OpenRaiser/Intern-Atlas huggingface dataset:
New Algorithms and Hard Instances for Non-Commutative Computation
Venue: arXiv cs.CC 2015
Year: 2015

Motivated by the recent developments on the complexity of non-com\-mu\-ta\-tive determinant and permanent [Chien et al.\ STOC 2011, Bläser ICALP 2013, Gentry CCC 2014] we attempt at obtaining a tight characterization of hard instances of non-commutative permanent. We show that computing Cayley permanent and determinant on weight\-ed adjacency matrices of graphs of component size six is $\#{\sf P}$ complete on algebras that contain $2\times 2$ matrices and the permutation group $S_3$. Also, we prove a lower bound of $2^{Ω(n)}$ on the size of branching programs computing the Cayley permanent on adjacency matrices of graphs with component size bounded by two. Further, we observe that the lower bound holds for almost all graphs of component size two. On the positive side, we show that the Cayley permanent on graphs of component size $c$ can be computed in time $n^{c{\sf poly}(t)}$, where $t$ is a parameter depending on the labels of the vertices. Finally, we exhibit polynomials that are equivalent to the Cayley permanent polynomial but are easy to compute over commutative domains.
Monoidal functional dependencies
Venue: arXiv cs.DB 2015
Year: 2015

We present a complete logic for reasoning with functional dependencies (FDs) with semantics defined over classes of commutative integral partially ordered monoids and complete residuated lattices. The dependencies allow us to express stronger relationships between attribute values than the ordinary FDs. In our setting, the dependencies not only express that certain values are determined by others but also express that similar values of attributes imply similar values of other attributes. We show complete axiomatization using a system of Armstrong-like rules, comment on related computational issues, and the relational vs. propositional semantics of the dependencies.
Generation and Analysis of Constrained Random Sampling Patterns
Venue: arXiv cs.DS 2015
Year: 2015

Random sampling is a technique for signal acquisition which is gaining popularity in practical signal processing systems. Nowadays, event-driven analog-to-digital converters make random sampling feasible in practical applications. A process of random sampling is defined by a sampling pattern, which indicates signal sampling points in time. Practical random sampling patterns are constrained by ADC characteristics and application requirements. In this paper authors introduce statistical methods which evaluate random sampling pattern generators with emphasis on practical applications. Furthermore, the authors propose a new random pattern generator which copes with strict practical limitations imposed on patterns, with possibly minimal loss in randomness of sampling. The proposed generator is compared with existing sampling pattern generators using the introduced statistical methods. It is shown that the proposed algorithm generates random sampling patterns dedicated for event-driven-ADCs better than existed sampling pattern generators. Finally, implementation issues of random sampling patterns are discussed.
Rate Optimal design of a Wireless Backhaul Network using TV White Space
Venue: arXiv cs.NI 2015
Year: 2015

The penetration of wireless broadband services in remote areas has primarily been limited due to the lack of economic incentives that service providers encounter in sparsely populated areas. Besides, wireless backhaul links like satellite and microwave are either expensive or require strict line of sight communication making them unattractive. TV white space channels with their desirable radio propagation characteristics can provide an excellent alternative for engineering backhaul networks in areas that lack abundant infrastructure. Specifically, TV white space channels can provide "free wireless backhaul pipes" to transport aggregated traffic from broadband sources to fiber access points. In this paper, we investigate the feasibility of multi-hop wireless backhaul in the available white space channels by using noncontiguous Orthogonal Frequency Division Multiple Access (NC-OFDMA) transmissions between fixed backhaul towers. Specifically, we consider joint power control, scheduling and routing strategies to maximize the minimum rate across broadband towers in the network. Depending on the population density and traffic demands of the location under consideration, we discuss the suitable choice of cell size for the backhaul network. Using the example of available TV white space channels in Wichita, Kansas (a small city located in central USA), we provide illustrative numerical examples for designing such wireless backhaul network.
Smart Sampling for Lightweight Verification of Markov Decision Processes
Venue: arXiv cs.DS 2015
Year: 2015

