196,033 research outputs found
Discreteness of asymptotic tensor ranks
No full textTensor parameters that are amortized or regularized over large tensor powers, often called “asymp-
totic” tensor parameters, play a central role in several areas including algebraic complexity theory
(constructing fast matrix multiplication algorithms), quantum information (entanglement cost and
distillable entanglement), and additive combinatorics (bounds on cap sets, sunflower-free sets,
etc.). Examples are the asymptotic tensor rank, asymptotic slice rank and asymptotic subrank.
Recent works (Costa–Dalai, Blatter–Draisma–Rupniewski, Christandl–Gesmundo–Zuiddam) have
investigated notions of discreteness (no accumulation points) or “gaps” in the values of such tensor
parameters.
We prove a general discreteness theorem for asymptotic tensor parameters of order-three tensors
and use this to prove that (1) over any finite field (and in fact any finite set of coefficients in any
field), the asymptotic subrank and the asymptotic slice rank have no accumulation points, and (2)
over the complex numbers, the asymptotic slice rank has no accumulation points.
Central to our approach are two new general lower bounds on the asymptotic subrank of tensors,
which measures how much a tensor can be diagonalized. The first lower bound says that the
asymptotic subrank of any concise three-tensor is at least the cube-root of the smallest dimension.
The second lower bound says that any concise three-tensor that is “narrow enough” (has one
dimension much smaller than the other two) has maximal asymptotic subrank.
Our proofs rely on new lower bounds on the maximum rank in matrix subspaces that are obtained
by slicing a three-tensor in the three different directions. We prove that for any concise tensor, the
product of any two such maximum ranks must be large, and as a consequence there are always two
distinct directions with large max-rank
Nondeterministic quantum communication complexity: the cyclic equality game and iterated matrix multiplication
No full textWe study nondeterministic multiparty quantum communication with a quantum
generalization of broadcasts. We show that, with number-in-hand classical
inputs, the communication complexity of a Boolean function in this
communication model equals the logarithm of the support rank of the
corresponding tensor, whereas the approximation complexity in this model equals
the logarithm of the border support rank. This characterisation allows us to
prove a log-rank conjecture posed by Villagra et al. for nondeterministic
multiparty quantum communication with message-passing.
The support rank characterization of the communication model connects quantum
communication complexity intimately to the theory of asymptotic entanglement
transformation and algebraic complexity theory. In this context, we introduce
the graphwise equality problem. For a cycle graph, the complexity of this
communication problem is closely related to the complexity of the computational
problem of multiplying matrices, or more precisely, it equals the logarithm of
the asymptotic support rank of the iterated matrix multiplication tensor. We
employ Strassen's laser method to show that asymptotically there exist
nontrivial protocols for every odd-player cyclic equality problem. We exhibit
an efficient protocol for the 5-player problem for small inputs, and we show
how Young flattenings yield nontrivial complexity lower bounds
Barriers for Fast Matrix Multiplication from Irreversibility
No full textDetermining the asymptotic algebraic complexity of matrix multiplication, succinctly represented by the matrix multiplication exponent omega, is a central problem in algebraic complexity theory. The best upper bounds on omega, leading to the state-of-the-art omega <= 2.37.., have been obtained via the laser method of Strassen and its generalization by Coppersmith and Winograd. Recent barrier results show limitations for these and related approaches to improve the upper bound on omega.
We introduce a new and more general barrier, providing stronger limitations than in previous work. Concretely, we introduce the notion of "irreversibility" of a tensor and we prove (in some precise sense) that any approach that uses an irreversible tensor in an intermediate step (e.g., as a starting tensor in the laser method) cannot give omega = 2. In quantitative terms, we prove that the best upper bound achievable is lower bounded by two times the irreversibility of the intermediate tensor. The quantum functionals and Strassen support functionals give (so far, the best) lower bounds on irreversibility. We provide lower bounds on the irreversibility of key intermediate tensors, including the small and big Coppersmith - Winograd tensors, that improve limitations shown in previous work. Finally, we discuss barriers on the group-theoretic approach in terms of "monomial" irreversibility
Dr. Duane M. Jackson, Morehouse College, July 2011
No full textThis video is a conversation with Dr. Duane M. Jackson. Dr. Jackson talks about his paper, "Recall and the Serial Position Effect: The Role of Primacy and Recency on Accounting Students' Performance." Jackie Daniel, AUC Woodruff Library, is the interviewer
"Reflections on the subject of Emigration from Europe with a view to Settlement in the United States" By M. Carey.
No full text"Reflections on the subject of Emigration from Europe with a view to Settlement in the United States: containing bried sketches of the moral and political character of those states.
By M. Carey, member of the American philosophical, and of the American Antiquarian Society, and author of The Olive Branch, Cindiciae Hibernicae, essays on banking, on political economy, and on internal improvement.
