."
370 results on '"Przybylowski, P."'

1. KKL theorem for the influence of a set of variables

Author

Przybyłowski, Tomasz

Subjects
Mathematics - Combinatorics, Computer Science - Discrete Mathematics, Mathematics - Probability, 42C10, 60E15, 68R01
Abstract

We study the notion of the influence of a set of variables on a Boolean function, which was recently introduced by Tal. We show that for an arbitrary fixed $d$, every Boolean function $f$ on $n$ variables admits a $d$-set of influence at least $\frac{1}{10} \mathbf{W}^{\geq d}(f) (\frac{\log n}{n})^d$, which is a direct generalisation of the Kahn-Kalai-Linial theorem. We give an example demonstrating essential sharpness of this result. Further, we generalise a related theorem of Oleszkiewicz regarding influences of pairs of variables.

Published
2024

2. Random walks on Coxeter interchange graphs

Author

Buckland, Matthew, Kolesnik, Brett, Mitchell, Rivka, and Przybyłowski, Tomasz

Subjects
Mathematics - Combinatorics, Mathematics - Probability, 05C20, 11P21, 17B22, 20F55, 51F15, 51M20, 52B05, 60J10, 62J15
Abstract

A tournament is an orientation of a graph. Vertices are players and edges are games, directed away from the winner. Kannan, Tetali and Vempala and McShine showed that tournaments with given score sequence can be rapidly sampled, via simple random walks on the interchange graphs of Brualdi and Li. These graphs are generated by the cyclically directed triangle, in the sense that traversing an edge corresponds to the reversal of such a triangle in a tournament. We study Coxeter tournaments on Zaslavsky's signed graphs. These tournaments involve collaborative and solitaire games, as well as the usual competitive games. The interchange graphs are richer in complexity, as a variety of other generators are involved. We prove rapid mixing by an intricate application of Bubley and Dyer's method of path coupling, using a delicate re-weighting of the graph metric. Geometric connections with the Coxeter permutahedra introduced by Ardila, Castillo, Eur and Postnikov are discussed.

Published
2024

3. Coxeter interchange graphs

Author

Kolesnik, Brett, Mitchell, Rivka, and Przybyłowski, Tomasz

Subjects
Mathematics - Combinatorics, 05C20, 11P21, 17B22, 20F55, 51M20, 52B05, 62J15
Abstract

Brualdi and Li introduced tournament interchange graphs. In such a graph, each vertex represents a tournament. Traversing an edge corresponds to reversing a cyclically directed triangle. Such a triangle is neutral, in that its reversal does not affect the score sequence. An interchange graph encodes the combinatorics of the set of tournaments with a given score sequence, or equivalently, of a given fiber of the classical permutahedron from discrete geometry. Coxeter tournaments were introduced by the first author and Sanchez, in relation to the Coxeter permutahedra in Ardila, Castillo, Eur and Postnikov. Coxeter tournaments have collaborative and solitaire games, in addition to the usual competitive games in classical tournaments. We introduce Coxeter interchange graphs. These graphs are more intricate, as there are multiple neutral structures at play, which interact with one another. Our main result shows that the Coxeter interchange graphs are regular, and we describe the degree geometrically, in terms of distances in the Coxeter permutahedra. We also characterize the set of score sequences of Coxeter tournaments, generalizing a classical result of Landau., Comment: v3: revised discussions; added figures; results unchanged

Published
2023

4. Thresholds and expectation thresholds for larger p

Author

Przybyłowski, Tomasz and Riordan, Oliver

Subjects
Mathematics - Combinatorics, Mathematics - Probability, 60C05
Abstract

Let $p_\mathrm{c}$ and $q_\mathrm{c}$ be the threshold and the expectation threshold, respectively, of an increasing family $\mathcal{F}$ of subsets of a finite set $X$, and let $l$ be the size of a largest minimal element of $\mathcal{F}$. Recently, Park and Pham proved the Kahn-Kalai conjecture, which says that $p_\mathrm{c} \leqslant K q_\mathrm{c} \log_2 l$ for some universal constant $K$. Here we slightly strengthen their result by showing that $p_\mathrm{c} \leqslant 1 - \mathrm{e}^{-K q_\mathrm{c} \log_2 l}$. The idea is to apply the Park-Pham Theorem to an appropriate `cloned' family $\mathcal{F}_k$, reducing the general case (of this and related results) to the case where the individual element probability $p$ is small., Comment: 5 pages; minor edits; submitted

