OpenRaiser/Intern-Atlas huggingface dataset:
A Quasi-Random Approach to Matrix Spectral Analysis
Venue: arXiv cs.DS 2017
Year: 2017

Inspired by the quantum computing algorithms for Linear Algebra problems [HHL,TaShma] we study how the simulation on a classical computer of this type of "Phase Estimation algorithms" performs when we apply it to solve the Eigen-Problem of Hermitian matrices. The result is a completely new, efficient and stable, parallel algorithm to compute an approximate spectral decomposition of any Hermitian matrix. The algorithm can be implemented by Boolean circuits in $O(\log^2 n)$ parallel time with a total cost of $O(n^{ω+1})$ Boolean operations. This Boolean complexity matches the best known rigorous $O(\log^2 n)$ parallel time algorithms, but unlike those algorithms our algorithm is (logarithmically) stable, so further improvements may lead to practical implementations. All previous efficient and rigorous approaches to solve the Eigen-Problem use randomization to avoid bad condition as we do too. Our algorithm makes further use of randomization in a completely new way, taking random powers of a unitary matrix to randomize the phases of its eigenvalues. Proving that a tiny Gaussian perturbation and a random polynomial power are sufficient to ensure almost pairwise independence of the phases $(\mod (2π))$ is the main technical contribution of this work. This randomization enables us, given a Hermitian matrix with well separated eigenvalues, to sample a random eigenvalue and produce an approximate eigenvector in $O(\log^2 n)$ parallel time and $O(n^ω)$ Boolean complexity. We conjecture that further improvements of our method can provide a stable solution to the full approximate spectral decomposition problem with complexity similar to the complexity (up to a logarithmic factor) of sampling a single eigenvector.
Aircraft navigation based on differentiation-integration observer
Venue: arXiv cs.SY 2017
Year: 2017

In this paper, a generalized differentiation-integration observer is presented based on sensors selection. The proposed differentiation-integration observer can estimate the multiple integrals and high-order derivatives of a signal, synchronously. The parameters selection rules are presented for the differentiation-integration observer. The theoretical results are confirmed by the frequency-domain analysis. The effectiveness of the proposed observer are verified through the numerical simulations on a quadrotor aircraft: i) through the differentiation-integration observer, the attitude angle and the uncertainties in attitude dynamics are estimated synchronously from the measurements of angular velocity; ii) a control law is designed based on the observers to drive the aircraft to track a reference trajectory.
Arguments for the Effectiveness of Human Problem Solving
Venue: arXiv cs.AI 2017
Year: 2017

The question of how humans solve problem has been addressed extensively. However, the direct study of the effectiveness of this process seems to be overlooked. In this paper, we address the issue of the effectiveness of human problem solving: we analyze where this effectiveness comes from and what cognitive mechanisms or heuristics are involved. Our results are based on the optimal probabilistic problem solving strategy that appeared in Solomonoff paper on general problem solving system. We provide arguments that a certain set of cognitive mechanisms or heuristics drive human problem solving in the similar manner as the optimal Solomonoff strategy. The results presented in this paper can serve both cognitive psychology in better understanding of human problem solving processes as well as artificial intelligence in designing more human-like agents.
On the Interpretability of Conditional Probability Estimates in the Agnostic Setting
Venue: arXiv cs.LG 2017
Year: 2017

We study the interpretability of conditional probability estimates for binary classification under the agnostic setting or scenario. Under the agnostic setting, conditional probability estimates do not necessarily reflect the true conditional probabilities. Instead, they have a certain calibration property: among all data points that the classifier has predicted P(Y = 1|X) = p, p portion of them actually have label Y = 1. For cost-sensitive decision problems, this calibration property provides adequate support for us to use Bayes Decision Theory. In this paper, we define a novel measure for the calibration property together with its empirical counterpart, and prove an uniform convergence result between them. This new measure enables us to formally justify the calibration property of conditional probability estimations, and provides new insights on the problem of estimating and calibrating conditional probabilities.
Unbounded-Time Analysis of Guarded LTI Systems with Inputs by Abstract Acceleration (extended version)
Venue: arXiv cs.SY 2017
Year: 2017

