Form Of Bound Research Articles

Heuristic reoptimization of time‐extended multi‐robot task allocation problems

AbstractProviding high quality solutions is crucial when solving NP‐hard time‐extended multi‐robot task allocation (MRTA) problems. Reoptimization, that is, the concept of making use of a known solution to an optimization problem instance when the solution to a similar problem instance is sought, is a promising and rather new research field in this application domain. However, so far no approximative time‐extended MRTA solution approaches exist for which guarantees on the resulting solution's quality can be given. We investigate the reoptimization problems of inserting as well as deleting a task to/from a time‐extended MRTA problem instance. For both problems, we can give performance guarantees in the form of an upper bound of 2 on the resulting approximation ratio for all heuristics fulfilling a mild assumption. We furthermore introduce specific solution heuristics and prove that smaller and tight upper bounds on the approximation ratio can be given for these heuristics if only temporal unconstrained tasks and homogeneous groups of robots are considered. A conclusory evaluation of the reoptimization heuristic demonstrates a near‐to‐optimal performance in application.

Continuity bounds on observational entropy and measured relative entropies

We derive a measurement-independent asymptotic continuity bound on the observational entropy for general positive operator valued measures measurements, making essential use of its property of bounded concavity. The same insight is used to obtain continuity bounds for other entropic quantities, including the measured relative entropy distance to a convex set of states under a general set of measurements. As a special case, we define and study conditional observational entropy, which is an observational entropy in one (measured) subsystem conditioned on the quantum state in another (unmeasured) subsystem. We also study continuity of relative entropy with respect to a jointly applied channel, finding that observational entropy is uniformly continuous as a function of the measurement. But we show by means of an example that this continuity under measurements cannot have the form of a concrete asymptotic bound.

General Bound on the Performance of Counter-Diabatic Driving Acting on Dissipative Spin Systems.

Counter-diabatic driving (CD) is a technique in quantum control theory designed to counteract nonadiabatic excitations and guide the system to follow its instantaneous energy eigenstates, and hence has applications in state preparation, quantum annealing, and quantum thermodynamics. However, in many practical situations, the effect of the environment cannot be neglected, and the performance of the CD is expected to degrade. To arrive at general bounds on the resulting error of CD in this situation we consider a driven spin-boson model as a prototypical setup. The inequalities we obtain, in terms of either the Bures angle or the fidelity, allow us to estimate the maximum error solely characterized by the parameters of the system and the bath. By utilizing the analytical form of the upper bound, we demonstrate that the error can be systematically reduced through optimization of the external driving protocol of the system. We also show that if we allow a time-dependent system-bath coupling angle, the obtained bound can be saturated and realizes unit fidelity.

Event-Triggered Quantized Communication-Based Consensus in Multiagent Systems via Sliding Mode

To handle the common existing constraints, that is, limited energy supplies and limited communication bandwidth in multiagent systems (MASs), this article investigates the consensus problem in MASs with event-triggered communication (ETC) and state quantization. In order to compensate for the effect brought by mismatched disturbances, we also propose a novel multiple discontinuous sliding-mode surface, and the corresponding sliding-mode control law is constructed by considering the event-triggered and dynamic quantized mechanisms jointly. Under such a scheme, it is shown that the state trajectories of all the agents will be regulated to achieve consensus asymptotically and the Zeno behavior can be avoided completely. We further extend this work to self-triggered and periodic event-triggered cases. Particularly, in a periodic event-triggered approach, the new form of triggering conditions and upper bound of the sampling periods are provided explicitly. As a result, all agents can reach bounded consensus. Moreover, the upper bound of the consensus error can be arbitrarily adjusted by appropriately selecting parameters, and the periodic event-triggered case will be reduced to the event-triggered case when the bound approaches 0 (sampling periods approach 0 at the same time). A numerical example is illustrated to verify the effectiveness of the proposed algorithms.

Cramér-Rao bound for a mixture of real- and integer-valued parameter vectors and its application to the linear regression model

Performance lower bounds are known to be a fundamental design tool in parametric estimation theory. A plethora of deterministic bounds exist in the literature, ranging from the general Barankin bound to the well-known Cramér-Rao bound (CRB), the latter providing the optimal mean square error performance of locally unbiased estimators. In this contribution, we are interested in the estimation of mixed real- and integer-valued parameter vectors. We propose a closed-form lower bound expression leveraging on the general CRB formulation, being the limiting form of the McAulay-Seidman bound. Such formulation is the key point to take into account integer-valued parameters. As a particular case of the general form, we provide closed-form expressions for the Gaussian observation model. One noteworthy point is the assessment of the asymptotic efficiency of the maximum likelihood estimator for a linear regression model with mixed parameter vectors and known noise covariance matrix, thus complementing the rather rich literature on that topic. A representative carrier-phase based precise positioning example is provided to support the discussion and show the usefulness of the proposed lower bound.

