We introduce the concept of a k-dimensional matrix product D of k matrices A1,…,Ak of sizes n1×n,…,nk×n, respectively, where D[i1,…,ik] is equal to ∑ℓ=1nA1[i1,ℓ]×…×Ak[ik,ℓ]. We provide upper bounds on the time complexity of computing the product and solving related problems of computing witnesses and maximum witnesses of the Boolean version of the product in terms of the time complexity of rectangular matrix multiplication. The multi-dimensional matrix product framework is useful in the design of parameterized graph algorithms. First, we apply our results on the multi-dimensional matrix product to the fundamental problem of detecting/counting copies of a fixed pattern graph in a host graph. The recent progress on this problem has not included complete pattern graphs, i.e., cliques (and their complements, i.e., edge-free pattern graphs, in the induced setting). The fastest algorithms for the aforementioned patterns are based on a reduction to triangle detection/counting. We provide an alternative simple method of detection/counting copies of fixed size cliques based on the multi-dimensional matrix product. It is at least as time efficient as the triangle method in cases of K4 and K5. Next, we show an immediate reduction of the k-dominating set problem to the multi-dimensional matrix product. It implies the W[2] hardness of the problem of computing the k-dimensional Boolean matrix product. Finally, we provide an efficient reduction of the problem of finding the lowest common ancestors for all k-tuples of vertices in a directed acyclic graph to the problem of finding witnesses of the Boolean variant of the multi-dimensional matrix product. Although the time complexities of the algorithms resulting from the aforementioned reductions solely match those of the known algorithms, the advantage of our algorithms is simplicity. Our algorithms also demonstrate the versatility of the multi-dimensional matrix product framework.

We present MOTION, an efficient and generic open-source framework for mixed-protocol secure multi-party computation (MPC) . MOTION is built in a user-friendly, modular, and extensible way, intended to be used as a tool in MPC research and to increase adoption of MPC protocols in practice. Our framework incorporates several important engineering decisions such as full communication serialization, which enables MPC over arbitrary messaging interfaces and removes the need of owning network sockets. MOTION also incorporates several performance optimizations that improve the communication complexity and latency, e.g., \( 2\times \) better online round complexity of precomputed correlated Oblivious Transfer (OT) . We instantiate our framework with protocols for N parties and security against up to \( N-1 \) passive corruptions: the MPC protocols of Goldreich-Micali-Wigderson (GMW) in its arithmetic and Boolean version and OT-based BMR (Ben-Efraim et al., CCS’16), as well as novel and highly efficient conversions between them, including a non-interactive conversion from BMR to arithmetic GMW. MOTION is highly efficient, which we demonstrate in our experiments. Compared to secure evaluation of AES-128 with \( N=3 \) parties in a high-latency network with OT-based BMR, we achieve a 16 \( \times \) better throughput of 16 AES evaluations per second using BMR. With this, we show that BMR is much more competitive than previously assumed. For \( N=3 \) parties and full-threshold protocols in a LAN, MOTION is \( 10\times \) – \( 18\times \) faster than the previous best passively secure implementation from the MP-SPDZ framework, and \( 190\times \) – \( 586\times \) faster than the actively secure SCALE-MAMBA framework. Finally, we show that our framework is highly efficient for privacy-preserving neural network inference.

The author continues his previous works on preparation to develop generalized axiomatics of the probability theory. The approach is based on the study of set systems of a more general form than the traditional set algebras and their Boolean versions. They are referred to as Dynkin algebras. The author introduces the spectrum of a separable Dynkin algebra and an appropriate Grothendieck topology on this spectrum. Separable Dynkin algebras constitute a natural class of abstract Dynkin algebras, previously distinguished by the author. For these algebras, one can define partial Boolean operations with appropriate properties. The previous work found a structural result: each separable Dynkin algebra is the union of its maximal Boolean subalgebras. In the present note, leaning upon this result, the spectrum of a separable Dynkin algebra is defined and an appropriate Grothendieck topology on this spectrum is introduced. The corresponding constructions somewhat resemble the constructions of a simple spectrum of a commutative ring and the Zariski topology on it. This analogy is not complete: the Zariski topology makes the spectrum of a commutative ring an ordinary topological space, while the Grothendieck topology, which, generally speaking, is not a topology in the usual sense, turns the spectrum of a Dynkin algebra into a more abstract object (site or situs, according to Grothendieck). This suffices for the purposes of the work.

