Primitive Operator Research Articles

AdaMEC: Towards a Context-adaptive and Dynamically Combinable DNN Deployment Framework for Mobile Edge Computing

With the rapid development of deep learning, recent research on intelligent and interactive mobile applications (e.g., health monitoring, speech recognition) has attracted extensive attention. And these applications necessitate the mobile edge computing scheme, i.e., offloading partial computation from mobile devices to edge devices for inference acceleration and transmission load reduction. The current practices have relied on collaborative DNN partition and offloading to satisfy the predefined latency requirements, which is intractable to adapt to the dynamic deployment context at runtime. AdaMEC, a context-adaptive and dynamically combinable DNN deployment framework, is proposed to meet these requirements for mobile edge computing, which consists of three novel techniques. First, once-for-all DNN pre-partition divides DNN at the primitive operator level and stores partitioned modules into executable files, defined as pre-partitioned DNN atoms. Second, context-adaptive DNN atom combination and offloading introduces a graph-based decision algorithm to quickly search the suitable combination of atoms and adaptively make the offloading plan under dynamic deployment contexts. Third, runtime latency predictor provides timely latency feedback for DNN deployment considering both DNN configurations and dynamic contexts. Extensive experiments demonstrate that AdaMEC outperforms state-of-the-art baselines in terms of latency reduction by up to 62.14% and average memory saving by 55.21%.

A Logical Modeling of Severe Ignorance

In the logical context, ignorance is traditionally defined recurring to epistemic logic. In particular, ignorance is essentially interpreted as “lack of knowledge”. This received view has - as we point out - some problems, in particular we will highlight how it does not allow to express a type of content-theoretic ignorance, i.e. an ignorance of φ that stems from an unfamiliarity with its meaning. Contrarily to this trend, in this paper, we introduce and investigate a modal logic having a primitive epistemic operator I, modeling ignorance. Our modal logic is essentially constructed on the modal logics based on weak Kleene three-valued logic introduced by Segerberg (Theoria, 33(1):53–71, 1997). Such non-classical propositional basis allows to define a Kripke-style semantics with the following, very intuitive, interpretation: a formula φ is ignored by an agent if φ is neither true nor false in every world accessible to the agent. As a consequence of this choice, we obtain a type of content-theoretic notion of ignorance, which is essentially different from the traditional approach. We dub it severe ignorance. We axiomatize, prove completeness and decidability for the logic of reflexive (three-valued) Kripke frames, which we find the most suitable candidate for our novel proposal and, finally, compare our approach with the most traditional one.

DIFFERENCE AND PRIMITIVE OPERATORS ON THE DUNKL-TYPE FOCK SPACE $$\mathscr {F}_{\alpha }(\mathbb {C}^{d})$$

In 1961, Bargmann introduced the classical Fock space $$\mathscr {F}(\mathbb {C}^{d})$$ and in 1984, Cholewinsky introduced the generalized Fock space $$\mathscr {F}_{\alpha ,e}(\mathbb {C}^{d})$$ . These two spaces are the aim of many works, and have many applications in mathematics, in physics, and in quantum mechanics. In this work, we introduce and study the Fock space $$\mathscr {F}_{\alpha }(\mathbb {C}^{d})$$ associated to the Dunkl operators $$T_{\alpha _{j}}$$ with $$\alpha _{j}>-1/2$$ for all $$j=1,\ldots ,d$$ . This space is an extension of the Dunkl-type Fock space $$\mathscr {F}_{\alpha }(\mathbb {C})$$ constructed by Sifi and Soltani in 2002. We prove that the space $$\mathscr {F}_{\alpha }(\mathbb {C}^{d})$$ is a Hilbert space with reproducing kernel. Next, we give an application of the classical theory of reproducing kernels to the Tikhonov regularization problem for the bounded linear operator $$\mathscr {L}:\mathscr {F}_{\alpha }(\mathbb {C}^{d})\rightarrow \mathscr {H}$$ , where $$\mathscr {H}$$ is a Hilbert space. Finally, we come up with some results regarding the extremal functions, when $$\mathscr {L}$$ is the difference operator and the primitive operator, respectively.

