2,083 research outputs found
A Hyper-Relation Characterization of Weak Pseudo-Rationalizability
I provide a characterization of weakly pseudo-rationalizable choice functions---that is, choice functions rationalizable by a set of acyclic relations---in terms of hyper-relations satisfying certain properties. For those hyper-relations Nehring calls extended preference relations, the central characterizing condition is weaker than (hyper-relation) transitivity but stronger than (hyper-relation) acyclicity. Furthermore, the relevant type of hyper-relation can be represented as the intersection of a certain class of its extensions. These results generalize known, analogous results for path independent choice functions
The physics and the mixed Hodge structure of Feynman integrals
This expository text is an invitation to the relation between quantum field
theory Feynman integrals and periods. We first describe the relation between
the Feynman parametrization of loop amplitudes and world-line methods, by
explaining that the first Symanzik polynomial is the determinant of the period
matrix of the graph, and the second Symanzik polynomial is expressed in terms
of world-line Green's functions. We then review the relation between Feynman
graphs and variations of mixed Hodge structures. Finally, we provide an
algorithm for generating the Picard-Fuchs equation satisfied by the all equal
mass banana graphs in a two-dimensional space-time to all loop orders.Comment: v2: 34 pages, 5 figures. Minor changes. References added. String-math
2013 proceeding contributio
Luttinger States at the Edge
An effective wavefunction for the edge excitations in the Fractional quantum
Hall effect can be found by dimensionally reducing the bulk wavefunction.
Treated this way the Laughlin wavefunction yields a Luttinger
model ground state. We identify the edge-electron field with a Luttinger
hyper-fermion operator, and the edge electron itself with a non-backscattering
Bogoliubov quasi-particle. The edge-electron propagator may be calculated
directly from the effective wavefunction using the properties of a
one-dimensional one-component plasma, provided a prescription is adopted which
is sensitive to the extra flux attached to the electrons
Building Efficient Query Engines in a High-Level Language
Abstraction without regret refers to the vision of using high-level
programming languages for systems development without experiencing a negative
impact on performance. A database system designed according to this vision
offers both increased productivity and high performance, instead of sacrificing
the former for the latter as is the case with existing, monolithic
implementations that are hard to maintain and extend. In this article, we
realize this vision in the domain of analytical query processing. We present
LegoBase, a query engine written in the high-level language Scala. The key
technique to regain efficiency is to apply generative programming: LegoBase
performs source-to-source compilation and optimizes the entire query engine by
converting the high-level Scala code to specialized, low-level C code. We show
how generative programming allows to easily implement a wide spectrum of
optimizations, such as introducing data partitioning or switching from a row to
a column data layout, which are difficult to achieve with existing low-level
query compilers that handle only queries. We demonstrate that sufficiently
powerful abstractions are essential for dealing with the complexity of the
optimization effort, shielding developers from compiler internals and
decoupling individual optimizations from each other. We evaluate our approach
with the TPC-H benchmark and show that: (a) With all optimizations enabled,
LegoBase significantly outperforms a commercial database and an existing query
compiler. (b) Programmers need to provide just a few hundred lines of
high-level code for implementing the optimizations, instead of complicated
low-level code that is required by existing query compilation approaches. (c)
The compilation overhead is low compared to the overall execution time, thus
making our approach usable in practice for compiling query engines
What does inflation really predict?