To which are now added the English editor's comments on the subject; together with Important Advice to Emigrants, and Cautions Against Impositions Practiced in the Outports
Dispelling the Myths Behind First-author Citation Counts
No full textWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
Dr. Glendon Swarthout
No full textHosted by Roger M. Busfield, MSU Assistant Professor of Speech and Theater, Meet the Author is designed to introduce a general audience to a contemporary author and their work through in-depth interviews. This episode features a conversation between Dr. Glendon Swarthout, prolific author and English professor at MSU, and assistant professors Sam S. Baskett and Theodore B. Strandness
Simulation of thermal plant optimization and hydraulic aspects of thermal distribution loops for large campuses
No full textFollowing an introduction, the author describes Texas A&M University and its utilities system. After that, the author presents how to construct simulation models for chilled water and heating hot water distribution systems. The simulation model was used in a $2.3 million Ross Street chilled water pipe replacement project at Texas A&M University. A second project conducted at the University of Texas at San Antonio was used as an example to demonstrate how to identify and design an optimal distribution system by using a simulation model. The author found that the minor losses of these closed loop thermal distribution systems are significantly higher than potable water distribution systems. In the second part of the report, the author presents the latest development of software called the Plant Optimization Program, which can simulate cogeneration plant operation, estimate its operation cost and provide optimized operation suggestions. The author also developed detailed simulation models for a gas turbine and heat recovery steam generator and identified significant potential savings. Finally, the author also used a steam turbine as an example to present a multi-regression method on constructing simulation models by using basic statistics and optimization algorithms. This report presents a survey of the author??s working experience at the Energy Systems Laboratory (ESL) at Texas A&M University during the period of January 2002 through March 2004. The purpose of the above work was to allow the author to become familiar with the practice of engineering. The result is that the author knows how to complete a project from start to finish and understands how both technical and nontechnical aspects of a project need to be considered in order to ensure a quality deliverable and bring a project to successful completion. This report concludes that the objectives of the internship were successfully accomplished and that the requirements for the degree of Degree of Engineering have been satisfied
Algebraic complexity, asymptotic spectra and entanglement polytopes
No full textMatrix rank is multiplicative under the Kronecker product, additive under the direct sum, normalised on identity matrices and non-increasing under multiplying from the left and from the right by any matrices. It is the only real matrix parameter with these properties. Strassen studied the tensor extension: find all maps from k-tensors to the reals that are multiplicative under the tensor Kronecker product, additive under the direct sum, normalised on "identity tensors", and non-increasing under acting with linear maps on the k tensor factors. These maps form the "asymptotic spectrum of k-tensors" and capture the asymptotic relations among tensors, including the asymptotic tensor rank. We give the first explicit construction of an infinite family of elements in the asymptotic spectrum of complex k-tensors, based on information theory and entanglement polytopes. Other results on tensors include an extension of the Coppersmith-Winograd method to higher-order tensors. In graph theory, as a new instantiation of the abstract theory of asymptotic spectra, we introduce the asymptotic spectrum of graphs, which captures the Shannon capacity, a graph parameter characterizing zero-error communication complexity. Examples of elements in the asymptotic spectrum of graphs are the Lovász theta number and the fractional Haemers bounds. Finally, we study algebraic branching programs, an algebraic model of computation. Ben-Or and Cleve proved that width-3 abps can compute any polynomial efficiently in the formula size, and Allender and Wang proved that some polynomials cannot be computed by any width-2 abp. We prove that any polynomial can be efficiently approximated by a width-2 abp
Intern experience at CH���M Hill, Inc.: an internship report
No full textIncludes author's vita"Submitted to the College of Engineering of Texas A&M University in partial
fulfillment of the requirement for the degree of Doctor of Engineering."Includes bibliographical referencesA review of the author's internship experience with CH���M HILL, Inc.
during the period September 1975 through May 1976 is presented. During this nine month
internship the author worked as an Engineer II in the Industrial Processes discipline of this
large consulting engineering firm... The author's prime responsibility was as one of three
lead design engineers on the design of a large wastewater treatment facility for a pulp mill
in Hoquiam, Washington owned by ITT Rayonier Inc. The work generally consisted of the design
of individual treatment units and associated piping and pumping. The purpose of the project
was to provide wastewater treatment capabilities that would satisfy the effluent limitations
(standards) imposed upon the mill by the State of Washington Department of Ecology and the
U.S. Environmental Protection Agency. The author's assignment also entailed necessary
interaction with the project manager and other CH���M HILL design engineers and support staff
members, the client's representatives, and representatives of two other consulting engineering
firms working on the project. Thus, the internship position at CH���M HILL provided considerable
experience coordinating the author's work with the work of other engineers, guiding the design
and administrative efforts of a support staff, and interacting regularly with the client and
other consulting firms. This broad exposure to a variety of engineering and organizational
problems provided a valuable educational experience
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