Functional un|unparsing

Danvy??s functional unparsing problem (Danvy in J. Funct. Program. 8(6), 621?C625, 1998) is to implement a type-safe ??printf?? function, which converts a sequence of heterogeneous arguments to a string according to a given format. The dual problem is to implement a type-safe ??scanf?? function, which extracts a sequence of heterogeneous arguments from a string by interpreting (Friedman and Wand in LFP, pp. 348?C355, 1984 and in Essentials of Programming Languages, MIT Press, 2008) the same format as an equally heterogeneous sequence of patterns that binds zero or more variables. We derive multiple solutions to both problems (Wand in J. ACM 27(1), 164?C180, 1980) from their formal specifications (Wand in Theor. Comput. Sci. 20(1), 3?C32, 1982). On one hand, our solutions show how the Hindley-Milner type system, unextended, permits accessing heterogeneous sequences with the static assurance of type safety. On the other hand, our solutions demonstrate the use of control operators (Felleisen et al. in Proceedings of the 1988 ACM Conference on Lisp and Functional Programming, pp. 52?C62, ACM Press, New York, 1988; Wand in POPL 85: Conference Record of the Annual ACM Symposium on Principles of Programming Languages, vol. 16, ACM Press, New York, 1985; Meyer and Wand in Logics of Programs, Lecture Notes in Computer Science, vol. 193, pp. 219?C224, Springer, Berlin, 1985) to communicate with formats as coroutines (Wand in Proceedings of the 1980 ACM Conference on Lisp and Functional Programming, vol. 12, pp. 285?C299, ACM Press, New York, 1980 and Haynes et al. in LFP, pp. 293?C298, 1984).     

A Uniform Paradigm to Succinctly Encode Various Families of Trees

We propose a uniform method to encode various types of trees succinctly. These families include ordered (ordinal), k-ary (cardinal), and unordered (free) trees. We will show the approach is intrinsically suitable for obtaining entropy-based encodings of trees (such as the degree-distribution entropy). Previously-existing succinct encodings of trees use ad hoc techniques to encode each particular family of trees. Additionally, the succinct encodings obtained using the uniform approach improve upon the existing succinct encodings of each family of trees; in the case of ordered trees, it simplifies the encoding while supporting the full set of navigational operations. It also simplifies the implementation of many supported operations. The approach applied to k-ary trees yields a succinct encoding that supports both cardinal-type operations (e.g. determining the child label i) as well as the full set of ordinal-type operations (e.g. reporting the number of siblings to the left of a node). Previous work on succinct encodings of k-ary trees does not support both types of operations simultaneously (Benoit et al. in Algorithmica 43(4):275–292, 2005; Raman et al. in ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 233–242, 2002). For unordered trees, the approach achieves the first succinct encoding. The approach is based on two recursive decompositions of trees into subtrees. Recursive decomposition of a structure into substructures is a common technique in succinct encodings and has even been used to encode (ordered) trees (Geary et al. in ACM Trans. Algorithms 2(4):510–534, 2006; He et al. in ICALP, pp. 509–520, 2007) and dynamic binary trees (Munro et al. in ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 529–536, 2001; Storm in Representing dynamic binary trees succinctly, Master’s thesis, 2000). The main distinction of the approach in this paper is that a tree is decomposed into subtrees in a manner that the subtrees are maximally isolated from each other. This intermediate decomposition result is interesting in its own right and has proved useful in other applications (Farzan et al. in ICALP (1), pp. 451–462, 2009; Farzan and Munro in ICALP (1), pp. 439–450, 2009; Farzan and Kamali in ICALP, 2011).     

