Theoretical Upperbound Research Articles

Analytical derivation of the optimum triplicator

The analytical derivation of the phase profile of a diffractive optical element that produces three equi-intense replicas of an input beam with the maximum efficiency is presented. Such derivation, based on a functional minimization procedure, leads to a closed form for the phase profile and to an efficiency value slightly lower than the predicted theoretical upper bound.

Dynamic selection procedures for constrained inbreeding and their consequences for pedigree development

A novel selection algorithm for maximizing genetic response while constraining the rate of inbreeding is presented. It is shown that the proposed method controls the rate of inbreeding by maintaining the sum of squared genetic contributions at a constant value and represents an improvement on previous procedures. To maintain a constant rate of inbreeding the contributions from all generations are weighted equally and this is facilitated by modifying the numerator relationship matrix. By considering the optimization of the contributions of many generations the initial mating proportions (the genetic contributions to the next generation) are not equal to their long-term values, but are set equal to the expected long-term contributions given the current information. This is confirmed by the regression of the long-term contributions on the assigned mating proportions being close to one. The gain obtained from the selection algorithm is compared with the maximum theoretical genetic gain under constrained inbreeding. It is concluded that this theoretical upper bound is in general unattainable, but from this a concept of genetic efficiency in terms of resources and constraints is derived.

Low-temperature elastic coefficients of polycrystalline indium

Using an ultrasonic pulse-echo method, we measured the elastic coefficients of polycrystalline indium from 300 to 5 K. All elastic coefficients showed regular temperature behavior, as predicted by an Einstein-oscillator model. The shear and Young moduli showed the largest change, increasing ≈55% during cooling. The Poisson ratio was unusually high at 0.45, just below the theoretical upper bound of 0.5. Using a Marx composite oscillator, we measured the internal friction at room temperature. We calculated the acoustic Debye temperature, 108.4 K, that agreed well with a monocrystal acoustic value, 111.3 K and the specific-heat value, 108.8 K. Also, we calculated the Grüneisen parameters, γ L=2.04, γ H=2.68, that agreed well with the specific-heat value, γ=2.48 and the shock-wave value, γ=2.24.

Caps Embedded in Grassmannians

This paper is concerned with constructing caps embedded in line Grassmannians. In particular, we construct a cap of size q3 +2q2+1 embedded in the Klein quadric of PG(5,q) for even q, and show that any cap maximally embedded in the Klein quadric which is larger than this one must have size equal to the theoretical upper bound, namely q3+2q2+q+2. It is not known if caps achieving this upper bound exist for even q > 2.

Linear cellular automata and Fischer automata

We study the sizes of minimal finite state machines associated with linear cellular automata. In particular, we construct a class of binary linear cellular automata whose corresponding minimal automata exhibit full exponential blow-up. These cellular automata have Hamming distance 1 to a permutation automaton. Moreover, the corresponding minimal Fischer automata as well as the minimal DFAs have maximal complexity. By contrast, the complexity of higher iterates of a cellular automaton always stays below the theoretical upper bound.

Hebbian learning, its correlation catastrophe, and unlearning

Learning and associative memory are concerned with storing and retrieving activity patterns of a neuronal net. It is considered to be a minimal requirement that the number of patterns that can be stored faithfully is extensive, i.e. is at least proportional to the number of neighbours each neuron interacts with. The main drawback of Hebbian learning, and of any one-shot local learning procedure, is that it cannot store extensively many patterns with activities which vary from pattern to pattern because, being local, it cannot discern global correlations. We critically review the performance of Hebbian unlearning—also proposed as a model of REM sleep—in a network of formal neurons with a distribution of axonal delays. Hebbian unlearning, though as local and unsupervised as Hebbian learning, eliminates undesirable global correlations, handles any spatio-temporal pattern, and improves the network performance greatly—sometimes even saturating a theoretical upper bound. Furthermore, it is shown that unlearning has an optimal and critical number of unlearning loops (‘dreams’) at and above which, respectively, storage and retrieval are optimal and break down completely. In applications, ‘blinking’ is a most useful property: after having unlearned stationary patterns, the network, when presented with a noisy pattern, either converges to the original one or to a blinking state signalling that the final pattern has not been learned. In a daily context, data acquisition and REM sleep alternate. Numerical simulations have shown that, alternating between learning bundles of patterns and unlearning, a network only stores and retrieves the most recently learned data and ‘forgets’ the past. A key property of unlearning being the elimination of undesirable correlations, the process would give a straightforward explanation of Freudian condensation. In other words, the unlearning viewpoint offers a comprehensive perspective.

