4,494 research outputs found
Invariable generation of the symmetric group
We say that permutations invariably
generate if, no matter how one chooses conjugates
of these permutations, generate
. We show that if are chosen randomly from
then, with probability tending to 1 as ,
they do not invariably generate . By contrast it was shown
recently by Pemantle, Peres and Rivin that four random elements do invariably
generate with positive probability. We include a proof of this
statement which, while sharing many features with their argument, is short and
completely combinatorial.Comment: 15 pages. Corrections and clarifications suggested by the referees.
Added a reference to a paper of Raouj and Stef which solves related problems
about divisor
Large gaps between consecutive prime numbers
Let denote the size of the largest gap between consecutive primes
below . Answering a question of Erdos, we show that where
is a function tending to infinity with . Our proof combines existing
arguments with a random construction covering a set of primes by arithmetic
progressions. As such, we rely on recent work on the existence and distribution
of long arithmetic progressions consisting entirely of primes.Comment: v2. very minor corrections. To appear in Ann. Mat
Attacking Without Provocation; Maintaining a Subsequent Occupation; All for the Sake of Democratization: The Constitutionality and Wisdom of Preventive War and Post-Conflict Nation-Building
This Note examines the constitutionality and wisdom of both aspects of the current warfare policy. Ultimately, the current United States warfare strategy that includes using preventive wars followed by post-conflict military nation-building is constitutional; however, underlying policy concerns suggest that this approach to warfare should be reconsidered and reframed
Unfair, Abusive, and Unlawful: Protecting Debtors and Society from Unrestrained Bank Account Garnishment
In the span of a generation, consumer credit has reshaped the financial lives of millions of Americans. Today, some seventy million Americans have a debt in collections, and creditors file millions of actions annually to secure repayment of these loans. Despite the rapid expansion of consumer debt, the Consumer Credit Protection Act, the only federal law limiting garnishment, has not been updated since its enactment in 1968. Moreover, courts have narrowly construed its provisions to permit creditors to empty a debtor’s bank account to repay a delinquent debt.
To afford debtors the basic protections of the Consumer Credit Protection Act, this Note argues that courts should enforce its provisions to protect wages deposited into a bank account. Alternatively, considering the dramatic expansion of consumer credit and debt collection, this Note argues that the Consumer Financial Protection Bureau should engage in rulemaking to prohibit the unrestrained garnishment of bank accounts as an unfair and abusive practice. These federal interventions are critical in shielding debtors and their families from destitution and in protecting the public from the onerous social costs of unrestrained debt collection
Total Error and Variability Measures with Integrated Disclosure Limitation for Quarterly Workforce Indicators and LEHD Origin Destination Employment Statistics in OnThe Map
We report results from the first comprehensive total quality evaluation of five major indicators in the U.S. Census Bureau\u27s Longitudinal Employer-Household Dynamics (LEHD) Program Quarterly Workforce Indicators (QWI): total employment, beginning-of-quarter employment, full-quarter employment, total payroll, and average monthly earnings of full-quarter employees. Beginning-of-quarter employment is also the main tabulation variable in the LEHD Origin-Destination Employment Statistics (LODES) workplace reports as displayed in OnTheMap (OTM). The evaluation is conducted by generating multiple threads of the edit and imputation models used in the LEHD Infrastructure File System. These threads conform to the Rubin (1987) multiple imputation model, with each thread or implicate being the output of formal probability models that address coverage, edit, and imputation errors. Design-based sampling variability and finite population corrections are also included in the evaluation. We derive special formulas for the Rubin total variability and its components that are consistent with the disclosure avoidance system used for QWI and LODES/OTM workplace reports. These formulas allow us to publish the complete set of detailed total quality measures for QWI and LODES. The analysis reveals that the five publication variables under study are estimated very accurately for tabulations involving at least 10 jobs. Tabulations involving three to nine jobs have quality in the range generally deemed acceptable. Tabulations involving zero, one or two jobs, which are generally suppressed in the QWI and synthesized in LODES, have substantial total variability but their publication in LODES allows the formation of larger custom aggregations, which will in general have the accuracy estimated for tabulations in the QWI based on a similar number of workers
Lower Bounds for Oblivious Near-Neighbor Search
We prove an lower bound on the dynamic
cell-probe complexity of statistically
approximate-near-neighbor search () over the -dimensional
Hamming cube. For the natural setting of , our result
implies an lower bound, which is a quadratic
improvement over the highest (non-oblivious) cell-probe lower bound for
. This is the first super-logarithmic
lower bound for against general (non black-box) data structures.
We also show that any oblivious data structure for
decomposable search problems (like ) can be obliviously dynamized
with overhead in update and query time, strengthening a classic
result of Bentley and Saxe (Algorithmica, 1980).Comment: 28 page
Vote Properly Cast - The Constitutionality of the National Voter Registration Act of 1993, A;Note
Stretching the Twenty-First Amendment Beyond Its Limit: A Critique of S. Wine & Spirits of Am., Inc. v. Div. of Alcohol & Tobacco Control
-
A prototype system for detecting the radio-frequency pulse associated with cosmic ray air showers
The development of a system to detect the radio-frequency (RF) pulse
associated with extensive air showers of cosmic rays is described. This work
was performed at the CASA/MIA array in Utah, with the intention of designing
equipment that can be used in conjunction with the Auger Giant Array. A small
subset of data (less than 40 out of a total of 600 hours of running time),
taken under low-noise conditions, permitted upper limits to be placed on the
rate for pulses accompanying showers of energies around eV.Comment: 53 pages, LaTeX, 19 figures, published in Nuclear Instruments and
Methods. Revised version; some references update
- …