Toward more localized local algorithms: removing assumptions concerning global knowledge

Numerous sophisticated local algorithm were suggested in the literature for various fundamental problems. Notable examples are the MIS and $(\Delta +1)$ -coloring algorithms by Barenboim and Elkin (Distrib Comput 22(5–6):363–379, 2010), by Kuhn (2009), and by Panconesi and Srinivasan (J Algorithms 20(2):356–374, 1996), as well as the $O\mathopen {}(\Delta ^2)$ -coloring algorithm by Linial (J Comput 21:193, 1992). Unfortunately, most known local algorithms (including, in particular, the aforementioned algorithms) are non-uniform, that is, local algorithms generally use good estimations of one or more global parameters of the network, e.g., the maximum degree $\Delta $ or the number of nodes $n$ . This paper provides a method for transforming a non-uniform local algorithm into a uniform one. Furthermore, the resulting algorithm enjoys the same asymptotic running time as the original non-uniform algorithm. Our method applies to a wide family of both deterministic and randomized algorithms. Specifically, it applies to almost all state of the art non-uniform algorithms for MIS and Maximal Matching, as well as to many results concerning the coloring problem (In particular, it applies to all aforementioned algorithms). To obtain our transformations we introduce a new distributed tool called pruning algorithms, which we believe may be of independent interest.     

Generalising Unit-Refutation Completeness and SLUR via Nested Input Resolution

The class ${\mathcal{SLUR}}$ (Single Lookahead Unit Resolution) was introduced in Schlipf et al. (Inf Process Lett 54:133–137, 1995) as an umbrella class for efficient (poly-time) SAT solving, with linear-time SAT decision, while the recognition problem was not considered. ?epek et al. (2012) and Balyo et al. (2012) extended this class in various ways to hierarchies covering all of CNF (all clause-sets). We introduce a hierarchy ${\mathcal{SLUR}}_k$ which we argue is the natural “limit” of such approaches. The second source for our investigations is the class ${\mathcal{UC}}$ of unit-refutation complete clause-sets, introduced in del Val (1994) as a target class for knowledge compilation. Via the theory of “hardness” of clause-sets as developed in Kullmann (1999), Kullmann (Ann Math Artif Intell 40(3–4):303–352, 2004) and Ansótegui et al. (2008) we obtain a natural generalisation ${\mathcal{UC}}_k$ , containing those clause-sets which are “unit-refutation complete of level k”, which is the same as having hardness at most k. Utilising the strong connections to (tree-)resolution complexity and (nested) input resolution, we develop basic methods for the determination of hardness (the level k in ${\mathcal{UC}}_k$ ). A fundamental insight now is that ${\mathcal{SLUR}}_k = {\mathcal{UC}}_k$ holds for all k. We can thus exploit both streams of intuitions and methods for the investigations of these hierarchies. As an application we can easily show that the hierarchies from ?epek et al. (2012) and Balyo et al. (2012) are strongly subsumed by ${\mathcal{SLUR}}_k$ . Finally we consider the problem of “irredundant” clause-sets in ${\mathcal{UC}}_k$ . For 2-CNF we show that strong minimisations are possible in polynomial time, while already for (very special) Horn clause-sets minimisation is NP-complete. We conclude with an extensive discussion of open problems and future directions. We envisage the concepts investigated here to be the starting point for a theory of good SAT translations, which brings together the good SAT-solving aspects from ${\mathcal{SLUR}}$ together with the knowledge-representation aspects from ${\mathcal{UC}}$ , and expands this combination via notions of “hardness”.     

A new spatial IP assignment method for IP-based wireless sensor networks

Wireless sensor networks (WSNs), one of the commercial wireless mesh networks (WMNs), are envisioned to provide an effective solution for sensor-based AmI (Ambient Intelligence) systems and applications. To enable the communications between AmI sensor networks and the most popular TCP/IP networks seamlessly, the best solution model is to run TCP/IP directly on WSNs (Mulligan et al. 2009; Hui and Culler 2008; Han and Mam 2007; Kim et al. 2007; Xiaohua et al. 2004; Dunkels et al. 2004; Dunkels et al. 2004; Dunkels 2001; Dunkels et al. 2004). In this case, an IP assignment method is required to assign each sensor node a unique IP address. SIPA (Dunkels et al. 2004) is the best known IP assignment method that uses spatial relations and locations of sensor nodes to assign their IP addresses. It has been applied in Contiki (Dunkels et al. 2004), a famous WSN operating system, to support the 6LowPAN protocol. In Chang et al. (2009), we proposed the SLIPA (Scan-Line IP Assignment) algorithm to improve the assignment success rate (ASR) obtained by SIPA. SLIPA can achieve a good ASR when sensor nodes are uniformly distributed. However, if sensor nodes are deployed by other distributions, the improvements would be limited. This paper proposes a new spatial IP assignment method, called SLIPA-Q (SLIPA with equal-quantity partition), to improve SLIPA. Experiments show that, by testing the proposed method 1,000 times with 1,000 randomly deployed sensor nodes, the average ASR obtained by SLIPA-Q is over two times of that obtained by SLIPA. Under the same 88% ASR, the average numbers of sensor nodes those can be successfully assigned by SLIPA-Q, SLIPA, and SIPA are 950, 850, and 135, respectively. Comparing to previous spatial IP assignment methods, SLIPA-Q can achieve dramatic improvements in ASR for assigning IP addresses to a large set of sensor nodes.     

