Probabilistic Analysis of Facility Location on Random Shortest Path Metrics

The facility location problem is an NP-hard optimization problem. Therefore, approximation algorithms are often used to solve large instances. Such algorithms often perform much better than worst-case analysis suggests. Therefore, probabilistic analysis is a widely used tool to analyze such algorithms. Most research on probabilistic analysis of NP-hard optimization problems involving metric spaces, such as the facility location problem, has been focused on Euclidean instances, and also instances with independent (random) edge lengths, which are non-metric, have been researched. We would like to extend this knowledge to other, more general, metrics. We investigate the facility location problem using random shortest path metrics. We analyze some probabilistic properties for a simple greedy heuristic which gives a solution to the facility location problem: opening the $\kappa$ cheapest facilities (with $\kappa$ only depending on the facility opening costs). If the facility opening costs are such that $\kappa$ is not too large, then we show that this heuristic is asymptotically optimal. On the other hand, for large values of $\kappa$, the analysis becomes more difficult, and we provide a closed-form expression as upper bound for the expected approximation ratio. In the special case where all facility opening costs are equal this closed-form expression reduces to $O(\sqrt[4]{\ln(n)})$ or $O(1)$ or even $1+o(1)$ if the opening costs are sufficiently small.Comment: A preliminary version accepted to CiE 201

Probabilistic Analysis of Optimization Problems on Generalized Random Shortest Path Metrics

Simple heuristics often show a remarkable performance in practice for optimization problems. Worst-case analysis often falls short of explaining this performance. Because of this, "beyond worst-case analysis" of algorithms has recently gained a lot of attention, including probabilistic analysis of algorithms. The instances of many optimization problems are essentially a discrete metric space. Probabilistic analysis for such metric optimization problems has nevertheless mostly been conducted on instances drawn from Euclidean space, which provides a structure that is usually heavily exploited in the analysis. However, most instances from practice are not Euclidean. Little work has been done on metric instances drawn from other, more realistic, distributions. Some initial results have been obtained by Bringmann et al. (Algorithmica, 2013), who have used random shortest path metrics on complete graphs to analyze heuristics. The goal of this paper is to generalize these findings to non-complete graphs, especially Erd\H{o}s-R\'enyi random graphs. A random shortest path metric is constructed by drawing independent random edge weights for each edge in the graph and setting the distance between every pair of vertices to the length of a shortest path between them with respect to the drawn weights. For such instances, we prove that the greedy heuristic for the minimum distance maximum matching problem, the nearest neighbor and insertion heuristics for the traveling salesman problem, and a trivial heuristic for the $k$-median problem all achieve a constant expected approximation ratio. Additionally, we show a polynomial upper bound for the expected number of iterations of the 2-opt heuristic for the traveling salesman problem.Comment: An extended abstract appeared in the proceedings of WALCOM 201

Npas4 is activated by melatonin, and drives the clock gene Cry1 in the ovine pars tuberalis

Seasonal mammalsintegrate changes in the duration of nocturnal melatonin secretion to drive annual physiologic cycles. Melatonin receptors within the proximal pituitary region, the pars tuberalis (PT), are essential in regulating seasonal neuroendocrine responses. In the ovine PT, melatonin is known to influence acute changes in transcriptional dynamics coupled to the onset (dusk) and offset (dawn) of melatonin secretion, leading to a potential interval-timing mechanism capable of decoding changes in day length (photoperiod). Melatonin offset at dawn is linked to cAMP accumulation, which directly induces transcription of the clock gene Per1. The rise of melatonin at dusk induces a separate and distinct cohort, including the clock-regulated genes Cry1 and Nampt, but little is known of the upstream mechanisms involved. Here, we used next-generation sequencing of the ovine PT transcriptome at melatonin onset and identified Npas4 as a rapidly induced basic helix-loop-helix Per-Arnt-Sim domain transcription factor. In vivo we show nuclear localization of NPAS4 protein in presumptive melatonin target cells of the PT (α-glycoprotein hormone-expressing cells), whereas in situ hybridization studies identified acute and transient expression in the PT of Npas4 in response to melatonin. In vitro, NPAS4 forms functional dimers with basic helix loop helix-PAS domain cofactors aryl hydrocarbon receptor nuclear translocator (ARNT), ARNT2, and ARNTL, transactivating both Cry1 and Nampt ovine promoter reporters. Using a combination of 5'-deletions and site-directed mutagenesis, we show NPAS4-ARNT transactivation to be codependent upon two conserved central midline elements within the Cry1 promoter. Our data thus reveal NPAS4 as a candidate immediate early-response gene in the ovine PT, driving molecular responses to melatonin

A Tonnetz Model for pentachords

This article deals with the construction of surfaces that are suitable for representing pentachords or 5-pitch segments that are in the same $T/I$ class. It is a generalization of the well known \"Ottingen-Riemann torus for triads of neo-Riemannian theories. Two pentachords are near if they differ by a particular set of contextual inversions and the whole contextual group of inversions produces a Tiling (Tessellation) by pentagons on the surfaces. A description of the surfaces as coverings of a particular Tiling is given in the twelve-tone enharmonic scale case.Comment: 27 pages, 12 figure

Minsky machines and algorithmic problems

This is a survey of using Minsky machines to study algorithmic problems in semigroups, groups and other algebraic systems.Comment: 19 page

Allocating the Burdens of Climate Action: Consumption-Based Carbon Accounting and the Polluter-Pays Principle