Markov decision processes (MDP) are useful to model optimisation problems in concurrent systems. To verify MDPs with efficient Monte Carlo techniques requires that their nondeterminism be resolved by a scheduler. Recent work has introduced the elements of lightweight techniques to sample directly from scheduler space, but finding optimal schedulers by simple sampling may be inefficient. Here we describe "smart" sampling algorithms that can make substantial improvements in performance.
Universal Phase Transition in Community Detectability under a Stochastic Block Model
Venue: arXiv cs.SI 2015
Year: 2015

We prove the existence of an asymptotic phase transition threshold on community detectability for the spectral modularity method [M. E. J. Newman, Phys. Rev. E 74, 036104 (2006) and Proc. National Academy of Sciences. 103, 8577 (2006)] under a stochastic block model. The phase transition on community detectability occurs as the inter-community edge connection probability $p$ grows. This phase transition separates a sub-critical regime of small $p$, where modularity-based community detection successfully identifies the communities, from a super-critical regime of large $p$ where successful community detection is impossible. We show that, as the community sizes become large, the asymptotic phase transition threshold $p^*$ is equal to $\sqrt{p_1\cdot p_2}$, where $p_i~(i=1,2)$ is the within-community edge connection probability. Thus the phase transition threshold is universal in the sense that it does not depend on the ratio of community sizes. The universal phase transition phenomenon is validated by simulations for moderately sized communities. Using the derived expression for the phase transition threshold we propose an empirical method for estimating this threshold from real-world data.
Recurrent Neural Network Regularization
Venue: arXiv cs.NE 2015
Year: 2015

We present a simple regularization technique for Recurrent Neural Networks (RNNs) with Long Short-Term Memory (LSTM) units. Dropout, the most successful technique for regularizing neural networks, does not work well with RNNs and LSTMs. In this paper, we show how to correctly apply dropout to LSTMs, and show that it substantially reduces overfitting on a variety of tasks. These tasks include language modeling, speech recognition, image caption generation, and machine translation.
The Interplay between Massive MIMO and Underlaid D2D Networking
Venue: arXiv cs.IT 2015
Year: 2015

In a device-to-device (D2D) underlaid cellular network, the uplink spectrum is reused by the D2D transmissions, causing mutual interference with the ongoing cellular transmissions. Massive MIMO is appealing in such a context as the base station's (BS's) large antenna array can nearly null the D2D-to-BS interference. The multi-user transmission in massive MIMO, however, may lead to increased cellular-to-D2D interference. This paper studies the interplay between massive MIMO and underlaid D2D networking in a multi-cell setting. We investigate cellular and D2D spectral efficiency under both perfect and imperfect channel state information (CSI) at the receivers that employ partial zero-forcing. Compared to the case without D2D, there is a loss in cellular spectral efficiency due to D2D underlay. With perfect CSI, the loss can be completely overcome if the number of canceled D2D interfering signals is scaled with the number of BS antennas at an arbitrarily slow rate. With imperfect CSI, in addition to pilot contamination, a new asymptotic effect termed underlay contamination arises. In the non-asymptotic regime, simple analytical lower bounds are derived for both the cellular and D2D spectral efficiency.
Grouping-based Interference Alignment with IA-Cell Assignment in Multi-Cell MIMO MAC under Limited Feedback
Venue: arXiv cs.IT 2015
Year: 2015

