Computing the Least-core and Nucleolus for Threshold Cardinality Matching Games

Cooperative games provide a framework for fair and stable profit allocation in multi-agent systems. \emph{Core}, \emph{least-core} and \emph{nucleolus} are such solution concepts that characterize stability of cooperation. In this paper, we study the algorithmic issues on the least-core and nucleolus of threshold cardinality matching games (TCMG). A TCMG is defined on a graph $G=(V,E)$ and a threshold $T$, in which the player set is $V$ and the profit of a coalition $S\subseteq V$ is 1 if the size of a maximum matching in $G[S]$ meets or exceeds $T$, and 0 otherwise. We first show that for a TCMG, the problems of computing least-core value, finding and verifying least-core payoff are all polynomial time solvable. We also provide a general characterization of the least core for a large class of TCMG. Next, based on Gallai-Edmonds Decomposition in matching theory, we give a concise formulation of the nucleolus for a typical case of TCMG which the threshold $T$ equals $1$. When the threshold $T$ is relevant to the input size, we prove that the nucleolus can be obtained in polynomial time in bipartite graphs and graphs with a perfect matching

Disorderless quasi-localization of polar gases in one-dimensional lattices

One-dimensional polar gases in deep optical lattices present a severely constrained dynamics due to the interplay between dipolar interactions, energy conservation, and finite bandwidth. The appearance of dynamically-bound nearest-neighbor dimers enhances the role of the $1/r^3$ dipolar tail, resulting, in the absence of external disorder, in quasi-localization via dimer clustering for very low densities and moderate dipole strengths. Furthermore, even weak dipoles allow for the formation of self-bound superfluid lattice droplets with a finite doping of mobile, but confined, holons. Our results, which can be extrapolated to other power-law interactions, are directly relevant for current and future lattice experiments with magnetic atoms and polar molecules.Comment: 5 + 2 Page

Period halving of Persistent Currents in Mesoscopic Mobius ladders

We investigate the period halving of persistent currents(PCs) of non-interacting electrons in isolated mesoscopic M\"{o}bius ladders without disorder, pierced by Aharonov-Bhom flux. The mechanisms of the period halving effect depend on the parity of the number of electrons as well as on the interchain hopping. Although the data of PCs in mesoscopic systems are sample-specific, some simple rules are found in the canonical ensemble average, such as all the odd harmonics of the PCs disappear, and the signals of even harmonics are non-negative. {PACS number(s): 73.23.Ra, 73.23.-b, 68.65.-k}Comment: 6 Pages with 3 EPS figure

An approximation algorithm for feedback vertex sets in tournaments

We obtain a necessary and sufficient condition in terms of forbidden structures for tournaments to possess the min-max relation on packing and covering directed cycles, together with strongly polynomial time algorithms for the feedback vertex set problem and the cycle packing problem in this class of tournaments. Applying the local ratio technique of Bar-Yehuda and Even to the forbidden structures, we find a 2.5-approximation polynomial time algorithm for the feedback vertex set problem in any tournament.published_or_final_versio

Magnetic Moments of JP=3/2+J^P={3/2}^+ Pentaquarks

If the $J^P$ of $\Theta_5^+$ and $\Xi_5^{--}$ pentaquarks is really found to be ${1\over 2}^+$ by future experiments, they will be accompanied by $J^P={3\over 2}^+$ partners in some models. It is reasonable to expect that these $J^P={3\over 2}^+$ states will also be discovered in the near future with the current intensive experimental and theoretical efforts. We estimate $J^P={3/2}^+$ pentaquark magnetic moments using different models.Comment: 13 page

The spike weight contribution of the photosynthetic area above the upper internode in a winter wheat under different nitrogen and mulching regimes

Besides leaves, non-foliar green organs such as stem and spike are also considered photosynthetic organs. To assess the photosynthetic contributions of these organs, the correlations between these photosynthetic areas and single-spike weight were investigated in a winter wheat (Triticum aestivum L.) under four nitrogen and mulching treatments: N120, N150, N195, and N195 + M. Two-year repeated field experiments were conducted on the Loess Plateau of China. Non-foliar photosynthetic area, grain-filling ratio and duration, grain yield, and in particular, single-spike weight, were measured, recorded and analyzed. Under the N195 + M treatment, plants showed the largest area of photosynthetic organs (flag leaf and non-foliar organs) and the highest grain yield and single spike weight. Single-spike weight was positively correlated with the areas of all examined non-foliar photosynthetic organs, in particular with the area above the flag leaf node (R2 = 0.761⁎) and the area above the exposed part of the peduncle (EXP) (R2 = 0.800⁎⁎). In addition, single-spike weight was highly correlated with average grain-filling ratio (R2 = 0.993⁎⁎), whereas it was less highly correlated with grain-filling duration (R2 = 0.533). The morphological traits of non-foliar photosynthetic organs were also more highly correlated with average grain-filling ratio than with average grain-filling duration. The significant correlation between each of the morphological traits (area, length and width) of EXP and single-spike weight indicates that morphological traits of EXP are important in determining spike weight in the Loess Plateau environment

Aberrant posterior cingulate connectivity classify first-episode schizophrenia from controls: A machine learning study

Background Posterior cingulate cortex (PCC) is a key aspect of the default mode network (DMN). Aberrant PCC functional connectivity (FC) is implicated in schizophrenia, but the potential for PCC related changes as biological classifier of schizophrenia has not yet been evaluated. Methods We conducted a data-driven approach using resting-state functional MRI data to explore differences in PCC-based region- and voxel-wise FC patterns, to distinguish between patients with first-episode schizophrenia (FES) and demographically matched healthy controls (HC). Discriminative PCC FCs were selected via false discovery rate estimation. A gradient boosting classifier was trained and validated based on 100 FES vs. 93 HC. Subsequently, classification models were tested in an independent dataset of 87 FES patients and 80 HC using resting-state data acquired on a different MRI scanner. Results Patients with FES had reduced connectivity between PCC and frontal areas, left parahippocampal regions, left anterior cingulate cortex, and right inferior parietal lobule, but hyperconnectivity with left lateral temporal regions. Predictive voxel-wise clusters were similar to region-wise selected brain areas functionally connected with PCC in relation to discriminating FES from HC subject categories. Region-wise analysis of FCs yielded a relatively high predictive level for schizophrenia, with an average accuracy of 72.28% in the independent samples, while selected voxel-wise connectivity yielded an accuracy of 68.72%. Conclusion FES exhibited a pattern of both increased and decreased PCC-based connectivity, but was related to predominant hypoconnectivity between PCC and brain areas associated with DMN, that may be a useful differential feature revealing underpinnings of neuropathophysiology for schizophrenia