Slope Intervals,Generalized Gradients,Semigradients, Slant Derivatives,and Csets

Many practical optimization problems are nonsmooth, and derivative-type methods cannot be applied. To overcome this difficulty, there are different concepts to replace the derivative of a function f : : interval slopes, semigradients, generalized gradients, and slant derivatives are some examples. These approaches generalize the success of convex analysis, and are effective in optimization. However, with the exception of interval slopes, it is not clear how to automatically compute these; having a general analogue to the chain rule, interval slopes can be computed with automatic differentiation techniques. In this paper we study the relationships among these approaches for nonsmooth Lipschitz optimization problems in finite dimensional Euclidean spaces. Inclusion theorems concerning the equivalence of these concepts when there exist one sided derivatives in one dimension and in multidimensional cases are proved separately. Valid enclosures are produced. Under containment set (cset) theory, for instance, the cset of the gradient of a locally Lipschitz function f near x is included in its generalized gradient.     

Electrical engineering department,Heriot-Watt university,Edinburgh, UK

This review describes research work which is just starting in the Electrical Engineering Department of Heriot-Watt University. It is based on a directed-graph method of describing the structure of a computation, and as such can be equally applied to hardware and software. It is a computer aid to the logical and program designer, rather than to the drawing office and production department, like most present day digital c.a.d. systems. The project is based on the results of various workers, and much of this paper contains a summary of their work as a necessary introduction.It is possible to write a good many pages¹ on the lack of c.a.d. for computer designers: the shortest summary is to say that it is not possible to be sure what a normal hardware logic structure will do except by simulation or exhaustive tests. The alternatives for $\text{n}$ Boolean variables must have some relation to 2²ⁿ, a number which can rapidly outstrip any speed improvement in computer simulation as $\text{n}$ increases. Since programming uses hardware-built functions there is a similar effect, and once again the structure of a program is no guarantee of correct performance-exhaustive testing or whether exhaustive testing or machine simulation is needed. Lastly, since the design methods are so different for programs and logic there is a considerable interface problem.     

Worlds,Events, and Inertia

The semantics of progressive sentences presents a challenge to linguists and philosophers alike. According to a widely accepted view, the truth-conditions of progressive sentences rely essentially on a notion of inertia. Dowty (Word meaning and Montague grammar: the semantics of verbs and times in generative grammar and in Montague’s PTQ, D. Reidel Publishing Company, Dordrecht, 1979) suggested inertia worlds to implement this “inertia idea” in a formal semantic theory of the progressive. The main thesis of the paper is that the notion of inertia went through a subtle, but crucial change when worlds were replaced by events in Landman (Nat Lang Semant 1:1–32, 1992) and Portner (Language 74(4):760–787, 1998), and that this new, event-related concept of inertia results in a possibility-based theory of the progressive. An important case in point in the paper is a proof that, despite its surface structure, the theory presented in Portner (1998) does not implement the notion of inertia in Dowty (1979); rather, it belongs together with Dowty’s earlier, 1977 theory according to which the progressive is a possibility operator.     

Preprocess, Set, Query!

Thorup and Zwick (J. ACM 52(1):1–24, 2005 and STOC’01) in their seminal work introduced the notion of distance oracles. Given an n-vertex weighted undirected graph with m edges, they show that for any integer k≥1 it is possible to preprocess the graph in $\tilde {O}(mn^{1/k})$ time and generate a compact data structure of size O(kn ^1+1/k ). For each pair of vertices, it is then possible to retrieve an estimated distance with multiplicative stretch 2k?1 in O(k) time. For k=2 this gives an oracle of O(n ^1.5) size that produces in constant time estimated distances with stretch 3. Recently, Pǎtra?cu and Roditty (In: Proc. of 51st FOCS, 2010) broke the theoretical status-quo in the field of distance oracles and obtained a distance oracle for sparse unweighted graphs of O(n ^5/3) size that produces in constant time estimated distances with stretch 2. In this paper we show that it is possible to break the stretch 2 barrier at the price of non-constant query time in unweighted undirected graphs. We present a data structure that produces estimated distances with 1+ε stretch. The size of the data structure is O(nm ^1?ε′) and the query time is $\tilde {O}(m^{1-\varepsilon '})$ . Using it for sparse unweighted graphs we can get a data structure of size O(n ^1.87) that can supply in O(n ^0.87) time estimated distances with multiplicative stretch 1.75.     