Query-Efficient Locally Decodable Codes of Subexponential Length

A k-query locally decodable code (LDC) C : Σ ⁿ → Γ ^N encodes each message x into a codeword C(x) such that each symbol of x can be probabilistically recovered by querying only k coordinates of C(x), even after a constant fraction of the coordinates has been corrupted. Yekhanin (in J ACM 55:1–16, 2008) constructed a 3-query LDC of subexponential length, N = exp(exp(O(log n/log log n))), under the assumption that there are infinitely many Mersenne primes. Efremenko (in Proceedings of the 41st annual ACM symposium on theory of computing, ACM, New York, 2009) constructed a 3-query LDC of length ${N_{2}={\rm exp}({\rm exp} (O(\sqrt{\log n\log\log n})))}$ with no assumption, and a 2 ^r -query LDC of length ${N_{r}={\rm exp}({\rm exp}(O(\sqrt[r]{\log n(\log \log n)^{r-1}})))}$ , for every integer r ≥ 2. Itoh and Suzuki (in IEICE Trans Inform Syst E93-D 2:263–270, 2010) gave a composition method in Efremenko’s framework and constructed a 3 · 2 ^r-2-query LDC of length N _r , for every integer r ≥ 4, which improved the query complexity of Efremenko’s LDC of the same length by a factor of 3/4. The main ingredient of Efremenko’s construction is the Grolmusz construction for super-polynomial size set-systems with restricted intersections, over ${\mathbb{Z}_m}$ , where m possesses a certain “good” algebraic property (related to the “algebraic niceness” property of Yekhanin in J ACM 55:1–16, 2008). Efremenko constructed a 3-query LDC based on m = 511 and left as an open problem to find other numbers that offer the same property for LDC constructions. In this paper, we develop the algebraic theory behind the constructions of Yekhanin (in J ACM 55:1–16, 2008) and Efremenko (in Proceedings of the 41st annual ACM symposium on theory of computing, ACM, New York, 2009), in an attempt to understand the “algebraic niceness” phenomenon in ${\mathbb{Z}_m}$ . We show that every integer m =  pq = 2 ^t ?1, where p, q, and t are prime, possesses the same good algebraic property as m = 511 that allows savings in query complexity. We identify 50 numbers of this form by computer search, which together with 511, are then applied to gain improvements on query complexity via Itoh and Suzuki’s composition method. More precisely, we construct a ${3^{\lceil r/2\rceil}}$ -query LDC for every positive integer r < 104 and a ${\left\lfloor (3/4)^{51} \cdot 2^{r}\right\rfloor}$ -query LDC for every integer r ≥ 104, both of length N _r , improving the 2 ^r queries used by Efremenko (in Proceedings of the 41st annual ACM symposium on theory of computing, ACM, New York, 2009) and 3 · 2 ^r-2 queries used by Itoh and Suzuki (in IEICE Trans Inform Syst E93-D 2:263–270, 2010). We also obtain new efficient private information retrieval (PIR) schemes from the new query-efficient LDCs.     

Consistency properties and set based logic programming

Blair et al. (2001) developed an extension of logic programming called set based logic programming. In the theory of set based logic programming the atoms represent subsets of a fixed universe X and one is allowed to compose the one-step consequence operator with a monotonic idempotent operator O so as to ensure that the analogue of stable models in the theory are always closed under O. Marek et al. (1992, Ann Pure Appl Logic 96:231–276 1999) developed a generalization of Reiter’s normal default theories that can be applied to both default theories and logic programs which is based on an underlying consistency property. In this paper, we show how to extend the normal logic programming paradigm of Marek, Nerode, and Remmel to set based logic programming. We also show how one can obtain a new semantics for set based logic programming based on a consistency property.     

