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

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

Room temperature reversible colossal volto-magnetic effect in all-oxide metallicmagnet/topotactic-phase-transition material heterostructures

Multiferroic materials have undergone extensive research in the past two decades in an effort to produce a sizable room-temperature magneto-electric (ME) effect in either exclusive or composite materials for use in a variety of electronic or spintronic devices. These studies have looked into the ME effect by switching the electric polarization by the magnetic field or switching the magnetism by the electric field. Here, an innovative way is developed to knot the functional properties based on the tremendous modulation of electronics and magnetization by the electric field of the topotactic phase transitions (TPT) in heterostructures composed of metallic-magnet/TPT-material. It is divulged that application of a nominal potential difference of 2-3 Volts induces gigantic changes in magnetization by 100-250% leading to colossal Voltomagnetic effect, which would be tremendously beneficial for low-power consumption applications in spintronics. Switching electronics and magnetism by inducing TPT through applying an electric field requires much less energy, making such TPT-based systems promising for energy-efficient memory and logic applications as well as opening a plethora of tremendous opportunities for applications in different domains

Bounds on the Complexity of Halfspace Intersections when the Bounded Faces have Small Dimension

We study the combinatorial complexity of D-dimensional polyhedra defined as the intersection of n halfspaces, with the property that the highest dimension of any bounded face is much smaller than D. We show that, if d is the maximum dimension of a bounded face, then the number of vertices of the polyhedron is O(n^d) and the total number of bounded faces of the polyhedron is O(n^d^2). For inputs in general position the number of bounded faces is O(n^d). For any fixed d, we show how to compute the set of all vertices, how to determine the maximum dimension of a bounded face of the polyhedron, and how to compute the set of bounded faces in polynomial time, by solving a polynomial number of linear programs

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

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

Orexin receptors exert a neuroprotective effect in Alzheimer's disease (AD) via heterodimerization with GPR103

Orexins are neuropeptides that regulate the sleep-wake cycle and feeding behaviour. QRFP is a newly discovered neuropeptide which exerts similar orexigenic activity, thus playing an important role in energy homeostasis and regulation of appetite. The exact expression and signalling characteristics and physiological actions of QRFP and its receptor GPR103 are poorly understood. Alzheimerâ €™ s disease (AD) patients experience increased nocturnal activity, excessive daytime sleepiness, and weight loss. We hypothesised therefore that orexins and QRFP might be implicated in the pathophysiology of AD. We report that the down-regulation of hippocampal orexin receptors (OXRs) and GPR103 particularly in the cornu ammonis (CA) subfield from AD patients suffering from early onset familial AD (EOFAD) and late onset familial AD (LOAD). Using an in vitro model we demonstrate that this downregulation is due to to Aβ-plaque formation and tau hyper-phosphorylation. Transcriptomics revealed a neuroprotective role for both orexins and QRFP. Finally we provide conclusive evidence using BRET and FRET that OXRs and GPR103 form functional hetero-dimers to exert their effects involving activation of ERK 1/2. Pharmacological intervention directed at the orexigenic system may prove to be an attractive avenue towards the discovery of novel therapeutics for diseases such as AD and improving neuroprotective signalling pathways

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

MR-trackable intramyocardial injection catheter

There is growing interest in delivering cellular agents to infarcted myocardium to prevent postinfarction left ventricular remodeling. MRI can be effectively used to differentiate infarcted from healthy myocardium. MR-guided delivery of cellular agents/therapeutics is appealing because the therapeutics can be precisely targeted to the desired location within the infarct. In this study, a steerable intramyocardial injection catheter that can be actively tracked under MRI was developed and tested. The components of the catheter were arranged to form a loopless RF antenna receiver coil that enabled active tracking. Feasibility studies were performed in canine and porcine myocardial infarction models. Myocardial delayed-enhancement (MDE) imaging identified the infarcted myocardium, and real-time MRI was used to guide left ventricular catheterization from a carotid artery approach. The distal 35 cm of the catheter was seen under MRI with a bright signal at the distal tip of the catheter. The catheter was steered into position, the distal tip was apposed against the infarct, the needle was advanced, and a bolus of MR contrast agent and tissue marker dye was injected intramyocardially, as confirmed by imaging and post-mortem histology. A pilot study involving intramyocardial delivery of magnetically labeled stem cells demonstrated the utility of the active injection catheter system. © 2004 Wiley-Liss, Inc

Knowledge-based energy functions for computational studies of proteins

This chapter discusses theoretical framework and methods for developing knowledge-based potential functions essential for protein structure prediction, protein-protein interaction, and protein sequence design. We discuss in some details about the Miyazawa-Jernigan contact statistical potential, distance-dependent statistical potentials, as well as geometric statistical potentials. We also describe a geometric model for developing both linear and non-linear potential functions by optimization. Applications of knowledge-based potential functions in protein-decoy discrimination, in protein-protein interactions, and in protein design are then described. Several issues of knowledge-based potential functions are finally discussed.Comment: 57 pages, 6 figures. To be published in a book by Springe