Practical Sentences, Their Meaning and Their Validity

Following Richard M. Hare1 I think that we use practical sentences as decision criteria. We understand their meaning if we know what decision to take according to them. But it is not clear, how exactly decision criteria are related to decisions and how they function as criteria. To fully understand this role, we need a formal semantics of practical sentences. For this I have to introduce a formal language and give an interpretation of it. This language has to be constructed in such a way that a translation into ordinary language is always possible in principle. Thus, we make sure that our semantics and logic will have an impact on the solution of concrete practical problems. According to this program I will first introduce the formal language ‘LP1’. To give an interpretation of it I will then clarify what a decision is and show how practical sentences function as decision criteria. On this basis I give an interpretation of the primitive two-place operator ‘PT p,q’ and the one-place operator ‘VTp’. I further argue that we make meta-decisions concerning the application of first-order decision-criteria. This allows me to introduce a new concept of practical validity, which differs radically from the concept of truth. Using this concept, I then give an interpretation of the deontic operators ‘OTp’, ‘FTp’, ‘ATp’ and ‘ITp’. The concept of practical validity makes it also possible to introduce practical logical connectors and mixed logical connectors on the basis of practical or mixed value tables. These connectors are used – among others – in bridge-principles, which play an important role in ethical and juridical theories. Finally, I shortly explain the semantics of the main kinds of practical sentences, i.e. value judgments, imperatives, norms and intentions, and I argue that we need a deontic logic in order to use practical sentences in a correct way.

The Modal Logic LEC for Changing Knowledge, Expressed in the Growing Language

We present the propositional logic LEC for the two epistemic modalities of current and stable knowledge used by an agent who system-atically enriches his language. A change in the linguistic resources of an agent as a result of certain cognitive processes is something that commonly happens. Our system is based on the logic LC intended to formalize the idea that the occurrence of changes induces the passage of time. Here, the primitive operator C read as: it changes that, defines the temporal succession of states of the world. The notion of current knowledge concerns variable components of the world and it may change over time. We represent it by the primitive operator k read as: the agent currently knows that, and assume that it has S5 properties. The second type of knowledge, symbolized by the primitive operator K read as: the agent stably knows that, relates to constant components of the world and it does not change. As a result of the axiomatic entanglement of C, K and k we show that stable knowledge satisfies axioms of S4.3. K and k modalities are not mutually definable, stable knowledge implies the current one and if the latter never changes, then it comes to be stable. The combination of K and k with the idea of an expanding language allows questioning of the so-called perfect recall principle. It cannot be maintained for both types of knowledge just because of changes in the vocabulary of the agent and possibly the growing spectrum of possible states of the world. We interpret LEC in the semantics of histories of epistemic changes and show that it is complete. Finally, we compare our logic with selected epistemic logics based on the concept of linear discrete time.

Boolean negation and non-conservativity I: Relevant modal logics

Abstract Many relevant logics can be conservatively extended by Boolean negation. Mares showed, however, that E is a notable exception. Mares’ proof is by and large a rather involved model-theoretic one. This paper presents a much easier proof-theoretic proof which not only covers E but also generalizes so as to also cover relevant logics with a primitive modal operator added. It is shown that from even very weak relevant logics augmented by a weak K-ish modal operator, and up to the strong relevant logic R with a S5 modal operator, all fail to be conservatively extended by Boolean negation. The proof, therefore, also covers Meyer and Mares’ proof that NR—R with a primitive S4-modality added—also fails to be conservatively extended by Boolean negation.

The logic of modal changes LMC

ABSTRACTThe logic of change formulated by K. Świętorzecka, has its motivation coming from the Aristotelian theory of substantial change which is undrstood as a transformation consisting in the disappearing and becoming of individual substances. The transition: becoming/disapearing (and conversely) is expressed in by the primitive operator C, to be read: it changes that …, and it is mapped by the progressively expanding language. We are interested in attributive changes of individual substances. We consider a formalism with two non-normal and not mutually definable operators of possible and necessary change, inspired by Aristotelian distinction of accidental and essential attributes. From we adopt the idea that temporal concepts are defined via change operators, and the idea of an expanding language. In what follows, We axiomatise our new logic and describe its semantics, giving the proof of its completeness. We compare our formalism with selected modal logics.