Multi-player epistemic games: Guiding the enactment of classroom knowledge-building communities

Teachers and students face many challenges in shifting from traditional classroom cultures to enacting the Knowledge-Building Communities model (KBC model) supported by the CSCL environment, Knowledge Forum (Bereiter, 2002; Bereiter & Scardamalia, 1993; Scardamalia, 2002; Scardamalia & Bereiter, 2006). Enacting the model involves socializing students into knowledge work, similar to disciplinary communities. A useful construct in the field of the Learning Sciences for understanding knowledge work is “epistemic games” (Collins & Ferguson, 1993; Morrison & Collins 1995; Perkins, 1997). We propose that a powerful means for supporting classroom enactments of the KBC model entails conceptualizing Knowledge Forum as a collective space for playing multi-player epistemic games. Participation in knowledge-building communities is then scaffolded through learning the moves of such games. We have designed scaffolding tools that highlight particular knowledge-building moves for practice and reflection as a means of supporting students and teachers in coming to understand how to collectively work together toward the progressive improvement of ideas. In order to examine our design theories in practice, we present research on Ideas First, a design-based research program involving enactments of the KBC model in Singaporean primary science classrooms (Bielaczyc & Ow, 2007, 2010; Ow & Bielaczyc, 2007; 2008).     

Fair online load balancing

We revisit from a fairness point of view the problem of online load balancing in the restricted assignment model and the 1-∞ model. We consider both a job-centric and a machine-centric view of fairness, as proposed by Goel et al. (In: Symposium on discrete algorithms, pp. 384–390, 2005). These notions are equivalent to the approximate notion of prefix competitiveness proposed by Kleinberg et al. (In: Proceedings of the 40th annual symposium on foundations of computer science, p. 568, 2001), as well as to the notion of approximate majorization, and they generalize the well studied notion of max-min fairness. We resolve a question posed by Goel et al. (In: Symposium on discrete algorithms, pp. 384–390, 2005) proving that the greedy strategy is globally O(log?m)-fair, where m denotes the number of machines. This result improves upon the analysis of Goel et al. (In: Symposium on discrete algorithms, pp. 384–390, 2005) who showed that the greedy strategy is globally O(log?n)-fair, where n is the number of jobs. Typically, n?m, and therefore our improvement is significant. Our proof matches the known lower bound for the problem with respect to the measure of global fairness. The improved bound is obtained by analyzing, in a more accurate way, the more general restricted assignment model studied previously in Azar et al. (J. Algorithms 18:221–237, 1995). We provide an alternative bound which is not worse than the bounds of Azar et al. (J. Algorithms 18:221–237, 1995), and it is strictly better in many cases. The bound we prove is, in fact, much more general and it bounds the load on any prefix of most loaded machines. As a corollary from this more general bound we find that the greedy algorithm results in an assignment that is globally O(log?m)-balanced. The last result generalizes the previous result of Goel et al. (In: Symposium on discrete algorithms, pp. 384–390, 2005) who proved that the greedy algorithm yields an assignment that is globally O(log?m)-balanced for the 1-∞ model.     

The stable topology for residuated lattices

The spectrum of a residuated lattice L is the set Spec(L) of all prime i-filters. It is well known that Spec(L) can be endowed with the spectral topology. The main scope of this paper is to introduce and study another topology on Spec(L),?the so called stable topology, which turns out to be coarser than the spectral one. With this and in view, we introduce the notions of pure i-filter for a residuated lattice and the notion of normal residuated lattice. So, we generalize to case of residuated lattice some results relative to MV-algebras (Belluce and Sessa in Quaest Math 23:269–277, 2000; Cavaccini et?al. in Math Japonica 45(2):303–310, 1997) or BL-algebras (Eslami and Haghani in Kybernetika 45:491–506, 2009; Leustean in Central Eur J Math 1(3): 382–397, 2003; Turunen and Sessa in Mult-Valued Log 6(1–2):229–249, 2001).     