Linear Time Invariant (LTI) systems are ubiquitous in control applications. Unbounded-time reachability analysis that can cope with industrial-scale models with thousands of variables is needed. To tackle this problem, we use abstract acceleration, a method for unbounded-time polyhedral reachability analysis for linear systems. Existing variants of the method are restricted to closed systems, i.e., dynamical models without inputs or non-determinism. In this paper, we present an extension of abstract acceleration to linear loops with inputs, which correspond to discrete-time LTI control systems under guard conditions. The new method relies on a relaxation of the solution of the linear dynamical equation that leads to a precise over-approximation of the set of reachable states, which are evaluated using support functions. In order to increase scalability, we use floating-point computations and ensure soundness by interval arithmetic. Our experiments show that performance increases by several orders of magnitude over alternative approaches in the literature. In turn, this tremendous gain allows us to improve on precision by computing more expensive abstractions. We outperform state-of-the-art tools for unbounded-time analysis of LTI system with inputs in speed as well as in precision.
The computational complexity of calculating partition functions of optimal medians with Hamming distance
Venue: arXiv cs.CC 2017
Year: 2017

In this paper, we show that calculating the partition function of optimal medians of binary strings with Hamming distance is \#P-complete for several weight functions. The case when the weight function is the factorial function has application in bioinformatics. In that case, the partition function counts the most parsimonious evolutionary scenarios on a star tree under several models in bioinformatics. The results are extended to binary trees and we show that it is also \#P-complete to calculate the most parsimonious evolutionary scenarios on an arbitrary binary tree under the substitution model of biological sequences and under the Single Cut-or-Join model for genome rearrangements.
Stable Separation and Super-Resolution of Mixture Models
Venue: arXiv cs.IT 2017
Year: 2017

We consider simultaneously identifying the membership and locations of point sources that are convolved with different band-limited point spread functions, from the observation of their superpositions. This problem arises in three-dimensional super-resolution single-molecule imaging, neural spike sorting, multi-user channel identification, among other applications. We propose a novel algorithm, based on convex programming, and establish its near-optimal performance guarantee for exact recovery in the noise-free setting by exploiting the spectral sparsity of the point source models as well as the incoherence between point spread functions. Furthermore, robustness of the recovery algorithm in the presence of bounded noise is also established. Numerical examples are provided to demonstrate the effectiveness of the proposed approach.
Efficient computation of middle levels Gray codes
Venue: arXiv cs.DS 2017
Year: 2017

For any integer $n\geq 1$ a middle levels Gray code is a cyclic listing of all bitstrings of length $2n+1$ that have either $n$ or $n+1$ entries equal to 1 such that any two consecutive bitstrings in the list differ in exactly one bit. The question whether such a Gray code exists for every $n\geq 1$ has been the subject of intensive research during the last 30 years, and has been answered affirmatively only recently [T. Mütze. Proof of the middle levels conjecture. Proc. London Math. Soc., 112(4):677--713, 2016]. In this work we provide the first efficient algorithm to compute a middle levels Gray code. For a given bitstring, our algorithm computes the next $\ell$ bitstrings in the Gray code in time $\mathcal{O}(n\ell(1+\frac{n}{\ell}))$, which is $\mathcal{O}(n)$ on average per bitstring provided that $\ell=Ω(n)$.
Fast and Vectorizable Alternative to Binary Search in O(1) Applicable to a Wide Domain of Sorted Arrays of Floating Point Numbers
Venue: arXiv cs.DS 2017
Year: 2017