Interference alignment (IA) is a promising technique to efficiently mitigate interference and to enhance the capacity of a wireless communication network. This paper proposes a grouping-based interference alignment (GIA) with optimized IA-Cell assignment for the multiple cells interfering multiple-input and multiple-output (MIMO) multiple access channel (MAC) network under limited feedback. This work consists of three main parts: 1) a complete study (including some new improvements) of the GIA with respect to the degrees of freedom (DoF) and optimal linear transceiver design is performed, which allows for low-complexity and distributed implementation; 2) based on the GIA, the concept of IA-Cell assignment is introduced. Three IA-Cell assignment algorithms are proposed for the setup with different backhaul overhead and their DoF and rate performance is investigated; 3) the performance of the proposed GIA algorithms is studied under limited feedback of IA precoders. To enable efficient feedback, a dynamic feedback bit allocation (DBA) problem is formulated and solved in closed-form. The practical implementation, the required backhaul overhead, and the complexity of the proposed algorithms are analyzed. Numerical results show that our proposed algorithms greatly outperform the traditional GIA under both unlimited and limited feedback.
The Q-curve construction for endomorphism-accelerated elliptic curves
Venue: arXiv cs.CR 2015
Year: 2015

We give a detailed account of the use of $\mathbb{Q}$-curve reductions to construct elliptic curves over $\mathbb{F}\_{p^2}$ with efficiently computable endomorphisms, which can be used to accelerate elliptic curve-based cryptosystems in the same way as Gallant--Lambert--Vanstone (GLV) and Galbraith--Lin--Scott (GLS) endomorphisms. Like GLS (which is a degenerate case of our construction), we offer the advantage over GLV of selecting from a much wider range of curves, and thus finding secure group orders when \(p\) is fixed for efficient implementation. Unlike GLS, we also offer the possibility of constructing twist-secure curves. We construct several one-parameter families of elliptic curves over $\mathbb{F}\_{p^2}$ equipped with efficient endomorphisms for every $p \textgreater{} 3$, and exhibit examples of twist-secure curves over $\mathbb{F}\_{p^2}$ for the efficient Mersenne prime $p = 2^{127}-1$.
Tangent Codes
Venue: arXiv cs.IT 2015
Year: 2015

The present article studies the finite Zariski tangent spaces to an affine variety X as linear codes, in order to characterize their typical or exceptional properties by global geometric conditions on X. The discussion concerns the generic minimum distance of a tangent code to X, its lower semi-continuity under a deformation of X, as well as the existence of Zariski tangent spaces to X with exceptional minimum distance. Tangent codes are shown to admit simultaneous decoding. The duals of the tangent codes to X are realized by gradients of polynomials from the ideal of X. We provide constructions of affine varieties with near MDS, cyclic or Hamming tangent codes. Puncturing, shortening and extending finite Zariski tangent spaces are related to the corresponding operations on affine varieties. The (u|u+v) construction of tangent codes is associated with a fibered product of varieties. Explicit constructions realize linear Hamming isometries as differentials of morphisms of affine varieties.
Fast MATLAB assembly of FEM matrices in 2D and 3D: Edge elements
Venue: arXiv cs.MS 2015
Year: 2015

We propose an effective and flexible way to assemble finite element stiffness and mass matrices in MATLAB. We apply this for problems discretized by edge finite elements. Typical edge finite elements are Raviart-Thomas elements used in discretizations of H(div) spaces and Nedelec elements in discretizations of H(curl) spaces. We explain vectorization ideas and comment on a freely available MATLAB code which is fast and scalable with respect to time.
Probabilistic thread algebra
Venue: arXiv cs.LO 2015
Year: 2015

We add probabilistic features to basic thread algebra and its extensions with thread-service interaction and strategic interleaving. Here, threads represent the behaviours produced by instruction sequences under execution and services represent the behaviours exhibited by the components of execution environments of instruction sequences. In a paper concerned with probabilistic instruction sequences, we proposed several kinds of probabilistic instructions and gave an informal explanation for each of them. The probabilistic features added to the extension of basic thread algebra with thread-service interaction make it possible to give a formal explanation in terms of non-probabilistic instructions and probabilistic services. The probabilistic features added to the extensions of basic thread algebra with strategic interleaving make it possible to cover strategies corresponding to probabilistic scheduling algorithms.
A Note on Selling Optimally Two Uniformly Distributed Goods
Venue: arXiv cs.GT 2015
Year: 2015

