Conditions for the Light-Traffic Insensitivity to Loss Probability in a GI/G/m/0 Queueing System

A loss queueing system GI/G/m/0 is considered. Let a(x) be a p.d.f. of interarrival intervals. Assume that this function behaves like cx^-1 for small x. Further let B(x) be a d.f. of service time; (1/) be the mean service time. Conditions are derived for the light-traffic insensitivity of the loss probability to the form of B(x) as (/ ) 0. In particular, the condition = 1 is necessary. Estimates for the loss probability are obtained.     

Generating Boolean \mu-expressions

In this paper, we consider the class of Boolean -functions, which are the Boolean functions definable by -expressions (Boolean expressions in which no variable occurs more than once). We present an algorithm which transforms a Boolean formulaE into an equivalent -expression-if possible-in time linear in E times , where E is the size ofE andn _m is the number of variables that occur more than once inE. As an application, we obtain a polynomial time algorithm for Mundici's problem of recognizing -functions fromk-formulas [17]. Furthermore, we show that recognizing Boolean -functions is co-NP-complete for functions essentially dependent on all variables and we give a bound close to co-NP for the general case.     

Deep X-ray lithography using mask with integrated electrothermal actuator

We present a deep X-ray mask with integrated bent-beam electrothermal actuator for the fabrication of 3D microstructures with curved surface. The mask absorber is electroplated on the shuttle mass, which is supported by a pair of 20-m-thick single crystal silicon bent-beam electrothermal actuators and oscillated in a rectilinear direction due to the thermal expansion of the bent-beams. The width of each bent-beam is 10 m or 20 m and the length and bending angle are 1 mm and 0.1 rad, respectively, and the shuttle mass size is 1 mm × 1 mm. For 10-m-wide bent-beams, the shuttle mass displacement is around 15 m at 180 mW (3.6 V) dc input power. For 20-m-wide bent-beams, the shuttle mass displacement is around 19 m at 336 mW (4.2 V) dc input power. Sinusoidal cross-sectional PMMA microstructures with a pitch of 40 m and a height of 20 m are fabricated by 0.5 Hz, 20-m-amplitude sinusoidal shuttle mass oscillation.This research, under the contract project code MS-02-338-01, has been supported by the Intelligent Microsystem Center, which carries out one of the 21st centurys Frontier R & D Projects sponsored by the Korea Ministry of Science & Technology. Experiments at PLS were supported in part by MOST and POSCO.     

Constructing strongly convex hulls using exact or rounded arithmetic

One useful generalization of the convex hull of a setS ofn points is the -strongly convex -hull. It is defined to be a convex polygon with vertices taken fromS such that no point inS lies farther than outside and such that even if the vertices of are perturbed by as much as , remains convex. It was an open question as to whether an -strongly convexO()-hull existed for all positive . We give here anO(n logn) algorithm for constructing it (which thus proves its existence). This algorithm uses exact rational arithmetic. We also show how to construct an -strongly convexO( + )-hull inO(n logn) time using rounded arithmetic with rounding unit . This is the first rounded-arithmetic convex-hull algorithm which guarantees a convex output and which has error independent ofn.     

A variotherm mold for micro metal injection molding

In this paper, a variotherm mold was designed and fabricated for the production of 316L stainless steel microstructures by micro metal injection molding (MIM). The variotherm mold incorporated a rapid heating/cooling system, vacuum unit, hot sprue and cavity pressure transducer. The design of the variotherm mold and the process cycle of MIM using the variotherm mold were described. Experiments were conducted to evaluate the molded microstructures produced using variotherm mold and conventional mold. The experiments showed that microstructures of higher aspect ratio such as 60 m × height 191 m and 40 m × height 174 m microstructures could be injection molded with complete filling and demolded successfully using the variotherm mold. Molded microstructures with dimensions of 60 m × height 191 m were successfully debound and sintered without visual defects.     