Networks used in biological applications at different scales (molecule, cell and population) are of different types: neuronal, genetic, and social, but they share the same dynamical concepts, in their continuous differential versions (e.g., non-linear Wilson-Cowan system) as well as in their discrete Boolean versions (e.g., non-linear Hopfield system); in both cases, the notion of interaction graph G(J) associated to its Jacobian matrix J, and also the concepts of frustrated nodes, positive or negative circuits of G(J), kinetic energy, entropy, attractors, structural stability, etc., are relevant and useful for studying the dynamics and the robustness of these systems. We will give some general results available for both continuous and discrete biological networks, and then study some specific applications of three new notions of entropy: (i) attractor entropy, (ii) isochronal entropy and (iii) entropy centrality; in three domains: a neural network involved in the memory evocation, a genetic network responsible of the iron control and a social network accounting for the obesity spread in high school environment.

Abstract Dynkin algebras are studied. Such algebras form a useful instrument for discussing probabilities in a rather natural context. Abstractness means the absence of a set-theoretic structure of elements in such algebras. A large useful class of abstract algebras, separable Dynkin algebras, is introduced, and the simplest example of a nonseparable algebra is given. Separability allows us to define appropriate variants of Boolean versions of the intersection and union operations on elements. In general, such operations are defined only partially. Some properties of separable algebras are proved and used to obtain the standard intersection and union properties, including associativity and distributivity, in the case where the corresponding operations are applicable. The established facts make it possible to define Boolean subalgebras in a separable Dynkin algebra and check the coincidence of the introduced version of the definition with the usual one. Finally, the main result about the structure of separable Dynkin algebras is formulated and proved: such algebras are represented as set-theoretic unions of maximal Boolean subalgebras. After preliminary preparation, the proof reduces to the application of Zorn’s lemma by the standard scheme.

Abstract Dynkin algebras are studied. Such algebras form a useful instrument for discussing probabilities in a rather natural context. Abstractness means the absence of a set-theoretic structure of elements in such algebras. A large useful class of abstract algebras, separable Dynkin algebras, is introduced, and the simplest example of a nonseparable algebra is given. Separability allows us to define appropriate variants of Boolean versions of the intersection and union operations on elements. In general, such operations are defined only partially. Some properties of separable algebras are proved and used to obtain the standard intersection and union properties, including associativity and distributivity, in the case where the corresponding operations are applicable. The established facts make it possible to define Boolean subalgebras in a separable Dynkin algebra and check the coincidence of the introduced version of the definition with the usual one. Finally, the main result about the structure of separable Dynkin algebras is formulated and proved: such algebras are represented as set-theoretic unions of maximal Boolean subalgebras. After preliminary preparation, the proof reduces to the application of Zorn’s lemma by the standard scheme.

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Reachability and recurrence in a modular generalization of annihilating random walks (and lights-out games) to hypergraphs

A quantum Boolean image processing methodology is presented in this work, with special emphasis in image denoising. A new approach for internal image representation is outlined together with two new interfaces: classical to quantum and quantum to classical. The new quantum Boolean image denoising called quantum Boolean mean filter works with computational basis states (CBS), exclusively. To achieve this, we first decompose the image into its three color components, i.e., red, green and blue. Then, we get the bitplanes for each color, e.g., 8 bits per pixel, i.e., 8 bitplanes per color. From now on, we will work with the bitplane corresponding to the most significant bit (MSB) of each color, exclusive manner. After a classical-to-quantum interface (which includes a classical inverter), we have a quantum Boolean version of the image within the quantum machine. This methodology allows us to avoid the problem of quantum measurement, which alters the results of the measured except in the case of CBS. Said so far is extended to quantum algorithms outside image processing too. After filtering of the inverted version of MSB (inside quantum machine), the result passes through a quantum-classical interface (which involves another classical inverter) and then proceeds to reassemble each color component and finally the ending filtered image. Finally, we discuss the more appropriate metrics for image denoising in a set of experimental results.