An Industrial Dynamic Skyline Based Similarity Joins For Multidimensional Big Data Applications

In the era of data deluge, data analysis has become a key task for many industrial applications, e.g., master data management, and data integration. In particular, similarity join is an important primitive operator to support data analysis, which is to find similar pairs based on similarity functions and thresholds. In this article, we first propose a new similarity join operation called the dynamic skyline join without having to specify any similarity function or similarity threshold, which measures the similarity through multicriteria optimization. The dynamic skyline join operator makes the similarity join more flexible to support different criteria in multidimensional space. However, it is nontrivial to achieve dynamic skyline joins as both join operations and dynamic skyline queries are computationally complex in the increasing volume of real-world data. Therefore, we further propose Grid-SkyJoin, a framework to enable efficient parallel dynamic skyline joins on a shared-nothing cluster. Specifically, we use a grid partitioning to facilitate the data filtering and grouping strategies to provide load balancing and reduce the number of replicas. We also propose a multilevel filtering scheme to prune away a large fraction of unpromising points that do not fit into join results without actual join operations. Extensive experiments using benchmark datasets demonstrate that our filtering scheme can greatly reduce the number of data points to be joined, and our approach is about two times faster compared with the straightforward method in average.

Construction of a magnetostrictive hysteresis operator using a tripod-like primitive hopfield neural network

It is well known that accurate modeling of magnetostrictive hysteresis is crucial to different industrial applications. Although several magnetostrictive models have been developed in the past, the accuracy-efficiency balance has always been crucial. Recently, the possibility of constructing a primitive vector hysteresis operator using a tri-node Hopfield Neural Network (HNN) was demonstrated. Based upon the fact that mechanical stress along a certain direction results in dimensional deformation, this paper introduces a novel extension to the aforementioned recently developed approach. More specifically, a stress-driven evolution of a tri-node HNN hysteresis operator pair is proposed, thus yielding a tripod-like HNN pair having different input offset values. Model identification, sample simulation results and comparison with experimental measurements are given in the paper.

Disentangling FDE-Based Paraconsistent Modal Logics

The relationships between various modal logics based on Belnap and Dunn’s paraconsistent four-valued logic FDE are investigated. It is shown that the paraconsistent modal logic $$\mathsf{BK}^\Box $$ , which lacks a primitive possibility operator $$\Diamond $$ , is definitionally equivalent with the logic $$\mathsf{BK}$$ , which has both $$\Box $$ and $$\Diamond $$ as primitive modalities. Next, a tableau calculus for the paraconsistent modal logic KN4 introduced by L. Goble is defined and used to show that KN4 is definitionally equivalent with $$\mathsf{BK}^\Box $$ without the absurdity constant. Moreover, a tableau calculus is defined for the modal bilattice logic MBL introduced and investigated by A. Jung, U. Rivieccio, and R. Jansana. MBL is a generalization of BK that in its Kripke semantics makes use of a four-valued accessibility relation. It is shown that MBL can be faithfully embedded into the bimodal logic $$\mathsf{BK}^\Box \times \mathsf{BK}^\Box $$ over the non-modal vocabulary of MBL. On the way from $$\mathsf{BK}^\Box $$ to MBL, the Fischer Servi-style modal logic $$\mathsf{BK}^\mathsf{FS}$$ is defined as the set of all modal formulas valid under a modified standard translation into first-order FDE, and $$\mathsf{BK}^\mathsf{FS}$$ is shown to be characterized by the class of all models for $$\mathsf{BK}^{\Box }\times \mathsf{BK}^{\Box }$$ . Moreover, $$\mathsf{BK}^\mathsf{FS}$$ is axiomatized and this axiom system is proved to be strongly sound and complete with respect to the class of models for $$\mathsf{BK}^{\Box }\times \mathsf{BK}^{\Box }$$ . Moreover, the notion of definitional equivalence is suitably weakened, so as to show that $$\mathsf{BK}^\mathsf{FS}$$ and $$\mathsf{BK}^{\Box }\times \mathsf{BK}^{\Box }$$ are weakly definitionally equivalent.

