The General N-Location Distribution Problem

This paper studies the one-period, general network distribution problem with linear costs. The approach is to decompose the problem into a transportation problem that represents a stocking decision, and decoupled newsboy problems that represent the realization of demand with the usual associated holding and shortage costs. This approach leads to a characterization of optimal policies in terms of the dual of the transportation problem. Specifically, it is shown that there is a correspondence between the optimal policies and the extreme points, edges, faces etc. of the dual feasible region. This method is not directly suitable for the solution of large problems but the exact solution for small problems can be obtained. It is shown that the three location case involves 37 policies as compared to seven for the two location case. For the numerical solutions of large problems, the problem has been formulated as a linear program with column generation. This latter approach is quite robust in the sense that it is easily extended to incorporate capacity constraints and the multiproduct case. Extensions of this work are briefly discussed.Supported in part by the Office o Naval Research under contract 67-A-0204-007

Random Costs in Combinatorial Optimization

The random cost problem is the problem of finding the minimum in an exponentially long list of random numbers. By definition, this problem cannot be solved faster than by exhaustive search. It is shown that a classical NP-hard optimization problem, number partitioning, is essentially equivalent to the random cost problem. This explains the bad performance of heuristic approaches to the number partitioning problem and allows us to calculate the probability distributions of the optimum and sub-optimum costs.Comment: 4 pages, Revtex, 2 figures (eps), submitted to PR

Efficacy and Tolerability of Intramuscular Dexketoprofen in Postoperative Pain Management following Hernia Repair Surgery

Objective. To evaluate the safety and efficacy of intramuscular dexketoprofen for postoperative pain in patients undergoing hernia surgery. Methodology. Total 202 patients received single intramuscular injection of dexketoprofen 50 mg or diclofenac 50 mg postoperatively. The pain intensity (PI) was self-evaluated by patients on VAS at baseline 1, 2, 4, 6, and 8 hours. The efficacy parameters were number of responders, difference in PI (PID) at 8 hours, sum of analogue of pain intensity differences (SAPID), and onset and duration of analgesia. Tolerability assessment was done by global evaluation and adverse events in each group. Results. Dexketoprofen showed superior efficacy in terms of number of responders (P = .007), PID at 8 hours (P = .02), and SAPID 0–8 hours (P < .0001). It also showed faster onset of action (42 minutes) and longer duration of action (6.5 hours). The adverse events were comparable in both groups. Conclusion. Single dose of dexketoprofen trometamol 50 mg given intramuscularly provided faster, better, and longer duration of analgesia in postoperative patients of hernia repair surgery than diclofenac 50 mg, with comparable safety

Distortions of Subjective Time Perception Within and Across Senses

Background: The ability to estimate the passage of time is of fundamental importance for perceptual and cognitive processes. One experience of time is the perception of duration, which is not isomorphic to physical duration and can be distorted by a number of factors. Yet, the critical features generating these perceptual shifts in subjective duration are not understood. Methodology/Findings: We used prospective duration judgments within and across sensory modalities to examine the effect of stimulus predictability and feature change on the perception of duration. First, we found robust distortions of perceived duration in auditory, visual and auditory-visual presentations despite the predictability of the feature changes in the stimuli. For example, a looming disc embedded in a series of steady discs led to time dilation, whereas a steady disc embedded in a series of looming discs led to time compression. Second, we addressed whether visual (auditory) inputs could alter the perception of duration of auditory (visual) inputs. When participants were presented with incongruent audio-visual stimuli, the perceived duration of auditory events could be shortened or lengthened by the presence of conflicting visual information; however, the perceived duration of visual events was seldom distorted by the presence of auditory information and was never perceived shorter than their actual durations. Conclusions/Significance: These results support the existence of multisensory interactions in the perception of duration and, importantly, suggest that vision can modify auditory temporal perception in a pure timing task. Insofar as distortions in subjective duration can neither be accounted for by the unpredictability of an auditory, visual or auditory-visual event, we propose that it is the intrinsic features of the stimulus that critically affect subjective time distortions