Computation, Implementation, Cognition

Putnam (Representations and reality. MIT Press, Cambridge, 1988) and Searle (The rediscovery of the mind. MIT Press, Cambridge, 1992) famously argue that almost every physical system implements every finite computation. This universal implementation claim, if correct, puts at the risk of triviality certain functional and computational views of the mind. Several authors have offered theories of implementation that allegedly avoid the pitfalls of universal implementation. My aim in this paper is to suggest that these theories are still consistent with a weaker result, which is the nomological possibility of systems that simultaneously implement different complex automata. Elsewhere I (Shagrir in J Cogn Sci, 2012) argue that this simultaneous implementation result challenges a computational sufficiency thesis (articulated by Chalmers in J Cogn Sci, 2012). My focus here is on theories of implementation. After presenting the basic simultaneous implementation construction, I argue that these theories do not avoid the simultaneous implementation result. The conclusion is that the idea that the implementation of the right kind of automaton suffices for a possession of a mind is dubious.     

Complexity,convexity, and unimodality

A class of polygons termedunimodal is introduced. LetP = P₁,p ₂,...,p _n be a simplen-vertex polygon. Given a fixed vertex or edge, several definitions of the distance between the fixed vertex or edge and any other vertex or edge are considered. For a fixed vertex (edge), a distance measure defines a distance function as the remaining vertices (edges) are traversed in order. If for every vertex (edge) ofP a specified distance function is unimodal thenP is a unimodal polygon in the corresponding sense. Relationships between unimodal polygons, in several senses, andconvex polygons are established. Several properties are derived for unimodal polygons when the distance measure is the euclidean distance between vertices of the polygons. These properties lead to very simple 0(n) algorithms for solving a variety of problems that occur in computational geometry and pattern recognition. Furthermore, these algorithms establish that convexity is not the key factor in obtaining linear-time-complexity for solving these problems. The paper closes with several open questions in this area.     

Invariants,composition, and substitution

In the literature the notion of asystem invariant has been formalized in two different ways, differing in the treatment of unreachable transitions. We call the more general notion, which ignores unreachable transitions,invariant sets of a system, the more restricted notion, which considers unreachable transitions,inductive sets of a system.It turns out that even if we are only interested in invariant sets of a system, inductive sets play an important rôle for proving invariant sets of system in a compositional way. This paper shows the interplay of both kinds of invariants; particularly, we show that inductive sets arefully abstract with respect to invariant sets.One essential difference between invariant and inductive sets is that thesubstitution rule is only valid for invariant sets, and thecomposition rule is only valid for inductive sets. Sometimes it seems desirable to have a notion of invariants for which both rules are valid. We show that every notion of an invariant enjoying both rules is very restrictive.Supported by the DFG SFB 342, TP A3: SEMAFOR and the ESPRIT Basic Research WG 6067 Caliban     

Differences in typing forces,muscle activity,comfort, and typing performance among virtual,notebook, and desktop keyboards

The present study investigated whether there were physical exposure and typing productivity differences between a virtual keyboard with no tactile feedback and two conventional keyboards where key travel and tactile feedback are provided by mechanical switches under the keys. The key size and layout were same across all the keyboards. Typing forces; finger and shoulder muscle activity; self-reported comfort; and typing productivity were measured from 19 subjects while typing on a virtual (0 mm key travel), notebook (1.8 mm key travel), and desktop keyboard (4 mm key travel). When typing on the virtual keyboard, subjects typed with less force (p's < 0.0001) and had lower finger flexor/extensor muscle activity (p's < 0.05). However, the lower typing forces and finger muscle activity came at the expense of a 60% reduction in typing productivity (p < 0.0001), decreased self-reported comfort (p's < 0.0001), and a trend indicating an increase in shoulder muscle activity (p's < 0.10). Therefore, for long typing sessions or when typing productivity is at a premium, conventional keyboards with tactile feedback may be more suitable interface.     

Household technology adoption,use, and impacts: Past,present, and future

Since the 1980s, researchers have been studying the phenomenon associated with technology being diffused to the household. In this paper, three themes in that stream of research, specifically adoption, use, and impacts, are explored. Key studies from prior research within each theme are discussed and directions for future research are offered. The directions for future research range from investigating adoption issues associated with the digital divide to understanding the impacts of new technology and social networking sites on individuals and families. The evolving nature of the technology continues to offer interesting research directions and challenges, with the study of unintended consequences of technology use presenting, perhaps, the greatest opportunities.