Published
2023

40. International Tuberculum Sellae Meningioma Study: Preoperative Grading Scale to Predict Outcomes and Propensity-Matched Outcomes by Endonasal Versus Transcranial Approach

Author

Magill, Stephen T., Schwartz, Theodore H., Couldwell, William T., Gardner, Paul A., Heilman, Carl B., Sen, Chandranath, Akagami, Ryojo, Cappabianca, Paolo, Prevedello, Daniel M., McDermott, Michael W., Przybylowski, Colin J., Almefty, Kaith K., Patel, Akash J., Khan, A. Basit, Wu, Kyle C., Bi, Wenya Linda, Dunn, Ian F., Mamelak, Adam N., Ehsan, Mohammad U., Bruce, Jeffrey N., Englander, Zachary K., Wang, Linda M., Youngerman, Brett, Anand, Vijay K., Kacker, Ashutosh, Tabaee, Abtin, Clarke, David B., Walling, Simon A., Hebb, Andrea L. O., Macki, Mohamed, Anand, Sharath K., Rock, Jack P., Baskin, David S., Yewah Gwei, Larisse K., Guthikonda, Bharat, Kosty, Jennifer, Nanda, Anil, Sun, Hai, Culicchia, Frank, Morrow, Kevin, Fannin, Erin, Germanwala, Anand V., Prabhu, Vikram C., Patel, Chirag R., Chaichana, Kaisorn, Quinones-Hinojosa, Alfredo, ReFaey, Karim, Chandler, James P., Fernandez, Luis G., Oyon, Daniel E., Youngblood, Mark W., Golfinos, John G., Placantonakis, Dimitris G., Pacione, Donato, Delavari, Nader, Albonette-Felicio, Thiago, Otto, Bradley A., Carrau, Ricardo L., Han, Seunggu J., Shahin, Maryam N., Brahimaj, Bledi C., Beer-Furlan, André, Byrne, Richard W., Munich, Stephan A., Munoz, Lorenzo F., Liu, James K., Zhao, Kevin, Agarwalla, Pankaj K., Hsueh, Wayne D., Eloy, Jean Anderson, Chang, Steven D., Meola, Antonio, Teng, Hao, Goulart, Carlos R., Rai, Shawn S., Chin, Lawrence S., Ahye, Nicholas, Weaver, Michael, Mangham, William M., Michael, L. Madison, Robertson, Jon H., Dowd, Richard S., Amenta, Peter S., Scullen, Tyler A., de Divitiis, Oreste, Solari, Domenico, Cavallo, Luigi M., Makarenko, Serge, Rizzuto, Michael, Prakash, Swetha, Chen, William C., El-Sayed, Ivan H., Nguyen, Minh P., Morshed, Ramin A., Theodosopoulos, Philip V., Aghi, Manish K., Santarius, Thomas, Stastna, Daniela, Williams, Brian J., Andaluz, Norberto, Adappa, Nithin D., Palmer, James N., Grady, M. Sean, Lee, John Y. K., Buch, Love, Sharma, Nikhil, Joshi, Disha, Champagne, Pierre-Olivier, Valappil, Benita, Kumar, Jay I., Agarwalla, Pankaj K., Agazzi, Siviero, van Loveren, Harry, Zada, Gabriel, Strickland, Benjamin, Garrett, Norman E., Plitt, Aaron R., Barnett, Samuel L., Mickey, Bruce E., Garzon-Muvdi, Tomas, Nassiri, Farshad, Gentili, Fred, Kalyvas, Aristotelis, Zadeh, Gelareh, Karsy, Michael, Sayyahmelli, Sima, Baskaya, Mustafa K., Morone, Peter J., Cavallo, Claudio, Sylvester, Peter T., and Chicoine, Michael R.