Log-Space Algorithms for Paths and Matchings in k-Trees

Reachability and shortest path problems are NL-complete for general graphs. They are known to be in L for graphs of tree-width 2 (Jakoby and Tantau in Proceedings of FSTTCS’07: The 27th Annual Conference on Foundations of Software Technology and Theoretical Computer Science, pp. 216–227, 2007). In this paper, we improve these bounds for k-trees, where k is a constant. In particular, the main results of our paper are log-space algorithms for reachability in directed k-trees, and for computation of shortest and longest paths in directed acyclic k-trees. Besides the path problems mentioned above, we also consider the problem of deciding whether a k-tree has a perfect matching (decision version), and if so, finding a perfect matching (search version), and prove that these two problems are L-complete. These problems are known to be in P and in RNC for general graphs, and in SPL for planar bipartite graphs, as shown in Datta et al. (Theory Comput. Syst. 47:737–757, 2010). Our results settle the complexity of these problems for the class of k-trees. The results are also applicable for bounded tree-width graphs, when a tree-decomposition is given as input. The technique central to our algorithms is a careful implementation of the divide-and-conquer approach in log-space, along with some ideas from Jakoby and Tantau (Proceedings of FSTTCS’07: The 27th Annual Conference on Foundations of Software Technology and Theoretical Computer Science, pp. 216–227, 2007) and Limaye et al. (Theory Comput. Syst. 46(3):499–522, 2010).     

Playing Mastermind with Constant-Size Memory

We analyze the classic board game of Mastermind with n holes and a constant number of colors. The classic result of Chvátal (Combinatorica 3:325–329, 1983) states that the codebreaker can find the secret code with Θ(n/logn) questions. We show that this bound remains valid if the codebreaker may only store a constant number of guesses and answers. In addition to an intrinsic interest in this question, our result also disproves a conjecture of Droste, Jansen, and Wegener (Theory Comput. Syst. 39:525–544, 2006) on the memory-restricted black-box complexity of the OneMax function class.     

On sunflowers and matrix multiplication

We present several variants of the sunflower conjecture of Erd?s & Rado (J Lond Math Soc 35:85–90, 1960) and discuss the relations among them. We then show that two of these conjectures (if true) imply negative answers to the questions of Coppersmith & Winograd (J Symb Comput 9:251–280, 1990) and Cohn et al. (2005) regarding possible approaches for obtaining fast matrix-multiplication algorithms. Specifically, we show that the Erd?s–Rado sunflower conjecture (if true) implies a negative answer to the “no three disjoint equivoluminous subsets” question of Coppersmith & Winograd (J Symb Comput 9:251–280, 1990); we also formulate a “multicolored” sunflower conjecture in ${\mathbb{Z}_3^n}$ and show that (if true) it implies a negative answer to the “strong USP” conjecture of Cohn et al. (2005) (although it does not seem to impact a second conjecture in Cohn et al. (2005) or the viability of the general group-theoretic approach). A surprising consequence of our results is that the Coppersmith–Winograd conjecture actually implies the Cohn et al. conjecture. The multicolored sunflower conjecture in ${\mathbb{Z}_3^n}$ is a strengthening of the well-known (ordinary) sunflower conjecture in ${\mathbb{Z}_3^n}$ , and we show via our connection that a construction from Cohn et al. (2005) yields a lower bound of (2.51 . . .) ⁿ on the size of the largest multicolored 3-sunflower-free set, which beats the current best-known lower bound of (2.21 . . . ) ⁿ Edel (2004) on the size of the largest 3-sunflower-free set in ${\mathbb{Z}_3^n}$ .     

