Cake Cutting Algorithms for Piecewise Constant and Piecewise Uniform Valuations

Cake cutting is one of the most fundamental settings in fair division and mechanism design without money. In this paper, we consider different levels of three fundamental goals in cake cutting: fairness, Pareto optimality, and strategyproofness. In particular, we present robust versions of envy-freeness and proportionality that are not only stronger than their standard counter-parts but also have less information requirements. We then focus on cake cutting with piecewise constant valuations and present three desirable algorithms: CCEA (Controlled Cake Eating Algorithm), MEA (Market Equilibrium Algorithm) and CSD (Constrained Serial Dictatorship). CCEA is polynomial-time, robust envy-free, and non-wasteful. It relies on parametric network flows and recent generalizations of the probabilistic serial algorithm. For the subdomain of piecewise uniform valuations, we show that it is also group-strategyproof. Then, we show that there exists an algorithm (MEA) that is polynomial-time, envy-free, proportional, and Pareto optimal. MEA is based on computing a market-based equilibrium via a convex program and relies on the results of Reijnierse and Potters [24] and Devanur et al. [15]. Moreover, we show that MEA and CCEA are equivalent to mechanism 1 of Chen et. al. [12] for piecewise uniform valuations. We then present an algorithm CSD and a way to implement it via randomization that satisfies strategyproofness in expectation, robust proportionality, and unanimity for piecewise constant valuations. For the case of two agents, it is robust envy-free, robust proportional, strategyproof, and polynomial-time. Many of our results extend to more general settings in cake cutting that allow for variable claims and initial endowments. We also show a few impossibility results to complement our algorithms.Comment: 39 page

Social Welfare in One-sided Matching Markets without Money

We study social welfare in one-sided matching markets where the goal is to efficiently allocate n items to n agents that each have a complete, private preference list and a unit demand over the items. Our focus is on allocation mechanisms that do not involve any monetary payments. We consider two natural measures of social welfare: the ordinal welfare factor which measures the number of agents that are at least as happy as in some unknown, arbitrary benchmark allocation, and the linear welfare factor which assumes an agent's utility linearly decreases down his preference lists, and measures the total utility to that achieved by an optimal allocation. We analyze two matching mechanisms which have been extensively studied by economists. The first mechanism is the random serial dictatorship (RSD) where agents are ordered in accordance with a randomly chosen permutation, and are successively allocated their best choice among the unallocated items. The second mechanism is the probabilistic serial (PS) mechanism of Bogomolnaia and Moulin [8], which computes a fractional allocation that can be expressed as a convex combination of integral allocations. The welfare factor of a mechanism is the infimum over all instances. For RSD, we show that the ordinal welfare factor is asymptotically 1/2, while the linear welfare factor lies in the interval [.526, 2/3]. For PS, we show that the ordinal welfare factor is also 1/2 while the linear welfare factor is roughly 2/3. To our knowledge, these results are the first non-trivial performance guarantees for these natural mechanisms

Social Welfare in One-Sided Matching Mechanisms

We study the Price of Anarchy of mechanisms for the well-known problem of one-sided matching, or house allocation, with respect to the social welfare objective. We consider both ordinal mechanisms, where agents submit preference lists over the items, and cardinal mechanisms, where agents may submit numerical values for the items being allocated. We present a general lower bound of $\Omega(\sqrt{n})$ on the Price of Anarchy, which applies to all mechanisms. We show that two well-known mechanisms, Probabilistic Serial, and Random Priority, achieve a matching upper bound. We extend our lower bound to the Price of Stability of a large class of mechanisms that satisfy a common proportionality property, and show stronger bounds on the Price of Anarchy of all deterministic mechanisms

Clinicopathologic Characteristics of Stomach Cancer among Patients Admitted to the Surgical Departments of Teaching Hospitals in Sana'a, Yemen

Objective: To describe the characteristics of stomach cancer among patients admitted to the surgical departments of teaching hospitals in Sana’a city, Yemen. Methods: This retrospective, descriptive study was conducted to identify the characteristics of stomach cancer among patients admitted to the surgical departments of two major teaching hospitals in Sana’a; namely, Kuwait University Hospital of Sana’a University and University of Science & Technology Hospital, in the period from January 2011 to June 2015. Sociodemographic and clinical data in addition to the characteristics of stomach cancer among 106 documented cases admitted over the study period were retrieved from the medical records and analyzed. Results: Of the stomach cancer patients admitted over the study period, 55.7% were males and 52.8% were aged 50–70 years old. The most frequent symptom was dyspepsia (96.2%) followed by weight loss (88.7%) and loss of appetite (81.1%). Dysphagia was present in 56.6% of the patients, while upper and lower gastrointestinal bleedings were present in 15.1% and 6.0% of the patients, respectively. Palpable masses were present among 35.8% of the patients, being most frequently observed in the pylorus and antrum (22.1%) and the body of the stomach (18.9%) as revealed by abdominal computed tomography. Regarding the histopathologic findings of endoscopic biopsies, tumors were well-differentiated in 32.1% and moderately or poorly differentiated in 26.4% of the patients each. However, moderately-to-poorly differentiated and lymphoma were less frequent (5.7%, each) and the gastrointestinal stromal tumor was observed in 1.9% of the patients. Conclusions: Clinicopathologic characteristics of stomach cancer among Yemeni patients are consistent with those documented internationally

