168 research outputs found
Optimal Composition Ordering Problems for Piecewise Linear Functions
In this paper, we introduce maximum composition ordering problems. The input
is real functions and a constant
. We consider two settings: total and partial compositions. The
maximum total composition ordering problem is to compute a permutation
which maximizes , where .
The maximum partial composition ordering problem is to compute a permutation
and a nonnegative integer which maximize
.
We propose time algorithms for the maximum total and partial
composition ordering problems for monotone linear functions , which
generalize linear deterioration and shortening models for the time-dependent
scheduling problem. We also show that the maximum partial composition ordering
problem can be solved in polynomial time if is of form
for some constants , and . We
finally prove that there exists no constant-factor approximation algorithm for
the problems, even if 's are monotone, piecewise linear functions with at
most two pieces, unless P=NP.Comment: 19 pages, 4 figure
Surrogate Optimization for p-Norms
In this paper, we study the effect of surrogate objective functions in optimization problems. We introduce surrogate ratio as a measure of such effect, where the surrogate ratio is the ratio between the optimal values of the original and surrogate objective functions.
We prove that the surrogate ratio is at most mu^{|1/p - 1/q|} when the objective functions are p- and q-norms, and the feasible region is a mu-dimensional space (i.e., a subspace of R^mu), a mu-intersection of matroids, or a mu-extendible system. We also show that this is the best possible bound. In addition, for mu-systems, we demonstrate that the ratio becomes mu^{1/p} when p q. Here, a mu-system is an independence system such that for any subset of ground set the ratio of the cardinality of the largest to the smallest maximal independent subset of it is at most mu. We further extend our results to the surrogate ratios for approximate solutions
Online Knapsack Problems with a Resource Buffer
In this paper, we introduce online knapsack problems with a resource buffer. In the problems, we are given a knapsack with capacity 1, a buffer with capacity R >= 1, and items that arrive one by one. Each arriving item has to be taken into the buffer or discarded on its arrival irrevocably. When every item has arrived, we transfer a subset of items in the current buffer into the knapsack. Our goal is to maximize the total value of the items in the knapsack. We consider four variants depending on whether items in the buffer are removable (i.e., we can remove items in the buffer) or non-removable, and proportional (i.e., the value of each item is proportional to its size) or general. For the general&non-removable case, we observe that no constant competitive algorithm exists for any R >= 1. For the proportional&non-removable case, we show that a simple greedy algorithm is optimal for every R >= 1. For the general&removable and the proportional&removable cases, we present optimal algorithms for small R and give asymptotically nearly optimal algorithms for general R
Towards Optimal Subsidy Bounds for Envy-freeable Allocations
We study the fair division of indivisible items with subsidies among
agents, where the absolute marginal valuation of each item is at most one.
Under monotone valuations (where each item is a good), Brustle et al. (2020)
demonstrated that a maximum subsidy of and a total subsidy of
are sufficient to guarantee the existence of an envy-freeable
allocation. In this paper, we improve upon these bounds, even in a wider model.
Namely, we show that, given an EF1 allocation, we can compute in polynomial
time an envy-free allocation with a subsidy of at most per agent and a
total subsidy of at most . Moreover, we present further improved
bounds for monotone valuations.Comment: 14page
The Outcome of Eating Disorders: Relapse, Childbirth, Postnatal Depression, Family Support
This study was aimed to identify eating disorder (ED) relapse, childbirth, postnatal depression,and the family support. Of the ED patients during treatment from 1994 to 2004,55 were pregnant and had ED recovery. Of them, 25 (21 Bulimia Nervosa (BN)and 4 Anorexia Nervosa (AN)) agreed to take part in this study. We interviewed them every 2 wk. both during the pregnancy and after childbirth. We also interviewed family members each month. The Eating Attitudes Test-26 (EAT-26) and Edinburgh Postnatal Depression Scale (EPDS) were helpful for diagnosing the EDs and postnatal depression. As the statistical analysis, We conducted t-test.67%relapsed ED while pregnant and 50%relapsed postnatal. In the non-relapse group, all the subjects had vaginal delivery and their infants were male. 50% of the subjects had postnatal depression. Non-Postnatal depression group had average body- weight infants. With regard to family support, there was no relationship between ED relapse and postnatal depression. We found that the rate of ED relapse and that of suffering from postnatal depression were remarkable in this group, suggesting the necessity for long-term follow-up for the EDs
A STUDY ON GROUP DYNAMICS OF THE FORMAL-INFORMAL RELATIONS IN A MAXIMUM SECURITY PRISON SOCIAL PSYCHOLOGY OF A COERCIVE ORGANIZATION
Effective meson masses, effective meson-nucleon couplings and neutron star radii
Using the generalized mean field theory, we have studied the relation among
the effective meson masses, the effective meson-nucleon couplings and the
equation of state (EOS) in asymmetric nuclear matter. If the effective
omega-meson mass becomes smaller at high density, the EOS becomes stiffer.
However, if we require that the omega-meson mean field is proportional to the
baryon density, the effective omega-nucleon coupling automatically becomes
smaller at the same time as the effective omega-meson mass becomes smaller.
Consequently, the EOS becomes softer. A similar relation is found for the
effective rho-meson mass and the effective rho-nucleon coupling. We have also
studied the relation among the effective meson masses, the effective
meson-nucleon couplings and a radius R of a neutron star. The R depends
somewhat on the value of the effective omega-meson mass and the effective
omega-nucleon coupling.Comment: 29pages, 24 figure
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