Deduction, Strategies, and Rewriting

Automated deduction methods should be specified not procedurally, but declaratively, as inference systems which are proved correct regardless of implementation details. Then, different algorithms to implement a given inference system should be specified as strategies to apply the inference rules. The inference rules themselves can be naturally specified as (possibly conditional) rewrite rules. Using a high-performance rewriting language implementation and a strategy language to guide rewriting computations, we can obtain in a modular way implementations of both the inference rules of automated deduction procedures and of algorithms controling their application. This paper presents the design of a strategy language for the Maude rewriting language that supports this modular decomposition: inference systems are specified in system modules, and strategies in strategy modules. We give a set-theoretic semantics for this strategy language, present its different combinators, illustrate its main ideas with several examples, and describe both a reflective prototype in Maude and an ongoing C++ implementation.     

Petri nets, algebras, morphisms, and compositionality

It is shown how a category of Petri nets can be viewed as a subcategory of two sorted algebras over multisets. This casts Petri nets in a familiar framework and provides a useful idea of morphism on nets different from the conventional definition—the morphisms here respect the behaviour of nets. The categorical constructions which result provide a useful way to synthesise nets and reason about nets in terms of their components; for example, various forms of parallel composition of Petri nets arise naturally from the product in the category. This abstract setting makes plain a useful functor from the category of Petri nets to a category of spaces of invariants and provides insight into the generalisations of the basic definition of Petri nets—for instance, the coloured and higher level nets of Kurt Jensen arise through a simple modification of the sorts of the algebras underlying nets. Further, it provides a smooth formal relation with other models of concurrency such as Milner's calculus of communicating systems (CCS) and Hoare's communicating sequential processes (CSP), though this is only indicated in this paper.     

Cyberculture,symbiosis, and syncretism

The impact of Cyberculture, of digital devices on young people as extensions of the body, can be seen in terms of the decreasing structuring of thoughts and information, increasing impulsivity in perception and action, and the development of more primitive defense mechanisms. These adverse impacts result in the feeling of isolation and devaluation, frustration of present and uncertainty of the future, exteriorization and floating identities, mimetic and adhesive identifications, less cohesion of the self, and decreasing tolerance of the other. This paper focuses on the following themes: Symbiosis versus syncretism: The affirmations of symbiosis. The dilutions of syncretism. Synopsis: Too much syncretism, too little symbiosis. Lack of a deeper co-construction of knowledge, more lasting, and sustainable. Lack of increased more independent personal cognitive deepening. Lack of ability to be alone. Causality and free will: Symbiotic versus syncretic causality. Conclusions: Cyber-selfs—either distributed or not at all?     

Motility,mixing, and multicellularity

A fundamental issue in evolutionary biology is the transition from unicellular to multicellular organisms, and the cellular differentiation that accompanies the increase in group size. Here we consider recent results on two types of “multicellular” systems, one produced by many unicellular organisms acting collectively, and another that is permanently multicellular. The former system is represented by groups of the bacterium Bacillus subtilis and the latter is represented by members of the colonial volvocalean green algae. In these flagellated organisms, the biology of chemotaxis, metabolism and cell–cell signaling is intimately connected to the physics of buoyancy, motility, diffusion, and mixing. Our results include the discovery in bacterial suspensions of intermittent episodes of disorder and collective coherence characterized by transient, recurring vortex streets and high-speed jets of cooperative swimming. These flow structures markedly enhance transport of passive tracers, and therefore likely have significant implications for intercellular communication. Experiments on the Volvocales reveal that the sterile flagellated somatic cells arrayed on the surface of Volvox colonies are not only important for allowing motion toward light (phototaxis), but also play a crucial role in driving fluid flows that transport dissolved molecular species. These flows, generated by the collective beating of flagella, confer a synergistic advantage with regard to transport of nutrients and chemical messengers. They allow these species to circumvent a nutrient acquisition bottleneck which would exist if transport were purely diffusive, and thereby evolve to larger multicellular individuals. In both cases, a higher level of organization, specialization and complexity counteract the higher costs inherent to larger groups.     

Robustness,stability, recoverability,and reliability in constraint satisfaction problems

Many real-world problems in Artificial Intelligence (AI) as well as in other areas of computer science and engineering can be efficiently modeled and solved using constraint programming techniques. In many real-world scenarios the problem is partially known, imprecise and dynamic such that some effects of actions are undesired and/or several unforeseen incidences or changes can occur. Whereas expressivity, efficiency, and optimality have been the typical goals in the area, there are several issues regarding robustness that have a clear relevance in dynamic Constraint Satisfaction Problems (CSPs). However, there is still no clear and common definition of robustness-related concepts in CSPs. In this paper, we propose two clearly differentiated definitions for robustness and stability in CSP solutions. We also introduce the concepts of recoverability and reliability, which arise in temporal CSPs. All these definitions are based on related well-known concepts, which are addressed in engineering and other related areas.     