Targeted Advertising in Public Transportation Systems with Quantitative Evaluation

In spite of vast business potential, targeted advertising in public transportation systems is a grossly unexplored research area. For instance, SBS Transit in Singapore can reach 1 billion passengers per year but the annual advertising revenue contributes less than $35 million. To bridge the gap, we propose a probabilistic data model that captures the motion patterns and user interests so as to quantitatively evaluate the impact of an advertisement among the passengers. In particular, we leverage hundreds of millions of bus/train boarding transaction records to quantitatively estimate the probability as well as the extent of a user being influenced by an ad. Based on the influence model, we study a top- k retrieval problem for bus/train ad recommendation, which acts as a primitive operator to support various advanced applications. We solve the retrieval problem efficiently to support real-time decision making. In the experimental study, we use the dataset from SBS Transit as a case study to verify the effectiveness and efficiency of our proposed methodologies.

Injection-Locked Spin Hall-Induced Coupled-Oscillators for Energy Efficient Associative Computing

In this paper, we show that the dynamics of injection-locked Spin Hall Effect Spin-Torque Oscillator (SHE-STO) cluster can be exploited as a robust primitive computational operator for non-Boolean associative computing. A cluster of SHE-STOs can be locked to a common frequency and phase with an injected ac current signal. DC input to each STO from external stimuli can conditionally unlock some of them. Based on the input dc signal, the degree of synchronization of SHE-STO cluster is detected by CMOS interface circuitry. The degree of synchronization can be used for associative computing/matching. We present a numerical simulation model of SHE-STO devices based on Landau–Lifshitz–Gilbert equation with spin-transfer torque term and Spin Hall Effect. The model is then used to analyze the frequency and phase locking properties of injection-locked SHE-STO cluster. Results show that associative computing based on the injection locked SHE-STO cluster can be energy efficient and relatively immune to device parameter variations and thermal noise.

Some Examples of Extremal Functions on the Dunkl-Type Fock Space $$F_k(\mathbb {C})$$ F k ( C )

In this work, we recall some properties of the generalized Fock space \(F_k(\mathbb {C})\) and the Hilbert space \(H_k(\mathbb {C})\) (defined by the squared norm \(\Vert f\Vert ^2_{H_k(\mathbb {C})}:=\Vert f\Vert ^2_{F_k(\mathbb {C})}+\langle zf',f\rangle _{F_k(\mathbb {C})}\)). Next, we give the best approximation of the bounded operators \(L:F_k(\mathbb {C})\rightarrow H_k(\mathbb {C})\). As applications, we come up with some results regarding the approximate formulas for the difference operator, the Dunkl difference operator and the primitive operator.

Biologically Inspired Computing Technique for Optimizing Discontinuous Mathematical Functions

This paper explores the immense capabilities of the recently proposed biologically inspired soft computing technique named Particle Swarm Optimization for the optimization of non-convex, nonlinear and discontinuous mathematical functions; which primarily focus upon the attainment of the global optimum, despite of the existence of local multi-optimums in the vicinity. This technique uses an innovative distributed intelligent paradigm for solving optimization problems that originally took its inspiration from the biological examples like bird flocking and fish schooling. This is also a population-based optimization tool, which could be implemented and applied easily to solve various function optimization problems. But unlike Genetic Algorithm it uses only primitive mathematical operator and does not uses cross-over, mutation and reproduction. Potential of this technique is illustrated by implementing it on the well known bench mark mathematical problems which includes Rastrigins, Ackley, Alpine, and Schaffer's F6 functions.

Parameterised Multiparty Session Types

For many application-level distributed protocols and parallel algorithms, the set of participants, the number of messages or the interaction structure are only known at run-time. This paper proposes a dependent type theory for multiparty sessions which can statically guarantee type-safe, deadlock-free multiparty interactions among processes whose specifications are parameterised by indices. We use the primitive recursion operator from G\"odel's System T to express a wide range of communication patterns while keeping type checking decidable. To type individual distributed processes, a parameterised global type is projected onto a generic generator which represents a class of all possible end-point types. We prove the termination of the type-checking algorithm in the full system with both multiparty session types and recursive types. We illustrate our type theory through non-trivial programming and verification examples taken from parallel algorithms and Web services usecases.