FRI0076 Ra patients with the highest scores for the 2010 ra classification criteria are less prone to achieve remission after 2 years of follow-up in a very early arthritis clinic

FRI0561 The role of patient global disease activity score in the definition of acr/eular remission in very early ra - results from the nor-veac study

In the years to come new solutions will be required to overcome the limitations of scaled CMOS technology. One approach is to adopt Nano-Magnetic Logic Circuits, highly appealing for their extremely reduced power consumption. Despite the interesting nature of this approach, many problems arise when this technology is considered for real designs. The wire is the most critical of these problems from the circuit implementation point of view. It works as a pipelined interconnection, and its delay in terms of clock cycles depends on its length. Serious complications arise at the design phase, both in terms of synthesis and of physical design. One possible solution is the use of a delay insensitive asynchronous logic, Null Convention Logic (NCL TM ). Nevertheless its use has many negative consequences in terms of area occupation and speed loss with respect to a Boolean version. In this article we analyze and compare different solutions: nanomagnetic circuits based on full NCL, mixed Boolean-NCL, and fully Boolean logic. We discuss the advantages of these logics, but also the issues they raise. In particular we analyze feedback signals, which, due to their intrinsic pipelined nature, cause errors that still have not found a solution in the literature. The innovative arrangement we propose solves most of the problems and thus soundly increases the knowledge of this technology. The analysis is performed using a VHDL behavioral model we developed and a microprocessor we designed based on this model, as a sound and realistic test bench.

E. Remy, P. Ruet and D. Thieffry have proved a Boolean version of Thomas' conjecture: if a map $F$ from $\{0,1\}^{n}$ to itself has several fixed points, then there exists a positive circuit in the corresponding interaction graph. In this paper, we prove that the presence of a positive circuit in a local interaction graph is also a necessary condition for the presence of several attractive cycles in the Boolean synchronous dynamics.

Incremental view maintenance for XPath queries asks to maintain a materialized XPath view over an XML database. It assumes an underlying XML database D and a query Q . One is given a sequence of updates U to D , and the problem is to compute the result of Q ( U ( D )): the result of evaluating query Q on database D after having applied updates U . This article initiates a systematic study of the Boolean version of this problem. In the Boolean version, one only wants to know whether Q ( U ( D )) is empty or not. In order to quickly answer this question, we are allowed to maintain an auxiliary data structure. The complexity of the maintenance algorithms is measured in, (1) the size of the auxiliary data structure, (2) the worst-case time per update needed to compute Q ( U ( D )), and (3) the worst-case time per update needed to bring the auxiliary data structure up to date. We allow three kinds of updates: node insertion, node deletion, and node relabeling. Our main results are that downward XPath queries can be incrementally maintained in time O(depth( D )·poly(| Q |)) per update and conjunctive forward XPath queries in time O(depth( D ) · log(width( D ))·poly(| Q |)) per update, where | Q | is the size of the query, and depth( D ) and width( D ) are the nesting depth and maximum number of siblings in database D , respectively. The auxiliary data structures for maintenance are linear in | D | and polynomial in | Q | in all these cases.

Gene silencing, also called RNA interference, requires reliable assessment of silencer impacts. A critical task is to find matches between silencer oligomers and sites in the genome, in accordance with one-to-many matching rules (G-U matching, with provision for mismatches). Fast search algorithms are required to support silencer impact assessments in procedures for designing effective silencer sequences. The article presents a matching algorithm and data structures specialized for matching searches, including a kernel procedure that addresses a Boolean version of the database task called the skyline search. Besides exact matches, the algorithm is extended to allow for the location-specific mismatches applicable in plants. Computational tests show that the algorithm is significantly faster than suffix-tree alternatives. Source code, executable, data and test results are freely available at ftp://ftp.csiro.au/Horn/RapidMatch.

