527 research outputs found
Trees with an On-Line Degree Ramsey Number of Four
On-line Ramsey theory studies a graph-building game between two players. The player called Builder builds edges one at a time, and the player called Painter paints each new edge red or blue after it is built. The graph constructed is called the background graph. Builder's goal is to cause the background graph to contain a monochromatic copy of a given goal graph, and Painter's goal is to prevent this. In the S[subscript k]-game variant of the typical game, the background graph is constrained to have maximum degree no greater than k. The on-line degree Ramsey number [˚over R][subscript Δ](G) of a graph G is the minimum k such that Builder wins an S[subscript k]-game in which G is the goal graph. Butterfield et al. previously determined all graphs G satisfying [˚ over R][subscript Δ](G)≤3. We provide a complete classification of trees T satisfying [˚ over R][subscript Δ](T)=4.National Science Foundation (U.S.) (Grant DMS-0754106)United States. National Security Agency (Grant H98230-06-1-0013
Looking for evidence of noncompetitive behavior in Minnesota's banking industry
Banks and banking - Minnesota
Towards an integrated understanding of neural networks
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2018.Cataloged from PDF version of thesis.Includes bibliographical references (pages 123-136).Neural networks underpin both biological intelligence and modern Al systems, yet there is relatively little theory for how the observed behavior of these networks arises. Even the connectivity of neurons within the brain remains largely unknown, and popular deep learning algorithms lack theoretical justification or reliability guarantees. This thesis aims towards a more rigorous understanding of neural networks. We characterize and, where possible, prove essential properties of neural algorithms: expressivity, learning, and robustness. We show how observed emergent behavior can arise from network dynamics, and we develop algorithms for learning more about the network structure of the brain.by David Rolnick.Ph. D
Neural Networks as Paths through the Space of Representations
Deep neural networks implement a sequence of layer-by-layer operations that
are each relatively easy to understand, but the resulting overall computation
is generally difficult to understand. We consider a simple hypothesis for
interpreting the layer-by-layer construction of useful representations: perhaps
the role of each layer is to reformat information to reduce the "distance" to
the desired outputs. With this framework, the layer-wise computation
implemented by a deep neural network can be viewed as a path through a
high-dimensional representation space. We formalize this intuitive idea of a
"path" by leveraging recent advances in *metric* representational similarity.
We extend existing representational distance methods by computing geodesics,
angles, and projections of representations, going beyond mere layer distances.
We then demonstrate these tools by visualizing and comparing the paths taken by
ResNet and VGG architectures on CIFAR-10. We conclude by sketching additional
ways that this kind of representational geometry can be used to understand and
interpret network training, and to describe novel kinds of similarities between
different models.Comment: 10 pages, submitted to ICLR 202
How to be causal: time, spacetime, and spectra
I explain a simple definition of causality in widespread use, and indicate
how it links to the Kramers Kronig relations. The specification of causality in
terms of temporal differential eqations then shows us the way to write down
dynamical models so that their causal nature /in the sense used here/ should be
obvious to all. To extend existing treatments of causality that work only in
the frequency domain, I derive a reformulation of the long-standing Kramers
Kronig relations applicable not only to just temporal causality, but also to
spacetime "light-cone" causality based on signals carried by waves. I also
apply this causal reasoning to Maxwell's equations, which is an instructive
example since their casual properties are sometimes debated.Comment: v4 - add Appdx A, "discrete" picture (not in EJP); v5 - add Appdx B,
cause classification/frames (not in EJP); v7 - unusual model case; v8 add
reference
Single Top Quark Production as a Probe for Anomalous Moments at Hadron Colliders
Single production of top quarks at hadron colliders via fusion is
examined as a probe of possible anomalous chromomagnetic and/or chromoelectric
moment type couplings between the top and gluons. We find that this channel is
far less sensitive to the existence of anomalous couplings of this kind than is
the usual production of top pairs by or fusion. This result is
found to hold at both the Tevatron as well as the LHC although somewhat greater
sensitivity for anomalous couplings in this channel is found at the higher
energy machine.Comment: New discussion and 10 new figures added. uuencoded postscript fil
Online Ramsey theory for a triangle on -free graphs
Given a class of graphs and a fixed graph , the online
Ramsey game for on is a game between two players Builder and
Painter as follows: an unbounded set of vertices is given as an initial state,
and on each turn Builder introduces a new edge with the constraint that the
resulting graph must be in , and Painter colors the new edge either
red or blue. Builder wins the game if Painter is forced to make a monochromatic
copy of at some point in the game. Otherwise, Painter can avoid creating a
monochromatic copy of forever, and we say Painter wins the game.
We initiate the study of characterizing the graphs such that for a given
graph , Painter wins the online Ramsey game for on -free graphs. We
characterize all graphs such that Painter wins the online Ramsey game for
on the class of -free graphs, except when is one particular graph.
We also show that Painter wins the online Ramsey game for on the class of
-minor-free graphs, extending a result by Grytczuk, Ha{\l}uszczak, and
Kierstead.Comment: 20 pages, 10 page
Design, Construction, Operation and Performance of a Hadron Blind Detector for the PHENIX Experiment
A Hadron Blind Detector (HBD) has been developed, constructed and
successfully operated within the PHENIX detector at RHIC. The HBD is a
Cherenkov detector operated with pure CF4. It has a 50 cm long radiator
directly coupled in a window- less configuration to a readout element
consisting of a triple GEM stack, with a CsI photocathode evaporated on the top
surface of the top GEM and pad readout at the bottom of the stack. This paper
gives a comprehensive account of the construction, operation and in-beam
performance of the detector.Comment: 51 pages, 39 Figures, submitted to Nuclear Instruments and Method
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