Minimization of norms and logarithmic norms by diagonal similarities

It is a commonly occurring problem to find good norms · or logarithmic norms (·) for a given matrix in the sense that they should be close to respectively the spectral radius (A) and the spectral abscissa (A). Examples may be the certification thatA is convergent, i.e. (A)A<1 or stable, i.e. (A)(A)<0. Often the ordinary norms do not suffice and one would like to try simple modifications of them such as using an ordinary norm for a diagonally transformed matrix. This paper treats this problem for some of the ordinary norms.

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Minimisierung von Normen und Logarithmischen Normen durch Diagonale Transformationen

Zusammenfassung Ein oft vorkommendes praktisches Problem ist die Konstruktion von guten Normen · und logarithmischen Normen (·) für eine gegebene MatrixA. Mit gut wird dann verstanden, daß A den Spektralradius (A)=max |₁| und (A) die Spektralabszisse (A)=max Re _i gut approximieren. Beispiele findet man für konvergente Matrizen wo (A)A<1 gewünscht ist, und für stabile Matrizen wo (A)(A)<0 zu zeigen ist. Wir untersuchen hier, wie weit man mit Diagonaltransformationen und dengewöhnlichsten Normen kommen kann.

     

The dynamic clusters method in nonhierarchical clustering

Given a finite setE R ⁿ, the problem is to find clusters (or subsets of similar points inE) and at the same time to find the most typical elements of this set. An original mathematical formulation is given to the problem. The proposed algorithm operates on groups of points, called samplings (samplings may be called multiple centers or cores); these samplings adapt and evolve into interesting clusters. Compared with other clustering algorithms, this algorithm requires less machine time and storage. We provide some propositions about nonprobabilistic convergence and a sufficient condition which ensures the decrease of the criterion. Some computational experiments are presented.     

On the minimal number of trajectories determining a multidimensional system

The minimal number(S) of generators of a multidimensional systemS is constructively determined. Such anS is the solution space of a linear system of partial differential or difference equations with constant coefficients. The main theorem generalizes recent results of Heij and Zampieri who calculated the number(S) in the one- (resp. two-) dimensional discrete case. There is also a direct connection with Macaulay's inverse systems in the multidimensional discrete situation, in particular with his principal systems characterized by the relation(S)1. It is surprising that, for dimensions greater than one, very many large systems are principal in this sense.     

Local determinacy of abstract local dynamical systems

O. Hájek proved in his book Dynamical Systems in the Plane (Chapter III) that there isat most one abstract local dynamical system which is locally equivalent to, or equivalently an extension of, a given elementary dynamical system, and suggested a question of finding reasonable conditions on the latter for the existence ofat least one such abstract local dynamical system. An elementary dynamical system is said to satisfy the No-Intersection Axiom and is called an abstract germ if(x ₁, t) = (x ₂,t) impliesx ₁ =x ₂. We show that is (uniquely) extendable to an abstract local dynamical system if and only if is an abstract germ, and hence the question is completely answered. After introducing various kinds of isomorphisms of abstract germs and abstract local dynamical systems corresponding to those of continuous germs and continuous local dynamical systems, we obtain some sufficient conditions for extendability of isomorphisms and possibility of restriction of them, and thus establish the local determinacy of abstract local dynamical systems up to isomorphisms in some wider categories.Dedicated to Professor Yusuke HAGIHARA in Commemoration of His Seventy-Seventh Anniversary     

A Representation of the Interval Hull of a Tolerance Polyhedron Describing Inclusions of Function Values and Slopes

Given a nonempty set of functions

Almost surely continuous solutions of a nonlinear stochastic integral equation

A nonlinear stochastic integral equation of the Hammerstein type in the formx(t; ) = h(t, x(t; )) + _s k(t, s; )f(s, x(s; ); )d(s) is studied wheret S, a measure space with certain properties, , the supporting set of a probability measure space (,A, P), and the integral is a Bochner integral. A random solution of the equation is defined to be an almost surely continuousm-dimensional vector-valued stochastic process onS which is bounded with probability one for eacht S and which satisfies the equation almost surely. Several theorems are proved which give conditions such that a unique random solution exists. AMS (MOS) subject classifications (1970): Primary; 60H20, 45G99. Secondary: 60G99.     