Periodic-like words, periodicity, and boxes

We introduce the notion of periodic-like word. It is a word whose longest repeated prefix is not right special. Some different characterizations of this concept are given. In particular, we show that a word w is periodic-like if and only if it has a period not larger than , where is the least non-negative integer such that any prefix of w of length $\geq R'_{w}$ is not right special. We derive that if a word w has two periods , then also the greatest common divisor of p andq is a period ofw. This result is, in fact, an improvement of the theorem of Fine and Wilf. We also prove that the minimal period of a word w is equal to the sum of the minimal periods of its components in a suitable canonical decomposition in periodic-like subwords. Moreover, we characterize periodic-like words having the same set of proper boxes, in terms of the important notion of root-conjugacy. Finally, some new uniqueness conditions for words, related to the maximal box theorem are given. Received: 10 July 2000 / Accepted: 24 January 2001     

Randomness, Stochasticity, and Approximations

Polynomial time unsafe approximations for intractable sets were introduced by Meyer and Paterson [9] and Yesha [19], respectively. The question of which sets have optimal unsafe approximations has been investigated extensively; see, e.g., [1], [5], [15], and [17]. Recently, Wang [15], [17] showed that polynomial time random sets are neither optimally unsafe approximable nor Δ -levelable. In this paper we show that: (1) There exists a polynomial time stochastic set in the exponential time complexity class which has an optimal unsafe approximation. (2) There exists a polynomial time stochastic set in the exponential time complexity class which is Δ -levelable. The above two results answer a question asked by Ambos-Spies and Lutz [2]: What kind of natural complexity property can be characterized by p -randomness but not by p -stochasticity? Our above results also extend Ville's [13] historical result. The proof of our first result shows that, for Ville's stochastic sequence, we can find an optimal prediction function f such that we will never lose our own money betting according to f (except the money we have earned), that is to say, if at the beginning we have only $1 and we always bet $1 that the next selected bit is 1 , then we always have enough money to bet on the next bit. Our second result shows that there is a stochastic sequence for which there is a betting strategy f such that we will never lose our own money betting according to f (except the money we have earned), but there is no such optimal betting strategy. That is to say, for any such betting strategy, we can find another betting strategy which could be used to make money more quickly. Received May 1997, and in final form September 1998.     

U-shaped, iterative, and iterative-with-counter learning

This paper solves an important problem left open in the literature by showing that U-shapes are unnecessary in iterative learning from positive data. A U-shape occurs when a learner first learns, then unlearns, and, finally, relearns, some target concept. Iterative learning is a Gold-style learning model in which each of a learner’s output conjectures depends only upon the learner’s most recent conjecture and input element. Previous results had shown, for example, that U-shapes are unnecessary for explanatory learning, but are necessary for behaviorally correct learning. Work on the aforementioned problem led to the consideration of an iterative-like learning model, in which each of a learner’s conjectures may, in addition, depend upon the number of elements so far presented to the learner. Learners in this new model are strictly more powerful than traditional iterative learners, yet not as powerful as full explanatory learners. Can any class of languages learnable in this new model be learned without U-shapes? For now, this problem is left open.     

Disjunctions, independence, refinements

An important question in constraint satisfaction is how to restrict the problem to ensure tractability (since the general problem is NP-hard). The use of disjunctions has proven to be a useful method for constructing tractable constraint classes from existing classes; the well-known ‘max-closed’ and ‘ORD-Horn’ constraints are examples of tractable classes that can be constructed this way. Three sufficient conditions (the guaranteed satisfaction property, 1-independence and 2-independence) that each ensure the tractability of constraints combined by disjunctions have been proposed in the literature. We show that these conditions are both necessary and sufficient for tractability in three different natural classes of disjunctive constraints. This suggests that deciding this kind of property is a very important task when dealing with disjunctive constraints. We provide a simple, automatic method for checking the 1-independence property—this method is applicable whenever the consistency of the constraints under consideration can be decided by path-consistency. Our method builds on a connection between independence and refinements (which is a way of reducing one constraint satisfaction problem to another.)