EFFECTS OF NEUTRINO OSCILLATION ON THE SUPERNOVA RELIC NEUTRINO BACKGROUND

We investigate to what extent the oscillation or conversion of neutrinos enhances the expected event rate of the supernova relic neutrino background (SRN) at the SuperKamiokande detector (SK). The SRN [Formula: see text] can be almost completely exchanged with vμ-like neutrinos by the MSW oscillation under the inverse mass hierarchy with Δm2~ 10−8–105[eV2], or by the magnetic moment of Majorana neutrinos with μv≳10−12μB and Δm2~10−4–10° [eV2]. In the standard calculation of the SRN flux, the event rate of the SRN [Formula: see text] at the SK in the observable energy range of 15–40 MeV can be enhanced from 1.2 yr−1 to 2.4 yr−1 if all [Formula: see text] are exchanged with vμ-like neutrinos. The enhancement is prominent especially in the high energy range (≳ 25 MeV). In the astrophysically optimistic calculation, the event rate becomes as high as 9.4 yr−1. Because the theoretical upper bound of the SRN events without oscillation is about 5 yr−1 taking into account the various astrophysical uncertainties, we might have to resort to the neutrino oscillation if more than 5 events in a year, as well as a significantly harder spectrum, were observed in the SK.

Naturalness and superpartner masses or when to give up on weak scale supersymmetry.

Superpartner masses cannot be arbitrarily heavy if supersymmetric extensions of the standard model explain the stability of the gauge hierarchy. This ancient and hallowed motivation for weak scale supersymmetry is often quoted, yet no reliable determination of this upper limit on superpartner masses exists. In this paper we compute upper bounds on superpartner masses in the minimal supersymmetric model, and we identify which values of the superpartner masses correspond to the most natural explanation of the hierarchy stability. We compare the most natural value of these masses and their upper limits to the physics reach of current and future colliders. As a result, we find that supersymmetry could explain weak scale stability naturally even if no superpartners are discovered at the CERN LEP II or the Fermilab Tevatron (even with the Main Injector upgrade). However, we find that supersymmetry cannot provide a complete explanation of weak scale stability, if squarks and gluinos have masses beyond the physics reach of the CERN LHC. Moreover, in the most natural scenarios, many sparticles, for example, charginos, squarks, and gluinos, lie within the physics reach of either LEP II or the Tevatron. Our analysis determines the most natural value of the chargino (squark) [(gluino)] mass consistent with current experimental constraints is \ensuremath{\sim}50 (250) [(250)] GeV and the corresponding theoretical upper bound is \ensuremath{\sim}250 (700) [(800)] GeV.

Analysis of polling protocols for fieldbus networks

Roll-call polling mechanisms are considered for fieldbus networks. Based on a producer/consumer communication model, two different protocols are presented, namely the standardized FIP (Factory Instrumentation Protocol) and a modified FIP protocol that we propose here. The modified protocol uses redundancy to eliminate local timers used by the FIP protocol. The two protocols are analyzed for efficiency, jitter and robustness. We compare the two protocols based on implementation and analytical results. Practical aspects concerning: clock precision; computing time; and hard real-time constraints are also discussed. The results show that: (1) the original FIP protocol is fractionally more efficient with respect to its execution time than the modified one; (2) the modifications proposed, however, reduce the jitter and improve the robustness considerably; (3) the slot time of the original FIP protocol has theoretical upper bound but the modified protocol has no such limitations.

Twisted GFSR generators

The generalized feed back shift register (GFSR) algorithm suggested by Lewis and Payne is a widely used pseudorandom number generator, but has the following serious drawbacks: (1) an initialization scheme to assure higher order equidistribution is involved and is time consuming; (2) each bit of the generated words constitutes an m -sequence based on a primitive trinomials, which shows poor randomness with respect to weight distribution; (3) a large working area is necessary; (4) the period of sequence is far shorter than the theoretical upper bound. This paper presents the twisted GFSR (TGFSR) algorithm, a slightly but essentially modified version of the GFSR, which solves all the above problems without loss of merit. Some practical TGFSR generators were implemented and passed strict empirical tests. These new generators are most suitable for simulation of a large distributive system, which requires a number of mutually independent pseudorandom number generators with compact size.

Analysis and evaluation of message management functions for bidimensional transputer networks

This work is focused on the analysis of the T800 transputer as the message manager of a multicomputer system. The studied topologies are a 4 × 4 mesh and a 4 × 4 torus. A model for the message manager has been developed and implemented in Occam. A random communication pattern and store-and-forward flow control have been used. Using this model, message latency and throughput have been studied for different traffic levels, ranging from null traffic up to the saturation point of the network. The influence of the message length on the network behaviour has also been considered. Finally, the theoretical upper bound of the throughput is discussed and compared with the experimental data.