Interpretations of open default theories in non-monotonic logics

It is shown that the translation of an open default into a modal formula x(L(x)LM ₁ (x)...LM _m (x)w(x)) gives rise to an embedding of open default systems into non-monotonic logics.     

The conjoinability relation in Lambek calculus and linear logic

In 1958 J. Lambek introduced a calculusL of syntactic types and defined an equivalence relation on types: x y means that there exists a sequence x=x₁,...,x_n=y (n 1), such thatx _i x _i+1 or x_i+ x _i (1 i n). He pointed out thatx y if and only if there is joinz such thatx z andy z. This paper gives an effective characterization of this equivalence for the Lambeck calculiL andLP, and for the multiplicative fragments of Girard's and Yetter's linear logics. Moreover, for the non-directed Lambek calculusLP and the multiplicative fragment of Girard's linear logic, we present linear time algorithms deciding whether two types are equal, and finding a join for them if they are.The author was sponsored by project NF 102/62-356 (Structural and Semantic Parallels in Natural Languages and Programming Languages), funded by the Netherlands Organization for the Advancement of Research (N.W.O.).     

Hierarchy theorems for two-way finite state transducers

Summary For a family of languages , CAL() is defined as the family of images of under nondeterministic two-way finite state transducers, while FINITE · VISIT() is the closure of under deterministic two-way finite state transducers; CAL⁰()= and for n0, CAL ⁿ⁺¹()=CAL ⁿ (CAL()). For any semiAFL , if FINITE · VISIT() CAL(), then CAL ⁿ () forms a proper hierarchy and for every n0, FINITE · VISIT(CALⁿ()) CAL ⁿ⁺¹() FINITE · VISIT(CAL ⁿ⁺¹()). If is a SLIP semiAFL or a weakly k-iterative full semiAFL or a semiAFL contained in any full bounded AFL, then FINITE · VISIT() CAL() and in the last two cases, FINITE · VISIT(). If is a substitution closed full principal semiAFL and FINITE · VISIT(), then FINITE · VISIT() CAL(). If is a substitution closed full principal semiAFL generated by a language without an infinite regular set and ₁ is a full semiAFL, then is contained in CAL^m(₁) if and only if it is contained in ₁. Among the applications of these results are the following. For the following families , CAL ⁿ () forms a proper hierarchy: =INDEXED, =ETOL, and any semiAFL contained in CF. The family CF is incomparable with CAL ^m (NESA) where NESA is the family of one-way nonerasing stack languages and INDEXED is incomparable with CAL ^m (STACK) where STACK is the family of one-way stack languages.This work was supported in part by the National Science Foundation under Grants No. DCR74-15091 and MCS-78-04725     