We consider time-space tradeoffs for static data structure problems in the cell probe model with word size 1 (the bit probe model). In this model, the goal is to represent n -bit data with s = n + r bits such that queries (of a certain type) about the data can be answered by reading at most t bits of the representation. Ideally, we would like to keep both s and t small, but there are tradeoffs between the values of s and t that limit the possibilities of keeping both parameters small. In this paper, we consider the case of succinct representations, where s = n + r for some redundancy r ≪ n . For a Boolean version of the problem of polynomial evaluation with preprocessing of coefficients, we show a lower bound on the redundancy–query time tradeoff of the form ( r + 1 ) t ≥ Ω ( n / log n ) . In particular, for very small redundancies r , we get an almost optimal lower bound stating that the query algorithm has to inspect almost the entire data structure (up to a logarithmic factor). We show similar lower bounds for problems satisfying a certain combinatorial properties of a coding theoretic flavor, and obtain ( r + 1 ) t ≥ Ω ( n ) for certain problems. Previously, no ω ( m ) lower bounds were known on t in the general model for explicit Boolean problems, even for very small redundancies. By restricting our attention to systematic or index structures ϕ satisfying ϕ ( x ) = x ⋅ ϕ ∗ ( x ) for some map ϕ ∗ (where ⋅ denotes concatenation), we show similar lower bounds on the redundancy–query time tradeoff for the natural data structuring problems of Prefix Sum and Substring Search.

We develop a framework for natural language semantics which handles intensionality via metalogical constructions and deals with degree truth values in an integrated way. We take an axiomatic set theory, ZF, as the foundation for semantic representations, but we make ZF a metalanguage for part of itself by embedding a language L within ZF which is basically a copy of the part of ZF consisting of set expressions. This metalogical set-up is used for handling propositional attitude verbs (limited to believe in this paper). We define a truth function T which determines the truth value τ(p, T) of an L-proposition p with respect to a theory T. Theories are sets of L-propositions with associated truth values, and can be viewed as a (much more well-defined) replacement for possible worlds. We develop a mechanism for defining belief worlds as theories. We simultaneously develop two different versions of our system - a Boolean version where the set Ω of truth values is {0,1}, and a degree-truth version where Ω is the interval [0,1] of real numbers. We use degrees of truth in handling a broad class of semantic predicates that we call base-focus predicates, which include generalized quantifiers as well as many adverb and adjective senses and certain discourse-level predicates.

In this paper we establish a theory of stochastic integration with respect to the basic field operator processes in the Boolean case. This leads to a Boolean version of quantum Itô's product formula and has applications to the theory of dilations of quantum dynamical semigroups.

In the cell probe model with word size 1 (the bit probe model), a static data structure problem is given by a map f : {0,1}^n * {0,1}^m -> {0,1}, where {0,1}^n is a set of possible data to be stored, {0,1}^m is a set of possible queries (for natural problems, we have m << n) and f(x,y) is the answer to question y about data x.<br /> <br />A solution is given by a representation phi : {0,1}^n -> {0,1}^s and a query algorithm q so that q(phi(x), y) = f(x,y). The time t of the query algorithm is the number of bits it reads in phi(x).<br /> <br />In this paper, we consider the case of <em>succinct</em> representations where s = n + r for some <em>redundancy</em> r << n. For a boolean version of the problem of polynomial evaluation with preprocessing of coefficients, we show a lower bound on the redundancy-query time trade-off of the form <br />(r + 1) t >= Omega(n/log n).<br /> In particular, for very small redundancies r, we get an almost optimal lower bound stating that the query algorithm has to inspect almost the entire data structure (up to a logarithmic factor). We show similar lower bounds for problems satisfying a certain combinatorial property of a coding theoretic flavor. Previously, no omega(m) lower bounds were known on t in the general model for explicit functions, even for very small redundancies.<br /> <br />By restricting our attention to <em>systematic</em> or <em>index</em> structures phi satisfying phi(x) = x · phi*(x) for some map phi* (where · denotes concatenation) we show similar lower bounds on the redundancy-query time trade-off for the natural data structuring problems of Prefix Sum and Substring Search.

Creating a text classifier to detect radiology reports describing mediastinal findings associated with inhalational anthrax and other disorders