Die Ortsfrequenzgrenze und das Auflösungsvermögen des visuellen Systems der Taube

The spatial contrast transfer function of the visual system of the pigeon was determined by recording from the optic tectum evoked potentials or extracellular unit activity in response to a pattern stimulus contrast transfer function, determined as a "response function", describes the relationship between the contrast in the pattern--which consisted of vertically oriented stripes of sinusoidally varying luminance--and the amplitude of the response at various spatial frequencies (c/deg). The transfer function yields an estimate of the high frequency limit, which in turn is a measure of visual resolving power. Action potentials were recorded extracellularly using glass microelectrodes; for evoked potentials, stainless steel electrodes were used. Recordings were made from the stratum griseum et fibrosum superficiale of the optic tectum. The highest spatial frequency detectable in a visual system is limited by various factors, including the diffraction of light at the pupil and the anatomical spacing of the photoreceptors. The pupil factor can be controlled in experiments in a suitable way. In this paper, the electrophysiologically determined high-frequency limit was compared with the theoretical resolution limit imposed by the photoreceptor mosaic. The experimental results show that the visual system of the pigeon has a high-frequency limit at a spatial frequency of 15.5 c/deg, corresponding to a visual acuity of 1.9 min of arc. The attempt to relate visual acuity in the pigeon to the anatomical spacing of the photoreceptors shows that the Nyquist frequency of the photoreceptor mosaic, the theoretical upper bound of the spatial resolution, agrees with measurement.

Statistical mechanics of a multilayered neural network.

Statistical mechanics is applied to estimate the maximal information capacity per synapse (${\mathrm{\ensuremath{\alpha}}}_{\mathit{c}}$) of a multilayered feedforward neural network, functioning as a parity machine. For a large number of hidden units, K, the replica-symmetric solution overestimates dramatically the capacity, ${\mathrm{\ensuremath{\alpha}}}_{\mathit{c}}$\ensuremath{\propto}${\mathit{K}}^{2}$. However, a one-step replica-symmetry breaking gives ${\mathrm{\ensuremath{\alpha}}}_{\mathit{c}}$\ensuremath{\sim}lnK/ln2, which coincides with a theoretical upper bound. It is suggested that this asymptotic behavior is exact. Results for finite K are also discussed.

Optimal Design of a Rotating Bar for Kinetic Energy Storage

A thin homogeneous rotating bar of variable width is considered for the purpose of storing kinetic energy. The objective of the design is to find the shape of the bar for which, in the presence of constraints on the geometry and strength of the bar, the Specific Kinetic Energy (SKE) is maximal. An upper bound for the SKE of a finite length bar is derived and a discrete formulation is presented by which an approximate optimal profile for arbitrary design parameters and rotational speeds can be obtained numerically. Applying a parametric study, in which optimal designs for a sequence of rotational speeds were observed, a general configuration of the exact optimal profile was concluded. The parametric study reveals the existence of three speed intervals, each characterized by a common type of optimal design. The optimal SKE corresponding to the ultimate rotational speed reaches a value very close to the theoretical upper bound, namely, that of a thin ring. The model gives insight into the nature of optimal designs and serves as a simple and rapid computational tool for finding the optimal profile for arbitrary bar parameters and rotational speeds.

Optimal Design of a Rotating Disk for Kinetic Energy Storage

A thin homogeneous rotating disk of variable thickness is considered for the purpose of storing kinetic energy. The objective of the design is to find the optimal shape of the disk for which, in the presence of constraints on the geometry and strength of the disk, the Specific Kinetic Energy (SKE) is maximal. An upper bound for the SKE of a finite diameter disk is derived and a discrete formulation is presented by which an approximate optimal profile for arbitrary design parameters and rotational speeds can be obtained numerically. Applying a parametric study in which optimal designs for a sequence of rotational speeds are observed, a general configuration of the exact optimal profile is presented. The parametric study reveals the existence of three speed intervals, each characterized by a common type of optimal design. The optimal SKE corresponding to the ultimate rotational speed reaches a value very close to the theoretical upper bound, namely twice that of a thin ring. The model gives insight into the nature of optimal designs and serves as a simple and rapid computational tool for finding the optimal profile for arbitrary disk parameters and rotational speeds.