Is high active share always good?

More and more asset managers are committing to an explicit active share target, which takes the form of a lower bound (e.g. at least 75%) or a range of values (e.g. between 75 and 85%). The active share target is used either in conjunction with, or as a substitute for a tracking error limit. We analyse the implications of active share targets on the portfolio construction process using a simple optimisation framework. Our results suggest, counter to conventional wisdom, that in certain situations the portfolio construction process benefits from imposing a limit on active share rather than from boosting active share. In particular, if the signal used in a strategy is weak, then a constraint on active share can help mitigate the effects of model uncertainty.

Semilocal convergence of a continuation method in Banach spaces

This paper is concerned with the semilocal convergence of a continuation method between two third-order iterative methods, namely, the Halley’s and the convex acceleration of Newton’s method, also known as the Super-Halley’s method. This convergence analysis is discussed using the recurrence relations approach. This approach simplifies the analysis and leads to improved results. The convergence analysis is established under the assumption that the second Frechet derivative satisfies Lipschitz continuity condition. An existence-uniqueness theorem is given. Also, a closed form of error bound is derived in terms of a real parameter α ∈ [0, 1]. Two numerical examples are worked out to demonstrate the efficacy of our approach. On comparing the existence and uniqueness region and error bounds for the solution obtained by our analysis with those obtained by using majorizing sequences [15], we observed that our analysis gives better results. Further, we have observed that for particular values of the α, our analysis reduces to those for the Halley’s method (α = 0) and the convex acceleration of Newton’s method (α = 1), respectively, with improved results.

Uncertainty Relations for Some Central Potentials in N-Dimensional Space

We study the uncertainty relation for three quantum systems in the N-dimensional space by using the virial theorem (VT). It is shown that this relation depends on the energy spectrum of the system as well as on the space dimension N. It is pointed out that the form of lower bound of the inequality, which is governed by the ground state, depends on the system and on the space dimension N. A comparison between our result for the lower bound and recent results, based on information-theoretic approach, is pointed out. We examine and analyze these derived uncertainties for different angular momenta with a special attention made for the large N limit.

Lower bound for the hyperfine populations of spin-2 condensates against a magnetic field under the single-spatial-mode approximation

The variation of the hyperfine populations $N{\ensuremath{\rho}}_{\ensuremath{\mu}}$ of the ground state (g.s.) of spin-2 condensates against a magnetic field $B$ is studied. A $N$-body theory which is rigorous in dealing with the spin degrees of freedom has been adopted. The conservation of the total magnetization $M$ is assumed. A combined hyperfine population $N{\ensuremath{\rho}}_{\text{comb}}=N({\ensuremath{\rho}}_{0}\ensuremath{-}3{\ensuremath{\rho}}_{2}\ensuremath{-}3{\ensuremath{\rho}}_{\ensuremath{-}2})$, which is an observable, is defined. The lower bound for this population has been derived analytically. It turns out that the lower bound is identical to the actual population when $B=0$ and $\ensuremath{\infty}$, and the population is monotonically uprising in between. Thus, via the analytical form of the lower bound, the variation of the population against $B$ can be roughly known in advance. Numerical examples are given to demonstrate the applicability of the bound. When $M=0$, the g.s. in the polar phase was found to be highly unstable against $B$ because the neighboring level density is extremely high. When $M=N$, the g.s. in the cyclic phase was also found to be highly unstable. This is because the appearance of $B$, even if it is very weak, will break the high degeneracy of the g.s. and result in having numerous levels emerging in the neighborhood of the g.s.

Multi-Receiver Wiretap Channel With Public and Confidential Messages

We study the multi-receiver wiretap channel (MR-WC) with public and confidential messages. In this channel, there is a transmitter that wishes to communicate with two legitimate users in the presence of an external eavesdropper. The transmitter sends a pair of public and confidential messages to each legitimate user. While there are no secrecy constraints on the public messages, confidential messages need to be transmitted in perfect secrecy. We study the discrete memoryless MR-WC as well as its Gaussian multi-input multi-output (MIMO) counterpart. First, we propose an inner bound for the general, not necessarily degraded, discrete memoryless MR-WC by using Marton's inner bound and rate splitting in conjunction with superposition coding and binning. Second, we specialize this inner bound for the degraded discrete memoryless case. This specialized form of the inner bound can be obtained by using superposition coding and binning only. Next, we obtain an outer bound for the capacity region of the degraded channel, which matches the inner bound for some special cases. Third, we consider the degraded Gaussian MIMO channel, and show that, to evaluate both the inner and outer bounds, considering only jointly Gaussian auxiliary random variables and channel input is sufficient. Similar to the discrete memoryless case, for the Gaussian MIMO case as well, these bounds match for some special cases.