Given an array $X$ of $N+1$ strictly ordered floating point numbers and a floating point number $z$ in the interval $[X_0,X_N)$, a common problem is to find the index $i$ of the interval $[X_{i},X_{i+1})$ containing $z$. This problem arises for instance in the context of spline interpolation or the computation of empirical probability distribution from empirical data. Often it needs to be solved for a large number of different values $z$ and the same array $X$, which makes it worth investing resources upfront in pre-processing the array $X$ with the goal of speeding up subsequent search operations. In some cases the values $z$ to be processed are known simultaneously in blocks of size $M$, which offers the opportunity to solve the problem vectorially, exploiting the parallel capabilities of modern CPUs. The common solution is to sequentially invoke $M$ times the well known binary search algorithm, which has complexity $O(log_2 N)$ per individual search and, in its classic formulation, is not vectorizable, i.e. is not SIMD friendly. This paper describes technical improvements to the binary search algorithm, which make it faster and vectorizable. Next it proposes a new vectorizable algorithm, based on an indexing technique, applicable to a wide family of $X$ partitions, which solves the problem with complexity $O(1)$ per individual search at the cost of introducing an initial overhead to compute the index and requiring extra memory for its storage. Test results using streaming SIMD extensions compare the performance of the algorithm versus various benchmarks and demonstrate its effectiveness. Depending on the test case, the algorithm can produce a throughput up to two orders of magnitude larger than the classic binary search. Applicability limitations and cache-friendliness related aspects are also discussed.
On an almost-universal hash function family with applications to authentication and secrecy codes
Venue: arXiv cs.CR 2017
Year: 2017

Universal hashing, discovered by Carter and Wegman in 1979, has many important applications in computer science. MMH$^*$, which was shown to be $Δ$-universal by Halevi and Krawczyk in 1997, is a well-known universal hash function family. We introduce a variant of MMH$^*$, that we call GRDH, where we use an arbitrary integer $n>1$ instead of prime $p$ and let the keys $\mathbf{x}=\langle x_1, \ldots, x_k \rangle \in \mathbb{Z}_n^k$ satisfy the conditions $\gcd(x_i,n)=t_i$ ($1\leq i\leq k$), where $t_1,\ldots,t_k$ are given positive divisors of $n$. Then via connecting the universal hashing problem to the number of solutions of restricted linear congruences, we prove that the family GRDH is an $\varepsilon$-almost-$Δ$-universal family of hash functions for some $\varepsilon<1$ if and only if $n$ is odd and $\gcd(x_i,n)=t_i=1$ $(1\leq i\leq k)$. Furthermore, if these conditions are satisfied then GRDH is $\frac{1}{p-1}$-almost-$Δ$-universal, where $p$ is the smallest prime divisor of $n$. Finally, as an application of our results, we propose an authentication code with secrecy scheme which strongly generalizes the scheme studied by Alomair et al. [{\it J. Math. Cryptol.} {\bf 4} (2010), 121--148], and [{\it J.UCS} {\bf 15} (2009), 2937--2956].
Robust Monotone Submodular Function Maximization
Venue: arXiv cs.DS 2017
Year: 2017

We consider a robust formulation, introduced by Krause et al. (2008), of the classical cardinality constrained monotone submodular function maximization problem, and give the first constant factor approximation results. The robustness considered is w.r.t. adversarial removal of up to $τ$ elements from the chosen set. For the fundamental case of $τ=1$, we give a deterministic $(1-1/e)-1/Θ(m)$ approximation algorithm, where $m$ is an input parameter and number of queries scale as $O(n^{m+1})$. In the process, we develop a deterministic $(1-1/e)-1/Θ(m)$ approximate greedy algorithm for bi-objective maximization of (two) monotone submodular functions. Generalizing the ideas and using a result from Chekuri et al. (2010), we show a randomized $(1-1/e)-ε$ approximation for constant $τ$ and $ε\leq \frac{1}{\tildeΩ(τ)}$, making $O(n^{1/ε^3})$ queries. Further, for $τ\ll \sqrt{k}$, we give a fast and practical 0.387 algorithm. Finally, we also give a black box result result for the much more general setting of robust maximization subject to an Independence System.
Distributed First Order Logic
Venue: arXiv cs.LO 2017
Year: 2017