Exponential stability of impulsive stochastic fuzzy cellular neural networks with mixed delays and reaction–diffusion terms

The problem of mean square exponential stability for a class of impulsive stochastic fuzzy cellular neural networks with distributed delays and reaction–diffusion terms is investigated in this paper. By using the properties of M-cone, eigenspace of the spectral radius of nonnegative matrices, Lyapunov functional, Itô’s formula and inequality techniques, several new sufficient conditions guaranteeing the mean square exponential stability of its equilibrium solution are obtained. The derived results are less conservative than the results recently presented in Wang and Xu (Chaos Solitons Fractals 42:2713–2721, 2009), Zhang and Li (Stability analysis of impulsive stochastic fuzzy cellular neural networks with time varying delays and reaction–diffusion terms. World Academy of Science, Engineering and Technology 2010), Huang (Chaos Solitons Fractals 31:658–664, 2007), and Wang (Chaos Solitons Fractals 38:878–885, 2008). In fact, the systems discussed in Wang and Xu (Chaos Solitons Fractals 42:2713–2721, 2009), Zhang and Li (Stability analysis of impulsive stochastic fuzzy cellular neural networks with time varying delays and reaction–diffusion terms. World Academy of Science, Engineering and Technology 2010), Huang (Chaos Solitons Fractals 31:658–664, 2007), and Wang (Chaos Solitons Fractals 38:878–885, 2008) are special cases of ours. Two examples are presented to illustrate the effectiveness and efficiency of the results.     

On anonymizing transactions with sensitive items

K-anonymity (Samarati and Sweeny 1998; Samarati, IEEE Trans Knowl Data Eng, 13(6):1010–1027, 2001; Sweeny, Int J Uncertain, Fuzziness Knowl-Based Syst, 10(5):557–570, 2002) and its variants, l-diversity (Machanavajjhala et al., ACM TKDD, 2007) and tcloseness (Li et al. 2007) among others are anonymization techniques for relational data and transaction data, which are used to protect privacy against re-identification attacks. A relational dataset D is k-anonymous if every record in D has at least k-1 other records with identical quasi-identifier attribute values. The combination of released data with external data will never allow the recipient to associate each released record with less than k individuals (Samarati, IEEE Trans Knowl Data Eng, 13(6):1010–1027, 2001). However, the current concept of k-anonymity on transaction data treats all items as quasi-identifiers. The anonymized data set has k identical transactions in groups and suffers from lower data utility (He and Naughton 2009; He et al. 2011; Liu and Wang 2010; Terrovitis et al., VLDB J, 20(1):83–106, 2011; Terrovitis et al. 2008). To improve the utility of anonymized transaction data, this work proposes a novel anonymity concept on transaction data that contain both quasi-identifier items (QID) and sensitive items (SI). A transaction that contains sensitive items must have at least k-1 other identical transactions (Ghinita et al. IEEE TKDE, 33(2):161–174, 2011; Xu et al. 2008). For a transaction that does not contain a sensitive item, no anonymization is required. A transaction dataset that satisfies this property is said to be sensitive k-anonymous. Three algorithms, Sensitive Transaction Neighbors (STN) Gray Sort Clustering (GSC) and Nearest Neighbors for K-anonymization (K-NN), are developed. These algorithms use adding/deleting QID items and only adding SI to achieve sensitive k-anonymity on transaction data. Additionally, a simple “privacy value” is proposed to evaluate the degree of privacy for different types of k-anonymity on transaction data. Extensive numerical simulations were carried out to demonstrate the characteristics of the proposed algorithms and also compared to other types of k-anonymity approaches. The results show that each technique possesses its own advantage under different criteria such as running time, operation, and information loss. The results obtained here can be used as a guideline of the selection of anonymization technique on different data sets and for different applications.     

Finding and Counting Vertex-Colored Subtrees

The problems studied in this article originate from the Graph Motif problem introduced by Lacroix et al. (IEEE/ACM Trans. Comput. Biol. Bioinform. 3(4):360–368, 2006) in the context of biological networks. The problem is to decide if a vertex-colored graph has a connected subgraph whose colors equal a given multiset of colors M. It is a graph pattern-matching problem variant, where the structure of the occurrence of the pattern is not of interest but the only requirement is the connectedness. Using an algebraic framework recently introduced by Koutis (Proceedings of the 35th International Colloquium on Automata, Languages and Programming (ICALP), Lecture Notes in Computer Science, vol. 5125, pp. 575–586, 2008) and Koutis and Williams (Proceedings of the 36th International Colloquium on Automata, Languages and Programming (ICALP), Lecture Notes in Computer Science, vol. 5555, pp. 653–664, 2009), we obtain new FPT algorithms for Graph Motif and variants, with improved running times. We also obtain results on the counting versions of this problem, proving that the counting problem is FPT if M is a set, but becomes #W[1]-hard if M is a multiset with two colors. Finally, we present an experimental evaluation of this approach on real datasets, showing that its performance compares favorably with existing software.     