Violation of a local form of the Lieb-Oxford bound

In the framework of density-functional theory, several popular density functionals for exchange and correlation have been constructed to satisfy a local form of the Lieb-Oxford bound. In its original global expression, the bound represents a rigorous lower limit for the indirect Coulomb interaction energy. Here we employ exact-exchange calculations for the G2 test set to show that the local form of the bound is violated in an extensive range of both the dimensionless gradient and the average electron density. Hence, the results demonstrate the severity in the usage of the local form of the bound in functional development. On the other hand, our results suggest alternative ways to construct accurate density functionals for the exchange energy.

ESTIMATING A PARAMETER WHEN IT IS KNOWN THAT THE PARAMETER EXCEEDS A GIVEN VALUE

SummaryIn some statistical problems a degree of explicit, prior information is available about the value taken by the parameter of interest, θ say, although the information is much less than would be needed to place a prior density on the parameter's distribution. Often the prior information takes the form of a simple bound, ‘θ > θ1’ or ‘θ < θ1’, where θ1 is determined by physical considerations or mathematical theory, such as positivity of a variance. A conventional approach to accommodating the requirement that θ > θ1 is to replace an estimator, , of θ by the maximum of and θ1. However, this technique is generally inadequate. For one thing, it does not respect the strictness of the inequality θ > θ1, which can be critical in interpreting results. For another, it produces an estimator that does not respond in a natural way to perturbations of the data. In this paper we suggest an alternative approach, in which bootstrap aggregation, or bagging, is used to overcome these difficulties. Bagging gives estimators that, when subjected to the constraint θ > θ1, strictly exceed θ1 except in extreme settings in which the empirical evidence strongly contradicts the constraint. Bagging also reduces estimator variability in the important case for which is close to θ1, and more generally produces estimators that respect the constraint in a smooth, realistic fashion.

Reducing mechanism design to algorithm design via machine learning

We use techniques from sample-complexity in machine learning to reduce problems of incentive-compatible mechanism design to standard algorithmic questions, for a broad class of revenue-maximizing pricing problems. Our reductions imply that for these problems, given an optimal (or β-approximation) algorithm for an algorithmic pricing problem, we can convert it into a ( 1 + ϵ ) -approximation (or β ( 1 + ϵ ) -approximation) for the incentive-compatible mechanism design problem, so long as the number of bidders is sufficiently large as a function of an appropriate measure of complexity of the class of allowable pricings. We apply these results to the problem of auctioning a digital good, to the attribute auction problem which includes a wide variety of discriminatory pricing problems, and to the problem of item-pricing in unlimited-supply combinatorial auctions. From a machine learning perspective, these settings present several challenges: in particular, the “loss function” is discontinuous, is asymmetric, and has a large range. We address these issues in part by introducing a new form of covering-number bound that is especially well-suited to these problems and may be of independent interest.

Convergence Analysis and BER Performance of Finite-Length Turbo Codes

We propose the signal-to-noise ratio (SNR) transfer characteristic band (TCB) chart of extrinsic information (EI) as a basic tool for the probabilistic convergence analysis of iterative decoding. The proposed SNR TCB chart is a general version of the widely used SNR transfer chart, and it can model the behavior of EI in iterative decoding with any blocklength. We propose an algorithm using the SNR TCB chart to obtain the information, which is both quantitative and qualitative, on the probabilistic convergence behavior of iterative decoding. We also propose the bit-error rate (BER) estimate, in the form of a lower bound, of turbo codes over an additive white Gaussian noise channel. The proposed estimate is especially useful in estimating the BER of finite-length turbo codes in a waterfall region, while it is meaningful for all blocklengths and all Eb/N0

Stable Laws and the Present Value of Fixed Cash Flows

In this paper, the authors consider the present value of a series of fixed cash flows under stochastic interest rates. To model these interest rates, they don’t use the common lognormal model, but stable laws, which better fit in with reality. Their main intention is to derive a result for the distribution function of such a present value. However, due to the dependencies between successive discounted payments, the calculation of an exact analytical distribution is impossible. Therefore, use is made of the methodology of comonotonic random variables and the convex ordering of risks, introduced by the same authors in some previous papers. The present paper starts with a brief overview of properties and features of stable laws, and of the possible application of the concept of convex ordering to sums of risks, which is also the situation for a present value of future payments. Afterwards, the authors show how, for the present value under investigation, an approximation in the form of a convex upper bound can be derived. This upper bound has an easier structure than the original present value, and they derive elegant calculation formulas for the distribution of this bound. Finally, they provide some numerical examples that illustrate the precision of the approximation. Due to the design of the present value and the construction of the upper bound, these illustrations show great promise concerning the accuracy of the approximation.