Distributed First Order Logic (DFOL) has been introduced more than ten years ago with the purpose of formalising distributed knowledge-based systems, where knowledge about heterogeneous domains is scattered into a set of interconnected modules. DFOL formalises the knowledge contained in each module by means of first-order theories, and the interconnections between modules by means of special inference rules called bridge rules. Despite their restricted form in the original DFOL formulation, bridge rules have influenced several works in the areas of heterogeneous knowledge integration, modular knowledge representation, and schema/ontology matching. This, in turn, has fostered extensions and modifications of the original DFOL that have never been systematically described and published. This paper tackles the lack of a comprehensive description of DFOL by providing a systematic account of a completely revised and extended version of the logic, together with a sound and complete axiomatisation of a general form of bridge rules based on Natural Deduction. The resulting DFOL framework is then proposed as a clear formal tool for the representation of and reasoning about distributed knowledge and bridge rules.
Identification, location-domination and metric dimension on interval and permutation graphs. I. Bounds
Venue: arXiv cs.DM 2017
Year: 2017

We consider the problems of finding optimal identifying codes, (open) locating-dominating sets and resolving sets of an interval or a permutation graph. In these problems, one asks to find a subset of vertices, normally called a \emph{solution} set, using which all vertices of the graph are distinguished. The identification can be done by considering the neighborhood within the solution set, or by employing the distances to the solution vertices. Normally the goal is to minimize the size of the solution set then. Here we study the case of interval graphs, unit interval graphs, (bipartite) permutation graphs and cographs. For these classes of graphs we give tight lower bounds for the size of such solution sets depending on the order of the input graph. While such lower bounds for the general class of graphs are in logarithmic order, the improved bounds in these special classes are of the order of either quadratic root or linear in terms of number of vertices. Moreover, the results for cographs lead to linear-time algorithms to solve the considered problems on inputs that are cographs.
Efficiently list-decodable punctured Reed-Muller codes
Venue: arXiv cs.IT 2017
Year: 2017

The Reed-Muller (RM) code encoding $n$-variate degree-$d$ polynomials over ${\mathbb F}_q$ for $d < q$, with its evaluation on ${\mathbb F}_q^n$, has relative distance $1-d/q$ and can be list decoded from a $1-O(\sqrt{d/q})$ fraction of errors. In this work, for $d \ll q$, we give a length-efficient puncturing of such codes which (almost) retains the distance and list decodability properties of the Reed-Muller code, but has much better rate. Specificially, when $q =Ω( d^2/ε^2)$, we given an explicit rate $Ω\left(\fracε{d!}\right)$ puncturing of Reed-Muller codes which have relative distance at least $(1-ε)$ and efficient list decoding up to $(1-\sqrtε)$ error fraction. This almost matches the performance of random puncturings which work with the weaker field size requirement $q= Ω( d/ε^2)$. We can also improve the field size requirement to the optimal (up to constant factors) $q =Ω( d/ε)$, at the expense of a worse list decoding radius of $1-ε^{1/3}$ and rate $Ω\left(\frac{ε^2}{d!}\right)$. The first of the above trade-offs is obtained by substituting for the variables functions with carefully chosen pole orders from an algebraic function field; this leads to a puncturing for which the RM code is a subcode of a certain algebraic-geometric code (which is known to be efficiently list decodable). The second trade-off is obtained by concatenating this construction with a Reed-Solomon based multiplication friendly pair, and using the list recovery property of algebraic-geometric codes.
Factor Graphs for Quantum Probabilities
Venue: arXiv cs.IT 2017
Year: 2017

A factor-graph representation of quantum-mechanical probabilities (involving any number of measurements) is proposed. Unlike standard statistical models, the proposed representation uses auxiliary variables (state variables) that are not random variables. All joint probability distributions are marginals of some complex-valued function $q$, and it is demonstrated how the basic concepts of quantum mechanics relate to factorizations and marginals of $q$.
Finding Points in General Position
Venue: arXiv cs.CG 2017
Year: 2017

We study computational aspects of the General Position Subset Selection problem defined as follows: Given a set of points in the plane, find a maximum-cardinality subset of points in general position. We prove that General Position Subset Selection is NP-hard, APX-hard, and give several fixed-parameter tractability results as well as a subexponential running time lower bound based on the Exponential Time Hypothesis.
Resource Oblivious Sorting on Multicores
Venue: arXiv cs.DS 2017
Year: 2017