Fuzzy measurement in the Mishnah and the Talmud

I discuss the attitude of Jewish law sources from the 2nd–:5th centuries to the imprecision of measurement. I review a problem that the Talmud refers to, somewhat obscurely, as impossible reduction. This problem arises when a legal rule specifies an object by referring to a maximized (or minimized) measurement function, e.g., when a rule applies to the largest part of a divided whole, or to the first incidence that occurs, etc. A problem that is often mentioned is whether there might be hypothetical situations involving more than one maximal (or minimal) value of the relevant measurement and, given such situations, what is the pertinent legal rule. Presumption of simultaneous occurrences or equally measured values are also a source of embarrassment to modern legal systems, in situations exemplified in the paper, where law determines a preference based on measured values. I contend that the Talmudic sources discussing the problem of impossible reduction were guided by primitive insights compatible with fuzzy logic presentation of the inevitable uncertainty involved in measurement. I maintain that fuzzy models of data are compatible with a positivistic epistemology, which refuses to assume any precision in the extra-conscious world that may not be captured by observation and measurement. I therefore propose this view as the preferred interpretation of the Talmudic notion of impossible reduction. Attributing a fuzzy world view to the Talmudic authorities is meant not only to increase our understanding of the Talmud but, in so doing, also to demonstrate that fuzzy notions are entrenched in our practical reasoning. If Talmudic sages did indeed conceive the results of measurements in terms of fuzzy numbers, then equality between the results of measurements had to be more complicated than crisp equations. The problem of impossible reduction could lie in fuzzy sets with an empty core or whose membership functions were only partly congruent. Reduction is impossible may thus be reconstructed as there is no core to the intersection of two measures. I describe Dirichlet maps for fuzzy measurements of distance as a rough partition of the universe, where for any region A there may be a non-empty set of - _A (upper approximation minus lower approximation), where the problem of impossible reduction applies. This model may easily be combined with probabilistic extention. The possibility of adopting practical decision standards based on -cuts (and therefore applying interval analysis to fuzzy equations) is discussed in this context. I propose to characterize the uncertainty that was presumably capped by the old sages as U-uncertainty, defined, for a non-empty fuzzy set A on the set of real numbers, whose -cuts are intervals of real numbers, as U(A) = 1/h(A) ₀ ^h(A) log [1+(A)]d, where h(A) is the largest membership value obtained by any element of A and (A) is the measure of the -cut of A defined by the Lebesge integral of its characteristic function.     

The input/output complexity of transitive closure

Suppose a directed graph has its arcs stored in secondary memory, and we wish to compute its transitive closure, also storing the result in secondary memory. We assume that an amount of main memory capable of holdings values is available, and thats lies betweenn, the number of nodes of the graph, ande, the number of arcs. The cost measure we use for algorithms is theI/O complexity of Kung and Hong, where we count 1 every time a value is moved into main memory from secondary memory, or vice versa.In the dense case, wheree is close ton ², we show that I/O equal toO(n ³/s) is sufficient to compute the transitive closure of ann-node graph, using main memory of sizes. Moreover, it is necessary for any algorithm that is standard, in a sense to be defined precisely in the paper. Roughly, standard means that paths are constructed only by concatenating arcs and previously discovered paths. For the sparse case, we show that I/O equal toO(n ²e/s) is sufficient, although the algorithm we propose meets our definition of standard only if the underlying graph is acyclic. We also show that(n ²e/s) is necessary for any standard algorithm in the sparse case. That settles the I/O complexity of the sparse/acyclic case, for standard algorithms. It is unknown whether this complexity can be achieved in the sparse, cyclic case, by a standard algorithm, and it is unknown whether the bound can be beaten by nonstandard algorithms.We then consider a special kind of standard algorithm, in which paths are constructed only by concatenating arcs and old paths, never by concatenating two old paths. This restriction seems essential if we are to take advantage of sparseness. Unfortunately, we show that almost another factor ofn I/O is necessary. That is, there is an algorithm in this class using I/OO(n ³e/s) for arbitrary sparse graphs, including cyclic ones. Moreover, every algorithm in the restricted class must use(n ³e/s/log³ n) I/O, on some cyclic graphs.The work of this author was partially supported by NSF grant IRI-87-22886, IBM contract 476816, Air Force grant AFOSR-88-0266 and a Guggenheim fellowship.     