If the inflaton potential has multiple minima, as may be expected in, e.g.,
the string theory "landscape", inflation predicts a probability distribution
for the cosmological parameters describing spatial curvature (Omega_tot), dark
energy (rho_Lambda, w, etc.), the primordial density fluctuations (Omega_tot,
dark energy (rho_Lambda, w, etc.). We compute this multivariate probability
distribution for various classes of single-field slow-roll models, exploring
its dependence on the characteristic inflationary energy scales, the shape of
the potential V and and the choice of measure underlying the calculation. We
find that unless the characteristic scale Delta-phi on which V varies happens
to be near the Planck scale, the only aspect of V that matters observationally
is the statistical distribution of its peaks and troughs. For all energy scales
and plausible measures considered, we obtain the predictions Omega_tot ~
1+-0.00001, w=-1 and rho_Lambda in the observed ballpark but uncomfortably
high. The high energy limit predicts n_s ~ 0.96, dn_s/dlnk ~ -0.0006, r ~ 0.15
and n_t ~ -0.02, consistent with observational data and indistinguishable from
eternal phi^2-inflation. The low-energy limit predicts 5 parameters but prefers
larger Q and redder n_s than observed. We discuss the coolness problem, the
smoothness problem and the pothole paradox, which severely limit the viable
class of models and measures. Our findings bode well for detecting an
inflationary gravitational wave signature with future CMB polarization
experiments, with the arguably best-motivated single-field models favoring the
detectable level r ~ 0.03. (Abridged)Comment: Replaced to match accepted JCAP version. Improved discussion,
references. 42 pages, 17 fig
Judging the Rationality of Decisions in the Presence of Vague Alternatives
The standard framework of the decision theory is subjected to partial revision in regard to the usage of the notion of alternative. An approach to judging the rationality of decision-maker's behavior is suggested for various cases of incomplete observability and/or controllability of alternatives. The approach stems from the conventional axiomatic treatment of rationality in the general choice theory and proceeds via modifying the description of alternative modes of behavior into a generalized model that requires no explicit consideration of alternatives. The criteria of rationality in the generalized decision model are proposed. For the conventional model in the choice theory, these criteria can be reduced to the well known criteria of the regularity (binariness) of choice functions. Game and economic examples are considered
Portfolio Selection in Multidimensional General and Partial Moment Space.
This paper develops a general approach for the single period portfolio optimization problem in a multidimensional general and partial moment space. A shortage function is defined that looks for possible increases in odd moments and decreases in even moments. A main result is that this shortage function ensures suffcient conditions for global optimality. It also forms a natural basis for developing tests on the infuence of additional moments. Furthermore, a link is made with an approximation of an arbitrary order of a general indirectutility function. This nonparametric effciency measurement framework permits to dfferentiate mainly between portfolio effciency and allocative effciency. Finally, information can,in principle, be inferred about the revealed risk aversion, prudence, temperance and otherhigher-order risk characteristics of investors.shortage function, efficient frontier, K-moment portfolios
Next-to-leading order predictions for Z gamma+jet and Z gamma gamma final states at the LHC
We present next-to-leading order predictions for final states containing
leptons produced through the decay of a Z boson in association with either a
photon and a jet, or a pair of photons. The effect of photon radiation from the
final state leptons is included and we also allow for contributions arising
from fragmentation processes. Phenomenological studies are presented for the
LHC in the case of final states containing charged leptons and in the case of
neutrinos. We also use the procedure introduced by Stewart and Tackmann to
provide a reliable estimate of the scale uncertainty inherent in our
theoretical calculations of jet-binned Z gamma cross sections. These
computations have been implemented in the public code MCFM.Comment: 30 pages, 10 figure
Learning Models over Relational Data using Sparse Tensors and Functional Dependencies
Integrated solutions for analytics over relational databases are of great
practical importance as they avoid the costly repeated loop data scientists
have to deal with on a daily basis: select features from data residing in
relational databases using feature extraction queries involving joins,
projections, and aggregations; export the training dataset defined by such
queries; convert this dataset into the format of an external learning tool; and
train the desired model using this tool. These integrated solutions are also a
fertile ground of theoretically fundamental and challenging problems at the
intersection of relational and statistical data models.
This article introduces a unified framework for training and evaluating a
class of statistical learning models over relational databases. This class
includes ridge linear regression, polynomial regression, factorization
machines, and principal component analysis. We show that, by synergizing key
tools from database theory such as schema information, query structure,
functional dependencies, recent advances in query evaluation algorithms, and
from linear algebra such as tensor and matrix operations, one can formulate
relational analytics problems and design efficient (query and data)
structure-aware algorithms to solve them.
This theoretical development informed the design and implementation of the
AC/DC system for structure-aware learning. We benchmark the performance of
AC/DC against R, MADlib, libFM, and TensorFlow. For typical retail forecasting
and advertisement planning applications, AC/DC can learn polynomial regression
models and factorization machines with at least the same accuracy as its
competitors and up to three orders of magnitude faster than its competitors
whenever they do not run out of memory, exceed 24-hour timeout, or encounter
internal design limitations.Comment: 61 pages, 9 figures, 2 table
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