3,494 research outputs found
Judicial Incoherence, Capital Punishment, and the Legalization of Torture
This brief essay responds to the Supreme Court’s recent decision in Bucklew v. Precythe. It contends that the argument relied upon by the Court in that decision, as well as in Glossip v. Gross, is either trivial or demonstrably invalid. Hence, this essay provides a nonmoral reason to oppose the Court’s recent capital punishment decisions. The Court’s position that petitioners seeking to challenge a method of execution must identify a readily available and feasible alternative execution protocol is untenable, and must be revisited
Regularity lemmas in a Banach space setting
Szemer\'edi's regularity lemma is a fundamental tool in extremal graph
theory, theoretical computer science and combinatorial number theory. Lov\'asz
and Szegedy [L. Lov\'asz and B. Szegedy: Szemer\'edi's Lemma for the analyst,
Geometric and Functional Analysis 17 (2007), 252-270] gave a Hilbert space
interpretation of the lemma and an interpretation in terms of compact- ness of
the space of graph limits. In this paper we prove several compactness results
in a Banach space setting, generalising results of Lov\'asz and Szegedy as well
as a result of Borgs, Chayes, Cohn and Zhao [C. Borgs, J.T. Chayes, H. Cohn and
Y. Zhao: An Lp theory of sparse graph convergence I: limits, sparse random
graph models, and power law distributions, arXiv preprint arXiv:1401.2906
(2014)].Comment: 15 pages. The topological part has been substantially improved based
on referees comments. To appear in European Journal of Combinatoric
Asymptotic independence for unimodal densities
Asymptotic independence of the components of random vectors is a concept used
in many applications. The standard criteria for checking asymptotic
independence are given in terms of distribution functions (dfs). Dfs are rarely
available in an explicit form, especially in the multivariate case. Often we
are given the form of the density or, via the shape of the data clouds, one can
obtain a good geometric image of the asymptotic shape of the level sets of the
density. This paper establishes a simple sufficient condition for asymptotic
independence for light-tailed densities in terms of this asymptotic shape. This
condition extends Sibuya's classic result on asymptotic independence for
Gaussian densities.Comment: 33 pages, 4 figure
Weighted counting of solutions to sparse systems of equations
Given complex numbers , we define the weight of a
set of 0-1 vectors as the sum of over all
vectors in . We present an algorithm, which for a set
defined by a system of homogeneous linear equations with at most
variables per equation and at most equations per variable, computes
within relative error in time
provided for an absolute constant and all . A similar algorithm is constructed for computing
the weight of a linear code over . Applications include counting
weighted perfect matchings in hypergraphs, counting weighted graph
homomorphisms, computing weight enumerators of linear codes with sparse code
generating matrices, and computing the partition functions of the ferromagnetic
Potts model at low temperatures and of the hard-core model at high fugacity on
biregular bipartite graphs.Comment: The exposition is improved, a couple of inaccuracies correcte
A robust scheme for free surface and pressurized flows in channels with arbitrary cross-sections
Flows in closed channels, such as rain storm sewers, often contain transitions from free surface flows to pressurized flows, or viceversa. These phenomena usually require two different sets of equations to model the two different flow regimes. Actually, a few specifications for the geometry of the channel and for the discretization choices can be sufficient to model closed channel flows using only the open channel flow equations. Transitions can also occur in open channels, like those from super- to subcritical flow, or vice versa. These particular flows are usually difficult to reproduce numerically and strong restrictions are imposed on the numerical scheme to simulate them. In this paper, an implicit finite-difference conservative algorithm is proposed to deal properly with these problems. In addition, a special flux limiter is described and implemented to allow accurate flow simulations near hydraulic structures such as weirs. A few computational examples are given to illustrate the properties of the scheme and the numerical solutions are compared with experimental data, when possible
Deterministic polynomial-time approximation algorithms for partition functions and graph polynomials
In this paper we show a new way of constructing deterministic polynomial-time
approximation algorithms for computing complex-valued evaluations of a large
class of graph polynomials on bounded degree graphs. In particular, our
approach works for the Tutte polynomial and independence polynomial, as well as
partition functions of complex-valued spin and edge-coloring models.
More specifically, we define a large class of graph polynomials
and show that if and there is a disk centered at zero in the
complex plane such that does not vanish on for all bounded degree
graphs , then for each in the interior of there exists a
deterministic polynomial-time approximation algorithm for evaluating at
. This gives an explicit connection between absence of zeros of graph
polynomials and the existence of efficient approximation algorithms, allowing
us to show new relationships between well-known conjectures.
Our work builds on a recent line of work initiated by. Barvinok, which
provides a new algorithmic approach besides the existing Markov chain Monte
Carlo method and the correlation decay method for these types of problems.Comment: 27 pages; some changes have been made based on referee comments. In
particular a tiny error in Proposition 4.4 has been fixed. The introduction
and concluding remarks have also been rewritten to incorporate the most
recent developments. Accepted for publication in SIAM Journal on Computatio
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