We provide a new, much simplified and straightforward proof to a result of Pavlov [2011] regarding the revenue maximizing mechanism for selling two goods with uniformly i.i.d. valuations over intervals $[c,c+1]$, to an additive buyer. This is done by explicitly defining optimal dual solutions to a relaxed version of the problem, where the convexity requirement for the bidder's utility has been dropped. Their optimality comes directly from their structure, through the use of exact complementarity. For $c=0$ and $c\geq 0.092$ it turns out that the corresponding optimal primal solution is a feasible selling mechanism, thus the initial relaxation comes without a loss, and revenue maximality follows. However, for $0<c<0.092$ that's not the case, providing the first clear example where relaxing convexity provably does not come for free, even in a two-item regularly i.i.d. setting.
Joint Transceiver Design for Wireless Sensor Networks through Block Coordinate Descent Optimization
Venue: arXiv cs.IT 2015
Year: 2015

This paper considers the joint transceiver design in a wireless sensor network where multiple sensors observe the same physical event and transmit their contaminated observations to a fusion center, with all nodes equipped with multiple antennae and linear filters. Under the mean square error (MSE) criterion, the joint beamforming design problem can be formulated as a nonconvex optimization problem. To attack this problem, various block coordinate descent (BCD) algorithms are proposed with convergence being carefully examined. First we propose a two block coordinate descent (2-BCD) algorithm that iteratively designs all the beamformers and the linear receiver, where both subproblems are convex and the convergence of limit points to stationary points is guaranteed. Besides, the thorough solution to optimizing one single beamformer is given, which, although discussed several times, is usually incomplete in existing literature. Based on that, multiple block coordinate descent algorithms are proposed. Solving the joint beamformers' design by cyclically updating each separate beamformer under the 2-BCD framework gives birth to a layered BCD algorithm, which guarantees convergence to stationary points. Besides that, a wide class of multiple BCD algorithms using the general essentially cyclic updating rule has been studied. As will be seen, by appropriately adjusting the update of single beamformer, fast converging, highly efficient and stationary point achieving algorithms can be obtained. Extensive numerical results are presented to verify our findings.
An Efficient Topology-Based Algorithm for Transient Analysis of Power Grid
Venue: arXiv cs.OH 2015
Year: 2015

In the design flow of integrated circuits, chip-level verification is an important step that sanity checks the performance is as expected. Power grid verification is one of the most expensive and time-consuming steps of chip-level verification, due to its extremely large size. Efficient power grid analysis technology is highly demanded as it saves computing resources and enables faster iteration. In this paper, a topology-base power grid transient analysis algorithm is proposed. Nodal analysis is adopted to analyze the topology which is mathematically equivalent to iteratively solving a positive semi-definite linear equation. The convergence of the method is proved.
Census: Fast, scalable and robust data aggregation in MANETs
Venue: arXiv cs.NI 2015
Year: 2015

This paper describes Census, a protocol for data aggregation and statistical counting in MANETs. Census operates by circulating a set of tokens in the network using biased random walks such that each node is visited by at least one token. The protocol is structure-free so as to avoid high messaging overhead for maintaining structure in the presence of node mobility. It biases the random walks of tokens so as to achieve fast cover time; the bias involves short albeit multi-hop gradients that guide the tokens towards hitherto unvisited nodes. Census thus achieves a cover time of O(N/k) and message overhead of O(Nlog(N)/k) where N is the number of nodes and k the number of tokens in the network. Notably, it enjoys scalability and robustness, which we demonstrate via simulations in networks ranging from 100 to 4000 nodes under different network densities and mobility models.
Revisiting Algebra and Complexity of Inference in Graphical Models
Venue: arXiv cs.AI 2015
Year: 2015

