Two Structural Results for Low Degree Polynomials and Applications

In this paper, two structural results concerning low degree polynomials over finite fields are given. The first states that over any finite field $\mathbb{F}$, for any polynomial $f$ on $n$ variables with degree $d \le \log(n)/10$, there exists a subspace of $\mathbb{F}^n$ with dimension $\Omega(d \cdot n^{1/(d-1)})$ on which $f$ is constant. This result is shown to be tight. Stated differently, a degree $d$ polynomial cannot compute an affine disperser for dimension smaller than $\Omega(d \cdot n^{1/(d-1)})$. Using a recursive argument, we obtain our second structural result, showing that any degree $d$ polynomial $f$ induces a partition of $F^n$ to affine subspaces of dimension $\Omega(n^{1/(d-1)!})$, such that $f$ is constant on each part. We extend both structural results to more than one polynomial. We further prove an analog of the first structural result to sparse polynomials (with no restriction on the degree) and to functions that are close to low degree polynomials. We also consider the algorithmic aspect of the two structural results. Our structural results have various applications, two of which are: * Dvir [CC 2012] introduced the notion of extractors for varieties, and gave explicit constructions of such extractors over large fields. We show that over any finite field, any affine extractor is also an extractor for varieties with related parameters. Our reduction also holds for dispersers, and we conclude that Shaltiel's affine disperser [FOCS 2011] is a disperser for varieties over $F_2$. * Ben-Sasson and Kopparty [SIAM J. C 2012] proved that any degree 3 affine disperser over a prime field is also an affine extractor with related parameters. Using our structural results, and based on the work of Kaufman and Lovett [FOCS 2008] and Haramaty and Shpilka [STOC 2010], we generalize this result to any constant degree

Quantum Advantage without Entanglement

We study the advantage of pure-state quantum computation without entanglement over classical computation. For the Deutsch-Jozsa algorithm we present the maximal subproblem that can be solved without entanglement, and show that the algorithm still has an advantage over the classical ones. We further show that this subproblem is of greater significance, by proving that it contains all the Boolean functions whose quantum phase-oracle is non-entangling. For Simon's and Grover's algorithms we provide simple proofs that no non-trivial subproblems can be solved by these algorithms without entanglement.Comment: 10 page

Motivations and Barriers Associated with the Adoption of Battery Electric Vehicles in Beijing: A Multinomial Logit Model Approach

The recent surge of the Chinese Plug-in Hybrid Electric Vehicle (PEV) market makes China the world’s largest PEV stock. A series of supportive policies in China contributed greatly to the rapid PEV adoption by limiting regular vehicles and reducing the price of PEVs. However, the role these policies play in changing references and encouraging consumers to purchase PEVs rather than conventional vehicles is not fully known. Other factors, rather than incentives, that could help maintain the current adoption trend are still unclear. The latter is especially critical in understanding how the market reacts to a gradually decreasing level of incentives to achieve the next goal of 5 million PEVs on the road by 2020 in China. Therefore, in this study the authors explored these research questions through a cross-sectional study of the current PEV market on consumers in Beijing by employing a multinomial logit model. Beijing has high levels of PEV adoptions in addition to a specific policy stimulus. The model results show significant influences of stimuli, individual socio-demographics, attitudes, charging infrastructure, and charging experiences on the adoption of PEVs over conventional vehicles. The results may help find out key interventions for policy makers to promote more PEV adoptions in China as well as other countries

Rate Amplification and Query-Efficient Distance Amplification for Linear LCC and LDC

The main contribution of this work is a rate amplification procedure for LCC. Our procedure converts any q-query linear LCC, having rate ? and, say, constant distance to an asymptotically good LCC with q^poly(1/?) queries. Our second contribution is a distance amplification procedure for LDC that converts any linear LDC with distance ? and, say, constant rate to an asymptotically good LDC. The query complexity only suffers a multiplicative overhead that is roughly equal to the query complexity of a length 1/? asymptotically good LDC. This improves upon the poly(1/?) overhead obtained by the AEL distance amplification procedure [Alon and Luby, 1996; Alon et al., 1995]. Our work establishes that the construction of asymptotically good LDC and LCC is reduced, with a minor overhead in query complexity, to the problem of constructing a vanishing rate linear LCC and a (rapidly) vanishing distance linear LDC, respectively

Transduplication resulted in the incorporation of two protein-coding sequences into the Turmoil-1 transposable element of C. elegans

Transposable elements may acquire unrelated gene fragments into their sequences in a process called transduplication. Transduplication of protein-coding genes is common in plants, but is unknown of in animals. Here, we report that the Turmoil-1 transposable element in C. elegans has incorporated two protein-coding sequences into its inverted terminal repeat (ITR) sequences. The ITRs of Turmoil-1 contain a conserved RNA recognition motif (RRM) that originated from the rsp- 2 gene and a fragment from the protein-coding region of the cpg-3 gene. We further report that an open reading frame specific to C. elegans may have been created as a result of a Turmoil-1 insertion. Mutations at the 5' splice site of this open reading frame may have reactivated the transduplicated RRM moti

Charging for Charging: The Paradox of Free Charging and its Detrimental Effect on the Use of Electric Vehicles

A survey of plug-in electric vehicle (PEV) owners was conducted focusing on workplace charging suggesting that pricing and a mix of high and low power chargers could efficiently meet the needs of workplace charging and increase electric vehicle miles traveled (eVMT). Respondents reported that in California, 38% of drivers who have chargers at work are unable to charge at least once per week due to congestion at chargers. When asked about price, answers indicated that 4 chargers would be needed for every 10 vehicles if free, versus 1 chargers for every 10 PEVs if the price were double (assuming 1 charger serves 2 cars/day). Since a price of double that of home electricity is still likely to save money, the implication is that people are using free workplace infrastructure 4 times more than they need to. This usage pattern suggests that that simply charging a small fee could encourage more efficient use of infrastructure. If charging is given away for free to spur the market, level 1 or low power level 2 (similar in power to level 1) could be used to install the maximum number of chargers on an existing electricity panel. Level 2 at work could be priced higher to discourage those who don’t need it. More dependability for BEVs could encourage their sale and use. In the case of PHEVs, they would only use level 2 when needed or default to a lower power alternative

Exploring the Impact of High Occupancy Vehicle (HOV) Lane Access on Plug-in Vehicle Sales and Usage in California

Allowing single-occupant advanced clean vehicles to use carpool or high occupancy vehicle (HOV) lanes is an important non-monetary sales incentive. This incentive needs to be balanced against the potential cost of increased congestion on those lanes and reduced revenue of high occupancy toll (HOT) lanes, especially during peak travel periods. In a 2013 survey, when Plug-In in vehicle buyers were asked about their primary motivation to buy a plug in car, 57% of Plug-in Priuses, 34% of Volts and 38% of LEAFs identified the HOV sticker. Current legislation in California allows a limited number of stickers for plugin hybrid vehicles and an unlimited number for full battery electric vehicles. This paper offers an analysis on the impact of these stickers on the vehicle purchase decision and the resulting electric miles traveled. We also offer an analysis of the potential cost in terms of miles driven on HOV lanes. The results can help policy makers optimize the benefit for each additional permit while understanding the impact of different vehicle types