Tuning the quality factor of bulk micromachined structures using squeezed-film damping

This report demonstrates the tuning the quality factor of a micromachined structure using the air damping of a small squeezed-film area (300 m² to 800 m²). Two micromachining processes have successfully been established to fabricate novel stationary structures using thin films and bulk silicon, in which the stationary structure and a vibrating micromachined cantilever form a squeezed-film region. Measurements showed that, under the assistant of bulk silicon stationary structure, the quality factor of the vibrating beam decreased by 48% when the squeezed-film area was increased from 300 m² to 800 m² under a 760-torr ambient pressure. Moreover, even when the ambient pressure was only 20 mtorr, the quality factor of the beam still decreased by 20% for the same increase in area. Under the assistant of thin film stationary structure, the quality factor of the vibrating beam decreased by 35% when the squeezed-film area was increased from 300 m² to 500 m² under a 760-torr ambient pressure. Consequently, the proposed two stationary structures can be exploited to significantly alter the quality factor of dynamic systems.This material is based (in part) upon work supported by the Ministry of Economic Affairs, R.O.C. under contract No. 91-EC-17-A-07-S1-0011, and the Asia Pacific Microsystems Inc. The author would like to express his appreciation to the NSC Central Regional MEMS Research Center (Taiwan), Electrical Engineering Department of National Tsing Hua University (Taiwan), Semiconductor Center of National Chiao Tung University (Taiwan), and National Nano Device Laboratories (Taiwan) in providing fabrication facilities.     

Best Huffman trees

Summary Given a sequence of positive weights, W=w ₁...w _n >0, there is a Huffman tree, T (T-up) which minimizes the following functions: max{d(w_i)}; d(w_i); f(d(w_i)) w _i(here d(w _i) represents the distance of a leaf of weight w _i to the root and f is a function defined for nonnegative integers having the property that g(x) = f(x + 1) – f(x) is monotone increasing) over the set of all trees for W having minimal expected length. Minimizing the first two functions was first done by Schwartz [5]. In the case of codes where W is a sequence of probabilities, this implies that the codes based on T have all their absolute central moments minimal. In particular, they are the least variance codes which were also described by Kou [3]. Furthermore, there exists a Huffman tree T, (T-down) which maximizes the functions considered above.However, if g(x) is monotone decreasing, T and T, respectively maximize and minimize f(d(w_i) w _i) over the set of all trees for W having minimal expected length. In addition, we derive a number of interesting results about the distribution of labels within Huffman trees. By suitable modifications of the usual Huffman tree construction, (see [1]) T and T can also be constructed in time O(n log n).     

Optimal multilayer channel routing with overlap

This paper presents algorithms for multiterminal net channel routing where multiple interconnect layers are available. Major improvements are possible if wires are able to overlap, and our generalized main algorithm allows overlap, but only on everyKth (K 2) layer. Our algorithm will, for a problem with densityd onL layers,L K + 3,provably use at most three tracks more than optimal: (d + 1)/L/K + 2 tracks, compared with the lower bound of d/L/K. Our algorithm is simple, has few vias, tends to minimize wire length, and could be used if different layers have different grid sizes. Finally, we extend our algorithm in order to obtain improved results for adjacent (K = 1) overlap: (d + 2)/2L/3 + 5 forL 7.This work was supported by the Semiconductor Research Corporation under Contract 83-01-035, by a grant from the General Electric Corporation, and by a grant at the University of the Saarland.     

Property preserving abstractions for the verification of concurrent systems

We study property preserving transformations for reactive systems. The main idea is the use of simulations parameterized by Galois connections (, ), relating the lattices of properties of two systems. We propose and study a notion of preservation of properties expressed by formulas of a logic, by a function mapping sets of states of a systemS into sets of states of a systemS'. We give results on the preservation of properties expressed in sublanguages of the branching time -calculus when two systemsS andS' are related via (, )-simulations. They can be used to verify a property for a system by verifying the same property on a simpler system which is an abstraction of it. We show also under which conditions abstraction of concurrent systems can be computed from the abstraction of their components. This allows a compositional application of the proposed verification method.This is a revised version of the papers [2] and [16]; the results are fully developed in [28].This work was partially supported by ESPRIT Basic Research Action REACT.Verimag is a joint laboratory of CNRS, Institut National Polytechnique de Grenoble, Université J. Fourier and Verilog SA associated with IMAG.