This paper studies the form and complexity of inference in graphical models using the abstraction offered by algebraic structures. In particular, we broadly formalize inference problems in graphical models by viewing them as a sequence of operations based on commutative semigroups. We then study the computational complexity of inference by organizing various problems into an "inference hierarchy". When the underlying structure of an inference problem is a commutative semiring -- i.e. a combination of two commutative semigroups with the distributive law -- a message passing procedure called belief propagation can leverage this distributive law to perform polynomial-time inference for certain problems. After establishing the NP-hardness of inference in any commutative semiring, we investigate the relation between algebraic properties in this setting and further show that polynomial-time inference using distributive law does not (trivially) extend to inference problems that are expressed using more than two commutative semigroups. We then extend the algebraic treatment of message passing procedures to survey propagation, providing a novel perspective using a combination of two commutative semirings. This formulation generalizes the application of survey propagation to new settings.
Upper bound on list-decoding radius of binary codes
Venue: arXiv cs.IT 2015
Year: 2015

Consider the problem of packing Hamming balls of a given relative radius subject to the constraint that they cover any point of the ambient Hamming space with multiplicity at most $L$. For odd $L\ge 3$ an asymptotic upper bound on the rate of any such packing is proven. Resulting bound improves the best known bound (due to Blinovsky'1986) for rates below a certain threshold. Method is a superposition of the linear-programming idea of Ashikhmin, Barg and Litsyn (that was used previously to improve the estimates of Blinovsky for $L=2$) and a Ramsey-theoretic technique of Blinovsky. As an application it is shown that for all odd $L$ the slope of the rate-radius tradeoff is zero at zero rate.
Strong Steiner Tree Approximations in Practice
Venue: arXiv cs.DS 2015
Year: 2015

In this experimental study we consider Steiner tree approximations that guarantee a constant approximation of ratio smaller than $2$. The considered greedy algorithms and approaches based on linear programming involve the incorporation of $k$-restricted full components for some $k \geq 3$. For most of the algorithms, their strongest theoretical approximation bounds are only achieved for $k \to \infty$. However, the running time is also exponentially dependent on $k$, so only small $k$ are tractable in practice. We investigate different implementation aspects and parameter choices that finally allow us to construct algorithms (somewhat) feasible for practical use. We compare the algorithms against each other, to an exact LP-based algorithm, and to fast and simple $2$-approximations.
Cache Serializability: Reducing Inconsistency in Edge Transactions
Venue: arXiv cs.DC 2015
Year: 2015

Read-only caches are widely used in cloud infrastructures to reduce access latency and load on backend databases. Operators view coherent caches as impractical at genuinely large scale and many client-facing caches are updated in an asynchronous manner with best-effort pipelines. Existing solutions that support cache consistency are inapplicable to this scenario since they require a round trip to the database on every cache transaction. Existing incoherent cache technologies are oblivious to transactional data access, even if the backend database supports transactions. We propose T-Cache, a novel caching policy for read-only transactions in which inconsistency is tolerable (won't cause safety violations) but undesirable (has a cost). T-Cache improves cache consistency despite asynchronous and unreliable communication between the cache and the database. We define cache-serializability, a variant of serializability that is suitable for incoherent caches, and prove that with unbounded resources T-Cache implements this new specification. With limited resources, T-Cache allows the system manager to choose a trade-off between performance and consistency. Our evaluation shows that T-Cache detects many inconsistencies with only nominal overhead. We use synthetic workloads to demonstrate the efficacy of T-Cache when data accesses are clustered and its adaptive reaction to workload changes. With workloads based on the real-world topologies, T-Cache detects 43-70% of the inconsistencies and increases the rate of consistent transactions by 33-58%.
Interference Functionals in Poisson Networks
Venue: arXiv cs.IT 2015
Year: 2015

We propose and prove a theorem that allows the calculation of a class of functionals on Poisson point processes that have the form of expected values of sum-products of functions. In proving the theorem, we present a variant of the Campbell-Mecke theorem from stochastic geometry. We proceed to apply our result in the calculation of expected values involving interference in wireless Poisson networks. Based on this, we derive outage probabilities for transmissions in a Poisson network with Nakagami fading. Our results extend the stochastic geometry toolbox used for the mathematical analysis of interference-limited wireless networks.