We present a deterministic sorting algorithm, SPMS (Sample, Partition, and Merge Sort), that interleaves the partitioning of a sample sort with merging. Sequentially, it sorts $n$ elements in $O(n \log n)$ time cache-obliviously with an optimal number of cache misses. The parallel complexity (or critical path length) of the algorithm is $O(\log n \cdot \log\log n)$, which improves on previous bounds for optimal cache oblivious sorting. The algorithm also has low false sharing costs. When scheduled by a work-stealing scheduler in a multicore computing environment with a global shared memory and $p$ cores, each having a cache of size $M$ organized in blocks of size $B$, the costs of the additional cache misses and false sharing misses due to this parallel execution are bounded by the cost of $O(S\cdot M/B)$ and $O(S \cdot B)$ cache misses respectively, where $S$ is the number of steals performed during the execution. Finally, SPMS is resource oblivious in Athat the dependence on machine parameters appear only in the analysis of its performance, and not within the algorithm itself.
Graph Codes for Distributed Instant Message Collection in an Arbitrary Noisy Broadcast Network
Venue: arXiv cs.IT 2017
Year: 2017

We consider the problem of minimizing the number of broadcasts for collecting all sensor measurements at a sink node in a noisy broadcast sensor network. Focusing first on arbitrary network topologies, we provide (i) fundamental limits on the required number of broadcasts of data gathering, and (ii) a general in-network computing strategy to achieve an upper bound within factor $\log N$ of the fundamental limits, where $N$ is the number of agents in the network. Next, focusing on two example networks, namely, \textcolor{black}{arbitrary geometric networks and random Erd$\ddot{o}$s-R$\acute{e}$nyi networks}, we provide improved in-network computing schemes that are optimal in that they attain the fundamental limits, i.e., the lower and upper bounds are tight \textcolor{black}{in order sense}. Our main techniques are three distributed encoding techniques, called graph codes, which are designed respectively for the above-mentioned three scenarios. Our work thus extends and unifies previous works such as those of Gallager [1] and Karamchandani~\emph{et. al.} [2] on number of broadcasts for distributed function computation in special network topologies, while bringing in novel techniques, e.g., from error-control coding and noisy circuits, for both upper and lower bounds.
Microscopic Analysis of the Uplink Interference in FDMA Small Cell Networks
Venue: arXiv cs.NI 2017
Year: 2017

In this paper, we analytically derive an upper bound on the error in approximating the uplink (UL) single-cell interference by a lognormal distribution in frequency division multiple access (FDMA) small cell networks (SCNs). Such an upper bound is measured by the Kolmogorov Smirnov (KS) distance between the actual cumulative density function (CDF) and the approximate CDF. The lognormal approximation is important because it allows tractable network performance analysis. Our results are more general than the existing works in the sense that we do not pose any requirement on (i) the shape and/or size of cell coverage areas, (ii) the uniformity of user equipment (UE) distribution, and (iii) the type of multi-path fading. Based on our results, we propose a new framework to directly and analytically investigate a complex network with practical deployment of multiple BSs placed at irregular locations, using a power lognormal approximation of the aggregate UL interference. The proposed network performance analysis is particularly useful for the 5th generation (5G) systems with general cell deployment and UE distribution.
Using Thought-Provoking Children's Questions to Drive Artificial Intelligence Research
Venue: arXiv cs.AI 2017
Year: 2017

We propose to use thought-provoking children's questions (TPCQs), namely Highlights BrainPlay questions, as a new method to drive artificial intelligence research and to evaluate the capabilities of general-purpose AI systems. These questions are designed to stimulate thought and learning in children, and they can be used to do the same thing in AI systems, while demonstrating the system's reasoning capabilities to the evaluator. We introduce the TPCQ task, which which takes a TPCQ question as input and produces as output (1) answers to the question and (2) learned generalizations. We discuss how BrainPlay questions stimulate learning. We analyze 244 BrainPlay questions, and we report statistics on question type, question class, answer cardinality, answer class, types of knowledge needed, and types of reasoning needed. We find that BrainPlay questions span many aspects of intelligence. Because the answers to BrainPlay questions and the generalizations learned from them are often highly open-ended, we suggest using human judges for evaluation.