A finite state machine algorithm for finding restriction sites and other pattern matching applications

Existing algorithms for finding restriction endonuclease recognition sites use brute-force algorithms which run in time 0(NM) where N is the number of nucleotides in the sequence under analysis and M is the total number of nucleotides in all the different sites being searched for. This paper presents a deterministic finite state machine algorithm which runs in time 0(N). Memory use can be as high as 0(M4) but a slight modification to the basic algorithm can impose a theoretical upper bound of 0(M) at the cost of some added complexity in the execution of the state machine. The algorithm can operate with a single pass through the sequence under analysis, with no need to back up or (for non-circular sequences) store more than a single input character at a time. This type of algorithm can be adapted to many pattern-matching tasks and is simple enough to implement in hardware that it could, for example, be built into a disk controller as part of a specialized database machine.

Comparison of Policies for Routing Customers to Parallel Queueing Systems

This paper studies a queueing system with two groups of servers, each with a separate queue, and with arriving customers routed irrevocably to one of the two queues. One natural policy for routing arriving customers is to send them to the queue with the shortest expected delay. Although this shortest delay routing policy (SDR) is known to be optimal if each server group has one server and the service time distribution has nondecreasing failure rate, little is known about the general multiserver case, even with exponential service times. In this paper we show, using a theoretical upper bound, that an optimal policy would produce delays that are almost identical to what would result from combining the two groups. In addition, our simulation results show that SDR performs nearly optimally in every case considered.

A theoretical and numerical approach to the plastic behaviour of steels during phase transformations—II. Study of classical plasticity for ideal-plastic phases

The response of phase-transforming steels to variations of the applied stress (i.e. the ∑-term of the classical plastic strain rate Ė cp defined in Part I) is studied both theoretically and numerically for ideal-plastic individual phases. It is found theoretically that though the stress-strain curve contains no elastic portion, it is nevertheless initially tangent to the elastic line with slope equal to Young's modulus. Moreover an explicit formula for the beginning of the curve is derived for medium or high proportions of the harder phase, and a simple upper bound is given for the ultimate stress (maximum Von Mises stress). The finite element simulation confirms and completes these results, especially concerning the ultimate stress whose discrepancy with the theoretical upper bound is found to be maximum for low proportions of the harder phase. Based on these results, a complete model is proposed for the ∑-term of the classical plastic strain rate Ė cp in the case of ideal-plastic phases.

Computer simulation study of hysteresis and free energy in the fcc Ising antiferromagnet

A method for estimating the entropy $S$ from a Monte Carlo simulation, suggested previously by the author, is applied to the fcc Ising antiferromagnet with nearest-neighbor interactions and external magnetic field $h$. The estimated accuracy for $S$ is 0.01% to 0.5%, which is, at least, 1 order of magnitude higher than has been obtained with thermodynamic integration by Binder. Comparison of the free-energy results for the coexisting ordered and disordered phases enables us to determine with high accuracy the first-order transition points and the discontinuities in the thermodynamic functions. For the residual ground-state entropies per spin $\frac{S(0)}{{k}_{B}}$ at the critical fields $\frac{{h}_{c}}{J}=12$ and 4, we obtain 0.249 89(2) [=0.369 51(3)ln2] and 0.239(1) [=0.345(1)ln2], respectively. The first result is significantly larger than the theoretical upper bound, ${\ensuremath{\sigma}}_{u}^{\ensuremath{'}}=0.2398$ (=0.3460ln2), conjectured by Hadjukovi\ifmmode \acute{c}\else \'{c}\fi{} and Milo\ifmmode \check{s}\else \v{s}\fi{}evi\ifmmode \acute{c}\else \'{c}\fi{}. Our results are also significantly larger than Binder's result, ~⅓ ln2, obtained for both critical fields.

Unrecorded Human Assets and the "Hold Up" Problem

Human resource accountants claim that financial statements understate firms' assets by failing to recognize the value of human assets. In a recent paper in this Journal, Dittman, Juris, and Revsine (DJR) [1976] employed a model developed by Becker [1964; 1975] to show that the total costs of specific training constitute an upper bound on the value of unrecorded human assets to employers. The purpose of this note is to point out an omission in DJR's analysis' which suggests that this theoretical upper bound is even lower than DJR claimed.2 In Becker's model, employee training is partitioned into general training and training which is completely firm specific. By definition, general training increases the worker's posttraining marginal productivity to current and alternative employers by equal amounts. In a competitive labor market, workers compensate employers for general training by accepting a lower (than current marginal product) wage during the training period. Specific training,3 by definition, increases the wo'rker's