A framed temporal logic programming language

We discuss the projection temporal logic (PTL), based on a primitive projection operator, prj. A framing technique is also presented, using which a synchronization operator, await, is defined within the underlying logic. A framed temporal logic programming language (FTLL) is presented. To illustrate how to use both the language and framing technique, some examples are given.

Evolutionary design and adaptation of high performance digital filters within an embedded reconfigurable fault tolerant hardware platform

Finite impulse response filters (FIRs) are crucial devices for robust data communication and manipulation. Multiplierless filters have been shown to produce high performance systems with fast signal processing and reduced area. Furthermore, the distributed architecture inherent in multiplierless filters makes it a suitable candidate for fault tolerant design. Alternative approaches to the design of fault tolerant systems have been proposed using evolutionary algorithms (EAs) and the concept of evolvable hardware (EHW). This paper presents an evolvable hardware platform for the automated design and adaptation of multiplierless digital filters. Filters are realised within a dedicated programmable logic array (PLA) based on the Primitive Operator Filter design principle. The platform employs a genetic algorithm to autonomously configure the PLA for a given set of coefficients. The ability of the platform to adapt to increasing numbers of faults was investigated through the “evolution” of a 31-tap low-pass FIR filter. Results show that the functionality of filters evolved on the PLA was maintained despite an increasing number of faults covering up to 25% of the PLA area. Additionally, three PLA initialisation methods were investigated to ascertain which produced the fastest fault recovery times. It was shown that seeding a population of random configuration-strings with the best configuration currently obtained resulted in a 6 fold increase in fault recovery speed over other methods investigated.

Genetic synthesis of reduced complexity filters and filter banks using primitive operator directed graphs

Using integer coefficient filters, which can be efficiently implemented using primitive operator directed graphs, a multi-objective optimisation using genetic algorithms is used to jointly optimise filter performance and complexity. Complexity is measured using a variation of the RAG-n algorithm (Dempster and MacLeod, 1995). The optimisation maintains a non-dominated set of best-compromise solutions, which allows the designer greater choice. A flexible design tool is described which allows the designer to interactively vary many of the optimisation parameters. The proposed techniques are demonstrated for the design of both one- and two-dimensional linear phase FIR filters with both low-pass and band-pass characteristics. The method is shown to provide significantly better results than previous methods. Also considered is the design of perfect reconstruction filter pairs, which are the main building block within discrete wavelet transforms. To achieve this the use of a combination of transformation and factorisation approaches is proposed. In this way, the problem is significantly simplified, allowing a GA to successfully find high performance filter banks with significantly better results than previous methods.

Modal fictionalism and the imagination

Journal Article Modal fictionalism and the imagination Get access Thomas Baldwin Thomas Baldwin University of YorkYork, Y01 5DD, UKtrb2@york.ac.uk Search for other works by this author on: Oxford Academic Google Scholar Analysis, Volume 58, Issue 2, April 1998, Pages 72–75, https://doi.org/10.1093/analys/58.2.72 Published: 01 April 1998

Modal fictionalism and the imagination

So far Gideon Rosen's intriguing 'fictionalist' analysis of modality appears to have surmounted the problems that have been directed at it, by Rosen among others (see Rosen 1993 and Noonan 1994). I want to argue, however, that further reflection on a problem that Rosen himself raises in his original paper points to a difficulty which undermines the merits of Rosen's analysis. In order to appreciate the problem which Rosen raises it is important to be clear about the relationship between Rosen's position and that of Lewis. Rosen's basic idea (1990: 332) was that one should add the primitive operator 'According to the modal realist's hypothesis of a plurality of worlds' (PW) as a 'fictional' prefix to Lewis's analysis of modality (in 1986: 5). Thus where Lewis's analysis is exemplified by