DNF sparsification and a faster deterministic counting algorithm

Given a DNF formula f on n variables, the two natural size measures are the number of terms or size s(f) and the maximum width of a term w(f). It is folklore that small DNF formulas can be made narrow: if a formula has m terms, it can be ${\epsilon}$ -approximated by a formula with width ${{\rm log}(m/{\epsilon})}$ . We prove a converse, showing that narrow formulas can be sparsified. More precisely, any width w DNF irrespective of its size can be ${\epsilon}$ -approximated by a width w DNF with at most ${(w\, {\rm log}(1/{\epsilon}))^{O(w)}}$ terms. We combine our sparsification result with the work of Luby & Velickovic (1991, Algorithmica 16(4/5):415–433, 1996) to give a faster deterministic algorithm for approximately counting the number of satisfying solutions to a DNF. Given a formula on n variables with poly(n) terms, we give a deterministic ${n^{\tilde{O}({\rm log}\, {\rm log} (n))}}$ time algorithm that computes an additive ${\epsilon}$ approximation to the fraction of satisfying assignments of f for ${\epsilon = 1/{\rm poly}({\rm log}\, n)}$ . The previous best result due to Luby and Velickovic from nearly two decades ago had a run time of ${n^{{\rm exp}(O(\sqrt{{\rm log}\, {\rm log} n}))}}$ (Luby & Velickovic 1991, in Algorithmica 16(4/5):415–433, 1996).     

pth Moment Exponential Stability of Stochastic Recurrent Neural Networks with Markovian Switching

This paper investigates the problem of the pth moment exponential stability for a class of stochastic recurrent neural networks with Markovian jump parameters. With the help of Lyapunov function, stochastic analysis technique, generalized Halanay inequality and Hardy inequality, some novel sufficient conditions on the pth moment exponential stability of the considered system are derived. The results obtained in this paper are completely new and complement and improve some of the previously known results (Liao and Mao, Stoch Anal Appl, 14:165–185, 1996; Wan and Sun, Phys Lett A, 343:306–318, 2005; Hu et al., Chao Solitions Fractals, 27:1006–1010, 2006; Sun and Cao, Nonlinear Anal Real, 8:1171–1185, 2007; Huang et al., Inf Sci, 178:2194–2203, 2008; Wang et al., Phys Lett A, 356:346–352, 2006; Peng and Liu, Neural Comput Appl, 20:543–547, 2011). Moreover, a numerical example is also provided to demonstrate the effectiveness and applicability of the theoretical results.     

On the modelling of time-interleaved sequential lamination micromixers

We develop a novel and simple theoretical model of time-interleaved sequential lamination micromixers that improves the model proposed by Nguyen and coworkers (Microfluid Nanofluid 1:373–375, 2005a, Lab Chip 5:1320–1326, b, J Phys Conf Ser 34:136–141, 2006) based on the Taylor–Aris dispersion theory. The Nguyen model takes into account the non uniform structure of the velocity profile through an effective dispersion coefficient. However, it is essentially a one-dimensional model that is not suitable to describe (i) neither the behavior of mixing occurring at short length-scales, and characterized by the growth of a mixing boundary layer near the channel walls, (ii) nor the exponential decay of the concentration field occurring at larger length-scales. The model we propose, which is based upon the theory of imaginary potential developed by Giona et?al. (J Fluid Mech 513:221–237, 2004, Europhys Lett 83:34001, 2008, J Fluid Mech 639:291–341, 2009a), is able to provide quantitative predictions on the evolution of the L ²-norm of the concentration fields as function of the axial coordinate ξ,?both for short and asymptotic lengthscales. The quantitative comparison with respect to the Nguyen model is illustrated and discussed. Finally, the coupling between parallel lamination and sequential segmentation is analyzed, and leads to unexpected and apparently counter-intuitive findings.