4,179 research outputs found

### Vertex Ramsey problems in the hypercube

If we 2-color the vertices of a large hypercube what monochromatic
substructures are we guaranteed to find? Call a set S of vertices from Q_d, the
d-dimensional hypercube, Ramsey if any 2-coloring of the vertices of Q_n, for n
sufficiently large, contains a monochromatic copy of S. Ramsey's theorem tells
us that for any r \geq 1 every 2-coloring of a sufficiently large r-uniform
hypergraph will contain a large monochromatic clique (a complete
subhypergraph): hence any set of vertices from Q_d that all have the same
weight is Ramsey. A natural question to ask is: which sets S corresponding to
unions of cliques of different weights from Q_d are Ramsey?
The answer to this question depends on the number of cliques involved. In
particular we determine which unions of 2 or 3 cliques are Ramsey and then
show, using a probabilistic argument, that any non-trivial union of 39 or more
cliques of different weights cannot be Ramsey.
A key tool is a lemma which reduces questions concerning monochromatic
configurations in the hypercube to questions about monochromatic translates of
sets of integers.Comment: 26 pages, 3 figure

### Improving Natural Language Interaction with Robots Using Advice

Over the last few years, there has been growing interest in learning models
for physically grounded language understanding tasks, such as the popular
blocks world domain. These works typically view this problem as a single-step
process, in which a human operator gives an instruction and an automated agent
is evaluated on its ability to execute it. In this paper we take the first step
towards increasing the bandwidth of this interaction, and suggest a protocol
for including advice, high-level observations about the task, which can help
constrain the agent's prediction. We evaluate our approach on the blocks world
task, and show that even simple advice can help lead to significant performance
improvements. To help reduce the effort involved in supplying the advice, we
also explore model self-generated advice which can still improve results.Comment: Accepted as a short paper at NAACL 2019 (8 pages

### Applications of a tunable dye laser for atomic fluoresence spectrometry

Imperial Users onl

### Ask, and shall you receive?: Understanding Desire Fulfillment in Natural Language Text

The ability to comprehend wishes or desires and their fulfillment is
important to Natural Language Understanding. This paper introduces the task of
identifying if a desire expressed by a subject in a given short piece of text
was fulfilled. We propose various unstructured and structured models that
capture fulfillment cues such as the subject's emotional state and actions. Our
experiments with two different datasets demonstrate the importance of
understanding the narrative and discourse structure to address this task

### Adaptively Secure Coin-Flipping, Revisited

The full-information model was introduced by Ben-Or and Linial in 1985 to
study collective coin-flipping: the problem of generating a common bounded-bias
bit in a network of $n$ players with $t=t(n)$ faults. They showed that the
majority protocol can tolerate $t=O(\sqrt n)$ adaptive corruptions, and
conjectured that this is optimal in the adaptive setting. Lichtenstein, Linial,
and Saks proved that the conjecture holds for protocols in which each player
sends a single bit. Their result has been the main progress on the conjecture
in the last 30 years.
In this work we revisit this question and ask: what about protocols involving
longer messages? Can increased communication allow for a larger fraction of
faulty players?
We introduce a model of strong adaptive corruptions, where in each round, the
adversary sees all messages sent by honest parties and, based on the message
content, decides whether to corrupt a party (and intercept his message) or not.
We prove that any one-round coin-flipping protocol, regardless of message
length, is secure against at most $\tilde{O}(\sqrt n)$ strong adaptive
corruptions. Thus, increased message length does not help in this setting.
We then shed light on the connection between adaptive and strongly adaptive
adversaries, by proving that for any symmetric one-round coin-flipping protocol
secure against $t$ adaptive corruptions, there is a symmetric one-round
coin-flipping protocol secure against $t$ strongly adaptive corruptions.
Returning to the standard adaptive model, we can now prove that any symmetric
one-round protocol with arbitrarily long messages can tolerate at most
$\tilde{O}(\sqrt n)$ adaptive corruptions.
At the heart of our results lies a novel use of the Minimax Theorem and a new
technique for converting any one-round secure protocol into a protocol with
messages of $polylog(n)$ bits. This technique may be of independent interest