Action must be taken to combat climate change. Yet, how the costs of climate action should be allocated among states remains a question. One popular answer—the polluter-pays principle (PPP)—stipulates that those responsible for causing the problem should pay to address it. While intuitively plausible, the PPP has been subjected to withering criticism in recent years. It is timely, following the Paris Agreement, to develop a new version: one that does not focus on historical production-based emissions but rather allocates climate burdens in proportion to each state’s annual consumption-based emissions. This change in carbon accounting results in a fairer and more environmentally effective principle for distributing climate duties

Delivery of sTRAIL variants by MSCs in combination with cytotoxic drug treatment leads to p53-independent enhanced antitumor effects

Mesenchymal stem cells (MSCs) are able to infiltrate tumor tissues and thereby effectively deliver gene therapeutic payloads. Here, we engineered murine MSCs (mMSCs) to express a secreted form of the TNF-related apoptosis-inducing ligand (TRAIL), which is a potent inducer of apoptosis in tumor cells, and tested these MSCs, termed MSC.sTRAIL, in combination with conventional chemotherapeutic drug treatment in colon cancer models. When we pretreated human colorectal cancer HCT116 cells with low doses of 5-fluorouracil (5-FU) and added MSC.sTRAIL, we found significantly increased apoptosis as compared with single-agent treatment. Moreover, HCT116 xenografts, which were cotreated with 5-FU and systemically delivered MSC.sTRAIL, went into remission. Noteworthy, this effect was protein 53 (p53) independent and was mediated by TRAIL-receptor 2 (TRAIL-R2) upregulation, demonstrating the applicability of this approach in p53-defective tumors. Consequently, when we generated MSCs that secreted TRAIL-R2-specific variants of soluble TRAIL (sTRAIL), we found that such engineered MSCs, labeled MSC.sTRAIL DR5, had enhanced antitumor activity in combination with 5-FU when compared with MSC.sTRAIL. In contrast, TRAIL-resistant pancreatic carcinoma PancTu1 cells responded better to MSC.sTRAIL DR4 when the antiapoptotic protein XIAP (X-linked inhibitor of apoptosis protein) was silenced concomitantly. Taken together, our results demonstrate that TRAIL-receptor selective variants can potentially enhance the therapeutic efficacy of MSC-delivered TRAIL as part of individualized and tumor-specific combination treatments. © 2013 Macmillan Publishers Limited All rights reserved

The gray matter volume of the amygdala is correlated with the perception of melodic intervals: a voxel-based morphometry study

Music is not simply a series of organized pitches, rhythms, and timbres, it is capable of evoking emotions. In the present study, voxel-based morphometry (VBM) was employed to explore the neural basis that may link music to emotion. To do this, we identified the neuroanatomical correlates of the ability to extract pitch interval size in a music segment (i.e., interval perception) in a large population of healthy young adults (N = 264). Behaviorally, we found that interval perception was correlated with daily emotional experiences, indicating the intrinsic link between music and emotion. Neurally, and as expected, we found that interval perception was positively correlated with the gray matter volume (GMV) of the bilateral temporal cortex. More important, a larger GMV of the bilateral amygdala was associated with better interval perception, suggesting that the amygdala, which is the neural substrate of emotional processing, is also involved in music processing. In sum, our study provides one of first neuroanatomical evidence on the association between the amygdala and music, which contributes to our understanding of exactly how music evokes emotional responses

Sensory Electrical Stimulation Improves Foot Placement during Targeted Stepping Post-Stroke

Proper foot placement is vital for maintaining balance during walking, requiring the integration of multiple sensory signals with motor commands. Disruption of brain structures post-stroke likely alters the processing of sensory information by motor centers, interfering with precision control of foot placement and walking function for stroke survivors. In this study, we examined whether somatosensory stimulation, which improves functional movements of the paretic hand, could be used to improve foot placement of the paretic limb. Foot placement was evaluated before, during, and after application of somatosensory electrical stimulation to the paretic foot during a targeted stepping task. Starting from standing, twelve chronic stroke participants initiated movement with the non-paretic limb and stepped to one of five target locations projected onto the floor with distances normalized to the paretic stride length. Targeting error and lower extremity kinematics were used to assess changes in foot placement and limb control due to somatosensory stimulation. Significant reductions in placement error in the medial–lateral direction (p = 0.008) were observed during the stimulation and post-stimulation blocks. Seven participants, presenting with a hip circumduction walking pattern, had reductions (p = 0.008) in the magnitude and duration of hip abduction during swing with somatosensory stimulation. Reductions in circumduction correlated with both functional and clinical measures, with larger improvements observed in participants with greater impairment. The results of this study suggest that somatosensory stimulation of the paretic foot applied during movement can improve the precision control of foot placement

Identifying component modules

A computer-based system for modelling component dependencies and identifying component modules is presented. A variation of the Dependency Structure Matrix (DSM) representation was used to model component dependencies. The system utilises a two-stage approach towards facilitating the identification of a hierarchical modular structure. The first stage calculates a value for a clustering criterion that may be used to group component dependencies together. A Genetic Algorithm is described to optimise the order of the components within the DSM with the focus of minimising the value of the clustering criterion to identify the most significant component groupings (modules) within the product structure. The second stage utilises a 'Module Strength Indicator' (MSI) function to determine a value representative of the degree of modularity of the component groupings. The application of this function to the DSM produces a 'Module Structure Matrix' (MSM) depicting the relative modularity of available component groupings within it. The approach enabled the identification of hierarchical modularity in the product structure without the requirement for any additional domain specific knowledge within the system. The system supports design by providing mechanisms to explicitly represent and utilise component and dependency knowledge to facilitate the nontrivial task of determining near-optimal component modules and representing product modularity