Magnetic control of large room-temperature polarization

Numerous authors have referred to room-temperature magnetic switching of large electric polarizations as The Holy Grail of magnetoelectricity.We report this long-sought effect using a new physical process of coupling between magnetic and ferroelectric relaxor nano-regions. Here we report magnetic switching between the normal ferroelectric state and the ferroelectric relaxor state. This gives both a new room-temperature, single-phase, multiferroic magnetoelectric, PbZr0.46Ti0.34Fe0.13W0.07O3, with polarization, loss (<4%), and resistivity (typically 108 -109 ohm.cm) equal to or superior to BiFeO3, and also a new and very large magnetoelectric effect: switching not from +Pr to negative Pr with applied H, but from Pr to zero with applied H of less than a Tesla. This switching of the polarization occurs not because of a conventional magnetically induced phase transition, but because of dynamic effects: Increasing H lengthens the relaxation time by x500 from 100 ?s, and it couples strongly the polarization relaxation and spin relaxations. The diverging polarization relaxation time accurately fits a modified Vogel-Fulcher Equation in which the freezing temperature Tf is replaced by a critical freezing field Hf that is 0.92 positive/negative 0.07 Tesla. This field dependence and the critical field Hc are derived analytically from the spherical random bond random field (SRBRF) model with no adjustable parameters and an E2H2 coupling. This device permits 3-state logic (+Pr,0,negative Pr) and a condenser with >5000% magnetic field change in its capacitance.Comment: 20 pages, 5 figure

Phase transition and landscape statistics of the number partitioning problem

The phase transition in the number partitioning problem (NPP), i.e., the transition from a region in the space of control parameters in which almost all instances have many solutions to a region in which almost all instances have no solution, is investigated by examining the energy landscape of this classic optimization problem. This is achieved by coding the information about the minimum energy paths connecting pairs of minima into a tree structure, termed a barrier tree, the leaves and internal nodes of which represent, respectively, the minima and the lowest energy saddles connecting those minima. Here we apply several measures of shape (balance and symmetry) as well as of branch lengths (barrier heights) to the barrier trees that result from the landscape of the NPP, aiming at identifying traces of the easy/hard transition. We find that it is not possible to tell the easy regime from the hard one by visual inspection of the trees or by measuring the barrier heights. Only the {\it difficulty} measure, given by the maximum value of the ratio between the barrier height and the energy surplus of local minima, succeeded in detecting traces of the phase transition in the tree. In adddition, we show that the barrier trees associated with the NPP are very similar to random trees, contrasting dramatically with trees associated with the $p$ spin-glass and random energy models. We also examine critically a recent conjecture on the equivalence between the NPP and a truncated random energy model

Analysis of the intraspinal calcium dynamics and its implications on the plasticity of spiking neurons

The influx of calcium ions into the dendritic spines through the N-metyl-D-aspartate (NMDA) channels is believed to be the primary trigger for various forms of synaptic plasticity. In this paper, the authors calculate analytically the mean values of the calcium transients elicited by a spiking neuron undergoing a simple model of ionic currents and back-propagating action potentials. The relative variability of these transients, due to the stochastic nature of synaptic transmission, is further considered using a simple Markov model of NMDA receptos. One finds that both the mean value and the variability depend on the timing between pre- and postsynaptic action-potentials. These results could have implications on the expected form of synaptic-plasticity curve and can form a basis for a unified theory of spike time-dependent, and rate based plasticity.Comment: 14 pages, 10 figures. A few changes in section IV and addition of a new figur

An update on the Hirsch conjecture

The Hirsch conjecture was posed in 1957 in a letter from Warren M. Hirsch to George Dantzig. It states that the graph of a d-dimensional polytope with n facets cannot have diameter greater than n - d. Despite being one of the most fundamental, basic and old problems in polytope theory, what we know is quite scarce. Most notably, no polynomial upper bound is known for the diameters that are conjectured to be linear. In contrast, very few polytopes are known where the bound $n-d$ is attained. This paper collects known results and remarks both on the positive and on the negative side of the conjecture. Some proofs are included, but only those that we hope are accessible to a general mathematical audience without introducing too many technicalities.Comment: 28 pages, 6 figures. Many proofs have been taken out from version 2 and put into the appendix arXiv:0912.423