Classical generalized constant coupling model for geometrically frustrated antiferromagnets

A generalized constant coupling approximation for classical geometrically frustrated antiferromagnets is presented. Starting from a frustrated unit we introduce the interactions with the surrounding units in terms of an internal effective field which is fixed by a self consistency condition. Results for the magnetic susceptibility and specific heat are compared with Monte Carlo data for the classical Heisenberg model for the pyrochlore and kagome lattices. The predictions for the susceptibility are found to be essentially exact, and the corresponding predictions for the specific heat are found to be in very good agreement with the Monte Carlo results.Comment: 4 pages, 3 figures, 2 columns. Discussion about the zero T value of the pyrochlore specific heat correcte

Trafficking activity of myosin XXI is required in assembly of Leishmania flagellum

Actin-based myosin motors have a pivotal role in intracellular trafficking in eukaryotic cells. The parasitic protozoan organism Leishmania expresses a novel class of myosin, myosin XXI (Myo21), which is preferentially localized at the proximal region of the flagellum. However, its function in this organism remains largely unknown. Here, we show that Myo21 interacts with actin, and its expression is dependent of the growth stage. We further reveal that depletion of Myo21 levels results in impairment of the flagellar assembly and intracellular trafficking. These defects are, however, reversed by episomal complementation. Additionally, it is shown that deletion of the Myo21 gene leads to generation of ploidy, suggesting an essential role of Myo21 in survival of Leishmania cells. Together, these results indicate that actin-dependent trafficking activity of Myo21 is essentially required during assembly of the Leishmania flagellum

Differential Expression of Proteoglycans in Tissue Remodeling and Lymphangiogenesis after Experimental Renal Transplantation in Rats

BACKGROUND: Chronic transplant dysfunction explains the majority of late renal allograft loss and is accompanied by extensive tissue remodeling leading to transplant vasculopathy, glomerulosclerosis and interstitial fibrosis. Matrix proteoglycans mediate cell-cell and cell-matrix interactions and play key roles in tissue remodeling. The aim of this study was to characterize differential heparan sulfate proteoglycan and chondroitin sulfate proteoglycan expression in transplant vasculopathy, glomerulosclerosis and interstitial fibrosis in renal allografts with chronic transplant dysfunction. METHODS: Renal allografts were transplanted in the Dark Agouti-to-Wistar Furth rat strain combination. Dark Agouti-to-Dark Agouti isografts and non-transplanted Dark Agouti kidneys served as controls. Allograft and isograft recipients were sacrificed 66 and 81 days (mean) after transplantation, respectively. Heparan sulfate proteoglycan (collXVIII, perlecan and agrin) and chondroitin sulfate proteoglycan (versican) expression, as well as CD31 and LYVE-1 (vascular and lymphatic endothelium, respectively) expression were (semi-) quantitatively analyzed using immunofluorescence. FINDINGS: Arteries with transplant vasculopathy and sclerotic glomeruli in allografts displayed pronounced neo-expression of collXVIII and perlecan. In contrast, in interstitial fibrosis expression of the chondroitin sulfate proteoglycan versican dominated. In the cortical tubular basement membranes in both iso- and allografts, induction of collXVIII was detected. Allografts presented extensive lymphangiogenesis (p<0.01 compared to isografts and non-transplanted controls), which was associated with induced perlecan expression underneath the lymphatic endothelium (p<0.05 and p<0.01 compared to isografts and non-transplanted controls, respectively). Both the magnitude of lymphangiogenesis and perlecan expression correlated with severity of interstitial fibrosis and impaired graft function. INTERPRETATION: Our results reveal that changes in the extent of expression and the type of proteoglycans being expressed are tightly associated with tissue remodeling after renal transplantation. Therefore, proteoglycans might be potential targets for clinical intervention in renal chronic transplant dysfunction

The First National Study of Neighborhood Parks

An extensive infrastructure of neighborhood parks supports leisure time physical activity in most U.S. cities; yet, most Americans do not meet national guidelines for physical activity. Neighborhood parks have never been assessed nationally to identify their role in physical activity

Diabetes Alters Contraction-Induced Mitogen Activated Protein Kinase Activation in the Rat Soleus and Plantaris

The prescription of anaerobic exercise has recently been advocated for the management of diabetes; however exercise-induced signaling in diabetic muscle remains largely unexplored. Evidence from exercise studies in nondiabetics suggests that the extracellular-signal-regulated kinases (Erk1/2), p38, and c-JUN NH2-terminal kinase (Jnk) mitogen-activated protein kinases (MAPKs) are important regulators of muscle adaptation. Here, we compare the basal and the in situ contraction-induced phosphorylation of Erk1/2- p38- and Jnk-MAPK and their downstream targets (p90rsk and MAPKAP-K2) in the plantaris and soleus muscles of normal and obese (fa/fa) Zucker rats. Compared to lean animals, the time course and magnitude of Erk1/2, p90rsk and p38 phosphorylation to a single bout of contractile stimuli were greater in the plantaris of obese animals. Jnk phosphorylation in response to contractile stimuli was muscle-type dependent with greater increases in the plantaris than the soleus. These results suggest that diabetes alters intramuscular signaling processes in response to a contractile stimulus