Published
2023
Full Text
View/download PDF

41. International Tuberculum Sellae Meningioma Study: Surgical Outcomes and Management Trends

Author

Magill, Stephen T., Schwartz, Theodore H., Couldwell, William T., Gardner, Paul A., Heilman, Carl B., Sen, Chandranath, Akagami, Ryojo, Cappabianca, Paolo, Prevedello, Daniel M., McDermott, Michael W., Przybylowski, Colin J., Almefty, Kaith K., Patel, Akash J., Khan, A. Basit, Wu, Kyle C., Bi, Wenya Linda, Dunn, Ian F., Mamelak, Adam N., Ehsan, Mohammad U., Bruce, Jeffrey N., Englander, Zachary K., Wang, Linda M., Youngerman, Brett, Anand, Vijay K., Kacker, Ashutosh, Tabaee, Abtin, Clarke, David B., Walling, Simon A., Hebb, Andrea L. O., Macki, Mohamed, Anand, Sharath K., Rock, Jack P., Baskin, David S., Yewah Gwei, Larisse K., Guthikonda, Bharat, Kosty, Jennifer, Nanda, Anil, Sun, Hai, Culicchia, Frank, Morrow, Kevin, Fannin, Erin, Germanwala, Anand V., Prabhu, Vikram C., Patel, Chirag R., Chaichana, Kaisorn, Quinones-Hinojosa, Alfredo, ReFaey, Karim, Chandler, James P., Fernandez, Luis G., Oyon, Daniel E., Youngblood, Mark W., Golfinos, John G., Placantonakis, Dimitris G., Pacione, Donato, Delavari, Nader, Albonette-Felicio, Thiago, Otto, Bradley A., Carrau, Ricardo L., Han, Seunggu J., Shahin, Maryam N., Brahimaj, Bledi C., Beer-Furlan, André, Byrne, Richard W., Munich, Stephan A., Munoz, Lorenzo F., Liu, James K., Zhao, Kevin, Agarwalla, Pankaj K., Hsueh, Wayne D., Eloy, Jean Anderson, Chang, Steven D., Meola, Antonio, Teng, Hao, Goulart, Carlos R., Rai, Shawn S., Chin, Lawrence S., Ahye, Nicholas, Weaver, Michael, Mangham, William M., Michael, L. Madison, Robertson, Jon H., Dowd, Richard S., Amenta, Peter S., Scullen, Tyler A., de Divitiis, Oreste, Solari, Domenico, Cavallo, Luigi M., Makarenko, Serge, Rizzuto, Michael, Prakash, Swetha, Chen, William C., El-Sayed, Ivan H., Nguyen, Minh P., Morshed, Ramin A., Theodosopoulos, Philip V., Aghi, Manish K., Santarius, Thomas, Stastna, Daniela, Williams, Brian J., Andaluz, Norberto, Adappa, Nithin D., Palmer, James N., Grady, M. Sean, Lee, John Y. K., Buch, Love, Sharma, Nikhil, Joshi, Disha, Champagne, Pierre-Olivier, Valappil, Benita, Kumar, Jay I., Agarwalla, Pankaj K., Agazzi, Siviero, van Loveren, Harry, Zada, Gabriel, Strickland, Benjamin, Garrett, Norman E., Plitt, Aaron R., Barnett, Samuel L., Mickey, Bruce E., Garzon-Muvdi, Tomas, Nassiri, Farshad, Gentili, Fred, Kalyvas, Aristotelis, Zadeh, Gelareh, Neurosurgery, Division of, Hospital, Toronto Western, Toronto, University of, Toronto, Ontario, Karsy, Canada; Michael, Sayyahmelli, Sima, Baskaya, Mustafa K., Morone, Peter J., Cavallo, Claudio, Sylvester, Peter T., and Chicoine, Michael R.

Published
2023
Full Text
View/download PDF

Catalog

Books, media, physical & digital resources
See catalog results