Time-space trade-off lower bounds for randomized computation of decision problems

We prove the first time-space lower bound trade-offs for randomized computation of decision problems. The bounds hold even in the case that the computation is allowed to have arbitrary probability of error on a small fraction of inputs. Our techniques are extension of those used by Ajtai and by Beame, Jayram, and Saks that applied to deterministic branching programs. Our results also give a quantitative improvement over the previous results.Previous time-space trade-off results for decision problems can be divided naturally into results for functions with Boolean domain , that is, each input variable is {0,1}-valued, and the case of large domain , where each input variable takes on values from a set whose size grows with the number of variables.In the case of Boolean domain, Ajtai exhibited an explicit class of functions, and proved that any deterministic Boolean branching program or RAM using space S = o ( n ) requires superlinear time T to compute them. The functional form of the superlinear bound is not given in his paper, but optimizing the parameters in his arguments gives T = Ω( n log log n /log log log n ) for S = O ( n 1-ϵ ). For the same functions considered by Ajtai, we prove a time-space trade-off (for randomized branching programs with error) of the form T = Ω( n √ log( n/S )/log log ( n/S )). In particular, for space O ( n 1-ϵ ), this improves the lower bound on time to Ω( n √ log n /log log n ).In the large domain case, we prove lower bounds of the form T = Ω( n √ log( n/S )/log log ( n/S )) for randomized computation of the element distinctness function and lower bounds of the form T = Ω( n log ( n/S )) for randomized computation of Ajtai's Hamming closeness problem and of certain functions associated with quadratic forms over large fields.

Kekuatan Mengikat UDHR 1948 terhadap Negara Anggota PBB, Khususnya Indonesia

Although, the Constitution of Human Rights 1948 accepted by General Assembly of the United Nations on December 10 1948 does not have a tightening power yurisdically, it has a more tightening power in the form of moral bound. This is due to an assumption issued by civilized nations of the United Nation members that the contain of the Article of Human Rights constitutes a minimum standard for human rights. Indonesia, which was admitted as a member of the United Nations after the Article of Human Rights 1948 issued, has morally responsible for this point. Therefore, this issue was also stated in the Temporary Constitution of the Republic of lndonesia 1950, and has been reflected on the 1945 Constitution following other regulations.

On Four-Connecting a Triconnected Graph

We consider the problem of finding a smallest set of edges whose addition four-connects a triconnected graph. This is a fundamental graph-theoretic problem that has applications in designing reliable networks and improving statistical database security. We present an O(n·α(m,n)+m)-time algorithm for four-connecting an undirected graph G that is triconnected by adding the smallest number of edges, where n and m are the number of vertices and edges in G, respectively, and α(m,n) is the inverse Ackermann function. This is the first polynomial time algorithm to solve this problem exactly.In deriving our algorithm, we present a new lower bound for the number of edges needed to four-connect a triconnected graph. The form of this lower bound is different from the form of the lower bound known for biconnectivity augmentation and triconnectivity augmentation. Our new lower bound applies for arbitrary k and gives a tighter lower bound than the one known earlier for the number of edges needed to k-connect a (k−1)-connected graph. For k=4, we show that this lower bound is tight by giving an efficient algorithm to find a set of edges whose size equals the new lower bound and whose addition four-connects the input triconnected graph.

Confidence bounds for neural network representations

With the continuing strategic interest in the application of neural networks for inferential estimation across a range of industrial processes, it is desirable that some form of confidence bound is placed upon the resulting predictions. In this paper, a novel method for the calculation of confidence bounds for feedforward neural network models is proposed. Once the model structure has been determined, the two important factors that determine prediction reliability are (i) the accuracy of the neural network to predict the unknown data and (ii) the distribution of the available training data. These two factors are taken into consideration in the derivation of the confidence bounds presented here. The new technique is then applied to the modelling of specific quality variables in a batch polymerisation process. Encouraging results have been achieved.

Orthomodularity and quadratic transformations in probabilistic theories of physics

A characterization of orthomodularity of a set of effects is given in terms of a triangle closedness of this set. This leads to a simple (probabilistic) characterization of observables with a Boolean range. Quadratic transformations on expectation functionals of observables are studied in order to investigate the derivability of the Heisenberg inequality and the form of the lower bound of such an inequality for a pair of observables.