### Pseudo-Deterministic Streaming

A pseudo-deterministic algorithm is a (randomized) algorithm which, when run multiple times on the same input, with high probability outputs the same result on all executions. Classic streaming algorithms, such as those for finding heavy hitters, approximate counting, ?_2 approximation, finding a nonzero entry in a vector (for turnstile algorithms) are not pseudo-deterministic. For example, in the instance of finding a nonzero entry in a vector, for any known low-space algorithm A, there exists a stream x so that running A twice on x (using different randomness) would with high probability result in two different entries as the output.
In this work, we study whether it is inherent that these algorithms output different values on different executions. That is, we ask whether these problems have low-memory pseudo-deterministic algorithms. For instance, we show that there is no low-memory pseudo-deterministic algorithm for finding a nonzero entry in a vector (given in a turnstile fashion), and also that there is no low-dimensional pseudo-deterministic sketching algorithm for ?_2 norm estimation. We also exhibit problems which do have low memory pseudo-deterministic algorithms but no low memory deterministic algorithm, such as outputting a nonzero row of a matrix, or outputting a basis for the row-span of a matrix.
We also investigate multi-pseudo-deterministic algorithms: algorithms which with high probability output one of a few options. We show the first lower bounds for such algorithms. This implies that there are streaming problems such that every low space algorithm for the problem must have inputs where there are many valid outputs, all with a significant probability of being outputted

### Students Have Their Own Minds. A Response to âBeyond the Catch-22 of School-Based Social Action Programs: Toward a More Pragmatic Approach for Dealing with Powerâ

In response to the authorsâ work on finding a more pragmatic approach to dealing with power, this commentary calls into question the possibility of a preestablished agenda by the researchers, who struggled to engage high school students. There might have been a case of overly ambitious expectations at work; also, the authors confess to being in the school only once a week and that their students were themselves struggling to find their place in a new charter school with an emphasis on social action. This response challenges the authors to reexamine their wish to engage students with institutional power by suggesting that they consider their own positions of power inside the school and classroom. Lastly, the response posits that rather than focusing on the limitations of service-learning and/or public achievement, which may make them appear as less desirable models for social action, we should consider such approaches as providing the very thingâsmall winsâthe authors sought in and that educators should prepare their students for more substantial engagements with power

### Near-Linear Time Insertion-Deletion Codes and (1+$\varepsilon$)-Approximating Edit Distance via Indexing

We introduce fast-decodable indexing schemes for edit distance which can be
used to speed up edit distance computations to near-linear time if one of the
strings is indexed by an indexing string $I$. In particular, for every length
$n$ and every $\varepsilon >0$, one can in near linear time construct a string
$I \in \Sigma'^n$ with $|\Sigma'| = O_{\varepsilon}(1)$, such that, indexing
any string $S \in \Sigma^n$, symbol-by-symbol, with $I$ results in a string $S'
\in \Sigma''^n$ where $\Sigma'' = \Sigma \times \Sigma'$ for which edit
distance computations are easy, i.e., one can compute a
$(1+\varepsilon)$-approximation of the edit distance between $S'$ and any other
string in $O(n \text{poly}(\log n))$ time.
Our indexing schemes can be used to improve the decoding complexity of
state-of-the-art error correcting codes for insertions and deletions. In
particular, they lead to near-linear time decoding algorithms for the
insertion-deletion codes of [Haeupler, Shahrasbi; STOC `17] and faster decoding
algorithms for list-decodable insertion-deletion codes of [Haeupler, Shahrasbi,
Sudan; ICALP `18]. Interestingly, the latter codes are a crucial ingredient in
the construction of fast-decodable indexing schemes

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